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C:nc..Ci Library System
Univc-rcity of Wisconsin-Madison
72S State Street
ft^adison, Wl 53706-1494
U.SA
HANDBOOK OF SMALL TOOLS
COMPRISING
THREADING TOOLS, TAPS, DIES,
CUTTERS, DRILLS, AND
REAMERS
TOOKTHBR WITH A COMPLETE TREATISE ON
SCREW-THREAD SYSTEMS
BY
ERIK OBERG
Associate Editor of " Machinery," Author qf
" Shop Arithmetic for the Machinist "
FIRST EDITION
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS
London: CHAPMAN & HALL, Limited
1908
Ck>PYBIOHT, 1908.
BY
ERIK OBERG
Stanbope I>resft
F. H. GILSON COMPANY
BOSTON, U.S.A.
137313
PREFACE.
In the following pages the author has endeavored to
present an original and, as far as possible, complete
treatise on the design and construction of small cutting
tools, such as threading tools, taps, dies, milling cut-
ters of all classes, reamers, drills, counterbores, hollow
mills, etc. The material has been prepared with special
regard to the requirements of the tool-maker, tool drafts-
man, foreman, inspector, and superintendent, for specific
information relating to tools of the class mentioned. The
immediate reason for the placing of this book on the mar-
ket is the lack of definite data on this class of work in
existing treatises on shop practice, and the book has been
written to supply a distinct demand in this direction.
The author also wishes to emphasize the fact that the
information given is authentic, and that the book places
on record the most modem practice in tool manufacture,
the experience gained by him during several years con-
nection with one of the foremost tool-making firms in
the country, the Pratt & Whitney Company, being the
basis of the treatise.
In arranging the material, a great deal of space has
been devoted to tables, formulas, and general data, giving
j the tool-maker and the designer of tools specific working
I figures; and while methods and processes have not been
[ neglected, the author's personal experience has been that
the demand. of the tool-making trade is for directions what
to do rather than how to do it. An effort has been made
to prepare the material for this book so as to give specifi-
cally, in plain figures, in tables, and in formulas, the
iii
iv PREFACE
desired mformation. While the book is of a practical
character, and intended for the use of practical men,
theoretical considerations have Hot been overlooked, and
formulas and deductions of formulas are included where-
ever considered advisable. Those who have no interest
in the deduction or use of formulas will find the results
sought for directly in the tables, without calculations.
The portion of Chapter II devoted to change gearing for
the lathe has been prepared with the intention of present-
ing this matter in as simple a manner as possible, in order
to meet the requirements of those whose knowledge of
mathematics is limited; hence the rather extended and
elementary treatment of this subject.
The majority of the tables are original, and have never
been published before, except those which have appeared
under the author's name in Machinery^ in which, in the
form of separate articles, a great deal of the material has
already been published. In the preparation of the mate-
rial the author has also made use of some portions of
articles contributed from time to time to Machinery by
Mr. A. L. Valentine, Mr. E. R. Markham, and Mr. A. E.
Johnson, and credit is here given to these writers.
The author is also under obligation to the publishers of
Mdchinery for the use of a considerable number of engrav-
ings and for permission to use several articles previously
contributed by him to this journal, and copyrighted by
The Industrial Press, publishers of Machinery.
ERIK OBERG.
Brooklyn, N. Y., November, 1908.
CONTENTS.
CHAPTER I.
SCREW-THREAD SYSTEMS.
PAOB
Introductory .- 1
The United States Standard Thread 2
Formulas for Determining the Number of Threads per Inch 7
Principal Requirements for a Desirable Screw Thread 8
The Sharp V-Thread 9
Comparison between the United States Standard and the
Sharp V-Thread 13
The Advantage of Fine Pitches 14
Points of Advantage of the Sharp V-Thread 15
Threads for Machine Screws 16
The Whitworth Standard Thread 16
Advantages and Disadvantages of the Whitworth Thread 20
The British Standard Fine Screw Thread 20
British Association Standard Thread 22
Briggs Standard Pipe Thread 25
Whitworth Standard Thread for Gas and Water Piping 27
Square Threads 28
The Acme Thread 29
French and International Standard Threads 31
Miscellaneous Systems of Threads in Common Use 34
Standard Proportions for Machine Screws 38
CHAPTER II.
METHODS AND PRUfCIPLES OF THREAD-CUTTING.—
MEASURING THREADS.
Thread-Cuiting 43
Determining the Change Gears for Thread-Cutting 50
Simple Gearing 52
Lathes with Reduction Gearing in Head-Stock 54
Compound Gearing , 55
V
VI CONTENTS
PAGB
Fractional Threads 57
Cutting Metric Threads with an English Lead Screw 58
Cutting an English Thread with a Metric Lead Screw 61
General Principles op Thread-Cutting 66
Measuring Threads 69
Testing the Lead op Taps and Screws 92
Testing the Lead by Gauges 93
Comparators for the Lead op Taps and Screws 95
CHAPTER III.
THREADING TOOLS. — DEFINITIOIfS OF TAPS.
Simple Forms of Thread Tools 99
Thread-Tool Holders 102
Single-Point Cutters 104
Chasers 105
The Making op Threading Tools 106
Thread Tools with Side Clearance 121
Threading Toous for Taper Taps 124
The Influence of the Thread Miller on Threading Tools .... 129
Square-Thread Tools 132
Special Thread Tool Holder 136
Definitions op Different Kinds of Taps 138
CHAPTER IV.
HAND TAPS.
Hand Taps Made in Sets 142
CumNG Taps with Dies 157
Requirements for Correctly Threaded Taps 158
Fluting 159
Grinding Fluting Cutters 166
Relief of Taps 176
Change of Pitch in Hardening 178
Hardening Taps 187
Dimensions of Ordinary Hand Taps 190
Dimensions of Acme and Square Thread Taps 192
Machinb Screw Taps 194
Pulley Taps 207
CONTENTS vii
CHAPTER V.
TAPPER TAPS AND MACHUfE TAPS. — SCREW MACHINE
TAPS.— HOBS AND DIE TAPS.
PAGE
Tapper Taps 210
Machine Taps 216
Screw Machine Taps 226
Hobs and Die Taps. 228
CHAPTER VI.
TAPER TAPS. -.MISCELLANEOUS TAPS.
Taper Taps in General 236
PiPB Taps 242
English Taper Pipe Taps 247
Pipe Hobs 250
Taper Boiler Taps 253
Patch-Bolt Taps 255
Mud and Wash-out, Taps 256
Blacksmiths' Taper Taps 257
Pipe Taps and Drills Combined 258
Stay-Bolt Taps 259
Straight Boiler Taps 263
Straight Pipe Taps 265
Adjustable Taps 268
Kind op Si'bel Used for Taps 276
CHAPTER VII.
THREADING DIES.
Spring Screw Threading Dies 278
Roughing and Finishing Spring Screw Dies 293
Classes op Threading Dies 297
Solid Dies 298
Split Adjustable Dies 303
Die Holders 308
Holder por Spring Screw Dies 310
Inserted Chaser Dies 312
Grinding Threading Dies 315
Selpk>pening Dibs 317
viii CJONTENTS
CHAPTER VIII.
PLAIN AND SIDE MILLING CUTTERS.
PAGE
Introductory 319
Plain Milling Cutters 320
Number of Teeth in Plain Milling Cutters 325
Hardening 337
Grinding 339
Side or Straddle Milling Cutters 343
Number of Teeth in Side Milling Cutters 348
Interlocked Cutters 351
High-speed Steel for Milling Cutters 355
CHAPTER IX.
MISCELLANEOUS MILLING CUTTERS.
End Mills 360
Angular Milling Cutters 367
Cutters for Fluting Spiral-teeth Milling Cutters 368
Fixture for Grinding Angular Milling Cutters 369
Formed Cutters 371
Importance of Grinding Eccentrically Relieved Cutter
Teeth Radially » 379
Forming Tools 381
T-Slot Cutters 389
Metal Slitting Cutters 392
Inserted-Blade Milling Cutters 393
Inserted-Tooth Formed Milling Cutter 397
Special Form of Milling Cutters 399
CHAPTER X.
REAMERS.
Introductory 403
Hand Reamers 403
Relief 407
Reamers with Helical Flutes 409
Threaded-End Hand Reamers 410
Precautions in Hardening Reamers 421
Principles of Grinding Reamers 421
Fluted Chucking Reamers 423
Rose Chucking Reamers 426
CONTENTS ix
PAOS
JoBBEBs' Reamebs • 430
Shell Reamers 432
Taper Reamers 438
Grooved Chucking Reamers 456
Center Reamers 450
FLAT-sn>ED Reamers 461
Adjustable Reamers 462
CHAPTER XI.
DRILLS. — COUIVTERBORES. — HOLLOW MILLS. — LATHE
ARBORS.
Twist Drilib 469
Thickness op Web 474
Relieving the Land of Twist Drills 476
Hardening Twist Drills 478
Grinding Twist Drilea 480
Factors Determining the Keenness and Durability of the
Cutting Edge 481
Dimensions of Twist Drills 482
The Drilling of Deep Holes 486
Counterbores 490
Counxerbores with Inserted Pilots 496
Counx'erbores with Interchangeable Bodies and Guides 497
Hollow Milu3 500
Solid ' Lathe Arbors 502
SMALL TOOLS.
CHAPTER I.
SCREW-THREAD SYSTEMS.
Introductory.
Notwithstanding all . that has been written about
standard screw-thread systems, data which completely
cover all the recognized standards are very scattered,
and it is often necessary to search for information in
many various handbooks and works of reference. For
this reason we will of necessity, before entering upon the
subject of taps and tap-making, devote our attention to
the different kinds and systems of thread in common use.
While a great many more systems than we will review in
the following have been proposed from time to time, only
those which are mentioned below have been officially
recognized by mechanical men, or gained prestige by
means of universal use and adoption. It will be found
that the list given embraces all standards, whether in
use principally in the United States, in Great Britain, or
on the European continent. Any one having to do with
tool-making, and, of course, tap-making in particular,
must be equally familiar with the systems abroad as with
those of this coimtry, because the trade relations between
the United States and Great Britain and the continent
make it necessary to produce a great number of tools in
this country, made in accordance with the systems in
vogue in the country where the tools are to be used.
The recognized British standards are also used to a great
1
2 SMALL TOOLS
extent by machine builders in this country, and even
the number of American manufacturers who introduce
what is termed the French and International standards
in their establishments is steadily growing. To question
the advisability of such a course is not within the limi-
tations of this treatise, but the fact is referred to merely
in order to point out the universal use of all the standard
systems of screw threads, and to call attention to the
necessity of a complete record of the peculiarities of each
system.
Standard Systems.
The most common systems which will be treated in
detail in the following pages are:
The United States standard thread,
The sharp V-thread,
The Whitworth standard thread.
The British standard fine screw thread,
The British Association standard thread,
The Briggs standard pipe thread.
The Whitworth standard thread for gas and water
piping.
The square thread,
The Acme thread, and finally
The French and International standard threads.
The United States Standard Thread.
The United States standard thread, usually denoted
U. S. S., has a cross section as shown in Fig. 1. The
sides of the thread form an angle of 60 degrees with one
another. The top and bottom of the thread are flattened,
the width of the flat in both cases being equal to one-
eighth of the pitch of the thread. In this connection it
SCREW-THREAD SYSTEMS 8
may be appropriate to define the expression " pitch " as
well as "lead/' as these two are often confused and the
word " pitch/' in particu- ] ,
lar, often, though improperly, 1" ^ i
used in place of "number .^f"''^^^^^'^^,
of threads per inch." The ,^^^^ >^^pK
pitch of a thread is the dis- ,^11^^^^,^^^: \^
tance from center to center of f : ^""^^^^^^^^'"^^
two adjacent threads. It is F^gl i/^S^S^^^aitdard
equal to the reciprocal value Thread
of the number of threads per inch, or, if expressed in a
formula,
number of threads per inch
If, for instance, the number of threads per inch in a cer-
tain case is 16, then
pitch = :j^ = 0.0625 inch.
The lead of a screw thread is the distance the screw will
travel forward if turned around one complete revolution.
It is evident that for a single-threaded screw the pitch
and the lead are equal. If the screw is provided with
a double thread, then the lead is equal to two times the
pitch. These definitions should be strictly adhered to,
as great confusion is often caused by the different
meanings being given to the expressions "pitch'' and
"lead."
If we now return to the United States standard thread,
we will notice that if the thread is flattened one-eighth of
the pitch at top and bottom, the depth of the thread is
equal to three-quarters of the depth of a corresponding
thread sharp both at top and bottom. If p equals the
pitch of the thread, d the depth, and / the width of the
4 SMALL TOOLS
flat, we can express the relation between these quantities
in the following formulas :
1
number of threads per inch
d = I X p X cos 30° = 0.64952 p,
•^ 8
Assuming again a case with 16 threads per inch, we
find by using our formulas,
depth of thread = 0.64952 X :;^ = 0.0406 inch,
10
and the width of the flat = — = 0^0078 inch.
8
In Table I the depth of the thread and the width of the
flat for the most common number of threads per inch are
given. A column is also given for the double depth of
the thread. This quantity is of value when wanting to
find the root diameter of the thread, this diameter evi-
dently being equal to the outside or standard diameter
less the double depth of the thread. As this figure there-
fore is of particular importance it is given in all the fol-
lowing tables for various forms of thread.
There will be noticed in some cases in Table I apparent
errors in the last decimal figure in the column for the
double depth of the thread, this figure not being in all
cases exactly two times the figure for the depth of the
thread as stated in the second column. This depends, of
course, upon that the figures given are not even decimal
values, and in all cases wherever the fifth decimal, which
is not given, is above 5, the fourth figure is raised to the
nearest higher digit.
SCREW-THREAD SYSTEMS
TABLE I.
ELEMENTS OF THE UNITED STATES STANDARD THREAD.
No. of
Threads
per
Inch.
Depth of
Thread.
Width of
Flat.
Double
Depth of
Thread.
No. of
Threads
per
Inch.
Depth of
Thread.
Width of
Flat.
Double
Depth of
Thread.
2i
0.2887
0.0556
0.5774
18
0.0361
0.0069
0.0722
2i
0.2735
0.0526
0.5470
20
0.0325
0.0062
0.0650
^
0.2598
0.0500
0.5196
22
0.0295
0.0057
0.0590
2|
0.2474
0.0476
0.4949
24
0.0271
0.0052
0.0541
2f
0.2362
0.0455
0.4724
26
0.0250
0.0048
0.0500
2i
0.2259
0.0435
0.4518
28
0.0232
0.0045
0.0464
3
0.2165
0.0417
0.4330
30
0.0217
0.0042
0.0433
31
0.1999
0.0385
0.3997
32
0.0203
0.0039
0.0406
3i
0.1856
0.0357
0.3712
34
0.0191
0.0037
0.0382
4
0.1624
0.0312
0.3248
36
0.0180
0.0035
0.0361
4i
0.1443
0.0278
0.2887
38
0.0171
0.0033
0.0342
5
0.1299
0.0250
0.2598
40
0.0162
0.0031
0.0325
5i
0.1181
0.0227
0.2362
42
0.0155
0.0030
0.0309
6
0.1083
0.0208
0.2165
44
0.0148
0.0028
0.0295
7
0.0928
0.0179
0.1856
46
0.0141
0.0027
0.0282
8
0.0812
0.0156
0.1624
48
0.0135
0.0026
0.0271
9
0.0722
0.0139
0.1443
60
0.0130
0.0025
0.0260
10
0.0650
0.0125
0.1299
62
0.0125
0.0024
0.0250
11 •
0.0590
0.0114
0.1181
56
0.0116
0.0022
0.0232
12
0.0541
0.0104
0.1083
60
0.0108
0.0021
0.0217
13
0.0500
0.0096
0.0999
64
0.0101
0.0020
0.0203
14
0.0464
0.0089
0.0928
68
0.0096
0.0018
0.0191
15
0.0433
0.0083
0.0866
72
0.0090
0.0017
0.0180
16
0.0406
0.0078
0.0812
80
0.0081
0.0016
0.0162
In Table II are given the number of threads per inch
corresponding to a given diameter, as well as the root
diameter for all standard screws. When denoting that a
certain thread is to be of the same shape as the United
States standard, but the number of threads per inch is
not in accordance with the standard number of threads
for the diameter in question, it is usual to state the num-
ber of threads and add "United States Form," U. S. F.
Thus, while IJ — U. S. S. means a tap or a screw IJ inches
in diameter with 6 threads per inch, this being the stand-
ard number for this diameter, if 12 threads per inch are
6
SMALL TOOLS
wanted, the tap or screw would be denoted 1 J — 12
U. S. F. The United States standard thread is some-
times, though at the present time rarely, called the
Sellers thread, naming it from its ori^nator, Mr. William
Sellers.
TABLE II.
NUMBER OF THREADS PER INCH CORRESPONDING TO A GIVEN
DIAMETER.
United States Standard Thread.
No. of
Threads.
Diameter at
No. of
Threads.
Diameter at
Diameter.
Root of
Thread.
Diameter.
Root of
Thread.
A
64
0.0422
If
5
1.4902
A
50
0.0678
lif
5
1.5527
^
40
0.0925
If
5
1.6152
A
36
0.1202
1«
5
1.6777
^
32
0.1469
2
^
1.7113
j^
28
0.1724
n
4i
1.8363
i
20
0.1850
2i
4i
1.9613
A
18
0.2403
2f
4
2.0502
i
16
0.2938
^
4
2.1752
A
14
0.3447
2f
4
2.3002
i
13
0.4001
2f
4
2.4252
h
12
0.4542
2f
3^
2.5038
11
0.5069
3
3i
2.6288
'.
i
11
0.5694
3f
3J
2.7538
.
10
0.6201
3i
3f
2.8788
i
10
0.6826
3f
3i
2.9753
9
0.7307
^i
3i
3.1003
f
9
0.7932
3f
3f
3.2253
r
8
0.8376
3f
3
3.3170
lA
7
0.8769
3f
3
3.4420
H
7
0.9394
4
3
3.5670
4
7
1.0019
4i
2J
3.7982
li
7
1.0644
4i
2f
4.0276
lA
6
1.0960
4f
2f
4.2551
If
6
1.1585
5
2^
4.4804
lA
6
1.2210
5i
^
4.7304
H
6
1.2835
5i
2f
4.9530
lA
6i
1.3263
5t
2f
5.2030
If
6*
1.3888
6
2
5.4226
i«
5i
1.4513
SCREW-THREAD SYSTEMS 7
Formulas for Determining the Number of Threads
PER Inch.
In order to fix definitely the proper number of threads
per inch for any given diameter of screw in the United
States standard system, the following formula is used:
p = 0.24 \/ Z) + 0.625 - 0.175,
in which formula p equals the pitch of the thread for any
bolt or screw of the diameter D. To illustrate the use of
this formula, we take, for example, a two-inch bolt, and
by proper substitution we find
p = 0.24 V2 + 0.625 - 0.175
= 0.2138 inch.
The reciprocal value of this, or
1
0.2138
4.68,
is the proper number of threads per inch for a two-inch
bolt. It is evident that the fraction is not used in such a
form, but is approximated by the value 4J threads per
inch, as otherwise the screw-cutting operation and selec-
tion of change gears would be altogether too complicated.
The formula given above is the one originally pro-
posed by William Sellers, the originator of the United
States standard thread. It is applicable to all screws
one-quarter inch and larger in diameter. For diameters
below one-quarter inch the formula should be changed to
p = 0.23 V D -\- 0.625 - 0.175.
The modification above, which has met with general
acceptance, changing the coefficient 0.24 to 0.23, was pro-
posed by Mr. George M. Bond in 1882. The purpose of
the change was to make the formula applicable to screw
8 SMALL TOOLS
threads for bolts which are smaller in diameter than
one-quarter inch, inasmuch as Mr. Bond's formula tends to
increase the number of threads per inch more rapidly as
the diameter decreases than is found to result from the
use of the original formula.
It will be proper to remark in this connection that
screws |^, ^|, and || inch in diameter according to the
formula ought to have 10, 9, and 8 threads per inch respec-
tively, but in Table II the number of threads is given as
11, 10, and 9, because this conforms with the usual manu-
facturing practice.
Principal Requirements for a Desirable Screw
Thread.
The principal requirements for a screw thread, and in
fact the required conditions which led to the adoption of
the United States standard thread, are as follows:
1. That it shall possess a strength that, in the length
or depth of a nut, shall be equal to the strength of the
weakest part of the bolt, which, of course, is at the bottom
of the thread of the screw.
2. That the tools required to produce the thread shall
be easily made, and shall not appreciably change their
form by reason of wear.
3. That these tools shall be capable of being easily
sharpened, and set to the correct position in a lathe.
4. That a minimum of measuring and gauging shall be
required to test the diameter and form of the thread.
5. That the angles of the sides shall be as acute as
consistent with required strength.
6. That the thread shall not be unduly liable to become
loose in cases where the nut may require to be fastened
and loosened occasionally.
SCREW-THREAD SYSTEMS 9
From the comparisons which we shall make in the
following between the United States and other kinds of
threads it will be apparent that the former thread form
fills the requirements better than any other kind of
thread hitherto proposed.
The Sharp V-Thread.
The sharp V-Thread, a diagram of which is shown in
Fig. 2, is very similar to the United States standard
thread, except that theoreti- i i
cally it is not provided with
any fiat either at the top or
bottom of the thread. In
common practice, however, it
has proven necessary to pro-
vide this thread with a slight ^. ^ ^, ^^^
^ , , ^ , Fig. 2. KUapp V-Thread
flat on the top of the thread. u.^,5.
Several reasons may be mentioned necessitating this.
In the first place, it is very difficult to produce a per-
fectly sharp edge on the top of the thread, and, in the
case of a tap, the sharp edge would be very likely to be
impaired in hardening, leaving the top of the thread less
perfect than if provided with a slight, uniform flat. In
the second place, the sharp edge would wear away very
rapidly, both in the case of a tap and a screw, and as tl^e
wear could not be expected to be uniform, the ultimate
result would be far less desirable than the one obtained
by slightly flattening the top of the thread from the
beginning.
The necessity of providing the sharp V-thread with a
flat at the top of the thread has, however, caused some
difficulty. A standard outside diameter must necessarily
be adhered to, and if then a flat is provided, there must
NNs^i<<^.^x c^ .^cS^^^$^^$^^<<<:<^^
10
SMALL TOOLS
be an increase in the angle diameter of the thread, or the
diameter measm^d halfway between the theoretical top
and bottom of the thread as shown in Fig. 3. This
diameter is evidently of the greatest importance, since it
is obvious that if there are any variations in this dimen-
sion it will directly influence the fit between the screw
and the nut. Inasmuch as there is no recognized standard
as to how much of a flat the top of the thread ought to be
>l Depth of Tttcud
Fig. 3.
J i'ltcii '^_ DeptJi of Thiiead
Definitions of Screw-Thread Terms
provided with, various manufacturers each have their
own practice in this particular, which necessarily causes
much confusion. The gauges made by one firm do not
always correspond to the taps manufactured by another.
Tjje question is still more confusing on account of the
fact that many manufacturers do not even have a definite
standard for all gauges and taps manufactured by them,
but working to their old established plug gauges often
produce large taps with smaller flats on the top of the
thread, proportionally, than the flats on smaller taps.
The conditions mentioned are evidently a serious draw-
back in regard to the sharp V-thread, and it is to be
expected that the manufacturers as well as the users of
SCREW-THREAD SYSTEMS
11
taps with shaxp V-thread will before long settle upon a
definite standard. Some manufacturers have used the
same flat for the sharp V-thread as is used for the Briggs
standard pipe tap thread, which, although theoretically
roimded at top and bottom, is, in this country at least,
made with a small flat on the top of the thread. The
width of this flat is selected so as to give exactly the same
angle diameter as is obtained when rounding the top of
the thread in accordance with Briggs' original proposition.
This flat is equal to about one-twenty-fifth of the pitch.
TABLE III.
ELEMENTS OF THE SHARP V-THREAD.
No. of
Threads
per
Inch.
Depth of
Thread.
Width of
Flat.
Double
Depth of
Thread.
No. of
Threads
per
Inch.
Depth of
Thread.
Width of
Flat.
Double
Depth of
Thread.
2i
0.3849
0.0178
0.7698
18
0.0481
0.0022
0.0962
2f
0.3646
0.0168
0.7293
20
0.0433
0.0020
0.0866
2i
0.3464
0.0160
0.6928
22
0.0394
0.0018
0.0787
2f
0.3299
0.0162
0.6598
24
0.0361
0.0017
0.0722
2J
0.3149
0.0145
0.6298
26
0.0333
0.0015
0.0666
2i
0.3012
0.0139
0.6025
28
0.0309
0.0014
0.0619
3
0.2887
0.0133
0.5774
30
0.0289
0.0013
0.0577
3i
0.2665
0.0123
0.5329
32
0.0271
0.0012
0.0541
3J
0.2474
0.0114
0.4949
34
0.0255
0.0012
0.0509
4
0.2165
0.0100
0.4330
36
0.0241
0.0011
0.0481
4i
0.1925
0.0089
0.3849
38
0.0228
0.0011
0.0456
5
0.1732
0.0080
0.3464
40
0.0217
0.0010
0.0433
5i
0.1575
0.0073
0.3149
42
0.0206
0.0010
0.0412
6
0.1443
0.0067
0.2887
44
0.0197
0.0009
0.0394
7
0.1237
0.0057
0.2474
46
0.0188
0.0009
0.0377
8
0.1083
0.0050
0.2165
48
0.0180
0.0008
0.0361
9
0.0962
0.0044
0.1925
50
0.0173
0.0008
0.0346
10
0.0866
0.0040
0.1732
52
0.0167
0.0008
0.0333
11
0.0787
0.0036
0.1575
56
0.0155
0.0007
0.0309
12
0.0722
0.0033
0.1443
60
0.0144
0.0007
0.0289
13
0.0666
0.0031
0.1332
64
0.0135
0.0006
0.0271
14
0.0619
0.0029
0.1237
68
0.0127
0.0006
0.0255
15
0.0577
0.0027
0.1155
72
0.0120
0.0006
0.0241
16
0.0541
0.0025
0.1083
80
0.0108
0.0005
0.0217
In Table III the depth of the thread and the flat for
various pitches, as figured from the formulas below, are
12
SMALL TOOLS
given. The standard pitches corresponding to certain
diameters are stated in Table IV in the same manner as
for the United States standard thread. In the formulas
p equals the pitch, d the depth, and / the flat on the top
of the thread.
1
number of threads per inch'
d = p X cos 30° = 0.86603 p,
25
TABLE IV.
NUMBER OF THREADS PER INCH CORRESPONDING TO A GIVEN
DIAMETER.
Sharp V-Thread.
No. Of
Threads.
Diameter at
No. of
Threads.
Diameter at
Diameter.
Root of
Thread.
Diameter.
Root of
Thread.
A
72
0.0384
If
5
1.4036
^
66
0.0628
lit
5
1.4661
40
0.0817
It
4i
1.4901
^
32
0.1021
Itf
4i
1.5526
' t
24
0.1153
2
4i
1.6151
24
0.1465
2i
4i
1.7401
}
20
0.1634
21
4i
1.8651
A
18
0.2163
H
4i
1.9901
f
16
0.2667
^
4
2.0670
A
14
0.3138
H
4
2.1920
i
12
0.3557
2}
4
2.3170
A
12
0.4182
^
4
2.4420
1
11
0.4675
3
3i
2.5051
tt
11
0.5300
3i
^
2.6301
10
0.5768
3i
H
2.7551
i
10
0.6393
3f
3i .
2.8421
9
0.6825
3i
3J
2.9671
1
9
0.7450
H
3i
3.0921
1
8
0.7835
3f
3
3.1726
lA
8
0.8460
3}
3
3.2976
H
7
0.8776
4
3
3.4226
lA
7
0.9401
4i
2i
3.6475
li
7
1.0026
4i
2
3.8702
lA
7
1.0651
4i
2
4.0902
11
6
1.0863
5
2
4.3072
lA
6
1 . 1488
5i
2
4.5572
li
6
1.2113
5h
2
4.7707
6
1.2738
5i
2
2
5.0207
IJ
5
1.2786
6
5.2302
Itt
5
1.3411
■ I
SCREW-THREAD SYSTEMS 18
In applying these formulas let us assume a case of a
screw with 12 threads per inch. We then find :
depth of thread = 0.86603 X — = 0.0722 inch, and
JL
flat on' top of thread = 1^ = -i- = 0.0033 inch.
^ 25 300
Attention must be called to the fact that the formula
for the width of the flat is selected simply to give an
arbitrary value, which is not recognized as any standard
Element of the sharp V-thread. In figuring the depth of
the thread this flat is disregarded, and the depth is
arrived at as if the thread were exactly sharp.
Comparison between the United States Standard
AND THE Sharp V-Thread.
The two standards referred to hitherto are the two
forms of thread most commonly used in the United States.
The objection to the sharp V-thread as compared with
the United States standard thread is that the compara-
tively sharp points of the teeth are very frail and liable to
injury from contact with other objects. The groove at
the bottom of the thread also being sharp, facilitates
fracture under strain, and is a source of weakness in the
screw. The depth of the thread being considerably
greater than that of the United States standard thread,
subtracts from the effective area of the screw, or the
sectional area at the bottom of the thread, thus impairing
the tensile strength of the threaded bolt. It is true that
the V-thread in itself is a trifle stronger than the United
States standard thread, but the increased danger of a
screw with the latter form of thread failing, due to the
threads stripping, as compared with that of a screw with
14 SMALL TOOLS
sharp V-threads, is more apparent than real, as experience
has shown that a screw with a full United States standard
thread will fail almost invariably by breaking across the
diameter at the bottom of the threads before the threads
themselves will shear or strip.
Experiments carried out with the object of determining
the exact relation between the strength of the two forms
of thread in question have proven that smaller screws
provided with the United States standard thread have
approximately one-quarter more strength, medium-sized
ones one-sixth more, and larger ones one-eighth more
strength to resist tension than screws having an ordinary
sharp V-thread. The resistance to torsion of screws with
the former thread is about one-third, one-quarter, and
one-fifth greater, respectively, than those provided with
a sharp V-thread.
The Advantage of Fine Pitches.
Another valuable feature of the United States standard
thread as compared with the sharp V-thread is the greater
endurance or life of a tap provided with the former thread
and the greater duty of which it is capable, owing to the
liberal flats at the top and bottom of the thread. Still
another feature of superiority of the former system is the
tendency in some sizes to employ finer pitches than those
of the V-thread. This can be easily seen in regard to a
number of sizes by referring to Tables II and IV. It may
be well to point out that even the pitches of the United
States standard thread are rather coarse for many pur-
poses, and manufacturers of special machinery are inclined
to modify the system. If this could be done in such a
way that a recognized system with finer threads could be
universally adopted, to be used in cases where the United
States standard proved too coarse, then all would be well.
SCREW-THREAD SYSTEMS 16
But if various branches of manufacturers adopt standards
of their own, great confusion will result. In Great
Britain, as we will see later, great pains have been taken
to establish a system of fine screw threads, to be used in
special cases as a substitute for the regular Whitworth
thread. This system of fine screw threads promises to
be generally adopted. Such an organized efifort should
be effected in this country in regard to the United States
standard thread, so that, while both the form and the
number of threads per inch corresponding to certain
diameters are retained for such purposes, where they
prove effective, in accordance with the original system, a
series of finer pitches with the same thread form should
also be adopted to be used where the coarser thread does
not answer the purpose as well.
One such system has been proposed and adopted by the
Association of Licensed Automobile Manufacturers. As
this system has been favored only by a limited group of
manufacturers it can hardly be classed with the standard
systems of thread. We will, however, return to this sub-
ject later and give more detailed information regarding
this system.
Points of Advantage of the Sharp V-Thread.
In spite of all that we have said in favor of the United
States standard thread, the sharp V-thread will long con-
tinue to be in general use, due primarily to the fact that
it has so thoroughly established itself in the mechanical
industries. This form of thread has also another strong
claim because of being admirably adapted to the mak-
ing of steam-tight joints. It answers this purpose best,
perhaps, of all common forms of thread, and all patch-
bolt taps, boiler taps, stay-bolt taps, and arch-pipe taps
are as a rule provided with a sharp V-thread. There is
16 SMALL TOOLS
no variation of any consequence at the top and bottom of
the thread, as there may be in the United States standard
form of thread, with the resulting liability of leakage
through the clearance thus formed.
Threads for Machine Screws.
The sharp V-thread is also used for machine screws.
In these screws, however, while the bottom of the thread
is sharp, the top is flattened considerably. No data can
be given for this latter flat, as it does not conform to any
system or standard, the flat being large or small only to
conform to the manufacturer's once established gauges.
There has been, however, a strong movement for adopting
the United States standard thread form for machine
screws, which, of course, would be of great advantage.
The only objection to using this thread form for small
screws is that flattening only one-eighth of the depth of a
full V-thread provides practically a sharp thread on very
fine pitches, and a larger proportion than one to eight
between the width of the flat and the pitch of the thread
would be desirable in such cases. The standard pro-
portions for machine screw threads adopted by the
American Society of Mechanical Engineers fills this
requirement, and we will return to this system later.
The Whitworth Standard Thread.
The Whitworth standard thread is used chiefly in Great
Britain, but to a certain extent also in the United States.
Its use here, however, has greatly diminished since the
United States standard thread commenced to gain general
approval. The Whitworth standard is the older one of
the two, and is the first recognized screw thread system.
For this reason as well as for its decided merits, which will
be referred to later, it commands close attention.
• SCREW-THREAD SYSTEMS 17
In the Whitworth standard the sides of the thread form
an angle of 55 degrees with one another. The top and the
bottom of the thread are rounded as shown in Fig. 4,
The radii for these rounded portions are determined by the
w ,
Fig. 4. Whitworth Standard Thread. Fig. 6.
depth of the thread, which is two-thirds of the depth of a
thread of the same angle, sharp at top and bottom.
The radii at the top and at the bottom are the same. If
p and d mean the pitch and the depth of the thread,
respectively, and r the radius of the top or bottom,
d = I X f X cot 27° 30' = 0.64033 p,
r = 0.1373 p.*
* In any thread system where the thread is rounded at top and
bottom, the radius can be determined by the formula given below, if
the pitch, the depth of the thread, and the angle between the sides of
the thread are given. Let
p =» pitch of thread,
d = depth of thread,
w = inclusive angle of thread, and
r =■ radius at top and bottom. (See Fig. 5.)
Then
fp .w d \ .
w
sin 2
l-8in^
As an example of the application of this formula let us figure the
radius required for a Whitworth thread having say 10 threads to the
18
SMALL TOOLS
TABLE V.
ELEMENTS OF WHITWORTH STANDARD THREAD.
No. of
Threads
per
Inch.
Depth of
Thread.
Radius.
Double
Depth of
Thread.
No. of
Threads
per
Inch.
Depth of
Thread.
Radius.
Double
Depth of
Thread.
2i
0.2846
0.0610
0.5692
18
0.0356
0.0076
0.0711
2|
0.2696
0.0578
0.5392
20
0.0320
0.0069
0.0640
2^
0.2561
0.0549
0.5123
22
0.0291
0.0062
0.0582
2i
0.2439
0.0523
0.4879
24
0.0267
0.0057
0.0634
2}
0.2328
0.0499
0.4657
26
0.0246
0.0053
0.0493
21
0.2227
0.0478
0.4454
28
0.0229
0.0049
0.0457
3
0.2134
0.0458
0.4269
30
0.0213
0.0046
0.0427
3i
0.1970
0.0422
0.3940
32
0.0200
0.0043
0.0400
Si
0.1830
0.0392
0.3659
34
0.0188
0.0040
0.0377
4
0.1601
0.0343
0.3202
36
0.0178
0.0038
0.0356
4*
0.1423
0.0305
0.2846
38
0.0169
0.0036
0.0337
5
0.1281
0.0275
0.2561
40
0.0160
0.0034
0.0320
5i
0.1164
0.0250
0.2328
42
0.0152
0.0033
0.0305
6
0.1067
0.0229
0.2134
44
0.0146
0.0031
0.0291
7
0.0915
0.0196
0.1830
46
0.0139
0.0030
0.0278
8
0.0800
0.0172
0.1601
48
0.0133
0.0029
0.0267
9
0.0711
0.0153
0.1423
50
0.0128
0.0027
0.0256
10
0.0640
0.0137
0.1281
52
0.0123
0.0026
0.0246
11
0.0582
0.0125
0.1164
56
0.0114
0.0025
0.0229
12
0.0534
0.0114
0.1067
60
0.0107
0.0023
0.0213
13
0.0493
0.0106
0.0985
64
0.0100
0.0021
0.0200
14
0.0457
0.0098
0.0915
68
0.0094
0.0020
0.0188
15
0.0427
0.0092
0.0854
72
0.0089
0.0019
0.0178
16
0.0400
0.0086
0.0800
80
0.0080
0.0017
0.0160
inch. The pitch, p, is 0.1 ; the depth of the thread, d, according to
the formula given for the depth of Whitworth threads is 0.064; the
angle, w, is 55 degrees. The
radius = -
Carrying out this calculation we find
radius = 0.0137,
which corresponds to the result which would have been obtained from
the simplified formula
r = 0.1373 p
already given for the radius of the Whitworth thread.
SCREW-THREAD SYSTEMS
19
If we apply these formulas to the case of a screw with
8 threads per inch, we find :
depth of thread = 0.64033 X ^ = 0.0800 inch, and
o
radius at top and bottom = 0.1373 X - = 0.0172 inch.
o
The values of d and r are given in Table V for different
numbers of threads per inch. Table VI gives the number
of threads per inch corresponding to different diameters.
TABLE VI.
NUMBER OF THREADS PER INCH CORRESPONDING TO A GIVEN
DIAMETER.
Whitworth Standard Thread.
No. of
Threads.
Diameter at
No. of
Threads.
Diameter at
Diameter.
Root of
Thread.
Diameter.
Root of
Thread.
A
60
0.0412
If
5
1.4939
A
48
0.0670
1«
5
1.5564
*
40
0.0930
li
4*
1.5904
32
0.1162
1«
4i
1.6529
1
24
0.1341
2
4i
1.7154
24
0.1653
2i
4i
1.8404
i
20
0.1860
21
1.9298
A
18
0.2414
2|
2.0548
i
16
0.2950
2i
2.1798
A
14
0.3460
2f
2.3048
h
12
0.3933
2f
^h
2.3841
^
12
0.4558
2i
H
2.5091
11
0.5086
3
H
2.6341
i
11
0.5711
3i
H
2.7591
10
0.6219
3i
3i
2.8560
i
10
0.6844
3|
31
2.9810
9
0.7327
3i
31
3.1060
i
9
0.7952
3f
31
3.2310
1
8
0.8399
3f
3
3.3231
lA
8
0.9024
3i
3
3.4481
li
7
0.9420
4
3
3.5731
lA
7
1.0045
4i
21
3.8046
U
7
1.0670
^
2i
4.0546
ift
7
1 . 1295
^
2i
4.2843
1}
6
1.1616
5
2i
2f
4.5343
lA
6
1.2241
5i
4.7621
li
6
1.2866
5i
2f
5.0121
lA
6
1.3491
51
21
5.2377
i|
5
1.3689
6
21
5.4877
itt
5
1.4314
20 SMALL TOOLS
Advantages and Disadvantages of the Whitworth
Thread.
The Whitworth form of thread has two points of merit
that commend it highly where heavy service is required.
First, screws with this form of thread have all of the
strength possessed by screws with United States standard
threads, with the advantage over the latter of having no
sharp edges or corners from which fractures may "start.
Secondly, screws and nuts with this form of thread will
work well together after continued heavy service where
the other forms of thread would fail. Whitworth threads
are used in the United States chiefly on special screws,
such, for instance, as screws for gasoline needle valves
where a liquid-tight and yet working fit is desired. It is
also often used for locomotive boiler stay bolts.
The objections to the Whitworth form of thread are
that the angle of 55 degrees cannot be measured or simply
laid out with ordinary tools, and that the rounded comers
at the top and the bottom of the threads are extremely
difficult to produce with the degree of precision required
in tools for thread cutting. Here the United States
standard thread has a decided advantage, as the angle is
easily obtained, and the flat at the top and bottom of the
thread can be easily and accurately made. The Whit-
worth standard thread system is denoted B. S. W. (British
Standard Whitworth screw thread) in Great Britain, where
it is the recognized standard.
The British Standard Fine Screw Thread.
The British Standard fine screw thread is a system of
threads recently adopted in Great Britain. The form of
the thread is the same as that for the Whitworth stand-
ard, but there is a greater number of threads per inch
SCREW-THREAD SYSTEMS 21
corresponding to a certain diameter than in the Whit-
worth system. The fine screw-thread system is denoted
B. S. F., and applies to screws one-quarter inch in diameter
and larger. The reason for adopting this standard was
fomided on the complaints of many manufactm^rs that
the regular Whitworth standard gave altogether too
coarse pitches for a number of purposes, and while the
old system was well adapted for a variety of construc-
tions, it was not the best obtainable for those designs
where shocks and vibrations had to be taken into con-
sideration.
The pitches for the system of fine screw threads are
based apiM^oximately on the formula
P = -— for sizes up to and including one inch; and
on the formula
P = -— for sizes larger than one inch in diameter.
In the above formulas
P = pitch, or lead of single-threaded screw,
d = diameter of screw.
As an example of the application of these formulas let
us find the required number of threads per inch for a
half-inch and a 3-inch screw. In the former case the
first formula would be used :
ix^ u ^^(?? >/a25 0.630 ^^^. .
Rtch = ^ = -j^ = -^ = 0.063 mch.
The number of threads per inch = -ttt = 777:;^^ = 16
pitch 0.063
(approx.).
22 SMALL TOOLS
In order to find the number of threads per inch for a
3-inch screw we employ the second formula given:
p.,, W V243 1.99 ^-^. ,
The number of threads per inch = -t-t- = — -z-: = 5
^ pitch 0.199
(approx.).
It is evident that where the number of threads would be
a fractional value it is approximated to the nearest whole
number, except in the case of 3^ and 4J threads per inch,
where fractional values are used.
In Table VII the number of threads per inch cor-
responding to certain diameters is given. It must be
plainly understood that this standard is not supposed to
make the regular Whitworth standard thread superfluous,
but is simply intended to offer a possibility of a standard
fine screw thread for purposes where the regular Whitworth
thread would be too coarse. This standard applies only to
screws larger than one -quarter inch in diameter. For
smaller screws the British Association standard is used.
British Association Standard Thread.
The British Association standard thread is the stand-
, ard system for screws of small
diameter in Great Britain.
It is hardly used at all in the
United States, excepting in
the manufacture of tools for
. XX- \ X ..X V . x^ X xxxx ^v X ^^^ English market. The
%^^^^^^$.^^M§m^$^l^ features of the thread form
Fig. 6. British Association Stan- ^^^ ^^^^^^ ^^ ^^^^^ ^f ^^^
dard Thread
Whitworth thread, but the
angle between the two sides of the thread is only 47 de-
grees 30 minutes, and the radius at the top and the bottom
SCREW-THREAD SYSTEMS
28
of the thread (see Fig. 6) is proportionally larger, the reason
being that the depth of the thread is smaller in relation
to the pitch than in the Whitworth standard thread. If
p, d, and r signify the pitch, the depth, and the radius
at the top and bottom of the thread, respectively, then
d = 0.6 p,
2p
11
TABLE VII.
NUMBER OF THREADS PER INCH CORRESPONDING TO A CERTAIN
DIAMETER.
British Standard Fine Screw Thread.
No. of
Threads.
Diameter at
No. of
Threads.
Diameter at
Diameter.
Root of
Thread.
Diameter.
Root of
Thread.
i
25
0.1988
It*
7
1.7545
^
22
0.2543
2
7
1.8170
f
20
0.3110
2J
7
1.9420
A
18
0.3664
2i
6
2.0366
i
16
0.4200
2|
6
2.1616
V
16
0.4825
2i
6
2.2866
14
0.5335
2*
6
2.4116
i
14
0.5960
2|
6
2.5366
12
0.6433
2i
6
2.6616
*
12
0.7058
3
5
2.7439
: ■
11
0.7586
3i
5
2.8689
i
11
0.8211
3i
5
2.9939
1
10
0.8719
3|
5
3.1189
lA
10
0.9344
3i
^
3.2154
1*
9
0.9827
H
^
3.3404
lA
9
1.0452
3i
4i
3.4654
li
9
1.1077
3i
41
3.5904
lA
9
1.1702
4
4i
3.7154
U
8
1.2149
4i
4
3.9298
lA
8
1.2774
^
4
4.1798
li
8
1.3399
4f
4
4.4298
lA
8
1.4024
5
4
4.6798
If
8
1.4649
5i
31
4.8841
m
8
1.5274
5^
31
5.1341
If
7
1.5670
5f
31
5.3841
iH
7
1.6295
6
31
5.6341
li
7
1.6920
24
SMALL TOOLS
The various sizes of screws in this system are numbered,
and a certain number of threads per inch always corre-
sponds to a given diameter. Table VIII gives all the
detailed information in regard to diameter of screws,
pitches, and depth and radius of thread, which is neces-
sary for originating tools with this form of thread. The
system is founded on metric measurements, hence diame-
ter and pitch are given also in millimeters.
TABLE VIII.
ELEMENTS OF BRITISH ASSOCIATION STANDARD THREAD.
British
Associ-
Diameter.
Pitch.
Depth of
Thread.
Radius.
Double
Depth
of Thread.
at ion
Num-
Milli-
Milli-
ber.
meters.
Inches.
meters.
Inches.
Inches.
Inches.
Inches.
0
6.0
0.2362
1.0
0.0394
0.0236
0.0072
0.0472
1
5.3
0.2087
0.90
0.0354
0.0212
0.0064
0.0425
2
4.7
0.1850
0.81
0.0319
0.0191
0.0058
0.0383
3
4.1
0.1614
0.73
0.0287
0.0172
0.0052
0.0345
4
3.6
0.1417
0.66
0.0260
0.0156
0.0047
0.0312
5
3.2
0.1260
0.59
0.0232
0.0139
0.0042
0.0279
6
2.8
0.1102
0.53
0.0209
0.0125
0.0038
0.0250
7
2.5
0.0984
0.48
0.0189
0.0113
0.0034
0.0227
8
2.2
0.0866
0.43
0.0169
0.0101
0.0031
0.0203
d
1.9
0.0748
0.39
0.0154
0.0092
0.0028
0.0184
10
1.7
0.0669
0.35
0.0138
0.0083
0.0025
0.0165
11
1.5
0.0591
0.31
0.0122
0.0073
0.0022
0.0146
12
1.3
0.0511
0.28
0.0110
0.0066
0.0020
0.0132
13
1.2
0.0472
0.25
0.0098
0.0059
0.0018
0.0118
14
1.0
0.0394
0.23
0.0091
0.0055
0.0016
0.0109
15
0.90
0.0354
0.21
0.0083
0.0050
0.0015
0.0099
16
0.79
0.0311
0.19
0.0075
0.0045
0.0014
0.0090
17
0.70
0.0276
0.17
0.0067
0.0040
0.0012
0.0080
18
0.62
0.0244
0.15
0.0059
0.0035
0.0011
0.0071
19
0.54
0.0213
0.14
0.0055
0.0033
0.0010
0.0066
20
0.48
0.0189
0.12
0.0047
0.0028
0.0009
0.0057
21
0.42
0.0165
0.11
0.0043
0.0026
0.0008
0.0052
22
0.37
0.0146
0.098
0.0039
0.0023
0.0007
0.0046
23
0.33
0.0130
0.089
0.0035
0.0021
0.0006
0.0042
24
0.29
0.0114
0.080
0.0031
0.0019
0.0006
0.0038
25
0.25
0.0098
0.072
0.0028
0.0017
0.0005
0.0034
SCREW-THREAD SYSTEMS 25
This system was originated in Switzerland as a stand-
ard for screws used in watch and clock making; it is
therefore also, at times, referred to as the Swiss small
screw-thread system.
Briggs Standard Pipe Thread.
The Briggs standard pipe thread is made with an angle
of 60 degrees; it is slightly rounded off both at the top
and at the bottom, so that the depth of the thread, instead
of being equal to the depth of a sharp V-thread (0.866
0 8
X pitch), is only four-fifths of the pitch, or equal to -^,
n
if n be the number of threads per inch. The difficulty of
producing a thread with rounded top and bottom has,
however, caused the manufacturers in this country to
modify the original standard. In-
stead of rounding the bottom of
the thread it is made sharp as
shown in Fig. 7. The top is slightly \ / \ M
flattened instead of rounded, the . ■ /
flat being carried down just far
enough to tangent the top circle Fig. 7. Brigg's Standard
of the correct thread form. ^'^ ^^'^^^ ^^"^
This thread is used for pipe joints, as indicated by the
name, and for many purposes in locomotive boiler work.
The taps for producing Briggs standard pipe thread are
provided with a taper of three-quarters inch per foot on
the diameter. The pipe size is expressed by its nominal
size, which, however, is considerably smaller than the
actual size. In Table IX the nominal and actual sizes of
the tube are given, as well as the corresponding number
of threads per inch, the depth and the double depth of the
thread. These latter values are figured as being 0.833 X p
and 2 X 0.833 X p, respectively, p being the pitch of the
26
SMALL TOOLS
thread. This ^ves the correct depth of a V-thread with
a flat on the top as called for by the formula
number of threads per inch '
but ^ves a thread sharp at the bottom of the thread, this
being at variance with the original standard as expressed
by the formula, but conforming to practical usage. The
flat on the top of the thread = ^. -; : — -,
number of threads per mch
or approximately one-twenty-fifth of the pitch.
TABLE IX.
ELEMENTS OF BRIGGS STANDARD PIPE THREAD.
Nominal
Size of
Tube.
Actual
Outside
Size of
Tube.
No. of
Threads
per Inch.
Depth of
Thread.
Width of
Flat on
Top of
Thread.
Double
Depth of
Thread.
i
0.405
27
0.0309
0.0014
0.0617
i
0.540
18
0.0463
0.0021
0.0926
i
0.675
18
0.0463
0.0021
0.0926
h
0.840
14
0.0595
0.0027
0.1190
f
1.050
14
0.0595
0.0027
0.1190
1
1.315
m
0.0724
0.0033
0.1449
H
1.660
m
0.0724
0.0033
0.1449
H
1.900
Hi
0.0724
0.0033
0.1449
2
2.375
IH
0.0724
0.0033
0.1449
^
2.875
8
0.1041
0.0048
0.2082
3
3.500
8
0.1041
0.0048
0.2082
^
4.000
8
0.1041
0.0048
0.2082
4
4.500
8
0.1041
0.0048
0.2082
^
5.000
8
0.1041
0.0048
0.2082
5
5.563
8
0.1041
0.0048
0.2082
6
6.625
8
0.1041
0.0048
0.2082
7
7.625
8
0.1041
0.0048
0.2082
8
8.625
8
0.1041
0.0048
0.2082
9*
9.688
8
0.1041
0.0048
0.2082
10
10.750
8
0.1041
0.0048
0.2082
* By the action of the Manufacturers of Wrought-iron Pipe and Boiler Tubes
at a meeting held in New York, May 9, 1889, a change in size of actual outside
diameter of 9-inch pipe was adopted, making the latter 9.625 instead of 9.688
inches, as given in the table of Briggs Standard Pipe Diameters.
SCREW-THREAD SYSTEMS
27
Whitworth Standard Thread for Gas and Water
Piping.
The Whitworth standard thread for gas and water
piping is used to some extent in this country. Tlie form
of this thread is the Whitworth form, and the only differ-
ence from the regular Whitworth standard is the number
of threads per inch. The sizes and number of threads
per inch, with corresponding depth of thread, are given in
Table X.
TABLE X.
ELEMENTS OF WHITWORTH STANDARD THREAD FOR
GAS AND WATER PIPING.
Nominal
Actual
No. of
Depth of
Thread.
Double
Size of
Size of
Threads
Radius.
Depth of
Tube.
Tube.
per Inch.
Thread.
-
0.386
28
0.0229
0.0049
0.0467
i
0.620
19
0.0337
0.0072
0.0674
0.666
19
0.0337
0.0072
0.0674
^
0.822
0.0467
0.0098
0.0916
0.902
0.0467
0.0098
0.0916
1
1.034
0.0467
0.0098
0.0915
{
1.189
0.0467
0.0098
0.0915
1.302
0.0682
0.0126
0.1164
li
1.492
0.0682
0.0126
0.1164
1.660
0.0682
0.0126
0.1164
l|
1.746
0.0682
0.0126
0.1164
1^
1.882
0.0682
0.0126
0.1164
2.021
0.0682
0.0126
0.1164
2.160
0.0682
0.0126
0.1164
2.246
0.0682
0.0126
0.1164
2
2.347
0.0682
0.0126
0.1164
2i
2.467
0.0682
0.0126
0.1164
2i
2.687
0.0682
0.0126
0.1164
2}
2.794
0.0682
0.0126
0.1164
2i
3.001
0.0682
0.0125
0.1164
2f
3.124
0.0682
0.0125
0.1164
2}
3.247
0.0682
0.0126
0.1164
2i
3.367
0.0682
0.0126
0.1164
3
3.486
0.0682
0.0126
0.1164
3i
3.698
0.0682
0.0126
0.1164
^
3.912
0.0682
0.0126
0.1164
3*
4.126
0.0682
0.0126
0.1164
4
4.339
11 1 0.0582
0.0126
0.1164
28
SMALL TOOLS
Fig. 8. Square Thread
Square Threads.
The square thread is shown in Fig. 8. The sides of the
thread are parallel, and as the name indicates, the depth
of the thread is equal to the
width of space between the
teeth, this space being equal
to one-half of the pitch. In
Table XI the depth of the
thread is given for certain
numbers of threads^ per inch.
The square fonn of thread
is usually made about twice as coarse in pitch as the V
or United States standard threads, and partly for this
reason and partly because of the perpendicular walls of
the thread it is a troublesome thread to cut with taps
and dies. There is also difficulty where more than one
cut is made to produce the finished screw, due to the
succeeding taps or dies not having a lead exactly like
the one of the partly cut thread, and consequently
the thread already formed is cut away. This form of
thread is largely used on adjusting and power-conveying
screws.
While, theoretically, the space between the teeth is
equal to the thickness of the tooth, each being one-half of
the pitch, it is evident that the thickness of the tooth
must be enough smaller than the space to admit at least
an easy sliding fit. In threads with angular sides this
slight variation may be taken care of by a small increase
of the angle diameter in the nut, but in the case of
a square thread with perpendicular sides it is obvious
that the only provision possible is a slight increase
of the width of the space above the thickness of the
tooth.
SCREW-THREAD SYSTEMS
29
TABLE XI.
ELEMENTS OF THE SQUARE THREAD.
No. of
Threads
per Inch.
Depth of
Thread.
Double
Depth of
Thread.
No. of
Threads
per Inch.
Depth of
Thread.
Double
Depth of
Thread.
1
0.5000
1.0000
8
0.0625
0.1250
11
0.3750
0.7500
9
0.0556
0.1111
H
0.3333
0.6667
10
0.0500
0.1000
U
0.2857
0.5714
11
0.0455
0.0909
2
0.2500
0.5000
12
0.0417
0.0833
2i
0.2000
0.4000
13
0.0385
0.0769
3
0.1667
0.3333
14
0.0357
0.0714
3i
0.1429
0.2857
15
0.0333
0.0667
4
0.1250
0.2500
16
0.0312
0.0625
41
0.1111
0.2222
18
0.0278
0.0556
5
0.1000
0.2000
20
0.0250
0.0500
5i
0.0909
0.1818
22
0.0227
0.0455
6
0.0833
0.1667
24
0.0208
0.0417
7
0.0714
0.1429
^^30^
The Acme Thread.
The Acme thread, shown in Fig. 9, has of late become
widely used, having in most instances taken the place of
the square thread on account
of its better wearing quali-
ties and the comparative ease
with which this thread can be
produced. Of all the thread
systems which we have
treated, this is the only one
where a standard provision
has been made for clearance at the top and in the bottom
of the thread. The screw provided with an Acme thread is
made of standard diameter, but the nut into which it is
to fit is made over size in its total diameter. The rela-
tionship between screw and nut is plainly illustrated in
Fig. 10. If the diameter of the screw is A over the top of
.,^:^'
Fig. 9. Acme Standard
Thread Form
30 SMALL TOOLS
the thread, and B at the bottom or root of the thread,
the corresponding diameters in the nut are A + 0.020
and B + 0.020 inch. Referring _ ^.^..^^^^^..^^^^^
again to Fig. 9, it will be noticed ==^-^>--
that the sides of the thread form
an angle of 29 degrees with one .,^,„^ i -
another. Considering the screw ** ^ ^ I
only, if p is the pitch, d the > ,.„, .^ :
depth of the thread, / the width / :':-^ -'kU-^.-^^Jju^
of the flat at the top of the >:^^s^s^^^?^^^§^^^
thread, and C the width of the Fig. 10. Dimensions of
flat at the root of the thread, ISST'^"''"'*'
then
d = 2 + 0.010 inch,
f = 0.3707 p,
c = 0.3707 p - 0.0052 inch.
Table XII contains the values of d, /, and c for certain
common numbers of threads per inch. Having given the
formula for the depth of the thread it is clear that
Diameter at root of thread = total diameter- (p + 0.020).
This formula regards screws as well as taps for Acme
thread nuts. The formulas for d and / given above refer
to screws only. On taps the flats at the top and the
bottom are alike and equal c, or 0.3707 p — 0.0052 inch.
The diameter of the tap equals diameter of screw + 0.020,
which is evident from what has previously been said about
the size of the thread in Acme thread nuts.
The Acme thread has many good points, not the least
of which is its strength and the ease with which it may be
cut, compared with the square thread. This is due to the
greater strength of the teeth in both taps and dies, as well
as to the facility with which the cuttings free themselves.
SCREW-THREAD SYSTEMS
31
This thread is recommended as a substitute for, and in
preference to, the square form of thread.
TABLE XII.
ELEMENTS OF THE ACME STANDARD THREAD.
No. of
Depth of
Thread.
Width of
Width of
Double
Threads per
Flat at Top
Flat at Root
Depth of
Inch.
of Thread.
of Thread.
Thread.
1
0.5100
0.3707
0.3655
1.0200
H
0.3433
0.2471
0.2419
0.6867
2
0.2600
0.1853
0.1801
0.5200
2*
0.2100
0.1483
0.1431
0.4200
3
0.1767
0.1236
0.1184
0.3533
^
0.1529
0.1059
0.1007
0.3057
4
0.1350
0.0927
0.0875
0.2700
^
0.1211
0.0824
0.0772
0.2422
5
0.1100
0.0741
0.0689
0.2200
5*
0.1009
0.0674
0.0622
0.2018
6
0.0933
0.0618
0.0566
0.1867
7
0.0814
0.0530
0.0478
0.1629
8
0.0725
0.0463
0.0411
0.1450
9
0.0666
0.0412
0.0360
0.1311
10
0.0600
0.0371
0.0319
0.1200
12
0.0517
0.0309
0.0257
0.1033
French and International Standard Threads.
The French and International standard threads are of
the same form as the United States standard, and the
formulas given for the latter form of thread apply to the
former. The pitches, however, are stated in the metric
measure, and are somewhat finer for corresponding diame-
ters than the United States standard thread. This is a
distinct advantage, especially on the smaller sizes. The
standard thread of the International system, denoted S. I.,
was adopted by the International Congress for the uni-
fying of screw threads, held at Ziirich, 1898. This system
conforms in general with the system earlier adopted in
France, the French standard thread, denoted S. F., but
some slight variations occur, as can be easily seen from
32
SMALL TOOLS
Table XIV, where the diameters and corresponding
pitches are given.
In order to provide for clearance at the bottom of the
thread, the Congress referred to above specified that
"the clearance at the bottom of the thread shall not
exceed one-sixteenth part of the height of the original
triangle. The shape of the bottom of the thread resulting
from said clearance is left to the manufacturers. How-
ever, the Congress recommends rounded profile for said
bottom.'' By this provision, choice is given manu-
facturers in the several countries interested of making the
bottoms of their threads flat or rounded, as desired, and
yet have them conform to a common standard so as to
interchange if necessary.
TABLE XIII.
ELEMENTS OF THE FRENCH AND INTERNATIONAL SYSTEM
STANDARD THREAD.
Pitch,
Mm.
Depth of
Thread,
Inches.
Width of
Flat,
Inches.
Double
Depth of
Thread.
Inches.
Pitch,
Mm.
Depth of
Thread,
Inches.
Width of
Flat,
Inches.
Double
Depth of
Thread,
Inches.
8
0.2046
0.0394
0.4092
3.25
0.0831
0.0160
0.1662
7.75
0.1982
0.0382
0.3964
3
0.0767
0.0148
0.1534
7.5
0.1918
0.0369
0.3836
2.75
0.0703
0.0135
0.1406
7.25
0.1854
0.0357
0.3708
2.5
0.0639
0.0123
0.1279
7
0.1790
0.0344
0.3580
2.25
0.0575
0.0111
0.1151
6.75
0.1726
0.0332
0.3452
2
0.0511
0.0098
0.1023
6.5
0.1662
0.0320
0.3324
1.75
0.0448
0.0086
0.0895
6.25
0.1598
0.0308
0.3196
1.5
0.0384
0.0074
0.0767
6
0.1534
0.0295
0.3068
1.25
0.0320
0.0062
0.0639
6.75
0.1470
0.0283
0.2940
1
0.0256
0.0049
0.0511
5.5
0.1406
0.0271
0.2812
0.9
0.0230
0.0044
0.0460
5.25
0.1343
0.0259
0.2685
0.8
0.0205
0.0039
0.0409
5
0.1279
0.0246
0.2557
0.75
0.0192
0.0037
0.0384
4.75
0.1215
0.0234
0.2429
0.7
0.0179
0.0034
0.0358
4.5
0.1151
0.0221
0.2301
0.6
0.0153
0.0030
0.0307
4.25
0.1087
0.0209
0.2174
0.5
0.0128
0.0025
0.0256
4
0.1023
0.0197
0.2046
0.4
0.0102
0.0020
0.0205
3.75
0.0959
0.0185
0.1918
0.3
0.0077
0.0015
0.0153
3.5
0.0895
0.0172
0.1790
0.25
0.0064
0.0012
0.0128
SCREW-THREAD SYSTEMS
33
In Table XIII the necessary data as to depth of thread
and flat at top and bottom of thread are given. We
may remark that in this country the rounded profile at
the bottom is not in vogue, the form of the thread being
made an exact duplicate of the United States standard
form,
TABLE XIV.
DIAMETERS AND CORRESPONDING PITCHES.
French and International Systems Standard Thread.
French System.
International System.
Diameter,
Pitch,
Diameter at
Diameter,
Pitch,
Diameter
Mm.
Mm.
Root of
Thread, Mm.
Mm.
Mm.
at Root of
Thread, Mm.
3
0.5
2.35
6
1.0
4.70
4
0.75
3.03
7
1.0
5.70
5
0.75
4.03
8
1.25
6.38
6
1.0
4.70
9
1.25
7.38
7
1.0
5.70
10
1.5
8.05
8
1.0
6.70
11
1.5
9.05
9
1.0
7.70
12
1.75
9.73
10
1.5
8.05
14
2.0
11.40
12
1.5
10.05
16
2.0
13.40
14
2.0
11.40
18
2.5
14.76
16
2.0
13.40
20
2.5
16.75
18
2.5
14.75
22
2.5
18.75
20
2.5
16.75
24
3.0
20.10
22
2.5
18.75
27
3.0
23.10
24
3.0
20.10
30
3.5
25.45
26
3.0
22.10
33
3.5
28.45
28
3.0
24.10
36
4.0
30.80
30
3.6
25.45
39
4.0
33.80
32
3.5
27.45
42
4.5
36.15
^54
3.5
29.45
45
4.5
39.15
3b
4.0
30.80
48
5.0
41.51 .
38
4.0
32.80
52
5.0
45.51
40
4.0
34.80
56
5.5
48.86
42
4.5
36.15
60
5.5
52.86
44
4.5
38.15
64
6.0
56.21
46
4.5
40.15
68
6.0
60.21
48
5.0
41.51
72
6.5
63.56
50
5.0
43.51
76
6.5
67.56
80
7.0
70.91
34
SMALL TOOLS
In order to facilitate any necessary conversion of milli-
meters into inches a metric conversion table is appended.
(See Table XV.)
TABLE XV.
MILLIMETERS CONVERTED INTO INCHES.
Mm.
Inches.
Mm.
Inches.
Mm.
Inches.
Mm.
Inches.
Mm.
Inches.
0.01
0.0004
0.35
0.0138
0.69
0.0272
4
0.1575
38
1.4961
0.02
0.0008
0.36
0.0142
0.70
0.0276
5
0.1969
39
1.5354
0.03
0.0012
0.37
0.0146
0.71
0.0280
6
0.2362
40
1.5748
0.04
0.0016
0.38
0.0150
0.72
0.0283
7
0.2756
41
1.6142
0.05
0.0020
0.39
0.0154
0.73
0.0287
8
0.3150
42
1.6535
0.06
0.0024
0.40
0.0157
0.74
0.0291
9
0.3543
43
1.6929
0.07
0.0028
0'.41
0.0161
0.75
0.0295
10
0.3937
44
1.7323
0.08
0.0031
0.42
0.0165
0.76
0.0299
11
0.4331
45
1.7716
0.09
0.0035
0.43
0.0169
0.77
0.0303
12
0.4724
46
1.8110
0.10
0.0039
0.44
0.0173
0.78
0.0307
13
0.5118
47
1.8504
0.11
0.0043
0.45
0.0177
0.79
0.0311
14
0.5512
48
1.8898
0.12
0.0047
0.46
0.0181
0.80
0.0315
15
0.5905
49
1.9291
0.13
0.0051
0.47
0.0185
0.81
0.0319
16
0.6299
50
1.9685
0.14
0.0055
0.48
0.0189
0.82
0.0323
17
0.6693
51
2.0079
0.15
0.0059
0.49
0.0193
0.83
0.0327
18
0.7087
52
2.0472
0.16
0.0063
0.50
0.0197
0.84
0.0331
19
0.7480
53
2.0866
0.17
0.0067
0.51
0.0201
0.85
0.0335
20
0.7874
54
2.1260
0.18
0.0071
0.52
0.0205
0.86
0.0339
21
0.8268
55
2.1653
0.19
0.0075
0.53
0.0209
0.87
0.0343
22
0.8661
56
2.2047
0.20
0.0079
0.54
0.0213
0.88
0.0346
23
0.9055
57
2.2441
0.21
0.0083
0.55
0.0217
0.89
0.0350
24
0.9449
58
2.2835
0.22
0.0087
0.56
0.0220
0.90
0.0354
25
0.9842
59
2.3228
0.23
0.0091
0.57
0.0224
0.91
0.0358
26
1.0236
60
2.3622
0.24
0.0094
0.58
0.0228
0.92
0.0362
27
1.0630
61
2.4016
0.25
0.0098
0.59
0.0232
0.93
0.0366
28
1.1024
62
2.4409
0.26
0.0102
0.60
0.0236
0.94
0.0370
29
1.1417
63
2.4803
0.27
0.0106
0.61
0.0240
0.95
0.0374
30
1.1811
64
2.5197
0.28
0.0110
0.62
0.0244
0.96
0.0378
31
1.2205
65
2.5590
0.29
0.0114
0.63
0.0248
0.97
0.0382
32
1.2598
66
2.5984
0.30
0.0118
0.64
0.0252
0.98
0.0386
33
1.2992
67
2.6378
0.31
0.0122
0.65
0.0256
0.99
0.0390
34
1.3386
68
2.6772
0.32
0.0126
0.66
0.0260
1
0.0394
35
1.3779
69
2.7165
0.33
0.0130
0.67
0.0264
2
0.0787
36
1.4173
70
2.7559
0.34
0.0134
0.68
0.0268
3
0.1181
37
1.4567
Miscellaneous Systems of Thread in Common Use.
Besides the systems previously treated, which we have
classified as standard systems of thread, there are a
SCREW-THREAD SYSTEMS
35
number of systems which have never become recognized
standards, but which nevertheless are used to a greater or
smaller extent in special trades.
Instrument and Watch Makers' Systems, — The standard
screw thread of the Royal Microscopical Society of Lon-
don, England, is employed for microscope objectives, and
the nose pieces of the microscope into which these objec-
tives screw. The form of the thread is the Whitworth
form; the diameter of the male gauge is 0.7626 inch.
The number of threads per inch is 36.
TABLE XVI.
WHITWORTH STANDARD THREAD SYSTEM FOR WATCH
AND MATHEMATICAL INSTRUMENT MAKERS.
No.
No.
No.
Diameter
of
Diameter
of
Diameter
of
of Screw,
Thrds.
of Screw,
Thrds.
of Screw,
Thrds.
Inches.
per
Inches.
per
Inches.
per
Inch.
Inch.
Inch.
0.010
400
0.022
210
0.050
100
0.011
400
0.024
210
0.055
100
0.012
350
0.026
180
0.060
100
0.O13
350
0.028
180
0.065
80
0.014
300
0.030
180
0.070
80
0.015
300
0.032
150
0.075
80
0.016
300
0.034
150
0.080
60
0.017
250
0.036
150
0.085
60
0.018
250
0.038
120
0.090
60
0.019
250
0.040
120
0.095
60
0.020
210
0.045
120
0.100
50
In Table XVI are given the sizes and corresponding
number of threads for Whitworth standard screw pitch
system for watch and mathematical instrument makers.
This system is adopted by many instrument makers
both in the United States and Europe.
Lag Screw Threads. — There is no recognized standard
for the sizes and corresponding number of threads for
SMALL TOOLS
lag screws. Table XVII gives the number of threads
according to common practice. While lag screws are
largely made according to this system, there is, however,
a number of varying systems in use.
TABLE XVII.
LAG SCREW THREADS.
Diameter of
Screw.
Number of
Threads per
Inch.
Diameter of
Screw.
Number of
Threads per
Inch.
A
10
9
8
7
6
6
i
?
i
.1
5
5
6
4
4
Gas-Fixture Threads, — Thin brass tubing is threaded
with 27 threads per inch, irrespective of diameter. The
so-called "Ornament brass sizes" have 32 threads per
inch. The standard sizes of the thread are 0.196 inch
(large ornament brass size) and 0.148 inch (small orna-
ment brass size).
Fine Screw-Thread Systems. — We have previously
referred to the desirability of the adoption of a standard
system with the United States standard form of thread
but with a finer pitch than called for by this standard.
We also mentioned the system which has been proposed by
the Association of Licensed Automobile Manufacturers.
In this system the diameters and corresponding number
of threads are as follows:
i-.
A-
i..
A.
J..
A*
28
24
24
20
20
18
f..
«.
1..
»..
1..
18
16
16
14
14
SCREW-THREAD SYSTEMS
37
The objection to the adoption of this standard by a
single body of manufacturers is obvious. Even if the
standard is one which would recommend itself for general
use, it would have been better if the opinions and the
needs of machine builders in general had been taken
into consideration. Besides, there is reasonable doubt
whether the standard referred to is not too fine for ordi-
. nary construction even where the need of a fine-pitch
standard has presented itself. Automobile construction is,
of course, so specialized a manufacture that here doubtless
may arise requirements which do not. present themselves
elsewhere.
It seems as if the pitches of the British standard fine
screw thread were well selected for a fine-pitch screw
thread, at least with a few slight modifications. It would
be well if a system of such a kind could be adopted.
The number of threads corresponding to a certain diam-
eter given in Table XVIII will be found very suitable for a
fine pitch screw standard, and may serve as a guide in
selecting fine pitches until a recognized standard is pro-
posed and adopted.
TABLE XVIII.
PROPOSED FINE SCREW-TmiEAD SYSTEM.
Diam-
eter
of
Screw.
Number
of
Threads.
Diam-
eter
of
Screw.
Number
of
Threads.
Diam-
eter
of
Screw.
Number
of
Threads.
•
Diam-
eter
of
Screw.
Number
of
Threads.
I
i
26
24
22
20
18
16
16
14
i
a
1
n
It
14
13
13
12
12
11
11
10
If
1}
2
2J
2i
2f
10
9
9
9
8
8
8
7
2i
2i
3
3}
3i
4
7
7
7
6
6
6
38 SMALL TOOLS
Standard Proportions for Machine Screws.
Finally, we will give our attention to a new standard
system for machine screws which promises to gain uni-
versal recognition. A committee appointed by the Ameri-
can Society of Mechanical Engineers to investigate the
subject of machine screw proportions and to recommend
standard specifications for machine screws, made its
first report at the December meeting, 1905. Some
criticism, however, of this report made it necessary to call
for a second, and what was intended to be a final, report
at the May meeting, 1906. In the discussion that fol-
lowed this report there were, however, several diverging
opinions expressed on this subject, and the committee was
therefore continued and was supposed to report at the
December meeting in the same year. For some reason
the report, however, was not accepted by the Association
imtil the Indianapolis meeting in May, 1907. Below are pre-
sented some of the most important points of consideration
in the new standard for machine screws which has been
accepted by the American Society of Mechanical Engineers.
The standard diameters of machine screws are to be 21
in number. The included angle of the thread is 60
degrees, and the flat at the top and bottom of the thread
for the basic standard is one-eighth of the pitch. The
uniform increment between all sizes from 0.060 inch to
0.190 inch is 0.013 inch, and for larger sizes 0.026 inch,
making the largest size 0.450 inch in diameter. The ,
number of threads is made a function of the diameter as i
expressed by the formula '
6 5 '
Number of threads per inch = — — ^— — • |
This formula, however, gives the results approximately i
only, as even numbers of threads are chosen in order to |
avoid fractional or odd numbers.
SCREW-THREAD SYSTEMS 89
TABLE XIX.
FORMULAS FOR PROPOSED STANDARD FOR MACHINE SCREWS
AND TAPS. BASIC STANDARD THREAD.. U. 8. FORM.
T.P.I. = Number of Threads per inch.
Screws.
Max. external diam. = basic external diam.
Max. pitch diam. = basic pitch diam.
Max. root diam. = basic root diam.
Min. external diam. = basic external diam. —
Min. pitch diam. = basic pitch diam. —
T.P.I. +40
0.168
T.P.I. + 40"
0.10826 . 0.168
nvr- .A' V. • .A' r0.10826 . 0.168 1
Mm. root diam. = basic root diam. - i ^^^ + T. PI. 4- 40 J *
Taps.
^ ^A^ y. ' . ^A' . 0.10826 , 0.224
Max. external diam. ^ basic external diam. + +
Max. pitch diam. «= basic pitch diam. +
Max. root diam. = basic root diam. +
Min. external diam. = basic external diam. +
Min. pitch diam. = basic pitch diam. +
Min. root diam. = basic root diam. +
T.P.I. ■ T.P.I.+40
0.224
T.P.L+40
0.336
T.P.I. +40
0.112
T.P.I. + 40
0.112
T.P.I. +40
0.112
T.P.I. +40
In regard to the limits for variation from the basic
standard, the maximum screw shall conform practically
in all respects to the basic standard. The minimum screw
shall have a flat at the bottom of the thread of one-six-
teenth of the pitch, and the difference between the maxi-
mum and the minimum root diameter will allow at the
bottom of the thread any width of flat between one-
sixteenth and one-eighth of the pitch. (See Figs. 11 and
12.) The maximum tap shall have a flat at the top
of the thread equal to one-sixteenth of the pitch, and
the difference between the maximum and the minimum
40
SMALL TOOLS
TOP OF THREAD
Figs. 11 aud 12. Machine Screw Thread Standard Adopted by the
American Society of Mechanical Engineers ; 16 and 72 Threads per
Inch
SCREW-THREAD SYSTEMS
41
external diameter will allow at the top of the thread any
width of fiat between one-sixteenth and one-eighth of the
pitch. The minimum tap shall conform to the basic
standard in all respects except in diameter, as plainly
shown in the cuts. The difiference between the minimum
tap and the maximum screw is settled upon in order to
allow for errors in pitch and for the wear of the tap in
service. The formulas in Table XIX give the relations
between the various dimensions determining the sizes of
taps and screws in this standard.
TABLE XX.
DOUBLE END TEMPLET THREAD GAUGES FOR INSPECTION OF
SCREWS.
Thicknoaa = N/Pitch X 1443.
Threads per Inch.
Thickness.
Threads per Inch.
Thickness.
80
0.161
30
0.263
72
0.170
28
0.273
64
0.180
24
0.295
56
0.193
22
0.308
48
0.208
20
0.323
44
0.217
18
0.345
40
0.228
16
0.361
36
0.240
14
0.385
32
0.255
The reference thread gauges should be made from
unhardened steel, 0.35 per cent carbon, and a set should
include both reference thread gauges for screws and refer-
ence thread gauges for taps, each of these to represent the
maximum and minimum diameters. Table XX gives the
thickness of double end templet thread gauges, for each
pitch of the standard screws recommended, for the prac-
tical inspection of machine screws. The formula
Thickness = Vpitch x 1.443
42 SMALL TOOLS
provides a limit for the error in lead on screws and taps.
These templet thread gauges are to be made of steel,
hardened, and being double ended and having maximum
and minimum limits, respectively, are to represent at the
largest end the pitch and root diameters of the basic stand-
ard, while at the small end they should represent the
minimum limits for the pitch and root diameters of screws.
The threads of these templet gauges should be made by
taps having the thread enough larger than the standard in
the outside diameter to insure clearance at the top of the
thread of the screw. In addition to the threaded holes,
these gauges should have plain cylindrical holes represent-
ing, respectively, the external diameter of the maximum
and minimum screw.
In Chapter IV, tables are given' stating all dimensions
for taps and screws made according to this system of
standard machine screw threads.
CHAPTER II.
METHODS AND PRINCIPLES OF THREAD-CUTTING.
— MEASURING THREADS.
Thread-Cutting.
Comparison between Usual Methods. — There are two
common ways of producing screw threads, cutting the
threads in a lathe or cutting them by means of dies. The
first method, and the one with which we will deal here, is
the one used whenever any greater degree of accuracy of
pitch and diameter is desired. By special methods, and
by extreme care in making the dies as well as cutting the
thread, screws within close limits of accuracy may be
produced by means of dies; but for cutting the threads of
taps, where any original error or imperfection would be
duplicated in all the pieces of work afterward threaded by
the tap, thfe only desirable method is the cutting of the
thread in a lathe. All screws of any considerable length
must also be cut in this manner, as accuracy in lead can-
not be insured unless the accuracy of a tested lead screw
is duplicated in the piece threaded.
Examples have been pointed out where, in using dies
for thread cutting, the inaccuracy of ordinary commer-
cial dies in the pitch has been so great as to cut a thread
which, if continued for a foot in length, would have had
an error of one-eighth inch in the lead. If the thread is
cut with dies by hand there is also a chance for error in
the starting of the die. The thread may not be true with
the axis of the work, for although most dies intended for
use by hand are either themselves provided with a guide
48
44 SMALL TOOLS
or mounted so that the piece to be threaded enters a
guide before reaching the die, this guide does not always
fit the piece closely enough to start the die perfectly true.
In all these respects lathe threading is superior, and can-
not be too strongly recommended in all cases where a
thread of good qualities is required.
Cviting Screws without the Aid of a Lead Screw. —
Because the lead of a screw being cut always depends
upon the lead of a thread that has been previously cut,
any incorrectness in the master thread (as in a lathe, in
the thread of the lead screw) will be reproduced in the
screw. For ordinary purposes, the errors in the lead of
lead screws of lathes of good manufacture are insignifi-
cant, but occasions arise when these errors must be taken
into consideration. In order to avoid the duplication of
errors of this character, Messrs. de Fries & Co., Diissel-
dorf, Germany, have designed a new screw-cutting lathe,
working on the principle of producing a thread independ-
ently of a previously cut lead screw. The lathe employed
for this purpose is of common design, the feature of
extraordinary interest being the arrangement for feeding
the carriage; a flexible steel band is used for this purpose
instead of the lead screw. This band is located centrally
between the two ways of the bed, and one end of the band
is fastened to the front end of the carriage, while the
other end extends under the head-stock and is fastened to
a drum, turned accurately to a definite diameter. When
this drum is revolving, the steel band is wound up on it,
and thus feeds the carriage. The drum, of course, must
be large enough so that the steel band when winding up
does not reach fully one complete turn around the drum,
because if it reached more than one turn around, the
band in winding up on itself would be wound up on a
larger diameter than that of the drum, thus causing
THREAD-CUTTING — MEASURING THREADS 46
incorrect results. The drum is driven from the cone
pulley by means of a worm and worm wheel.
For the return, another steel band is fastened to the
rear end of the carriage, this band extending to the rear
end of the lathe and running over an idle pulley. A
coimterweight is suspended from this band heavy enough
to pull the carriage back when released from the pull at
its front end. This lathe is not used for cutting the whole
screw from start to finish, but simply for finishing the
thread. The arrangement is by its construction too weak
to stand up for the heavy cuts necessary for rough thread-
ing. The thread is therefore cut in an ordinary screw-
cutting lathe, somewhat over size, and then placed in this
special lathe mentioned and there finished. It is claimed
that by this machine it is possible to cut the most cor-
rect thread as yet produced for conmiercial purposes.
Cviting Threads in the Thread Milling Machine. — A
method of producing threads which has been but lately
brought into more general use is the milling of the
thread in special thread milling machines, which, while
embodying the principles of a lathe, are provided with a
cutter head in place of the lathe tool-post, and a cutter,
driven from the countershaft in place of the ordinary
tool. As this method contains all the principles which
insure accuracy in thread-cutting in a lathe, equally per-
fect threads will result from milling. The cutting of
threads in a thread milling machine is also more economi-
cal, at least when fairly long threads are to be cut. The
thread is milled to its full depth at once, and as the center
of the cutter is always at the same height as the center of
the work, there is no risk of improper setting of the tool.
The only objection that could be advanced is that the
cutter head is tilted to the angle of helix of the thread,
and consequently, if the same cutter is used for all diam-
46
SMALL TOOLS
eters with the same number of threads per inch, the thread
form will be slightly inaccurate, owing to the different angles
to which the cutter head is tilted. For all ordinary angles
of helix, that is, for all diameters provided with a pro-
portionate pitch, this inaccuracy, however, is so small as
to command no consideration.
Method of Rolling Threads, — Some manufacturers of
taps finish the thread by a process named rolling. The
tap is first rough threaded, and afterward passed through
a set of three rollers, mounted in a kind of a chuck.
Fig. 13. Device for Rolling Threads on Small Screws
These rollers are provided with circular grooves of the
same shape as the thread, and in order to insure the cor-
rect lead, each roller must be cut with its grooves one-
third of the pitch in advance of the next preceding roller.
All the rollers are mounted in the same horizontal plane
if the tap passes through them vertically, or in the same
vertical plane if the tap passes through them in a hori-
zontal direction. What has been said in regard to rolling
threads may be better understood by referring to Fig.
13, where the outline of a chuck with three rollers is
shown. The pieces A provided with circular grooves are
THREAD-CUTTING — MEASURING THREADS 47
the rollers. These are mounted in adjustable blocks B,
the back ends of which are tapered to correspond to the
taper of the ring (7, which encloses the whole arrange-
ment and serves the purpose of providing for the adjust-
ment. By screwing the ring C down, the rollers are
evidently pushed toward the center of the chuck, and
screwing the ring up permits the rollers and the blocks
to recede. The blocks, when adjusted, are held in posi-
tion in relation to the center line of the body D by means
of binding screws entering from the front face at an angle
of 45 degrees and binding in grooves in the blocks.
This arrangement is used for rolling smaller taps. For
larger ones the ring C is eliminated, and the rollers are
mounted in blocks, adjustable by screws in a similar
manner to the jaws in universal chucks. This manner of
finishing tap threads is very economical, and the tap
thread fills all reasonable requirements. It is particu-
larly of advantage for finishing taps with thread forms
having radii at top and bottom, as it saves the necessity
of complicated thread tools, the roughing operation taking
no account of the round at top and bottom, this being
impressed in the tap by the rollers when finishing.
One special way of producing threads by rolling, which,
however, can hardly be considered as directly concerning
the tool-maker, is the process of rolling threads on rough
wire or forged blanks without previous rough threading.
The blank is then rolled between two dies or blocks having
grooves of the right pitch, form, and angle of lead, and
the thread is formed by displacement of the metal, which
causes the finished screw to be larger in diameter than the
blank. One die is usually stationary, while the other has
a reciprocating motion.
A device of this description, intended to be used for
thread-rolling on a punch press, was shown by Mr. S.
48
SMALL TOOLS
Oliver in the July, 1907, issue of Machinery, In Fig. 14,
A is a punch holder to fit the punch press. jB is the
bolster, or a piece of cast iron about 1 inch thick, upon
which are located two cast-iron blocks, one made station-
ary and the other adjustable by slotting B, so that the
block can be forced ahead by the set screw C. There is
a groove in the stationary block and a tongue in the
punch holder A to prevent the dies from getting out of
Fig. 14. Device for Thread-Rolling in a Punch Press
line. The screw D is for holding a thin piece of steel as a
stop so that the thread can be cut to the desired length.
The screw E holds a wire supporting the piece to be
threaded until the upper die, F, comes down and carries it
past the lower die, G. In cutting the die, it may be made
in one piece, H being the circumference of the thread to be
rolled and G^ the desired length for the lower die. F^ is
the desired length for the upper die, which must be longer
than the lower die so that it will roll the wire past the die
THREAD-CUTTING — MEASURING THREADS 49
G and permit it to drop out of the way. The part K must
be cut out when cutting in two parts. The proper
angle to which to cut the die depends on the pitch of the
thread. The pitch divided by the circumference of the
screw to be rolled will give the tangent of the angle. In
cutting the die, which must be of good tool steel and
hardened after making, the shaper is used. The cut is
taken with a tool that can be taken off and put back
again without changing its location, such a tool, for
instance, as a circular threading tool. In case the point
should happen to get dull, the tool can then be removed
for grinding. If the feed screw should not have the
desired graduations on it, a brass index plate can be made
very quickly and used on the machine. The brass plate
should be of a good size and cut accurately in a milling
machine, and a pointer clamped on the shaper.
Cutting Threads by Rapidly Revolving Hardened Disk. —
An interesting method for producing threads was shown
in the January, 1908, issue of Machinery, by Mr. Oskar
Kylin. In Fig. 15 this method is illustrated. It is used
for threading studs, pins, etc., of manganese steel, this
material being so hard that it cannot be cut by any
kind of tool steel. A plain, hardened tool-steel disk, hav-
ing the edge made according to the angle of thread, is
employed. This disk is revolved at a high speed, and at
the same time forced into the work, which is revolved
slowly. Due to the friction between the edge of the disk
and the work, and the softening of the material, owing
to the heat generated by the friction, the disk wears
away the stock and by means of this creates the thread.
The stock is coming ofif in very small, thin scales like
chips, which to some extent remind one of the scales of
a fish. An ordinary lathe has been rigged up for the
purpose by removing the tool-post and top rest and
60
SMALL TOOLS
substituting for them the fixture shown in the cut. The
disk must be driven independently by an overhead drum
or some similar arrangement. The peripheral speed of
the disk is usually between 3000 and 4000 feet per minute.
The operation is unavoidably slow and expensive, and the
method is used only when no other way is possible.
CvUing Threads in the Lathe. — Having mentioned the
most common methods for producing threads we will now
review the fundamental principles of cutting threads in the
Fig. 15. Cutting Threads by a Rapidly Revolving Disk
lathe. While well known to all mechanics, it is necessary
to dwell upon this question to some extent in order to
complete the subject in hand.
Determining the Change Gears for Thread-Cutting.
The determining of the change gears for gearing the
lathe to cut the desired thread seems to be a never
decreasing source of difficulty. Of course, all lathes are
now provided with a gear-cutting index for gearing the
lathe to cut standard threads. When it is required, how-
THREAD-CUTTING— MEASURING THREADS 51
ever, to determine the change gears for an odd or a frac-
tional pitch, many a man otherwise efficient is at a loss.
While the principles and rules governing the calculation
of change gears are very simple, they of course pre-
suppose some fundamental knowledge of the use of com-
mon fractions. If such knowledge is at hand, the subject
of figuring change gears, if once thoroughly understood,
can hardly ever be forgotten. It should be impressed
upon the minds of all who have found difficulties with
this subject that the matter is not approached in a logi-
cal manner, and is usually grasped by the memory rather
than* by the intellect. Before answering the question in
regard to any rules for figuring change gears, let us there-
fore analyze the subject. The lead screw B of the lathe
(see Fig. 16) must be recognized as our first factor, and
the spindle as the second. If
the lead screw has six threads
per inch, then, if the lead
screw makes six revolutions,
the carriage travels one inch,
and the thread-cutting tool
travels one inch along the
piece to be threaded. If the
spindle makes the same num-
ber of revolutions in a given
time as the lead screw, it is
clear the tool will cut six
threads per inch. In such
the spindle stud J, and gear
are alike,
revolutions
Fig. 16.
Simple Gearing
the gear D on
lead screw,
a case
E on the
If the spindle makes twice the number of
of the lead screw, the spindle revolves
twelve times while the tool moves one inch, and conse-
quently twelve threads per inch will be cut. But in
order to make the spindle revolve twice as fast as the
62 SMALL TOOLS
lead screw, it is necessary that a gear be put on the
spindle stud of only half the number of teeth of the gear
on the lead screw, so that when the lead screw revolves
once the spindle-stud gear makes two revolutions.
Simple Gearing.
Suppose we wish to cut nine threads per inch with a
lead screw of six threads per inch, as referred to above.
Then the six threads of the lead screw correspond to nine
threads on the piece to be threaded, which is the same as
sa3dng that six revolutions of the lead screw correspond
to nine revolutions of the spindle; or in other words,
one revolution of * the lead screw corresponds to 1 J of
the spindle. From this it is evident that the gear on the
lead screw must make only one revolution while the
spindle^tud gear makes IJ. Thus, if the lead-screw gear
has, for instance, 36 teeth, the gear on the spindle stud
should have only 24, the smaller gear, of course, revolving
faster than the larger. If we express what has been pre-
viously said in a formula we have
threads per inch of lead screw _ teeth in gear on spindle stud
threads per inch to be cut ~' teeth in gear of lead screw
Applying this to the case above, we have
6^24
9 36*
The values 24 and 36 are obtained by multiplying 6 and
9, respectively, by 4. By multiplying both the numerator
and the denominator by the same number we do not
change the proportion. As a general rule we may then
say that the change gea:^ necessary to cut a certain num-
ber of threads per inch are found by placing the number
of threads in the lead screw in the numerator, the num-
THREAD-CUTTING — MEASURING THREADS 53
ber of threads to be cut in the denominator, and then
multiplying numerator as well as denominator by the same
number, by trial, until two gears are obtained the numbers
of teeth of which are both to be found in the set of gears
accompanying the lathe. The gear with the number of
teeth designated by the new numerator is to be placed on
the spindle stud (at J, Fig. 16), and the gear with the
number of teeth corresponding to the denominator on the
lead screw B.
A few examples of this will more clearly explain the
rule. Suppose the number of teeth of the change gears
of a lathe are 24, 28, 32, 36, and so forth, increasing by
4 teeth up to 100. Assume that the lead screw is pro-
vided with 6 threads per inch, and that 10 threads per
inch are to be cut. Then
6 _ 6 X4 _24
10 10X4 40*
By multiplying both numerator and denominator by
4 we obtain two available gears with 24 and 40 teeth,
respectively. The 24-tooth gear goes on the spindle stud,
and the 40-tooth gear on the lead screw. Assuming the
same lathe and gears, let us find the gears for cutting
UJ threads per inch, this being the standard number of
threads for certain sizes of pipe thread. Then
6 _ 6 X8 _48
Hi Hi X 8 92 *
It will be found that multiplying by any other number
than 8 would not, in this case, have given us gears
with such numbers of teeth as we have in our set with
this lathe. Until we get accustomed to figuring of this
kind, we can, of course, only by trial find out the correct
number by which to multiply numerator and denominator.
54 SMALL TOOLS
The number of teeth in the intermediate gear F, Fig. 16,
which meshes with both the spindle-stud gear and the
lead-screw gear, is of no consequence.
Lathes with Reduction Gearing in Head-Stock.
In some lathes, however, there is a reduction gearing in
the head-stock of the lathe, so that if equal gears are
placed on the lead screw and the spindle stud, the spindle
does not make the same number of revolutions as the
lead screw, but a greater number. Usually in such lathes
the ratio of the gearing in the head-stock is 2 to 1, so that
with equal gears the spindle makes two revolutions to one
of the lead screw. This is particularly common in lathes
intended for cutting fine pitches or, in general, in small
lathes. In figuring the gears this must, of course, be
taken into consideration. As the spindle makes twice as
many revolutions as the lead screw with equal gears, if
the ratio of the gears be 2 to 1, that means that if the
head-stock gearing were ehminated, and the lead screw
instead had twice the number of threads per inch as it
has, with equal gears the spindle would still revolve the
same as before for each inch of travel along the piece to
be threaded. In other words, the gearing in the head-
stock may be disregarded if the number of threads of the
lead screw is midtiplied by the ratio of this gearing. Sup-
pose, for instance, that in a lathe the lead screw has eight
threads per inch, that the lathe is geared in the head-
stock with a ratio of 2 to 1, and that 20 threads are to be
cut. Then
2X8 _ 16 _ 16. ><_£ _ 64,
20 20 20 X 4 80'
which two last values signify the numbers of teeth in the
gears to use.
THREAD-CUTTING — MEASURING THREADS 66
Sometimes the ratio of the gearing in the head-stock
cannot be determined by counting the teeth in the gears,
because the gears are so placed that they cannot be plainly
seen. In such a case, equal gears are placed on the lead
screw and the spindle stud, and a thread cut on a piece
in the lathe. The number of threacls per inch of this
piece should be used for the numerator in our calculation
instead of the actual number of threads of the lead
screw. The ratio of the gearing in the head-stock is
equal to the ratio between the number of threads cut on
the piece in the lathe and the actual number of threads
per inch of the lead screw.
Compound Gearing.
The cases with only two gears in a train referred to
are termed simple gearing. Sometimes it is not possible
to obtain the correct ratio excepting by introducing
two more gears in the train, which, as hardly need be
mentioned, is termed com-
pound gearing. This class of
gearing is shown in Fig. 17.
The rules for figuring com-
pound gearing are exactly the
same as for simple gearing
excepting that we must divide
both our numerator and de-
nominator into two factors,
each of which is multiplied
by the same number in
order to obtain the change
gears.
Suppose a lathe has a lead screw with six threads per
inch, that the numbers of the teeth in the gears available
are 30, 35, 40, and so forth, increasing by 5 up to 100.
Fig. 17. Compound Gearing
66 SMALL TOOLS
Assume that it is desired to cut 24 threads per inch. We
have then
6
- = ratio.
By dividing up the numerator and denominator into
factors, and multiplying each pair of factors by the same
number y we find the gears :
6 __ 2 X 3 _ (2 X 20) X (3 X 10) _ 40 X 30
24 4X6 (4 X 20) X (6 X 10) 80 X 60 *
The last four numbers indicate the gears which should be
used. The upper two, 40 and 30, are driving gears, the
lower two, with 80 and 60 teeth, are driven gears. Driv-
ing gears are, of course, the gear D, Fig. 17, on the spindle
stud, and the gear P on the intermediate stud K, meshing
with the lead-screw gear. Driven gears are the lead-
screw gear, E, and the gear N on the intermediate stud,
meshing with the spindle-stud gear. It makes no differ-
ence which of the driving gears is placed on the spindle
stud, or which of the driven is placed on the lead screw.
Suppose, for a final example, that we wish to cut If
threads per inch on a lathe with a lead screw having six
threads per inch, and that the gears run from 24 and up
to 100 teeth, increasing by 4. Proceeding as before we
have
A ^ 2X3 _ (2 X 36) X (3 X 16) _ 72 X 48
If 1 X If (IX 36) X (If X 16) 36 X 28*
This is the case directly illustrated in Fig. 17. The
gear with 72 teeth is placed on the spindle stud J, the one
with 48 on the intermediate stud Kj meshing with the
lead-screw gear. These two gears (72 and 48 teeth) are
the driving gears. The gears with 36 and 28 teeth are
placed on the lead screw and on the intermediate stud, as
shown, and are the driven gears.
THREAD-CUTTING — MEASURING THREADS 67
Fractional Threads.
Sometimes the lead of the thread is expressed by a
fraction of an inch instead of stating the number of
threads per inch. For instance, a thread may be required
to be cut having a three-eighths-inch lead. In such a
case the expression "three-eighths lead'' should first be
transformed to "number of threads per inch/' after which
we can proceed in the same way as has already been
explained. To find how many threads per inch there is
when the lead is stated, we simply find how many times
the lead is contained in one inch, or, in other words, we
divide one by the ^ven lead. Thus one divided by three-
eighths gives us 2§, which is the number of threads per
inch of a thread having three-eighths-inch lead. To find
change gears to cut such a thread we would proceed as
follows :
Assume that the lead screw has 6 threads per inch and
that the change gears run from 24 up to 100 teeth,
increasing by 4. Proceeding to find the gears as before
we have
6 2X3 (2 X 36) X (3 X 24) _ 72 X 72
2§ 1 X 21 (IX 36) X (2§ X 24) 36 X 64 '
The rule for finding the number of threads per inch,
when the lead is ^ven, may be expressed by the formula
1
number of threads per inch
lead of thread'
What has been said in the foregoing in regard to the
figuring of change gears for the lathe may be summed up
in the following rules :
1. To find the number of threads per inch if the lead of
a thread is given, divide one by the lead.
68 SMALL TOOLS'
2. To find the change gears used in simple gearing,
when the number of threads per inch on the lead screw and
the number of threads per inch to be cut are given, place
the number of threads on the lead screw as numerator and the
number of threads to he cut as denominator in a fraction, and
multiply numerator and denominator by the same number
uhtil a new fraction results representing suitable numbers of
teeth for the change gears. In the new fraction, the numera-
tor represents the number of teeth on the spindle stud, and
the denominator the number of teeth in the gear on the
lead screw.
3. To find the change gears used in compound gearing,
place the number of threads per inch on the lead screw as
numerator and the number of threads per inch to be cvi as
denominator in a fraction, divide up both numerator and
denominator into two factors each, and multiply each pair of
factors (one factor in the numerator and one in the denomi-
nator making "a pair^') by the same number until new
fractions result representing suitable numbers of teeth for the
change gears. The gears represented by the numbers in
the new numerators are driving gears, and those in the
denominators are driven gears.
Cutting Metric Threads wiph an English Lead Screw.
It often happens that screws or taps having threads
cut according to the metric system are required. The
lead of these screws is expressed in millimeters. Thus,
instead of saying that a screw has so many threads per inch,
it is said that the screw has so many millimeters lead. Sup-
pose, for example, that we have a lathe having a lead screw
with 6 threads per inch, and that a screw with 3 millimeters
lead is required to be cut. We can find the change gears to
be used in the same manner as has been previously explained
THREAD-CUTTING — MEASURING THREADS 69
for screws cut according to the English system, if we only
first find out how many threads per inch we wUl have if we
cut a screw with a certain lead given in millimeters. Thus,
in this case, we must find out how many threads there will
be in one inch if we cut a screw with 3 millimeters lead.
There are 25.4 millimeters to one inch, so that, if we find
out how many times 3 is contained in 25.4, we evidently
get the number of threads in one inch. To find out how
many times 3 is contained in 25.4, we divide 25.4 by 3.
It is not necessary to carry out the division. We can
25 4
simply write it as a fraction in the form — ^, this then being
the number of threads per inch. We now proceed as if
we had to do only with English threads. We place the
number of the threads on the lead screw in the lathe as the
numerator in a fraction, and the number of threads to be
cut, which number is expressed by the fraction -—-^ as the
it
denominator. Then we have
J..
25.4
This seems very complicated, but as we remember that
the line between the numerator and the denominator in a
fraction really means that we are to divide the numerator
by the denominator, then if we carry out this division we
get
25.4 6X3 18
6^
3 25.4 25.4
If we now proceed as in the case of figuring change
gears for any number of threads per inch we multiply
numerator and denominator by the same number until
we find suitable numbers of teeth for our gears. In the
60 SMALL TOOLS
case above we can find by trial that the first number by
which we can multiply 25.4 so that we get a whole num-
ber as result is 5. Multiplying 25.4 by 5 gives us 127.
This means that we must have one gear with 127 teeth
whenever we cut metric threads by means of an English
lead screw. The gear to mesh with the 127-teeth gear in
this case has 90 teeth, because 5 times 18 equals 90.
If we summarize what we have just said in rules, we
would express them as follows :
1. To find the number of threads per inch, when the
lead is given in millimeters, divide 25.4 by the number of
millimeters in the given lead.
2. To find the change gears for cutting metric threads
with an English lead screw, place the number of threads per
inch in the lead screw multiplied by the number of mUli-
meters in the lead of the thread to be cut as the numerator of
a fraction and 25.4 as the denominaior, and multiply
numerator and denominator by 5. The numerator and
denominator of the new fraction are the gears to be used.
These same rules expressed in formulas would be
number of threads per inch = , — -j-. '7^. — - —
lead in millimeters
and
number of threads per lead in millimeters ^
inch in lead screw of screw to be cut gear on spindle stud
25.4 X 6 ~" gear on lead screw
Of course it is sometimes necessary to compound the
gears, because the gear on the spindle stud would other-
wise get too many teeth, that is, would be too large. Sup-
pose, for an example, that we wish to cut a screw having
6 millimeters lead on a lathe having a lead screw with
8 threads per inch. According to our rule and formula
the gear on the spindle stud would then have 8x6x5,
or 240 teeth. As no lathe is provided with a change gear
THREAD-CUTTING — MEASURING THREADS 61
with so many teeth, we must use compound gearing. In
this case we would proceed as follows :
8 X6 X5 .48 X 5_ 48 X 120
25.4X5 127X1 127x24'
which is exactly the same method as has already been
explained under the head of compound gearing in con-
nection with the figuring of change gears for English
screws. The method of mounting these gears is shown
in the diagram, Fig. 18.
What should in particular
be impressed upon the mind
of the student is that there
is no difference in method of
figuring the gears whether
the thread to be cut is given lacT^
in the English or in the
metric system. If given in
the latter system, simply
transform the "lead in mil-
Kmeters'' to "number of
threads per inch" and pro-
ceed in exactly the same
way as if the thread had
been given according to the
English system.
Fig. 18
The 127-tooth gear is always placed on the lead screw
when cutting metric threads with an English lead screw.
Cutting an English Thread with a Metric Lead
Screw.
The method of figuring the change gears for a case
where an English screw is to be cut by a metric lead screw
is simply the reverse of the one already explained. We
62 SMALL TOOLS
simply transform the millimeter lead of the metric lead
screw into "number of threads per inch." This we do
in the same way as explained before, by dividing 25.4
(which is the number of millimeters in one inch) by the
number of millimeters in the lead of the metric lead screw.
After having obtained ithis number of threads per inch,
we proceed as usual, putting the number of threads per
inch of the lead screw in the numerator and the number
of threads per inch to be cut in the denominator of a
fraction, simplifying the fraction, and multiplying numer-
ator and denominator by 5 to get the number of teeth in
the change gears.
Suppose, for example, that we wish to cut 5 threads
per inch with a lead screw having 4 millimeters lead.
The number of threads per inch of the lead screw is then
25 4
-J- , and we find our gears by writing our fraction
25.4
4
5
This fraction can be simplified by actually dividing
25 4 25 4
-~ by 5, in which case we get ^ ' , as a result.
4 ^ ' ^5X4
Multiplying both numerator and denominator by 5
gives us then
25.4 X 5 _ 127
5X4X5 100'
which gives us the numbers of teeth in our change
gears.
The formula expressing this calculation would take
this form:
26.4 X 6 _ gear on spindle stud
number of threads lead in millimeters y 5 ~ gear on lead screw
per inch to be cut ^ of lead screw
THREAD-CUTTING— MEASURING THREADS 63
Expressed as a rule this formula would read :
To find the change gears for cutting English threads on
a metric lead screw, place 25.4 as the numerator and the
threads per inch to be cut multiplied by the number of milli-
meters in the lead of the lead screw in the denominator of a
fraction, and multiply numerator and denominator by 5.
The numerator and denominator of the new fraction are the
change gears to be used.
In this case too, of course, it sometimes becomes neces-
sary to compound the gears, in order to get gears which
are to be found in the set of gears provided with the lathe.
Sometimes the gears may be available, but they are so
large that the capacity of the lathe does not permit them
to be placed in a direct train; then, also, it becomes
necessary to compound the gears. Take the case which
we have already referred to, where we were to cut a screw
with 5 threads per inch, using a lead screw having 4 milli-
meters lead. We then obtained the gears with 127 and
100 teeth respectively. Now suppose that the lathe does
not possess a change gear with 100 teeth to be placed
in a direct train. The gears to be used in a compound
train would then have to be found as has already been
described and as shown in the following calculation :
25.4 X 5 127 127 X 1 127 X 25
5X4X5 100 50 X2 50x50
The 127-tooth gear is always put on the spindle stud
when cutting English screws with a metric lead screw.
A diagram of the arrangement of the gears in the last
example is shown in Fig. 19.
If there is any special reduction gearing in the head of
the lathe, this must of course be taken into consideration,
in the manner already described under the heading " Lathes
with Reduction Gearing in Head-Stock."
64
SMALL TOOLS
For those who prefer formulas to rules expressed in
words the whole previous discussion may be simply stated
as follows :
Let us first take the
case of an English thread
to be cut on a lathe pro-
vided with a metric lead
screw. As there are 25.4
millimeters in one inch,
the number of threads per
inch on the metric lead
screw equals 25.4 divided
by the pitch of the lead
screw expressed in milli-
meters; in other words, if
a is the pitch of the lead
screw in millimeters and C is the number of threads per
inch of same lead screw, then
^ 25.4
Fig. 19
Let c be the number of threads per inch to be cut on the
piece to be threaded; then the ratio of the change gears is
C _ 25.4 i- g _ 25.4
c c a X c
Change gears conforming to this ratio will cut an exactly
correct pitch. Multiply both denominator and numera-
tor by 5, thus making the formula read
127
5aX c
Thus it will be seen that if a gear with 127 teeth is
introduced in the train of gears and other gears are
selected, as indicated by the values a and c, the correct
change gears can be found without any trouble whatever.
THREAD-CUTTING — MEASURING THREADS 66
Let us assume for an example that the pitch of the
lead screw (a) equals 4 millimeters, and that 5 threads
per inch (c) are to be cut.
rru ^u V f 127 127 driver.
Then the ratio of gears = — = — — • , .
^ 20 X 5 100 driven.
If the lathe has a capacity of taking a 127- and 100-
tooth gear in a direct train, these gears are used; other-
wise, gears have to be compounded, and it is readily seen
that trains of gears composed as follows :
drivers drivers drivers
127 - 24. 127 - 30. 127 -32.
40 - 60' 50 - 60' 64 - 50'
driven driven driven
and many other combinations will serVe the purpose, the
gears above being such as generally go with any lathe.
The 127-tooth gear in this case ought to be mounted on
the spindle stud.
If we now take the case of a metric thread to be cut on
a lathe provided with an English lead screw, we will find
a formula for the ratio in the same manner.
Suppose d = the number of threads per inch on the
lead screw,
e — the pitch in millimeters on the screw to
be cut, and
/ = the number of threads per inch of same
screw.
Then referring to what has previously been said,
25 4 d d
f = — ^and the ratio of the change gears- == --— =
e f 25.4 -^ e
dx e _5dXe
25.4 127
Then, as before, it will be readily seen that even in this
case a gear with 127 teeth is necessary, and no other
gear can replace it, either in the first case or in this,
66 SMALL TOOLS
as 127 is a prime factor. In order to illustrate this for-
mula with an example, let us assume that the lead screw
has 8 threads per inch (d), and that a screw with 6 milli-
meters pitch (e) is to be cut. The ratio of gears is then
40 X 6
127 '
and trains of gears composed as follows :
drivers drivers drivers
96 - 90. • 100 - 60. • 80 - 75.
127 - 36' 127 - 25' 127 - 25'
driven driven driven
and others can be used in this case. Of course the 127-
tooth gear ought to be mounted on the screw in this case.
General Principles of Thread-Cutting.
The operations for cutting a thread are shortly as fol-
lows. The first step is to turn to the exact outside diameter.
This of course is more or less modified in the case of taps,
which are often wanted to be a trifle over-size. When
turning a blank to be threaded with Whitworth thread,
or with any thread form with a round top, the piece should
be turned from 0.002 inch over-size for quarter-inch size
to 0.004 inch for 1-inch size to insure that the rounded
form shall be perfect on the top of the threads. In cutting
the thread, the threading tool, which will be treated in
detail later, is of course the first consideration. If the tool
is correct in itself, it must also, in order to produce a
correct thread, be set square with the axis of the work,
which is done by a thread gauge. The height of the top
face of the tool should be exactly at the same height as
the center line of the piece to be threaded. If it is not,
the form of the thread will not be correct even if the thread
THREAD-CUTTING — MEASURING THREADS 67
tool be perfect, inasmuch as the latter must be duplicated
in a plane through the center of the piece to be threaded.
The thread is cut by successive small cuts; the last or
finishing cuts should be made with a very fine feed to
insure a smooth surface of the thread. A thin lubricant
of lard oil and turpentine is excellent for thread-cutting.
Mr. F. E. Shailor, in M achinery ,' MsiTchj 1907, says that
when meeting with difficulty in obtaining a smooth thread,
such as is required for screw gauges and taps, one good
way to obtain a smooth thread is to turn the tap nearly
to size and harden it, then draw the temper to a. "light
blue." When turning to size, if the tool does not stand
up weU, draw still lower, the object being to leave just
enough temper in the tap to make the steel firm. By
making light chips with a hard thread tool a glossy,
smooth thread will result. Another advantage gained by
hardening the tap before finishing is that it will greatly
eliminate the chances of the lead changing after the final
hardening. It is, however, not advisable to follow this
practice except in certain cases when a smooth thread is
the very highest object desired, because it is well known
that steel will, as a rule, lose its qualities of endurance and
strength by successive hardening and annealing.
Multiple Threads, — Multiple threads, double, triple, etc.,
are used in cases where a quick lead is required but a
deep thread is not desirable. It may be that the diameter
of the screw is so small, comparatively, that a deep thread
would seriously impair its strength or be entirely impos-
sible. Two, three, or more threads of less depth but
with the same lead as the coarse thread may then be
substituted. This condition is plainly illustrated in the
upper part, Aj of Fig. 20. The lead of a multiplertbreaded
screw is the distance it will travel in the nut for one
turn of the screw, or in other words, the distance from
68
SMALL TOOLS
center to center of the same thread. The pitch is the
distance from center to center of adjacent threads (see
Fig. 20). A great deal of confusion has always existed in
regard to the correct way to designate a multiple-threaded
SINGLE THREAD DOUBLE THREAD TRIPLE THREAD
Fig. 20. Single and Multiple Threads
screw. The safest way is to state the lead and the class
of thread, whether double or triple, etc. Thus, one-quarteT-
inch lead, double, means a screw with double thread, which,
when cut, has the lathe geared for 4 threads per inch, but
THREAD-CUTTING — MEASURING THREADS 69
each thread is cut only to a depth corresponding to 8
threads per inch. This same condition is also expressed by
4 threads per inchj dovble. These two ways of expressing the
number of multiple threads are both correct, but the former
is always the safer to use in order to avoid misunder-
standings, provided of course that the word ''lead'^ is used
and understood in its correct sense. A way of expression
which under no circumstances could be misunderstood, and
if misunderstood, would be inexcusable, would be to say:
one-quarter lead, one-eighth pitch, double thread.
When cutting a multiple thread it is obvious that the
lathe must be geared the same as if cutting a single thread
of the same lead as the multiple one. One thread is then
cut at a time, and the tool advanced after each thread an
exact amount corresponding to the pitch of the screw, by
disconnecting the spindle and the lead screw; the other
thread is then cut independently of the first, and so forth.
Multiple threads are cut even more advantageously by
means of chasers having several teeth. In such a case
there is no need of advancing the thread tool, as all the
threads will be cut at once. The lathe must be geared, of
course, to correspond to the lead of the screw to be cut, not
to the pitch of the chaser. If the latter were done, a single-
threaded screw would evidently result.
Measurino Threads.
When the thread of a screw or a tap is cut, the necessary
measuring or gauging of the outside diameter as well as of
the angle diameter, and the testing of the lead, is commonly
the next thing required if accuracy is of importance. The
outside diameter can be measured by ordinary micrometers.
The angle diameter, which is the most important, must be
measured by special means.
70
SMALL TOOLS
Brovm and Sharpe Thread Micrometers. — The Brown
and Sharpe Manufacturing Company are the originators
of a system of measuring the angle diameters of taps
by means of a special micrometer shown in Fig. 21. The
fixed anvil is V-shaped so as to fit over the thread, while
the movable point is cone-shaped so as to enable it to
enter the space between two threads and at the same
time be at liberty to revolve. The contact points are on
the sides of the thread, as they necessarily must be if it is
the angle diameter which is to be determined. The cone-
Fig. 21. Brown and Sharpe Thread Micrometer
shaped point of the measuring screw is slightly rounded so
as to insure that the point will not bear in the bottom of
the thread; there is also provision for sufficient clearance
at- the bottom of the V-shaped anvil to prevent the top of
the thread bearing at this point.
Considering this, it is evident that the actual outside
diameter of a screw or a tap has no influence upon the
reading of the micrometer, and as screws, at least those
made according to the United States standard system,
are not intended to bear upon the top of the thread when
screwed into a nut, but upon the angular sides, it is obvious
THREAIMIJUTTING — MEASURING THREADS 71
that measuring in this manner constitutes the only real test
of the size of a screw or tap. As we measure one-half of the
depth of the thread from the top, on each side, the diameter
of the thread as indicated by the micrometer, or the pitch
diameter, is the full size of the thread less the depth of one
thread. Referring to Fig. 22, when the point and anvil are
in contact, zero on the micrometer barrel represents a line
drawn through the plane ABj and if the caliper is opened,
say to 0.500, it represents the distance of the two planes
0.500 inch apart.
While the movable point measures all pitches, the fixed
anvil is Umited in its capacity, for if made large enough to
measure eight threads per inch it would be too wide at the
ezM
Fig. 22, Principle of Brown and Sharpe Thread Micrometer
top to measure twenty threads per inch, and if made to
measm-e twenty threads per inch it would be so small that
the coarser thread would not obtain a proper bearing in the
anvil.
The V anvil swivels, however, and therefore adapts
itself automatically to different angles of helix of the
thread. The only criticism that might be advanced in
regard to this tool is that the V anvil has flat sides, which,
when pressed against the helical surface of the screw
thread, will theoretically cause an over-size reading. This
point was not lost sight of in designing this tool, but
the difference between the micrometer reading and the
theoretically correct figure is so slight as to permit of
being wholly disregarded in practical work.
72
SMALL TOOLS
To find the theoretical angle diameter, which is
measured by the micrometer, one subtracts the depth of
the thread from the standard outside diameter. The
depths of the threads for all LTnited States, V, and Whit-
worth standard threads were given in the first chapter.
In Tables XXI and XXII in this chapter are given the
angle diameters for all standard United States and V
thread screws, that is, the reading of the Brown and
Sharpe thread micrometer if the screw or tap is correct.
TABLE XXI.
ANGLE DIAMETERS (BROWN AND SHARPE TmiEAD MICROMETER
READING) FOR UNITED STATES STANDARD SCREWS.
Diam-
eter '
TtiftLj,
Angle
Diam-
eter
Thrds.
Angle
Diam-
eter
Thrds.
Angle
of
Screw.
huh.
Diameter.
of
Screw.
per
Inch.
Diameter.
of
Screw.
per
Inch.
Diameter.
■h
64
0.0524
«
9
0.8653
2
^
1.8557
^!y
50
0.0807
1
8
0.9188
2i
4i
1.9807
40
0.1088
lA
7
0.9697
2i
4i
2.1057
, jy
36
0.1382
U
7
1.0322
21
4
2.2126
A
32
0.1672
lA
7
1.0947
2i
4
2.3376
A
28
0.1955
• H
7
1.1572
2f
4
2.4626
1
20
0.2175
lA
6
1.2042
2^
4
2.5876
t
18
0.2764
li
6
1.2667
2i
3}
2.6894
16
0.3344
lA
6
1.3292
3
3i
2.8144
A
14
0.3911
li
6
1.3917
3J
^
2.9394
}
13
0.4500
lA
5i
1.4444
3i
^
3.0644
A
12
0.5084
If
5i
1.5069
3|
3i
3.1751
J.
1
11
0.5660
IH
H
1.5694
3i
3i
3.3001
i
11
0.6285
If
5
1.6201
3f
3i
3.4251
10
0.6850
m
5
1.6826
3f
3
3.5335
f
10
0.7475
n
5
1.7451
3i
3
3.6585
9
0.8028
m
5
1.8076
4
3
3.7835
Ball-Point Micrometers, — If one has standard plug
gauges on hand, and it is thus not necessary to actually
measure the angle diameter but merely compare it
with the standard gauge, a ball-point micrometer, such
THREAD-CUTTING — MEASURING THREADS 73
TABLE XXII.
ANGLE DIAMETERS (BROWN AND SHARPE THREAD MICROMETER
READING) FOR STANDARD SHARP V-THREAD SCREWS.*
Diam-
eter
Thrds.
Angle
Diam-
eter
Tlirdfi,
Angle
Dlam-
Thrds.
Angle
of
Screw.
per
Inch.
Diameter.
of
Screw.
per
Iiic»h.
Diameter.
of
SCTPW.
per
Inch.
Diameter.
tV
72
0.0505
H
9
0.8413
2
4*
1.8075
^
56
0.0783
1
8
0.8917
2*
4*
1.9325
i
40
0.1033
iiV
8
0.9542
2i
4*
2.0575
32
0.1292
1*
7
1.0013
2|
4*
2.1825
A
24
0.1514
lA
7
1.0638
2*
4
2.2835
"h
24
0.1826
U
7
1.1263
2
4
2.4085
i
20
0.2067
lA
7 •
1.1888
2
4
2.5335
A
18
0.2644
i»
6
1.2307
2
4
2.6585
1
16
0.3209
lA
6
1.2932
3
3*
2.7526
A
14
0.3756
H
6
1.3557
3i
3*
2.8776
1
12
0.4278
lA
6
1.4182
3i
3*
3.0026
A
12
0.4903
1
5
1.4518
3*
31
3.1085
11
0.5463
U
5
1.5143
3*
3i
3.2335
i
11
0.6088
1
5
1.5768
3t
3i
3.3585
10
0.6634
1*
5
1 . 6393
3f
3
3.4613
«
10
0.7269
ij
4*
1.6825
3t
3
3.5863
1
9
0.7788
m
4i
1 . 7450
4
3
3.7113
as shown in Fig. 23, is all that is necessary. The balls,
which are made in one piece with stems which are
Enlarged view ^"^
of ball-point
Fig. 23. Ball-point Micrometer for Comparing Angle Diameters
* The figures given are for the theoretical angle diameter. If the sharp
V-thread for practical purposes is provided with a flat on the top of the thread,
the figures for the angle diameter, as given, should be increased by an amount
equal to width of flat x 1.732.
74
SMALL TOOLS
inserted in the anvil and the face of the measuring screw
respectively, are made in certain sizes corresponding
each to a certain series of pitches. It is evident that
as the object is not measuring but only comparing the
angle diameters, there is no need of the balls being in
any exact relation to the pitch, nor does one need a certain
size of ball for each pitch of thread. A certain relation
between the size of the ball points and the pitch of the
thread, however, must be maintained, inasmuch as the
Fig 24. Determining the Size of Ball Points
ball point used for a certain pitch must not be so large as
to bear only at the top or edge of the thread and not on
the sides, nor be so small as to tangent the flat in the
bottom of the thread.
The most desirable size of ball point would of course
be one that would tangent the sides of the thread at the
angle diameter as shown in Fig. 24. The diameter of
such a ball for the United States or V standard threads
is easily figured. If the point of tangent, Ay is located
at the angle diameter of the thread, the line AB equals
one-half the pitch. The radius AG of the ball point
THREAD-GUTTING — MEASURING THREADS 76
equals two times CD, if we consider only 60-degree
threads, the angle DAC then being 30 degrees. Conse-
quently, if d is the diameter of the ball point and p the
pitch of the thread,
CD =^ ADx tan 30°,
CD -^' AD --^ -^'
consequently
^ = 2 X tan 30°, or d = p X tan 30°.
4 4
From this we see that the best size of ball point for a
certain pitch is a diameter equal to 0.577 times the pitch.
But ball points may be used that are only about one-
third of the pitch or that are as large as to be 0.8 times
the pitch in diameter. In Table XXIII are given the
sizes of balls suitable for the most common numbers of
threads per inch. This table applies to threads of United
States standard and sharp V form.
TABLE XXIII.
BALL POINTS FOR MICROMETERS FOR COMPARING
ANGLE DIAMETERS.
Threads
Diameter
Threads
Diameter
per Inch.
of Ball.
per Inch.
of Ball.
24
0.022
9
0.060
22
0.025
8
0.070
20
0.028
7
0.080
18
0.030
6
0.090
16
0.035
5*
0.100
14
0.035
5
0.110
13
0.040
4i
0.120
12
0.045
4
0.130
11
0.050
3i
0.150
10
0.055
3
0.170
76
SMALL TOOLS
Three-Wire System for Measuring Threads. — A method
for measuring very correctly the angle diameter by means
of ordinary micrometers and three wires of equal dia-
meter has long been known. In this system three wires
are used as shown in Fig. 25, one wire being placed in the
angle of the thread on one side of the piece and the other
two on the opposite side, one on each side of the corre-
sponding thread, measuring over the whole with a microm-
[— <=:^ 17^^
-i«_.
Fig. 25. Measuring Threads by the Three-Wire System
eter. The formula for the micrometer reading is obtained
as follows :
In Fig. 26 assume that m is the bottom of a *V thread,
the circle showing one wire in place. Then angle
710
a = 30°; sin 30° = 0.5; —-= mn or 2 no = mn. As no
0.5
and np are radii of the same circle, it follows that
wp = 3 no = IJ X diameter of wire.
Multiplying by 2 to add a length mp for the opposite
THREAD-CUTTING — MEASURING THREADS 77
Bide gives 2 mp = 3 X diameter of wire. Hence for V
thread,
Diameter of screw -. ■=-rr ^ : — r
number of threads per inch
+ (3 X diameter of wire used) = micrometer reading.
For United States form we have to take into account
the flat at the bottom of the thread, so instead of using
the United States constant 1.299 we add to it one-eighth
Fig. 26. Deducing the Formula for the Micrometer Reading
of 1.732, or 0.2165, giving as a constant 1.5155, making the
formula
T^ . f 1-5155
Diameter of screw ^-j- -z : — =-
number of threads per inch
+ (3 X diameter of wire used) = micrometer reading.
These formulas may be expressed in a shorter form by
denoting the measurements as follows (see Fig. 25) :
T8 SMALL TOOLS
D = diameter of screw,
M = measurements over wires,
W = diameter of wires,
P = pitch of thread =
number of threads per inch
The following formulas will then apply to V threads*
M = D - 1.732 P + ZW.
D ^M + 1.732 P - 3 Tf .
The same formulas for the United States standard thread
are
M = D - 1.5155 P + 3 Tf ,
D = M + 1.5155 P ~ZW.
Suppose that we apply these formulas to a screw with
United States standard thread form; the screw is IJ inches
in diameter, with 12 threads per inch. The wires used for
measuring are 0.070 inch in diameter. The micrometer
reading for a correct screw should then be
H - 1.5155 X :f|- + 3 X 0.070 = 1.5837.
If the micrometer reading happens to be 1.591 in the
above case, that would indicate that the angle diameter of
the screw is not correct. The amount of the error would be
found by using the second formula, which gives the diameter
of the screw when the dimension over the wires is known.
1.591 + 1.5155 X r^ - 3 X 0.070 = 1.5073 = the actual
diameter of the screw.
From this we see that our screw is 0.0073 too large in
angle diameter. The outside diameter of course may be
correct, 1 J inches, but the flat on the top of the thread may
be incorrect so as to account for the difiference.
THREAI>-CUTTING — MEASURING THREADS 79
The above formulas together with a table giving the
values of 1.732 P and 1.5155 P for various numbers of
threads were given by Mr. J. Dangerfield in the American
Machinist, issue of May 31, 1906. The table has been
extended somewhat, so as to ^ve all standard pitches in
common use. (See Table XXIV.)
TABLE XXIV.
VALUES OF CONSTANTS USED IN FORMULAS FOR MEASURING ANGLE
DIAMETERS OF SCREWS BY THE THREE-WIRE SYSTEM.
No. of
No. of
Threads
V Thread.
U. S. Thread,
Threads
V Thread,
U. S. Thread,
per
1.732 P.
1.6156 P.
per
1.732 P.
1.5155 P.
Inch.
Inch.
2i
0.7698
0.6736
18
0.0962
0.0842
2i
0.7293
0.6381
20
0.0866
0.0768
^
0.6928
0.6062
22
0.0787
0.0689
^
0.6598
0.5773
24
0.0722
0.0631
H
0.6298
0.6511
26
0.0666
0.0583
2}
0.6025
0.5271
28
0.0619
0.0541
3
0.5774
0.5052
30
0.0577
0.0506
31
0.5329
0.4663
32
0.0541
0.0474
Zh
0.4949
0.4330
34
0.0509
0.0446
4
0.4330
0.3789
36
0.0481
0.0421
41
0.3849
0.3368
38
0.0456
0.0399
5
0.3464
0.3031
40
0.0433
0.0379
51
0.3149
0.2755
42
0.0412
0.0361
6
0.2887
0.2526
44
0.0394
0.0344
7
0.2474
0.2165
46
0.0377
0.0329
8
0.2165
0.1894
48
0.0361
0.0316
9
0.1925
0.1684
50
0.0346
0.0303
10
0.1732
0.1515
52
0.0333
0.0291
11
Q..1575
0.1378
56
0.0309
0.0271
12
0.1443
0.1263
60
0.0289
0.0263
13
0.1332
0.1166
64
0.0271
0.0237
14
0.1237
0.1082
68
0.0255
0.0223
15
0.1155
0.1010
72
0.0241
0.0210
16
0.1083
0.0947
80
0.0217
0.0189
This system for measuring the angle diameter of thread
has also been treated at some length by Mr. Joseph M.
Stabel in the January, 1904, issue of Machinery. He shows
a special micrometer gauge adapted for the purpose of meas-
80
SMALL TOOLS
uring with the aid of three wires. This instrument is illus-
trated in Fig. 27. It is composed of a regular micrometer
with its anvil cut off and its frame fixed into a base plate,
which in turn rests upon three hardened feet. Great care
should be taken when miUing the slot for the micrometer
frame in the base plate, as the frame must stand perfectly
perpendicular with the base if accurate results in measuring
are to be obtained. Upon the base plate rests the plate 6,
Pig. 27. Special Micrometer for Measuring Threads by Three -Wire
System
which serves as the anvil of the micrometer. This anvil
should be hardened, ground, and lapped perfectly parallel.
It is held in position by the screws c. The screw holes
should not pass entirely through the plate b, but leave the
top surface of this plate perfectly solid and free from any
obstructions. The wires are shown in positions at e. It is
of course not necessary to have this special measuring
instrument, as an ordinary micrometer answers the purpose
THREAD-CUTTING — MEASURING THREADS 81
for at least all fine pitches, but it is apparent that the tool
shown makes this measuring very much easier to handle
than it would be with regular micrometers.
In Machinery, March, 1907, Mr. F. E. Shailor shows a
method for securing and holding the wires while measuring
with ordinary micrometers. As shown in Fig. 28, the three
wires are fastened in a small wooden handle. It is evident
that each handle with its wires can be used only for a
o
END VIEW OF
WOOD HANDLE
WITH WIRES
WOOD HANDLE
Fig. 28. Method of Holding Wires
comparatively small number of pitches, and for diameters
which are within close range. Where a great deal of
measuring is to be done the arrangement shown in Fig. 27
is therefore to be recommended.
82
SMALL TOOLS
TABLE XXV.
MEASURING V AND UNITED STATES STANDARD THREADS BY
MEANS OF THE THREE-WIRE SYSTEM.
Diameter of
Number of
Diameter of
Dimension
Dimension
Screw.
Threads
Wire Used.
over Wires,
over Wires,
per Inch.
V Thread.
U. S. Thread.
i
18
0.035
0.2588
0.2708
i
20
0.035
0.2684
0.2792
i
22
0.035
0.2763
0.2861
24
0.035
0.2828
0.2919
^
18
0.035
0.3213
0.3333
^
20
0.035
0.3309
0.3417
ft
22
0.035
0.3388
0.3486
ft
24
0.035
0.3453
0.3544
i
16
0.040
0.3867
0.4003
18
0.040
0.3988
0.4108
}
20
0.040
0.4084
0.4192
A
14
0.050
0.4638
0.4793
T^
16
0.050
0.4792
0.4928
■ 1
12
0.050
0.5057
0.5237
■'
13
0.050
0.5168
0.5334
'
14
0.050
0.5263
0.5418
ft
12
0.050
0.5682
0.5862
V
14
0.050
0.5888
0.6043
10
0.070
0.6618
0.6835
■
11
0.070
0.6775
0.6972
.
12
0.070
0.6907
0.7087
X
10
0.070
0.7243
0.7460
-l
11
0.070
0.7400
0.7597
10
0.070
0.7868
0.8085
J .
11
0.070
0.8025
0.8222
J .
12
0.070
0.8157
0.8337
1
9
0.070
0.8300
0.8541
*
10
0.070
0.8493
0.8710
8
0.090
0.9285
0.9556
9
0.090
0.9525
0.9766
10
0.090
0.9718
0.9935
i
8
0.090
0.9910
1.0181
«
9
0.090
1.0150
1.0391
1
8
0.090
1.0535
1.0806
1
9
0.090
1.0775
1.1016
11
7
0.090
1.1476
1.1785
li
7
0.090
1.2726
1.3035
u
6
0.150
1.5363
1.5724
u
6
0.150
1.6613
1.6974
If
5i '
0.150
1.7601
1.7995
If
5
0.150
1.8536
1.8969
H
5
0.150
1.9786
2.0219
THREAI>-CUTTING — MEASURING THREADS 83
TABLE XX\,— Continued.
Diameter of
Number of
Diameter of
Dimension
Dimension
Screw.
Threads
per Inch.
Wire Used.
over Wires,
V Thread.
over Wires,
U. S. Thread.
2
4i
0.150
2.0651
2.1132
21
4i
0.150
2.3151
2.3632
^
4
0.150
2.5170
2.5711
2}
4
0.150
2.7670
2.8211
3
3J
0.200
3.1051
3.1670
3i
^
0.200
3.3551
3.4170
Zi
3i
0.250
3.7171
3.7837
3|
3
0.250
3.9226
3.9948
4
3
0.250
4.1726
4.2448
4i
21
0.250
4.3975
4.4729
^
2}
0.250
4.6202
4.6989
4}
2f
0.250
4.8402
4.9227
5
2*
0.250
5.0572
5.1438
In Table XXV are given the most common diameters
and corresponding pitches, and, for given wires used in
measuring, the dimension over the wires. If the sizes of
wires stated are used, this table will save all figuring in the
cases where the diameter and the pitch of the screw or tap
to be measured can be found in the table. The dimensions
are given for sharp V thread as well as for United States
standard thread.
Limits for Diameter of Wires Used in the Three-Wire
System. — It is evident that there are certain maximum
and minimum limits for the sizes of the wire which can be
used for measuring the diameters of screws and taps with
the three-wire system. The most desirable size of wire
would be that which is of the same diameter as the ball
points for ball-point micrometers previously referred to.
The wires would then tangent the sides of the thread at the
points over which the angle diameter is measured. This
size of wire, however, is rather small, too small, in fact,
for measuring taps with sharp V thread, as the anvil and
84
SMALL TOOLS
the point or face of the micrometer screw would be liable
to bear upon the top edges of the thread before bearing
upon the wire.
We can, however, determine the limits between which
wires may be selected for each particular pitch. The
limits must be such, for the minimum dimension, that the
wires extend beyond the top of the thread so as to prevent
Fig. 29. Limits for Wires Used when Measuring Threads by the
Three -Wire System
the micrometer bearing on the threads, as mentioned, and
for the maximum limit, that the wires tangent the sides
of the thread, and do not bear upon the comers or edges
of the top of the thread. These maximum and minimum
limits with regard to the United States and V standard
threads are clearly indicated in Fig. 29.
If we first refer to the minimum size of wire for the
United States standard thread, we find that to be reached
THREAD-CUTTING — MEASURING THREADS 85
when the line AB (Fig. 29) tangents the wire. The length
of the side AB of the triangle into which the circle repre-
7
senting the wire is inscribed equals - X pitch. But
o
AB X cos 30° = BD, and CD = \bD (the radius of the
circle inscribed in an equilateral triangle being equal to
one-third the altitude). Consequently
1 17
CD = -^ AJS X cos 30° = ~ X ~ X pitch X cos 30°
o o o
= 0.2526 X pitch.
The minimum size of wire would then be twice this, or
Minimum wire = 0.5052 X pitch = r=^ 7-77-^ — \ : — r •
No. of threads per mch
The maximum size for the United States standard
thread would be a wire which would tangent the thread
7
at E and H, Fig. 29. We have here EH ^ ^x pitch,
o
EF = \eH, and EG = -^^^ • Consequently
2 cos 30
The maximum size of wire would be twice this, or
1.0104
Max. wire = 1.0104 X pitch = _ _ . . , . , -
No. of threads per inch
In a similar manner we find the minimum and maxi-
mum wires for the sharp V thread.
Min. wire = -^ '^ pitch X cos 30° = ;
3 No. of threads per inch
M • s pitch ^ L15^ .
cos 30° No. of threads per inch
86 SMALL TOOLS
While the figures found give the extreme linuts, it is
evident that the wires used ought not to be near to these
limits, particularly not to the larger one, as that gives a
poor place for contact with the thread. We may say that
if the wires vary between 0.65 X pitch and 0.9 X pitch,
that will give us satisfactory results. Allowing these
limits, it is evident that the same size wire may be
used for a number of sizes, as is the case in Table
XXV.
Formulas for Whitworth Thread. — When measuring
Whitworth threads with the three-wire system the formula
used is
Diameter of screw — — T-~r — ^ : — ? + (3.1657
No. of threads per inch
X diameter of wire used) = micrometer reading.
In other words, if
D = diameter of screw,
M = measurement over wires,
W = diameter of wires,
P = pitch of thread = r= t—. ~ -, — - ,
No. of threads per mch
then
M = D - 1.6008 P + 3.1657 W and
D = M + 1.6008 P - 3.1657 W.
In Table XXVI are given the values of the constant
1.6008 P for various pitches.
The maximum and minimum limits of the wires used
for measuring Whitworth threads are determined by the
formulas
Maximum limit = 0.81 pitch and
Minimum limit = 0.51 pitch.
THREAD-CUTTING — MEASURING THREADS 87
TABLE XXVI.
VALUES OF OONSTANTS USED IN FORMULAS FOR MEASURING
ANGLE DIAMETERS OFWHITWORTH SCREWS WITH THE THREE-
WIRE SYSTEM.
No. of
Whit-
No. of
Whit-
No. of
Whit-
No. of
Whit-
Threads
worth
Threads
worth
Threads
worth
Thread.'
worth
per
Thread,
per
Thread,
per
Thread,
per
Thread,
Inch.
1.6008 P.
Inch.
1.6008 P.
Inch.
18
1.6008 P.
Inch.
1.6008 P.
2i
0.7115
5i
0.2911
0.0889
42
0.0381
2|
0.6740
6
0.2668
So
0.0800
44
0.0364
2^
0.6403
7
0.2287
22
0.0728
46
0.0348
2g
0.6098
8
0.2001
24
0.0667
48
0.0334
2f
0.5821
9
0.1779
26
0.0616
60
0.0320
2t
0.5568
10
0.1601
28
0.0572
52
0.0308
3
0.5336
11
0.1455
30
0.0534
56
0.0286
3i
0.4926
12
0.1334
32
0.0500
60
0.0267
H
0.4574
13
0.1231
34
0.0471
64
0.0250
4
0.4002
14
0.1143
36
0.0445
68
0.0235
^
0.3557
15
0.1067
38
0.0421
72
0.0222
5
0.3202
16
0.1001
40
0.0400
80
0.0200
Measuring Acrne Threads with the Three-Wire System. —
The three-wire system may also be used for measuring
Acme threads in the angle. As there are no standard
diameters corresponding to certain pitches in the Acme
standard, we cannot make up a table in the same manner
as we have done for the V and United States standard
threads. In Table XX\ni, however, all the figures necessary
to facihtate measuring Acme threads with three wires are
given. In the second column the size of wire to use for
certain pitches is stated. The third column in the table
gives the amount which must be added to the root diameter
of an Acme tap or screw to find the dimension over the
wires. The last column ^ves the amount which must be
added to the standard outside diameter to find the size over
the wires. The convenience of this last column is that
it makes it unnecessary to find the root diameter of the
screw in order to measure the angle diameter.
88
SMALL TOOLS
If it should, for instance, be desired to cut a one-inch
screw or tap with six threads per inch, the only computation
necessary is to add the value found in the last column in
Table XXVII, opposite six threads per inch, to the outside
diameter of the screw :
1.000 + 0.0521 = 1.0521,
which is the size that the screw or tap should measure over
wires 0.0916 inch in diameter.
In regard to the points of 'tangency between the wires and
the sides of the thread, these points would evidently be
most correctly located if they coincided with the points over
'"^^mm^
Fig. 30. Determining Formula for Measuring Acme Threads by
Tliree-Wire System
which the angle diameter is measured, that is, the points
C and D in Fig. 30. This would be permissible for Acme
thread screws, but in the case of taps with fine pitch the
wire would be too small to reach above the top of the thread,
which on Acme thread taps is 0.010 inch higher than on the
screws. For this reason the points of tangency must ' be
located a trifle further toward the top of the thread, say at
3
AB (Fig. 30) which is r^ X pitch from the top of the thread.
THREAD-CUTTING — MEASURING THREADS 89
The diameter of the wire for measuring will be found as
follows. CD = ^, if p signifies the pitch, and is located at
a distance of - p from the top of the thread, inasmuch as
CT> is at the location of the pitch line over which the angle
diameter is measured.
lb
The diameter of the wire =
C!onsequently
AB
cos 14i°
2 + 2x^^14^
Diam. of wire == --— = 0.5498 p.
cos 14$°
The diameter according to this formula is given in Table
XXVII.
TABLE XXVII.
MEASURING ACME THREAD SCREWS BY THE THREE-WmE SYSTEM.
Dimen-
Dimen-
Dimen-
Dimen-
No. of
Threads
Diam-
eter of
sion over
Wires
minus
sion over
Wires
minus
No. of
Threads
Diam-
eter of
sion over
Wires
minus
sion over
Wires
minus
per
Inch.
Wires
Used.
Root
Diam.
Standard
Diam.
per
Inch.
Wires
Used.
Root
Diam.
Standard
Diam.
(=2 a).
(=2 6).
(=2 a).
(=2 6).
1
0.5498
1.3324
0.3124
5
•
0.1100
0.2825
0.0625
li
0.3665
0.8950
0.2083
51
0.1000
0.2586
0.0568
2
0.2749
0.6762
0.1562
6
0.0916
0.2388
0.0521
21
0.2199
0.5450
0.1250
7
0.0785
0.2075
0.0446
3
0.1833
0.4574
0.1041
8
0.0687
0.1840
0.0390
31
0.1571
0.3950
0.0893
9
0.0611
0.1658
0.0347
4
0.1375
0.3481
0.0781
10
0.0550
0.1512
0.0312
41
0.1222
0.3116
0.0694
12
0.0458
0.1293
0.0260
90 SMALL TOOLS
The formula for determining the distance b is easily found.
Let R be the radius of the wire. Then
But EF = R X sin 14^°, and R = 0.2749 p, according
to our previous formula for the diameter of wire.
Consequently
6 = 0.1562 p.
Fig. 31. Measuring Acme Threads by Three-wire System
The dimension a in Fig. 31 and Table XXVII is simply
b + depth of thread, or, as given in the table, 2 o = 2 6 +
double depth of thread = 2 6 + p + 0.020.
The best and most handy tool for measuring the depth
of Acme and square threads is the micrometer depth gauge.
As this tool is fairly common in the shop, a description
seems unnecessary.
Sensitive Micrometer Attachinent. — When testing the
diameters of taps or other pieces that are handled in
great quantities and are all supposed to be within cer-
tain close limits of a standard dimension, the ordinary
micrometer presents the difficulty of having to be moved
for each piece, and small variations in diameters have to
be carefully read off from the graduations on the barrel.
THREAD-CUTTING — MEASURING THREADS 91
Not only does this take a comparatively long time but
it also easily happens that the differences from the
standard diameter are not carefully noted and pieces are
liable to pass inspection that would not pass if a con-
venient arrangement for reading off the differences were at
hand. Fig. 32 shows a regular Brown and Sharpe microm-
eter fitted with a sensitive arrangement for testing and
inspecting the diameters of pieces which must be within
certain close limits of variation. The addition to the ordi-
Fig. 82. Sensitive Micrometer Attachment
nary micrometer is all at the anvil end of the instrument.
The anvil itself is loose and consists of a plunger B,
held in place by a small pin A. The pin has freedom
to move in a slot in the micrometer body, as shown in the
enlarged view in the cut. A spring C holds the plunger B
up against the work to be measured and a screw D is pro-
vided for obtaining the proper tension in the spring. The
screw and the spring are contained in an extension E
screwed and doweled to the body of the micrometer. A
pointer or indicator is provided which is pivoted at F and
has one extension arm resting against the pin A, which
92 SMALL TOOLS
is pointed in order to secure a line contact. At the end
of the indicator is a small scale graduated with the zero
mark in the center, and as the indicator swings to one
side or the other, the variations in the size of the piece
measured are easily determined. A small spring G is
provided for holding the pointer up against the pin A.
The case H simply serves the purpose of protecting the
spring mentioned. As the plunger B takes up more space
than the regular anvil, the readings of the micrometer
cannot be direct. The plunger B can be made of such
dimensions, however, that- 0.100 inch deducted from the
barrel and thimble reading will give the actual dimensions.
Such a deduction is easily made in all cases. In other
words, the reading of the micrometer should be 0.100
when the face of the measuring screw is in contact with the
face of the plimger; the 0.100 inch mark is thus the zero
of this measuring tool.
When wanting to measure a number of pieces, a stand-
ard size piece or gauge is placed between the plunger B and
the face L of the micrometer screw and the instrument is
adjusted until the indicator points exactly to zero on the
small scale provided on the body of the micrometer.
After this the micrometer is locked and the pieces to be
measured are pushed one after another between the face
L and the plunger B, the indications of the pointer M
being meanwhile observed. Whenever the pointer shows
too great a difference the piece of course does not pass
inspection. All deviations are easily detected, and any
person of ordinary common sense can be employed for
inspecting the work.
Testing the Lead of Taps and Screws.
In cases where there is no necessity of ascertaining the
exact error in the lead of a screw or tap, and when only
THREAD-CUTTING — MEASURING THREADS 98
a limited number are to be tested, a fairly good test is
afforded by simply screwing the thread into a female gauge.
The threaded portion of this latter should then, however,
be fairly long, so that errors in lead, which are liable to
be very small m a short distance, may be detected by tak-
ing account of the error in the comparatively long length.
Ordinarily, however, when quantities of taps are to be
tested, the errors in lead are most easily ascertained by
some device particularly intended for the testing of the
lead of a screw thread alone. Some devices which test
both the lead and the diameter within certain limits are
,/^v/ V V v"y'^w.'V^v''^^v/V'
ft
ro
V
T^.
:^
^M3
Fig. 33. British Grauge for Simultaneoius Testing of Lead and Angle
Diameter
also in use. Of these latter, two examples are shown in a
report on British Standard Systems for Limit Gauges for
Screw Threads, presented to the Engineering Standards
Committee of Great Britain.
Testing the Lead by Gauges.
The first of these gauges is shown in Fig. 33. In this
gauge, allowance is made for a permissible error in angle
diameter and lead. As is plainly shown in the cut, the
screw thread enters between three fixed points, shaped
like the thread, two of which are located in the lower jaw
94 SMALL TOOLS
of the gauge and one in the upper. The distance between
the two points on the lower part of the gauge should be
equal to about twice the diameter of the screw. The fixed
point in the upper jaw should, of course, be placed midway
between the points in the lower jaw. At A is shown a
ground flat face which is so adjusted that the small cylinder
C, of such diameter that it will touch the thread about
half way down its depth, will barely enter between the
flat face and the thread of the bolt for the minimum
permissible diameter, but will ''not go" as a general rule.
This device then gives a practical test for both diameter
and lead. If the lead were out too much, the screw would
not enter the gauge, because the two points in the lower
jaw would not fit the pitch of the thread, these points
being, of course, set to a standard gauge. If, again, it
could be conceived that the diameter was so much smaller
than the standard that the screw or tap could be placed
in the gauge in spite of the lead being an appreciable
amount long or short, then the feeler C would enter so
freely between the face A and the screw as to indicate
that the screw was not within permissible limits. It
will be noticed that provision is made for getting the
points entering the threads placed exactly in the center
of the screw. In the end view the screw is shown rest-
ing with one side up against the back of the gauge, the
distance from the back of the gauge to the center of the
points being equal to half the diameter of the screw. It
is evident that gauges of this kind will have to be made
for each different diameter and pitch.
Another form of gauge intended to deal with shorter
lengths of thread than the one just described is shown in
Fig. 34. In this case two separate gauges are applied,
one minimum and one maximum. The screw is supposed
to enter into the one and refuse to enter into the other.
THREAD-CUTTING — MEASURING THREADS 95
In this gauge the top plates T are made of hardened steel
and contain V teeth set as shown, the distance L repre-
senting the next even num-
_ f^n nn/T^
.Ml
T 0^
O* K'0 T
ber of threads immediately
above the number con-
tained in a length of screw
equal to the diameter of the
thread, while the distance
Lj is one thread shorter.
The plates are screwed,
and preferably doweled, to
a base plate, and are, of
course, made and adjusted
to a standard plug. At s
are shown screws which can
be so adjusted that the
measurement can be made
exactly at the center of
the screw, the distance
from the faces of screws s
to the center of the gauge plates being equal to one-half
the diameter of the screw.
0)^' O' i<lQ>
Fig. 34. Maximum and Minimum
Gauge for Lead and Angle Di-
ameter
Comparators for the Lead of Taps and Screws.
When it is wanted, however, to determine the errors in
pitch with some exactitude and not to find out only
whether the error is between certain limits, then the
instrument termed 'thread comparator'' is used. This
consists, in its simplest form (see Fig. 35), of a fixed block
A and a sliding block B provided with ball points. The
sliding block operates a pointer C, which on a large scale
indexes the errors of lead. The manner of using this
instrument is as follows. A standard plug is first placed
96
SMALL TOOLS
against the device so that the ball points enter in threads,
say one inch apart. The position of the pointer on the
scale is noted when the standard plug engages the ball
points, the free block B adjusting itself to the thread into
which its ball point enters, and carrying with it the
pointer C. Next the tap or screw to be tested is placed
in position against the device. If the lead of this screw
/VVV\AA/VVVVVV
Tap or Thread Plug
Fig. 35. Simple Form of Comparator for Lead of Screw Threads
or tap is correct and is the same as that of the plug,
the pointer will evidently occupy the same position in
relation to the scale as in the case of the plug. If the
tap or screw is long or short in the lead, the pointer
will show the amount on the scale by swinging either
to the left or to the right. The scale should, of course,
preferably be graduated so as to show thousandths of an
inch.
THREAD-CUTTING — MEASURING THREADS 97
A more elaborate device for measuring the errors in lead
of taps is shown in Fig.. 36. Here one ball point A, which
we may call the fixed, is mounted in a slide D, which latter
is operated by a knurled head screw B. Ball point A may
be screwed into any of the holes C, which may be one-half
K.
if
1 r
I 9
!
/
r . w
1 '' 1
6 1
1 <L 1
ilr
-.
rt*t
■iifi
1 1 • 1 1
lU^
^^b
?l
1
I
M
i
S
I
ttfD
inch apart; thus one may with this device measure the
lead in one inch, or in any length up to six inches, as may be
desired, by moving the ball point A to different positions in
the slide D. The ball point E is inserted in a movable block
98 SMALL TOOLS
resting on a ball bearing. This block, in turn, is connected
through the lever F with the indicator or sensitive gauge (?,
which should be so arranged and graduated that thou-
sandths of an inch can be easily read. When the standard
plug is placed against this device, the ball points entering
between threads in the same way as in the device previously
described, the slide D can be so adjusted by the knurled
head screw B that the indicator points to zero. When the
screw or tap to be tested is placed against the ball points,
any error will then be apparent by jbhe motion imparted by
too long or too short lead to the movable ball point E.
This motion is, of course, carried to the indicator through
the lever arm F. If the latter is graduated in thousandths
of an inch, the graduations below or above zero will indicate
the amount in thousandths of an inch that a tap or screw-
is short or long in the lead in the distance originally meas-
ured on the plug, Le., the distance between the ball points
when the plug was placed in position against the device.
In the device shown, the length of the lever F, between its
pivot and that end which is operated by the movable block,
is half of the length between the pivot and the end operating
the gauge. Consequently, if the gauge be graduated to show
movements of 0.001 inch on its own plunger, it will indicate
a motion of 0.001 inch on the movable ball point by moving
two graduations on its own scale. Very close measurements
are consequently possible.
Of course this device is only one modification of the many
possible for obtaining the same results. Very likely there
are others equally good, but this one is shown as an example
of a satisfactory design, and at the same time as an indi-
cation of the principles involved in the design of compara-
tors for the lead of screw and tap threads.
CHAPTER III
threading tools. — definitions of taps.
Simple Forms of Thread Tools.
Thread tools for V, United States, and Whitworth Threads,
— A threading tool of the simplest forai is shown in
Fig. 37. This tool is provided with a shank held in the
tool-post and ground on the
T^
end to the shape of the thread ~
to be cut, in this case a sharp
V thread. The tool should
be ground flat on the top face ^
AB, and the sides CD and EF
should form an angle of 60
degrees. It should be noted
that this angle must measure
60 degrees in the plane AB, ^'S' ^^,; ^"^^^^'^ ^f ™ ^^
,, , . n . 1 . V Thread Tool
as the angle in tnis plane is
the one which will be duplicated in the thread-cutting. The
angle between the two faces in the section GH, perpendic-
ular to the line KL, the tool being given clearance, will be
slightly more than 60 degrees. In grinding an ordinary tool
as shown, it is unimportant what this latter angle is so
long as the tool fits the thread gauge measured in the plane
AB. When making special thread-cutting tools which are
groimd in special fixtures, or grinding machines, however,
the angle in the section GH is the one taken into account.
It is, of course, of great importance that the clearance
angle KLM should be permanently settled upon in such
cases, as the difference between the angle between the faces
99
100
SMALL TOOLS
Fig. 38. Simplest Form of
Thread Tool for United
States Standard Thread
measured in the section GH and the angle measured in the
plane AB is directly dependent upon the clearance angle.
This clearance angle is usually made 15 degrees.
In the case of a United States standard thread tool,
shown in Fig. 38, the diflSculty of correctly measuring the
flat is the one of the greatest
importance. In ordinary practice
this flat is made in accordance
with standard thread gauges,
such as are sold for instance by
the Brown and Sharpe Ciompany ;
but if the flat must be fully cor-
rect, as is required in thread
tools manufactured for the market
or for making thread gauges, a
more complicated method must
be resorted to. This method will
be treated in detail in connection with single-point cutters
used in standard thread tool holders.
Thread tools for the Whitworth standard thread form
in fact are forming tools. As
seen from Fig. 39, the tool is
provided with round comers
on the sides of the tool to
form the round points of the
top of the thread, while the
point of the tool of course forms
the actual groove or thread.
Thread Tools for Square
Threads. — Tools for cutting
square threads must be given
"side clearance" as well as
clearance for the cutting edge. The latter is 15 degrees,
as commonly used for all threading tools. The former
Fig. 89.
Thread Tool for Whit-
worth Thread
THREADING TOOLS — DEFINITIONS OF TAPS 101
depends upon the diameter of the screw to be cut and the
pitch of the thread. A tool for cutting square threads is
shown in Pig. 40. The angle DCE is the side clearance
angle, or the angle which the sides of the tool must make
with the vertical line in order to clear the sides of the
thread in the cutting operation. This angle should be
equal to the helical angle of the thread. In other words,
the tangent for the side clearance angle is equal to the
p
Fig. 40. Square-Thread Tool
lead divided by the circumference
expressed in a formula,
I
of the screw, or if
tan DCE =
7:d
if I equals the lead of the thread and d the outside diame-
ter of the screw. Instead of using the outside diameter of
the screw it would be more correct to use the angle diame-
ter of the screw in the formula, although this is seldom
done. In such a case the formula would be transformed
into
tsinDCE = ,J ...
7t{d- ip)
in which formula I and d denote the same quantities as
102 SMALL TOOLS
before, and p the pitch of the thread. In the case of a
single-threaded screw, of course, the pitch and the lead
would be the same.
This clearance angle can be constructed graphically in a
very simple manner. In Fig. 41, draw a line AB equal to
the circumference of the screw and at JS a line BC at
right angles to AB; the length of BC should be equal to
the lead of the thread. Draw a line from A to C. The
angle BAC in the required clearance angle, provided the
drawing has been made fairly accurate. This angle can
be measured by means of a protractor and the tool
Fig. 41. Laying out the Clearance Angle for a Square-Thread Tool
ground according to it without the use of trigonometrical
tables.
Tools for the Acme standard thread are similar to those
for square thread, but as a rule do not need side clearance
except for steep pitches. The width of the flat is deter-
mined by a thread gauge, the same as for the United States
standard thread.
Thread-Tool Holders.
Ordinarily, however, it is cheaper to use threading tools
held in special holders. The same holder can be used for
all sizes of threading tools, and the tools themselves are
made with a constant cross section from the beginning, so
that all grinding takes place on the top of the tool, the
thread form remaining perfect until the thread tool is
THREADING TOOLS — DEFINITIONS OF TAPS 108
used up by grinding. A holder which is manufactured by
the Pratt and Whitney Company and imiversally used, is
shown in Fig. 42. Threading tools for use with this holder
are shown in Figs. 43 and 44. Referring to the holder it
will be noticed that the tool is held in position by means
of a tongue A, and clamped tightly by a clamp B and the
nut C. An elevating screw D is provided by means of
which the threading tool proper, which has a thread on
Fig. 42. Pratt and Whitney Thread-Tool Holder
its back part, may be raised or lowered so as always to be
adjusted to its proper height. The screw D is stationary
as far as longitudinal movement is concerned, being held
in place by the pin E; consequently the tool will move
whenever the adjusting screw is turned. The screw F is
for adjusting the height of the clamp B in relation to the
body of the holder, so that if the threading tool proper
should be either a little too thick or too thin, a perfect
bearing can still be obtained by adjusting this screw.
104
SMALL TOOLS
Single-Point Cutters.
In Figs. 43 and 44 the ordinary thread tool or single-
point cutters used with this holder are shown. The
former cut shows the form of tool for all pitches smaller
than 4 threads per inch, while Fig. 44 shows the tool used
for coarse pitches, say from 2^ to 4 threads per inch.
This form for coarse pitches is necessitated by the width of
the body of the tool, which is only one-quarter inch, and
Fig. 43. Single-Point Cutter used in Pratt and Whitney Thread-Tool
Holder for Pitches finer than 4 Threads per Inch
it is obvious that the, cutting part of the tool itself must
at least be equal to the pitch, hence for pitches coarser
than 4 threads per inch the front or cutting part is made
seven-sixteenths inch wide.
Special forms of single-point cutters are shown in
Fig. 45. Here the cutting point is offset with regard to
the body of the tool in order to make it possible to cut a
thread close up to a shoulder. The tool to the left is
termed a right-hand offset tool, and the one to the right
is a left-hand offset thread tool.
THREADING TOOLS — DEFINITIONS OF TAPS 105
Fig. 44. Single-Point Cutter used in Pratt and Whitney Thread-Tool
Holder, 2^ to 4 Threads per Inch
Fig. 45. Offset Single-Point Cutters
Chasers.
In Fig. 46 is shown the common form of thread chaser
used in the thread-tool holder referred to. While the
part of this chaser having provision for being clamped in
a holder and adjusted can be of a description to suit any
106
SMALL TOOLS
holder, the part containing the thread can in all cases
be made according to the dimensions given in Table
XXVIIL
Fig. 46
TABLE XXVIII.
DIMENSIONS OF THREADING CHASERS.
No. Of
Threads
No. of
No. of
No. of
A.
B.
Teeth
Threads
A.
B.
Teeth
per Inch.
in
Chaser.
per
Inch.
in
Chaser.
3
1.333
a
4
12
0.667
ft
8
31
1.231
1
4
13
0.615
ft
8
3i
1.143
1
4
14
0.571
i
8
4
1.000
4
16
0.500
i
8
^
1.111
1
5
18
0.500
i
9
5
1.000
i
5
20
0.450
i
9
5i
0.909
i
5
22
0.409
ft
9
6
0.833
i
5
24
0.375
9
7
0.714
f
5
26
0.385
ft
10
8
0.750
6
28
0.357
ft
10
9
0.667
1
6
30
0.333
ft
10
10
0.700
1
7
32
0.312
i
10
11
0.636
1
7
36
0.278
i
10
m
0.696
f
8
48
0.250
i
12
The Making of Threading Tools.
United States Thread Tools. — The chief requirements for
cutting a correct thread are correct threading tools, a
correct setting of the tool, and a lathe with a reasonably
THREADING TOOLS — DEFINITIONS OF TAPS 107
accurate lead screw. In making the thread tool a correct
60-degree angle gauge is necessary. To produce such a
gauge first plane up a piece of steel in the shape of an
equilateral triangle as shown at a in Fig. 47. After
hardening this triangle, grind and lap the edges until the
three comer angles prove to be exactly alike when meas-
ured with a protractor. This is now the master gauge.
To produce the female gauge make two pieces, one right
hand and one left, like that shown at h in Fig. 47; harden
Fig. 47. Gauge for Making a 60-Degree Tiiread Tool
them and lap the edges that form the 150-degree angle so
that they are straight, and square with both sides. When
this is done the two pieces should be screwed, and doweled
to a backing plftte d as shown in Fig. 47, using the master
triangle to locate them, thus producing a practically per-
fect female gauge.
In making up the tool some form of cutter to be used in
a holder should be chosen in preference to a forged tool
on account of convenience in handling and measuring and
the facility with which it may be reground without
108 SMALL TOOLS
destroying the shape. The tool should be made so that
the top will stand level when in the holder, and the clear-
ance should be about 15 degrees, which is ample for a
single thread unless the pitch is very coarse. With that
amount of clearance the included angle between the sides
of the tool in a plane perpendicular to the front edge
is approximately 61° 44'. The tool should be planed to
that angle as nearly as is possible by measuring with a
protractor, then, to test its accuracy, it should be placed
top down on a flat piece of glass c and tried with the
60-degree gauge as shown in Fig. 47. After lapping the
tool until it shuts out the light when tried in this man-
ner, the angle may be considered as nearly correct as is
possible to obtain with ordinary means. To adapt the
V thread tool thus made to cut the United States standard
form of thread, it is only necessary to grind ofif the sharp*
edge an amount equal to one-eighth of the depth of a
V thread of the required pitch, or for 20 threads per inch
' ^ Q "^ 0.0054 inch. To test the accuracy of this
grinding, a piece of steel should be turned up to the correct
outside diameter and a short shoulder turned down at
the end to the correct diameter of the bottom of the
thread; then the piece is threaded and the tool fed in
imtil the flat of the tool just tangents the shoulder. Then
cut a nick in the edge of a piece of sheet steel with the
threading tool. This sheet steel piece is now applied like
a gauge to the threaded cylindrical piece. If the nick in
the sheet steel fits the thread so that it shuts out the light,
the flat of the tool is correct.
In preparing a plug gauge for threading it should be
made the same as the cylindrical test piece above, with a
part turned down to the root diameter of the thread,
except that for V thread it is customary to leave the
THREADING TOOLS — DEFINITIONS OF TAPS 109
shoulder 0.005 inch large on account of the impossibility
of producing a perfectly sharp point on the tool. The
thread tool should be set level, with the top at the same
height as the center line of the spindle of the lathe,
otherwise the correct angle will not be reproduced. After
a master plug has once been produced, it is not necessary
to turn down a portion to the root diameter of the thread,
as the work can be compared with the master plug by
means of a micrometer fitted with either ball or V points
for measuring in the angle of the thread.
It occasionally happens that a tap is to be threaded, or
other external threading is to be done, of an odd size or
pitch where it is desired to originate a master plug. In
such cases it is best to use the three-wire system for
measuring the angle of the thread.
Measuring Width of Flat on United States Standard
Thread Tools. — When making United States standard
threading tools, as described, it is comparatively easy to
arrange for gauging the angle, but the measuring of the
width of the flat is a more difficult task, if by measuring
we understand the process of making sure that the flat is
fully correct, and not merely comparing the thread tool we
make with a manufactured thread gauge, which is a very
uncertain test for accurate work. The common method
already described is a ''cut and try" scheme, first cutting
a thread on a cylindrical piece with the tool supposed to
be approximately correct, and afterward using the same
thread tool with which this thread was cut to plane a
groove in a flat piece of steel. The groove in the flat piece
of steel is then a duplicate of the thread previously cut
and should also be an exact duplicate of the section GACF
of the thread cut on the cylindrical piece. (See Fig.
48.) When testing, if the groove proves to be an exact
duplicate of the thread form, the flat evidently is correct,
110
SMALL TOOLS
inasmuch as the flats at the bottom and at the top of the
thread are alike, it being supposed that the angle was
previously tested and found correct. However, if the
groove in the flat steel piece does not exactly fit the sec-
tion of the thread on the cylindrical piece, it is necessary
to grind the tool again and make another trial, continuing
this until a tool with a correct flat is produced. The ideal
^^m^^
Fig. 48.
Section of U. S. Standard
Thread
Fig. 49. U. S. Standard Thread
Tool before Grinding Flat
method would be to measure the flat by micrometers, if
that could be done, in which case there would be no
uncertainties, and a correct tool could be produced more
directly and with less work. It is, of course, not possible
to measure with micrometers the distance AC in Fig. 48,
as such a measurement would be at best uncertain for
large pitches, and absolutely impossible to make on smaller
ones, even when using an eyeglass. If, however, the ver-
THREADING TOOLS — DEFINITIONS OF TAPS 111
tical distance BD from the top of the thread down to the
flat can be measured, the width of the flat is easily figured,
as for a United States standard thread,
A(7=2BDxtan30^.
This distance cannot, of course, be measured with
ordinary micrometers, but a micrometer can be simply
\
iJiN
/
°s
^^ ..
1
S F
.._.__ — __
^-— -'
y
J
G ' D i
Fig. 50. Micrometer for Measuring Flat of Thread Tools
designed which may be used for obtaining this distance.
Such a micrometer is shown in Fig. 50. If it were only a
case of measuring a threading tool without clearance, the
angle CBD in Fig. 50 would simply need to be 60 degrees,
and the micrometer so graduated that the reading would
be zero when the face A of the measuring screw was
exactly in line with the point B of the angle CBD. When
112 SMALL TOOLS
wanting to measure the width of the flat of a threading
tool, the tool would be placed in the angular space pro-
vided for it and the micrometer adjusted until the face of
the measuring screw would touch the flat. The reading
should then be multiplied by two times the tangent for
30 degrees, or 1.155.
As the threading tool is provided with clearance, the
case, however, is not quite so simple, but still presents no
actual difficulties. Referring to Fig. 49, where a thread-
ing tool is provided with 15 degrees clearance, it is evident
that the measurement taken by the micrometer will have
to be along the line CD in a plane AB at right angles to
the line EK. The length of the line CD is equal to MI
multiplied by cosine of 15 degrees, or, reversing the
expression.
COS 15°
The width of the flat HG again is equal to 2 X MI X tan-
gent for 30 degrees. Thus :
CD
HG = 2 X -^oXtan30°
cos 15
or in other words, the width of the flat of the threading
tool equals two times the distance measured by the microm-
eters in the plane AB divided by cosine of 15 degrees, the
quotient multiplied by the tangent for 30 degrees. We
naturally would reverse the formula when wanting to
produce a threading tool for a ^ven pitch, the width of
the flat HG being then given from the beginning and the
distance we require to know being CD. Knowing this
distance, we can grind down the sharp V tool until we
read off on the micrometer the required figure for CD.
The formula for determining CD is
OD ^^X cot 30° X cos 15°.
THREADING TOOLS — DEFINITIONS OF TAPS 113
For United States standard thread,
1
HG = ^X
8 number of threads per inch
If N denotes the number of threads per inch, the for-
mula may be written:
CD =
cot 30^ X cos 15°
16 iV
In Table XXIX the values of CD are given for a num-
ber of United States standard pitches when the clearance
angle of the tool is 15 degrees.
TABLE XXIX.
MICROMETER READINGS FOR MEASURING THE FLAT OF UNITED
STATES STANDARD THREAD TOOLS.
Clearance angle 15 degrees.
No. of
Threads
per Inch.
Micrometer
Reading.
No. of
Threads
per Inch.
Micrometer
Reading.
No. of
Threads
per Inch.
Micrometer
Reading.
2i
0.0465
9
0.0116
34
0.0031
2t
0.0440
10
0.0105
36
0.0029
2f
0.0418
11
0.0095
38
0.0027
0.0398
12
0.0087
40
0.0026
2i
0.0380
13
0.0080
42
0.0025
2}
0.0364
14
0.0075
44
0.0024
3
0.0349
15
0.0070
46
0.0023
3i
0.0322
16
0.0065
48
0.0022
3i
0.0299
18
0.0058
50
0.0021
4
0.0261
20
0.0052
52
0.0020
4i
0.0232
22
0.0048
56
0.0019
5
0.0209
24
0.0044
60
0.0017
6i
0.0190
26
0.0040
64
0.0016
6
0.0174
28
0.0037
68
0.0015
7
0.0149
30
0.0035
72
0.0015
8
0.0131
32
0.0033
80
0.0013
Referring now to Fig. 50, the micrometer consists of an
ordinary micrometer head fitted into a block F. This
block is provided with an angular groove CBD to receive
the tool. The angle to which to plane this block equals
114
SMALL TOOLS
61° 44', which is the angle between the faces IH and IG
in Fig. 49, measured in the plane AB. In the center of the
block, where the micrometer head is attached, part of
the block is cut away, leaving a free view of the tool and
the face of the measuring screw when the former is placed
in position for measuring. The micrometer head em-
ployed may be an ordinary one with regular graduations,
in which case the reading of the micrometer must be
carefully noted when the face A of the screw is in line
with the point B of the angular groove, but it is still
better, if one wants to go to the expense, to make the
head with a special graduation having the zero mark
where the face and point of the angle coincide. Li this
latter case the graduations would evidently be made
in a direction opposite to the
one on an ordinary micrometer
barrel. In the former case it
would be necessary to subtract
the measured reading from
the reading when A and B
coincide in order to obtain the
length of the line CD in Fig. 49.
To facilitate the holding of
the tool when measuring, it is
advisable to knurl it on the top
at G.
This manner of measur-
ing can be conveniently
employed when testing or in-
specting tools with round
points like the tools used for
originating the thread tools
used to cut the Whitworth or the British Association
standard thread. In this case the length of a line CD
Fig. 51. Whitworth standard
Thread Tool
THREADING TOOLS — DEFINITIONS OF TAPS 116
from the point / to the highest part M of the radius
measured in a plane at right angles to EF as shown in
Fig. 51, must be determined. The angle CBD (Fig. 50)
of the block must of course be made according to the
angle of the thread which is measured. If the angle of
the thread is v, the angle CBD is determined from the
formula
tan
CBD
COS 15°'
provided that the clearance angle is 15 degrees. The
values for the length of the line CD measured on a tool
with 15 degrees clearance angle are given in Table XXX
for the Whitworth standard thread and in Table XXXI
for the most common pitches of the British Association
standard thread.
TABLE XXX.
MICROMETER READINGS FOR TESTING WHITWORTH FORM OF TOOL.
Clearance angle 15 degrees.
No. of
Threads
per Inch.
Micrometer
Reading.
No. of
Threads
per Inch.
Micrometer
Reading.
No. of
Threads
per Inch.
Micrometer
Reading.
21
0.0687
9
0.0172
34
0.0045
^
0.0651
10
0.0155
36
0.0043
^
0.0619
11
0.0141
38
0.0041
2|
0.0589
12
0.0129
40
0.0039
2|
0.0562
13
0.0119
42
0.0037
2}
0.0538
14
0.0110
44
0.0035
3
0.0515
15
0.0103
46
0.0034
3i
0.0476
16
0.0097
48
0.0032
H
0.0442
18
0.0086
50
0.0031
4
0.0387
20
0.0077
52
0.0030
4i
0.0344
22
0.0070
56
0.0028
5
0.0309
24
0.0064
60
0.0026
5i
0.0281
26
0.0059
64
0.0024
6
0.0258
28
0.0055
68
0.0023
7
0.0221
30
0.0052
72
0.0021
8
• 0.0193
32
0.0048
80
0.0019
116
SMALL TOOLS
TABLE XXXI.
MICROMETER READINGS FOR TESTING BRITISH ASSOCIATION
FORM OF TOOLS.
Clearance angle 15 degrees.
British
Micrometer
British
Micrometer
British
Micrometer
Asso. No.
Reading.
Asso. No.
Reading.
Asso. No.
Reading.
0
0.0102
9
0.0040
18
0.0015
1
0.0092
10
0.0036
19
0.0014
2
0.0083
11
0.0032
20
0.0012
3
0.0075
12
0.0029
21
0.0011
4
0.0068
13
0.0025
22
0.0010
5
0.0060
14
0.0023
23
0.0009
6
0.0054
15
0.0021
24
0.0008
7
0.0049
16
0.0019
25
0.0007
8
0.0044
17
0.0017
Making Wkitworth Thread Tools. — While the develop-
ment of a correct United States or V-thread tool is a
thing requiring a great deal of skill and patience, it is
easy compared to the task of producing a tool, for the
round top and bottom thread, of which the Whitworth and
British Association standards are the leading examples.
In testing for accuracy, threads of this type are not
only measured by gauges and micrometers, but the curves
must match the angle so evenly that when the male gauge
is tried in the female from either end no difference can be
detected. The difficulty attending this will be better
appreciated when it is known that some of the leading
tap and die manufacturers of this country and Europe
have failed in producing threads that would pass the
British government's inspection.
It may be laid down as a cardinal principle that the
best results are obtained by developing the form first with
a flat top and bottom as in the United States thread,
roimding the comers afterward. The first step of all is
THREADING TOOLS — DEFINITIONS OF TAPS 117
to produce a correct angle gauge; assuming that we are to
work out the Whitworth thread, this would be a gauge
measuring 55 degrees. Make and harden a steel triangle,
A, Fig. 52, with the angle x as near 55 degrees as is possi-
ble by using a bevel protractor; the other two angles are
to be equal. Then make an angle iron JS, making sure
that ab and cd are parallel, and that be is square with ab.
Assuming that C and D are accurate two-inch and one-
half-inch plugs, we put in the pins E, E in such a position
that a line drawn through the centers of C and D, at right
angles to their axes, will make an angle of 27J degrees
Fig. 62. Making Angle Gauge for Whitworth Thread Tool
with ab. This can be done by figuring the distance fg
as follows : In the triangle Ihkj hk = I — 0.25 = 0.75
inch.
0.75 0.75
z^' = ■
= 1.4406 inch.
tan 27i° 0.5206
1.4406 + J diameter of C — i diameter of D =
1.4406 + 1 - 0.25 = 2.1906 inch = fg.
Set the pin F near enough to D to keep the corner of
the triangle from striking the angle iron B. Mount the
triangle A as shown, and set up the fixture on surface
grinder table, using a toe strap in the small hole in A to
118
SMALL TOOLS
hold it in position, and grind first one edge, then the
other. This gives us the male angle gauge. A female
gauge can now be made from this by the method described
in connection with United States standard thread tools.
The tools to be used in making the thread tool (see
Pig. 53) include an angular tool with a flat point, the
width of the point to be such that it reaches to the center
of the round in the bottom of the thread, the angle of the
tool matching the gauge previously made; a female radius
tool for forming the point; and a male radius tool for the
side radii. For convenience in measuring and getting
the exact form required, these tools should be made with
A
A
A
^
Fig. 53. Tools for Making Whitworth Thread Tools
the top square with the face at the cutting edge, i.e.,
without clearance. The sides and back of all should be
ground as well as the top. The tool a can be ground by
means of an angular block made in the same manner as
the male angle gauge and should be finished by lapping.
The tool h can be made in two pieces, one a hardened,
ground, and lapped wire, and the other a soft piece made
up in such shape that the wire can be soldered or otherwise
firmly fastened to it in the correct position. The tool c
should be made up first as at c' and hardened. Then
lap the hole carefully to size and grind the outside.
After measuring the distance from the hole to the back
of the tool, the front can be ground off to ef and the
THREADING TOOLS — DEFINITIONS OF TAPS 119
bevels ground until the depth of the round part is
right.
We now require a shaper with an apron made up to
hold the tool holder at an angle of 15 degrees, as shown in
Fig. 54. The apron should fit the clapper box perfectly.
If it does not, it is better to fasten it solid and let the
Fig. 64. Method of Planing a Whitworth Thread Tool
tools drag back through the cut, sharpening the tools over
again before finishing. Otherwise one runs the risk of
side shake. With this angular apron we can use the tools
made without clearance to produce a tool with correct
clearance for the lathe. Two thread-tool blanks, one, a,
of tool steel and one, b, of machinery steel, should be set
up on the table adapter as shown in the cut with spacing-
120 SMALL TOOLS
parallels between to avoid interfering with one while
planing the other. The blanks should be planed off
to exactly the same height, and all measurements for
height should be figured from the line cd, allowance being
made for the difference caused by the 15-degree clearance.
Then, after carefully measuring the tools previously made
to determine where the exact center is, we can start form-
ing the blanks, setting the tools sidewise successively by
positive measurement from the rib of the adapter. The
angular tool comes first, and with it we plane down the
sides of the tool a and the center of b so that the point
of the tool just reaches the center of the radius. Then
using the female radius tool we round the point of a and
the two points of 6, coming down until the circle of the
tool is just tangent to the top of the blanks. The male
tool will round out the two lower comers of a and the
center of b, being fed down to exact depth.
We now have the thread tool a, which can be hardened
and the machinery steel blank used as a lap to correct
errors in it, reversing the lap occasionally, and using oil-
stone powder or other fine abrasive as the cutting medium.
Great care must be used in putting on the abrasive, as in
all lapping operations of this kind points and comers are
apt to lap faster than wide surfaces. This operation
does not really correct the tool, but equalizes the errors
due to imperfect matching of the different cuts, and it
can be done so effectively that whatever errors of that
kind are left cannot be detected.
To test the tool, turn up a blank plug with a teat equal
to the diameter at the bottom of the thread. When this
is threaded, the point of the tool should touch the teat
just as the outer comers touch the top of the thread. In
the angle, the thread should measure by wires according
to the formula
THREADING TOOLS — DEFINITIONS OF TAPS 121
T^ ^ - 1.6008
Diameter of screw — ; r— ; ;; : — r
number of threads per inch
-I- (3.1659 X diameter of wire used) = micrometer reading.
For the final test of the fit of the curves with the angle,
a tap must be threaded with the tool, and a female gauge
tapped with the tap. The plug made before must screw
into this with an equal amount of friction from either end
and show a full contact on the thread. If this last test
is not successful it shows that the lapping is not good
enough and must be done over. If the plug does not
measure right it is necessary to go back to the planing and
plane up another tool, making such allowances as one
judges will correct the error. It is sometimes necessary
to do this several times before a perfect tool is produced.
In the use of the tool in the lathe great care is necessary
to see that it is set at the center of the spindle, and so
that the two side curves will scrape the top of the thread
at the same time. With the exception of making the
angle gauge and tool-grinding block, this whole procedure
has to be carried out for every pitch required.
Thread Tools with Side Clearance.
The tool most commonly used requiring side clearance
is the square-thread tool. We have previously referred
to the method of determining the amount of this clear-
ance. Acme thread tools for steep pitches often also
require side clearance, and as the matter of determining
the exact amount of this is more complicated than in the
former case, a more detailed analysis is necessary.
In figuring the side clearance as well as the angle to
which to plane threading tools, the angle of clearance is,
of course, the determining factor. In Fig. 55 a diagram
122
SMALL TOOLS
illustrating the planing of thread tools is shown. By
means of the fonnulas on next page the angles to which
the planer or shaper head should be set can be easily
detennined. By reference to the diagram, the formulas are
readily understood. The expressions ^Hhe leading" and
''the following" side of the tool may need a short explana-
tion. The former indicates the side of the tool which
first enters the work when a thread is cut; the latter, of
course, is the side which would last leave the work if it is
Fig. 55. Tool with Side Clearance
supposed that the tool traveled along the full length of
the work.
The diagrams and the formulas are given with special
reference to the tools used in the Pratt and Whitney
thread-tool holder, this holder being the one most used
in general practice. Evidently the formulas are equally
applicable to any thread tool which can be planed or
shaped in a similar manner to the one particularly
referred to.
If we first consider a tool with side clearance, as shown
in the cut, we will first find it necessary to determine the
THREADING TOOLS — DEFINITIONS OF TAPS 123
angle of the helix of the thread, the same as for square-
thread tools mentioned in the first pages of this chapter.
In the formulas,
a = depth of thread,
b = width of flat on offset tool,
c = actual width of flat,
d = outside diameter of screw,
4? = clearance angle,
w = one-half angle of thread,
y = angle of helix,
X = normal angle (to which to set planer head
when planing tool on side).
For finding the angle of hehx of the thread we have
then
, lead of thread
tan j/ = — ri r •
(a — a) 7z
For the normal angle we have
, _ cos y ± (cot II? X sin y X sin y)
xan X — •
cot ly X COS v
Use -I- for leading side and — for following side.
For Acme (29 degrees) thread and 15 degrees clear-
ance angle, the formula can, for all practical purposes, be
written
tan X - CQS y±sini/
^''''" 3.735 •
The width of flat on the offset tool is figured from
the formula 6 = c X cos j/.
If the tool has no side clearance, the angle of helix can
be considered = 0 degrees, and above formula reduces
., ,ir X i. tan w
itself to tan x = .
cos V
124 SMALL TOOLS
For 60-degree screw thread, United States standard,
the formula will thus have this appearance:
tan X = ^^^o = 0-5977; x = 30° 52'.
cos 15°
In this latter case the width of flat of tool (c) remains
unchanged.
It will be noticed that formulas are given first for
''tools with side clearance'' and second for "tools without
side clearance." Of course any thread tool ought to be
given a side clearance, the amount of which depends on
the angle of hehx of thread to be cut; but on account of
the small angle of helix on fine-pitch threads the necessity
of using a tool with side clearance in such cases is reduced
to a minimum, and can for practical reasons be dispensed
with, the clearance of 15 degrees in the front of the
tool being sufficient to carry the parts of the tool not
cutting far enough back so as not to interfere with the
thread.
Threading Tools for Taper Taps.
Threading tools for taper taps may, in fact, be said
to constitute a class by themselves, particularly if the
threading tool be a chaser. The cutting of taper-threaded
taps, such as pipe taps, with chasers is more or less com-
mon in shops where taper taps are manufactured, but the
operation usually causes some difficulties. In itself the
problem is very simple and the difficulty has probably
originated in an insufficient analysis of the subject. We
will consider the conditions of cutting a taper thread with
a chaser, and particularly consider the case of a pipe tap
with a total taper of three-quarters inch per foot, cut with
a chaser supposed to be held in a threading tool holder.
In Fig. 56 a chaser is shown such as would be held in
THREADING TOOLS — DEFINITIONS OF TAPS 126
the threading-tool holder made by the Pratt and Whitney
Company. It is evident that if either a single-point
cutter or a chaser used for ordinary straight-thread cut-
ting were put in a holder and the holder swiveled around
so as to present the chaser to the work at right angles to
the outside of the tapered blank to be threaded, the
thread formed would not be correct, inasmuch as a line
drawn through the center of the thread perpendicular to
rADCD a/ DCD CT ' V V \
Fig. 56. Taper Tap cut with Chaser made According to the Method
shown in Fig. 67
the axis of the tap would not bisect the angle of the
thread. This last condition, that the line perpendicular to
the axis of the tap should bisect the angle of the thread as
shown in Fig. 56, is the main requirement for producing a
correct thread on a tapered piece. In order to produce
such a thread with a chaser, the chaser must be made in
a way specially adapting it for this class of work only.
There are two ways in which such a chaser can be made,
depending upon the way in which the chaser is to be
presented to the work. In the first place, the chaser may
126
SMALL TOOLS
be presented to the work perpendicular to the axis of the
tap, as shown in Fig. 56, or the chaser may be presented
perpendicular to the outside surface of the tap Wank, as
shown in Fig. 59.
We will first discuss the former case. If the chaser
were not provided with clearance it is evident that the
miUing cutter for milling the grooves in the chaser would
be a 60-degree angular cutter, being 30 degrees on each
side. The chaser would be held in the vise as shown in
Fig. 57 and the cutter fed down, for each consecutive
Fig. 68
Two Methods of Milling the Teeth of Chasers for Taper Taps
tooth cut, an amount depending upon the taper and the
pitch of the thread. The values of a (Fig. 56) for pipe
thread and other common taper tap pitches, when the
taper is f inch per foot, are as follows:
Threads per Inch. a
8 0.0039
Hi 0.0027
12 0.0026
14 0.0022
18 0.0017
27 0.0012
THREADING TOOLS — DEFINITIONS OF TAPS 127
However, as the chaser must be made with 15 degrees
clearance, the milling cutter cannot be made 60 degrees,
but must be made 61° 44', this being the angle between
the two sides of a single-point cutter with 15 degrees
clearance angle, if measured in a plane at right angles to
the front face of the tooth. The arrangement for holding
the chaser when milling, and the angles required for the
milling cutter, are shown in Fig. 57. The feeding down of
the cutter will not equal a (Fig. 56) on account of the
15-degree clearance angle, but will be equal to a X cos
15 degrees. This distance is shown as 6 in Fig. 57. The
values of b for various pitches are given below:
Threads per Inch. b
8 0.0038
Hi 0.0026
12 0.0025
14 0.0021
18 • 0.0016
27 0.0011
While 6 is theoretically different from a, it will be seen
by comparing the two tables that the difference is so
small as to be insignificant for all practical purposes.
We will now consider the case where the tap is cut
with a chaser at right angles to the outside tapered sur-
face of the blank. We will find that in cutting this chaser
with a milling cutter and holding it as shown in Fig. 58,
we will not need to feed down the milling cutter for each
consecutive tooth to be cut, but the milling cutter itself
must be provided with . different angles for the different
sides of the thread. In Fig. .59 the actual angles of the
sides of the thread with a line perpendicular to the outside
surface of the blank are given as 28° 13' and 31° 47',
respectively, the sum of these angles being 60°. The
chaser being cut with 15 degrees clearance, these angles
128
SMALL TOOLS
in the cutter will be 29'' 3' and 32^ 41' respectively, the
sum of these two angles being 61° 44'. In Fig. 58 the
manner of holding the chaser in a vise and the angles of
the cutter are plainly shown. In the view to the left in
Fig. 59 are indicated the angles to which to plane a single-
point cutter held in the same manner as the chaser and
provided with a clearance of 15 degrees.
Care must be taken when making chasers to be used in
the manner indicated in the first case that the elevating
Fig. 69. Taper Tap cut with Chaser made According to the Method
shown in Fig. 68
screw of the milling machine, by means of which the
chaser is raised up toward the milling cutter for each
consecutive tooth cut, is correct, and that no back lash
enters as a factor in the operation. As this is difficult to
insure against, it is advisable to cut the threads according
to the second method, as there the chances of error are
smaller, it only being required that the milling cutter be
ground to the exact angles wanted, and that the chaser
afterward be presented to the work fully perpendicular to
THREADING TOOLS — DEFINITIONS OF TAPS 129
the outside surface. The angle which the face of the
chaser in the latter case will make with the axis of the
tap to be cut is 1° 47'. This angle, however, would be
difficult to measure unless the threading tool were held in
a tool-post provided with some kind of a graduated swivel.
In such a case a chaser could be placed so that its face
would be parallel with the axis of the tap, clamped to
the tool-post swivel, and this swivel afterward moved
around in an arc corresponding to 1° 47'. Ordinarily,
however, if the tap blank is turned to a correct taper, the
chaser can be set from the outside surface of the blank,
its face being parallel to this surface in a horizontal plane
through the axis of the tap.
The Influence of the Thread Miller on Threading
Tools.
With the advent of the thread milling machine the
extreme accuracy of thread forms hitherto scrupulously
adhered to was sacrificed for the greater commercial
advantages in rapid thread-cutting. The thread milling
cutter, while, as a rule, itself ground to the correct form of
the thread, is, when in use, swiveled around a horizontal
axis at right angles to the axis through the center of the
hole of the cutter in order to conform to the angle of helix
of the thread to be cut. By swiveling the cutter in this
way the exact form of thread is not duplicated in "the
screw to be cut, inasmuch as the correct angle of the
thread will not be measured in a horizontal plane through
the axis of the screw as it ought to be, but in a plane at
right angles to the direction of the helix of the thread. It
is obvious that the inaccuracy is increased in proportion
to the angle of helix. For fine pitches the inaccuracy is
so small as to be insignificant for practical consideration,
180 SMALL TOOLS
but as the pitches grow coarser, the same diameter being
retained, the differences between the correct thread form
and the one produced become enough pronounced to
demand attention.
It is particularly when cutting Acme threads that this
difference is great enough to cause difficulties, because of
the fact that the pitches on Acme screws are usually
twice as coarse as those on United States or V standard
screws. The head of the thread milling machine carry-
ing the cutter has to be tilted over so much in cutting the
screw that the dimensions of the thread produced differ
by measurable amounts from the standard thread, and if
a screw with such a thread is placed in a nut cut with a
tap having a correct thread, a very poor fit will result.
The variations are, of course, even greater in the case of
multiple-threaded screws, and the use of the thread milling
machine for cutting such screws may be prohibitive in
extreme cases unless the taps for the nuts are produced in
a manner similar to the one used for the screws.
One way would be to mill the taps on screw milling
machines. This is also done to a certain extent by man-
ufacturers of these taps. But if it is desired to cut the
taps in a lathe, and there are not enough taps to be made
to warrant the making of thread tools to suit all the
different angles of helix which may occur, a correct thread
tool or single-point cutter may be used and placed in a
tool-post or holder capable of swiveling adjustment, so
that the tool can be tilted over to the same angle as the
milling cutter would be set to in cutting the screw. Such
a tool holder is shown in Fig. 60. An incidental advan-
tage and saving of expense is gained by the use of such
a holder, because the tool or single-point cutter, being
set over to conform to the angle of the thread, does not
need to be provided with side clearance, but can be made
THREADING TOOLS — DEFINITIONS OF TAPS 181
as if intended for cutting a circular groove or a thread of
very fine pitch.
The tool holder shown is provided with a tongue A and a
clamp B to hold single-point cutters of the kind manufac-
liSiiiniiliiiiil! ' " =
I
-JL-
Fig. 60. Swiveling Thread-Tool Holder
tured by the Pratt and Whitney Company. The stem C of
the holder is fitted to a cast-iron bracket Z), which is clamped
to the cross slide of the lathe. The screw E clamps the
holder in position. The shoulder F of the holder is grad-
uated in degrees in order to indicate the angle to which
the tool is tilted. The holder, as shown, is of the very
132
SMALL TOOLS
simplest construction in order to merely convey the idea
of the tool. With a little more elaboration in the design
a still more efficient tool may result, but for temporary use
the one shown will prove efficient.
Square-Thread Tools.
The top of the thread of square-threaded screws with
coarse lead is always thicker or wider than the thread at
Fig. 61. Extreme Example Showing the Difference in Width at Top
and Bottom of the Square Thread
the bottom. The space between the thread is still of the
same square section. The explanation of the difiference
between the thickness of the thread at the top and
bottom is that a thread with a steep lead is approximating
a groove cut parallel with the axis of a screw as shown in
Fig. 61. We see that in this extreme case, while the
groove is of correct square section, the portion between
the grooves, or the "thread," is far wider at the top than
at the bottom. Evidently this imperfection in square
threads is greater the steeper the pitch is. Where the
THREADING TOOLS — DEFINITIONS OF TAPS 138
lead is small compared with the diameter, the difference
in width at the top and bottom of the thread is not
noticeable.
It is clear that if a nut is to perfectly fit a screw having
the top of the thread wider than the width at the bottom,
the thread in the nut must be cut accordingly. The
tool for cutting the thread in the nut must be wider at the
point and its sides must be ground convex. The thread
in such a case is first cut with parallel sides to the required
depth with an ordinary square threading tool; then this
special tool is used for widening the thread to the required
shape. The exact shape of the square threading tool is
obtained by drilling a hole in a piece of steel, which
latter is of the same diameter as the screw, inserting a
plug in this hole and threading the piece the same as the
screw, so that the inserted plug is located in the middle of
a thread with the grooves on each side cutting into it. If
the plug is then removed, it will show the exact section of
the thread in the screw and the shape which should be
^ven to the thread tool for threading the nut.
When cutting square threads it is customary to make
the screws exactly according to the theoretical standard of
the square thread. The width of the point of the tool for
cutting screws with square threads is therefore exactly
one-half of the pitch, but the width of the point of the tool
for cutting taps, which afterwards are used for tapping
nuts, is slightly less than one-half the pitch, so that the
groove in the tap becomes narrower, and the land or cut-
ting point wider than the theoretical square thread,
thereby cutting a groove in the nut which will be slightly
wider than the thread in the screw, so as to provide for
clearance. An inside threading tool for threading nuts
evidently must be of the same width as the land on the
tap would be, or in other words, slightly wider than one-
184
SMALL TOOLS
half the pitch. This provides, then, the required clear-
ance. Table XXXII gives the width of the point of the
tool for all ordinary pitches from one to twenty-four
threads per inch. The second column gives the width of
the point for cutting taps to be used for producing square-
thread nuts. The third column gives the width of the
point of the tool for cutting screws, which, as we have
said, equals one-half the pitch; and the fourth colunm
^ves the width of the point for inside threading tools for
nuts. While the table has been carried to as fine pitches
as those having twenty-four threads per inch, square-
threaded screws having so fine a pitch are very seldom
used. Some manufacturers of square threading tools,
however, make square threading tools for pitches as fine
as these, and for this reason they have been included.
TABLE XXXII.
WIDTH OF TOOL FOR CUTTING SQUARE THREADS.
Width of Point of Tool.
No. of
Threads
per
Inch.
Width of Point of Tool.
No. of
Threads
per
Inch.
For
Taps.
For
Screws.
For
Inside
Thread
Tools
for Nuts.
For
Taps.
For
For
Inside
Thread
Tools
for Nuts.
1
1*
H
li
2
2h
3
^
4
4*
5
5i
6
7
0.4965
0.3715
0.3303
0.2827
0.2475
0.1975
0.1641
0.1408
0.1235
0.1096
0.0985
0.0894
0.0818
0.0699
0.5000
0.3750
0.3333
0.2857
0.2500
0.2000
0.1666
0.1428
0.1250
0.1111
0.1000
0.0909
0.0833
0.0714
0.5035
0.3785
0.3363
0.2887
0.2525
0.2025
0.1691
0.1448
0.1265
0.1126
0.1015
0.0924
0.0848
0.0729
8
9
10
11
12
13
14
15
16
18
20
22
24
0.0615
0.0545
0.0490
0.0444
0.0407
0.0375
0.0352
0.0328
0.0307
0.0272
0.0245
0.0222
0.0203
0.0625
0.0655
0.0500
0.0454
0.0417
0.0385
0.0357
0.0333
0.0312
0.0277
0.0250
0.0227
0.0208
0.0635
0.0565
0.0510
0.0464
0.0427
0.0395
0.0362
0.0338
0.0317
0.0282
0.0255
0.0232
0.0213
THREADING TOOLS — DEFINITIONS OF TAPS 135
In Fig. 62 a diagram is presented which will facilitate
the calculation of the clearance angles required by square
threading tools.
>* >i K 1 1>4 l>i ^^ ^ 1^>i ^ii '^^ 3 3>4 3>i ax ^
Diameter, Inches
Fig. 62. Diagram of Clearance Angles for Square Thread Tools
Referring to Fig. 63, the angle on the leading side is
figured to correspond to the root diameter of the screw
to be cut, whereas the angle on the following side is
determined by the outside diameter of the screw. The
use of the diagram, Fig. 62, is best indicated by an
136 SMALL TOOLS
example. Suppose it is required to find the angles for
the square threading tool for a screw 2 inches in diameter,
having 4 threads per inch. The root diameter equals
2 - J = If inches. To find the angle for the leading side
of the tool, follow the vertical line from If inches diameter
to the intersection with the horizontal line from 4 threads
per inch, and from the intersection follow the nearest
diagonal line, thus finding the clearance angle of the
leading side of the tool equal to 2J degrees. To find the
angle for the following side, follow the vertical line from
2 inches diameter to its intersection with the horizontal
Une from 4 threads per inch. From the intersection
follow the nearest diagonal line, finding thus the clear-
Fig. 63. Clearance Angles of Square Threading Tools
ance angle for the following side equal to 2J degrees.
These angles are the theoretical clearance angles. For
practical purposes, slightly greater clearance should be
given.
Special Thread Tool Holder.
The cut. Fig. 64, shows a spring thread tool holder
the object of which is to permit the thread tool to spring
away from the work if too heavy a cut is taken. This
tool consists of a holder A, which is provided with a
projection into which a hole is drilled for obtaining the
spring effect, and the usual clamp and binding nut. The
slot B is cut from the lower side of the holder into the
hole, and permits the front part of the holder to recede
THREADING TOOLS — DEFINITIONS OF TAPS 137
under a too heavy cut. Proper resistance is given to the tool
by the set screw C, which has a spring at the lower end,
acting upon the front part of the holder. The part D is
an inserted blade or key which keeps the front part of the
holder from bending to one side while cutting. A great
many designs of spring tool holders have been tried, and
the one shown in Fig. 64 is comparatively common.
Kg. 64. Example of Spring Thread Tool Holder
The difficulty with holders of this kind is that it is almost
impossible to adjust the screw for each particular pitch
to be threaded so that the spring will have proper tension.
It is evident that in cutting a coarse thread there is no
need of the tool being as sensitive as when cutting a very
fine thread, but there is no means for judging when in
each particular case the proper springing action has been
attained. Another objection to the design shown is that
it prevents a full and clear view of the thread being cut,
the projecting part extending partly above the work.
138 SMALL TOOLS
Of all spring thread tool holders hitherto designed, how-
ever, this one is about as good as any. A spring tool
holder for threading tools which will overcome the objec-
tions mentioned is greatly in demand, and many attempts
have been made to solve the problem, but none have been
entirely successful.
Definitions of Different Kinds of Taps.
Before entering into a detailed discussion of the require-
ments and qualifications of taps, we will here briefly
review the uses of various kinds of taps and define the
names for different classes commonly used. In some
cases there are doubts as to the proper name for a cer-
tain tap, and some confusion exists for instance as to the
difference between a tapper tap and a machine tap. Per-
sons not very familiar with the nomenclature of tool-
making would also easily confuse such names as screw
machine tap, machine screw tap, and machine tap. In
order to avoid any misunderstandings throughout this
treatise we will settle definitely upon the meaning of the
terms used. The same names as are used by leading
tap-makers and manufacturers of small tools will be
adhered to.
Hand taps, as the name implies, are taps used for tap-
ping holes by hand. All taps used in this manner, how-
ever, are not termed hand taps, the name as commonly
used referring only to straight taps used by hand. In fact,
not even all taps which would come within this descrip-
tion are properly termed hand taps. The machine screw
tap is nothing but a hand tap, but is not ordinarily
termed so, inasmuch as all taps used for tapping holes for
standard machine screws are classified as machine screw
taps.
THREADING TOOLS — DEFINITIONS OF TAPS 189
Tapper taps and machine taps are both used for tapping
nuts in special nut-tapping machines. There is, however,
a distinct difference between these two kinds of taps,
although the names are often confused. The tapper tap
is the original and older form used for machine nut tap-
ping, and is simpler in its construction, consisting simply
of a long chamfered and a straight portion, and usually
relieved only on the top of the thread of the chamfered
part. The construction of the machine tap is more com-
plex, and will be described in detail later. The latter tap
is capable of greater endurance, and is used preferably
in tough material and when good cutting qualities are
necessary.
Screw machine taps, as the name implies, are used for
tapping in the screw machine. They are provided with
shanks fitting either the turret holes of the machine or
bushings inserted in these holes. As these taps ordi-
narily cut threads down to the bottom of a hole they are
provided with very short chamfer.
Pulley taps are used for tapping holes which cannot be
reached by ordinary hand taps, as for instance the set-
screw or oil-cup holes in the hub of a pulley which can be
reached only through a hole drilled in the pulley rim.
The pulley tap, practically, is nothing but a hand tap
with a very long shank.
Die taps are used for cutting threads in dies. They
are provided with a very long chamfer, and, while used
by hand, resemble in their construction the machine
tap.
Hob taps are used for sizing dies. Because of their
construction they cannot be used for actual thread-cutting,
but can only take a slight finishing chip. A special form
is the Sellers hob, which is used with a special guiding
arrangement and is provided with a long guide at the
140 SMALL TOOLS
end of the thread. The commonly used hob tap, or the
short-shank hob tap, is in all particulars similar to an
ordinary hand tap, except in regard to fluting.
Taper taps, as properly understood, are any taps which
have the diameter of the part of the thread nearest the
shank larger than the diameter of the point, the inter-
mediate portion being formed by a gradual taper from
the point to the end of the thread at the shank. It is
necessary to note this proper meaning of the expression
^' taper tap ^' because of the fact that the first tap in a
set of hand taps is commonly, but not properly, referred to
as a taper tap. As this expression is used to denote two
widely different things, and as its common usage pre-
cludes any possible change, we will in the following pages
distinctly state which of the two meanings is referred to
in any particular case. The most common of all taper
taps is the pipe tap, which is used for tapping holes for
standard pipe sizes. There is also a particular form of
pipe tap termed the straight pipe tap, which, as the name
implies, is straight. This latter tap, in fact, is nothing
but a hand tap, the name merely indicating the standard
sizes in regards to diameter and pitch conforming to which
this tap is made.
Other less common forms of taper taps, which, how-
ever, are largely used in boiler and locomotive work, are
mud or wash-out taps, sometimes termed arch pipe taps,
taper boiler taps, and patch-hoU taps.
Pipe hobs are used for sizing pipe dies. They are
longer than ordinary pipe taps and fluted in a different
manner.
Stay-bolt taps are used in locomotive boiler work.
Their action is that of a hand tap, but they are usually
provided with a reamer portion preceding the threaded
part. A special form of stay-bolt taps is embodied in
THREADING TOOLS — DEFINITIONS OF TAPS 141
the spindie stay-bolt tap, which revolves on a central
spindle provided with a taper guide on the front end.
Straight boiler taps are used in boiler work. They
differ in construction somewhat from the taper boiler tap,
and are provided with a straight portion, which in fact
puts them in the same class as ordinary hand taps.
A number of taps for special purposes have been named
after the persons with whom they ori^nated, or after the
devices with which they are used. They embody, how-
ever, no principles of construction differing from any of
those mentioned, in so far as the tap part is concerned.
Inserted cutter taps may belong to any of the classes
mentioned before, and are in a class by themselves only
because of not being solid but having the cutting teeth
on blades which are inserted and held in a body in a
suitable manner.
CHAPTER IV.
HAND TAPS.
Of all taps, the ones most commonly used are hand
taps. While there is a great deal of difference of opinion
in regard to the proper way in which to make most
machinists' tools, hand taps have been made so long and
in such quantities as to have nearly settled all disputes
regarding their necessary qualifications. There is only
one point on which opinions dififer, and this will be referred
to later. Even on this point it is probably not so much
a difference of opinion as a difference in common usage.
Hand Taps Made in Sets.
Hand taps are, as a rule, made in sets of three, the
taps being termed taper, plug, and bottoming taps respec-
tively. When using all three for tapping a hole they are
used in the order named. A set of three taps is shown in
Fig. 65. As indicated in the cut, the point of the taper
tap is turned down to the diameter at the bottom of the
thread for a length of about three or four threads. This
turned-down portion acts as a guide and aids in securing
a straight tapped hole. From the upper end of this
guide the thread is chamfered until it reaches the full
diameter of the tap. The length of this chamfered por-
tion should be from six to seven threads. The remaining
part of the threaded portion of the tap is turned straight
or parallel. The plug tap is chamfered at the point for
a length corresponding to about three threads. The
remaining portion of the thread of this tap is then turned
142
HAND TAPS
148
parallel. The bottoming tap is made practically in the
same way as the plug tap, with the exception that only
about one thread is chamfered at the point of this tap.
It is understood that the diameter of the straight or
parallel portion of the thread of all the taps in the set is
the same.
The question of the principle according to which hand
taps should be made in sets is the point about which
^WV\VWVVVVVVV
Bottominir
T
I
^/WNAAAAAAA/VSOir
w-/VVVV\AA/VVVNAI
Ping
Fig. 65. Set of Three Taps made According to Prevailing Practice
there may be some difference of opinions. It is evident
that from a critical point of view this way of making taps
intended to be used in sets cannot be considered correct,
inasmuch as the work to be done by the taps will be very
imevenly distributed on account of the fact that all the
taps in the set have the same diameter. The chamfered
portion of the first or taper tap will have the bulk of the
work to do, while the two following taps practically have
no work to do except in a case where a full thread is
144
SMALL TOOLS
required at the bottom of a hole; but even then the
duties of the different taps in the set are rather unevenly
distributed.
For this reason it is very obvious that taps intended for
use in sets should vary in diameter, as shown in Fig. 66,
so that each tap will have a reasonable amount of work to
do; of course, the last tap, being a finishing tap, should
have less work to do than the first two. The making of
rvVVVVVVV\VsAA/V
liniihinffTap (SrdTap)
-y-VVVVVWVWWV
SndTap
1st Tap
Fig. 66. Set of Three Taps made with Gradually Increasing Diameters
hand taps in sets, in this manner, although being both for
practical and theoretical reasons the only correct and the
best way, does not seem to have met with the favor of
the tap manufacturers, there being only one leading firm
(the Pratt and Whitney Company) which manufactures
hand taps made in this manner.
Objection to Making Hand Taps in Sets. — The prin-
cipal objection to making hand taps in sets as described
above, and the probable cause for their slow introduction,
HAND TAPS 146
must be that when using taps of such description the
whole set always has to be used, whereas for a short hole
to be tapped clear through a piece the taper tap alone
will be found sufficient, if the straight portion of the tap
is up to the full diameter; and in fact all three taps,
when all made with the same diameter, are seldom used
except when a full thread is wanted at the bottom of a
hole. However, the cutting of the full thread tapped
clear through a piece, by the taper tap in one operation,
places an imdue stress on this tap, and will not give as
smooth a thread as if the hole had been run through by a
set of taps of varying diameter, each of which cuts a fair
amount of the thread.
Proportioning the Work to be Done by Each Tap in a Set.
— The question of making the taps in a set with diflfer-
ent diameters is of so great importance, and will prob-
ably be given more or less attention by tap-makers in
the future, that it may be well worth to analyze the
problem of just how much each succeeding tap should be
larger in diameter than the preceding one. We must
also remark at the outset that it is not enough that there
is a variation in the diameters of the taps as measured on
the top of the thread; there must also be a difference in
the diameters measured in the angle of the thread. The
two diagrams Figs. 67 and 68 show by means of different
cross-sectioning the amounts of metal removed by the
different taps in a set made as outlined above. The
first diagram represents the cutting of a V thread, the
second a United States standard thread. The differences
in the outside diameters of the taps as well as in the
angle diameters are clearly indicated.
We will now proceed to express these differences by
formulas, and it is, of course, evident that the values will
vary with the pitch of the thread. In the formulas given
146
SMALL TOOLS
in the following the proportions between the amount of
metal removed by each succeeding tap are so adjusted
that the first tap cuts the greater part of the thread, the
second tap a somewhat smaller amount, and, finally, the
last tap in the set a comparatively slight proportion of
the total thread. If we first consider the V thread, and
take the pitch of the thread as the working factor, the
distances from the top of the full thread to the top of the
thread of the plug and taper taps respectively will be
found according to the following formulas:
a = 0.15 X pitch.
h = 0.47 X pitch.
• I
Fig. 67. Section Showing Relative Amount Removed by each Tap in
a Set of Three Taps, Sharp V Thread
The relative values of a and h are shown in the
diagram of the sharp V thread, Fig. 67. Considering
the differences in the angle diameter of the thread, these
ought to be the amounts c and d, respectively, smaller
than the correct angle diameter, for the plug and taper
taps :
For plug tap c = 0.09 X pitch.
For taper tap d = 0.17 X pitch.
HAND TAPS 147
For United States standard thread the fonnulas would
be
e = 0.05 X pitch and
/ = 0.33 X pitch
for the differences on the top of the thread (for the rela-
tive values of e and /see diagram, Fig. 68).
The angle diameter perhaps should, strictly considered,
vary differently from that of a sharp V thread, but the
variation would be so slight that it can be eliminated in
all practical considerations, and the variations between
the correct angle diameter and those of the plug and taper
tap can be made the same as for sharp V thread, viz..
f
Fig. 68. Section Showing Relative Amount Removed by each Tap in
a Set of Three Taps, U. S. Standard Thread
0.09 X pitch for the plug tap and 0.17 X pitch for the
taper tap.
For convenience, and in order to save the trouble of
figuring the values from the formulas in each individual
case. Table XXXIII, showing the amounts found from
the formulas, is given herewith. The quantities a, 6, c, and
/ are given as 2 a, 2 &, 2 e, and 2 /, thus giving the differ-
ences for the diameter (a, b, e, and / being the difference
on one side only). Only as many decimals are given as
are necessary for all practical purposes. The differ-
ences in the angle diameters, although alike for United
148
SMALL TOOLS
States standard thread and sharp V thread, have been
repeated in both columns in order to secure unifonnity.
TABLE XXXIII.
DIMENSIONS FOR MAKING HAND TAPS IN SETS.
No. of
U. S. Standard Thread.
Standard Sharp V Thread.
Thread
Pitch.
per
Inch.
2/.
2 c.
d.
c.
2 6.
2 a.
d.
c.
3
0.3333
0.222
0.033
0.056
0.030
0.312
0.100
0.056
0.030
3*
0.2857
0.190
0.029
0.048
0.026
0.269
0.086
0.048
0.026
4
0.2500
0.167
0.025
0.042
0.023
0.235
0.075
0.042
0.023
^
0.2222
0.148
0.022
0.037
0.020
0.209
0.067
0.037
0.020
5
0.2000
0.133
0.020
0.033
0.018
0.188
0.060
0.033
0.018
5*
0.1818
0.121
0.018
0.030
0.016
0.171
0.055
0.030
0.016
6
0.1667
0.111
0.017
0.028
0.015
0.157
0.050
0.028
0.015
7
0.1429
0.095
0.014
0.024
0.013
0.134
0.043
0.024
0.013
8
0.1250
0.083
0.012
0.021
0.011
0.118
0.037
0.021
0.011
9
0.1111
0.074
0.011
0.018
0.010
0.104
0.033
0.018
0.010
10
0.1000
0.067
0.010
0.017
0.009
0.094
0.030
0.017
0.009
11
0.0909
0.061
0.009
0.015
0.008
0.085
0.027
0.015
0.008
12
0.0833
0.056
0.008
0.014
0.008
0.078
0.025
0.014
0.008
13
0.0769
0.051
0.008
0.013
0.007
0.072
0.023
0.013
0.007
14
0.0714
0.048
0.007
0.012
0.006
0.067
0.021
0.012
0.006
16
0.0625
0.042
0.006
0.010
0.006
0.059
0.019
0.010
0.006
18
0.0556
0.037
0.0055
0.009
0.005
0.052
0.017
0.009
0.005
20
0.0500
0.033
0.005
0.008
0.0045
0.047
0.015
0.008
0.0045
22
0.0455
0.030
0.0045
0.0075
0.004
0.043
0.014
0.0075
0.004
24
0.0417
0.028
0.004
0.007
0.004
0.039
0.0125
0.007
0.004
26
0.0385
0.026
0.004
0.0065
0.0035
0.036
0.0115
0.0065
0.0035
28
0.0357
0.024
0.0035
0.006
0.003
0.034
0.0105
0.006
0.003
30
0.0333
0.022
0.0035
0.0055
0.003
0.031
0.010
0.0055
0.003
32
0.0312
0.021
0.003
0.005
0.003
0.029
0.0095
0.005
0.003
34
0.0294
0.020
0.003
0.005
0.0025
0.028
0.009
0.005
0.0025
36
0.0278
0.019
0.003
0.0045
0.0025
0.026
0.0085
0.0045
0.0025
38
0.0263
0.018
0.0025
0.0045
0.0025
0.025
0.008
0.0045
0.0025
40
0.0250
0.017
0.0025
0.004
0.0025
0.0235
0.0075
0.004
0.0025
42
0.0238
0.016
0.0025
0.004
0.002
0.0225
0.007
0.004
0.002
44
0.0227
0.015
0.0025
0.004
0.002
0.0215
0.0065
0.004
0.002
46
0.0217
0.0145
0.002
0.0035
0.002
0.0205
0.0065
0.0035
0.002
48
0.0208
0.014
0.002
0.0035
0.002
0.0195
0.006
0.0035
0.002
50
0.0200
0.0135
0.002
0.0035
0.002
0.019
0.006
0.0035
0.002
52
0.0192
0.013
0.002
0.003
0.0015
0.018
0.006
0.003
0.0015
54
0.0185
0.0125
0.002
0.003
0.0015
0.0175
0.0055
0.003
0.0015
56
0.0179
0.012
0.002
0.003
0.0015
0.017
0.0055
0.003
0.0015
58
0.0172
0.0115
0.0015
0.003
0.0015
0.016
0.005
0.003
0.0015
60
0.0167
0.011
0.0015
0.003
0.0015
0.0155
0.005
0.003
0.0015
HAND TAPS 149
In regard to the chamfer at the point of the thread it is
good practice to chamfer 6 threads on the first, 3 on the
second, and 1 on the last tap in a set when made as out-
lined above.
What has been said before in regard to making hand
taps in sets has special reference to taps with United States
standard thread and sharp V thread. It has also bearing
upon taps with International or French standard thread. No
table, however, can be considered necessary for these stand-
ards. As the shape of the threads for the latter standards
is the same as for the United States standard, the values
in the column under ''United States Standard Thread,"
if selected for the pitch which comes nearest to a giv^n
pitch in millimeter, will give satisfactory working figures.
Acme Taps in Sets. — While it has not become the
generally adopted custom to make the three taps in a set
of hand taps with the United States or V standard thread
of different diameters, so that each tap cuts a certain
proportion of the metal to be removed in forming the
thread, this construction becomes imperative when mak-
ing taps with Acme or square threads. The reason for
this is that the pitch of the thread of taps with the latter
class of threads is usually coarser for corresponding
diameters, and the same size tap is therefore required to
remove more metal in this case than if it were provided
with 60-degree threads. The shape of the Acme and
square threads, with their wide flats at the top of the
thread, also increases the resistance to the cut, if the full
depth of the thread should be produced with one tap.
For these reasons Acme and square thread taps, intended
for cutting a complete thread from a nut blank, and not
intended merely for finishing a thread cut in a lathe, are
always made in sets, each tap in the set being smaller in
diameter than the one following.
160 SMALL TOOLS
While for Acme and square thread taps three taps in a
set are undoubtedly the most coromon, these taps may be
made with only two taps in a set for very fine pitches,
and with as many as five taps in a set for very coarse
pitches. The last tap in these sets is not made on the
principle of a bottoming tap, as Acme and square threads
are seldom used except in nuts which are threaded straight
through. There is, in fact, a more liberal chamfer on all
the taps in the set than is common with ordinary taps.
In giving formulas and definite data we will first turn
our attention to the Acme tap. On accoimt of the clear-
ance required on the top of an Acme thread between the
screw and the nut, the actual diameter of the last or
finishing tap in the set must be larger than the standard
or nominal diameter of the screw or nut. If
A = actual diameter of finishing tap and
B = root diameter of the thread,
the relations of these values to the nominal or standard
diameter of the tap are
A = nominal diameter -f 0.020 inch,
B = nominal diameter — ( -, r— i ;; : — i-
V \number of threads per inch
+ 0.020 inchj .
Table XXXIV gives the proportions for the diameters
of Acme taps in sets of two up to and including five.
Referring to the table, C = the actual diameter of the suc-
ceeding taps in the sets, D = the diameter at the point of
the thread, and E = the length of the straight or parallel
portion of the thread in relation to the whole length of
the thread L. In order to simplify the expressions in the
formulas the difference between the actual diameter of
the finishing tap A and the root diameter B is termed G,
HAND TAPS
TABLE XXXIV.
ACME THREAD TAPS IN SETS.
161
No. of
Taps
in Set.
Tap.
C
D
E
2
1st
B + 0.65 G
B + 0.010 inch
L
6
2nd
A
Con 1st tap - 0.005 inch
L
3
Ist
fi+ 0.45 G
B + 0.010 inch
L
6
3
2nd
B+ (J.8G
C on ist tap - 0 . 005 inch
4
3rd
A
C on 2nd tap - 0.005 inch
L
3
1st
B-f 0.4(?
B+ 0.010 inch
L
8
4
2nd
B+ 0.7(?
C on 1st tap — 0.005 inch
L
6
3rd
B + 0.9C?
C on 2nd tap - 0 . 005 inch
L
4
4th
A
C on 3rd tap - 0.005 inch
L
3
1st
B+ Q.37G
B + 0.010 inch
L
8
2nd
B+ 0.63 (?
C on 1st tap - 0.005 inch
L
6
5
3rd
B+ 0.S2G
C on 2nd tap — 0 . 005 inch
L
5
4th
B+ 0.94 G
C on 3rd tap — 0 . 005 inch
L
4
5th
A
C on 4th tap - 0.005 inch
3
Square-Thread Taps in Sets. — If we now turn to the
square-thread tap, and let the letters represent the same
dimensions as in the case of Acme taps, we will find our
dimensions in Table XXXV. We must, however, take
into accoimt that there is no clearance allowed on the
152
SMALL TOOLS
top of the thread, and that the depth of a square thread
eguals one-half of the pitch. Therefore
A = the nominal diameter of the tap and
B = the nominal diameter — pitch of thread.
TABLE XXXV.
SQUARE-THREAD TAPS IN SETS.
No. of
Taps
in Set.
Tap.
C
D
E
2
Ist
B+ 0.67 (?
B - 0.005 inch
L
6
2nd
A
Con 1st tap - 0.005 inch
L
3
1st
B+ 0.41 G
B- 0.005 inch
L
6
3
2nd
B+ O.SG
C on 1st tap - 0.005 inch
L
4
3rd
A
C on 2nd tap - 0.005 inch
L
3
1st
B+ 0.32 (?
B- 0.005 inch
L
8
4
2nd
B+ 0.62 (?
C on 1st tap — 0.005 inch
L
6
3rd
B + 0.90 G
C on 2nd tap - 0.005 inch
L
4
4th
A
C on 3rd tap - 0.005 inch
L
3
1st
B+0.26G
B - 0.005 inch
L
8
2nd
B + 0.50G
C on 1st tap — 0.005 inch
L
6
5
3rd
B+ 0.72 G
C on 2nd tap — 0.005 inch
L
5
4th
B + 0.92G
C on 3rd tap - 0.005;;inch
L
4
5th
A
C on 4th tap - 0.005 inch
L
3
HAND TAPS 168
By comparing the tables given for the Acme and the
square thread taps it will be noticed that the differences
occur in the columns for the values of C and D, for the
latter, however, only in the case of the first tap in each
set. That the values for C should differ is evident, inas-
much as there is a decided difference in the cutting action
of an Acme and a square thread tap. In a set of square-
thread taps each tap is a finishing tap in itself, because
the lands of each tap are alike. In a set of Acme taps each
tap may be considered as a finishing tap for the preceding
one. The last tap in each set has less work to do in order
to assure a smooth bottom of the thread in the nut tapped.
In regard to the dimension D, this is larger than the root
diameter of the tap in the case of an Acme tap, because
the nut is supposed to be bored out with a clearance of
O.020 inch, as explained when reference was made to vari-
ous forms of threads. This, then, still permits the tap to
enter into the nut. In the case of a square-thread tap
there is no standard as to how much the hole in the nut
should clear the root of the thread, and therefore the
point of the tap is made below the root diameter on the
first tap in each set to insure that the tap can enter
the nut. In order to further facilitate the entering of the
tap in the nut, there should be, besides the long chamfer
referred to above, a slight chamfer at the point of the
thread, by means of which the tap will easily find its
way into the nut to be tapped. This chamfer should not
be lacking on any of the taps in the set.
Acme and Square Thread Taps in Sets of Three. —
As was mentioned before, the most conmion way of
making Acme and square thread taps is to make them
with three taps in a set. The values necessary to obtain
C in Tables XXXIV and XXXV have therefore been
figured for a set of three taps for the most common
164
SMALL TOOLS
pitches and are given in Table XXXVI. It must be
understood that the formulas given and the tables
figured from them possess a certain degree of flexibility,
inasmuch as the making up of the formulas necessarily
required some assumed standard to be selected as
embodying the best practice. Certain conditions may
require deviations from the rules given. While, how-
ever, the formulas which are given may not suit all pos-
sible conditions, they are made up to suit ordinary needs,
and they are particularly valuable in suggesting the possi-
bility of systematizing the making of tools too often given
up to "guesswork."
TABLE XXXVl.
TABLE FOR MAKING ACME AND SQUARE THREAD TAPS IN SETS OF
THREE.
Acme Thread.
Square Thread.
Number of
Threads
per Inch.
Amount in Inches to
add to Root Diameter of
Tap to obtain Diameter
of Straight Part of
Thread of
Amount in Inches to
add to Root Diameter of
Tap to obtain Diameter
of Straight Part of
Thread of
1st Tap.
2nd Tap.
1st Tap.
2nd Tap.
1
li
2
2i
3
3i
4
4i
5
5i
6
7
8
9
10
12
0.468
0.318
0.243
0.198
0.168
0.147
0.130
0.118
0.108
0.100
0.093
0.082
0.074
0.068
0.063
0.055
0.832
0.566
0.432
0.352
0.298
0.261
0.232
0.210
0.192
0.178
0.166
0.146
0.132
0.121
0.112
0.098
0.410
0.273
0.205
0.164
0.137
0.117
0.102
0.091
0. 82
0.075
0.068
0.059
0.051
0.046
0.041
0.034
0.800
0.533
0.400
0.320
0.267
0.229
0.200
0.178
0.130
0.146
0.133
0.114
0.100
0.089
0.080
0.067
HAND TAPS 165
In using Table XXXVI it is necessary first to find the
root diameter by subtracting the double depth of the
thread, plus the clearance in the case of Acme thread,
from the nominal diameter of the tap, and then add the
amount stated opposite the pitch for the respective taps
in the set.
It is difficult to draw a distinct line between hand taps
and machine taps when these are provided with Acme or
square threads, for while these taps are as a rule used as
hand taps, the construction is that of a machine tap. In
general practice, however, these taps are generally classified
as hand taps.
General Constmction of Acme and Square Thread Taps. —
Before we leave the Acme and square thread taps to return
^
■
ic V .
L *V* i
\
TKPER IN BOTTOM^
OF THREAD
Fig. 69. Greneral Appearance of Acme and Square Thread Taps
to the regular hand taps, we will point out some of the
peculiarities in their construction. The first tap in a set
should be turned to a taper in the bottom of the thread for
a distance of about one-quarter of the whole length of the
threaded part as indicated in Fig. 69. The diameter at
the root of the thread at the point of the first tap should
thus be less than the standard root diameter. If the taper
selected is such that the root diameter will be about one-
thirty-second inch smaller at the point than the root diame-
ter proper of the tap, that will be found to greatly increase
the ease with which the tap can be started in the nut. The
first tap in the set should also be provided with a groove or
a secondary thread on top of the ordinary thread. This
win aid in preventing the tap from reaming, instead of
166 SMALL TOOLS
actually cutting a thread in the nut. This secondary
thread may continue the full length of the chamfered por-
tion of the first tap. The first tap should also preferably
be provided with a short pilot as shown in Fig. 70 to guide
the tap straight into the nut. When the pitch is very
coarse as compared with the diameter of the tap, or when
the number of taps in a set is small in proportion to the
work they are to perform, the first tap in the set should be
provided with spiral flutes, forming a right angle with the
angle of direction of the thread. In other words, the
spiral of the flutes should be left-hand for a right-hand tap,
and vice versa. This will greatly increase the cutting
qualities of the tap. In fact, it evidently would increase
n 1 ■ hr-
L- ! i_
Fig. 70. Difference between First and Subsequent Taps in a Set of
Acme or Square Thread Taps
the efficiency of all taps to flute them in this manner, but
whenever it is not imperative it is avoided on account of
the increased expense and difiiculty.
When the first tap in a set is provided with a pilot, the
diameter of this should be made a trifle smaller than the
hole in the nut to be tapped (from 0.002 to 0.005 inch
smaller). The length of the pilot should be about equal
to the diameter of the tap, or, at least, not shorter than 0.75
times the diameter. The length of the pilot should project
from the regular length of the thread of the taps in the set,
but in order to make the total length of all the taps in the
set the same, the length of the pilot should be subtracted
from the length of the shank in the first tap. This is indi-
cated by the dotted lines in the cut. Fig. 70, where the full
HAND TAPS 167
lines show the second and third taps in a set, and the dotted
the pilot and the modification in the shank of the first tap.
At the end of this chapter we shall return to these taps
when giving formulas and length dimensions for all kinds
of hand taps. We shall now again take up ordinary hand
taps with United States, sharp V, or Whitworth form of
thread. What will be said in regard to the fluting of these
taps applies of course to Acme and square thread taps as
well. The relief of the latter taps will be specially men-
tioned later.
Cutting Taps with Dies.
While it is rather common to cut the threads on taps
with dies instead of cutting the thread in a lathe, it
is a practice which can hardly be recommended. Any
inaccuracy in the lead of the thread of the die will be
duplicated in the tap, and still further augmented by the
change in lead in the tap due to hardening. Sometimes,
when the threads on small taps are cut with dies in screw
machines, it is found that the taps have a "stretched''
thread, or in other words, that the lead of the thread is
longer than the standard lead. On examination the die
may be found to be properly made, but further investi-
gation may show that the heavy turret slide of the screw
machine was dragged along with the die, and this has
caused the thread to stretch, making the lead long.
For this reason it is not advisable to cut the thread of
taps which are required to have the highest possible
degree of accuracy in a screw machine. It is particu-
larly bad practice in the case of taps with a long threaded
portion or taps used for threading long holes, as the
inaccuracies in lead will be so much the more pronounced.
The opinion that taps stretch or become long in the
lead when cut by dies in screw machines is one that is
158 SMALL TOOLS
not universally accepted, and it must be admitted that
the reason given for this occurrence does not seem entirely
plausible. Whatever be the cause, however, the fact that
taps cut in screw machines are liable to be inaccurate
remains undisputed.
It is true that it is the practice with some firms manu-
facturing taps to cut the thread with dies in a screw
machine, but in the case of manufacturing some factors
enter which make this permissible. In the first place, the
difference in price when threading in a screw machine or
cutting the thread in a lathe is so great that a number of
taps can be thrown out at the final inspection if their
inaccuracy in lead is greater than the limits of error per-
mitted, and a saving may still be the result of the method
employed. It must be understood, however, that such a
procedure is applicable only to small taps, where the loss
of material is not very significant should a tap not pass
the inspector, but this process should not be applied to
taps where great accuracy is especially desired. In such
cases nothing can compare with a thread cut in a lathe
provided with a lead screw which itself has been properly
tested as to its own accuracy. For ordinary machine
screw taps, however, in manufacturing, the screw machine
may answer the purpose and prove economical.
Requirements for Correctly Threaded Taps.
In correctly threading a tap, there are six distinct points
to be taken into consideration. The tap must be pro-
vided with the correct diameter in the angle of the thread,
a correct outside diameter, correct lead, correct angle
between the sides of the thread, correct relation of this
angle to the axis of the tap, and finally, correct flats or
radii at the top and bottom of the threads, as required
by the standard thread form. The angle diameter, for
HAND TAPS 169
instance, may be correct while the outside diameter would
be a trifle large or small, depending upon whether the flat or
radius at the top of the thread were either too small or too
large. The lead, of course, may be incorrect while the other
factors are practically correct. The angle of the thread
may be larger or smaller than the standard angle, and if
the lead, the outside diameter, and the angle diameter
were ^till approximately correct, the tap would produce a
very poorly fitting thread. The angle between the sides
of the thread may be correct in itself, but the thread-
cutting tool may have been presented to the work at an
oblique angle, thus producing a thread that would not be
symmetrical about a Kne through the center of the thread
at right angles to the axis of the tap. It is evident that all
these requirements in regard to threading must be filled in
order to make a perfect tap.
In manufacturing, where tools and holders specially
made for the purpose are used in threading taps, there is
little danger of inaccurate or unsymmetrical angles of
the thread. It is therefore the practice simply to inspect
the angle diameter and the lead of the tap. If these two
prove correct within the prescribed limits, and if the out-
side diameter of the tap blank was inspected before
threading, there is little danger of any serious inaccuracies
in respect to the other details of the thread. It must,
however, be understood that the threading tools and the
alignment of the threading lathes must be subject to
inspection at certain intervals, if the chances of error are
to be guarded against as much as possible.
Fluting.
The flutes of a tap serve two purposes. They provide
for cutting edges for the threads and form channels for
the carrying off of the chips. The form of the flute is
160
SMALL TOOLS
very important, as it determines the cutting qualities
of the tap as well as the ease with which the chips will be
able to pass away from the cutting points. The main
qualities looked for in a tap are strength and ease of
working, provided the tap is otherwise correct. In order
to obtain strength a shallow flute with no sharp comers
is the first requirement. An easy-working tap, again,
requires a considerable amount of chip room, and con-
sequently a comparatively deep flute. The correct flute
therefore is a compromise between a flute which will give
the greatest amount of chip room and the greatest
Fig. 71. CommoD Forms of Tap Flutes
strength to the tap. Besides, the flute must be of a shape
easily produced, so as to limit the cost as far as con-
sistent with good results, and must carry away the chips
from the cutting edges in a manner offering the least
resistance. The present practice is to provide hand
taps with deep straight-sided flutes having a small round
in the bottom, as shown to the left in Fig. 71. This
method, while it provides an abundance of chip room, is
accompanied by some very grave disadvantages. The tap
will crack more easily in hardening, it will not carry away
the chips from the cutting edges as readily, and is not as
strong as a tap fluted in the manner shown in the section
HAND TAPS
161
to the right in Fig. 71. The making and maintenance of
the cutters for producing this latter flute, however, are
more expensive, and as the present practice of fluting is
becoming fairly universal it is evident that the objections,
while of a serious nature, do not outweigh the advantages
gained. The radius at the bottom of the flute ought,
however, not to be less than one-quarter of the diameter
of the tap. Some persons well familiar with this kind of
work claim that a radius of one-eighth of the diameter
Fig. 72. Tap Fluting Cutter
of the tap would serve the purpose equally well, besides
giving a larger space for chips. It has been proven
beyond doubt, however, that this slight difiference in the
radius at the bottom of the flute influences the endurance
qualities of the tap very materially.
Fluting Cutters. — The cutter used for cutting the
straight-sided flute is shown in Fig. 72. The included
angle between tl^e sides is 85 degrees, 55 degrees on one
side and 30 degrees on the other. The thickness of the
cutter should be approximately equal to ^ D + -^^^ inch if
D equals the diameter of the tap. The radius, as men-
tioned before, ought to be equal to --- , but should not
162
SMALL TOOLS
exceed ^^ inch. The diameter of the cutter depends, of
course, not only upon the diameter of the tap to be fluted
but also upon the size of the hole in the cutter for the
milling-machine arbor. If we assume that we use a three-
quarter-inch hole in the cutters for the smaller diameters
of taps, say up to and including three-quarter-inch, and
one-inch hole in cutters for large-diameter taps, we can
make
Diameter of cutter = — + 2 inches,
in which formula Z), as before, equals the diameter of
the tap to be fluted.
TABLE XXXVII.
DIMENSIONS OF FLUTING CUTTERS FOR HAND TAPS.
(See Fig. 72 for form of cutter.)
Diameter of
Thickness of
Radius.
Diameter of
Cutter.
Cutter.
Hole in Cutter.
Diameter of
Tap.
A
B
C
D
2
t
A
; ,
; •
2}
■J
^
^
21
^
1
\
21
jif
,
■
21
J
i
21
1
1
21
1
i
li
21
i
A
H
2}
1
H
2i
2
3
A
2}
3
1^
^
^
31
If
^
2f
3
31
31
1
1
31
31
l|
4
4
2
^
HAND TAPS
168
Table XXXVII is figured from the formulas given.
The figures ^ven in the table are, however, practical
working figures and are only approximately the values
figured from the formulas whenever these values give
dimensions unnecessarily fine and in too small fractions.
Of course the nearest quarter of an inch is near enough
for the dimension in regard to diameter, and the nearest
one-eighth inch in regard to thickness. The radius, how-
ever, must be given in finer subdivisions, as one-thirty-
second or even one-sixty-fourth inch makes a considerable
difference in this respect.
The cutter for the flute shown to the right in Fig. 71 is
shown in Fig. 73. The curve forming the cutting edge is
composed of two arcs tangent to each other
with their centers at A and B respectively.
The radius for the large arc should be about
equal to the diameter of the tap. The radius
of the small arc should be about one-sixth
of the diameter. It must be plainly under-
stood that when formulas and rules like
the above are given they are intended only
for guidance. It is evidently impossible to
have cutters conform to these formulas for
each different diameter of tap, as it would
require more cutters than necessary. The
formulas merely express a good average
working practice.
The lands of the* tap when fluted with the cutter last
described may be somewhat narrower than the lands in
taps fluted with straight-sided flutes, inasmuch as the
latter tap requires wide lands in order to make up for the
loss of strength due to the deep, more sharp cornered
flute.
Flviing Taps for Brass. — In the case of either flute it
/
^
^B
\
m
i
^B
<
A \.
Fig. 78. Special
Form of Tap
Fluting Cutter
164 SMALL TOOLS
is the practice to make the cutting edges of the taps radial
as in Pig. 71. This is, at least, the common practice
in regard to taps for steel and cast iron. In regard to
taps for brass there is some difference of opinion. The
general practice, however, if a tap is to be used entirely
a for brass, is to provide a cutting
^^L^ll^^^ edge which is slightly in advance of
y^^ the radial line, or in other words,
ry-^^J \ I parallel to the radial line, but ahead
It ^-^^TL ^^ *^^ center, as shown in Fig. 74.
'tt-^ IT This way of cutting the flute gives
W;; ;r^ > JJ a slight negative rake, and causes
j^^y the tap to cut more smoothly and
^^^^^ with less liability of chattering.
Fig. 74. s^tionof Tap r^Yie dimension a in Pig. 74 should
for Brass . *=»
be from one-sixteenth to one-tenth
of the diameter of the tap. However, a tap with the
cutting edges radial will cut brass fairly well if otherwise
properly made.
Number of Flutes. — Lastly, we have to consider the
number of the flutes in hand taps. The formula
Number of flutes = — h 2f ,
in which formula D equals the diameter of the tap, will
give approximately the correct nmnber of flutes. Figur-
ing a table from this formula, we will find the number of
flutes for various diameters as stated in Table XXXVIII.
It will be noticed that the numbers of flutes for hand
taps as given in Table XXXVIII are 4, 6, and 8, the
odd numbers 3, 5, and 7 not being used. The reason for
this is that an even number of flutes enables one to
measure the diameter of the tap in aU cases with ordinary
micrometers. If an odd number of flutes ia used the
HAND TAPS
165
measuring of the diameter is rather complicated and
requires a gauge to which to fit the tap. Even then there
will still be more or less uncertainty unless the tap is of a
standard diameter.
TABLE XXXVIII.
DIAMETERS OF HAND TAPS AND CORRESPONDING
NUMBER OF FLUTES.
Diameter
Number
Diameter
Number
of Tap.
of Flutes.
of Tap.
of Flutes.
i
li
6
2
6
'
2i
6
2i
6
•
2f
6
i
3
6
1
H
8
u
4
S
H
It must also be remarked, in connection with the flut-
ing of hand taps, that the width of the lands does not
depend only upon the necessary strength of the tap. As
a hand tap, as a rule, receives all its guidance from the
lands resting against the walls of the nut it is necessary to
have the lands wide enough so that they steady the tap
during the tapping operation.
In regard to the number of flutes there is, however,
some difference of opinion. There are those who con-
sider four flutes the proper number to use on all sizes of
hand taps with the land about one-fourth the diameter of
the tap. However, on large taps the land wiU be rather
wide if made according to this rule, and better results
will be obtained by increasing the number of flutes in
accordance with the formula previously given.
166 SMALL TOOLS
Convex Flviing Cutter. — Sometimes a regular convex
cutter is used for fluting taps. This is merely a way of
providing a flute similar: to the one shown to the right in
Fig. 71, but avoiding the expense of a special cutter. In
selecting half-round (convex) cutters for taps the formula
below can be used for determining the proper thickness of
the cutter:
8D
T =
in which formula
T = the thickness of the cutter,
D = the diameter of the tap,
A = the number of flutes.
If, for instance, we wish to flute a one-inch tap with
four flutes, the thickness of a convex cutter for the purpose
would be
g-^ = — =0.667, or — approximately.
Grinding Fluting Cutters.
In the case of formed cutters with regular milling cutter
teeth it is, of course, necessary that the teeth be ground
around the edges, instead of being ground only on the
faces as is always the case on cutters with eccentrically
relieved teeth. In Figs. 72 and 73 are shown two types
of milling cutters which may be ground with devices
working on the principles indicated and described below,
the cutter in Fig. 72, as mentioned above, being a regular
fluting cutter for taps, and the cutter in Fig. 73 a special
fluting cutter.
In Fig. 75 is shown the device used for grinding a
regular tap fluting cutter. The angle included between
HAND TAPS
167
the two faces on the fluting cutter is 85 degrees, and the
angle between the two faces 0 and D in the device for
grinding the teeth of these cutters is also 85 degrees, one
Fig, 76. Device for Grinding Tap Fluting Cutter Shown in Fig. 72
side making 30 and the other 55 degrees with a line at
right angles to the axis of stud A on which the cutter is
mounted while grinding. The device consists of a base
plate G having three feet which rest on a special table on
the grinding machine, shown in Fig. 76, which will be more
168
SMALL TOOLS
HAND TAPS 169
fully described later. On this base plate G slides a cutter
holding slide ff, which has a groove in the bottom fitting
a tongue projecting from the base plate. An oblong slot
is provided in the base plate as shown at P, so that the
slide H can be clamped to the base plate by the screw L
at any place within the length of the slot. The screw K
passing through the lug R driven into the base plate (?,
and acting upon the slide H, permits the necessary adjust-
ment. The slide H holds a stud or spindle A passing
through a projecting standard F of the slide. The cutter
to be ground is mounted on this stud.
It will be evident, upon explanation of the action of
this device, that when grinding the cutters these must be
so mounted upon the stud A that the apex of the included
angle between the two angular faces (that is, the point
where the angular sides would meet if extended) shall be
on^the same center line as the point N of the grinding
fixture, where the two sides C and D meet (see Fig. 75).
In order to obtain the fine adjustment necessary to bring
these two points on the same center line, that end of
stud A which enters into the bearing in the standard F is
provided with threaded portions on which adjusting nuts
are mounted. Collars are placed on the smaller diameter
of A against the shoulder ilf, so that the adjustment
necessary to be made by the nuts will be comparatively
small, the* collars taking up the main difference in width
of the various cutters to be ground. On the outside end
of the stud A is a collar B and a set screw having a large
round slotted head, which is used for binding the collar
against the cutter. It will be noted that this collar is
'cut off on one side to an angle. This is done in order to
permit the collar to clear the emery wheel of the grinder
when the side of the cutter tooth next to the collar is
being ground.
170 SMALL TOOLS
As shown in Fig. 72, the cutters to be grouna have their
two faces connected with the small radius, different for
different kinds and sizes of fluting cutters. This radius is
obtained by permitting the faces of the cutter teeth to
project slightly outside of the faces C and D of the base
plate G, Fig. 75, when the cutter is in position on the
stud A, the point of the cutter, however, still being in line
with the point N of the device, as mentioned above.
When in use, the grinding device is placed on the table of
the grinding machine, as shown in Fig, 76. This table is
mounted directly on the grinding-machine knee, and is
provided with a guide strip E. The hardened shoe N in
Fig. 75 slides against this guide strip E in Fig. 76, and by
swinging the device around so that first the face 0 comes
along the guide strip Ej and then turning it around the
point N until the face D rests against the guide strip, the
cutter is ground to the same angle as that of the base plate
G in Fig. 75, and a radius will be formed at the point
of the cutter, depending upon how far the faces of the
cutter teeth project outside of the faces G and D of the
base plate G, Different angles may be obtained by put-
ting tapered strips along the sides C and D, the angle
included between the face of the strips being the same as
the angle between the faces of the teeth of the cutter.
The base plate for this device should be made of machine
steel, and the faces C and D should be case-hardened.
If tapered strips are screwed onto the faces G and D to
accommodate other angles than the ones referred to,
these strips should also be made of machine steel and
case-hardened. Slide H is made of cast iron.
Referring now to Fig. 76, in which the special table on the*
cutter grinding machine is shown, this table consists of a
cast-iron body, being provided with two tool-steel plates
S on the top, forming the table surface. These plates
HAND TAPS
171
are hardened and ground to prevent too rapid wear, as the
feet of the grinding device constantly slide on their top
surface. The guide strip E is also made of tool steel and
hardened.
At T in Fig. 76 a stud is shown projecting up from the
top of the table. From this stud projects an arm TF,
which is used for setting the cutter tooth, as shown, the
cutter being indicated by dotted lines. It is, of course,
necessary that each tooth be exactly at the same height
as the others, when ground, so that the diameter of the
cutter measured over any two teeth will be exactly the
same. The cutter is held simply by frictional resistance,
and the indexing around
is done by hand by the
operator. The table can
be fed out and in by
means of a feed screw
with a knurled head V,
thereby permitting a
greater or less amount to
be ground off from the
teeth of different cutters.
In Fig. 77 is shown
a device which is used
for setting the slide H in
Fig. 75 to such a position
that the correct radius
will be groimd at the
apex of the angle of the
cutter teeth. The stud C Fig- 77
is screwed into the top
of any kind of a base or
surface plate. This stud has a slot or groove cut in its
top surface, and a regular 4-inch machinist's scale, pref-
ij
1
Device for Setting Grinding
Fixture to Grind a Certain Radius
at Point of Cutter
172 SMALL TOOLS
erably graduated in lOOths or 64ths of an inch, is laid in
this slot at the top and held by means of the set screw B,
the upper part of the round stud C being split so that
the scale can be gripped in the slot cut for it, as if placed
in a split chuck.
When the device in Fig. 75 is to be set so as to grind a
certain radius, the pin A, Fig. 77, is placed against the
edge of the point N of the base plate (?, Fig. 75, and the
slide H is adjusted so that the cutter touches the end D
of the scale in Fig. 77. When the scale is so set that m
equals n, the cutter to be ground will have no radius but
will get a sharp edge at the point. When m is shorter
than n, the difference between n and m will give a rela-
tive measure of the radius that will result between the
faces of the cutter teeth; but it must be understood that
this difference does not give the exact actual radius. This
would be measured from the side D of the plate G to the
side of the cutter. Of course, the arrangement in Fig. 77
may be used for measuring this length also, by placing the
face D against pin A and the angular side of the cutter
tooth against the end of the scale.
The device in Fig. 78, finally, is used for inspecting the
cutters when ground. The cutter is placed on the stud
A J the stud entering the hole in the cutter, and the gauge
pin B, having a large head ground flat, is pushed up
against the ends of the teeth in the cutter. This permits
not only the length of the different teeth in the same
cutter to be gauged, but in cases where several cutters are
used in a set for fluting taps, all the cutters in the set can
be gauged to find out if they are of exactly the same diam-
eter. The gauge stud B is fed in and out by means of the
micrometer screw 0 which has a graduated head as shown.
When the stud B has been set to the size of one cutter in
the set of cutters, it is clamped in place by the clamp
HAND TAPS
173
screw D. If, however, the other cutters in the set should
prove to be smaller or larger than the first cutter, the
I Jiii|iiii|iiirpiii|iiMi
i
gauge screw D can be loosened and the micrometer screw
adjusted so as to move B in the desired direction, and
the amount that the cutters are smaller and larger than
174
SMALL TOOLS
the size of the other cutters in the set can be determined
by reading off the number of thousandths directly on the
graduated head of the micrometer screw C This head
should be graduated so that each graduation reads 0.001
Fig. 79. Device for Grinding Formed Fluting Cutter Shown in Fig. 73
inch. A pointer E is screwed to the end of the gauge
stud J5, to insure correct reading of the graduations.
Collars may be put on stud A to accommodate smaller or
larger thicknesses of cutters, or the binding screw F may
be loosened and the stud A moved up enough to accommo-
date thinner cutters, the cutters resting on the shoulder G.
HAND TAPS
175
In Fig. 79 is shown a device used in conjunction with
the grinding table in Pig. 76 for grinding formed fluting
cutters, with an outline similar to the one shown in
Fig. 73. The principle of this device is practically the same
as that in Fig. 75. It will be noticed, however, that in
order to permit the device to be swung around so as to
grind the complete form of the cutter a slot T cut on a
circular arc has been provided in the base of the device,
and the top portion is swiveled around the stud A. At
Fig. 80. Side View of Formed Fluting Cutter Grinding Device
the front end of the slide B a threaded hole D is provided
for the screw which holds the former for the various
formed cutters to this slide, the slide being adjustable to
take care of the different diameters of the cutters. In
Fig. 80 is shown a side view of this device, which plainly
shows the design of the cutter-holding slide, the arbor,
and its adjustment. It will be noticed that in this case,
instead of adjusting the cutter arbor by means of two
nuts on each side of standard F, the stud C has the
smaller end threaded directly into the upright F and the
nut E simply acts as a binding or check nut. A slot is
176 SMALL TOOLS
provided for a screw-driver in the end of the stud C to
facilitate adjustment. It will be noticed that in the
device in Pig. 79 the former is not attached directly to
the base of the device but is placed on an independent
slide. On account of this there is no need of having any-
sliding adjustment between the base H of the device and
the standard F, all adjustment being taken care of by the
slide B, having the formers attached at D, ag mentionied.
The general shape of the formers used is shown at K,
Fig. 79.
The device last described may also be used for grinding
cutters for fluting drills when these cutters are made with
regular milling cutter teeth. In fact, the former, shown
in place in Fig. 79, is one which in form most nearly corre-
sponds to the form of a drill fluting cutter.
Relief of Taps.
In the next place we must turn our attention to the
proper relieving of hand taps. The question of proper
relief is one of the most serious and particular met with in
tap-making. The old and until recently the most common
method was to ^ve all the teeth a relief on the top as
well as in the angle of the thread; i.e., the heels of the
teeth were made of smaller diameter than the diameter
measured over the cutting edges, both at the top and at
the root of the thread (as shown in Fig. 81). However,
this has been found to be wholly unnecessary, and taps
of this kind are now made without any relief at all in
the angle of the thread; but the top of the thread of the
chamfered part only is slightly relieved. To further improve
upon the cutting qualities of the tap, it should be made
smaller in diameter toward the shank than at the point.
This difference in diameter should, of course, vary for
HAND TAPS
177
different diameters, and the limits in variation of size
permitted must, of course, also be taken into consider-
ation. It may be said that in general practice it answers
the purpose if the tap is about 0.0015 inch smaller at
the shank end of the thread for taps up to one-half inch
diameter, and from 0.002 to 0.003 inch smaller at this
end than at the point for taps from one-half up to two
inches diameter. It may be added that although this is
an essentially good point in tap-making, most manufac-
turers do not make their taps that way, probably because
it would increase the expense in the manufacture and
require greater care in making.
Fig. 81. Section of Tap Relieved Fig. 82. Section of Tap Relieved
both on Top and in Angle of in Center of Land
Thread
Another improvement upon a hand tap, seldom seen in
taps manufactured for the market, is to give to the angle
of the thread a relief in the center of the land, as shown
in Fig. 82. The reason for so doing is obvious. The
tap gets the same support along its periphery as if not
relieved in the angle of the thread, because it retains its
bearing at the heel of the thread, but as can be clearly
178 SMALL TOOLS
seen a good portion of the resistance is eliminated, the
bearing surface of the tap thread which is presented to
the nut being considerably smaller.
Acme and square thread taps should be relieved on the
top of the thread on the chamfered portion on all the
taps in a set, and the finishing tap should be given relief
in the center of the land on its straight or parallel por-
tion. In cases where the taps are used as machine taps
rather than as hand taps, they should be relieved in the
angle of the thread as well as on the top on the chamfered
portion.
Change of Pitch in Hardening.
As is well known, the pitch of a tap as well as its diam-
eter will change in hardening, the pitch as a rule becom-
ing shorter and the diameter larger. This tendency of
change can be minimized by slow and even heating, com-
bined with hardening at as low a heat as is possible to
obtain the desired result in the tap, but it can never be
fully eliminated. For this reason it is necessary to cut
the thread of taps on lathes having lead screws slightly
longer in the pitch than the standard. The tap will
then also have a pitch slightly in excess of the standard
before hardening, and if the excess length is properly
selected, the tap will have a nearly correct pitch when
hardened. The amount that the pitch should be longer
before hardening varies, of course, according to the makes
and grades of steel. To give definite rules in this matter
would be impossible, more particularly so because the
result of hardening may not always be shrinkage in the
length of the piece to be hardened. Practical experi-
ments have proved that in some cases, although rare,
even when working with a most uniform grade of steel
and handling it with the utmost care, there is no sure way
of telling whether the result will be shrinkage or expan-
HAND TAPS 179
sion. However, it has been found that most kinds of steel
have an invariable tendency to contract lengthwise when
hardened, and if this contraction has been found to be
within certain limits in a few experiments, the steel may
be fairiy well depended upon to vary in the same way
in so great a number of cases as to permit neglecting
those in which unexpected results are obtained. It is of
interest to note, however, that exceptional cases have
been observed where different parts of the same pieces
have shown considerable difference in the amount of
shrinkage.
While,, as stated before, definite rules cannot be laid
down, it may be given as a guide that most steels have an
average shrinkage of from 0.016 to 0.020 inch per foot,
when the ratio between the diameter and the length of
the work does not exceed say 1 to 10. When, however,
the threaded piece is very long compared with the diameter,
as for instance in stay-bolt taps, the contraction is pro-
.portionally greater. For very large diameters a pro-
portionately smaller value of shrinkage between the
Umits given above can usually be assumed. Jessop's steel
changes about the least and is the most uniform of any
kind of ordinarily used steels. The average shrinkage of
this steel is so small that it gives it a great range of use-
fulness in cases where other steels make trouble. The
amount of change is only from about 0.004 inch to 0.006
inch per foot, these values being in proportion to smaller
' or larger diameters of work, as remarked above.
Of course many conditions will have to be taken into
consideration to obtain satisfactory results. The amount
of change depends not only upon the grade of steel but,
as said before, upon the uniformity and amount of heat
used when hardening, the rapidity and manner of cooling,
and also upon the number of times the work has been
180 SMALL TOOLS
through the fire. In regard to the effect upon steel of
repeated annealing, a few interesting remarks might be
made. If after having been through the fire once the
pitch of a tap is correct, and it is annealed and hardened
again, each consecutive repetition of this process will
invariably bring about a growing error. Again, if a cer-
tain kind of steel should be too long in the lead after the
first hardening, a second or, if necessary, a third harden-
ing is likely to bring about a satisfactory result so far
as the pitch is concerned, though this is not advisable, as
tool steel generally loses its good qualities by being put
through the fire too many times.
Lead Screw for Cutting Taps Long in the Lead, — In this
connection it may be appropriate to give some attention
to the process of producing a lead screw intended for
cutting a thread which is a certain amount longer in
the lead than the same thread would be if regularly
pitched. If such a lead screw is to be cut on a lathe pro-
vided with a standard screw there are some difficulties
in finding the change gears with which to obtain the
results desired. The following formula will aid in find-
ing the ratio of the gears to be used. In this formula
a = amount thread is longer in one foot than the same
number of threads would be if regularly pitched.
n = nominal number of threads per inch on work to be
threaded.
I = threads per inch on lead screw of lathe,
r = ratio of gears in head of lathe.
R = ratio of change gears to cut a thread a certain
amount, a, longer in one foot than same number
of threads regularly pitched.
Then
„ ; X r (12 -f g)
^= 127^
HAND TAPS 181
The ratio of change gears having been thus obtained, the
proper gears to use must be found by trial calculations.
The most common amount to cut hand taps long in the
lead in one foot is about 0.018 inch. Stay-bolt taps and
taps of a similar kind are often cut from 0.030 to 0.034
inch long in the lead in one foot. If we assume that we
wish to cut a lead screw which is 0.018 inch long in the
lead in one foot, and that the nominal number of threads
per inch in this lead screw is to be 8, that the correct lead
screw in the lathe used for cutting the screw has 6 threads
per inch, and finally that the ratio of the gearing in the
head-stock of the lathe is 2, then the ratio of change gears
required to cut the lead screw in question would be
6 X 2 (12 + 0.018) ^ J 50225.
12 X 8
The trials which will give the gears which most nearly
produce this ratio are more or less lengthy, but no
definite rule can be given except for finding the ratio
according to the above formula.
HUT HAVmH BEEN CUT WJTH TAPLONO \H THE LEA&
/ \ /A. / \ ' '
^>.:/' Y \^'
Fig. 83. Effect of Difference in Lead in Nut and Screw
Provision for Differences in Lead of Tap and Screw. —
The lead of a tap cannot, however, be depended upon to
be exactly correct even when the precautions referred to
above are taken, but it will be within very close limits.
If the tap is long in the lead the nut tapped will, of course,
also be long in the lead, and will not correctly fit a stand-
ard screw. The resulting fit is shown exaggerated in
Fig. 83. As this difficulty cannot be in any way elimi-
182
SMALL TOOLS
nated, the only way possible to arrange so that a screw of
standard diameter and correct lead will go into a nut of
incorrect lead is to make the diameter of the nut, and
consequently the tap for tapping the nut, a certain
amount over-size, as is evident from Fig. 83. This
amount depends upon the length of the nut to be tapped
and upon the unavoidable error in the lead of the tap.
As these quantities are difficult to determine particu-
larly when making taps for general purposes in great
quantities, some standard figures must be assumed which
will fill the requirements in all ordinary cases. Table
XXXIX gives the values of over-size near which the angle
diameter of hand taps ought to be after hardening. In
other words, the angle diameter must be between the
standard angle diameter and the standard plus the limits
of over-size stated in the table, and preferably nep,r the
larger value.
TABLE XXXIX.
LIMITS OF OVER-SIZE IN DIAMETER OF HAND TAPS.
Size of
Limit of
Size of
Limit of
Tap in
Inches.
Over-size.
Tap in
Inches.
Over-size.
A
0.00075
li
0.00275
0.001
li
0.003
1
0.00125
2
0.0.03
{
0.0015
2i
0.0035
^
0.00175
^
0.0035
0.002
2i
0.004
0.00225
3
0.004
0.0025
H
0.0045
0.0025
' 4
0.005
u
0.00275
Swelling of Taps in Hardening. — Table XXXIX is,
of course, only of value for inspecting taps after harden-
ing unless some data are given in regard to the amount
HAND TAPS
188
a tap is likely to increase in diameter in the hardening
process. If such data are ^ven, it will make it possible
to determine the angle diameter of the tap before harden-
ing, the only figure which is of use in making the tap.
It is extremely difficult to state anything with certainty
in this respect. Experiments with taps made from the
same kind of steel and under the same conditions prove
that there may be very great variations in the swelling
or increase in diameter of taps due to hardening. In
Table XL are given such values as may be considered
correct for average cases.
TABLE XL.
INCREASE OF TAPS IN DIAMETER DUE TO HARDENING.
Diameter
of Tap.
Increase
Due to
Hardening.
Diameter
of Tap.
Increase
Due to
Hardening.
i
!
1
H
IJ
2
3
3*
4
0.0025
0.0025
0.003
0.003
0.0035
0.0035
0.004
0.00025
0.0005
0.001
0.0015
0.002
0.002
As the amount of over-size necessary for a tap depends
on the pitch rather than upon the diameter, the data
given in Table XXXIX should be applied only to taps
with standard threads.
The relationship between the pitch, the length of the
nut, and the error in lead on the one hand, and the excess
in angle diameter on the other, is approximately expressed
by the formula
AXNXL
D,-D,^
tan 30^
184 SMALL TOOLS
in which formula
Dj = the theoretical angle diameter,
Dj = the actual angle diameter required in the tap to
compensate for the error in the lead,
A = the error in lead per each thread,
iV = the number of threads per inch, and
L = the length of the nut in inches.
Diagram of Relation betrveen Lead and Excess Diameter,
— The relationship expressed by the formula above is
shown in the diagram Fig. 84. This diagram gives the
excess in angle diameter required over the standard
angle diameter in taps to compensate for given errors in
the pitch of the thread due to shrinkage in hardening.
If the error in the pitch in a certain length T is given, the
diagram will give the excess in pitch diameter necessary
to compensate for this error, assuming that the length of
the piece to be tapped equals T. If the length of the piece
to be tapped does not equal T, the amount of excess in
pitch diameter required is obtained from the formula
jjX E = excess in pitch diameter necessary to permit a
correct screw to go into the tapped piece.
In this formula L = the length of the piece to be
tapped and E = the excess in pitch diameter required for
a piece to be tapped, the length of which equals T.
Let us assume that the given error in the pitch of the
thread in a length of 3 inches is 0.001 inch. Suppose the
nut to be tapped is IJ inches long. Then
r= 3; L= li; ^=0.00175 (found from the diagram),
and according to our formula
-f X 0.00175 = 0.00075 (approx.) = excess in angle
o
diameter required.
HAND TAPS
186
''^^~
GIVEN ERRORS IN PITCH OF THREAD,CAU8ED BY
SHRINKAGEJN HARDENING
Fig* 84. Diagram of Relation betweeu Knor in
Lead and Excess Piteli Diameter of Taps
186 SMALL TOOLS
The value of E is found from the diagram by finding
0.001 on the horizontal line AC; then follow the vertical
line from 0.001 to the Une AB; from the intersecting
point on this line follow the horizontal line to BC and
read off the nearest graduation on the scale on this line.
The value obtained is Ey or the excess in angle diam-
eter required, provided the length of thread in which
the error in lead is measured equals the length of
the nut. Otherwise the amount of excess is found by
the formula previously given, in the manner already
explained.
It is common practice that the length of nut taken as the
basis for various taps, when they are to be used on general
work, is assumed to equal the diameter of the tap. It is
evident, however, that this will be correct only for taps
with standard threads, because when threads finer than
standard are used for a certain diameter, the length of the
nut is usually shorter. The excess in angle diameter
should therefore properly be determined rather by the
pitch than by the diameter of the tap. This is done by
several firms when inspecting taps made for them by other
manufacturers.
The Westinghouse Electric and Manufacturing Company
makes use of a formula:
Excess in angle diameter = V pitch X 0.01.
By means of thi3 formula values a trifle larger than those
given for limits of over-^ize in Table XXXIX are obtained.
In this formula the excess angle diameter is made directly
dependent upon the pitch of the thread. In Table XLI
the v-alues of the excess for a number of pitches are given.
The corresponding diameters of United States standard
screws are also stated. This will permit comparison to
be readily made with the values in Table XXXIX. It
HAND TAPS
187
must be remembered that these values refer to the sizes
of the taps after they are hardened.
TABLE XLI.
LIMITS OF OVER-SIZE IN DIAMETERS OF HAND TAPS.
No. of
Threads
per
Inch.
Correspond-
ing
Diameter,
U.S.
Standard.
Limit of
Over-size =
VpitchXO.Ol
No. of
Threads
per
Inch.
Correspond-
ing
—Diameter,
U.S.
Standard.
Limit of
Over-size =
VpitchXO.Ol
3
4
5
31-4
21-2}
li-ij
1
i
i
0.0058
0.0050
0.0045
0.0041
0.0038
0.0035
0.0035
0.0032
0.0030
0.0029
0.0028
0.0027
0.0025
18
20
22
24
26
28
30
32
36
40
50
56
64
^
0.0024
0.0022
0.0021
6
0.0020
7
0 0020
8
9
A
0.0019
0.0018
10
11
12
13
14
i
i
A
0.0018
0.0017
0.0016
0.0014
0.0013
16
A
0.0012
Hardening Taps.
As mentioned before, the amount that a tap will change
in dimensions in hardening depends greatly upon the
manner in which it is hardened. The heating must be
made evenly throughout the tap, and it should be heated
slowly; the water used for dipping should not be very
cold; the tap, when dipped, should be held in a vertical
position. The amounts given in the preceding tables were
obtained from actual experieiuce in the manufacturing
of taps. But it must be clearly understood that the
rules for hardening are all very indefinite. It is easy
to say: ^^Heat slowly and uniformly,'' but not so easy
to do it; and only by experience is it possible to attain
188 SMALL TOOLS
uniform results in the hardening of a tap or any other
tool
Mr. E. R. Markham in Machinery, May, 1904, described
a method of hardening taps by means of which, he claims,
the original pitch and diametrical measurements can be
maintained. This method is termed "pack hardening."
Mr. Markham says :
"It is a well-known fact that small, thin pieces of steel
can be hardened by heating red hot and dipping in oil,
with little or no tendency to spring; but as steel is hard-
ened by rapid cooling from a red heat and as large pieces
of steel cool very slowly in oil, it is generally considered
advisable to cool them in water, brine, or some bath
which takes the heat quickly from the steel. Now it has
been ascertained by experiment that steel can be treated
in a manner that insures its hardening when dipped in oil,
thus eliminating the danger of cracking or breaking, and
reducing to the minimum the liability of springing. This
is accomplished by packing the articles with some car-
bonaceous material in an iron box which should be covered
with a flat piece of iron. The space between the edges
of the box and cover should be luted with fire clay which
has been mixed with water until it is of the consistency
of dough. This should be allowed to dry before placing
in the furnace, or the rapid drying will cause it to crack.
Should it crack when drying the cracks may be filled with
clay and this allowed to dry.
"The carbonaceous material used must not contain
any elements that are injurious to tool steel. For this
reason do not use bone in any form. Bone contains
phosphorus, and this is extremely injurious, as it
causes the steel to become brittle when it is in com-
bination with carbon. Burned bone does not contain as
high a percentage of phosphorus as the raw bone, but
HAND TAPS 189
will not give as good results as other material we can
use.
''If the steel used in making the tool does not con-
tain over IJ per cent carbon, 'charred leather' is an *
excellent material to use when packing in the iron box.
If steels of higher carbon are used, charred leather does
not act as well as charred hoofs, or a mixture of
charred hoofs and horns; for charred leather has a
tendency to give high-carbon steels a grain that resem-
bles steel made by the cementation process, when it is
subjected to heat for a considerable time. But there
is no such effect when charred leather is used in con-
nection with steels that do not contain more than IJ per
cent carbon/'
The box containing the articles is heated in the fur-
nace, and when heated throughout, the taps are taken
out and iihmersed in a bath of raw linseed oil, work-
ing the taps up and down and around in the oil while
cooling.
In drawing the temper, it is of course evident that a
certain temperature can hardly be settled upon, inasmuch
as various kinds of steel would not require to be drawn to
exactly the same temperature. It may be said, however,
that temperatures varying from 430 to 460° F. will not
prove to be far from the correct ones. The lower tem-
perature mentioned is commonly employed for the oil
baths used for drawing the temper in manufacturing
plants. If preference should be given to any exact tem-
•perature, it would be correct to make a rule of drawing
large taps to 430 degrees and smaller ones, say up to
seven-sixteenths inch inclusive, to 460° F.
When hardening in the ordinary way the tap can be
heated to the greatest advantage in a crucible of molten
lead heated to a red heat. There is, however, some
190 SMALL TOOLS
difficulty in regard to the lead sticking to the tap. While
there are some tool-makers who do not take any pre-
cautions to prevent this, it may be avoided by dipping
• the tap in a mixture of two parts charred leather, three
parts fine flour, and four parts table salt, all thoroughly
mixed while dry, and converted into a fluid by slowly
adding water until the mixture has the consistency of
varnish. The ingredients should be finely pulverized.
This mixture will prevent the lead from sticking to the
tap, and facilitates the hardening of the tap because of its
carbonaceous composition. After dipping, the tap must
be allowed to dry thoroughly, as otherwise, when plun^ng
the taps in the hot lead, the latter will fly and endanger the
operators.
Dimensions of Ordinary Hand Taps.
It has been a very common thing among manufacturers
of taps, and still more among persons who only occasion-
ally have been called upon to make these tools, to pro-
duce taps without following any definite rule as to the
proportions of the various details. Little attention has
been given to the possibility of expressing the relation
between the diameter and the total length, for instance,
by a single formula. For this reason it is very common
to find that the dimensions of taps, or of any other tools
of a similar character which are made in a great number
of sizes, -do not follow any definite rule in their propor-
tions, except the one that a larger size has most of its
dimensions a trifle larger than those of the preceding one. .
Various manufacturers also differ widely as to the pro-
portions of their tools. It is, however, not impossible to
express in simple formulas the rules according to which
taps of proper proportions could be made. The formulas
which follow are all worked out so that all the length
HAND TAPS 191
dimensions of the tap stand in a certain relation to the
diameter of the tap. This insures a tap which will be well
proportioned and at the same time be well adapted
for its work, even if the pitch of the thread should vary
for the same diameter. The formulas are worked out with
particular regard to taps with standard threads, either
United States standard or sharp V thread, but will be
equally serviceable for finer pitches. The' formulas, as
has been said, are based upon the tap diameter, this being
the most convenient working factor, as, of course, the
diameter is always given from the beginning. At the
first glance an observer might infer that the working
factor ought to be the number of threads per inch, but as
that number in all standard systems is dependent upon
and stands in a certain relation to the diameter, this latter
factor is just as correct to work from, and gives simpler
and more universal formulas.
It is obvious that formulas cannot be made up that
would suit the whole range of diameters from the very
smallest up to the very largest, and therefore it has been
necessary to divide the series into two groups in order to
obtain correct proportions, the one group including taps
from three-sixteenths inch up to one inch diameter; the
second from one inch up to four inches diameter.
In the formulas the following letters are used to denote
the dimensions :
A = the total length of the tap,
B . = the length of the thread,
C = the length of the shank,
D = the diameter of the tap,
E = the diameter of the shank,
F = the size of the square,
G = the length of the square.
192 SMALL TOOLS
For sizes up to and including one inch in diameter the
f onnulas are :
A = 3.5 Z) + If inches,
B = D + 1^ inches,
C = 1.25 2) + If inches,
E = root diameter of thread — 0.01 inch,
F = 0.75 E,
G =0.75D+ iVinch.
For sizes one inch and larger the formulas will be :
A = 2.25 D + 21 inches,
B = D + 1^ inches,
C = 1.25 Z) + If inches,
E = root diameter of thread — 0.02 inch,
F =0.75^,
G = 0.33 D + i inch.
Table XLII contains figures for the dimensions of hand
taps with standard threads based on these formulas. Of
course, where no necessity for close fractional dimensions
exists, the dimensions are only approximately those obtained
from the formulas, and are given as practical working
dimensions. As seen in the table the shanks for the three-
sixteenths-inch and the quarter-inch diameter taps are
made equal to the diameter of the tap, according to the
usual custom in manufacturing these taps.
Dimensions of Acme and Square Thread Taps.
It has been mentioned previously that Acme and square
thread screws are usually made with coarser pitches than
used for the V form of thread. For this reason the length
dimensions given for ordinary hand taps do not suit those
provided with the former kinds of threads. The Acme
HAND TAPS
198
TABLE XLII.
DIMENSIONS OF HAND TAPS.
— E-
r
Fig. 86
Diam-
Number of
Tom I
Lfiii^h
LefWtll
Dianit'ti?r
8(fe
Length
eter 1
ThreadB
of
of
of
of 1
of
of Tap.
pef Inch.
Thread
Shank.
^hank, E.
r^qnare.
Square.
D.
U.S.
V
A.
B.
a.
U. S.
St'd.
V
Si'.L
F,
0.
A
32
24
2i
i
H
ft
ft
A
A
i
20
20
24
14
I ,
i
ft
ft
18
18
2«
14
Ift
0.23
0.21
ft
1 1
A
16
16
24i
IJ
144
0.28
0.25
ft
•
14
14
34
1}
If
0.33
0.30
i
i
13
12
3f
14
1}
0.39
0.34
1 J
ft
12
12
3ft
I4i
0.44
0.40
A
1
11
11
3«
2ft
0.49
0.45
M
i I
H
11
11
4
l|
24
0.56
0.52
^
A
}
10
10
44
2
24
0.61
0.56
A
i
a
10
10
4ft
24
2ft
0.67
0.62
i
H
i
9
9
444
24
2.
h
0.72
0.67
i
i
a
'9
9
44
2|
2
0.78
0.73
A
i
1
8
8
54
24
2
0.82
0.77
i
H
ift
7
8
54
2ft
2^
^
0.86
0.83
t
u
7
7
5ft
2|
2^
1
0.92
0.86
«
1
ift
7
7
5ft
244
2j
0.98
0.92
a
■ ;
H
7
7
544
2}
2^
i
1.04
0.98
i
it
Ift
6
7
5«
f
3
1.08
1.05
a
a
If
6
6
6
34
1.14
1.07
a
H
Ift
6
6
64
244
3ft
1.20
1.13
i
1
H
6
6
64
3
34
1.26
1.19
«
1
1}
54
5
6ft
34
3ft
1.37
1.26
1
lA
IJ
5
5
6«
34
3ft
1.47
1.38
lA
lA
11
5
44
74
3f
34
1.59
1.46
li
li
2
4i
44
71
34
34
1.69
1.59
u
lA
2i
4i
44
744
3t
4ft
1.81
1.71
lA
lA
2i
44
44
74*
3}
4ft
1.94
1.84
lA
U
21
4
44
84
3}
4}
2.03
1.97
li
2|
4
4
84
44
2.15
2.04
lA
1ft
2|
4
4
m
44
444
2.28
2.17
i«
1}
2i
4
4
9ft
44
44i
2.40
2.29
1}
lA
2}
34
4
91
5
2.48
2.42
m
lA
3
34
34
9f
44
54
2.60
2.48
i{
li
3J
34
34
10ft
4f
6ft
2.85
2.73
2A
lA
34
3i
34
10}
5
5J
3.08
2.95
2i
i«
3f
3
3
iif
54
6ft
3.29
3.15
2A
1}
4
3
3
54
64
3.54
3.39
H
lii
194 SMALL TOOLS
and square thread taps should also be made in sets,
usually in sets of three. These conditions necessitate a
separate set of dimensions for taps with these systems of
thread.
When the dimensions for the diameter of each tap in the
set have been ascertained in accordance with Table XXXVI,
Table XLIII may be used for finding the length dimensions
for Acme taps, in sets of three taps, from one-half to 3 inches
diameter. The dimensions in this table apply to single-
threaded taps. For multiple-threaded taps, or taps with
very coarse pitch relative to the diameter, it is advisable to
lengthen the dimensions for the chamfered part of the thread,
leaving the other dimensions as given in the table. The
size of the square of these taps is not given, depending as it
does upon the varying diameters of the shank, which in
turn depend on the depth of the thread. The square should,
however, always be made equal to f X diameter of shank.
Square-thread taps are made according to the same table as
Acme taps, with the exception of .the figures in column K
in Table XLIII, representing the full diameter of the last
tap in a set of Acme-thread taps. In the case of square-
thread taps column K should be equal to the nominal
diameter of the tap, because, as has already been mentioned,
no over-size allowance is customary in making these taps.
Machine Screw Taps.
As has been previously said, machine* screw taps are
only a special form of hand taps, used for tapping holes
for standard machine screws. These taps are known by
numbers from one to thirty. A certain outside diameter
corresponds to each number, but there is no rigidly recog-
nized number of threads corresponding to the various
diameters. The form of the thread is the V shape, with
an angle of 60 degrees, sharp at the bottom of the thread,
HAND TAPS
195
TABLE XLIII.
LENGTH DIMENSIONS OF ACME TAPS IN SETS.
18T TAP IN SET
<— D-— »■<■
3
2nd tap in set
4 F ►♦^
3
FINI8HIN0 TAP
Fig. 86
Nom-
•
inal
A
B
C
D
E
F
G
H
I
K
Diam.
IJ
2f
1
*i
i
li
i
U
i
H
0.520
A
4*
2
2i
A
2A
2
IJ
0.682
5i
2
3i
2-
21
1 ■
2
0.645
*
6
2
3i
*
2*
*
2A
1
21
0.707
6i
2*
3i*
i
3r
1
2+il
1
2A
0.770
it
61
2 it
4A
3A
iiV
3
lA
2
0.832
r
7i
3
4i
3
u
31
^
2
0.895
i
7A
3i
4A
^ ,
3f
ivk
31
lA
2
0.957
7*
3i
4
3*
H
3|
3
1.020
li
8J
3A
M
4A
lA
3f
1
3A
1.145
1
9
3}
5
*
tf
H
3J
1
3
1.270
1
9i
4
5
1
lA
4tV
2
3
1.395
I-
10
4
5
1
4
U
4
2;
3
1.520
1
lOi
4
6
1
5
H
4
2;
3
1.646
1
11
4
6i
iiV
5A
lA
44
2
4
1.770
1-
11
4
6i
iiV
5A
lA
4*
2
4}
1.895
2
11
5
6}
1*
68
1
5 •
2
4t
2.020
2i
12
5
71
1*
6*
1
5
2
4f
2.270
H
13
6
7}
lA
6A
1
5:
2
5i
2.520
2J
14
5
81
11
7
2
6:
2
5*
2.770
3
IS
61
81
Jl
7i
2
61
3
5}
3.020
196 SMALL TOOLS
but provided with a considerable flat at the top of the
thread. There is no standard adopted for the size of this
flat. It varies with the different pitches and diameters,
and the only guidance in making these taps is to fol-
low the standards adopted by the tap manufacturers. A
list of sizes with a number of different pitches is ^ven
in Table XLIV. The outside diameter, which is con-
stant for each size or number of tap, and the angle diam-
eter, upon which the width of the flat depends, are ^ven
in the table. The root diameter of the thread is easily
found by subtracting the depth of the sharp V thread
from the angle diameter.
In regard to the making of these taps there is little to
say which has not already been touched upon in con-
nection with ordinary hand taps. They are made in sets
of three, on the same principles as are used in the common
method of making hand taps, that is, with the diameter of
all three taps in a set the same on the straight or parallel
portion. As these taps are very small, they cannot be
provided with female centers, excepting on the larger
sdzes, particularly not at the threaded end. It is custo-
mary to provide all these taps one-quarter inch in diame-
ter and smaller with male centers.
Machine screw taps are fluted in the same manner as
hand taps. The form of the fluting cutter, its size, thickness,
and the radius between the angular sides which produces
the fillet in the bottom of the flute are all dimensions
which may be figured from the same formulas as for
regular hand taps. The radius of the cutter is perhaps
the most important of these dimensions. It will be
found that according to the formula
Radius = --,
4
HAND TAPS 197
in which D = the diameter of the tap, the radius for
sizes Nos. 1 and 2 should be about one-sixty-fourth inch,
for No. 3 to No. 7 about one-thirty-second inch, for No. 8
to No. 11 about three-sixty-fourths inch, for No. 12 to
No. 18 about one-sixteenth inch, for No. 19 to No. 26
about three-thirty-seconds inch, and for No. 28 and No. 30
about one-eighth inch.
The number of flutes should properly be three for sizes
smaller than five-thirty-seconds inch in diameter, and four
for larger sizes.
Dimensions of Machine Screw Taps. — The various
length dimensions of machine screw taps may be ex-
pressed by simple formulas the same as in the case of
regular hand taps. The general appearance of the former
taps is shown in Fig. 87. The shank on the smaller sizes
is larger than the diameter of the tap itself, and on the
larger sizes equal to the diameter of the tap. On the
larger sizes there is a neck between the threaded portion
and the shank, but on the smaller the thread runs directly
into the shank part.
In the formulas for machine screw taps,
A = the total length of the tap,
B = the length of the thread,
C = the length of the neck,
D = the diameter of the tap,
E = the length of the shank,
F = the diameter of the shank,
G = the size of the square,
H = the length of the square
198
SMALL TOOLS
TABLE XLIV.
SIZES, PITCHES, AND ANGLE DIAMETERS OF MACHINE SCREW TAPS.
No. of
No. of
No. Of
Threads
Outside
Angle
No. of
Threads
Outside
Angle
Tap.
per
Inch.
Diameter.
Diameter.
Tap.
per
Inch.
Diameter.
Diameter.
72
0.071
0.0670
6
48
0.141
0.1291
64
0.071
0.0620
6
44
0.141
0.1250
60
0.071
0.0650
6
. 40
0.141
0.1290
56
0.071
0.0612
6
38
0.141
0.1245
li
56
0.081
0.0710
6
3d
0.141
0.1230
li
52
0.081
0.0715
6
34
0.141
0.1235
2
64
0.089
0.0800
6
32
0.141
0.1230
2
60
0.089
0.0790
6
30
0.141
0.1155
2
56
0.089
0.0795
6
28
0.141
0.1195
2
48
0.089
0.0785
6
26
0.141
0.1160
2
40
0.089
0.0747
6
24
0.141
0.1150
2
36
0.089
0.0710
48
0.154
0.1415
3
64
0.101
0.0912
40
0.154
0.1375
3
60
0.101
0.0925
36
0.154
0.1360
3
56
0.101
0.0957
32
0.154
0.1377
3
52
0.101
0.0875
30
0.154
0.1320
3
50
0.101
0.0895
28
0.154
0.1314
3
48
0.101
0.0870
26
0.154
0.1310
3
44
0.101
0.0910
24
0.154
0.1249
3
40
0.101
0.0890
8
48
0.166
0.1535
3
36
0.101
0.0860
8
44
0.166
01520
3
34
0.101
0.0840
8
42
0.166
0.1525
3
32
0.101
0.0812
8
40
0.166
0.1549
56
0.113
0.1035
8
38
0.166
0.1530
52
0.113
0.1005
8
36
0.166
0.1510
50
0.113
0.1003
8
34
0.166
0.1520
48
0.113
0.1045
8
32
0.166
0.1480
46
0.113
0.0975
8
30
0.166
0.1457
44
0.113
0.1000
8
28
0.166
0.1455
42
0.113
0.0992
8
26
0.166
0.1435
40
0.113
0.1031
8
24
0.166
0.1385
38
0.113
0.0960
8
22
0.166
0.1432
36
0.113
0.1000
8
20
0.166
0.1387
34
0.113
0.0965
9
40
0.180
0.1625
32
0.113
0.0970
9
38
0.180
0.1600
30
0.113
0.0970
9
36
0.180.
0.1652
5
50
0.125
0.1117
9
34
0.180
0.1630
5
48
0.125
0.1135
9
32
0.180
0.1630
5
44
0.125
0.1108
9
30
0.180
0.1603
5
40
0.125
0.1140
9
28
0.180
0.1590
5
36
0.125
0.1120
9
26
0.180
0.1535
5
32
0.125
0.1199
9
24
0.180
0.1616
5
30
0.125
0.1070
10
48
0.194
0.1806
HAND TAPS
199
TABLE XLIW —Continued.
No. of
No. of
No. of
Threads
Outside
Angle
No. of
Threads
Outside
Angle
Tap.
per
Inch.
Diameter.
Diameter.
Tap.
per
Inch.
Diameter.
Diameter.
10
40
0.194
0.1753
14
24
0.246
0.2221
10
38
0.194
0.1792
14
22
0.246
0.2160
10
36
0.194
0.1760
14
20
0.246
0.2113
10
34
0.194
0.1780
14
18
0.246
0.2140
10
32
0.194
0.1710
14
16
0.246
0.2035
10
30
0.194
0.1730
15
28
0.261
0.2390
10
28
0.194
0.1685
15
26
0.261
0.2325
10
26
0.194
0.1680
15
24
0.261
0.2309
10
24
0.194
0.1680
15
22
0.261
0.2345
10
22
0.194
0.1610
15
20
0.261
0.2270
10
20
0.194
0.1592
15
18
0.261
0.2225
10
18
0.194
0.1575
16
40
0.272
0.2530
11
40
0.206
0.1927
16
36
0.272
0.2520
11
36
0.206
0.1890
16
32
0.272
0.2512
11
32
0.206
0.1925
16
28
0.272
0.2504
11
28
0.206
0.1820
16
26
0.272
0.2500
11
26
0.206
0.1800
16
24
0.272
0.2450
11
24
0.206
0.1780
16
22
0.272
0.2421
11
22
0.206
0.1764
16
20
0.272
0.2370
11
20
0.206
0.1740
16
18
0.272
0.2326
12
48
0.221
0.2095
16
16
0.272
0.2295
12
44
0.221
0.2065
16
14
0.272
0.2232
12
40
0.221
0.2048
17
24
0.285
0.2570
12
36
0.221
0.2025
17
22
0.285
0.2540
12
34
0.221
0.2035
17
20
0.285
0.2520
12
32
0.221
0.2035
17
18
0.285
0.2435
12
30
0.221
0.2013
17
16
0.285
0.2397
12
28
0.221
0.2015
18
26
0.298
0.2735
12
26
0.221
0.1970
18
24
0.298
0.2710
12
24
0.221
0.1940
18
22
0.298
0.2680
12
22
0.221
0.1900
18
20
0.298
0.2686
12
20
0.221
0.1868
18
18
0.298
0.2608
13
32
0.234
0.2140
18
16
0.298
0.2550
13
28
0.234
0.2112
19
24
0.312
0.2850
13
24
0.234
0.2080
19
20
0.312
0.2803
13
22
• 0.234
0.2048
19
18
0.312
0.2762
13
20
0.234
0.2005
19
16
0.312
0.2704
13
18
0.234
0.1938
20
24
0.325
0.2970
14
44
0.246
0.2307
20
22
0.325
0.2940
14
40
0.246
0.2330
20
20
0.325
0.2980
14
36
0.246
0.2310
20
18
0.325
0.2886
14
32
0.246
0.2272
20
16
0.325
0.2830
14
30
0.246
0.2220
22
24
0.350
0.3235
14
28
0.246
0.2245
22
22
0.350
0.3200
14
26
0.246
0.2^31
22
20
0.350
0.3155
200
SMALL TOOLS
TABLE XLIY -^Concluded.
No. of
No. of
No. of
Threads
Outside
Angle
No. of
Threads
Outside
Angle
Tap.
per
Inch.
Diameter.
Diameter.
Tap.
per
Inch.
Diameter.
Diameter.
22
18
0.350
0.3150
26
16
0.404
0.3592
22
16
0.350
0.3065
26
14
0.404
0.3560
24
24
0.378 .
0.3495
28
18
0.430
0.3905
24
22
0.378
0.3462
28
16
0.430
0.3883
24
20
0.378
0.3425
28
14
0.430
0.3826
24
18
0.378
0.3420
30
18
0.456
0.4175
24
16
0.378
0.3340
30
16
0.456
0.4166
24
14
0.378
0.3305
30
14
0.456
0.4096
26
18
0.404
0.3660
The following formulas will apply to all sizes of machine
screw taps :
A = 5 D + 1^ inches,
B=3 D + finch,
G=0.75F,
ff=0.67D + iinch.
F, the diameter of the shank, is 0.125 inch up to and
including No. 5 machine screw tap, and equal to D
for larger sizes. Up to and including No. 7 machine
screw tap there is no neck between the shank and the
thread. For larger sizes,
C = 0.75 D.
For sizes up to and including No. 7,
^ = 2D + i|inch.
For larger sizes,
E = 1.25 i) + 11 inch.
The values in Table XLV are figured from these for-
mulas, but it must be remembered that here as in the
case of hand taps dimensions are only approximately
HAND TAPS
201
those obtained from the fonnulas, whenever no necessity
for close fractional dimensions exists.
TABLE XLV.
DIMENSIONS OF MACHINE SCREW TAPS.
f Boot IMametMr
T-
3r
- B—
->j*-C"»K- B «
Fig. 87
No. Of
Tap.
Diam.
of
Tap.
St'rd
No. of
Threads.
Total
Length.
Length
of
Thread.
Length
of
Neck.
Length
of
Shank.
Diam.
of
Shank.
Size
of
Square.
Tip.ngth
of
Square.
D
A
B
C
B
F
0
H
1
0.071
64
n
ft
1ft
0.125
A
A
H
0.081
56
1*
1ft
0.125
if
A
2
0.089
56
1
0.125
A
A
3
0.101
48
ii
*
11
0.125
\ r
A
4
0.113
36
1
4
1ft
0.125
\ r
A
5
0.125
36
1*
1ft
0.125
\ r
^
6
0.141
32
2
«
1ft
0.141
\ r
^
7
0.154
32
2iV
«
0.154
M
»
8
0.166
32
2i
: '
'
IJ
0.166
n
9
0.180
30
2A
•*
0.180
10
0.194
24
2i
«
,^
ll^
0.194
11
11
0.206
24
2A
2A
1
-.^
It if
0.206
M
Jr
12
0.221
24
ift
i!r
Jjy
0.221
13
0.234
22
2i
ift
A
11
0.234
A
?!r
14
0.246
20
2A
li
A
IJ
0.246
A
T^
15
0.261
20
2*
Ift
A
1^
0.261
A
s
16
0.272
. 18
2H
Ift
j^
1^
0.272
is
18
0.298
18
1;
ih
n
0.298
^
J J
20
0.325
16
21f'
It
if
"Si
H
0.325
^
22
24
0.350
0.378
16
16
3*
i
1 ■
0.350
0.378
J*
1
26
0.404
16
3A
lA
ft
lA
0.404
)
28
0.430
14
3^
1 *
ft
lA
0.430
%
30
0.456
14
3ft
li
ft
11
0.456
A
202
SMALL TOOLS
The limits of over-size in diameter of machine screw
taps after hardening should be made as indicated by
Table XLVI.
TABLE XLVI.
LIMIT OF OVER-SIZE IN DIAMETER OF MACHINE SCREW TAPS AFTER
HARDENING.
Diameter
of Tap.
Inches.
Limit
of
Over-size.
Diameter
of Tap.
Inches.
Limit
of
Over -size.
Diameter
of Tap
Inches.
Limit
of
Over-size.
i-i
0.00075
0.001
t-f
0.00125
0.0015
t4
0.002
0.0025
A. S. M. E. Standard Machine Screws.
We mentioned in Chapter I the standard for machine
screws, approved and adopted by the American Society
of Mechanical En^neers. The dimensions for the thread
quantities, according to this standard, are ^ven in Tables
XLVII, XLVIII, XLIX, and L, for both taps and screws,
regular and special.
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206
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HAND TAPS 207
Pulley Taps.
Pulley taps are another special form of hand taps.
Their particular use has been previously referred to. The
shank of the pulley tap is usually the full diameter of
the thread; this gives the long tap a guide in starting the
thread, inasmuch as the shank may be a fair fit in the
hole in the pulley rim, through which it must pass to
reach the hub.
The tap is provided with a neck between the thread
and the shank, the purpose of which is mainly to facili-
tate the threading when the tap is made. The diameter
of this neck should be about 0.005 inch below the root
diameter of the threp^d. The length of the thread is
shorter than on hand taps of corresponding size. The
chamfer is made like the chamfer on a plug tap in a set of
three taps, that is, the tap is chamfered at the point for
about three or four threads. As these taps are seldom
required to tap down to the bottom of a hole, a tap thus
chamfered will be the most suitable.
The tap should be relieved on the top of the thread of
the chamfered portion, but not on the straight or parallel
portion of the thread. This latter requirement is par-
ticularly important, as a pulley tap must always be
backed out, and if relieved on the straight portion, chips
might easily wedge in between the thread being cut and
the thread on the tap, surely injuring the former and not
unhkely to break off the teeth in the latter.
The form of flute and the number of flutes should be
the same as for regular hand taps. The flute should not
be continued at the upper end any longer than necessary
to provide the last thread of the tap with a cutting edge,
partly because it spoils the appearance of the tap if the
flutes run into the shank, but primarily because the tap is
208
SMALL TOOLS
greatly weakened and liable to break at the neck if the
flutes run through the neck to their full depth.
TABLE LI.
DIMENSIONS OF PULLEY TAPS WITH U. S. STANDARD THREAD.
'V
r
— Q-
i_
-Q-
-L.
■3-
k^-4-
A -rf
Fig. 88
Diameter
Length of
Diameter
Length of
Size of
of Tap.
Thread.
of Neck.
Square.
Square.
D
A
B
C
E
J
11
0.180
J
ft
A
1
0.235
^
}
0.289
1
A
0.340
A
A
i
1
0.395
}
I
ft
1:
0.449
ft
i
i
2
0.502
i
a
21
0.564
a
i
i
2i
0.615
i
ft
i
2h
0.726
i
1
2i
0.833
1
•
n
3
0.934
H
■
n
31
1.059
H
«
Dimensions of Pulley Taps. — In Table LI dimensions
are given for pulley taps for sizes from one-quarter to IJ
inches in diameter. These taps, however, are rarely made
in sizes larger than one inch diameter. The total length
cannot be given, as that dimension varies with the require-
ments. The only dimensions we can give besides the
diameter of the shank, which should equal the diameter of
the thread, and the diameter of the neck, which has been
referred to previously, are the length of the thread and the
HAND TAPS 209
length of the neck. If D equals the diameter of the tap
and A the length of the thread, we may write down the
formula
. 8Z) + 3
The length of the neck is made equal to the diameter of
the tap. The length of the square may also be made
equal to the diameter of the tap, and the size of the square
equal to three-fourths times the diameter.
The over-size limits of pulley taps after hardening are
the same as for regular hand taps (see Table XXXIX).
CHAPTER V.
TAPPER TAPS AND MACHINE TAPS. — SCREW MACfflNE
TAPS.— HOBS AND DIE TAPS.
Tapper Taps.
Definition and General Appearance. — The name tapper
tap as understood by tool-makers and tap manufacturers
is applied to one of the two kinds of taps used for tapping
nuts in tapping machines. It is often confused with the
expression ^^ machine tap/' which properly designates the
second kind of taps used for this purpose. The machine
tap, however, differs from the tapper tap in a number of
particulars, most important of which are the number and
the form of the flutes, the relief of the threads, and the
general design. The tapper tap is the earlier of the two,
and is simpler in its details. It is not adapted for the
same hard usage as a machine tap, but is largely used for
tapping nuts for general purposes in material which is
not of too tough a structure.
3-
! I<— B — ■>!
Pig. 89. General Appearance of Tapper Taps
The general appearance and design of the tap is shown
in Fig. 89. It consists of a threaded portion Ay cham-
fered on the top of the thread for a distance J5, and a
shank C, which as a rule is not provided with a square on
the end, this being unnecessary because the tap is usually
held firmly in a chuck by its circular shank. Some man-
210
TAPS 211
ufacturers using these taps prefer, however, to have the
shank flatted on two sides, enabling them to secure a
firmer hold on the tap in the machine. The diameter of
the shank should be at least 0.015 inch smaller than the
diameter at the root of the thread, in order to permit the
threaded nuts to slide freely over the shank.
Turning and Threading, — In turning and threading
tapper taps, as well as any other taps, it must be remem-
bered that the straight part of the threaded portion must
be left a certain amount over the standard size. The
screw which is to fit the nut threaded by the tap is usually
made of tf standard diameter, and the nut therefore must
evidently be somewhat in excess of this in order to per-
mit the screw to enter and to allow for slight unavoidable
differences in the lead of the thread between the screw and
the nut. The amount which a tap should thus be left
over the standard diameter is largely a matter of judg-
ment, inasmuch as this amount must vary according to
whether a tight, free, or loose fit is desired between the
screw and the nut made by t*he tap. For general pur-
poses, however, the tap should be made between the
limits of from 0.0005 inch to 0.0015 inch over-size before
hardening for sizes not over one-half inch diameter, from
0.001 inch to 0.002 inch for sizes between one-half and
one inch, and from 0.0015 inch to 0.003 inch for sizes
between one and two inches in diameter. Tapper taps
are rarely made in sizes larger than two inches. When
larger diameters of taps are required for nut tapping, the
taps should preferably be made on the principles of
machine taps.
Fluting. — It has been the general practice to flute
tapper taps practically the same as hand taps. It is,
however, not necessary to make the lands as wide as
on these latter taps, because there is not the same ten-
212 SMALL TOOLS
dency for a tapper tap to deviate from its true course, the
tapper tap being guided by the firm grip of the chuck,
while a hand tap depends solely upon the lands of its
threaded portion for guidance. In regard to the number
of flutes there is some difference of opinion. The practice
adhered to by prominent tool manufacturers is to ^ve
four flutes to all taps up to and inclusive of one and one-
half inches diameter, and five flutes for larger sizes. The
fluting cutter for straight-sided flutes should have an
inclusive angle of 85 degrees, 55 degrees on one side and
30 degrees on the other^ the same as for hand taps.
Relief. — The next question of importance is that
of the relief given to the thread. Tapper taps as a
rule are relieved only on the top of the thread of the
chamfered portion. They are not given any relief in the
angle of the thread. The straight part, which performs no
cutting, being nothing but the sizing part of the tap, should
not be relieved, or, if relieved, the relief should be very
slight in order to permit the tap to retain its size so much
longer. It may be remarked that if the tap is backed
out through the nut no relief at all should be permitted on
the parallel part of the thread, because of the liability of
chips getting in between the land and the thread in the
nut and injuring tap as well as nut.
Tapper taps when being hardened should be drawn to a
temper of 430° F. What has been said in the previous
chapter in regard to the influence, of hardening upon hand
taps is, of course, equally true of tapper taps. The general
tables given in that connection apply to all kinds of taps.
Dimensions of Tapper Taps, — The accompanying for-
mulas, and Table LII figured from them, give the common
proportions of length of thread and length of chamfered
part of tapper taps. The length over all depends solely
upon the kind of work on which the tap is to be used. It
TAPS 213
is the common manufacturing practice to make these taps
11 inches long over all. The formulas are based upon the
diameter of the tap, as this is the most convenient
working factor. In the table the values are given approxi-
mately, as there is no reason to work closer than to one-
sixteenth or even one-eighth inch in regard to length
dimensions of this character.
In the formulas,
A = the length of the thread,
B = the parallel part of the thread,
C = the chamfered part of the thread,
D = the diameter of the tap,
E = the diameter of the shank,
F = the diameter at the point of the thread.
The formulas for tapper taps up to and including nine-
sixteenths inch are as follows:
A = 4.5 D -f ^5 inch,
B = 2.75 D + ^Q inch,
C = 1.75 D + 1 inch,
E = root diameter of thread — 0.01 inch,
F = root diameter of thread - (0.005 D + 0.005 inch).
For sizes from five-eighths inch diameter to 2 inches
inclusive the formulas are:
A = 2 D + If inches,
B = 1.25 D + 1 inch,
C =0.75D + finch,
E = root diameter of thread — 0.02 inch,
F = root diameter of thread - (0.005 D+ 0.005 inch).
By means of the formulas given the dimensions for any
intermediate size between those tabulated in Table LII
may easily be determined. It is understood, of course,
that the formulas have a great degree of flexibility,
and that they are proposed only in order to facilitate
214
SMALL TOOLS
the work of the tool-maker or draftsman, to whom it is
often left to settle upon the dimensions for these tools.
The tables are worked out in order to save figuring in
each individual case, but, as stated previously, give only
approximate working dimensions, and do not give the
close theoretical, values figured from the formulas except-
ing when essential.
TABLE LII.
DIMENSIONS OF TAPPER TAPS.
^■
3
n
&■
-?k-
Fig. 90
A
>
Diam.
Number
Length
Length
of
Straight
Part.
Length
of
Diameter
Diameter
of
of Threads
of
Cham-
of
of
Tap.
per Inch.
Thread
fered
Part.
Shank, E.
Point, F.
U.S.
V
U.S.
V
U.S.
V
D.
St'd.
St'd.
A.
B-
C
St'd.
StM.
St'd.
St'd.
A
32
24
lA
i
A
0.14
0.11
0.140
0.110
i
20
20
i
A
0.17
0.15
0.179
0.157
A
18
18
1}
4
i
0.23
0.21
0.234
0.210
i
16
16
2
0.28
0.25
0.287
0.260
A
14
14
2A
lA
0.33
0.30
0.338
0.306
]
13
12
2A
lA
1
0.39
0.34
0.393
0.349
i
12
12
2J
1}
n
0.44
0.40
0.446
0.410
11
11
3
m
lA
0.49
0.45
0.499
0.460
i
11
11
34
n
li
0.56
0.52
0.561
0.522
10
10
34
i«
lA
0.61
0.56
0.611
0.568
i
10
10
34
2
H
0.67
0.62
0.673
0.630
9
9
34
2i
1»
0.72
0.67
0.722
0.674
i
9
9
3»
2A
lA
0.78
0.73
0.783
0.735
8
8
3*
2}
1*
0.82
0.77
0.828
0.774
1
7
7
4
2A
lA
0.92
0.86
0.928
0.867
7
7
4:
2A
1*
1.04
0.98
1.053
0.992
6
6
4
2}
1
1.14
1.07
1.147
1.074
6
6
4
2{
1
1.26
1.19
1.272
1.199
54
5
5
3tV
i«
1.37
1.26
1.376
1.266
5
5
64
3A
2A
1.47
1.38
1.476
1.390
1
5
44
54
3»
2i
1.59
1.46
1.601
1.476
2
4J
44
54
3i
2i
1.69
1.59
1.696
1.600
TAPS 216
Machine Taps.
Definition and General Appearance, — As the name
implies, the machine tap is used for nut tapping in tapping
machines, the same as the tapper tap. It has been
mentioned that the names of these two taps are often
confused. From a manufacturing point of view, however,
there is a distinct difference between the two kinds of
taps. The tapper tap embodies, in fact, the very simplest
design possible for its purpose. It cannot be successfully
used in many instances where the machine tap will be
satisfactory. The machine tap being threaded and re-
lieved in a different manner is adapted for use on very
tough material and for heavy duty.
1
I
I j<--D-
~EE^.-
. ^_j B — --^
Fig. 91. General Appearance of the Machine Tap
The general appearance of the tap is shown in Fig. 91.
It consists of a threaded portion fi, having a straight
part D and a chamfered portion Ej and a shank C
which is provided with a square, enabling the tap to be
securely held in a chuck without danger of slipping. The
extreme end of the threaded part is provided with a
secondary chamfer, the purpose of which is to facilitate
the entering of the tap in the hole in the nut blank. The
diameter of the shank should be from 0.01 to 0.02 inch
below the root diameter of the thread, the same as for
tapper taps, and for the same reason, viz., to permit the
threaded nuts to slide freely over the shank.
Turning and Threading. — In turning machine taps
the straight portion of the threaded part must be left a
216 SMALL TOOLS
certain amount over-size. The amount to be left over the
standard diameter before hardening may, for general pur-
poses, be between the limits of 0.0005 inch and 0.0015
inch for sizes not over one-half inch diameter, from.
0.001 inch to 0.002 inch for sizes between one-half and
1 inch, from 0.0015 inch to 0.003 inch for sizes between
1 and 2 inches, and from 0.002 inch to 0.0035 inch for
sizes between 2 and 3 inches in diameter.
The main difference between tapper taps and machine
taps will be found in the threading and relieving of the
taps. While the tapper tap is threaded straight for the
whole length of the threaded portion, the machine tap is
threaded on a taper for a certain distance from the point.
The length of this taper thread and also the length of the
part chamfered on the top of the thread depend, of
course, primarily upon the conditions under which the
tap is to be used, the material to be tapped, as well as the
length of the nut. When making taps in large quantities,
however, whether for the market or for shop use in a large
establishment, it is evidently impossible to know before-
hand exactly what the taps will be used for, and certain
standards must necessarily be adopted. Experienced
makers of machine taps adhere to the rule of chamfering
from twenty to twenty-five threads on the top of the
threads and tapering the root of the thread for a distance
equivalent to eight or nine threads from the point. For-
mulas will be found below which give the length of the
chamfered part and the length of the taper thread for
various sizes of taps. These dimensions will be so selected
as to provide for a length equivalent to at least twenty
and eight threads, respectively, on standard thread taps.
While a long taper on a tap is desirable because it
diminishes the amount of stock that each tooth of the
thread will remove, it has the disadvantage of making the
TAPS 217
cutting edges toward the point of the tap very broad with
a very small space between them. This impairs the cut-
ting quality of the tap, inasmuch as the action is rather
that of reaming than of cutting. It is in order to over-
come this disadvantage that machine taps are tapered in
the angle of the thread for some distance from the point.
This makes the width of the tooth smaller and increases
the cutting qualities of the tap considerably. This taper
in the angle of the thread constitutes one of the principal
differences between the machine tap and the tapper tap,
the latter being simply chamfered off on the top of the
threads. ^ If we analyze the action of the tap when pro-
vided with too many cutting edges we will find that the
metal is either ground down very fine, and an unnecessary
amount of power is consumed in doing this, or some
teeth may in fact not cut at all, simply compressing
the metal, making the work of removing it still harder for
the next cutting edge. ' On the other hand, a short taper
takes away considerable of the chip room necessary for
the removed metal. While this may not be of great con-
sequence in an ordinary hand tap, where the motion is
slow and the tap is often reversed, it is of great impor-
tance in machine taps and tapper taps, where the cut-
ting speed is high and always in one direction. The
tap as well as the nut to be threaded is liable to be injured
if ample space for the chips to pass away from the cutting
edges is not provided.
An ingenious method of decreasing the number of
cutting edges, as well as increasing the available chip
room, is embodied in the "Echols thread," where every
alternate tooth is removed, as shown in Fig. 92. The
removal of every other tooth in one of the lands is evi-
dently equivalent to the removal of the teeth of the continu-
ous thread in every other land of the tap. It is therefore
218
SMALL TOOLS
obvious that taps provided with this thread must be
made with an odd number of lands, so that removing the
tooth in alternate lands may result in removing every
other tooth in each individual land. If there were an
even number of flutes, the cutting away of the teeth in
alternate lands would result in removing all the teeth from
certain lands and none from the others. Machine taps are
often provided with the Echols threiEid.
Fig. 92. Interrupted or Echols Thread
Fluting. — In considering the fluting of machine taps
we find another difference between these and tapper taps.
The former tap requires greater strength on account of its
harder service, and at the same time as much chip room
as possible. The flute that best fills these requirements
may, however, not be the flute commercially possible for
the purpose, because the factor of cost is of much impor-
tance and unusual or formed shapes of cutters will cost
more to make and also require much slower cutting speed.
When treating hand taps in preceding chapter two forms
of flutes were shown. Another form of flute introduced
by the Pratt and Whitney Company for machine taps is
shown in Fig. 93. This latter form is to be recommended
in all cases where a tap of unusual quality is required.
The tap will not break as easily, and the chips are carried
off in a more satisfactory manner. A certain kind of
flute of late used extensively by certain concerns is the
"hook'' flute, shown exaggerated in Fig. 94. This flute
provides for a keener cutting edge, and is recommended
TAPS
219
for very tough materials. Some users, however, do not
look upon this flute as favorably as others, and opinions
Fig. 93. Form of Flute for Machine Taps, and Fluting Cutter Used
I
Fig. 94. Hook Flute
vary considerably as to the superiority of this flute,
unless the "hook^' be made very slight. It is advis-
able to make the lands fairly narrow as compared with
220
SMALL TOOLS
R =
hand taps, inasmuch as this will increase the chip room
and but slightly decrease the strength, the lands of hand
taps being made wide not only to secure strength but to
insure good guiding. If provided with a straight-sided
flute with a radius in the bottom, which is largely used
by manufacturers, this radius may be approximately
determined by the equation
32'
R being the radius in the bottom of the flute and D the
diameter of the tap.
Fluting Cut- .
ters. — The cutter /jV
used for cutting /^^ i
straight - sided
flutes is shown
in Fig. 95, and is
similar to the
straight - sided
fluting cutter
used for hand
taps, with the
exception of the Fig. 95.
smaller radius.
The inclusive
angle between the sides is 85 degrees, 55 degrees on one side
and 30 degrees on the other. The thickness of the cutter
should be approximately equal to f 2) + A inch, if D
equals the diameter of the tap to be fluted. The diame-
ter of the cutter depends, of course, not only upon the
diameter of the tap to be fluted but also upon the size of
the holes in the cutter for the milling-machine arbor. If
we assume that we use a three-quarter-inch arbor for the
cutters intended for the smaller diameters of taps, say up
Regular Fluting Cutter for
Machine Taps
TAPS
221
to and including three-quarter-inch, and one-inch hole in
cutters for larger diameters, then
Diameter of cutter = — + 2 inches,
in which formula D as before equals the diameter of tap to
be fluted.
Table LIII has been figured from these formulas. The
figures given are, of course, practical working figures, and
are only approximately the values obtained from the formu-
las whenever these values give dimensions unnecessarily
close and in too small fractions. The nearest quarter of an
inch is near enough for the dimensions in regard to diam-
eter, and the nearest one-sixteenth or one-eighth inch for
thickness. The radius, however, must be given more
accurately, as one-thirty-second and even one-sixty-fourth
inch makes a considerable difference in this respect, partic-
ularly in small taps.
TABLE LIII.
DIMENSIONS OF FLUTING CUTTERS FOR MACHINE TAPS.
(See Fig. 95 for form of cutter.)
Diameter
Thickness of
Diameter of
Diameter
of Cutter.
Cutter.
Radius.
Hole in
of Tap.
Cutter.
A
B
C
D
..
2
h
[
2i
\
2i
1 •
^
; •
2i
ft
^
2i
ft
1
: ■
2i
\
1
2i
«
\
H
2i
1
\
H
2i
i
If
2i
fk
2
3
X
2i
3
H
T7
2i
3i
ii
2|
3i
If
\
3
3i
3J
3f
1
A
4
4
A
222
SMALL TOOLS
In the case of a fluting cutter such as shown in Fig. 93
the radius A should be about one-eighth and the radius
B about one-third of the diameter of the tap for taps with
five flutes. For taps with four or six flutes these radii
should be slightly larger or smaller, respectively, relative
to the diameter of the tap.
The number of flutes for various diameters is given in
Table LIV.
TABLE LIV.
NUMBERS OF FLUTES IN MACHINE TAPS FOR VARIOUS
DIAMETERS.
Diameta
No. of
Diameter
No. of
Diameter
No. of
of Tap.
Flutes.
of Tap.
Flutes.
of Tap.
Flutes.
1
4
\
5
2
5
A
4
\
5
2i
6
1
4
1
5
2J
6
A
5
u
5
2J
6
5
H
5
3
6
5
If
5
3i
7
Relief, — Machine taps are relieved as well in the angle
of the thread as on the top of the thread for the whole of
the chamfered portion, or in other words, the diameter
measured over the heel of the thread should be smaller
than the diameter measured over the cutting edge; the
diameters measured in the angle of the thread at the
same respective places should also differ in the same
manner. The straight portion of the thread in a machine
tap is for sizing only, the same as in the case of a tapper
tap, and should as a rule not be relieved. However,
what was said about the relief of the straight part of a
tapper tap applies here also. When being hardened,
machine taps should be drawn to a temper of about 430° F.
This temperature should, perhaps, vary for different kinds
of steel, but the figure stated will be found a good average.
Dimensions of Machine Taps, — Below are given two
TAPS 223
sets of empirical formulas for the most important dimen-
sions of machine taps. In the formulas,
A = the total length of the tap,
B = the length of the thread,
C = the length of the shank,
D = the diameter of the tap,
E = the length of the parallel part of the thread,
F = the length of the taper threaded portion.
For taps up to and including two inches in diameter
the following formulas will be suitable:
A = 5f D + 3|,
JS=2iZ) + IJ,
C=3iD + 2i
E= iD^ r\,
^ 3D + 1
For taps two inches in diameter and larger the formulas
will be:
A = 3 Z) + 9f ,
B=lJZ) + 3},
C=nD + 6J,
„ 2D + 3
^ = -4
Table LV is based upon the formulas given. All dimen-
sions are given in convenient working sizes, and are approx-
imate in cases where the formulas give values which cannot
be expressed in even fractions, or give fractional values
inconvenient for working figures.
The diameter of the extreme end or point of the cham-
fered portion should be equal to the root diameter less the
depth of the thread, or in other ! words, equal to the full
diameter of the tap minus three times the depth of thread.
224
SMALL TOOLS
TABLE LV.
DIMENSIONS OF MACHINE TAPS.
Fig. 96
Diam.
of
Tap.
Total
Length.
Length
of
Thread.
Length
of
Shank.
Length
of
Full
Thread.
Length
of
Taper
in
Angle.
Length
below
Root
Diam.
Size
of
Square.
Length
of
Square.
D
A
B
C
B
F
G
H
K
i
5^
n
3A
i
A
A
i
4
A
5f
2
3|
A
i
:&
f
i
6A
2A
3J
i
A
A
ii
A
ti|
2A
4A
i
A
J
i
i
ei
2}
2}
ii
A
A
A
1
A
^^
4A
i
A
A
i»
4
7
21}
4«
tt
A
H
7il
If
4i
tt
■
M
8^
SA
}
i
A
ii
if
^
3i
Si
i«
i
i
m
3A
5i
i
t
i
«
H
3A
5ii
}
H
,
h
lA
'>
31
Si
it
A
i
li
n
lOf
4A
6A
lA
1}
i
.
i
lA
iiA
41
6ii
li
lA
A
:
iiH
4tt
7i
li
lA
k
■
i
H
]2i
5
7i
lA
li
W
lA
If
i3i
5A
7if
lA
li
i
i
1
If
13^1
H
8A
li
lA
lA
1
•
i|
Hli
5ii
8}
l«
lii
li
i
2
15^
6i
H
lii
1}
•
li
2i
15^
6A
9A
If
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•
lA
2i
16 1
61
9i
lit
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«
lA
li
2}
L^i
m
9ii
lii
la
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li
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le^
7
9i
li
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lA
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ni
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175
7f
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IS
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18}
7}
lOf
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a
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19i
8i
11
2A
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1
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3i
19}
20}
8i
Hi
2i
2i
lA
2i
1
31
8i
n}
2i
2}
lA
2A
4
21}
9i
12i
2A
2f
H
2f 2
TAPS 226
Screw Machine Taps.
Definition and General Appearance, — Screw machine
taps, as the name indicates, are used for tapping in
screw machines. The thread to be cut is usually short
and the taps therefore are essentially different from other
taps used for nut tapping in machines. It is difficult to
establish a standard for this kind of taps, as in many
cases the length of the thread, the length of the chamfer,
and the diameter of the shank largely depend upon
special conditions. When manufactured in quantities,
however, either for shop use or for the market, there is a
necessity for establishing a standard which will be correct
in most cases.
The chamfered end of the thread of these taps is usually
very short, as in most cases the tap is required to tap
down to the bottom of a hole. A neck is provided between
the tap and the shank, as the latter is usually larger in
diameter than the tap itself. In regard to the diameter of
the shank, manufacturers making a specialty of this kind
of taps recommend that this diameter be made to corre-
spond with the outside diameter of a spring screw die for
cutting the same size of thread as that for which the screw
machine tap is intended. This makes it possible to use the
same kind of holders for both tap and die. In Table LVI
the diameter of the shank is given in accordance with
this recommendation, but it must be understood that
this diameter depends in many cases upon the size of the
turret or the bushings which the tap shank is to fit.
The shank should be ground true with the thread, as
otherwise the resulting thread cut with the taps may be
out of true. A flat is milled on the shank for the turret
binding screws. This prevents the ground surface of the
shank from being spoiled by the burr that would result
from binding directly upon the circular surface. The
226 SMALL TOOLS
flutes of a screw machine tap are cut with double angle
cutters of 85 degrees inclusive angle, 55 degrees on one
side and 30 on the other. The thread is relieved only on
the top of the thread of the chamfered portion. The
straight portion ought not to be relieved, as the screw
machine tap must always be reversed at the end of the
cut, and if relieved, there would be danger of chips get-
ting in between the back of the threads on the lands of the
tap and the threads in the nut, which might result in
dama^ng not only the thread already cut but the tap
also.
Dimensions of Screw Machine Taps, — The following
formulas may be used for determining the dimensions of
screw machine taps for general use. In these formulas,
D = diameter of tap,
A = total length of tap,
B = length of thread,
C = length of neck,
E = length of shank,
G = width of flat on shank.
The dimensions in Table LVI are approximately figured
from the following formulas :
, 5 D + 20
B =
E =
8
Z) + 4
D + 3
~8"'
2 7) + 9
8
The diameter of the shank cannot be determined by any
formula, as it should conform to the diameters most com-
monly used for spring screw threading dies. The width of
TAPS
227
the flat, Gy depends of course upon the diameter of the shank
and should be made approximately according to the formula
2F + 1
G =
8
The dimensions given must, of course, be deviated from
in many cases, inasmuch as they would not suit all special
purposes but are intended only for taps made for general use.
Screw machine taps should have four flutes in all sizes
smaller than IJ inches, and six flutes for larger diameters.
TABLE LVI.
DIMENSIONS OF SCREW MACHINE TAPS.
'Bootdiameter^.OOS
f
*J
Fig. 97
Diameter
TntJil
Length
Length
Length
Diameter
Width
(A
Tap.
Length.
of
Thread.
of
Neck.
of
Shank.
of
Shank.
of
Flat.
D
A
B
C
E
F
O
\
H
lA
1
lA
\
A
2
lA
^A
A
f
2
itV
A
^A
A
2
1
A
ij
{
i
2
1 :
X
li
ft
2
1
xk
u
1
A
•
■
2
1
A
u
1
A
i
2it
2|t
lA
A
lA.
!• ■
A
J
lA
A
lA
A
i
3
lA
1 •
lA
1
■
;
3
lA
1 ■
lA
1
\
3
1
If
1
1
3
1
■r
If
1
.
1]
■
3
1
•f
If
2
3
^A
"
lA
2
■
3A
^A
A
lA
21
3^
1}
lu
2i
3A
If
A
1
21
3*
\t
*
lA
^1
1
2 1
3}
«
1
If
3i
4
228 SMALL TOOLS
Hobs and Die Taps.
Ordinary Hob Taps. — Hob taps are, as a rule, only
intended for final finishing or sizing of the thread in dies.
For this reason their construction differs widely from that
of ordinary hand taps. They are not primarily intended
for actual cutting, being used merely for burring a thread
already cut with ordinary taps. Straight hob taps are not
relieved either on the top or in the angle of the parallel
portion of the thread. Two or at most three threads,
however, are chamfered at the point of the tap, and
these chamfered threads are relieved on the top of
the thread the same as ordinary hand taps. A taper
hob, of course, should be slightly relieved on the top
as well as in the angle of the thread. The flutes of
a hob tap constitute the essential difference between
this tap and the hand tap. The number of flutes
is greater, and the cutters used are usually regular
angular cutters of 50 degrees inclusive angle, 25 de-
grees on each side, or 45 degrees inclusive angle, 22J
degrees on each side. They should have a very slight
round joining the angular sides. The dimensions of
ordinary hob taps are made the same as for regular hand
taps. These were given in Table XLII in the preceding
chapter. The number of flutes will be found from
Table LVII of Sellers hobs, the number of flutes being
made the same for these latter hobs as for regular
ones.
Sellers Hohs. — The Sellers hobs are a special kind
of hob taps, differing from the ordinary hob tap
in that they are provided with a guide at a point
of the thread. The diameter of this guide or pilot
is given in Table LVII according to the ordinary
method in practice. The other dimensions are
TAPS 229
given approximately according to formulas below, in
which
D = diameter of hob,
A = total length of the hob,
B = length of the pilot,
C = length of the thread,
E = length of the shank,
G = the size of the square, and
H = the length of the square.
Formulas for hobs up to two inches in diameter are :
A = 5|D + 3|,
J. 3D + 17
(r = f X diameter of shank,
3D + 5
H
8
For siz.es of Sellers hobs two inches in diameter and
more, use the formulas:
A = 3fZ> + 7f,
„ 3D + 17
G= I X diameter of shank,
„ 3D + 5
280 SMALL TOOLS
The diameter of the shank should be made about one-
sixty-fourth smaller than the diameter of the root of the
thread. The guide or pilot should always be hardened
and ground.
Die Taps. — Die taps are used for cutting the thread in
the die in one single operation from the blank and are sup-
posed to be followed by the hob tap. The die tap is pro-
vided with a long chamfered portion and a short straight
or parallel thread. If to be followed by a hob tap, the
parallel portion should be slightly under the standard
size so as to leave enough metal for the hob tap to remove
to insure the correct size of the die. This difference in
size should be not only on the top of the thread but in
the angle of the thread as well, so that any inaccuracy
in the lead of the thread may be taken care of. On the
other hand, it must be remembered that the difference
must be very slight, as the hob cannot remove very much
stock, having a very short chamfer and very small chip
room for the stock removed. If this is not taken into
consideration, the dies may be injured in the sizing
operation. It may not be out of the way to point out
that one should never try to cut the full thread in the
die with a hob, as this is purely impossible if any satis-
factory results are expected. There are cases known
where persons, supposedly well informed as to the
use of tools, have bought hob taps for the pur-
pose of cutting dies with these taps in one operation,
and after having met with failure in accomplishing this,
have complained that the tools supplied were not satis-
factory.
Returning to die taps we may say that they are very
similar to machine taps and are made in almost exactly
the same way. The flutes are cut with the same fluting
cutters as are used for machine taps. The die taps are
TAPS
231
TABLE LVII.
I
DIMENSIONS OF SELLERS HOBS,
j^^-^ <ItookDlamete&O.Olfi
1 t;
— 1 f
-->*<-
Pig. 98
Diam.
of
Total
Length
of
Length
of
Length
of
Diam.
of
Size
of
Length
of
No. of
Hob.
Length.
Pilot.
Thread.
Shank.
Pilot.
Square.
Square.
Flutes.
D
A
B
C
E
F
G-
H
i
4i
U
li
2i
A
J
»
6
A
5
If
H
2i
^
■ ■
6
f
5i
lA
ift
2i
A
A
■ ■
6
A
5«
Itt
itt
2ft
A
J
8
6
i
6A
1}
li
2ft
1
jtf
8
ft
6A
2
2
2ft
i
S
ii
8
6i
2A
2,1
2i
J
}
8
a
7
2A
•2 ft
21
i
H
}
8
7i
^l
2
2|
^
A
}
8
H
ni
2\
H
2ft
1
1
a
8
i
Si^
2J
*
m
2ft
11
1
a
8
it
^1
2
i
m-
21
«
ft
1
10
S}
3i
H
21
«
1
10
IJ
^hV
3A
3i^
2ft
T
11
lA
10
IJ
10 ^
3i
35
2ft
}
lA
10
m
4A
4i^
2i
lA
«
li
10
H
n^
4f
*i
2ii
lA
n
lA
10
If
I2k
4tt
4U
2}
lA
1
U
12
1}
121
5
5
2f
lA
1ft
H
12
1|
13,^
^A
5ft
2i*
H
H
lA
12
2
141
5f
5f
21
1'
11
li
12
2i
i^h
5^
511
21i
H
ift
lA
12
2i
H]^
6
6
21i
H
ift
lA
12
2|
15K
6A
6ft
3
U
1}
H
12
^
15 lit
6i
61
3ft
H
Ift
lA
12
2f
ui
6A
6ft
31
H
m
If
14
21
16^-
6i
6}
31
H
u
i|
14
2}
HrV
m
m
3ft
n
iH
itt
14
3
Hi
7i
74
31
H
n
li
14
3i
l^ift.
7h
7i
3ft
2|
2ft
m
16
3*
19A
7}
7i
3ft
2f
2}
m
16
3|
20
81
8i
31
2i
2ft
2
16
4
20}
8*
8f
31
2f
2t
21
16
282 SMALL TOOLS
relieved both on the top of the thread and in the angle
of the thread on the chamfered portion, and they are
threaded on a taper for a short distance from the point of
the tap the same as machine taps. On the end of the
die tap a straight pilot may be provided with advantage.
This will help in guiding the tap straight when starting
the thread. Some manufacturers do not provide their
taps with this straight pilot; they simply chamfer them
all the way down to the point, but make the diameter
of point below the root diameter of the thread for a dis-
tance equivalent to the length of the guide. This, of
course, serves no other purpose than to aid in facilitating
the point of the tap to easily enter the hole in the die
blank but does not guide or start the tap straight.
When these taps are to be used for threading dies which
have already been provided with clearance holes, they
should be fluted with somewhat narrower flutes than
otherwise, leaving the lands fairly wide, and preferably
be given a greater number of flutes than usual. This
will permit the tap to pass through the die without
deviating from its true course.
Dimensions of Die Taps, — Table LVIII gives com-
plete dimensions for these taps. The dimensions are
figured from the formulas below. In these formulas,
D = diameter of the thread,
A = total length of die tap,
B = length of the thread,
C = length of the shank,
E = length of the straight thread,
F = length of the pilot,
G = size of the square, and
H = length of the square.
TAPS
288
TABLE LVIII.
DIMENSIONS OF TAPER DIE TAPS.
t<-^->\
Fig. 99
Diam.
of
Tap.
Total
Length.
Length
of
Thread.
Length
of
Shank.
Length
of
Straight
Thread.
Length
of
Pilot.
Size
of
Square.
Length
of
Square.
No. of
Flutes.
D
A
B
C
E
F
a
H
i
SA
212
2}
1
i
J
A
5
H
3A
2A
A
A
5
}
51
3A
2^
2f
}
i
A
*■
5
A
6f
3i
A
A
i
i
5
^
6
3}
2f
^
;!«;
■
5
A
6rt
7^f
4i
1
A
; 1
fi
i ■
5
5
ik
7H
4tt
3
*
it
M
■
6
SA
^a
3i
i
A
■
6
«
Sf
i^
»
f
i
«
6
i
H
3A
H
i
6
«
n
5i
3i
«
i*
A
6
H
6
3i
{
lA
6
IJ
lOA
6i
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li
a
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6
11
7A
3i
Ij
lA
7
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7A
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lA
1
lA
7
H
121
8^
4i
H
H
1}
7
l3tV
ss
4^
li
1
lA
7
1}
I3M
9A
4f
1}
lA
lA
li •
8
l|
144
9«
4H
H
H
8
2
U\
lOi
5
2
lA
H
1*
8
2i
nn
10!
5A
2t
lA
lA
8
21
i6H
Ut^
5f
2i
1}
lA
1«
9
2}
171
11 H
5A
2|
lA
H
1«
9
^
18
]2f
5}
2i
H
lA
2
9
2f
iSA
12^
f
2t
li
itt
2
9
2i
19
121
2}
lA
1}
2
10
2i
19A
19{
13*
6A
2}
lit
2A
10
3
131
6*
3
li
2A
10
3i
20f
21|
m
6}
3i
14
2A
2A
10
H
14|
7i
7f
3i
2}
2i
10
3}
22J
Mi
3}
i«
2A
2J
10
4
23i
]5t
8
4
21
2A
10
284
SMALL TOOLS
For diameters below 2J inches the following formulas
are used:
il = 5f D + 3f ,
C=lJZ) + 2,
E=D,
G = f X the diameter of shank,
For sizes 2J inches and larger the following formulas
are used:
A = 3J Z) + 9|,
B = 2D + 7f,
C=liI> + 2,
E=D,
F=VD-\,
G= \X diameter of shank,
F=JD + 1H.
It must be plainly understood that the formulas given
are for guidance only, and that no hard and fast rule
TABLE LIX.
LIMIT OF OVER-SIZE IN DIAMETER OF HOBS AND DIE TAPS
AFTER HARDENING.
Diameter
Limit
Diameter
Limit
Diameter
Limit
of Tap.
of
of Tap.
of
of Tap.
of
Inches.
Oversize.
Inches.
Oversize.
Inches.
Oversize.
A
0.00025
}
0.002
2f
0.003
0.0005
1
0.00225
3
0.003
^
0.00075
li
0.00225
31
0.0035
i
0.001
li
0.0025
3i
0.0036
i
0.00125
u
0.0025
3i
0.004
0.0015
2
0.00275
4
0.004
1
0.00175
2i
0.00275
TAPS 285
could be made in regard to the dimensions. Formulas
are given for so insignificant a dimension as the length of
the squared portion of the shank only in order to facili-
tate a systematic arrangement of the values in the tables.
The limits of over-size in diameter permissible in hobs
and die taps after hardening are given in Table LIX.
Hobs and die taps are made to somewhat closer limits
in regard to the excess diameter. The figures given in
Table LiX should not be exceeded under any circum-
stances, as a hob with an error in lead so great as to
require a larger excess in diameter than given should not
pass inspection.
CHAPTER VI.
TAPER TAPS.— MISCELLANEOUS TAPS.
Taper Taps in General.
Taper taps, if the expression be properly understood,
are taps which have the diameter of the thread nearest
the shank larger than the diameter of the full thread at
the point, the intermediate portion being formed by the
gradual taper from one end of the thread to the other, as
has already been said when defining different kinds of taps
in Chapter III. It may be well to call attention again to
this proper meaning of the expression '' taper tap " because
of the fact that the first tap in a set of hand taps is com-
monly but not properly referred to as a taper tap. As
this expression is used to designate two widely different
things, and as its common usage as the name of the
first tap in a set of hand taps prevents any possible change,
it is always well, when speaking of taper taps, to state
which of the two meanings is referred to in any particu-
lar case. In the present discussion we are referring to
the taps properly termed taper taps, that is, those with the
diameter of the full thread at the point smaller than the
diameter of the thread at the end nearest the shank as
shown exaggerated in Fig. 100.
There are three particular points to take into considera-
tion when making taper taps. In the first place, the
threading tool must be presented to the tap at right angles
to the axis of the tap, and not at right angles to its tapered
surface, imless the tool is specially made for taper threading
of taps with a definite taper; in the second place, taper
TAPER TAPS — MISCELLANEOUS TAPS 287
taps should, if possible, be turned on lathes provided
with taper attachments, and not by setting over the tail-
stock of the lathe; and, finally, proper relief should in all
cases be given a taper tap. The first of these questions
^""^^^^^^vx,,,,
\V\A^
//'
Vv,/-^-^''"'
Fig. 100. General Appearance of Taper Taps
was treated at length in the chapter on threading tools,
under the heading ''Cutting Taper Threaded Taps with
Chasers/' The second and third questions will now be
taken up.
Effect of Setting Over Tail-Stock when Threading Taper
Taps. — The second consideration of importance when
threading taper taps is that, if possible, the thread should
not be cut by means of setting over the tail-stock but by
means of a taper attachment. If the old method of setting
over the tail-stock is used, two errors will be introduced,
and these errors will increase as the taper of the taps
increases. The first error consists in the pitch of the thread
becoming finer than the standard, which is readily seen by
referring to Fig. 101. The length of the work shown
between the centers of the lathe is a if measured along the
238 SMALL TOOLS
axis of the work. If measured along the tapered surface
the length is b; but 6 =
cos V
If the piece is threaded
with a certain number of threads per inch, c, the number
of threads when threading by means of a taper attachment-
Fig. 101. Effect of Setting Over Tall-Stock when Threading Taper Taps
would be a X c; but if the threading is done with the tail-
stock set over, as shown by the dotted lines, the number of
threads would be X c, or a greater number of threads,
cos V
and consequently a finer pitch than in the first case.
An example will plainly demonstrate the case. Let
the length a, measured parallel to the axis, be 12 inches.
Assume that we wish to cut 10 threads per inch and that
the angle v is 8 degrees. The number of threads on the
whole length of the piece, when cut in a correct way by
means of a taper attachment, will be 120. Now, the
length 6, or the length of the piece measured parallel to
12
the outside, is — — = 12.121, or 12 J inches approximately. ,
In this length we would get 121J threads instead of 120.
It is thus evident that for steep tapers the difference is
quite considerable and cannot be overlooked.
'^ Drunken^' Thread. — The second error due to setting
over the tail-stock when cutting a taper thread is that
the thread; instead of becoming a true, continuous helix,
TAPER TAPS — MISCELLANEOUS TAPS
239
becomes "drunken." An exaggerated drunken thread is
shown in Fig. 102. The drunken thread is due to the fact
that in taper turning with the tail-stock set over, the work
does not turn with a uniform angular velocity, while the
cutting tool is advancing along the work longitudinally
Fig. 102. Exaggerated Appearance of Drunken Thread
with a unifonn linear velocity. The change in the pitch
and the irregularity of the thread are so small as to be
imperceptible to the eye if the taper is slight, but as the
tapers increase to say one-half inch or three-quarters inch
per foot the errors become pronounced. While the setting
over of the tail-stock for cutting taper threads should be
discouraged as much as possible, in cases where it is neces-
sary the evil effects of the method may be partly overcome,
at least so far as the cutting qualities of the taps are con-
cerned, by relieving the threads liberally. Obviously this
will not correct the errors of incorrect pitch and imperfect
helix of the thread, but it will cause the tap to cjut freely.
Amount of Error Due to Settiug Over the Tail-Stock. — In
' Table LX figures are given stating the amount a tap will
be shxyrt in the lead in one inch for various tapers if
threaded with the tail-stock set over. When used in con-
nection with taps and reamers, ^'amount of taper" is
meant to express the difference in diameter per foot of length
measured along the center line or axis of the tool. From
the table given it is easily seen whether the inaccuracy
240
SMALL TOOLS
t
produced will be of consequence in a particular case or
not. The amount of the error in one inch equals
1 — cos V,
if V is figured from the formula
tan V = —
2 X 12
in which formula t is the taper per foot of the piece to be
threaded.
A numerical example will make the formulas more
easily understood. Suppose the taper per foot of a partic-
ular piece of work is five-dghths inch. The angle v is
then first determined :
0.625 ^ ^^^
*^^'=2"^0~2^°-^^^'
v=r3o\
The amount the l6ad of the thread will be short in one
inch if threaded with the tail-stock set over equals
1 - cos 1° 30' =0.00034,
or about 0.004 per foot. Being a fairly small taper we
see that the amount of the error is comparatively slight.
If the taper is increased, however, the error will soon
assume such proportions as to be negligible only in very
rough work.
TABLE LX.
AMOUNT OF SHORTAGE IN LEAD IN ONE INCH OF TAPS
THREADED BY SETTING OVER THE TAIL-STOCK.
Taper per
Foot.
Error in
Lead per
Inch.
Taper per
Foot.
Error in
Lead per
Inch.
i
■ •
1
li
0.00001
0.00005
0.00012
0.00022
0.00034
0.00048
0.0009
0.0014
H
2
2i
3
3i
4
0.0019
0.0026
0.0035
0.0054
0.0078
0.0106
0.0137
TAPER TAPS — MISCELLANEOUS TAPS 241
Relief of Taper Taps, — The third and perhaps the
main consideration in regard to making taper taps is the
question of a proper relief. This question has caused much
perplexity, particularly in the case of taps with steep
tapers. It is evident that a taper tap not relieved,
either on the top or in the angle of the thread, will
refuse to cut altogether, or if forced through a hole will
either leave a very rough and irregular thread or break
off its own teeth. This depends upon that, as the tap is
continuously tapering upward, the heels of the teeth are
always located in a circular section of a larger diameter
than the cutting edges of the corresponding teeth. Con-
sequently, if forced to cut a thread, the tap, if not
relieved, will squeeze the metal back of the cutting edge
Fig. 108. Relief of Taper Taps
in order to find room for the increasing diameter. While
the edge cuts, the space produced by the cutting point of
the thread is not large enough for the increasing diameter
of the part of the thread immediately following. On
account of this it is imperative that taper taps be relieved
the full length of the thread, on the top as well as in the
angle of the thread, for the full width of the land. The relief
should also be greater on the side D than on the side E of
the thread. (See Fig. 103.) This will lessen the friction
and the resistance while cutting a thread, inasmuch as it
is obvious that the greater pressure on the thread of the
tap created by the cutting process comes on the side Z>.
Thus, if this side is properly relieved, so as to permit only
242 SMALL TOOLS
the cutting edge to come in contact with the material
to be cut, the friction is reduced to the smallest possible
amount at the same time as the keenness of the cutting
edge is increased.
With the exception of the previous remarks there is
nothing to be added concerning taper taps which has not
already been discussed in relation to straight taps. As a
rule there is not the necessity for the extreme accuracy in
taper taps that is sometimes expected in hand taps, because,
with incidental exceptions, of course, taper taps are usually
employed on work of rougher character. Besides, being
tapered, there is never any requirement for a working fit
between the stud and the nut, and taper taps are used
mainly for tapping holes where a steam- or air-tight fit is
required.
Pipe Taps.
The most common of all taper taps is the pipe tap. The
number and form of threads for this tap were given in
Chapter I. The pipe tap tapers three-quarters inch per
foot, or one-sixteenth inch per inch measured along its axis.
The taps are known by the nominal size of the pipe for
which they are intended. Consequently a pipe tap is a
great deal larger than the size by which it is designated.
The largest diameter of a half-inch pipe tap, as seen from
Table LXII, is 0.887 inch.
Fluting, — Pipe taps are fluted with the same kind of
cutters as are used for hand taps. As there is consider-
able difference in the manner in which a hand tap and a'
pipe tap cut, there is also some difference in regard to the
required chip room. In the case of a hand tap, as soon
as the thread has been cut by the chamfered portion, the
straight part of the thread does not cut or produce any
chips. The pipe tap, again, being tapered, is constantly
cutting; no matter which part of the tap is in contact with
TAPER TAPS — MISCELLANEOUS TAPS
248
the work, and therefore there is necessity for large chip
room, and the flutes should be made as deep as possible
without impairing the strength of the tap.
The number of flutes for pipe taps may be approximately
determined by the formula
N =1.75 A + 3,
in which N is the number of flutes and A the diameter
of the tap at the size line.
This fonnula ^ves the following number of flutes for
sizes up to 4-inch pipe tap.
Nominal
Number of
Nominal
Size of Tap.
Flutes.
Sisse of Tap.
Flutes.
J
4
n
6
4
2
7
4
2i
8
4
3
9
5
3*
10
1
5
4
11
u
6
The formula ^ven for the number of flutes makes the
distance from cutting edge to cutting edge at the size Une
larger as the sizes grow larger, thereby making possible
deeper flutes in the larger sizes.
Testing Lead of Taper Taps. — In testing or inspecting
the lead of taper taps, it must be remembered that the
correct lead should be on a line parallel to the axis of the
tap, and the lead of the thread cannot be measured in
the same manner as with straight taps, unless due allow-
ance is made for the differences in length along the
axis and the tapered surface. In Table LXI the values
are given which should be measured along the tapered
surface to correspond to one inch along the axis for dif-
244
SMALL TOOLS
ferent tapers. In other words, if a tap is tapered three-
quarters inch per foot, and is provided with 8 threads per
inch, the distance covering 8 threads on the surface of the
tap is not one inch but 1.0005 inch, as seen from the table
opposite three-quarters taper per foot. If the lead of the
thread is tested by comparing it with a standard plug, this
need not, of course, be taken into consideration, as then
any device for comparing the lead of straight taps is
equally applicable to taper taps.
TABLE LXI.
AMOUNT MEASURED ALONG THE TAPERED SURFACE
CORRESPONDING TO 1 INCH ALONG THE AXIS.
Amount
Amount
Measured
Measured
along the
along the
Taper per
Tapered Sur-
Taper per
Tapered Sur-
^ Foot.
faoeOorre-
Foot.
face Corre-
sponding to
spondlng to
1 Inch along
1 Inch along
the Axis.
the Axis.
J
1.0000
H
1.002
1.0001
If
1.0025
•
1.0001
2
1.0035
.
1.0002
2i
1.0055
1.0003
3
1.008
1.0005
^
1.011
1
1.0009
4
1.014
u
1.0015
The distance on the tapered surface corresponding to
one inch along the axis is y if v is determined by the
cosv
formula
tan V
t
2X 12
where t is the taper per foot.
TAPER TAPS — MISCELLANEOUS TAPS 245
Thus, if a tap tapers 1 J inches per foot and has 8 threads
to the inch, if 16 threads were measured at the surface of
the taper, the length, if the lead be correct, should not be
2 inches but 2.003 inches, which we find from
V = 3° (approximately), and — = 1.0014;
cos o
2 X 1.0014 = 2.003 (approximately).
In Tables LX and LXI figures have been given for tapers
as steep as 4 inches per foot. Of course, such steep tapers
are very seldom used.
Dimensions of Pipe Taps. — The dimensions of pipe taps
are given in Table LXII. Referring to Fig. 105, a diameter
A is given at the distance B from the point of the tap.
This diameter is the essential diametrical measure of a pipe
tap, and the circular line which may be imagined to be
drawn around the tap at this place is termed the size line.
The two smallest sizes are provided with a neck between
the threaded part and the shank. On the remaining sizes
the shank is made small enough to come below the
root diameter of the thread, and a neck is therefore
unnecessary.
As pipe taps must be made according to the established
manufacturing standard, formulas for the dimensions
cannot be given, excepting for those measurements which
are unessential, like the dimensions for the shank and
square; but Table LXII gives all necessary information in
regard to all standard sizes, and formulas, even if they
could be given, would consequently be superfluous.
Limits of Accuracy. — The accuracy usually demanded
of taper pipe taps in regard to the exact location of the size
246
SMALL TOOLS
line is ^ven below. The method of testing or measuring
taper taps in order to insure that they are within the per-
mitted limits of variation in this respect is by means of a
ring gauge, as shown in Fig. 104, the diameter L at the large
end of which is the dimension at the size line; the diameter
S at the small end of the hole is the diameter at the point
of the tap, and the length M of the ring gauge equals the
dimension B in Fig. 105, representing the distance from the
Fig. 104. Gauge for Testing Taper Pipe Taps
size line to the point of the tap. Thus, in testmg the tap
with this ring gauge, if the end of the tap comes exactly
flush with the gauge, the location of the size line is exactly
correct. If the end of the tap projects through or comes
short of the face of the ring gauge at the small end of the
hole, such projection or shortage represents the error in the
location of the size line.
-.. «. Enx)r Permitted in the Loca«
«pe aizes. ^^^^ ^^ ^^^ ^^ ^^^
i-1 ±h
li-3 ±A
3i and up ± J
Plus in the above table signifies a projection of the tap
through the ring gauge, and minus, failure of the tap to
reach the end of the gauge.
TAPER TAPS — MISCELLANEOUS TAPS
247
TABLE LXII.
DIMENSIONS OF BRIGGS STANDARD PIPE TAPS.
Fig.
105
1 ^
1 ^
Is
hi
ill
5
1
•s
■s
ll
i
A
B
C
D
1*
F
G
^
ii:
3/
r
0.405
a
0.443
2f
2i
%
T%
1
%
■ i
0.540
A
0.575
1 •
u
A
t
M
•
0.675
A
0.718
1:
11
3
A
i
0.840
0.887
1' ■
2
3
'
^
1.050
1.104
2}
3
*
1
. .•
1
1.315
1.366
2}
4
H
' i •
n
1.660
1.717
1
2}
4
lA
g
a>
u
1.900
1
1.963
2
3
5
1
1
It
O
o
2
2.375
1
2.453
2
3i
5f
1
lA
^
A
c
2i
2.875
li
2.961
2
4
61
2
1*
*
^
§;
3
3.500
lA
3.605
3
4i
7i
2
li
i
03
,s
3*
4.000
1
4.125
3i
4A
8A
2*
lA
2j
t
S
?.
4
4.500
U
4.629
4*
8»
3
1
2J
:
N
N
4i
5.000
1
5.125
3
4*
8A
3t^
1*
2
;
OQ
OQ
5
5.563
2
5.687
4
4
8i
9g
3
1
2J
■
M
CO
6
6.625
2
6.766
4i
4
3
1
2J
■»
.13
7
7.625
2
7.773
4f
5
9f
4
2
3A
H
e3
8
8.625
2
8.773
4}
5
9t
4
2
3
9
9.625
2
9.781
5
5
lOi
4
2
3
10
10.750
2i
10.906
5
5i
101
5i
2i
3«
English Taper Pipe Taps.
English taper pipe taps constitute a special class of taper
taps. Most tap manufacturers in this country make them
exactly like the Briggs standard pipe taps in regard to
dimensions, the only difference being that the English taper
248 SMALL TOOLS
pipe taps are provided with the Whitworth form of thread and
with such a number of threads per inch as is called for by the
standard for Whitworth standard gas and water pipe thread.
It appears, however, that in England these taps are made
with 1 inch taper per foot, instead of three-quarters inch, and
at least one firm in this country follows the English practice.
The last statement is made on the authority of Mr. Charles
E. Smart of Greenfield, Mass., who in a communication to
Machinery in June, 1908, wrote as follows: "Mechanical
hand-books give nothing on the subject of the taper of
Whitworth pipe taps, and for that reason it is highly de-
sirable that the question of correct taper be brought up in
the discussion of this subject. The dimensions of these taps
should be based upon standard Whitworth pipe tap gauges,
which are made in England by the Whitworth Company.
These gauges all taper 1 inch to the foot and are so marked
upon the gauge.
''The accompanying table [LXIII] shows the dimensions
of Whitworth pipe taps as made by the A. J. Smart Manu-
facturing Company. It will be noticed by comparing this
table with the one for regular Briggs pipe taps, that the
diameters at the small end are not the same for the same
nominal sizes. This is because English pipe is smaller than
American pipe, according to all tables, so that the ends on
the Whitworth pipe taps should be made correspondingly
smaller. It is believed by the A. J. Smart Manufacturing
Company that the proper way to make the taps, therefore,
is to make the diameter at the smaller end correspondingly
smaller. The lengths of the pipe taps in the table will also
be found to be shorter, because it has been foimd that
all users of pipe taps, especially plumbers, prefer the
shorter lengths, and many of the tap manufacturers are
now making the lengths of the threaded part of pipe taps
the same as those given in the table. The A. J. Smart
TAPER TAPS — MISCELLANEOUS TAPS
249
TABLE LXIII.
WHITWORTH PIPE TAPS.
(A. J. Smart Maaufacturing Company's Standard.)
Taper per foot =« 1 inch.
Diam.
No. Of
Nomi-
nal
Size.
at
Large
End
of
Thread.
Total
Length
of
Tap.
Length
of
Thread.
Length
of
Shank.
Diam.
of
Shank.
Length
of
Square.
Threads
per
Inch,
Whit-
worth
No. of
Flutes.
Size'
of
Steel.
Form.
i
0.435
H
U
0.328
a
28
a
i
0.570
^
U
IJ
0.438
A
19
i!
•
0.718
H
ift
0.563
i
19
1
0.888
3
1^
ift
0.703
A
*l
0.964
H
1. J
Iff
0.781
1
1.103
3|
li
0.906
X
^ii
1
1.382
3}
r
If
2i
1.125
H
m
u
1.725
4i
2}
1.453
6
1}
H
1.958
4|
1}
^
1.609
1
6
Iff
H
2.130
^
i«
2A
1.766
lA
6
i
2
2.430
H
2
2f
2.063
li
6
Manufacturing Company also only makes 4 or 6 flutes
in its taps. The company has found that customers do
not like an odd number of flutes, as the taper with the
odd number of flutes can never be measured by microm-
eters after the flutes have been once milled. This is a
great disadvantage (or, to some people, an advantage) in
cases of disputes as to the sizes of the taps. In the table
given there will be found a column giving the size of the
steel used for the different taps. This information is
given for the convenience of the purchasing agent, the
superintendent, the foreman, etc., and has often been
foimd exceedingly useful."
In paragraph 7, page 6, of the "Report on British
Standard Pipe Threads for Iron or Steel Rpe and Tubes,"
of April, 1905, issued by the Engineering Standards Com-
250 SMALL TOOLS
mittee, however, the taper of Whitworth pipe is ^ven as
three-quarters inch per foot. Before this report was
issued it was the custom in England to make these taps
with a taper of one inch per foot.
Pipe taps and taper taps in general are often made
with the interrupted thread shown in Fig. 92, Chapter V.
This form of thread is very well adapted for taper taps,
and in case of a very steep taper is, in fact, almost essen-
tial if a smooth and perfect thread is to be cut.
In hardening, pipe taps should be drawn to a somewhat
higher temperature than ordinary hand taps of the same
sizes. The correct" temperature is about 470° F.
Pipe Hobs.
Pipe, hobs are used for sizing pipe dies after the thread
has been cut nearly to size either in a lathe or by a pipe
tap. The threaded portion of a pipe hob is made longer
than that of pipe taps, but there is no good reason why
this should be so, excepting that it has become customary,
and established custom is as unyielding in tool-making
as in anything else. Outside of the longer threaded
portion, the only essential difference from the pipe tap
is the number and the form of the flutes. These latter
are cut with a 50-degree double-angle cutter, 25-degree
angle on each side, which is the same kind of a cutter
as is used for ordinary straight hob taps. The number of
flutes may be approximately determined by the formula
8.5 B =N,
in which B = diameter at large end of thread of hob and
N = the number of flutes.
This formula gives the width of each land as about three-
sixteenths inch, and the width of the space or flute the
TAPER TAPS — MISCELLANEOUS TAPS
251
same amount. According to this foijnula the number of
flutes for various sizes of pipe hobs is as follows:
Size of Pipe
Number of
Size of Pipe
Number of
Hob.
Flutes.
Hob.
Flutes.
1
5
2
22
^
6
2i
26
"i
6
3
32
1 ■
8
3i
36
10
4
40
1
12
4*
44
li
16
5
48
u
18
6
58
Dimensions of Pipe Hobs, — The dimensions for lengths
and diameters of pipe hobs are given in Table LXIV.
The dimension A is given according to the estabKshed
standard of the manufacturers of taps. This is the essen-
tial diameter and is located 1^ inches from the large end of
the thread of the hob. The limit of error for the loca-
tion of this diameter is the same as the limit for the loca-
tion of the size line of pipe taps which has been previously
stated, and the gauging is done in the same manner. It is
evident that a separate set of ring gauges is required, and
that the length of the gauge in this case should always be
1 J inches, the large diameter of the hole in the gauge being
diameter B in Fig. 106, and the small diameter the dimen-
sion A. The taper of pipe hobs is, of course, the regular
pipe thread taper, three-quarters inch per foot.
The more important dimensions in Table LXIV are
figured from the formulas :
N + 16
C =
D =
8_^
dVN + 11
F = A — iV for pipe sizes up to and including 3 inches,
N
jP == — + 3 J for 3 J-inch pipe size and larger,
o
262
SMALL TOOLS
In these formulas,
A = size of the hob IJ inches from the large end of
the thread,
N = nominal size of hob (pipe size),
0 = length of shank,
D = length of thread, and
F = diameter of shank.
TABLE LXIV.
DIMENSIONS OF PIPE HOBS.
Fig
106
Nomi-
Actual
Size
Diameter
Length
Length
Length
Diam.
Size
Length
nal
at Large
of
of
Over
of
of
of
Size.
End.
Shank.
Thread.
All.
Shank.
Square.
Square.
A
B
C
D
E
F
G
^
h
0.445
0.539
2
3A
5t%
,
t
4
■
0.573
0.667
2
3
5*
■
•
0.719
0.813
2tV
3
5A
fj
0.885
0.979
2tV
3t
3}
5ti
%
1.104
1.198
2i
6
lA
1
1.363
1.457
2v
6i
lA
1
1 ;
u
1.721
1.815
2Yk
4
6A
1
li
1:
H
1.955
2.049
2V^
4
6A
1
lA
2
2.460
2.554
2-
4 ^
6}
2
!■*
24
2.963
3.057
2A
4*
7
2
2i
rtf
3
3.620
3.714
2*
4i
7
IS
2i
3i
4.062
4.156
2^
5A
7-
2
B
1
4
4.485
4.579
2*
5
7-
3
2^
4*
5.000
5.094
2A
5
7*
3*
2i
5
5.565
5.659
n
5
8-
3
2-
*
2
6
6.620
6.714
2i
5|
84
4
3
2
TAPER TAPS — MISCELLANEOUS TAPS 258
Relief. — Pipe hobs, being provided with a taper thready
must be relieved both in the angle and on the top of the
thread. In this respect they differ from straight-thread
hobs, which are relieved only on the top of the thread
of the short chamfer at the point.
Taper Boiler Taps.
Taper boiler taps, as the name indicates, are used in steam
boiler work, and, like the pipe tap, are used in this work
where a steam-tight fit is desired. The taper of these taps
is the same as the pipe tap taper, three-quarters inch per
foot. In regard to their construction there is nothing to
say that has not already been said either in connection with
pipe taps or about taper taps in general. The size by
which these taps are designated is located one-quarter inch
from the large end of the thread. The permissible limits
of error in the location of the size line are the same as
for pipe taps.
In Table LXV dimensions are given for taper boiler taps.
The most important of these are approximately figured
from the following formulas :
A = 3 D + 2f inches,
B = -— + 1| inches,
C' = -7 + t inch, .
^ = 2 D + i inch.
In these formulas,
A = total length of tap,
B = length of thread,
C = length of neck,
D = diameter of tap, measured one-quarter inch from
the large end of the thread.
254
SMALL TOOLS
These taps are provided with 4 flutes up to IJ inches
diameter, and with 5 flutes for sizes from If to 2 inches.
If made in sizes larger than 2 inches, 6 flutes should be ^ven
to the tap. Boiler taps are always provided with 12 sharp
V threads per inch, irrespective of the diameter of the tap.
TABLE LXV.
DIMENSIONS OF TAPER BOILER TAPS.
Fig
107
Diam.
Total
Length
Length
Length
Diam.
Length
Size
of
Tap.
Length.
of
Thread.
of
Neck.
of
Shank.
of
Neck.
of
Square.
of
Square.
D
A
B
C
E
F
G
H
i
4}
2i
i
^
tt
i
»
A
4A
2A
1
ri
h
A
tt
4ft
2
, ■
1
i
■
i
4+»
2
A
1
-J
i
5
2A
A
2
f
A
if
5A
2J
A
2-
\ h
«
«
51
2A
A
2
h
J
*
5A
2A
2
*
i
1
5}
2
2
fi
lA
5«
2ik
■ ^
2
t!
lA
*
1*
6*
2v
H
2
U
;
lA
6A
2;
2
lA
■
li
6*
2*
*
3
1^
*
lA
6+*
2
4
3-
1^^
1^
1*
6J
2*
4
3
1^
1}
1^
lA
7A
2i
^ ..
3
lA
1^
1^
1
7i
3
3
1*
1|
If
1}
?
3t
3A
t*
3}
4
IM
li
lA
1-
8f
3A
*
4i
m
li
^A
2
8f
3f
4i
li
li
TAPER TAPS — MISCELLANEOUS TAPS
265
Patch-Bolt Taps.
Patch-bolt taps are practically only a modified form of
taper boiler taps. The taper is the same, but the threaded
portion as well as the total length is shorter than the
corresponding lengths of a taper boiler tap. The taps are
used for similar purposes in boiler construction.
TABLE LXVI.
DIMENSIONS OF PATCH-BOLT TAPS.
Fig. 108
Diam.
Total
Length
Length
Length
Diam.
Diam.
Size
Length
of
Length.
of
of
of
of
of
of
of
Tap.
Shank.
Neck.
Thread.
Neck.
Shank.
Square.
Square.
D
A
B
C
E
F
Q
H
K
\
2i
l\
H
»
i
\
i
A
3
lA
■ •
lA
A
A
A
4
■
3A
1}
' '
iVk
h
■
ii
A
i
3*
lA
h
1^
A
i
i
1^
3A
1*
lA
A
I*
3|
3i
3A
lA
If
■J
2"
lA
If
1*
1**
t
lA
3A
1*
1 i-
ii
•4
^A
f
H
3
1
1 •
li'
1}
1
1
^A
3!
u
lA
^A
\i
M
IJ
1-
ij
H
n
i
I^
3i
1+it
^A
1
r
M,
3*
2
1^
IJ
If
lA
1
lA
4
2A-
:■
1^
lA
lA
lA
4A
2i
i
lA
If
14
li
1
266 SMALL TOOLS
The dimensions for patch-bolt taps are ^ven in Table
LXVL The essential dimensions are approximately figured
from the formulas:
A =: 1^ D -f 2A inches,
B = D + f inch,
^ = A ^ + lA inches,
F =D - \ inch.
In these formulas,
D = diameter of tap (measured five-eighths inch from
the large end of the thread),
A = total length of tap,
B = length of shank,
E = length of thread, and
F = diameter of neck.
The diameter of the shank equals the diameter of the tap.
Patch-bolt taps are always provided with 12 threads per
inch, V form, irrespective of diameter. All sizes are fluted
with 4 flutes up to 1\ inches diameter. Patch-bolt tape
are not manufactured in larger sizes.
Mud and Wash-out Taps.
Mud and wash-out taps are used in boiler work the same
as the taps previously referred to. These taps are some-
times referred to as arch pipe taps, but the former name is
by far the more conmion. They are made in six sizes,
usually known by numbers as stated in Table LXVII.
These taps taper 1} inches per foot, and have 12 sharp
V threads per inch. The dimensions as given in Table
LXVII conform in all essential details to the practice
of manufacturers of taps. Number 0 tap is provided with
5 flutes. No. 1 with 6, No. 2 with 7, and the others with
8 flutes.
TAPER TAPS — MISCELLANEOUS TAPS 267
TABLE LXVII.
DIMENSIONS OF MUD OR WASH-OUT TAPS.
— 2k-
-*^
-*H^
Fig. 109
hV
Number of
Diameter at
Diameter at
Diameter ol
Size of
Tap.
Small End.
Large End.
Shank.
Square.
A
B
C
D
0
lA
U
li
1
U
2A
1
1
2
2A
21
2
1
3
2
2ii
2
4
2i
3
2
li
5
3
3A
2
li
Blacksmiths' Taper Taps.
There is but one more class of taper taps generally
manufactured, the blacksmiths' taper tap. This tap has
a long taper thread and a very short shank, only suffi-
ciently long for a square and a collar to prevent the tap
wrench from slipping from the square down upon the body
of the tap. The taper of the thread is three-quarters inch
per foot; the size by which the tap is known is measured
five-eighths inch from the large end of the thread. These
taps are generally made with the standard number of
V threads per inch corresponding to their nominal diameter.
The sizes given in Table LXVIII are the sizes generally
made; all these sizes have four flutes.
258
SMALL TOOLS
TABLE LXVIII.
DIMENSIONS OF BLACKSMITHS' TAPER TAPS.
,H = SQUARE I* ^g" "i
k!
u::
^ INCH TAPER PER FT.
:::»_
■•-c-*K-
Fig.
110
Nomi-
nal
Diam.
of Tap.
Length
of
Shank.
Length
of
Neck.
Length
of
Thread.
Total
Length.
Length
of
Square.
Diam.
of
Shank.
Size
of
Square.
A
B
C
D
E
F
G
II
i
i
*
H
2*
i
A
i
A
A
m
2H
»
»
t
*
I^
u
m
i
A
A
I^
2A
H
i
i
i
J
*
i
2i
3A
A
A
A
:
i
2A
3 ;
i
M
1
■J
i
i
ss.
3if
t
)*
A
3
4A
*
1
■s
A
3A
4-
1
A
3f
4
i
^
i
1
3A
5A
*
1
1
lA
H
5A
lA
i
U
lA
- •
4*
6
i
lA
i
H
li
^ ■
^
6A
1*
1
1*
If
^
7
i
lA
li
lA
■ ■
5i
7A
1
lA
lA
Pipe Taps and Drills Combined.
Pipe taps are sometimes provided with a drill point as
shown in Fig. Ill, for drilling the hole previous to tapping.
Instead of a square for a wrench, they are then usually
provided with square taper shank for a taper drill socket.
The dimensions of the shank must of course suit the
TAPER TAPS — MISCELLANEOUS TAPS
259
requirements. The threaded portion is an exact dupli-
cate of the threaded part of a pipe tap. The drill part
has two flutes like a twist drill, and the point is ground to
X INCH TAPER PER FT.
Fig. 111. Pipe Tap and Drill Combined
the same angle, 59 degrees with the center line, as are
ordinary twist drills. The diameter and the length of
the drill point are the only dimensions necessary to state
in this connection.
Pipe Tap
Length of
Diameter of
Size.
Drill Point.
Drill.
i
i
ii
■■
^
1:
1
II
i
1
i
1
1
1
lA
li
1
li
Iff
2
1
If
2A
^
2
2|
Stay-Bolt Taps.
Stay-bolt taps are extensively used in locomotive boiler
work. The ordinary or radial stay-bolt tap is shown
in Fig. 112; in Fig. 113 is shown the spindle stay-bolt
tap, which has derived its name from the guiding spindle
upon which the tap proper revolyes.
Radial Stay-bolt Taps. — If we first give our attention
to the radial stay-bolt tap as shown in Fig. 112, the length
260 SMALL TOOLS
C represents the threaded portion. Of this part, the
portion F is straight or parallel, and the part G is cham-
fered. The part jE is a taper reamer which reams the hole
previous to tapping. The taper of this reamer is usually
three-thirty-seconds of an inch per foot. The diameter
at H is equal to the root diameter of the thread. The
diameter of the shank is about 0.005 inch below the root
diameter.
Stay-bolt taps are usually made with 12 threads per
inch of the sharp V form. Although practice has almost
universally favored the employment of the sharp V thread,
the main advantage (and perhaps the only real advantage)
of a thread of this sort is that it can be made tight in the
boiler sheets and kept tight without any great diffi-
culty. On the other hand, the use of the V thread
violates one of the fundamental principles of machine
design — the principle, namely, of avoiding all sharp
angles and of filleting every place where such angles tend
to occur.
This must have occurred many times to engineers and
designers, and yet no general movement has been made to
discard the V thread and substitute for it a form that
shall not be open to the same objection. The Whitworth
thread is receiving considerable attention at the present
time, however, for use upon stay-bolts, and it is regarded
with favor by certain builders of large experience, notably
by the Baldwin Locomotive Works, who are now using
this thread upon locomotive stay-bolts. If experience
shows that stay-bolts can be made tight and kept so when
fitted with this thread, it is probable that its adoption will
extend to other builders.
Stay-bolt taps receive very rough treatment, and are
exposed to hard usage, and should therefore be made
of an extra good quality of steeL The thread should be
TAPER TAPS— MISCELLANEOUS TAPS 281
relieved both on top and in the angle of the thread on the
chamfered portion. In order to prevent the existence of
too wide cutting edges toward the smaller end of the
chamfered portion, the tap is threaded taper about one-
half of the chamfered part. This prevents the tap from
reaming instead of cutting. In order to gain the same
end it is advisable never to make the chamfer any longer
than 6 inches.
The interrupted thread shown in Fig. 92, Chapter V, is
particularly of value in the case of stay-bolt taps, and is
probably used more on this class of taps than on any
other.
In Table LXIX the dimensions for standard radial
stay-bolt taps as made by a prominent tap-manufactur-
ing firm are given. However, stay-bolt taps are made in
a variety of sizes and designs for special requirements ;
but the two kinds given in the table are the most com-
monly used. All stay-bolt taps of sizes given in the table
should have 5 flutes.
The over-size limit of variation in diameter from the
correct size, is commonly assumed in stay-bolt taps to be
0.002 inch for taps smaller than 1 inch in diameter and
0.003 inch for larger sizes. It is evident that it is not
permissible for the tap to be under the correct size ; con-
sequently the diameter is required, after hardening, to be
between the standard diameter and a diameter 0.002 or
0.003 inch respectively, above the standard.
Sometimes stay-bolt taps are provided with a threaded
guide at the upper end of the thread. This guide is not
fluted and should be made slightly smaller in diameter
than the cutting size of the tap. The amount which the
diameter is smaller is usually about 0.010 inch, and should
apply to the angle diameter as well as to the top of the
thread. While not fluted, this threaded guide ought
262
SMALL TOOLS
still to be grooved by a small convex cutter for oil pas-
sages to the flutes.
TABLE LXIX.
DIMENSIONS OF REGULAR STAY-BOLT TAPS.
rt-i=->
* G-
Fig. 112
o
I-
1^
i
a
1
li
lA
li
ift
li
n
n
n
n
n
7J
7i
n
71
n
5i
51
51
51
51
51
51
51
51
51
51
11
11
U
U
11
11
U
U
U
11
U
i|
se
0.606
0.668
0.731
0.793
0.856
0.918
0.981
1.043
1.106
1.168
1.231
5-8
0.601
0.663
0.726
0.788
0.851
0.913
0.976
1.038
1.101
1.163
1.226
L
H
M
i
i
i
1*
1
1
1
li
IJ
u
}
H
1
«
1
lA
11
lA
li
0.606
0.668
0.731
0.793
0.856
0.918
0.981
1.043
1.106
1.168
1.231
0.601
0.663
0.726
0.788
0.851
0.913
0.976
1.038
1.101
1.163
1.226
a
f
f
I
1
1
1
1
li
u
Spindle Stay-BoU Taps. — The spindle stay-bolt tap,
as shown in Fig. 113, is not provided with a reamer, and
with but a short chamfer. It is fluted about half way of
TAPER TAPS — MISCELLANEOUS TAPS
268
the threaded part. The remaining part of the thread
acts as a guide and should be made in the same way as
threaded guides for radial stay-bolt taps. The guide E
on the end of the spindle holds the tap in place in rela-
tion to the inner tube sheet while the outer one is threaded.
The standard dimensions for these taps are given in
Fig. 113 and in Table LXX.
TABLE LXX.
DIMENSIONS OF SPINDLE STAY-BOLT TAPS.
I ^
T^
t^
innnnr.nnnnnnnn
'"A
4
^.
Fig. 113
Diameter of
Tap.
Diameter of
Shank.
Size of
Square.
Diameter of
Neck.
Diameter of
Guide.
D
A
B
C
E
i
It
1
i
IS
0.601
0.663
0.726
0.788
0.851
0.913
0.976
1.038
1.101
1.163
1.226
I.
\t
Straight Boiler Taps.
Straight boiler taps are, strictly speaking, only a special
class of hand taps. They have a long chamfer and a
264
SMALL. TOOLS
straight guide at the point. The chamfered portion is
relieved on the top of the thread. These taps are fluted
in the same way as hand taps. In Table LXXI the
dimensions for these taps are ^ven.
TABLE LXXI.
DIMENSIONS OF STRAIGHT BOILER TAPS.
ROOT MAIIETBI-1-O.a
BOOT MAMETBI-l-O.OOe;'
Fig.
114
Diam.
Total
Length
Lraigth
Length
Length
of
Length
of
Length
Length
Size
of
Tap.
Length.
<rf .
Shank.
of
Neck.
of
Thread.
Full
Thread.
Cham-
ta.
of
Pilot.
of
Square.
of
Square.
D
A
B
C
E
F
a
H
/
K
i
4i
1 J,
i
2
i
n
f
.f
f
A
4A
1 i
2*
A
lA
f
A
A
•
4»
1 i
^r
2A
tt
li
A
ft
ff
i
m
A
2A
lA
A
«
\
. :
5
1
A
2A
lA
i
f
A
«
5A
1*
A
2 i
*
If
f
+f
5f
2
A
2 i
lA
f
f
f
*
5A
2
21t
3i
*
If
i
+f
f
5i
2
lA
A
1
lA
If
2A
3-
lA
1
A
lA
*
li
2A
3A
1*
U
If
lA
6i
2A
■:
3A
lA
1
ft
lA
■
U
6
2*
3 i
U
1
H
f
lA
6*
2A
■:
3*
lA
1*
i
lA
1
If
ft
2i
1 :
3*
1«
li
i
If
lA
lA
7A
2i
4:
lA
If
lA
lA
7i
2i
4
1 ■
2
•
If
1
n
2A
4A
2f
f
If
1
1
8
2f
*
4»
1
2A
1*
lA
8J
2i
*
5A
2A
If
lA
2
8t
2J
•
5i
2
2A
«
If
If
TAPER TAPS — MISCELLANEOUS TAPS 265
The most important of these dimensions are determined
from the f onnulas :
il = 3 D + 2f inches,
E=^2\D + iinch,
H=iD + T^inch,
in which formulas,
A = total length of tap,
D = diameter of tap,
E = length of threaded portion,
F = length of full or parallel thread, and
H = length of guide.
In making these taps the same limits in regard to over-
size diameters as are employed for regular hand taps should
be adopted.
Straight Pipe Taps.
Straight pipe taps, as was mentioned in a previous
chapter, are only a variation of hand taps, having the
same number of threads per inch as the corresponding
sizes of taper pipe taps, and a diameter arbitrarily
adopted by the manufacturers of these taps. Table
LXXII gives the dimensions for taps up to and including
three-quarters inch nominal diameter. The larger sizes
are ^ven in Table LXXIIft It will be noticed that the
difference in appearance between the larger and smaller
sizes is simply that the latter is provided with a short
neck, turned down below the root diameter, while on the
larger sizes the whole shank is turned down below the
root of the thread.
266
SMALL TOOLS
TABLE LXXII.
STANDARD STRAIGHT PIPE TAPS.
H^MbARE
k-
1— !
T
¥
T
^
WWW44H^
■«e*f«
4
Fig
. 115
Nomi-
Diam.
Total
Length.
Length
Length
Length
Diam.
Diam.
Size
Length
nal
of
of
of
of
of
of
of
of
Size.
Tap.
Thread.
Neck.
Shank.
Neck.
Shank.
Square.
Square.
D
A
B
C
E
F
G
H
/
0.398
n
Yk
lA
0.335
i
A
A
0.531
2i
1
*
1»
0.440
f
i
0.672
3tV
1
i
lA
0.575
M
ft
0.828
3
1
^
lA
0.705
"fe
t
1.041
3f
1
li
0.915
1
i
i
Pb SQUARE-
TABLE LXXIII.
STANDARD STRAIGHT PIPE TAPS.
— r-
^JIIIIIIIIHHIIinillHITTTTM
-iE
1 nil 1 1 rm
<:
■■'■llMIIIIIIIlt;
I
Fig.
116
Nomi-
Diam.
Total
Length.
Length
Length
Diam.
Size
Length
nal
of
of
of
of
of
of
Size.
Tap.
Thread.
Shank.
Shank.
Square.
Square.
1
D
A
B
C
E
F
G
1.293
4
li
• 2i
1 1 •
t»
' I :
li
1.645
4A
If
2i
1
»
■^ ■
14
1.880
4
2i
1
lA
2
2.359
5*
2A
3i
1
^^
2*
2.836
6
2
3
lA
i\
3
3.461
7
3
2
11
^
3.971
8A
If
4J
2
i+»
li
4
4.398
9
6i
2{
114
itt
TAPER TAPS — MISCELLANEOUS TAPS
267
These taps are chamfered the same as plug hand taps,
and relieved only on the top of the thread on the cham-
fered part.
The number of flutes may be made the same as for corre-
sponding sizes of Briggs standard pipe taps; if it is
considered that fewer flutes would be more advisable,
approximately the same number of flutes as is given to
regular hand taps will be satisfactory. In cases like this
the number of flutes, within reasonable limits, is largely a
matter of judgment. The straight pipe tap, being actu-
ally a hand tap, should evidently be fluted like a hand tap.
But inasmuch as the tap has a greater number of threads
per inch than corresponding sizes of ordinary hand taps,
there is a reason for providing it with a greater number
of flutes.
English straight pipe taps having Whitworth form of
threads and made according to Whitworth's thread system
for gas and water piping are given in Tables LXXIV
and LXXV.
lABLE LXXIV.
ENGLISH STRAIGHT PIPE TAPS.
(See Fig. 115 for meaning of letters in table.)
Nomi-
Diam.
Total
Length
Length
Length
Diam.
Diam.
Size
Length
nal
of
Length.
of
of
of
of
of
of
of
Size.
Tap.
Thread.
Neck.
Shank.
Neck.
Shank.
Square.
Square.
D
A
B
C
E
F
G
H
/
i
0.385
^
1
^
lA
0.335
i
^
A
'. ■
0.520
2}
H
,
1*
0.448
\
f
h
■ ■
0.665
3A
1}
-
lA
0.593
i
\
: ■
0.822
3i
i|
A
lA
0.726
1
A
i
0.902
3A
H
A
11
0.806
*
^
«
1.034
3t
H
i
11
0.938
1
i
f
268
SMALL TOOI^
TABLE LXXV.
ENGLISH STRAIGHT PIPE TAPS.
(See Fis. 116 fior meuiins d letters in table.)
Nomi-
Diam.
Total
Length.
Length
Length
DxAoz.
Sae
l^ccth
oal
(rf
cf
(rf
of
«i
of
Size.
Tap.
Thread.
Shank.
sbuik.
Jiqiare.
S^tUUE^
Z>
A
B
C
f
r
ti
i
1.189
3«
Itt
2|
lA
13
H
1.30^
4
1}
21
i|
^
it
H
1.492
4i
1
2|
lA
}
i\
1.650
4t^i
Itt
2i
li
tf
ii
If
1.745
4ii
2A
2f
ift
1
H
1}
1.882
4J
2*
2|
If
lA
1
i|
2.021
5A
2^
2}
lA
lA
lA
If
2.160
5A
2A
3
li
It
lA
2.245
5i
21
3i
lA
lA
U
2
2.347
5tt
2A
3i
li
li
lA
21
2.467
5i
2i
3f
i«
li
lA
2i
2.587
6i
2i
3i
1)
li
2*
2.794
6A
2H
3f
i«
1}
lA
2i
3.001
•6i
2|
3|
1}
1^
lA
2f
3.124
6}
2J
3}
i«
1^
i|
2}
3.247
m
2H
4
2
li
lA
2i
3.367
n
3
4i
2A
lA
lA
3
3.485
7f
3i
4i
2i
1
li
3i
3.698
7|
3i
4i
2i
itt
lA
3i
3.912
8A
3A
4|
2|
lit
lii
3}
4.125
H
3f
5
2i
li
H
4
4.339
9
3f
5i
21
li*
lii
Adjustable Taps.
Purpose and Kinds of Adjiistable Taps. — Adjustable
taps are made for the purpose of permitting adjustment to
a correct standard size. As the solid tap, on account of
changes in hardening, cannot be depended upon to meas-
ure exactly the diameter for which it was intended, and
because of the impossibility of preventing a solid tap from
decreasing in diameter through wear, the adjustable tap
has a wide field of usefulness where correct-sized nuts
TAPER TAPS — MISCELLANEOUS TAPS 269
must be produced. The adjustable tap may either be made
from a solid piece, split in a suitable manner to permit
adjustments, or may be provided with inserted blades or
cutters, which are so held in the tap body that a slight
movement of these blades in the longitudinal direction of
the tap moves the cutting points of the thread nearer
or further from the axis of the tap, thus decreasing or
increasing the diameter as the case may be.
Another cause for inserted blade taps bfesides adjusta-
bility may also be mentioned. The efforts constantly
made by progressive manufacturers to decrease the cost
of tools without impairing their efficiency have resulted in
the designing of a number of taps of this type which permit
cheaper grades of material to be used in the tap body,
while the best quality steel may be used for the inserted
blades, the total cost, especially in the case of large taps,
being smaller than if the tap were made solid of ordinary
tool steel throughout. Incidentally another advantage
is also gained, in that, as the wear of the cutting portion
of the tap is the only reason for discarding the tap, the
inserted blade design makes it possible to retain the body
proper and replace the cutters only.
In the case of large taps and coarse pitches the adjust-
able tap does not give very good satisfaction if a thread is
cut by one passage of the tap, because the strain on the
tap is so great as to spring it to a certain extent. It is
evident that an adjustable tap cannot possibly be made
quite as rigid as a solid tap. But in such cases the tap
still retains its superiority as a "sizing" tap, used to finish
the thread after it has been roughed out by means of an
ordinary tap cut somewhat under size.
Examples of Adjustable Taps, — The form of adjustable
taps, previously referred to, which is cut from a solid
piece and split, is shown in Pig. 117. The body is split
270 SMALL TOOLS
straight through; a nut with a taper thread serves to hold
the tap together at the end, and a screw with a taper head
is used to expand the tap, as shown. As the expansion is
Fig. 117. Adjustable Tap Made from Solid Stock
effected by bending the cutting lands as the tapered head
of the screw travels inward, the thread form is not accu-
rately retained and the tap is not to be recommended.
When accurate work is required the inserted blade form
of adjustable taps is the preferable form.
The requirements for a good inserted blade tap are that
the blades when bound in place shall be practically solid
with the body; that the design shall permit a liberal adjust-
ment in regard to size; that this adjustment shall be easily
accomplished; and that the means employed for binding
and adjusting the blades shall not be of such a kind as to
prevent the use of the tap in any case where the solid tap
could be used. This latter requirement involves the
possibility of tapping clear through a hole as well as the
tapping down to the bottom of a hole.
A tap which fills fairly well all these requirements with
the exception of the one mentioned last is shown in Fig. 118.
The blades are held in place by nuts, beveled on the inside
to fit the tapered ends of the blade. In this manner
the blades are prevented from longitudinal motion as well
as from moving out or in in relation to the center line of
the tap. The blades fit into slots in the tap body and are
thus prevented from moving sideways. The adjustment
is provided for by the tapered bottom of the slots in the
TAPER TAPS — MISCELLANEOUS TAPS 271
fcK)dy> by means of which the cutting size of the tap increases
when the blades are moved upward toward the shank end
of the tap. The adjustment is easily accomplished, it only
being required to loosen the upper nut and push up the
blades, and then tighten the lower as well as the upper nut
solidly upon the blades. It is, however, not possible with
the design shown to tap down clear to the bottom of a hole.
c
Fig. 118. Adjustable Tap with Inserted Blades
nor is it possible to tap straight through a hole. This
latter requirement could, of course, be easily obtained by
niaking the slots deeper and the blades wider, thus making
it possible to decrease the outside diameter of the upper
binding nut so that it would be less than the root diameter
of the thread. This would permit the tap to pass clear
through a threaded hole.
There is, however, a more serious objection to this
design. The backing of the blade by means of a tapered
surface in the nut is not very positive, and the blades are
liable to be a trifle incorrect in their relative position in
regard to lead. It is evident that if that is the case the
thread cut will be incorrect in its shape, the space cut being
wider than the thread itself in the nut. A tap which over-
comes the objections raised in regard to the tap in Fig. 118
is shown in Fig. 119.
Pratt and Whitney Company Adjustable Tap. — This tap
consists of body, blades and binders, and a thrust nut and
a check nut mounted on a threaded part of the body.
272
SMALL TOOLS
On comparatively small sizes of taps the end of the body
is turned down to fit a hole in the shank, as shown in the
lower view, Fig. 119. The shank is then driven into place
and secured by a taper pin. On larger sizes the shank is
made solid with the body as shown in the upper view.
This difference in design is necessitated by the construction
of the tap. The shank if made solid with the body must
Fig. 119. Pratt and Whitney Company's Design of Adjustable Tap
obviously be below not only the root diameter of the tap
itself but also below the root diameter of the portion on
the body threaded for the thrust and check nut, as other-
wise these nuts could not be put in place. On small taps
this would require a diameter of shank altogether too
small compared with the diameter of the tap. In such
cases, therefore, the body is driven into a shank of larger
diameter than would otherwise be possible to use.
The body is slotted longitudinally to receive the blades,
and has a circular groove all around to receive the binders.
The latter are, by means of small screws threaded into the
body, pressed fimily against a shoulder formed by a small
groove in the blades, as shown plainly in the enlarged view
of the binding arrangement in Fig. 120. The hole shown
at the front end of the tap extending at the center of the
TAPER TAPS — MISCELLANEOUS TAPS
278
tap for some distance inward is for providing clearance for
the taps when tapping the binder screw holes. The blades
are squared off at the upper end to rest solidly against the
thrust nut. As it is important that each blade be placed
in a correct position in relation to the others, each blade
being a certain amount ahead of the next preceding one
in regard to lead for the purpose of securing a continuous
thread around the tap, it
is customary to replace all
the blades at once, prefer-
ably threading them in
the tap body itself or in a
master holder similar to
the tap. It is evident
that it would be difficult
to replace single blades, as
the replaced blade would
hardly come in such a
position in relation to the
others as to produce a
Fig. 120. Method of BiDding the
Blades in the Tap in Pig. 119
perfect continuous thread all aroimd the tap.
As the thrust nut only locates the blades longitudinally,
the binders are relied upon altogether for holding the blades
down. For this reason the binder is placed near the center
of the blade. In the case of a reamer constructed on this
same principle the binder is placed nearer the front
end, as in a reamer there is no objection to beveling the
thrust nut on the inside in a manner similar to that used
for the inserted blade tap formerly described. This beveling
of the nut and tapering of the upper end of the blade will,
of course, hold the blade very securely in place, but cannot,
for the reasons previously given, be adopted in a tap of
good design.
The binders are made from a solid ring which is turned,
274 SMALL TOOLS
chucked, reamed, and has the screw holes drilled and
counterbored before the ring is cut into pieces. This tap
fills all the requirements mentioned at the beginning of
the discussion of inserted blade taps. When the binders
are tightened against the shoulder in the blade, and the
nuts are screwed tightly up against the end of the blades,
the blade at the same time fitting the slot in the body
snugly, there is no possible chance for the blade to move.
The tapered bottom of the slots in the tap body provides
for the adjustment the same as in the case of the inserted
blade tap previously described. When the tap is to be
expanded, the binder screws are loosened and the nuts
at the upper end of the blades are screwed back. The
blades can then be moved upward as far as necessary for
obtaining the desired size, and the nuts and binders are
again tightened. The ease of accomplishing this adjust-
ment is apparent. No parts of the tap used either for
binding or adjustment project outside of the tap at the
end. Nor does any detail project beyond the root diam-
eter of the thread in the tap. Thus the tap can pass
entirely through a hole as well as tap clear down to the
bottom of a hole, provided only a short chamfer is given
to the thread. Very few taps of the adjustable or expan-
sion type fill the given requirements as well as does this
one. Of course, this is not intended to mean that the
design which we have described to some extent in detail
is the only one possible which will fill the requirements
outlined. There can, of course, be a great deal of vari-
ation in the design, and the example chosen is selected
simply because it embodies all the features which are of
importance. Taps of this construction are manufactured
by the Pratt and Whitney Company. Inserted blade taps
do not adapt themselves to very small sizes of taps. As a
rule, it should not be attempted to make such taps of
TAPER TAPS — MISCELLANEOUS TAPS
276
sizes smaller than 1 J inches or at least not below 1 J inches
in diameter.
Other Examples of Inserted Blade Taps. — In Fig. 121
an inserted blade tap of a design common for pipe taps
Fig. 121. Inseited Blade Pipe Tap
is shown. Here the chasers are held in place by means
of taper pins which wedge the metal of the body firmly
against the blade. The correct location of the blades in
a longitudinal direction is obtained by means of a ring
held to the body by screws. It is plainly seen from the
construction that this tap is not intended to be adjust-
able, but is simply made with inserted blades from an
economical point of view. This design being most com-
monly used for large taps affords a considerable saving in
material. The tap shown in the cut is provided with
interrupted thread as commonly used on pipe taps and
taper taps in general.
Another form of inserted blade tap is shown in Fig. 122.
The blades are here held in place by means of a ring
threaded on the inside to fit the thread of the blades or
chasers, and split and provided with binding screws so as
to make possible a positive grip over the blades. The
advantage of this design is that the threads of the vari-
276
SMALL TOOLS
ous chasers must necessarily be so located as to form a
continuous helix all around the tap, inasmuch as the
threaded ring fits upon the thread in the chasers. But
the design is open to the objection that the ring prevents
threading as far down in a hole as may sometimes be
f—-z
-gi
«!
t-:--.
U
^®
Fig. 122. Burritt's Design of Inserted Blade Pipe Tap
required, and the 'ring may interfere with lugs or pro-
jections in the piece to be threaded. In this respect the
former of the two taps last described is superior, as it is
free from any outside incumbrance and takes up no more
room than a solid tap.
Kind of Steel Used for Taps.
Ordinary carbon steel or tool steel should be used for
all kinds of taps. It is advisable to use a higher grade, or
at least a tougher kind, of steel for machine taps and
stay-bolt taps than for other kinds as they are subjected
to heavy twisting strains.
While high-speed steel has proven itself to be of great
usefulness for cutting tools of general description such as
lathe and planer tools, drills, etc., it has not as yet proven
practicable to make such tools as taps, threading dies, and
chasers, which cannot be ground after hardening, of this
material. The reason for this is that most grades of high-
TAPER TAPS — MISCELLANEOUS TAPS 277
speed steel have to be heated to such a high temperature
when hardening that the sharp edges of the tools to be
hardened are practically melted away, and as a rule, unless
the tool is of such a construction that it can be ground
after hardening, it is almost useless for cutting purposes.
It is not to be inferred from this that it is impossible to
make taps and threading dies from high-speed steel, but the
difficulties encountered in trying to successfully harden
these tools are such that prominent manufacturers hesitate
to undertake the making of tools, that cannot be ground
after hardening, from this material.
The substitution of machine steel for purposes for which
carbon steel was formerly employed is one of the improve-
ments about which Jittle is heard. Nevertheless, some
large concerns use it almost exclusively for dies, taps, and
other cutting tools which require toughness as well as
hardness. A machine-steel tap when skillfully case-hard-
ened will cut as freely and is said to wear practically as well
as one of carbon steel. Besides being cheaper to make, it
will not snap off suddenly when subjected to undue .stress.
It is said that the Singer Manufacturing Company use little
carbon steel in their Elizabethport works, and that all
punches, dies, taps, etc., are generally made from machine
steel, case-hardened.
CHAPTER Vn.
THREADING DIES.
It is undoubtedly true that there is, as a rule, a great
deal more said in the technical press as well as in text-
books on tool-making about making taps than there is
about making threading dies. The reason for this is
probably that while the principles governing tap-making
are fairly well settled and agreed upon, those appertaining
to the making of threading dies are not so well defined.
Besides, dies are not made in such variety as are taps,
nor do they differ from one another very materially, pro-
viding we except the spring screw threading die. How-
ever, the die is used for external thread-cutting just as
often as the tap is used to thread the corresponding
nut, and for this reason threading dies ought to be
given a place equally prominent with taps in the manu-
facture of shop tools.
Spring Screw Threading Dies.
At present no thread- >-- —^
ing dies are used to such / ^^'^^^ \w\
a great extent as are V<^II^33^TrHj
spring screw threading I ^Ty^
dies. Fig. 123. The in- \^ ^^ — ^^
creasing importance of j^. i^s. gp^^ screw Threadiog
automatic screw ma- ^le
chines has been the one
great factor which has added most to the demand for this
class of dies. There is, however, still a great deal to wish
278
THREADING DIES 279
for in regard to the making of these dies, as at present
they are not manufactured exactly as they ought to be.
A simple analysis will bear out this statement.
Requirements of a Threading Die. — There are in general
three main requirements for a threading die. The cut
should be smooth and clean, the thread should be of a
perfect form, and the threaded piece should be of the exact
diameter required. In order to obtain this there are
several points to be taken into consideration.
In the first place it must be observed that a die with a
thread cut perfectly straight or parallel would act exactly
the same as a tap without back taper, that is, a tap having
the same angle diameter at the shank end as at the point.
This question in relation to taps was mentioned in a previ-
ous chapter in connection with the relief of taps. The
trouble encoimtered in using taps made without back taper
will also appear in dies made in the same manner. To
overcome the difficulties arising, and in order to give to
the die a certain amount of back taper, usually called
clearance, dies for the market are generally made a certain
amount over the size required, and then the size to be cut
is obtained by means of an adjusting collar, forcing the
prongs of the die down sufficiently to produce the. correct
diameter required on the piece to be threaded. This will,
of course, give the die a certain back taper, the amount of
which will depend upon the amount over the actual size
the die was originally made. The collar being applied at
the front end of the die, will evidently spring the prongs
more at the point, where it is applied, than further up,
nearer the solid part of the die. This is the general pro-
cedure of making spring screw dies for the market, and we
will now analyze the results, and see whether this die fills
our three main requirements mentioned above.
The die has ample clearance and will abnost invariably
280
SMALL TOOLS
produce a smooth, cleancut thread. The size of the thread
on the threaded piece can also be exactly correct, as the
adjusting collar, usually called clamp collar, can be so
adjusted as to ^ve any size wished for within certain
limits.
Shortcomings of the Commercial Spring Screw Die. — The
form of the thread, however, will not be perfect, as can
wwwv
WWWL
Kg. 124. Distortion of Thread Form in Spring Screw Dies of Usual
Design when Adjusted
readily be seen from the cut, Fig. 124, where the case is
shown exaggerated. By bending the prongs inward the
thread will evidently not move inward at right angles to
the axis of the die, but will move along an arc, thus causing
the thread to be of incorrect angle in the piece cut, one
side of the thread making an angle of more, and one an
angle of less than 30 degrees with the axis.
That this inaccuracy is of importance is even more
evident if we refer to a die with a thread form such as
shown in Pig. 125. Here the angle of the thread is very
slight, and consequently, the bending of the prongs is
distorting the thread-form still more. The piece threaded
THREADING DIES
281
by adjusting a die of this class in this manner can never
be expected to fit very well into a nut provided with a
correct thread.
Fig. 126. Spring Screw Die with Special Threads, and Result of
Adjustment
Preferable Method of Making Spring Screw Dies. — In
order to eliminate the error produced by the -closing in of
the prongs for adjustment by means of a clamp-collar
and still maintain the necessary back taper or clearance,
the correct size should originally be at the front end of
the die, and the diameter of the thread in the die should
gradually increase backward, that is, the die should be
made with back taper from the beginning. On large sizes
this is, of course, very easily accomplished by setting over
the taper bar of the machine where the die is chased out
an amount equal to the amount of back taper desired.
On small sizes, however, this is impractical, and on very
small sizes absolutely impossible. Therefore, in order to
obtain a die made in a way that will produce the results
required, the die must be tapped out from the back end
with a tap that has been cut with the taper required in the
die.
The amount of the clearance mentioned should vary
according to the kind of metal the die is to be used upon,
the clearance being greater for brass than for steel.
Opinions vary as to what is the best amount of back
282 SMALL TOOLS
taper to ^ve to a die. While some consider that a clear-
ance of 0.003 inch per inch is ample for cutting steel or
iron, and 0.005 inch per inch for brass, others claim that
one might give even as much as 0.010 inch per inch
clearance for steel and iron, and 0.015 inch per inch for
dies cutting brass, copper and metals of similar structure.
It may be safe to say that any figure between the extreme
limits given above will prove satisfactory, and that the
exact amount of clearance is comparatively unimportant.
A die made according to the last mentioned method
would, when new, cut a perfectly correct thread. Sup-
pose now that the die should wear, and in order to obtain
the correct size of the thread the adjusting collar had to
be tightened. In such a case a slight error in the form of
the thread would occur, on the grounds mentioned pre-
viously, but considering the way in which this die is
made, the error is reduced to a minimum. In fact, it is
easily seen, that the maximum error, when a die of this
kind is almost worn out, cannot be any greater than
the minimum error occurring in a new die with the same
length of thread cut straight, and made a sufficient
amount oversize to produce the same amount of back
taper by forcing the prongs in at the point.
The reason for' continuing to manufacture spring screw
dies in the old manner, when the superiority of dies made
according to the system outlined is well known by manu-
facturers, is one merely of expense. It would make the
die more expensive to grind on the outside, true with
the thread, as a taper arbor would be more difficult to
make than a straight arbor, but it is unquestionable that
the increase in expense is very slight if compared with the
superior qualities of the die. The grinding of the outside
of the die should never be overlooked by those desiring a
good die, especially if a solid holder is used. It must,
THREADING DIES
288
however, be admitted that most dies made for the market
are not ground on the outside, a fact of which most users
probably are painfully aware, as it takes a great deal of
experimenting and attention to produce desirable results
with dies where the thread is not true with the outside.
It also seems unnecessary to spend so much time and care
in producing a good thread in the die, and then to over-
look a factor equally important to accomplish perfect
results.
Objections to the Method Described. — It has been
objected that it is rather difficult to grind the outside of
spring screw threading dies, particularly the outside of
small dies. It is true that it is difficult to grind some
sizes of dies, but certainly not impossible even under
manufacturing conditions. The advantages gained would
be fully worth the cost of trying to conquer the difficul-
Fig. 126. Spring Screw Die Mounted on Threaded Arbor for Grinding *
ties. As shown in Fig. 126, the die should be held on a
taper threaded arbor, corresponding to the taper in the
die, but the whole length of the die should not be ground
at once. There would, however, be no difficulty in
grinding the die from the point upward for a length about
equal to the length of the thread in the die, as the arbor
and the die for that distance are practically one solid
piece and are well supported by the centers of the
arbor, which of course should not project outside of the
die more than necessary. When this is done the die
should be taken — with the arbor still in place in the die
284 SMALL TOOLS
— and put into a machine equipped with a drawback
mechanism and a spring collet or step chuck (Fig. 127).
The die is then, of course, held by the outside of the
already ground portion of same, and the back can if neces-
sary be supported by the center of the arbor. Any one
making a business of manufacturing spring screw thread-
ing dies would find this operation very inexpensive. The
matter of cost is particularly pointed out in this con-
nection, as it has been claimed that it would be too expen-
sive in ordinary manufacturing to grind spring screw
dies on the outside. But if we consider that a die not
ground on the outside after hardening must be made from
=J3 BE
Kg. 127. Grinding the Outside of Spring Screw IMes
either drawn wire of the correct required size or made
from rough stock, which before being made into die
blanks had to be turned and ground, the question gets a
different aspect. A die ground on the outside after hard-
ening is made from rough stock, rough turned and ready
for grinding after hardening. Right here we have a sav-
ing of either the difference in price of drawn wire and
rough stock or the saving of the cost of grinding the soft
blanks. If we add to this saving the time saved in not
having to be so extremely particular in making the tapped
hole run perfectly true with the outside of the die as
we have to be if the die is not to be ground on the outside
after hardening, we have quite an item to deduct from our
grinding expenses after the dies are hardened. As regards
the difference in the expense in making the die taps and
THREADING DIES
285
hobs there is none. The only increase is the expense of
making the arbor used when grinding the outside of the
die, but when considering that this arbor is made exactly
the same and at the same time as the hob, the expense is
reduced to a minimum.
Clamp Collars. — Another point of great importance in
making spring screw dies cut correctly is the way in which
the prongs or lands of the die are being adjusted to cut the
proper size. The clamp collars generally used for this are
nothing but split steel rings. The adjustment is secured
by means of a screw, and it is readily seen from the cut,
Fig. 128. Usoal Form of Clamp Collar for Spring Screw Dies
Fig. 128, that the action of the steel collar on the prongs of
the die is not uniform, that is, it will not give an equal
pressure to the various prongs. The prongs A and B will
be forced in more than the prongs C and Z>. The result of
this will be a die with its thread out of round, and all the
care and precautions taken in making a perfect die have
become useless by the use of improper means for adjusting
the prongs. Being out of true the die cannot have all the
prongs cutting, which of course is essential in producing
good results.
The only correct principle to apply for adjusting the
286
SMALL TOOLS
prongs is a solid ring which will evenly force all the prongs
equally toward the center. This can be accomplished by
making a solid steel ring with the hole tapered, and tapering
the fluted end of the die to suit the taper in the ring.
-TAPER >■
^
Fig. 129. Taper Collar for Adjusting Spring Screw Dies
(See Fig. 129.) The amount of taper in the ring and on
the prongs will be directly dependent upon the adjustment
wanted in the die.
As, however, this taper ring would require all dies to be
Fig. 130. Special Types of Clamp Collars
tapered towards the point it has not met with general
acceptance. There have been, instead, attempts to improve
upon the old style of clamp collar. In Fig. 130, two such
improvements are shown. The one to the left actually
does embody a decided improvement on the old form, but
THREADING DIES 28T
whether the one shown to the right is superior in any
respect may be open to discussion.
Fluting. — Spring screw dies are generally made with
four flutes, but experience has taught that a die of this
kind wiU almost invariably have only two lands cutting.
A die with three flutes, however, will, even if sKghtly out
of true on account of spring in the hardening, have the
three lands cut evenly, and three flutes are therefore to be
recommended. There is also another advantage gained
by giving a die only three flutes. The lands become wide
and stiff, while the chip-room may still be equally large or
even larger. It may be said as an objection to wide lands
that they will necessarily produce more friction between
the die and the piece to be cut. This can easily be over-
come by milling the prongs as shown in Fig. 131.
When fluting, the kind of material
upon which the die is to be used should
also be considered. If the die is to be
used on soft metals, such as brass, the
cutting face of the prongs is usually
made to come a small amount back
of the center, while on dies used for
Fig. 131. Three-fluted ^^^^^ ^^ ^^^^ ^^ cutting face is radial.
Die with Lands Re- Fluting Cutters. — If the die is made
lieved to Reduce Fric- ^^h three flutes, these should be cut
with a 60-degree angular cutter. If
made with four flutes, however, the cutter should be 48, 45
or 40 degrees according to the size of the die, the 48-degree
cutter being used for the smallest dies, and a 45-degree
cutter for all ordinary sizes. Dies one-half inch in outside
diameter or smaller are usually never made with more than
three lands.
Hardening Spring Screw Dies. — The principal troubles
encountered in the manufacture of spring screw threading
288
SMALL TOOLS
dies are due to difficulties in hardening. In the first place
the lead is liable to be incorrect, due to the shortening of
the prongs in hardening. This difficulty is so much the
more pronounced as the prongs may alter differently from
one another, in which case the die may be perfectly useless.
Li the second place the prongs may spring out of shape in
the form of a curve outward, as shown exaggerated in Fig.
132. In the third place they may twist, as shown in Fig.
rig. 182. Exaggerated View of Prong of Die Sprung Outward in
Hardening
133. That in either case a good thread cannot be cut with
the die is obvious. In the case of the prong springing out
in a curve all the beneficial
effect of the back taper would
be lost. In the case of the
prong twisting, the contact with
the piece to be threaded is -
not on the cutting edge of the
teeth, but back of it, causing
a drag which always makes a
rough thread and is very likely
to break off the screw to be ^*
threaded.
In order to eliminate as much as possible these effects of
hardening it is well to take care not to heat the die back of
Prongs of Die Twisted
in Hardening
THREADING DIES
289
the line ab in Fig. 134, and not to heat it any more than
so that it will harden only to the line cd at the end of the
thread. It is, however, even more effective for preventing
the die from springing out of shape in hardening not to
flute right through the metal into the hole, but to leave a
small amount to be removed when grinding the flutes after
the die has been hardened and finish ground on the outside.
The temper should be drawn to about 430° F.
Chamfer of Threads. — The only point now remaining
to be considered is that of the chamfer, which is, of course,
greatly dependent upon the class of work to be done. It
d b
Fig. 134. Directions for Hardening Spring Screw Dies
is evident that the longer chamfer, or taper on the top of
the threads, one can allow in a die, the better results will
be obtained, as it is obvious that a greater number of
teeth will then do the cutting, and each tooth will have
less to remove. The result will be a smoother thread.
For general use one must, of course, settle upon a certain
length of chamfer. The practice is to chamfer about three
threads, if the die is not expected to cut close to a shoulder.
In the latter case, one, or at most one and one-half thread
of chamfer must suffice.
Dimensions. — The length of the threaded part of a
spring screw die should be directly depending upon the
290
SMALL TOOLS
pitch of the thread. It is common practice to make the
length of the thread equal to about 7 times the pitch. In
Table LXXVI, the length of thread for various pitches
is given.
TABLE LXXVI.
LENGTH OF TmiEAD IN SPRING SCREW DIES FOR VARIOUS
PITCHES.
No. of
Length
No. of
Length
No. of
Length
Threads
of
Threads
of
Threads
of
per Inch.
Thread.
per Inch.
Thread.
per Inch.
Thread.
40
A
16
A
8
{
36
A
14
i
7
1
32
13
A
6
lA
28
24
t
12
11
«
5i
5
20
1
10
^
lA
18
if
9
a
The outside diameters of spring screw dies are made in
certain standard sizes. It is difficult to say what outside
diameter should correspond to a certain diameter of
thread, as practice differs quite widely. In Table LXXVII
dimensions are given for spring screw dies which will be
found to embody the average practice very accurately.
The length of the flute should be about three-fifths of the
length of the die.
Sizes of Hobs for Spring Screw Dies. — It has been pre-
viously mentioned that while a superior die is produced
by threading the die with a taper hob from the back, the
general practice is still to tap the dies with straight taps
a certain amount oversize. The amount which the die
taps should be made oversize for different pitches when the
dies are produced in the latter manner is stated in Table
LXXVIIL
THREADING DIES
291
TABLE LXXVII.
PROPORTIONS OF SPRING SCREW THREADING DIEa
Fig.
186
Diameter
Outside
Length.
Diameter
Outside
Length.
of Cut.
Diameter.
of Cut.
Diameter.
A
B
C
A
B
C
i
i
H
2i
A
i
1
2
3
i
i
1:
2
3
1
f
V
2
3
A
}
I'
2
3
i
i
1
2
3
i
2
2i
31
A
2
21
31
1
2
2i
31
i
n
2*
3i
4
A
ll
2J
2
3i
4
f
11
2i
2i
3i
4
Dimensions of Clamp Collars. — As has been said al-
ready, the clamp collar shown in Fig. 136, although not
the best, is the one most commonly used. In Table LXXIX
dimensions for these clamp collars are given correspond-
ing to the diameters of dies given in Table LXXVII. In
order to facilitate the design of intermediate sizes a set of
approximate formulas for determining the relation between
the dimensions is given below. The various dimensions
denoted by the letters are seen from Fig. 136.
292
SMALL TOOLS
TABLE LXXVIII.
OVERSIZE OF TAPS FOR HOBBING SPRING SCREW DIES WHEN CUT
STRAIGHT.
No. of
No. of
No. of
Threads
Oversiae.
Threads
Oversize.
Threads
Oversize.
per Inch.
per Inch.
per Inch.
4i
0.015
12
0.006
28
0.004
5
0.013
13
0.006
30
0.004
5i
0.012
14
0.005
32
0.004
6
0.010
16
0.005
36
0.004
7
0.008
18
0.005
40
0.003
8
0.007
20
0.005
48
0.003
9
0.007
22
0.005
56
0.003
10
0.006
24
0.004
64
0.002
11
0.006
26
0.004
72
0.002
TABLE LXXIX.
DIMENSIONS OF CLAMP COLLARS FOR SPRING SCREW THREADING
DIES.
Fig.
186
A
B
c
D
E
F
i
A
i
t
%
A
1
1
A
7
u
i|
A
■ "1
1
2
2i
3}
11
If
If
1
THREADING
DIES
The formulas
are:
B-
= l\A
+ i
E
= AA + A
0"
-\A
+ r\
F
= iA + \
Z) =
-lA
+ ^\
298
Roughing and Finishing Spring Screw Dies.
In order to obtain uniform and well-finished threads
when cut with spring-screw threading dies it is well tnown
that it is necessary to use two dies, one for roughing and
one for finishing the thread. In general practice the
roughing die is obtained simply by adjusting a regular
spring screw die of standard size to cut a certain amount
oversize. This, of course, answers the purpose well enough
for most classes of work for which this kind of die is used.
It is evident, however, that there is no great certainty as
to the relative amount of metal removed by each die, and
it is most probable that the roughing die, at least on larger
sizes, is doing far more than its fair portion of the work,
leaving but a small amount of metal for the finishing die
to remove. The latter die should, of course, not perform
as heavy a duty as the former, but it is considered as a
fair proportion to let the roughing die remove two-thirds
and the finishing die one-third of the total amount of
metal to be removed. In order to obtain such a proportion
some firms who perform very close work by means of
spring-screw dies make special roughing dies, enough over
size to permit the finishing die to cut the predetermined
amount of the thread. These roughing dies are provided
with perfectly-shaped threads, simply hobbed out with a
tap which is the desired amount oversize on the top as
well as in the angle of the thread. In this manner the finish-
ing die will remove a certain amount of metal both on the
294
SMALL TOOLS
top and in the angle, thus finishing the whole thread per-
fectly smooth and to the correct fonn.
It must, of course, be determined how much oversize
the roughing die is required in order to leave one-third of
the metal to be removed by the finishing die. This can be
expressed in a simple formula with the pitch of the thread
as the variable. Li Fig. 137 the relative amounts of metal
removed by the respective dies are shown in a diagram;
we have here a United States standard thread where the
Fig. 187. Diagram of Metal Removed, United States Standard Thread
amount of metal represented by the area ABDC is to be
removed by the roughing die and the area BEFGHACD
by the finishing die. The derivation of the formula we
wish to obtain is as follows :
Formvlas for U. S, Standard Thread. — The area, of a
section of a full V thread with the pitch p is
\v^ X cos 30°.
Subtracting from this the amounts
J X 4: P' X cos 30°, and \ X ^p' X cos 30° H-|: p' X cos 30°,
J 04 z 04 04
THREADING DIES 295
which represent the areas deducted from a full V thread in
order to obtain the area of a section of a United States
standard thread, we find this latter area to be
|p'Xcos30°.
o
Consequently the amount of this sectional area to be
removed by the roughing die is
jP'Xcos30°,
and the amount to be removed by the finishing die
ip^X cos 30°.
o
Referring to Fig. 137 we therefore arrive at the following
equation :
KIp -2xX tan 30° Vos30° - J X -rp' X cos 30°
2V8 / 2 64
= |p^ X cos 30°.
Solving this equation gives x = 0.135 p approximately.
The diameter of the tap with which the roughing spring-
screw die is to be produced should thus equal the standard
diameter plus two times 0.135 p. This refers to United
States standard threads.
Formulas for Sharp V thread. — For the same pro-
portions between the amoimt of metal removed by each
die, if a full V thread is to be cut, the formulas are, of
course, derived in the same manner, but have a different
aspect. The area of a section of the thread is
5P^Xcos30°.
296
SMALL TOOLS
The amount of sectional area to be removed by the
roughing die is consequently
ip2Xcos30^
o
Referring to Fig. 138 we arrive at the following equation:
1
I (p -2 xx tan 30°)' cos 30° = ^ p' X cos 30°.
Solving this equation gives x = 0.160 approximately.
Using this value, the diameter of the roughing die is now
easily determined.
Fig. 188. Diagram of Metal Removed, Standard Sharp V Thread
If we wish to give formulas for the results obtained, we
can express them in the following manner:
For the United States standard thread, jB = Z> + 0.27 p.
For sharp V thread, R= D + 0.32 p, in which formulas
R = diameter of roughing die,
D = standard diameter of finishing die, and
1
p = pitch =
number of threads per inch
THREADING DIES 297
It is, of course, of no great importance if the amount
removed by each die is somewhat different from the values
given, the amounts to be removed being arrived at in a
purely arbitrary way from the beginning. But the pro-
portions given conform to the practice of a prominent tool-
manufacturing firm, and the calculations are given to show
that even in a domain largely given over to ''guesswork"
there can be exact calculations made and adhered to. In
tool-making, as a rule, calculations form a very small part,
and altogether too often is ''a few thousandths over" or
''a few thousandths under" considered the only way to
determine certain values which, if once settled upon,
could be formulated by simple figuring so as to serve as a
permanent guide for the tool-maker. It is a mistake to
think that tool-making is so widely different in its nature
from other fields of industrial progress that here no strict
rules can be followed. It must be admitted that there is
perhaps no field of mechanical achievement where opinions
differ so widely as they do in regard to tool-making. But
that is no reason for continuing to consider tool-making as
a business in which no principles or rules can be concen-
trated in simple formulas arrived at in a logical and
common-sense nianner.
Various Classes of Threading Dies.
We have in the preceding pages given particular atten-
tion to one class of dies in the same manner as in the
case of taps we devoted ourselves most particularly to one
class of taps, hand taps. The same fundamental prin-
ciples, of course, hold good for all kinds of dies as were
pointed out with reference to spring screw threading dies.
We can therefore in the following summarize our state-
ments, and shall only dwell upon the more important
points in regard to other classes of dies.
298 SMALL TOOLS
The remaining kinds of dies may be divided into three
general classes — solid dies, which may be either square or
roimd as shown in Fig. 139; adjustable split dies, which
usually are round; and inserted chaser dies, where the
blades, provided with the cutting teeth, are inserted in a
body and secured in some suitable manner.
Solid Dies.
The solid die is used to a great extent on general work,
either in cases where a correct size is not essential or for
roughing a thread before taking a finishing cut with an
Tig. 139. Square and Round Solid Dies
adjustable die. The solid die is not preferable to use when
threads are to be cut requiring a high degree of accuracy.
In the first place, the size when the die is hardened cannot
be depended upon to be exactly the size wanted, as dies
are very apt to ^' go " morQ or less in hardening, and, on
account of their construction, to " go " in an irregular
manner, one land closing up or departing more from the
true axis of the thread than the others. In the second
place, even if the die were correct from the be^nning,
there are no provisions for adjusting it to size when
worn.
Solid Square Dies. — The solid die, as a rule, is of a
square form. It is used principally for threading in bolt
THREADING DIES 299
cutters, and for work of this kind answers its purpose well.
It is also used for pipe dies. In this ease the thread
evidently must be tapered. As a tapered thread in order
to cut a thread smoothly and correctly requires to be
relieved in the angle, and as the difficulties of relieving an
internal thread like that of a pipe die are very great and
it is not customary to do so, pipe dies, and, of course, also
all other taper dies, cannot be used for cutting the
threads of taps, but can only be used for rough work on
pipes and similar soft metal where a perfect thread is not
essential.
Lands and Clearance Holes. — Solid square dies are
always provided with four lands excepting if very large,
when five lands may be preferable. The width of the land
should be about one-twelfth of the circumference of the
screw to be cut with the die, or approximately one-fourth
of the diameter of this screw. The clearance holes should
be laid out so as to provide for this width of land. The
center of the clearance holes should be located a trifle
outside of the circle which measures the diameter of the
screw to be cut. Some makers of dies locate the center
of the clearance holes exactly on this circle, but the clear-
ance holes then become rather small and are easily clogged
with chips which may tear the threads of the screw being
cut and occasionally break the teeth of the threads in the
die.
In very large dies it is not possible to make circular
clearance holes, as these would be required to be of too
large a diameter in order to make the lands of the correct
width. In such cases two clearance holes are drilled
between each two of the lands and connected with a
straight surface as shown in Fig. 140.
The chamfer on the top of the thread should extend for
about three to four threads. It is necessary to relieve the
800
SMALL TOOLS
dies on the top of the thread of the chamfered teeth in
order to make the die cut. If the die should be expected
to cut a thread close up to a
shoulder, the chamfer, of course,
would have to be made propor-
tionally shorter, the same as in
the case of spring screw dies
already mentioned.
As the clearance holes when
drilled do not produce a desirable
cutting edge on the face of the
teeth, the front face must be
filed after the holes are drilled.
They are as a rule filed radial
as shown in Fig. 141. When
the dies are used wholly for threading brass castings and
various other alloys of copper, it is conamon in many shops
o
Fig. 140. Large Size Square
Solid Die, showing Form of
Clearance Holes
Fig. 141. Cutting Edges as Ordi-
narily made
Fig. 142. Cutting Edges with
Negative Rake
to give the face of the cutting edges a negative rake as
shown in Fig. 142. However, opinions differ widely as
to the proper rake to ^ve to the lands of threading dies,
and it is probably as well to make the faces radial in all
cases. As a matter of fact the dies will cut all metals
THREADING DIES
301
ordinarily used in a machine shop to full satisfaction if
made in this manner.
Dimensions of Solid Square Dies. — In regard to the
sizes in which solid square dies should be made, the outside
dimensions evidently depend upon the size of the holders
in which the dies are used. The thickness of the die
should preferably be made not less than one and one-
quarter times the diameter of the screw to be cut with the
die, but manufacturers of dies do not as a rule make their
dies quite so thick. The general rule is to make the thick-
ness about equal to the diameter, at least for sizes of screws
larger than three-quarters inch diameter. In Tables LXXX
and LXXXI.are given the general dimensions of dies as
commonly manufactured, both for regular sizes and pipe
sizes. These dimensions are, of course, given only as a
guidance, there being no particular reason for making the
dies in these sizes excepting that the outside dimensions
being standardized, the number of holders necessary to
use with the dies is reduced to a minimum.
TABLE LXXX.
DIMENSIONS OF SQUARE SOLID BOLT DIES.
Diameter
Size of
Thick-
Diameter
Size of
Thick-
of Thread.
Square.
ness.
of Thread.
Square.
ness.
1
2i
i
i
2i
i
A
2i
i
1
2i
2i
i
li
A
2i
i
li
2\
i
2i
i
If
^
A
2|
i
H
3
i
2}
i
It
3
2i
i
1}
3
U
2i
\
li
3J
u
ll-
2i
i
2
3*
2
302 SMALL TOOLS
TABLE LXXXI.
DIMENSIONS OF SOLID SQUARE PIPE DIES.
Nominal
Size of
Thick-
Nominal
Size of
Thick-
Pipe Size.
Square.
ness.
Pipe Size.
Square.
ness.
2
}
1
3
f
■
2
•'
li
3
i
2
•"
li
4
1
2i
, L
li
4
1
^
2
4
1
■•
2J
. ,
2i
5
u
*
3
. :
3
5
u
It is, however, necessary to call attention to the fact
that on account of the clearance holes the size of the out-
side square must have some minimum relation to the
diameter of the thread to be cut, so that the metal where the
clearance holes are drilled will not become too thin. Even
if strong enough to stand the strain incident to the thread-
cutting operation, a die with too thin metal at the clearance
holes will spring badly out of shape in hardening and will
become a very poor tool for its purpose. The outside size
of the square ought not to be less than double the diameter
of the thread to be cut.
Number of Lands. — While four cutting edges or lands
are sufficient, at least for all dies up to four inches diameter
which cut a full thread, it is necessary to provide more than
four cutting edges in a die used for threading work in which
part of the circumference is cut away. A greater number
of cutting edges is here needed in order to steady and
guide the die and prevent the work from crowding into
the side where the metal is cut away. When more than
one-sixth of the circumference is cut away, it is not advis-
able to try to use dies for cutting the thread. The number
of cutting edges is proportional to the amoimt of the
THREADING DIES
808
circumference of the work cut away and should be as
follows:
Fraction of
Circumference
Cut Away.
Number of
Cutting Edges.
f
5
6
7
8
Split Adjustable Dies.
Split adjustable dies, as said before, are usually round,
as shown in Pig. 143. The split permits the die to be
■P3 H"
M
B
Fig. 143. Bound Split Adjustable
Die
Fig. 144. Die with Grooves for
Adjusting Screws
opened or closed up for adjustment. The countersink A
at the split is for the point of the adjusting screw. The
countersinks B are for the binding screws, which close up
the die to bear upon the point of the adjusting screw.
Instead of countersinking at A and B as shown in Fig. 143
it is cheaper when making these dies in quantities to mill
grooves as shown in Fig. 144. The groove as well as the
304 SMALL TOOLS
countersink for the adjusting screw is usually made 60
degrees inclusive angle, and those for the binding screws
90 degrees.
In order to make the dies more easily adjustable a small
hole is often drilled outside of the clearance hole opposite
the split, as shown at C in Fig. 143. If the dies made are
few they may be split before hardening, as shown in Fig. 145,
with a saw or narrow file, but should not be split all the way
through until after hardening in order to prevent springing
due to this process. When made in large quantities, a hole
Fig. 146. Manner of Splitting Fig. 146. Another Method of
Round Adjustable Die before Splitting Bound Adjustable
Hardening Dies before Hardening
may be drilled outside of the clearance hole where the split
is to come and the groove for the adjusting screw milled
so as to leave a narrow bridge of metal between the hole
and the bottom of the groove as shown in Fig. 146. This
bridge of metal is then removed after hardening by means
of grinding with a thin emery wheel or a bevel wheel with
an acute angle.
Round split dies for sizes up to and including three-
sixteenths inch are given only three lands. All other
sizes are provided with four lands. When hardening
these dies, draw to a blue back of the clearance holes,
in order to insure a good spring temper.
THREADING DIES 806
About three threads should be chamfered and relieved
on the top of the chamfer on the leading side of the die.
Such dies as are intended for use in die stocks should be
chamfered on both sides or ends, in order to permit the
turning of the die and its cutting close up to a shoulder.
In such cases the chamfer on the leading side should be
about three threads as before and on the back side from
one to one and one-half threads. The thread which is to
be cut close to a shoulder should, however, always be
started with the leading side of the die, both because this
side is provided with a longer chamfer and consequently
Fig. 147. Comparison between Common Ways used for Locating
Adjusting Screws
possesses better cutting qualities, and also because of
the guide with which the die stock is provided on the
leading side which is necessary to insure a straight
thread.
There is some difference of opinion as to the best man-
ner of arranging the binding screws for adjustable split
dies. The common arrangement, with two screws, has
been referred to; but an arrangement for four' screws, as
shown in Fig. 147, evidently will close up the various
lands more uniformly and the die will cut more freely.
If adjusted so that the lands do not come at a uniform
distance from the true axis of the die, all the lands will not
306
SMALL TOOLS
eut; or, if they cut, will produce a thread that will be out
of true.
Dimensions. — The outside dimensions of round split
dies are usually made to certain standards to fit a few
holders. Dimensions commonly used are stated in Table
Lxxxn.
TABLE LXXXII.
DIMENSIONS OF ROUND SPLIT ADJUSTABLE DIES.
Diameter
of Thread.
Outside
Diameter
of Die.
Thick-
ness.
Diameter
of Thread.
Outside
Diameter
of Die.
Thick-
ness.
A
a
J
i
2
. s
i
«
^
A
2
A
a
\
2
1
i
«
J
H
2
§
A
}
2
i
tt
2i
i :
A
1
2i
ft
i
f
t
2i
2i
i
n
^
1
2i
H
A
a
^
H
2i
li
i
n
3
H
2*
tt
If there is no necessity of adhering to certain outside
diameters in order to fit holders, the dimensions for these
dies published in the American Machinist, issue of June
29, 1905, answer the purpose very well. These dimen-
sions are given in Table LXXXIII. There is no necessity,
of course, to use as many die-holders as there are different
outside diameters of dies. A couple of holders may be
used, and intermediate sizes which do not fit the holders
may be held by using a split bushing or collar in the holder.
In Fig. 148 two circles C and D are shown. On these circles
are located the centers of the clearance holes, the three
holes having their centers on the inner circle, and the fourth
hole, the one opposite the split, on the outer circle. This
THREADING DIES
307
provides for the springing qualities of the die, and saves
the drilling of an extra, small hole to give necessary
adjusting possibilities. The last mentioned (fourth) hole
is also larger in diameter than the others.
TABLE LXXXIII.
DIMENSIONS OF ROUND SPLIT DIES.
— >
«-— E— >
Fig. 148
Diameter
of
Screw.
Diameter
of Die
Blank.
Diameter
of Large
Center
Circle.
Diameter
of Small
Center
Circle.
Thickness,
of Die.
Diameter
of lArge
Clearance
Hole.
Diameter ^
of Small '
Clearance
Hole.
1
i
i
21
21
2A
2A
2
m
m
H
lA
8
A
*f
M
I
i
A
i
Approximate formulas may be given to express the
relation between the various dimensions. In these for-
mulas.
808 SMALL TOOLS
A = diameter of the screw to be threaded,
B = diameter of the die blank,
C = diameter of outside circle locating clearance hole
opposite split,
D = diameter of inside circle locating other three
clearance holes,
E = thickness of the die,
F = diameter of clearance hole opposite split, and
G = diameter of the remaining three clearance holes.
The approximate formulas are:
5=2.62 A,
(7=1.68 A,
Z)=1.5A,
i?=0.75A,
2^ =0.69 A,
G=0.62A.
Die Holders.
An ordinary lathe die holder is shown in Fig. 149, and
dimensions for holders of this design for the dies in Table
LXXXII are given in Table LXXXIV. A holder for a
smaller size is also specified, as dies for small machine screw
sizes are often made with an outside diameter of five-eighths
inch and a thickness of one-quarter inch. The dimensions
camiot always be adhered to perhaps, but they will be of
value as guidance when proportioning holders of this or
similar kinds.
It will be noticed that the center line of the binding
screws does not fully coincide with the center of the die
in the longitudinal direction, but that the screws apparently
THREADING DIES 809
are located 0.010 inch too far in. This is for the purpose of
forcing the dies soUdly toward the bottom of the recess,
the screws exerting a wedge action on the dies in the
countersinks or milled grooves provided for the point of
the screws.
Approximate formulas may be found from which well-
proportioned holders for other sizes than those ^ven in
the table may be made. In the formulas,
d = outside diameter of die,
A = diameter of recess,
B = depth of recess = thickness of die,
C = outside diameter of holder,
D = diameter of hole in shank,
E = diameter of shank,
F = length of body,
G = length of shank,
H = total length,
/ = size of adjusting and binding screws, and
K = distance from end of holdera to center of screws.
The following formulas give results approximately as
stated in Table LXXXIV.
A-
= d + (0.004 d + 0.005),
C-
ll<i + l
= 8 '
G-
= 3B,
D-
9d
= I6'
H'
95
= 2'
E-
3d + l
= 4 '
I =
d, 3
"8+32'
F-
3B
= T'
K =
= 1 + 0.010.
310
SMALL TOOLS
TABLE LXXXIV.
I
DIMENSIONS OF DIE HOLDERS FOR USE IN ORDINARY LATHE.
Fig. 149
•3 ^
.S H £
1^
5-8
II
0.632
0.821
1.009
1.511
2.013
2.515
1
i
I
ft
1
3ft
I
i
1
H
H
i
i
ft
1
a
i
i
H
li
IJ
2ft
H
H
iti
2i
2«
3ft
i
A
i
0.135
0.135
0.197
0.260
0.322
0.354
Holder for Spring Screw Dies.
In Fig. 150 is shown a holder for spring screw threading
dies which gives to the spring screw die all the qualities of
a solid die without losing any of the adjustable qualities of
the spring die.
It will be seen from the cut that the die is held rigidly
within a solid holder A, the shank of which fits the regular
die holder or chuck. The screws B hold the die in place.
THREADING DIES
Sll
The screws C adjust the die in regard to the size indepen-
dently of one another. These separate adjustments are
convenient, for it is often necessary to adjust one jaw more
than another. The screws D give a backing to the jaws
and prevent them from springing away from the cut. A
hardened bushing E, held in front of the die, guides the
work when entering the die so that the thread will be con-
centric with the blank. The holes F permit the oil to
enter the die and the chips to pass away from the cut.
Fig. 160. Special Holder for Spring Screw Threading Dies
WTien adjusting the die use a master screw. Screw it
into the die through the bushing and adjust the jaws until
they barely touch the thread of the master screw. The
die is then ready for use. The first screw made should be
gauged, and readjustment should be made according to
requirements. A little practice will enable the operator
to adjust the die without any trouble. This holder will
also be found to be convenient for holding the die when
rehobbing it. Often one jaw needs more hobbing than
another, and by means of the screws C this can be accom-
plished. The bushing E will be found to be an excellent
guide for the hob.
312 SMALL TOOLS
Inserted Chaser Dies.
Inserted chaser dies may be of two kinds — those which
have the chasers driven solidly in place, and those having
chasers easily removable. It is evident that the latter
form is the superior, but it is also the more complicated
and expensive form.
Inserted Chaser Dies with Fixed Chasers. — If we first
consider the case of the dies with the blades solidly in place,
we may safely say that it is not advisable to attempt to
make small dies with inserted blades; but for dies larger
than If or 2 inches in many shops a ring of machine steel
or cast iron is made having slots in which are inserted
blades made of tool steel. The first cost of a die may not
be any less when made by this method, but the cost of new
blades is much less than the cost of a new solid die. Then,
again, unlcvss large dies are pack-hardened there is con-
siderable danger of cracking, which is, of course, largely
done away with when only the blades are hardened.
The slots to receive the blades should be so made that
the front edge of the blade will be radial, as was
shown in Fig. 151. The slot must
be wider at the bottom than at the
top, as shown, in order that the blade
may be drawn on to its seating and
kept from drawing away from it when
in use.
Inserted blade dies may be made
either solid or adjustable. When made 'ferted Biade^Die^"
solid they are tapped with a hob the same
size as the screw to be cut by the die; when made adjust-
able, they should be tapped with a hob a few thousandths
of an inch larger than the size of the screw, to provide
clearance to the land when cutting. For adjustable inserted
THREADING DIES
313
blade dies the method of adjusting for size varies in differ-
ent shops. Some mechanics consider it best to make them
to adjust as shown in Fig. 152, while others claim best
Fig. 162. Adjustable Inserted Blade Die
results if provided with adjustment as described under
adjustable dies in a previous portion of this chapter.
Fig. 153. Inserted Chaser Die with Adjustable Blades
Inserted Chaser Die vnth Removable Blades. — A typical
construction of inserted chaser dies with easily removable
blades is shown in Fig. 153, This die consists of four
314
SMALL TOOLS
chasers or blades inserted in radial slots in a body or
collet, the chasers as well as the collet being enclosed in a
die ring. This ring is beveled on the inside to fit a corre-
sponding bevel on the back of the chasers. It can be
screwed up or down on the collet, thus pushing the chasers
in or permitting them to recede from the center. Screws
are provided bearing in slots of the chasers for holding the
latter in place after having been adjusted by means of the
ring.
The chasers must, of course, be made in sets so that each
is, so to speak, one-quarter of a thread ahead of the follow-
ing one, or in other words, the teeth on the chasers must
Fig. 164. Another Type of Inserted Chaser Die with Adjustable Blades
all form one continuous thread around the die. The die
shown in Fig. 153 is known as the Wdodbridge adjustable
die. The shank is in one solid piece with the body. An-
other form of inserted chaser die is shown in Fig. 154.
Here the shank is screwed into the body and secured to
it by means of a pin G. The screw A serves the purpose
of locking the die ring B to the body as soon as the chasers
are properly adjusted. The principle of securing the
chasers is exactly the same as in the die previously de-
scribed.
THREADING DIES 316
The object of inserted chaser dies is the adjustment
possible and the saving caused by being able to use the
same body and ring for an indefinite period, the chasers
only being replaced when worn. Only the chasers are
made from tool steel, the remaining parts being machine
steel. As there is a considerable element of waste in being
obliged to throw away a solid or adjustable die made
from expensive steel whenever the cutting edges are worn
away, it is obvious that the economy of replacing the
cutting edges only is well worth consideration.
Grinding Threading Dies.
The grinding of the chamfer on the leading end of
(lies and die chasers is of great importance. The prin-
ciple involved is the same in all classes of dies, but
as an example we will refer to the spring screw dies
shown in Figs. 155 and 156. The die may be to all
appearances in perfect condition for doing good work
and have an equal chamfer on every land, but the
chamfer may not be of a kind that actually does much
good. In nine cases out of ten, in manufactured dies,
one will find that the chamfer is made on the lines
indicated in Fig. 155, which is, to any one analyzing
the subject, entirely wrong. This die has the appear-
ance, when examined, of having a very liberal cham-
fer, but the actual fact is that this die has only about
1 to IJ threads chamfered. Now, these 1^ threads will
have all the cutting to do, and, consequently, will have a
tendency to "dig in.'' The land that digs into the metal
first will, of coui-se, leave little or nothing for the other
lands to cut. If a die is otherwise well made in all respects,
and then has a chamfer like the one shown in Fig. 156,
there will be no difficulty. The thread of the die should
316
SMALL TOOLS
never be chamfered more than to the root of the thread.
Whatever chamfer is made below this line is absolutely
useless unless it be that the turret and spindle of the screw
Fig. 165. Incorrect Way of Grinding Chamfer on Dies
machine in which the die is used should be so much out of
line that the die would have to act as a guide for the blank ^
in which case a chamfer like that shown in Fig. 155 would
be quite useful. It might also be argued that a die held
Fig. 156. Correct Way of Grinding Dies
in a loose die holder must have a chamfer like that shown
in Kg. 155, in order to start properly, but even in this
case a chamfer as shown in Fig. 156 should be used, and
the blank to be threaded should be chamfered before it is
presented to the die.
THREADING DIES 317
Self-opening Dies.
A treatise on dies would not be complete without
mentioning self-opening dies. These are used particu-
larly when cutting long threads. When the die has cut
a screw the desired length, the cutting edges recede from
the work, ob\dating the necessity of backing oflf the die.
Thus for work on long screws valuable time is saved, and
the tendency of the die to alter the shape of the thread
when bacldng off is done away with.
There are many forms of self-opening dies, and to
attempt a description of them all would be out of the
question. One of the simpler ones was described by
E. R. Markham in Machinery^ June, 1904. This form,
however, is not claimed to be the most satisfactory when
in use, but some dies on the market which give excellent
results are made for the trade in shops equipped with
special tools which render it impossible with the ordinary
machine-shop equipment to make a die at anywhere near
the figure they can be purchased for. While the self-
opening die shown in Fig. 157 is not claimed as the best,
it works very well, and is commendable because it can
be made in the ordinary shop.
The cutting edges are located on the ends of two mov-
able jaws, or sliding pieces; these are placed in a slot
cut in the head. They are 'moved toward the center by
means of inclined cuts in the ring, as shown. To open
the die turn the ring to allow the end of the sliding pieces to
go into the deepest part of the inclined cut. A spring
in each slide forces them against the cut in the ring. The
ring B is made to fit on body A, which contains the slot to
receive the movable jaws C, C which, in turn, are kept in
place by means of the plate D.
The length of the threaded part of the screw is governed
818
SMALL TOOLS
by the location of the dog E, which is movable on and
fastened to plunger F. The dog projects through a slot
into the hole in the shank, making it possible for the screw
to strike it, thus forcing the plunger out of the hole in the
adjustable ring G. This ring is adjustable on head ring
B and is fastened to it by means of set screw //, which
adjustment is necessary in order to alter the cutting size
of the die. Plunger F is movable through collar /, which
.G
Fig. 157. Simple Design of Self-Opening Die
is securely fastened to the head by means of a pointed
set screw, as shown. A coil spring forces the plunger
into the hole in the adjustable collar G, when it is turned
to a position that insures the die cutting the correct size.
The movable pieces C, C are moved toward the center by
meaas of the inclined surfaces on the inner side of ring B,
When the plunger is forced out of the hole in collar G, the
springs acting on the sliding pieces C, C force them against
the inclined surfaces in the outer ring, causing it to turn,
thus allowing the die to open.
CHAPTER VIII.
PLAIN AND SIDE MILLING CUTTERS.
Introductory.
The milling cutter, although a comparatively recently
introduced tool, is probably one of the most universally
used in the modem machine shop. There is no tool which
has so completely revolutionized machine-shop practice,
changed the methods formerly in vogue as well as influ-
enced the design and development of machine tools, as
has the milling cutter and its necessary companion, the
milling machine. All this change has been brought
about in a comparatively short time. For although the
milling machine itself is not of so recent origin, it may be
said without exaggeration that the milling machine has
gained most of its prestige during the last fifteen years.
The general adaptation of the process of milling to so
many operations formerly done on as many machines,
and the decreased need for individual skill, have been the
greatest factors in its successful stride for recognition.
Not only is the milling machine to-day doing a great deal
of the work which years ago had to be done in the planer,
shaper, slotting machine, and the gear planing machine,
but during the last three or four years the newly developed
thread milling machine has to a great extent superseded
the old methods of cutting screw threads in the lathe.
The milling cutter, the development of which neces-
sarily had to follow the development of the machine,
must therefore perform almost any function performed
by any other machinist's tool, but evidently the variety
810
320 SMALL TOOLS
of duties calls for a great variety in the design of
cutters.
The forms of the teeth of milling cutters differ in many-
respects from the shape of the single-edged tool. The
teeth are usually weaker than the tools, inasmuch as the
back of the teeth must be milled away to provide clear-
ance for chips. The teeth are, as a rule, not provided
with top rake, or front rake, which is a more correct
expression in the case of milling cutter teeth', but are
usually milled radial. On all regular milling cutters,
when the grooves between the teeth are milled, a small
flat is left at the point of the teeth, which is termed " land;"
this land is backed off sufficiently to provide for the cut-
ting rake of the teeth.
After these general remarks we are ready to enter upon
a detailed description of milling cutters. As said pre-
viously, the great variety of work done by milling cutters
and the wide difference between the operations performed
necessitate so great a variety in kinds, styles, and forms,
that it would not be possible to treat them all under a
general heading. For this reason we will follow the prac-
tice we adopted in the case of taps and dies, that of treat-
ing the most commonly used as completely as possible,
analyzing the principles involved in connection with
them, and giving but the necessary general information
in regard to the less commonly used.
Plain Milling Cutters.
Conditions Limiting the Size of Plain Milling Cidters. —
By far the most commonly used of all cutters are plain
milling cutters. Fig. 158. These are generally manu-
factured in sizes from two to five inches in diameter, and
up to six inches in width or length. They may, of
PLAIN AND SIDE MILLING CUTTERS
321
course, be made in sizes even larger than this, and the
limit for the diameter given, five inches, for instanxje, is
only arbitrary. Cutters up to ten and twelve inches in
diameter are sometimes made solid. It must be remarked,
however, that cutters of more than five inches diameter
ought to be made of the inserted-tooth style, that is,
with tool-steel blades inserted into a body made of
machine steel or cast iron. If the cutter is made in this
manner, it will even be cheaper to have high-speed steel
blades inserted in a steel or cast-iron body than to make
Fig. 168. Plain Milling Cutter
the cutter solid out of common ordinary tool steel. The
inserted-blade milling cutter will, under all circumstances,
be cheaper in the long run, because when the tool-
steel cutters are worn out the body can be used for
another set of cutters or blades, it being necessary to
replace the latter only. In this connection it may be well
to say that the opinions of milling-machine operators
differ as to the superiority of high-speed steel for milling
cutters; and when we referred to the use of this steel for
blades for inserted-tooth milling cutters, it was done
more as a reference to common practice than as an
822 SMALL TOOLS
advice in the matter. We will return later to the
opinions as to the use of high-speed steel for milling
cutters.
In regard to the width of solid milling cutters, while
here too such dimensions as six or eight inches face pre-
vail more or less commonly, it is not good practice to
make cutters of such a width. Four inches width of
face may be considered as the maximum in good practice,
and when greater length of cutter is required it should be
made in two or more interlocking sections. The style of
interlock used for plain milling cutters will be treated
later. There are two very strong reasons why not only
the maker or manufacturer of cutters but also the user
should prefer wide-face cutters made in sections, at least
when the commercial side of the question is considered.
And the commercial side necessarily must be considered,
as this is the cause which has led to our present highly
developed machine-shop practice.
In the first place, the difficulty and the risk taken by
the manufacturer in the various operations when making
cutters of very large dimensions, and particularly the
risk due to the liability of such large tools cracking in
hardening, is a very pronounced reason why it is not
profitable to undertake to make large cutters solid. When
in use the risk taken with a solid cutter is greater than
with one made in sections. If for any reason some part
of the cutter should meet with an accident and become
damaged, the whole cutter must be replaced. If the cutter
is made in sections, only the portion which has been
injured will need to be replaced. It is evident that the
first cost of interlocked cutters will be somewhat higher
than that of solid cutters, but it is fairly safe to say that,
all considered, the cutter made in sections will in the end
prove to be by far the cheaper one.
PLAIN AND SIDE MILLING CUTTERS 323
The Influence of the Diameter of CvMer on Time Required
for Traversing the Work. — When speaking of the size of
milling cutters some attention must be paid to the desira-
bility of making the diameter of cutters as small as
consistent with practical considerations. This is of advant-
age, in the first place, on account of the saving in material
possible; secondly, because the power required for taking
the cut when the cutter is in use becomes smaller on
account of the smaller turning moment; and thirdly,
because the distance the center of the cutter has to move
for a given length of surface cut becomes smaller in pro-
portion to the size of the milling cutter itself. As this
distance evidently is proportional to the time used for
traversing the work, it is clear that a smaller diameter
cutter involves a saving in time needed to perform a
certain milling operation and consequently in the
expense. Small-diameter cutters are therefore a great
saving in many respects, provided, of course, that the
cutters are large enough to have sufficient strength, and
can be provided with teeth heavy enough for the opera-
tion for which they are intended.
The influence of the diameter of the cutter on the
time required to traverse a piece of work can be most
easily understood by referring to Fig. 159. If A is the
piece to be milled, B sl milling cutter of a diameter twice
as large as the diameter of the cutter C, and DE the
surface to be milled, it is plainly seen that the center
of large cutters must travel from F to G in order to
traverse the piece of work, while the small cutter must
travel only from H io K, s, considerably shorter distance.
It will be seen that the actual saving in length of travel,
FG — HKy is constant, whatever be the length of the
work, other conditions being equal. From this we can
draw the conclusion that the relative saving, that is, the
824
SMALL TOOLS
percentage of time saved, is greater in the case of short
cuts than in the case of long ones, and, in fact, for very
long surface cuts it probably will be so small as to be
disregarded altogether. However, for short cuts, the Brown
and Sharpe Company states that a difference of only half
an inch in diameter has been found to make a saving of
10 per cent in the cost of the work in their own shops.
Conditions Governing the Minimum Size of Cutters. —
While thus a small cutter is desirable, we must carefully
Fig. 159. Influence of Diameter of Cutter on Time Required for
Traversing the Work
note the conditions governing the minimum size practi-
cable. In the first place, the hole through the cutter
must be large enough to permit the use of an arbor
strong enough to transmit the necessary power for driv-
ing the cutter without undue vibrations. The metal
between the hole and the bottom of the grooves between
the teeth must be strong enough not only between the
hole and the groove as measured at A, Fig. 160, but
between the key-way and the bottom of the groove as
measured at 6. This is the place where cutters con-
structed too weak usually fail. It may be said that
PLAIN AND SIDE MILLING CUTTERS
325
less than three-eighths inch metal is not advisable to
use. Finally, the diameter must be large enough to per-
mit a groove of coirect shape to be cut and permit proper
space between the teeth. It
is obvious that if the teeth
are spaced close together the
groove will be proportionally
less in depth, and the diameter
of the cutter can consequently
be made smaller; however, the
spacing of the teeth should
not be influenced by the
endeavor to diminish the di-
ameter of the cutter, as this
would spoil the eflSciency of
the cutter in other respects.
It may also be proper to say that a narrow-face cutter
as a rule can be of less heavy construction, diametri-
cally, than a wide-face one, because, as a rule, the stresses
in the cutter become proportionally greater as the width
of the face increases.
Fig. 160. The Weakest Parts of
a Milling Cutter
Number of Teeth.
As to the number of teeth in plain milling cutters there
is considerable difference of opinion. The practice of the
Pratt and Whitney Company, which has been one of the
pioneers in cutter manufacturing, corresponds very nearly
to the formula
5 D -f 24
N-
in which formula
N = the number of teeth and
D = the diameter of cutter.
826
SMALL TOOLS
The numbers of teeth figured from this formula are
given in Table LXXXV. Of course, plain milling cutters
are always given an even number of teeth, and the values
figured from the formula will only be approximate.
TABLE LXXXV.
NUMBER OF TEETH IN PLAIN MILLING CUTTERS.
XT * * *u 5 X diam. + 24
No. of teeth = •
Diameter of
Number of
Diameter of
Number of
Cutter.
Teeth.
Cutter.
Teeth.
2
16
5i
26
2i .
18
6
26
2i
18
6i
28
2}
18
7
30
3
20
71
30
3i
20
8
32
4
22
9
34
4*
24
10
36
5
24
It will be noticed by examining the number of teeth
given in the table and comparing them with the diameters
that the spacing of the teeth becomes very much coarser
as the diameters increase. Thus, the pitch of the cutter,
or the distance on the circumference from cutting edge to
cutting edge, is about three-eighths inch for a two-inch
cutter, nine-sixteenths for a four-inch, and more than one
inch for a ten-inch diameter cutter. This practice has
been found to be satisfactory for all ordinary milling.
English Rule for Nnmber of Teeth. — When milling
cutters first were made very little attention was paid to
spacing the teeth of larger diameter cutters differently
from those of small diameters. The teeth were also too
fine, which resulted in the crowding of the chips as well as
PLAIN AND SIDE MILLING CUTTERS
327
the breaking of the teeth. Even now it is claimed by
some persons who deserve credit as authorities on the
subject that a spacing of one-quarter to three-eighths inch
distance from tooth to tooth is enough for any size milling
cutter. However, it is open to question if this works
well for anything but finishing cutters. Roughing cuttei's,
ajid cutters for brass in particular, should have coarser
pitch.
TABLE LXXXVI.
NUMBER OF TEETH IN PLAIN MILLING CUTTERS.
Pitch of teeth ••
Vdiam. x 8
16
Diameter of
Number of
Diameter of
Number of
Cutter.
Teeth.
Cutter.
Teeth.
2
26
5i
42
2i
26
6
44
2i
28
6J
46
2}
30
7
46
3
30
7J
48
Zi
34
8
50
4
38
9
54
4i
38
10
56
5
40
A rule given by an English writer for cutters from four
to fifteen inches in diameter is expressed in the formula
P =
VDXS
16
where
P = pitch of teeth and
D = diameter of cutter.
This rule gives a pitch of nearly three-eighths inch for a
four-inch cutter, one-half inch for an eight-inch, and five-
eighths inch for a twelve-inch diameter cutter. It will be
seen that this pitch, although gradually increasing, gives
328 SMALL TOOLS
far finer spacing, and consequently a larger number of
teeth, than the rule expressed in our first formula for the
niraiber of teeth in cutters. The numbers of teeth accord-
ing to the last formula are given in Table LXXXVI.
These values should be used onl}^ for cutters used for
finishing or for those taking very moderate roughing cuts.
German Rvle far Number of Teeth. — While it may seem
unnecessary to place on record any more formulas for
obtaining the number of teeth in milling cutters, still in
order to give a complete review of present practice the
following formula, of German origin, may be of interest.
According to this
in which formula
P — pitch of teeth,
D = diameter of cutter, and
C = a constant the value of which varies for various
diameters. Thus, for cutters up to 2 inches
diameter C = A. inch
For cutters from
2 inches to 4 inches diameter C = A inch
4 inches to 4f inches diameter C = \ inch
4f inches to 6 inches diameter C = A inch
6 inches to 7 J inches diameter C = A inch
7i inches to 8 inches diameter C = 0 inch.
According to this formula, which admittedly is rather
cumbersome to use, the pitch for a two-inch cutter would
be approximately three-eighths inch, for a four-inch about
nine-sixteenths, and for a ten-inch diameter cutter one
inch; these values correspond very closely with those found
from the formula based on the practice of the Pratt and
Whitney Company.
PLAIN AND SIDE MILLING CUTTERS 329
In the last formula, as well as in the former one where
the pitch was found and not the number of teeth, the latter
value is, of course, found by dividing the circumference of
the cutter by the pitch. Thus, if N equals the number of
teeth in the cutter, P the pitch, and D the diameter of the
cutter as before, we have
,, TzD 3.14 P
Suppose we wish to obtain the number of teeth in a
cutter 6 inches in diameter with the teeth spaced for finish-
ing according to the formula P = — -r — previously given.
We first find the pitch,
— jg — == "le" = 16 (approximately).
We now apply this value of the pitch to our formula for
the number of teeth:
,, 3.14X6 301.4 .^ , • 4. 1 X
N = z — = — =— = 43 (approximately).
16
The number of teeth selected would, of course, be an
even number, that is 44.
It may be well once more to remark that this fine
spacing, while it may be all right and even desirable for
smooth finishing cuts, is not well suited for general prac-
tice. Besides, experiments have proven that less power
is required to drive coarsely pitched cutters than those
of fine pitch. The result of these experiments shows that
for two four-inch cutters the one having 30 and the other
only 15 teeth to the circumference, the ratio of the power
required to drive the cutters, all conditions being equal,
was 13.5 : 10.5, or in other words, the finely pitched cut-
330
SMALL TOOLS
ter required nearly 30 per cent more power to perform a
certain amount of work than did the coarsely pitched
one. This certainly is eAddence that ought to prove
conclusively that fine pitches on milling cutters should be
avoided.
TABLE LXXXVII.
LEAD OF SPIRAL FOR PLAIN MILLING CUTTERS.
Spiral = 9 X diameter + 4.
Diameter of
Cutter.
Lead of
Spiral in
Inches.
Diameter of
Cutter.
Lead of
Spiral in
Inches.
2
2i
2i
2}
3
3i
4
^
5
22
24i
2^
28f
31
35i
40
44i
49
5i
6
?*
8
9
10
53^
58
62^
67
7H
76
85
94
Spiral-cut Milling Cutters. — The teeth of plain milling
cutters should preferably be cut spiral.* While all cutters
ought to be cut spiral, whatever be the width of the face,
it has become a practice among manufacturers of cutters
to cut the teeth straight on narrow cutters, that is, cutters
up to about three-quarters inch thickness. The amount
of spiral is commonly expressed by stating the distance
along the axis of the cutter corresponding to one com-
plete turn of the spiral. If we denote this amount by 8
and the diameter of the cutter by Z), we may write the
formula
5 = 9 Z) + 4.
* " Helical" is, of course, the more correct expression, but as the word
" spiral " is commonly used to express the helix of milling cutters, this
word will be used.
PLAIN AND SIDE MILLING CUTTERS
331
Thus, if a cutter is six inches in diameter, the spiral should
make one turn around the cutter in
9 X 6 + 4 = 58 inches.
The amount of spiral for various diameters figured
from this formula is given in Table LXXXVII.
Nicked Milling Cutters. — In some cases it is preferred
to have cutters with the teeth cut straight, no matter
what width of face. One reason for this is that a spiral
cutter necessarily produces a certain amount of end
thrust, and when used in special machines not properly
SECTION ON A-B
Fig. 161. Milling Cutters with Nicked Teeth
designed to take up a great deal of pressure in the longi-
tudinal direction of the spindle it may be desirable to use
a cutter with the teeth cut straight. Of course there
would be no need for this in any modem, standard milling
machine. When the teeth are cut straight, in order to break
up the length of the cut, small grooves are cut at proper
intervals in the lands of each tooth in such a manner that
the grooves in one tooth come in the center of the cutting
portion between the two grooves in the next tooth, as
shown in the upper and lower cutting edges in Fig. 161.
Cutters, the cutting edges of which are notched by this
332
SMALL TOOLS
method, are generally termed "cutters with nicked cut-
ting edges." Very often the cutting edges of spiral-teeth
cutters are also nicked, particularly when the face is wide;
but whether this actually improves the cutting qualities of
the cutter may be open to question inasmuch as the cut is
continually broken up anjrway owing to the spiral of the
cutting edge.
Fluting Cutters for Plain Milling Cutters. — Plain milling
Fig. 162 Fig. 163
Fluting Cutters for Plain Milling Cutters
cutters, with the teeth cut spiral, should be fluted with a
cutter having 60 degrees included angle, 12 degrees on
one side and 48 degrees on the other, as shown in Kg..
162. Most manufacturers of small tools make for the
market cutters for fluting spiral mills having an inclusive
angle of 52 degrees only, 12 degrees on one side and 40 on
the other. These cutters, however, produce too weak
and unsupported a tooth and as a matter of fact the
manufacturers themselves use a 60-degree cutter for
PLAIN AND SIDE MILLING CUTTERS
333
cutting the teeth of the cutters of their own manu-
facture. When cutters are provided with straight teeth a
grooving cutter as shown in Fig. 163 should be used.
This is a regular 60-degree angular cutter.
The angular cutter for producing the teeth should
have the comers of the teeth slightly rounded rather
than sharp. The amount of round need be but slight,
Fig. 164. Cutting Radial
Teetli in Milling Cutter
Fig. 166. Cutting Teeth
with Negative Rake
but it makes a stronger cutter when the grooves are cut a
trifle rounding in the bottom and it also reduces the ten-
dency to crack when the cutter is hardened, sharp comers
being an invitation to crack.
Cvtting the Teeth of Plain Milling Cviters. — While the
teeth of all ordinary milling cutters are cut radial as
shown in Fig. 164, some persons very familiar with the best
shop practice claim that a certain amount of negative
front rake, as shown in Fig. 165, is sometimes desirable,
834 SMALL TOOLS
particularly when the cutter is to be used on brass.
There are, however, differences of opinion in this respect,
because on the other hand there are good reasons why
milling cutters should be given a slight positive front
rake in order to improve their cutting qualities. This has
not been the practice so far, but it may become rec-
ognized . that here is an opportunity for improvement.
Mr. A. L. De Leeuw in Machinery for May, 1906, calls
attention to the fact that the use of a positive front rake
in milling cutter teeth is not as common as it ought to be.
He says that while it is true that not every cutter can be
used with front rake, a great number that ought to have
front rake are not provided with it. There are two
main reasons why the rake for a milling cutter may not
be advisable; one is that a cutter ground with rake is
liable to produce a rather poor surface; the other is that
the spaces between the teeth are liable to be filled up with
chips. It is generally easy to avoid trouble on the latter
score by providing means for washing the chips away.
As far as the first reason is concerned, this is not quite so
bad as it looks. In the first place, where one operation is
done on a great number of parts it would be easy to have
two cutters, one for roughing and one for finishing. This
is something which, for some reason, is too much neglected
in milling practice, perhaps for the reason that not so long
ago most shops had only one or two milling machines,
which were mainly used for tool work, or such operations
as could not possibly be done on any other machine. As
a consequence, there was a very great number of costly
milling cutters for only one or two machines. It was
quite natural, then, that this large number of cutters was
not doubled again so as to get one cutter for roughing and
one for finishing. As a rough surface was positively
inadmissible, it followed that the cutter had to be made in
PLAIN AND SIDE MILLING CUTTERS
335
such a way that a good surface was produced. That the
cutter was not a decided success as a roughing cutter
was only regretted (if it was noticed at all). Now that
the milling machine is beginning to be recognized as a
factor in the rapid production of work in manufacturing
shops, it seems that the time is past when people can be
satisfied* with a slow cut, because the same cutter which
takes a fast cut will not make
a good surface.
Fig. 166 shows a cutter milled
with positive front rake. It
must be understood that such
cutters are not suited for finish-
ing cuts, but only for roughing. I
In milling the teeth it is neces- \ -^j..
sary to leave a slight portion V I
at the top of the tooth flat; this
portion is termed "land," and ^. ^^^ ^^.,^. ^^ ^^ ^ ^^
. , -, , 1 . \ .1 Fig. 166. MiUing Cutter Teeth
IS ground after hardemng to the ^^^ p^gj^^^ ^,^^^ ^^^
required angle to give keenness
to the cutting edge. The width of the land varies for
different pitches of teeth, and consequently for different
diameters. The values for the dimension of the width
of the land are given in Table LXXXVIII.
\ !
TABLE LXXXVIII.
WIDTH OF LAND OF PLAIN AND SIDE MILLING CUTTERS.
Diameter of
Width of
Diameter of
Width of
Cutter.
Land.
Cutter.
Land.
2
A
5
A
2i
6
A
3
^
7
A
3i
A
8
4
• A
10
A
336
SMALL TOOLS
Allowance for Grinding. — The hole in the cutter should
be left about 0.005 inch under size before hardening and
ground to size when hardened. In order to facilitate this
grinding it is advisable to recess the hole as shown in Fig.
167. The ends of the cutter must also be ground so as to
oflFer true surfaces for the ground clamp collars to bear
against. A considerable saving when grinding the ends
is afforded by recessing as shown in Pig. 168, thereby
Fig. 167. Cutter with Hole
Recessed to Facilitate Grind-
ing
Fig. 168. Ends of Cutter Recessed
to Save Grinding more than
Actual Hubs
producing a hub, which is the only portion of the end
requiring to be ground. The diameter of the hub should
not be less than the diameter of the hole in the cutter
plus three-quarters inch. All corners should be care-
fully rounded when recessing, as any sharp corners are
liable to produce cracks in hardening.
Key-ways. — In commenting upon the diameter to select
for milling cutters, one of the conditions governing the size
was the strength of the metal betweeij the key-way and
the bottom of the groove between the teeth. This key-
PLAIN AND SIDE MILLING CUTTERS
887
way causes a great deal of confusion to users as well as to
makers of cutters, as there is not as yet any universally
adopted standard as to the size of the key-way. Manu-
facturers of cutters are trying to establish a standard for
square as well as for half-round splines, which, if adopted
by all users, would save a great deal of expense and diflS-
culty and add to the interchangeability of the cutters.
These standards are given in Tables LXXXIX and XC.
TABLE LXXXIX.
STANDARD KEY-WAYS FOR MILLING CUTTERS.— SQUARE.
D -= Diam. of Hole.
il= Width of
Key-way.
B = Depth
of Key-way.
C = Radius
of Ctornere.
1 to A inch.
f
A
0.002
to inch.
^
0.030
f to 1 inch.
A
A
0.035
1^ to 1 inch.
^
f
0.040
1^ to 1 inch.
i
0.050
l|} to 2 inch.
%
0.060
2 A to 2i inch.
1
0.060
2A to 3 inch.
A
A
0.060
Hardening.
With regard to the hardening of milling cutters a great
deal has been written, but there can be very little said
that is definite enough to actually benefit any one who is
trying to learn hardening theoretically. Experience and
338
SMALL TOOLS
TABLE XC.
STANDARD KEY-WAYS FOR MILLING CUTTERS.
— HALF ROUND.
D = Diam. of Hole.
A = Width
of Key-way.
B = Depth
of Key-way.
} to f inch.
U to If inch.
J to 1^ inch.
\\ to 1^ inch.
1} to 2 inch.
2A to 2A inch.
2i to 3 inch.
i
i
A
•a
1
acquaintance with the steels used are essential for success-
ful hardening. Slow heating is, of course, necessary. For
quenching bath some hardeners advocate the use of raw
linseed oil, some brine, and some nothing but water. The
bath should not be very cold. A brine bath of a temper-
ature of about 70° F. will prove satisfactory if the hardener
knows his business in other respects. Small cutters, say
those below 2\ inches in diameter, should be drawn to a
temperature of 430° F. The temper of large milling
cutters is usually not drawn.
It may be remarked that when quenching milling
cutters, after having heated them, the general principles to
be borne in mind are that long cutters should be plunged
vertically and thin ones edgewise. This will in both
cases tend to counteract distortion of the cutter.
PLAIN AND SIDE MILLING CUTTERS
389
Grinding.
The grinding of the teeth of plain milling cutters is done
in either of two ways. By the first and oldest method it
is done by an emery wheel of the disk type, the wheel
grinding the land of the tooth to the desired angle of
clearance. The principal objection to this method is that
Fig. 169. Comparison between Action of Disk Wheel and Cup
Wheel when Grinding Milling Cutter Teeth
the surface ground will become slightly concave, as shown
by^the dash-dotted line in Fig. 169. Another difficulty
in this method, particulariy, is also to be found in the care
necessary to so adjust the grinding wheel that the proper
degree of clearance will result. In this respect the tool-
maker is entirely dependent upon his own judgment. It
may, of course, be said that the angle of clearance should
be from 5 to 7 degrees, that is, the land of the tooth should
be in a plane making 5 to 7 degrees angle with the tangent
340
SMALL TOOLS
to the outside diameter of the cutter at the edge of the
tooth as shown in Fig. 170. In other words, if the, teeth
are cut radial, the included
angle between the top of
the tooth and the front
face should be from 83 to
85 degrees. This, however,
does not help the tool-maker
much, as it is very hard to
measure the angle referred to
with any degree of accuracy.
The common method of
finding out whether enough
clearance has been given to
the tooth is to place a
straight edge or a regular
scale on top of the ground
teeth as shown in Fig. 171. If the straight edge, when rest-
ing on adjacent cutting edges either coincides with the plane
Fig. 170.
Angle of Clearance of
Cutter Teeth
Fig. 171. Gauging the Clearance by Means of a Straight Edge
of the land of the tooth or shows a slight clearance between
the straight edge and the top of the tooth as shown in
Fig. 171, then the angle of clearance may be considered
approximately correct.
PLAIN AND SIDE MILLING CUTTERS
841
Grinding Clearance with Cup Wheel — The second
method of grinding the relief or clearance of plain milling
cutters is by means of a cup wheel. This method was
originated in Germany, and is at present gaining ground
everywhere. The difference in the surface produced by
this wheel and by the disk wheel is easily seen in Fig. 169.
The cup wheel produces a longer lasting tooth, as the latter
is not provided with so keen and unsupported a cutting
edge. This method of grinding is to be recommended in
all cases where it is possible to use it. By this method
of Catt<*«-
Pig. 172. Cup Wheel Inclined to the Angle of Clearance of Cutter
it is also possible to gauge the angle of clearance in a more
satisfactory manner. The grinding head may be made so
that the cup wheel spindle inclines say 6 degrees to the
horizontal. This of course gives the face of the cup wheel
an inclination of 6 degrees to a vertical plane. If now the
cutter is presented to the wheel so that the front face of
the tooth to be ground is in the horizontal plane going
through the center of the cutter, as shown in Fig. 172,
then the clearance angle of the tooth will evidently be 6
degrees. The advantages of the method referred to are
a flat top surface and a uniform clearance an^le on all the
teeth.
342 SMALL TOOLS
In order to diminish the disadvantage of the concave
form of the land of the tooth when the grinding is per-
formed with a disk wheel, it is necessary to select a wheel
of as large a diameter as possible, as then evidently the
conca\ity will becomo less pronounced.
Precautions in Grinding, — When grinding it is also
necessary to get the length of all the teeth as nearly equal as
possible, so that one tooth does not project further from the
common center than do the others. If one or a few teeth
project beyond the others, they will cut deeper into the
metal to be cut, and a surface of an uneven and wavy
appearance will result. In order to get the teeth ground
to an equal length they should all be ground with a stop
resting against the face of the tooth operated upon. It is
evident that in such a case they must all be identically the
same when ground. If the cutter were indexed around
by an index head when grinding, in the same way as when
the teeth are cut, an uneven lehgth of teeth would result,
because no index head is so perfect as to bring every tooth
to the very same position in relation to the grinding wheel
as was occupied by the former tooth. Every indexing
head will cause slight irregularity in the spacing of the
teeth. If, however, the teeth are all one after another
brought up against the same stop, which is held in a fixed
relation to the grinding wheel, every tooth will be ground
correctly, irrespective of slight irregularities in the spacing
of the teeth.
When a special grinding head with the spindle inclined
as mentioned previously cannot be had, the clearance
angle can be secured by using a cup wheel with a vertical
face and setting the stop pin or guide for the tooth some-
what below the center of the cutter to be ground, as shown
in Fig. 173. Evidently this will fill the purpose equally
well.
PLAIN AND SIDE MILLING CUTTERS
343
Setting the Tooth Guide. — The amounts to set the guide
below the cutter center are ^ven in Table XCI for 5- and
7-degree angles. This table is as given by the Cincin-
nati Milling Machine Company. When grinding with a
disk wheel the center of the wheel must be set a certain
distance above the center of the cutter, the guide pin in
this case being set at the same height as the cutter center.
The amounts to set the wheel center above the cutter
center for various cutter diameters are given in Table XCII.
It is evident that if too large a wheel is selected it may cut
Oenterline
^f Cnttwr
Fig. 173. Setting Stop Pin for Grinding Clearance on Milling
Cutter Teeth
into the tooth nearest to the one ground. In such a case
a smaller wheel must be used.
In regard to the clearance angle it may be added that
where special roughing and finishing cutters are made
5 degrees should be used for the latter and 7 degrees for
the former cutters.
Side or Straddle Milling Cutters.
The next class of cutters to be considered are side or
straddle milling cutters, Fig. 174, the latter name having
ori^nated through the use of these cutters in pairs or gangs.
344
SMALL TOOLS
TABLE XCI.
TABLE FOR SETTING TOOTH REST BELOW CUTTER CENTER TO
OBTAIN 5 AND 7 DEGREES CLEARANCE WHEN GRINDING MILL-
ING CUTTER TEETH WITH CUP WHEEL.
Diameter
5 Deg.
7 Deg.
Diameter
5 Deg.
7 Deg.
of Cutter.
Clearance.
Clearance.
of Cutter.
Clearance.
Clearance.
0.011
0.015
3
0.132
0.180
i
0.015
0.022
3i
0.143
0.195
0.022
0.030
3i
0.154
0.210
.
0.028
0.037
3i
0.165
0.225
0.033
0.045
4
0.176
0.240
0.037
0.052
4i
0.198
0.270
1
0.044
0.060
5
0.220
0.300
H
0.050
0.067
5i
0.242
0.330
U
0.055
0.075
6
0.264
. 0.360
H
0.066
0.090
6i
0.286
0.390
li
0.077
0.105
7
0.308
0.420
2
0.088
0.120
n
0.330
0.450
2
0.099
0.135
8
0.352
0.480
2
0.110
0.150
9
0.396
0.540
2}
0.121
0.165
10
0.440
0.600
TABLE XCII.
TABLE GIVING DISTANCE TO SET CENTER OF GRINDING WHEEL
ABOVE THE CUTTER CENTER WHEN USING DISK WHEEL.
Diameter
of Emery
Wheel.
5 Deg.
Clearance.
7 Deg.
Clearance.
Diameter
of Emery
Wheel.
5 Deg.
Clearance.
7 Deg.
Clearance.
2
2i
2i
2}
3
3}
3i
3)
4
i
4i
^
4}
5
H
5i
5f
6
i
• 1 ■
PLAIN AND SIDE MILLING CUTTERS
846
These cutters can be considered as a combination of a
plain milling cutter and an end mill, and consequently,
as far as the face is concerned, whatever has been said
about plain milling cutters applies also to side milling
cutters. As these cutters are very seldom made of any
coasiderable width of face, they are almost always cut
straight.
Fig. 174. Side Milling Cutter
Milling the Teeth on the Sides. — When milling the teeth
on the sides of a side milling cutter, the cutter to use and
the angle to which to set over the mill when being cut must
be selected with a great degree of judgment and care. It
would be almost impossible to give any definite rules or
figures, but for general guidance it may be said that a
cutter of the same form as for milling the teeth on the face
should be used except that the angle of the cutter should
be about 75 degrees instead of 60 degrees. The formula
for finding the angle to which to set over the cutter while
846
SMALL TOOLS
the teeth are being cut on the side can, however, easily be
derived. If iV be the number of teeth in the cutter to be
cut, V the angle of the cutter with which the teeth are cut,
and w the angle to which to set over the index head of the
milting machine on which the mill to be cut is mounted,
then
360^
cos XV = tan -rrr- X COt V.
N
This formula is proved as follows:
Let it be assumed that the number of teeth in the mill
to be cut and the angle of the angular cutter with which
the teeth are to be milled are given. The angle sought is
the one to which to set the index head of the milling machine.
In Fig. 175 the problem is shown diagrammatically, the
cutter angle ADB and the
number of teeth, N, being
given, while the angle to which
the index head is to be set
(which is to be determined)
is BEC. In order to simplify
the calculations, assume the
radius of the side mill to
equal 1. Evidently the length
of the radius has no influence
on the final result, or on our
formula, anyway. The angle
BCM represents the angle of
one tooth of the side mill.
Now produce CM to- A and
draw AB. The line CE represents the bottom of the tooth,
and the plane in which the angle of the cutter for milling
the teeth must be measured is at right angles to CE^ or in
the plane BD (lower view of Fig. 175).
Fig. 176. Deriving Formula
for the Setting of Side Milling
Cutter when Milling Teeth on
Side
PLAIN AND SIDE MILLING CUTTERS 347
We can now arrive at the following equation :
Angle ACfi=^-
N ■
, 360° , .^D AB
tan —rr- = tan ACB = 7— .
N EC
But BC = radius of side mill = 1, and consequently
^ 360° .„
tan— =45, (1)
The triangle ABD, shown at the right in Fig. 175, is in a
plane perpendicular to the bottom CE of the tooth, the
angle ADB being the cutter angle, as mentioned. Then
BD = AB X cot ADB = tan -^ X cot ADB. (2)
The line BD, however, also lies in the plane containing
the right triangle CDB. We have, therefore,
cosC5D = ^. (3)
But BC = radius of side mill = 1, and consequently,
from (2) and (3),
cos CBD ==BD = tan ^ X cot ADB. (4)
The angle CBD equals the angle BEC, or the angle to
which to set the index head; therefore
360°
cos BEC = tan — ^^ X cot ADB, or, expressed in words:
The cosine of the angle to which to set the index head eqicals
the tangent of the tooth angle multiplied by the cotangent of
the angle of the cutter by which the teeth are cut.
This proof was contributed by Irving Banwell in Machin-
ery, February, 1908.
Assume as an example that we wish to cut the teeth on
the side of a side milling cutter having 18 teeth with an
348
SMALL TOOLS
angular cutter of 75 degrees. Then the cosine for the
angle to which to set the index head in which the milling
cutter is held, or
cos w = tan 20° X cot 75° = 0.364 X 0.268 = 0.0975.
I/; = 84° 25'.
Number of Teeth.
The number of teeth in a side milling cutter may be a
trifle greater than that of a plain milling cutter, because
the former class of cutters usually are very much narrower
than the latter. If A^ is the number of teeth and D the
diameter of the cutter, the following formula for number
of teeth corresponds with the practice of the Pratt and
Whitney Company :
iV = 3.1 7) + 11.
Thus the number of teeth in a cutter 5 inches in diameter
would be
3.1 X 5 + 11 = 15.5 + 11 = 26.5,
which of course must be 26 teeth. The number of teeth
figured from this formula is given in Table XCIII.
TABLE XCIII.
NUMBER OF TEETH IN SIDE MILLING CUTTERS.
No. of teeth =« 3.1 diam. + 11.
Diameter of
Number of
Diameter of
Number of
Cutter.
Teeth.
Cutter.
Teeth.
2
18
5i
28
2i
18
6
30
2i
18
^
32
2}
20
7
32
3
20
7i
34
3J
22
8
36
4
24
9
38
4*
24
10
42
5
26
PLAIN AND SIDE MILLING CUTTERS
349
Relief of Teeth^ — What has been previously said about
the relief of plain milling cutters is equally applicable
to side milling cutters. The relief on the side of these
cutters need not, however, be as large as the relief on the
face of the tooth. In fact, some manufacturers do not
relieve their side milling cutters at all on the side, but that
cannot be considered good practice. A slight relief is
evidently called for if the tooth on the side is to be able
to cut at all.
Fig. 176. Comparison between Relief of Teeth on the Cylindrical
Surface and the Side of Catter
The reason why the relief on the side of the cutter may
and should be smaller than that on the face is very obvious
if one considers the difference in the relationship of the
tooth to the surface to be cut when this tooth is located
on a circular and on a plain surface. Referring to the cut.
Fig. 176, where the case is shown in exaggerated scale, it is
easily seen that if the same angle of relief is given to the tooth
A on a circular surface and to the tooth 5 on a flat surface
(the side of the cutter) the actual relief C will be con-
siderably larger on the tooth B and will be larger than the
360 SMALL TOOLS
relief on the tooth A according to the diameter of the circle
on which the tooth A is located. The same angle of reUef
gives a smaller actual relief C on a smaller diameter than
on a large one. «
Even if we do not consider this theoretically, there are
practical reasons why the relief on the sides need not be
as large as on the face; in fact, the main reason why a side
milling cutter is preferable to a narrow, plain milling cutter
for cutting slots is that the former has more chip room on
the sides because of having teeth and consequently space
for chips between them, thus making the sides of the slot
smoother, whereas, when using the plain milling cutter, the
chips will clog between the sides of the cutter and the
sides of the slot, producing rough places in the work. It is
well known that the actual cutting of a side mill is per-
formed by the face; this is proven also by the fact that
these cutters have to be ground more often on the face
than on the sides.
It may be inferred that no relief at all on the sides is
necessary if the teeth on the sides are not doing any actual
work. However, there are occasions when these cutters
will have to do actual work, and that is when no other
cutter than a side milling cutter with the teeth relieved on
the sides will produce desirable results, as, for example,
when an absolutely straight slot is required to be cut.
When cutting a slot a plain milling cutter will never cut
its way straight through the work, because when once out
of the straight line it has no means of correcting its path,
but must follow the direction in which it started to cut,
whereas a straddle milling cutter with its teeth relieved on
the sides will, even if started wrong, have an opportimity
of correcting its path by being able to cut with its sides.
It may be said that if the cutter or cutter arbor is running
out, the slot will obviously be wider than the cutter, but
PLAIN AND SIDE MILLING CUTTERS
851
the slot will in all cases be straight. In this connection
it is appropriate to mention various ways of making
cutters that will maintain standard widths. This is
accomplished by interlocking the cutters in such a manner
as to permit adjustment after the cutters have been reduced
in width by grinding on the sides or through wear.
Interlocked Cutters.
There are three different ways of interlocking cutters in
common use, viz.: (1) A straight slot through the center
Fig. 177. Simplest Form of Interlocked Cutteis
across one end of one cutter and a corresponding tongue on
one end of the other cutter fitting loosely , in the slot
(Fig. V^7); (2) Two or more sectors on one end of each
of the two cutters cut away in such a manner that the
remaining high sectors in the one cutter fit loosely into thfe
spaces cut away in the other cutter (Fig. 178) ; (3) Oppo-
site ever}'' other tooth on one side of each of the two
cutters is cut away a portion, leaving a space into which
the high portions of each of the cutters fit (Fig. 179).
Referring to the first kind of interlock mentioned, it
must be remarked that this interlock is poorly adapted for
maintaining a standard width and is mostly used where
852
SMALL TOOLS
cutters of unusual lengths are required which would be
impractical, if not entirely impossible, to make in one
piece. This interlock is to be recommended for such
purposes because of its being very simple and inexpensive
to make. It will be noticed from the cut that there ou^t
to be a clearance of 0.010 inch between the bottom of the
slot in one cutter and the top of the tongue in the other
cutter, thus giving a resting siuface between the two
cutters at A and 5, which faces ought to be ground. It
Fig. 178. Interlocked Cutters for Maintaining Standard Width
may also be remarked that between the sides of the slot
and the tongue there does not need to be a perfect fit and
consequently these sides do not need to be ground. As
mentioned above, this kind of interlock is not to be recom-
mended for maintaining a standard width, although it
could be used for such purpose by inserting thin pieces
between the ground faces A and B,
For maintaining a standard width, interlocks such as are
shown in Figs. 178 and 179 are the most desirable. In
these cases the cutters are provided with ground hubs,
PLAIN AND SIDE MILLING CUTTERS
358
the width being maintained by inserting thin washers
between these hubs. Between the hubs and the interlock-
ing sections there should be an annular recess of sufficient
width and depth to permit clearance for the milling cutter
when milling out the sections for the interlock. If such a
recess is not provided, or if it is not wide enough, the cutter
will cut into the hub, causing an unfinished appearance
as well as a poor surface for a good contact with the
hub in the other cutter with which it is interlocked.
Fig. 179. Interlocked Cutters with Every Other Tooth Recessed
Cutters for Maintaining Standard Widths by Means of
Beveled Fa/^s. — ; In the February, 1905, issue of Machin-
ery, Mr. E. R. Markham showed a method of making cutters
for maintaining a standard width which he claiins to be
very satisfactory, and which has, he says, in many shops
superseded the cutter with interlocking teeth for the pur-
pose mentioned. This cutter is shown in Fig. 180. To
make this form of cutter use an eccentric mandrel like that
in Fig. 181. This mandrel has two sets of centers; the
354
SMALL TOOLS
eccentric centers are located equidistant from the regular
centers but on opposite sides, on the opposite ends, as
shown. Half of the cutter is placed on the mandrel so
that the end to be cut at an angle shall be halfway between
the ends of the mandrel, as shown in Fig. 182. After
facing the end a by running the mandrel on the concentric
centers, the eccentric centers are placed on the lathe
centers and the end 6 is faced as shown. The two parts
Fig. 180. Spe-
cial Inter-
locked Mill-
ing Cutter
Fig. 181. Mandrel for Turning Halfs of Cutter shown
in Fig. 180
a
b
(
u
Fig. 182. Turning Cutter Halfs
are then put together on a stud and the hole drilled and
reamed for the dowel pin, a, Fig. 180. The cutter is then
placed in the vise of the shaper or planer and the key-way
cut, after which the teeth are milled. The necessary
adjustment for width of the slot is obtained by blocking
apart by means of collars of tin, thin sheet steel, or
paper.
Gang Cutters. — When two milling cutters, for instance,
one plain and one side milling cutter, are used together in
PLAIN AND SIDE MILLING CUTTERS
366
a gang, as it is usually termed, one should always let the
teeth of the larger cutter project outside of the hub, as
shown in Fig. 183, so that
when cutting no ridge in the
metal cut will result. When
the cutters are of equal or
nearly equal diameter, the
common methods of interlock-
ing evidently provide against
any ridge being left in the
surface milled. It is very
important, whenever arrang-
ing milling cutters in a gang
to finish a continuous width of surface, that all the cutters
either interlock or project inside one another. In Fig. 184
Fig. 183. Plain and Side Milling
Cutters in Gang
Tig. 184. Gang of Milling Cutters
is shown a gang of four cutters thus arranged. No ridge
can be left at any place when this gang is put together in
the manner shown.
High-speed Steel for Milling Cutters.
In regard to the material which can most advantage-
ously be used for milling cutters, opinions dififer as to the
366 SMALL TOOLS
higher efficiency gained by making the cutters from high-
speed steel. Mr. Robert Grimshaw of Hannover, Germany,
in Machinery, February, 1907, stated that his experience
with high-speed steels has shown that while they would
rough out about three to five times as fast as the carbon
steels, they were not to be recommended either for finish-
ing cuts on the lathe or for milling cutters, and that his
own rather expensive experience was backed up by the
results obtained by others in Germany.
It should hardly be necessary to say that the reason
why we should not expect proportionately as good work in
finishing as in roughing is that the new steels, almost
without exception, require to be almost, if not quite, red
hot in order that their molecules may arrange them-
selves in mechanical grouping or in chemical combination
so as to give the maximum hardness, and that in conse-
quence of the high speed required to get this temperature,
and the tearing rather than cutting action, the surfaces
obtained are not so smooth as those produced with the
carbon steels.
The experiments of Prof. Haussner of Brunn, Germany,
go to show that a slight increase in specific power required
to produce turnings accompanies an increase in the speed
of cutting; and this is at once the cause of the new tools
getting hot when roughing and the reason why they cut
so fast. But in finishing on the lathe or planer there is
less heat developed than in roughing. In milling there is,
in the first place, no machine that will give the speed
required to make the tool red hot; and in the second
place the weight and cross-section of the body of the mill,
in proportion to the cutting portion proper, is so great
that in any case the slight heat developed by the work
is rapidly carried away from the point of application of
the cutter. Further, the teeth are not constantly at
PLAIN AND SIDE MILLING CUTTERS 367
work, as is the case with the point of a lathe tool; and
each tooth has a chance to cool off ^^ between bites."
This being the case, we have not the combination of cir-
cumstances tending to produce that high temperature of
the cutting point, or points, necessary in the case of the
new steels to do fast work. In a paper before the Ameri-
can Society for Testing Materials, Mr. Metcalf said in
effect: "As far as we know, the users of high-speed steel
have not been able to make tools that will finish satis-
factorily; therefore they use for this purpose carbon-
steel tools, after they have done the heavier, rougher
work with the high-speed steels.'' Although this was said
about finishing in the lathe, it applies equally well to all
milling operations, roughing and finishing alike, as the
conditions encountered are in principle the same, as has
already been pointed out.
While these experiences, of course, have their value, and
while the reasoning underlying the opinions is undoubt-
edly correct, yet both in this country and in England a
number of the leading manufacturers, who are users of
milling cutters, find that although the cutting speed can
be only slightly increased, so that the saving in time
does not in itself outweigh the increased expense of
material for cutters of high-speed steel, such cutters
retain their cutting edges much longer than those made of
ordinary tool steel; and this fact, when considering the
question of economy, is nearly as important as that of
high cutting speed.
In large shops, where several hundred milling cutters
are in constant use, their grinding is a very important
item in the expense account, and as high-speed steel cut-
ters have to be ground less frequently, that is a distinct
saving. The labor cost in the making of milling cutters
is considerable, in many cases so great that the cost of
368 SMALL TOOLS
material is small in comparison; and the greater the labor
cost the more important it is to use material which adds
to the cutter's life. The greater cost of high-speed steel
becomes a heavy item in tools where the labor cost of
making the tool is comparatively small; but in the case of
a formed milling cutter, where the labor cost is large, the
difiference in the total cost between ordinary carbon steel
and high-speed steel becomes insignificant.
Li a discussion regarding the manufacture and up-keep
of milling cutters, at a meeting of the Institution of Mechan-
ical Engineers of Great Britain, one of the speakers
called attention to one valuable property of high-speed
steel, which he had not seen referred to, namely, that of
withstanding shocks. In one of the railway shops in
England the output of the crank-turning lathes had
been practically doubled by the use of high-speed steel
tools. The forgings were never very accurate, there
being perhaps one-quarter inch to take off one side of the
diameter, and IJ inches off the other, and a tool suited
to such wide variation was greatly appreciated. If the
high-speed steel tool dug in, it did not break, as invari-
ably happened with ordinary
carbon steel.
Another speaker called atten-
tion to an important factor
affecting the life of high-speed
steel milling cutters. The teeth,
besides being correctly relieved '\
at the back, should have a Fig. 186. Method of Making
front rake ot 5 dep««, a. f^^^r.J^"™' "
indicated in Fig. 185. The
number of teeth in milling cutters, particularly when made
of high-speed steel, plays a very important part. A cutter
made of this material with a large number of teeth has
PLAIN AND SIDE MILLING CUTTERS 869
a considerably shorter life than one with fewer but deeper
teeth. In a certain case two milling cutters, one with 16
teeth and one with 32 teeth, had been made. The one
with the coarser teeth, of helical shape, would finish an
article with as good a finish as the one with the finer
pitched teeth, but the cost of making the coarse-pitched
cutter was 35 per cent less than the cost of making the
one with the fine-pitched teeth and the life of the coarse-
pitched cutter was four or five times as long as that of
the other.
CHAPTER IX.
MISCELLANEOUS MILLING CUTTERS
End Mills.
The end mill, as the name indicates, is a cutter having
teeth on, and cutting with, the end rather than by the
face as in the case of face or side mills. However, the
end mill is provided with teeth on the face as well as on
the end, as shown in Fig. 186. This kind of cutter is usu-
y
■^
Fig. 186. End MiU with Taper Shank
ally made with a solid sh^nk, but is also made with a hole
through it to fit a removable shank and is then termed
shell end mill. Such a mill is shown in Fig. 187.
Pig. 187. Side View and Section of Shell End Mill
The end mill is a combination of a plain and side milling
cutter, and can be used for milling surfaces parallel to the
axis of the cutter as well as surfaces perpendicular to the
360
MISCELLANEOUS MILLING CUTTERS
361
axis. The teeth on the end are almost always radial, and
without front rake. The teeth on the cylindrical surface
are usually cut straight, but may be cut spiral as well.
The object of the spiral is the same as in the case of face
mills, viz., that the cut may be broken up into a number of
smaller portions. The amount of spiral should not exceed
20 degrees.
Direction of Spiral. — The direction of the spiral in end
mills is more important than in the case of plain mills,
where the spiral may be in either direction. In Fig. 188 are
shown two end mills, both cutting in the right-hand direc-
Fig. 188. Bight- and Left-hand Spiral Cut End Milla
tion, but one with right-hand and one with left-hand spiral
flutes. At first thought it seems as if a right-hand
end mill should be given a right-hand spiral, the same as
a twist drill. This would tend to force the chips out of
the grooves, while a left-hand spiral would tend to force
them down toward the cutting edges. The right-hand
spiral, however, tends to draw the whole mill into the piece
to be cut, the spiral acting as a thread of steep pitch.
This is a very grave objection in that it loosens the mill
shank, if tapered, from its socket, and may result in injury
to the work in hand. Manufacturers of end mills, there-
fore, as a rule use a left-hand spiral for right-hand miUs^
362 SMALL TOOLS
and vice versa, notwithstanding that this produces a
poorer cutting mill. Not only is there an obstruction to
the chips freely moving out of the flutes, which is very
important in taking deep cuts, but the teeth on the end
get a negative front rake, as seen from the cut, and for
this reason the mill is not suited to cut with the end,
but will cut freely only with the teeth on the cylindrical
sides. The fact that the left-handed spiral pushes the
mill firmly into the socket is, however, considered to out-
weigh the disadvantages mentioned. If the mill is to be
used as end mill only, then the spiral on a right-hand mill
should be right hand, because the teeth can be given posi-
tive front rake. For ordinary use the end mill with teeth
cut straight is preferable, as it does not cause any trouble
of the kind referred to above.
Size of Shank. — Solid-shank end mills are usually pro-
vided with either Brown and Sharpe or Morse taper shank.
In Table XCIV are given the different numbers of stand-
ard shanks corresponding to the ordinary sizes of end
mills. In some cases two numbers are given, indicating
that it is usual to make the mills in question with either of
two sizes of shanks. The numbers of the shanks given
for various sizes of mills correspond to the practice of end-
mill manufacturers.
Dimensions. — The only dimension necessary to give
in relation to end mills, besides the size of the shank, is
the length of the cut, or the length of the cylindrical
portion provided with cutting edges. This dimension is
also given in Table XCIV, together with the number of
teeth ordinarily cut in these mills. The length of the
rieck between the cutting part of the mill and the shank
is unimportant, and should only be long enough to prevent
the fluting cutter from cutting into the shank when the
teeth are milled.
MISCELLANEOUS MILLING CUTTERS
363
TABLE XCIV.
DIMENSIONS OF END MILLS.
Diameter of
Mill.
Length of
Cut.
Number of
Teeth.
Number of
Morse Taper
Shank.
Number of
B. and S.
Tapo: Shank.
J
6
4,5
A
8
4,5
1
8
4,6
A
8
1,2
4,6 •
J
n
8
1,2
5,7
k
1^
8
1,2
6,7
1}
10
2
6,7
i
ll
10
2
7,9
1 ■
10
2,3
7,9
10
2,3
7 9
10
2,3
7,9
" ij
2
12
3
7,9
ij
2
12
3,4 .
7,9
i|
2i
12
3,4
9
2i
14
3,4
9
2i
14
4
9
1
2}
14
4
9
ij
2i
16
4
11
2
2i
16
4
11
Milling the Teeth on the End of End Mills, — The milling
of the teeth on the end of end milling cutters, and the
selection of a cutter with a proper angle, require a great
deal of judgment and care. It is almost impossible to give
any definite rules or figures for the cutter to select, as this
varies with the size and the number of teeth in the mill;
as well as with the clearance it is wanted to give back of
the cutting edge. The angle of the angular cutter used
should, however, be selected between 55 and 75 degrees.
If the cutter is settled upon, the proper angle to which to
set over the index head in which the end mill is held (see
Fig. 189) can be found by the rule already referred to in
connection with the milling of the teeth on the sides of
side milling cutters. This was ^ven by Mr. George G.
Porter in Machinery, April, 1904,
364
SMALL TOOLS
If
N = number of teeth in end mill,
V = angle of cutter with which teeth are cut, and
W = angle to which to set the index head in which
the mill is held, then
cos W = tan -rr- X cot V.
N
70 OeOREE CUTTER
i
A'
I TABLE
Y'lg. 189. Milling the Teeth on the End of End Mills
The use of this formula is best explained by an
example. Suppose that an end mill is to be made having
10 teeth, and that a 70-degree cutter will be used for
cutting the teeth. We have then
cos W = tan 36° X cot 70° = 0.727 X 0.364 = 0.264.
From this we have W = 74° 40'.
MISCELLANEOUS MILLING CUTTERS 365
End Mills With Center Cut, — When it is necessary to
cut into the surface of a piece of work with the end of the
mill and then feed along, as in die work, internal cams,
etc., the teeth are sharpened or given clearance on the
inside, and so are able to cut a path from the point where
the mill is sunk into the work. The teeth, being very
coarse, allow of heavy cuts. This is especially the case
when cast iron is the material being machined. After
cutting the teeth on the end of the mill a thin metal
splitting saw of comparatively small diameter should be
run through close to the face of each tooth, making the
cut shown in Fig. 190 at A. This cut is to permit back-
ing off the inner edge of the tooth, which gives the mill a
-^
I
z
Fig. 190. End Mill with Center Cut
cutting tooth on the inside as well as on the outside, and
allows it to cut away the projection made when the mill
is fed into the work.
As mentioned, the number of teeth in end milling cut-
ters with center cut is smaller than that in ordinary end
mills. It is customary to put in four teeth for sizes smaller
than one-half inch, six teeth for sizes from one-half to IJ
inches inclusive, and eight teeth for sizes up to 2 inches.
In ordinary end mills there is a recess in the end the
same as in end mills with center cut, but the teeth are not
sharpened on their inside edge. The object of recessing
the end in that case is to furnish a cavity for the entrance of
the cutter that is used to cut the teeth on the end. It also
facilitates the operation of grinding the teeth on the end.
366
SMALL TOOLS
Shell End MiUs. — Shell end mills, Fig. 187, do not
differ in principle from ordinary end mills. They are
mounted on arbors such as are shown in Fig. 191. The
head of the screw in the end of the arbor fits into the recess
in the end of the mill. The keys A fit into the key-ways
at the upper end of the mill, and constitute the drive.
The important dimensions of shell end mills are given
in Table XCV. The number of teeth in these mills is
larger for the same diameters than the number in solid
<
Pig. 191. Arbor for Shell End Mills
end mills, because the coarser teeth of the latter would
require a deeper flute than would be permissible in the
thin shell of shell end mills.
TABLE XCV.
GENERAL DIMENSIONS OF SHELL END MILLS.
Diam.
of
Mill.
Total
Diam.
of
Hole.
No. of
Diam.
of
Mill.
Total
Diam.
of
Hole.
No. of
Length.
Teeth.
Length.
Teeth.
li
U
i
16
H
2
1
18
lA
li
1
16
2,
2
18
l»
1
■i
16
2i
2
■
18
lA
1
16
2
2
■
18
1:
16
2
2
1
20
If
l:r
18
2
2
1
20
U
1
18
2-
2
1
20
1
U
18
3
2
1
20
2
U
%
18
MISCELLANEOUS MILLING CUTTERS
Angular Milling Cutters.
367
Angular milling cutters are provided with teeth on the
angular face and on one side as shown in Fig. 192. They
are usually made with the angle A 45, 50, 60, 70, or 80
degrees for regular purposes. They are used mainly for
fluting milling cutters. They are designated by the angle
A, so that a 60-degree angular cutter means one having
this angle 60 degrees. Angular milling cutters are ordi-
m
Fig. 192. Angular Milling Cutter
narily made in three sizes, 2J, 2J, and 3 inches in diameter,
all one-half inch thick, with 1-inch hole in the two smaller
sizes and IJ-inch hole in the largest. A recess B is turned
in the side of the cutter provided with teeth. The depth
of this recess may be made five-sixty-fourths inch and the
diameter If, 1|, and 2J respectively, according to the
diameter of the cutter.
The number of teeth in angular cutters is made 20,
22, and 24 respectively for the three different sizes of
cutters.
368
SMALL TOOLS
The cutter shown in the cut is termed right hand. The
cutter is ordinarily mounted on the milling-machine arbor
with the side without teeth toward the milling-machine
head.
Cutters for Fluting SpiraltTeeth Milling Cutters.
Cutters for fluting spiral-teeth milling cutters, usually
termed cutters for spiral mills, are ordinarily made with a
Fig. 193. Cutter for Fluting Spiral Teeth Milling Cutters
52-degree inclusive angle, as shown in Fig. 193, 12 degrees
on one side and 40 degrees on the other. However, this
cutter produces a rather weak tooth, and it is preferable to
make the 40-degree angle on the one side equal to 48 degrees,
the inclusive angle then being equal: to 60 degrees. These
cutters are, of course, nothing but double angle cutters.
The one shown in the cut is termed a left-hand cutter; that
is, when mounted on the arbor of a milling machine the
MISCELLANEOUS MILLLNG CUTTERS
869
side with the larger angle, the 40- or48-degree angle, should
be toward the machine. The manner in which these cutters
are used is shown in Fig. 194, where
C is the cutter being milled and A
the cutter for cutting the spiral
grooves.
Cutters for spiral mills are usually
made in three sizes only, 2J, 2J, and
3 inches diameter; the width is made
one-half inch in all, and the hole
1 inch in the two smaller sizes and
1\ inches in the largest. The num-
ber of teeth is made 18, 20, and 22
respectively for the three sizes. The
teeth are cut with angular cutters,
the 40- or 48-degree side with a
60-degree cutter and the 12-degree
side with a 75-degree cutter.
Fig. IW. Setting Cutter
in Fig. 193 when Fluting
Milling Cutter
Fixture for Grinding Angular Milling Cutters. "
Fig. 195 shows a little device which has proved itself
very useful in grinding angular milling cutters when a
perfect angle is required. This device was shown in
Machinery J January, 1908, by Mr. P. Yorgensen. A radius
at the point of the angle can also be ground, radius and
angle being ground at one setting. This fixture consists
of a base plate C, which is clamped to the grinder table so
that it can be fed to and from the wheel by the feed arrange-
ment on the grinder. On this base plate rests a triangular
plate D, carried on three feet. This latter plate is free to
move in all directions, simply sliding on its feet on the plate
C, and is guided only by the hands of the operator. In
this triangular plate D there is a slot E, into which a tongue
370
SMALL TOOLS
of the bracket F is fitted, this bracket then being movable
back and forth on the plate D, and having arrangement for
clamping in any position. The cutters A are clamped to
this bracket F by a suitable screw and washer. For dif-
ferent widths of cutters, either different brackets must be
employed or washers may be interposed between the
-hr^
"@"q"
[ojBl
*?-A
Fig. 196. Simple Fixture for Grinding Angular Milling Cutters
bracket and the cutter, because it is evident that the center
line of the cutter must always coincide with the center Kne
of the triangular plate D. The cutter can be set to any
given radius between the two angular faces by placing a
gauge block, having the same thickness as the radius wanted,
against the side of the triangular block, and placing a
square against the gauge, and adjusting the cutter so that
MISCELLANEOUS MILLING CUTTERS 371
the blade of the square just touches the aiiigular face of the
teeth of the cutter A, If, for instance, we have a cutter
that we want to grind to a 60-degree angle, and want one-
sixteenth-inch radius at the point, we simply set the cutter
central with the triangular block and place a one-sixteenth-
inch gauge block between the square and the side of the
block, and then adjust the cutter until it touches the blade
of the square. The cutter is then clamped in place. The
grinding itself is performed by sliding the plate D first to
one side and then to the other, so that the sides G and H
alternately rest against the guide K on the bed plate C,
the side of the teeth of the cutter being meanwhile moved
back and forth across the face of the grinding wheel. The
turning around of the triangular block from one side to the
other with the point B against the guide K evidently
produces a radius at the point of the cutter between the
two angular sides. The height of the cutter tooth in a
horizontal direction, when setting, is determined by a gauge
block of such a height that the tooth face is in a horizontal
plane with the center line of the cutter. The cutters are
formed closely, before hardening and grinding, to the
desired shape, so that there is but a few thousandths inch
left to be removed when grinding.
Formed Cutters.
While " formed " cutters may be provided either with reg-
ular milling cutter teeth or with eccentrically relieved teeth,
the common usage of the term is for cutters with eccentri-
cally relieved teeth only. Such a cutter is shown in Fig.
196. The formed cutter is intended for milling surfaces
of irregular form, and the teeth are so constructed that
their form is exactly the same all the way from a to 6.
In order to give clearance to the cutting edge the tooth is
372
SMALL TOOLS
backed off along the periphery of a circle which is eccentric
with the outside periphery of the cutter itself, hence the
name eccentrically relieved. Owing to the peculiarity in
the construction of the cutter tooth, the face c can be
ground off, in order to sharpen the tooth, without changing
the form cut by the cutter. This grinding may be con-
tinued until only a very small part of the tooth remains.
A well used up cutter is shown in Fig. 197.
Formed milling cutters are first turned up in an ordinary
lathe to the simple outlines of the form. A forming tool
Fig. 196. Eccentrically Relieved Milling Cutter
is then applied, by means of which the cutter is shaped to
the desired form. This forming tool must be of the exact
form wanted on its top face, but must be provided with
clearance, usually 15 degrees. The cutter is then fluted,
or the teeth cut. After this the cutter is brought back to
the lathe and relieved. The lathe should be provided with
a relieving attachment for the performance of this oper-
ation. Of course, by elaborate devices a cutter may be
relieved in any lathe, but the time consumed in doing the
work under such difficulties as present themselves is
too great to be contemplated at the present time when
MISCELLANEOUS MILLING CUTTERS 373
there exist excellent facilities for performing this opera-
tion. Manufacturers of eccentrically relieved cutters
employ special machines for this work, which are suited
for performing this operation only. After hardening,
the cutters are ground on the front faces of the teeth
only.
In making or laying out formed cutters care should be
taken, as far as possible, not to have any part or surfaces
of the teeth at right angles to the axis of the cutter, as
Fig. 107. Formed Milling Cutter having been used until
but a Small Part of the Tooth remains
shown at a, Fig. 198. It is evident that this part would
not be relieved, because the vndth of the forming tool used
for relieving is constant. And even if this portion a
were relieved by filing or in some other manner, when the
tooth were ground, the space between the faces a and 6
would become wider and the exact form would be lost.
Whenever possible, all surfaces should be ^ven an inclina-
tion of at least 5 degrees to the line perpendicular to the
axis of. the cutter. This will permit the forming tool to
374
SMALL TOOLS
slightly relieve the whole tooth form; the cutter will con-
sequently cut easier, and at the same time retain its shape
when ground.
Interlocking Formed Cutters, — At times formed cutters
must be provided with surfaces which are perpendicular
to the axis of the cutter. In order to make these cutters
cut freely the perpendicular face is relieved by means of
filing. As said before, the grinding on the face of the
K --a-— ->
R_
^mz<^^;A9.^':v^,-.^./oy>A/y.yv
Fig. 198. Undesirable Construction Fig. 199. Interlocked Formed
of Formed Cutter Cutter
tooth will then widen the form or lengthen the distance a,
Fig. 199. In order to overcome this difficulty, such
cutters are often interlocked so that the hubs which rest
against each other may be ^ound off at the same time
as the faces of the teeth are ground, thus bringing the dis-
tance a back to the original dimension. But it must be
remembered that this way of overcoming the difficulty is
permissible only when the width a is the most essential
MISCELLANEOUS MILLING CUTTERS 375
nli ; dimension and the form otherwise can stand slight changes,
^ i because the grinding ofif of the hubs at 6 will evidently bring
the curved parts c and d closer together, and thus slightly
,x- change the shape of the cutter, while a standard width a
il:^ is maintained. This is often overiooked, but unless it
j( is taken into consideration interiocking of formed milling
•^. cutters of the kind mentioned for retaining a standard
)f I width is not permissible, and shows an incomplete concep-
tion of the principles involved .in and the purpose of eccen-
trically relieved cutters.
Number of Teeth. — The spacing of the teeth in eccen-
trically relieved cutters is far coarser than in ordinary
I milling cutters. The reason for this is obvious. The
tooth itself is so much wider than the ordinary milling-
cutter tooth, and the space required between the teeth
should be fairly wide, although not necessarily as wide as
required for ordinary teeth. The formed cutter cannot
cut as heavy chips as the regular milling cutter, and con-
sequently there is no need for quite as much chip room
between the teeth. There can be no exact rule given
for the number of teeth, as this must, to some extent,
vary with the form of the cutter, that is, whether the
difference between the largest and smallest cutting
diameters is large or ^mall, and also with the diameter
of the cutter. In this particular there is no way of
determining the correct number but by judgment and
experience.
The cutters used to mill the grooves in eccentrically
relieved cutters of all kinds vary according to the diam-
eter of the cutter and the number and depth of the teeth.
In general an angular cutter of 35 degrees inclusive angle
is used, but this angle may vary from 30 to 45 degrees.
Concave, Convex, and Comer-rounding Cutters. — The
most common of all formed cutters, outside of gear-teeth
376
SMALL TOOLS
cutters, which fonn a class by themselves, are concave,
convex, and corner-rounding cutters, as shown in Figs.
200, 201, and 202. The corner-rounding cutter may be
of two kinds, single or double. It is a distinct improve-
ment on this cutter not to let the rounded part be a full
quarter of a circle, but to let it be made with a tangent
5 degrees to a Une perpendicular to the axis of the cutter
as shown in Fig. 200. This permits the whole cutting
edge of the cutter to be relieved, and at the same time
prevents any ridge being visible in the piece worked
r"5rT-f
^
&-
-J'-..
^
^ ^
1
._
<J
...
1
1
.~:
'~rj
:i:
1.
d)
1
1
1
1
1
jL_.
—
^
...
k-y
Figs. 200, 201, and 202. Single and Doable Comer-rounding Cutters,
Concave Cutter, and Convex Cutter
upon by the cutter, as the side of the tooth gradually
recedes from the work instead of being perfectly parallel
to it.
Approximate dimensions for the common sizes of these
cutters are given in Tables XCVI, XCVII, XCVIII, and
XCIX. The diameters as given are for cutters with
one-inch hole. If the hole is larger or smaller than one
inch, the diameter of the cutter must vary accordingly.
For sizes not given in these tables the following formulas
will give correct proportions for cutters with one-inch
holes.
MISCELLANEOUS MILLING CUTTERS
377
Comer-rounding cutters:
B =— + 2 inches,
C =- + J inch,
A
D = -r H- J inch for single, and
o
A
D = - + J inch for double corner-rounding
o
cutters.
Concave and convex cutters :
A
B =-j -\' 2 inches,
11 A
C = -^ 4- \ inch (concave cutters only),
o
ZA
D = ■— + J inch (concave cutters only).
Id
For the denotation of the letters in these formulas see
Figs. 200, 201, and 202.
TABLE XCVI.
SINGLE CORNER-ROUNDING CUTTERS.
(See Fig. 200.)
Size
of
Radius.
Diam.
of
Cutter.
Width
of
Flange.
Total
Width.
No. of
Teeth.
Size
of
Radius.
Diam.
of
Cutter.
Width
of
Flange.
Total
Width.
No. of
Teeth.
A
B
C
D
A
B
C
D
A
21
t
h
16
i
3i
*
i
10
f
2i
%
16
A
3i
M
**
10
2i
A
16
i
3i
A
iiV
8
2i
2i
i
^
12
12
3f
3J
r
If
8
8
f
2h
\
4
12
t«
4
i
lA
8
2*
1
12
}
4i
A
lA
8
?
2f
3
t
8
10
10
1
4i
41
f
li
8
8
A
3
^
H
10
378
SMALL TOOLS
TABLE XCVII.
DOUBLE CORNER-ROUNDING CUTTERS.
(See Fig. 200.)
Size
of
Radius.
Diam.
of
CuttCT.
Width
of
Flange.
Total
Width.
No. of
Teeth.
Size
of
Radius.
Diam.
of
Cutter.
Width
of
Flange.
Total
Width.
No. of
Teeth.
A
B
C
D
A
B
C
D
A
2i
t
A
16
i
3i
»
1}
10
f
21
*
16
A
3*
i;
10
2i
A
16
3i
A
1
8
i
2J
^
12
*
3f
M
If
8
2i
^
H
12
3i
^
2
8
it
2i
}
12
It
4
*
21
8
2i
i
12
4i
A
2ft
8
A
21
«
10
1
4}
A
2A
8
i
3
A
iiV
10
1
^
«
2f
8
A
3
ii
lA
10
TABLE XCVIII.
DIMENSIONS OF CONCAVE CUTTERS.
(See Fig. 201.)
Diam.
of
Circle.
Diam.
of
Cutter.
Width
of
Cutter.
Width
of
Flanges.
No. of
Teeth.
Diam.
of
Circle.
Diam.
of
CJutter.
Width
of
Cutter.
Width
of
Flanges.
No. of
Teeth.
A
B
C
D
A
B
C
D
i
2i
A
iftr
16
J
3
1ft
^
10
A
2i
i
A
16
+i
3i
1ft
ft
10
2i
A
16
3i
1
10
A
2i
•1
ft
12
ly
H
1*
i
10
i
2i
ft
12
3i
1*
i
8
A
2i
A
12
3i
2i
• •
8
i
21
i
j^
12
3}
2ft
■ 1
8
A
2f
1
'h
10
1
4
2
J
8
21
U
1
10
1
4i
2ff
8
i
2}
lA
1
10
4i
2it
■ §
8
3
U
1
10
2
4*
3
8
«
3
li
A
10
MISCELLANEOUS MILLING CUTTERS
379
TABLE XCIX.
DIMENSIONS OF CONVEX CUTTERS.
(See Fig. 202.)
Diameter
Diameter
Number
Diameter
Diameter
Number
of Circle.
of Cutter.
of Teeth.
of Circle.
of Cutter.
of Teeth.
A
B
A
B
J
2i
16
i
3
10
A
2i
16
a
3i
10
}
2i
16
3i
10
A
2i
12
H
3i
10
f
2i
12
3i
8
■ff
2i
12
1}
3}
8
i
2i
12
H
3f
8
A
2}
10
ij
4
8
2}
10
1}
a
8
i
2}
10
li
4i
8
3
10
2
4i
8
a
3
10
I
Importance of Grinding Eccentrically Relieved
Cutter Teeth Radially.
A leaflet calling attention to the need of grinding
eccentrically relieved cutter teeth radially in order to
secure satisfactory results was issued in 1907 by the
Union Twist Drill Company, Athol, Mass., and from it is
reproduced the accompanying illustration, Fig. 203, for
the sake of conveying some elementary instruction in the
art of grinding formed cutters. The cut shows, diagram-
matically, how the teeth should be ground to secure the
best results; it also illustrates improper grinding. The
teeth A and B, of course, are ground correctly. The
lines AC and BC, Isdng in the plane of the cutting face,
are radial; that is, the faces of the teeth would pass
directly through the center of the cutter if projected to
380
SMALL TOOLS
the center. Tooth Z), however, shows an entirely differ-
ent condition, and one which, unfortunately, is not un-
common in gear-cutting practice. The top of the tooth
is ground back faster than the base, thus throwing the
face of the cutter into the plane indicated by the line DE;
consequently the shape of the tooth space cut is distorted,
and a gear with badly shaped teeth must necessarily be
produced by it.
Tooth correctly arround,
face of tooth radial.
Tooth incorrectly groond,
face of tooth not radial.
Fig. 203. Correctly and Incorrectly Ground Teeth of Eccentrically
Relieved Cutter
The expression "may be ground without changing the
form'' has evidently been taken too literally and without
the necessary qualification that it is necessary to grind in a
plane radial with the center of the cutter in order that the
form shall not be changed. It is evident to any one who
will give the matter a little thought that if a gear is cut with
a gear cutter having teeth ground like D the resulting tooth
space will be too wide at the top if the cutter is carried to
MISCELLANEOUS MILLING CUTTERS 881
the correct depth. Moreover, such a gear cutter works
badly, as the cutting faces of the teeth have a negative rake.
The importance of correct grinding of all formed cutters
cannot be too strongly emphasized. Unfortunately, formed
cutters that can be ground without changing the form do
not always have sufficient clearance to work well with all
classes of work, and if such cutters are carelessly used there
will be heating and rapid wearing away of the tops of the
teeth. If hard pressed and ignorant, the tendency of the
grinding operator, in order to hurry the sharpening of such
cutters, is to incline the wheel away from the radial plane.
On account of this defect in formed cutters, one large
concern making small tools has found it profitable in the use
of certain formed cutters to make them the same as an
ordinary milling cutter, with the same rake and clearance as
is the usual practice. When the cutters require sharpening,
the teeth are groimd on top, using a fixture which preserves
the correct tooth shape. This concern has foimd the
practice good, for the cutters are much more effective in
action, and notwithstanding the increased cost of grinding,
the increased efficiency more than makes up for the differ-
ence.
Of course in grinding eccentrically relieved cutters it is
equally important that all teeth be ground to the same
length as that they be ground ofif radially.
Forming Tools.
In connection with formed cutters it will be appropriate
to give some attention to forming tools. These are
used either in the lathe or screw machine for duplicate
work, or for forming and relieving formed milling cutters,
which in turn are used to produce a great many pieces of
exactly the same shape. When made for use in lathes or
382
SMALL TOOLS
screw machines, they may be either flat or circular, but
when used for forming and relieving milling cutters they
are always made flat. For screw-machine work the circular
form is the most common. •
Flat forming tools may either be made solid with the
shank, like an ordinary lathe tool, or the tool may be
Fig. 204. Making a Forming Tool in the Shaper
merely a cutter formed to the desired shape and held in a
holder. The tool is made solid with the shank only in the
case of very simple forms. Where forms are more com-
plicated, the tool should be made in a separate piece, and
provision made for holding it securely in a tool holder or
tool clamping device.
MISCELLANEOUS MILLING CUTTERS
883
The flat forming tool is first laid out on the piece from
which it is to be made, and machined to the desired form
without giving any clearance to the tool. In order to
obtain a tool with clearance, this first tool made, tenned
master tool, is used to produce a second tool. The clear-
ance in this second tool is secured by the process shown in
Fig. 204. The master tool is held at an angle in the tool-
post of a shaper, and the blank from which the second
forming tool is to be made is clamped to the shaper table,
being held in a vise at the same angle of incline as the master
Fig. 206. Circular Forming Tool with Clearance for Cutting Edge
tool. When the master tool, No. 1 in Fig. 204, commences
to form the tool No. 2, it is evident that the face of the
latter will become an exact duplicate of No. 1, but being
• held in an angular position, a clearance corresponding to
this inclination is produced. The common angle of clear-
ance on forming tools is 15 degrees. Forming tools used
for relieving formed milling cutters are frequently made
with a clearance of 25 degrees. This is necessary in order
to prevent the tool from interfering with the following
tooth of the cutters when the one opposite the tool is being
relieved.
384
SMALL TOOLS
Circular Forming Tools. — Circular forming tools are
used to a great extent in screw machines, as mentioned.
They are easily made either by a forming tool, being formed
in the same manner as a milling cutter, or by ordinary
turning if the shape of the finished tool is not too com-
plicated. In order to provide for a cutting edge the tool
must be milled as shown in Fig. 205. If the piece to be
formed should be a true duplicate of the forming tool it
would be necessary to mill down the forming tool to a radial
line only, as shown in Fig. 206. But the tool in such a
case does not receive a proper amount of front rake or clear-
Hib
Fig. 206. Forming Tool without Clearance
ance to cut freely. For this reason the tool is milled down
from one-quarter to three-eighths inch below the center,
and in making the forming tool the dimensions must be so
adjusted that when the tool is milled and ground as men-
tioned, the desired form is reproduced in the pieces to be
made. The allowance to be made must be determined in %
each case by calculation.
In Fig. 207, BC represents the actual distance to be
reproduced in the piece of work to be made. But it is
evident that the difference between the radii OC and OB
is less than BC. As the radii OC and OB determine the
shape of the forming tool, these dimensions must stand
in an exact relation to the actual distance BO to
MISCELLANEOUS MILLING CUTTERS
385
be reproduced,
formula
This relationship is expressed by the
BC= VOC^-OA^ - VOB^ - 0A\
This relationship may be better expressed by a general
formula. The distance A,
Fig. 208, in a piece to be
formed must equal the dis-
tance a on the forming tool,
but as this latter distance is
measured in a plane a cer-
tain distance 6 below the
horizontal plane through the
center of the forming tool,
it is evident that the differ-
ences of diameters in the
tool and the piece to be
formed are not the same.
Fig. 207
A general formula may, however, be deduced, by the use of
elementary geometry, by means of which various diameters
Pt=:^
FORMING TOOL
END VIEW OF PIECE
TO BE FORMED
Fig. 208
of the forming tool may be determined if the largest (or
smallest) diameter of the tool, the amount that the cutting
edge is below the center, and, of course, the diameters of
the piece to be formed, are known.
886
SMALL TOOLS
If R = the largest radius of the tool,
a = difference in radii of steps, and
b = amount cutting edge is below center,
then, if r be the radius looked for.
r = ViVR' -b'- ay + bK
If the smaller radius r is given and the larger radius R
sought, the fonnula takes the form
Suppose, for an example, that a tool is to be made to
form the piece in Fig. 209.
Assume that the largest di-
ameter of the tool is to be
3 inches, and that the cut-
ting edge is to be one-quarter
inch below the center of the
tool. Then the next diam-
eter below 3 inches is found
from the formulas given by
inserting the given values:
72 = IJ inches, & = } inch, and a = J inch (half the dif-
ference between 4 and 3 J inches; see Fig. 209).
Then
Fig. 209
= ^(y/ my - ay - ly + ar = V(^h -ir+^
5.017 , ^.. . ,
= — : — = 1.254 inches.
While the formula looks complicated, by means of a
table of squares the calculations are easily simplified and
can be carried out in three or four minutes. The value r
being 1.254 inches, the diameter to make the smaller step
of the forming tool will be 2.508 inches, instead of 2J
MISCELLANEOUS MILLING CUTTERS
387
inches exact, as would have been the case if the cutting
edge had been on the center line.
Sometimes forming tools are made in sections, as shown
in Fig. 210, so that all diameters, sides and angles can be
easily ground after hardening. This design is of value
especially when forming tools are made from high-speed
steel, as the finished surfaces and the edges are likely to
be impaired by the high heat necessary when hardening
high-speed steel.
Fig. 210. Forming Tool Made in Sections
Making Concave and Convex Forming Tools in the
Milling Machine. — A method for making the concave
forming tools used for forming and relieving convex
cutters in a milling machine was described by Mr. J. J.
Lynskey in Machinery, December, 1903. Referring to
Fig. 211, B represents the tool which is held in the holder A
at an angle of 75 degrees with the table of the milling
machine, this giving a 15-degree angle of clearance to the
finished tool. When the tool blank is placed in the holder
the top is milled off parallel with the table of the machine.
A half circle of the desired radius is then drawn on the
back of the tool and a semicircular groove milled nearly
388
SMALL TOOLS
1^
.2
i
■3
o
bo
MISCELLANEOUS MILLING CUTTERS 389
to the line scribed. For finishing the tool a plug C is made,
the end of which is hardened and ground. This plug is
held in a special holder D in the spindle of the milling
machine, and set so that the axis of the plug is perpen-
dicular to the face of the tool to be finished. The spindle
is then firmly locked, and the table of the machine moved
forward and backward by hand until the tool has got the
required shape.
By using the concave tool as a planing tool as shown at
G a convex tool can be formed, but both tools must be
held at an angle of 75 degrees to the milling-machine
table. Of course, this example is given only to suggest
what can be done in a milling machine if a shaper is not at
hand. The latter machine is the one used whenever
possible.
T-Slot Cutters.
The T-slot cutter has gradually and successfully out-
classed the old-style method of planing T slots in milling-
machine tables and other machine tool parts where
T slots are regularly used. The old method was far
more expensive, and the quality of the work obtained was
in no way superior. T-slot cutters, therefore, at the
present time constitute an important tool in the machine
shop, particularly where machine tools are manufactured.
The general appearance of the cutter is shown in Fig.
212. The cutting portion, A^ is provided with teeth on
its face as well as on both sides. A long neck, S, per-
mitting the cutter to advance in the narrow portion of the
T slot, which is already milled with a side milling cutter
before the T-slot cutter is presented, combines the cut-
ting portion with the shank, which latter as a rule is
either a Brown and Sharpe or a Morse taper shank.
In making the cutter, after having been turned all over,
390
SMALL TOOLS
the teeth on the face are first cut. Then the teeth are cut
on the end of the cutter, and finally on the back side at
the neck. In order to provide a cutter that will cut more
easily than would be the case if all the teeth were full, every
other tooth is cut away at the ends as indicated in Fig.
Fig. 212. T-slot Cutter
213, but it should be observed that where a tooth is cut
off at the end face it is left full at the back face and vice
versa. Some makers prefer to leave one tooth full at both
ends to facilitate measuring the thickness of the cutter.
In order to permit the grinding of T-slot cutters with-
out making the slot cut by them too small, they are origi-
Fig. 213. Teeth of T-slot Cutter Cut Away at Opposite Ends
nally made one-thirty-second inch larger in diameter
and one-sixty-fourth inch greater in thickness than the
nominal size-
It is advisable to harden mills of this description the
entire length of the necked portion marked B, Fig. 212,
especially if the neck is of small diameter. Draw the
MISCELLANEOUS MILLING CUTTERS
391
neck to a blue color when tempering, and the cutting
portion to a straw color. The teeth of T-slot cutters
should be coarse and of a form that insures the greatest
strength possible, allowing of course sufficient space between
the teeth to accommodate chips.
TABLE C.
DIMENSIONS OF T-SLOTS.
;^-— A—
• - — —8-- . ...
A
B
c
D
A
B
c
D
I
J
^
A
*
1ft
^
i
i
', 1
\
i
If
1
^
' ■ :
^
T^
1
It
lA
*
16
A
ft
TABLE CI.
SIZE OF SHANKS OF T-SLOT CUTTERS.
Nominal
Size of
Cutter.
Actual
Size of
Cutter.
Nominal
Thickness
of Cutter.
Actual
Thickness
of Cutter.
No. of
Morse
Taper
Shank.
No. of
B. and S.
Taper
Shank.
ift
n
If
1
lA
iJi
4,5
5,7
5,7
7,9
7,9
9
9
9
9
392
SMALL TOOLS
The dimensions of standard T slots for which these cut-
ters are made are given in Table C. As mentioned, the
cutter is originally made one-thirty-second inch larger in
diameter and one-sixty-fourth inch greater in thickness
than these dimensions. The numbers of Morse and Brown
and Sharpe taper shanks with which these cutters are com-
monly provided are given in Table CI.
Metal Slitting Cutters.
Thin cutters intended for cutting ofif or slitting pur-
poses are termed metal slitting cutters. The sides of
these cutters are ground to run true, and made slightly
thicker at the outside edge than at the hole or center, in
order to provide for proper clearance and prevent binding
in the slot cut. For cutting steel the number of teeth
used in these cutters is as follows :
Diameter
Number
Diameter
Number
of Cutter.
of Teeth.
of Cutter.
of Teeth.
2i
30
5i
56
3
36
6
60
3i
40
6i
64
4
44
7
68
4i
48
7J
70
5
52
8
72
For brass and very deep slots the pitch of the teeth
should be coarser in the proportion of about 2 to 3; that
is, if a 4J-inch cutter for steel has 48 teeth, one for brass
should have only two-thirds this number, or 32. In case
very heavy work is required of a metal slitting cutter the
teeth are eccentrically relieved; this permits the teeth to
be wider and stronger.
For light slotting, like screw slotting, etc., a cheaper
MISCELLANEOUS MILLING CUTTERS
393
grade of cutters with very fine teeth, and not ground on
the sides, is used. These are commonly tenned screw
slotting cutters. The number of teeth in these for the
most common diameters is as follows:
Diameter of Cutter.
Number of Teeth.
li
52
2
56
2i
60
2*
64
2}
68
3
72
Inserted-bladb Milling Cutters.
Large milling cutters, say from 6 to 7 inches in diameter
and upward, are usually made with inserted teeth. The
advantages gained are decreased cost, because the cutter
body may be made of either cast iron or machine steel,
and the elimination of loss due to the liability of cracking
in hardening. The cutter body is generally made from
cast iron and the blades from ordinary tool steel. Whether
high-speed steel blades are actually greatly superior to
carbon steel blades for these cutters some manufacturers
doubt. Many users of milling cutters, however, use high-
speed steel cutters, which then should be inserted in
machine steel bodies. The latter material is also used
for. the body of all xnserted-blade cutters smaller than
6 inches in diameter, or where the body is less than
IJ inches thick.
The blades are inserted in slots milled in the body either
parallel with the axis of the cutter or at an angle thereto.
When the cutter is to be used as a plain milling cutter the
blades are usually set at an angle. When the cutter is
394
SMALL TOOLS
used for side or straddle milling or for end milling the
blades are not set at an angle with the axis.
One of the most common methods for holding the
blades in the body is the one shown in Fig. 214. This
method combines simplicity and cheapness with strength
and durability. This method is employed by the Pratt
and Whitney Company. Whether set parallel with or at an
angle to the axis of the cutter, the method of holding the
SECTION B-B
j^
Fig. 214. Method of Securing Blades in Body of Axial' Cutter
blades is the same. As seen from the cut, the blades are set
into rectangular slots in the body and held in position by
means of taper pins which wedge the metal of the body
firmly against the sides of the blades. There is only one
taper pin for every other blade, the pin spreading the
metal equally on each side of a narrow slot A located
halfway between the slots for the blades. Attention
must be called to the fact that the distances between the
teeth must be such as to insure on the one hand perfect
MISCELLANEOUS MILLING CUTTERS
895
holding qualities (that is, the metal between the slot A
and the slots for the blades must not be so heavy as
to prevent good springing action when forced sideways
by the taper pin), and on the other hand a strong and
durable body.
In making these cutters the slots for the blades are first
milled. The taper-pin hole between every other pair of
teeth is then drilled, and reamed to receive the taper pin.
After reaming the holes the narrow slots A are cut with a
thin metal slitting cutter. When the blades are in position
^Projecting Part of
Blade on Back Side
Cutting Sid,e of Cutter
Fig. 215. Section of Inserted Blade End Milling Cutter
the taper pins are driven into the taper holes, closing up
the stock, as mentioned, and holding the cutters securely.
When removing the blades, the taper pins are driven out,
and the stock springing back into its normal position
leaves the cutter free. The blades are, of course, turned
and ground in position in the body. They are backed
off so that the backed-off surface makes an angle of
from 75 to 80 degrees with the front of the blade. The
angle which the slots into which the blades are inserted
should make with the center line when not milled parallel
with the axis should be between 12 and 15 degrees.
396
SMALL TOOLS
Li cutters for end milling, the blades should project a
considerable amount on the back side, as shown in Pig.
215, in order to allow for adjustment when the cutting
faces of the blades by frequent grinding have been worn
down near to the body of the cutter.
Simple Method of Holding Blades. — One very simple
method of fastening the inserted blades to the body is
shown in Fig. 216. This form has been long in use in the
Annstrong Manufacturing Company's shops. While not the
very best construction, for narrow inserted-blade cutters it
Fig. 216. Simple Method of Securing Blades in Inserted Blade Cutter
will prove .satisfactory, particularly because of being a com-
paratively inexpensive method of fastening. The body is
slotted as usual, the blades C are provided with a shoulder,
and against this shoulder bears the head of screw B. In
order to prevent side slip, the inner end of the blade is
notched so as to engage with the body as shown in the
sectional view, Fig. 216. This class of cutter does not
recommend itself for end milling, because the blades are
hardly held securely enough for heavy strains from the
sides or ends.
Fig. 217 shows an English method of securing the teeth
of inserted-blade milling cutters to the body. This arrange-
MISCELLANEOUS MILLING CUTTERS
397
ment is the joint patent of H. S. Moorwood of Onslow
House, Brocco Bank, Sheffield, and J. M. Moorwood of
Millhouses Lane, Millhouses, Sheffield, England. The
body A of the cutter is provided with slots B to receive the
cutter blades as usual, but the lower ends of the cutter
blades, as well as the portions of the body between the
blades, are grooved to .receive the annular projection D of
two disks E which are screwed tightly to the body, thus
holding the blades in place. The groove in the blades as
well as the annular projection on the side plates is slightly
tapered on the inside, so that the inserted blades are drawn
Fig. 217. English Method of Securing Blades in Milling Cutter
inward and held firmly against the bottom of the slots
for the blades in the body when the bolts are tightened.
While, without modification, this method may have its
difficulties, and may be rather expensive, the idea involved
is commendable, and may serve to suggest something of
better practical apphcation.
Inserted-Tooth Formed Milling Cutter.
Fig. 218 shows an inserted-tooth milling cutter, designed
to manufacture the brake shoes shown at ^, in which it is
necessary to keep both the form and the radius of the cut
to gauge. This cutter was shown in Machinery, January,
398
SMALL TOOLS
1908, by Mr. S. A. McDonald. The principle of the inserted
teeth is the same as that of the circular fonning tools used
on screw machines, the teeth being sharpened radially.
The taper studs are used to secure the teeth in place by
forcing the slots open and binding the body of the cutter
on the teeth. The cutter-holding body is grooved in the
center to reduce the body of metal to be sprung out in order
.^3
Fig. 218. Inserted-Tooth Formed Milling Cutter
to bind on the outer edges of the teeth or cutters. As the
teeth become dull they can be ground while in place a few
times before being loosened and again set radially. The
advantage of this form cutter is that the teeth can be ground
to shape after being hardened (because they are ciicular),
which is impossible with the ordinary form cutter, but
often very necessary when the pieces milled have to be
correct within small limits. This permits the use of Novo
or other high-speed steel, which ordinarily cannot be used
MISCELLANEOUS MILLING CUTTERS 399
for form cutters, as the outside is bumed in hardening.
Broken teeth can be easily replaced. No backing-oflf
machine, or fixture,' is needed for making the formed teeth,
which will appeal to small shops. The cost of material is
considerably reduced as compared with a solid form cutter.
Within its limits dififerent kinds of teeth can be used in the
same body, but this is only recommended when the removed
cutters are of no further use.
One weak point in this design of cutter seems to be the
cutting of the central groove J?, which naturally permits the
outer edges of the cutter body to bend inward when the nut
on the tapered pins is tightened for binding the blades.
Another objection is the projection of the nuts outside of
the cutter body, as it is never good practice to have pro-
jections of this kind on rotating bodies if it can be avoided.
These objections, however, are mere details, and can easily
be overcome. The principle of the cutter itself is very
commendable, and may also be of value as suggestive of
similar adaptations for a multiplicity of work.
Dimensions op Inserted-blade Milling Cutters.
Definite dimensions for the various quantities in inserted-
blade milling cutters are difficult to give, as opinions diflFer
considerably. Each type, of course, would require a
different set of dimensions. Table CII gives dimensions
for guidance in laying out cutters of the type shown in
Fig. 214.
Special Form of Milling Cutters.
The Hess Machine Company, Philadelphia, Pa., in 1903
brought out a new form of milling cutter working on a
different principle from the ordinary cutter.
400
SMALL TOOLS
TABLE CII.
DIMENSIONS OF INSERTED-BLADE MILLING CUTTERS.
Fig.
219
A
3
4
5
6
B
8
10
10
12
C
i
A
A
D
f
i
1
1*
E
4
4
5
5
F
2J
3J
4f
5}
Diameter of cutter
Number of blades
Thickness of blades
Width of blades
Size of standard taper pin.
Diameter of cutter body. .
Diameter of cutter
Number of blades
Thickness of blades
Width of blades
Size of standard taper pin
Diameter of cutter body. .
7
14
H
5
6i
A
8
9
10
11
B
16
16
18
20
C
A-
*
*
i
D
1*
H
H
U
E
5
6
6
6
F
71
81
9i
101
12
20
i\
6
111
The action of the ordinary milling cutter produces chips
that are comparatively wide and thin. Each successive
tooth removes a chip having a length equal to the full
width of the cut. The feed per revolution of the cutter is
MISCELLANEOUS MILLING CUTTERS
401
divided into as many chips as there are teeth in the cutter.
While it is true that if the teeth are nicked the continuity
of the chip is broken, still the action is substantially the
same. Cutting the. teeth on a spiral, although it makes
the turning moment uniform and preserves a constant
thrust in one direction, which means a more even cut, does
not change the principle of the cutting action.
In order to avoid the consequent heavy thrust at
right angles to the work the Hess milling cutter removes
the metal in a series of narrow chips, the cut of each tooth
being narrow and deep, similar to that of a planer roughing
-^
Teeth Fused
or Gut in Body
■T' .r. .?;. a
^ C7 Oi_J tJ \.j ..i w/ ujf wi i-x;.-
i;
__ _. _ ___ __ __ __ . J ..x^-^-jk
Merer teas, to allow grinding J »' Alwajrs
Length to suit, bat Maximnm ^ ^**
Length^Width of Machine +8
:=i'f
Fig. 220. Hess Machine Company's New Type Milling Cutter
tool. The cutter is not mounted on a keyed mandrel, but
instead the outer end of the cutter body is formed into a
journal, supported in an outboard bearing, and the other
end carries a plug fitting into the spindle. The end of the
spindle of the milling machine is provided with a flange,
and a corresponding flange is provided on the cutter body,
these flanges being united by bolts. Fig. 220 shows a
cutter made on this principle. The teeth are made of
high-speed steel, working successfully at a cutting speed
of 60 feet per minute. They are cast or fused into the
cast-iron body by being placed in the mold and the
metal poured around them.
402
SMALL TOOLS
The teeth are arranged in a double right-hand heUx
having a lead of 3 inches. Since there are two rows or
threads of teeth there are only two teeth in the same trans-
verse plane, and each tooth takes a cut whose thickness
in the direction of feed is one-half the feed per revolution
of the cutter.
Since the paths of adjacent teeth overlap it gives each
following tooth a finishing action so far as its overlapping
i*AaO HEMtP'
tfiAflPEH ej OfllM^iNa FACES f*A'
PARALLEL TO AXIS, BY DROPPING
A WHEEL OF MAXIMUM RADIOS
R:m\S^N RADIALLY..
Fig. 221. Teeth of Cutter in Fig. 220 shown in half Actual Size
portion is concerned. The thickness of the chip taken by
the overlapping part of a tooth is thin as compared with
the principal chip. The cutting action is very similar to
that of a gang planer tool, each tooth having more of a
side-cutting than an end-cutting action. Consequently
the thrust at right angles to the work is proportionately
reduced.
The teeth reduced to one-half actual size are shown in
Fig. 221. Here are also shown the angle of relief and
clearance.
CHAPTER X.
REAMERS.
Introductory.
Reamers, in the narrowest sense of the word, include
only tools intended for producing a hole that is smooth
and true to size. In a wider sense, however, the word is
applied to any solid circular tool with a number of cutting
edges, used for enlarging cored or drilled holes, little or
no account being taken of whether the resulting hole is
strictly true to size or not. With reference to the manner
in which reamers are made, we may distinguish be-
tween solid and inserted-blade reamers. The latter are
usually adjustable for size. With reference to the pur-
pose of reamers and the manner in which they are used,
"we distinguish mainly between hand reamers, chucking
reamers, shell reamers, and taper reamers. The latter
class of reamers is mostly, perhaps, used by hand, the
same as the hand reamer, but the hand reamer is considered
to mean only a straight reamer, and the taper reamer
forms a class by itself. On the boundary between
reamers and drills is the grooved chucking reamer, which
is used for roughing cored holes, and is fluted with spiral
grooves like a twist drill. Center reamers constitute a
special class of reamers, which are used for reaming the
centers in pieces to be held between the centers in the
lathe.
Hand Reamers.
The ordinary hand reamer, provided with guide, is
shown in Fig. 222. As seen from the cut, it consists of a
403
404 SMALL TOOLS
cutting portion, a shank, and a square by which it is
turned when in use. As is also shown, the end portion of
the shank on which the square is formed is turned down
below the diameter of the shank proper. The purpose of
this is to prevent any burrs that may be raised on the
edges of the square by the wrench by which the reamer is
tiuned from projecting outside of the diameter of the
shank, thus either preventing the reamer from being drawn
clear through the hole reamed or causing scratches in the
hole if the reamer be pulled through. Between the cutting
portion and the shank there is a short neck, the purpose
of which is, primarily, to provide for clearance for the
grinding wheel when grinding the cutting edges as well as
Fig. 222. Regular Hand Reamer
the shank of the reamer, and also to permit the cutter by
which the flutes are cut to clear the shank so as to give a
more finished appearance to the tool.
Requirements Placed on a Hand Reamer. — ^Hand reamers
are probably among the most diflScult and particular tools
to make and manufacture. In many reamers manu-
factured by firms considered to be leaders in the making of
small tools no regard or attention seems to have been
^ven to some of the most essential points in the making
of these tools. As of course everybody knows, it is abso-
lutely necessary when making a good hand reamer to take
into consideration that the reamer is expected to produce
(1) a smooth hole, (2) a straight hole, and (3) a round
hole.
REAMERS 405
If we now consider first what means are generally used
for making reamers that will produce a smooth hole, we
will find that three ways have been tried with more or less
success. The first and earliest method used to prevent
chattering was making an odd number of flutes in the
reamers, but this has been almost entirely discarded on
account of the difficulty in measuring the diameter of such
reamers, it being possible to gauge this diameter only with
ring gauges. At present some manufacturers, in order to
overcome the vibrations which mar the smoothness of
the hole, make their reamers with spiral flutes. This,
although partly overcoming the difficulty referred to, has
several serious disadvantages. In the first place, such a
reamer is more difficult and more expensive to flute, not
to mention the difficulty of giving such a reamer the proper
relief. In the second place, a reamer fluted in such a way
has the disadvantage of either working forward or resist-
ing, depending on whether right-hand or left-hand spiral
flutes have been given to the reamer in question. It may
be noted that it is preferable to make regular right-hand
reamers of this description with left-hand spiral flutes,
which will prevent the reamer from working forward.
Some one might think that the working forward of the
reamer (to a certain extent depending upon the amount
of spiral given to the flutes) would rather be an advan-
tage, and so it would provided that the forward motion
could be on the one hand perfectly uniform and on the other
hand small enough to advance the reamer a very limited
distance for each revolution. This result, however, can be
obtained in a very much simpler and cheaper way by using
straight flutes and threading the reamer on the point for a
short distance. The advance of the reamer in this case
will of course be governed by the pitch of the thread. The
outside diameter of the threaded portion must obviously
406 SMALL TOOLS
be slightly smaller than the diameter of the reamer
itself.
Returning to our original consideration in regard to the
means employed to prevent vibration, the third way used
is to "break up the flutes," which means that the cutting
edges are not equally spaced, although the reamer then is
given an even number of flutes. This unimifonnity in
spacing need not be greater than to permit a gauging of the
diameter of the reamer over two opposite cutting edges
that will be correct for all practical purposes. The " break-
ing up of the flutes" is the simplest and most effective way
to obtain the result wanted, viz., a smooth hole. Leading
manufacturers are commencing more and more to manu-
facture their reamers in this manner.
The second consideration which was mentioned above as
necessary in a good reamer is its capability of producing
a straight hole. This is the principal point referred to in
the beginning of this chapter which seems to have been
wholly disregarded by manufacturers of reamers. No
reamer will produce a straight hole unless it is properly
started, and no reamer will start properly unless it is
properly guided. It is obvious that even with the most
extreme care, and handled by the most experienced man,
a reamer without a guide will make the hole slightly
tapered, and too large at the end where the reamer first
enters the work.
The way hand reamers are generally made for the
market is to simply taper the point for a certain distance
up, leaving nothing to steady or guide whatsoever. This
is not right. Instead a fluted cylindrical portion of the
end of the reamer should be left without relief, and this
part should be as much less in diameter than the reamer
itself as is practical for various metals to be cut with the
reamer. As this amount is very small and is left entirely
REAMERS 407
to the judgment of the manufacturer, the practice of
making reamers with guides slightly smaller than the
diameter of the reamer would prevent the user from mis-
using and abusing the tool, as he cannot use it to remove a
greater amount of metal than the reamer is intended for,
because the guide will not enter a hole that is not roughed
out suflBciently large before hand reaming. When using
a reamer with a tapered point it is usually possible to
enter and start the reamer in holes so much smaller than
the finished size as to seriously injure and even spoil it
by trying to make it perform a duty for which it was not
intended, this being possible because the taper is made so
large by most manufacturers as to permit it.
The third consideration, previously referred to, and
essential m a good reamer, is its capability of producing
a round hole. Most of the reasons set forth in treating
the possibilities of getting a smooth and a straight hole
apply here also, and it may well be repeated that unevenly
spaced (broken up) cutting edges and a guide nicely
fitting the hole to be reamed are the most essential
requisites for obtaining the desired results.
Relief.
It will also be necessary to remark that giving too much
or too little relief to a reamer will tend to produce unsatis-
factory results. Too much relief invariably causes a
reamer to chatter. Too small relief, again, will wear the
reamer more, as the shavings get in between the cutting
edges and the work to be reamed and slowly grind away
the land; besides, there is a tendency to bind the reamer
in the hole, and as a consequence to injure the hole as well
as the reamer, and cause the expenditure of more exertion
in performing the reaming operation.
408 SMALL TOOLS
In this connection it may be mentioned that the flat
relief, although mostly used, is not the most desirable nor
the ideal one, because the cutting edge is not properly
supported. The best results are obtained by a relief as
shown in Fig. 223. The difference between this relief
and the flat is very obvious from the cut, where the
latter relief is shown in dotted lines. This special relief,
usually termed the eccentric relief, is used by only two
prominent tool manufacturers, but it is to be strongly
recommended because it adds greatly to the reamer's
Fig. 223. Comparison between Eccentric and Flat Relief
capability of producing a smooth hole. The relief is pro-
duced by placing the reamer in a grinding machine, as
usual, but not on centers in line with the spindle but on
auxiliary centers, provided with adjustment sideways, so
as to enable them to be set at different positions for differ-
ent relief wanted on different sizes and kinds of reamers.
The reamer is thus held eccentrically. A rocking motion
is then imparted to the spindles holding the auxiliary
centers, and in this manner the grinding wheel, traveling
back and forth along the reamer, produces an eccentric
relief.
This eccentric relief, however, is not in favor with all
REAMERS 409
users of reamers. The eccentrically relieved reamer is
purely a finishing reamer, and cannot with advantage be
used to remove any considerable amount of metal, because
it has practically a negative rake. When hand reamers
are used merely for the purpose of removing stock, or in
other words, simply for enlarging holes, the flat relief will
undoubtedly prove to be superior to the eccentric. The
primary use of straight hand reamers, however, is for
producing holes true to size and smoothly finished, remov-
ing meanwhile but a small amount of stock. For this
purpose nothing excels the eccentric relief. That there is
a distinct difference between the relief required, accord-
ing to the use to be made of the reamer, is best proved by
the fact that, while some manufacturers of tools always
relieve their reamers eccentrically, intending them to be
used as finishing reamers, some of their customers, after
receiving the reamers, place them in a grinding machine
and replace the eccentric relief with a flat one, because
they find this relief better for their purpose, viz., simply
enlarging holes, irrespective of the requirements of
accuracy and smoothness.
Reamers with Helical Flutes.
Although the advantages of helical or, as they are com-
monly called, spiral cutting edges are somewhat doubtful
for straight reamers for ordinary use, they are recom-
mended for work where the hole reamed is pierced
crosswise by openings. A right-handed reamer should
have left-hand spiral flutes, in order to prevent the tool
from drawing into the work. The angle of spiral should
be such that the cutting edges will make an angle of
15 degrees with a plane passed through the axis of the
reamer. The number of flutes may be the same as if the
410
SMALL TOOLS
reamer were provided with straight cutting edges, and
the same kind of fluting cutters are employed.
Threaded-end Hand Reamers.
As has ah-eady been mentioned, hand reamers are some-
times provided with a thread at the extreme point in order
to give them a uniform feed when performing the reaming
operation. The diameter on the top of this thread at the
point of the reamer is considerably smaller than the reamer
itself, and the thread tapers upward until it reaches a
dimension of from 0.003 to 0.008 inch, according to size,
below the size of the reamer; at this point the thread stops,
and a short neck, about one-sixteenth inch wide, separates
the threaded portion from the actual reamer, which is
provided with a short taper from three-sixteenths to seven-
sixteenths inch long, according to size, up to where the
standard diameter is reached. In fact, the reamer has the
appearance of the regular reamer in Fig. 222, excepting that
the guide is threaded and tapered.
The length of the threaded portion and the number of
threads per inch with which to pro'sdde the point are given
below.
Size of Reamer.
From i to A i^^ch
From li to i inch
From j| to I inch
From II upward . .
Length of
Number of
Threaded
Threads
Portion.
per Inch.
t
32
^
28
i
24
A
18
The kind of thread employed is the sharp V thread, as
this thread gets a better grip on the metal, and thus feeds
the reamer in a more certain manner.
REAMERS 411
The diameter measured over the top of the thread at the
end of the point of the reamer should be as follows.
Size of Reamer.
Diameter of Thread at Point of
Reamer.
From J^ to i inch
Standard size — 0 . 006 inch
From ^i to 1 inch
Standard size — 0 . 008 inch
From 1-JW to 14 inches
Standard size — 0.010 inch
From 1 II to 2 inches
Standard size — 0.012 inch
From 2ijC to 2i inches
Standard size — 0.015 inch
From 245 to 3 inches i
Standard size — 0 . 020 inch
Breaking up of the Flutes. — As has been previously
mentioned, the best way to obtain a good hand reamer is
to have the cutting edges irregularly spaced. This dif-
ference in spacing may in fact be made very slight. The
manner in which it is usually done is to move the index
head, in which the reamer is fixed, a certain amount more
or less than would be the case if the spacing were regular.
In Table CIII a chart is presented which will serve as
a guide in fluting reamers with irregular spacing. This
chart gives the amount that the index head should be
moved more or less than would be the case for even spacing.
The figures designate the number of holes to move in a
certain index plate used in each special case. It is, of
course, understood that this table is given only as an
example of how tables of this kind may be worked out, as
there evidently is an unlimited number of variations.
Dimensions, — In Table CIV the principal dimensions
for hand reamers are ^ven. These dimensions are figured
from the formulas which are given below. No figures are
given in the table for the diameter of the shank, as on any
size reamer the general rule to make the shank very slightly
below (0.001 to 0.002 inch) the diameter of the reamer may
be adopted. The part of the shank which is squared should
412
SMALL TOOLS
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REAMERS
418
be turned enough smaller in diameter than the shank itself
so that when appl3dng a wrench no burr may result which
eventually would interfere with the reamed hole if the
reamer were passed clear through.
Figures for the diameter of the guide will not be found
in the table, as here no definite rule can be given. For
different metals it is obvious that different amounts should
be left for the reamer to remove. As a guidance for all-
around work it may be said that the guide should be made
from 0.005 to 0.010 inch smaller than the standard size of
the reamer for diameters up to 1 inch, and from 0.010 to
0.015 inch smaller for diameters from 1 to 3 inches. At the
upper end of the guide there is a tapered portion (shown
^E-^
r-Sfze
of Square
____3^_-_J
i%
^ B
^
Fig. 224
exaggerated in Fig. 224) extending from about three-
eighths to five-eighths inch for the smaller and from
three-quarters to 1{ inches for the larger sizes mentioned.
In all the formulas the diameter of the reamer is con-
sidered as the fundamental factor. In the formulas
A = the diameter of the reamer,
B = the total length,
C = the length of the flute,
D = the length of the shank,
E = the length of the square,
F = the size of the square,
G = the length of the guide.
TABLE CIV.
PROPORTIONS OF HAND REAMERS.
(See Fig. 224.)
Diameter.
Total
Length.
Length
of
Flute.
Length
of
Shank.
Length
of
Squared
Part.
Size of
Square.
Length
of
Guide.
i
A
i
t
i
^
i
;*
r
«
lA
u
lA
11
lA
H
If
iH
!l*
1«
2
2A
2i
2A
2i
if
2A
2J
2A
2f
2f
2ii
2}
2«
. 3
2A
2f
3A
3J
3«
41
m
SJ
Stt
6*
6A
7
7A
7t
8A
8f
9A
9A
9f
lOA
lOi
lOit
lOi
iiA
111
iiA
iifl
12
12A
'H
12A
12}
12tt
13J
13A
13i
13H
131
14A
^H
14A
14f
im
16
i
li
If
1{
2J
^
3
3i
31
If
4i
41
J!
5A
5A
51
51
5f
51
51*
6A
6A
61
«i
61
6
6
6
;f
71
71
71
7A
711
7"
8
81
81
lA
11
111
If
2A
'A
ill
3
3A
3f
3A
3f
3«
41
*^
4A
41
4A
411
41
41f
5A
51
5A
51
5f
5A
51
5A
511
51
51*
5f
6
It
6A
6A
**,
6A
61
\i
If
\i
lA
U
lA
lA
IM
If
IS
14§
11
IH
lA
V
REAMERS
415
For reamers from one-sixteenth to 1 inch diameter the
following formulas are used:
^_7(4A + 1)^
C = 4A+f,
D=3A + li,
2 16
jr. 3A
G =
QA + 1
8
For reamers .from li^ inches to 3 inches the following
formulas are used:
B = 3A +6,
^=2-^16'
^ 7 A + 12
,.U,
r^ 5A + 12
D— . >
« = 4A+3
8
In Table CIV some dimensions are given in even six-
teenths when the formulas give uneven values.
Number of Flutes. — The following table gives the
number of flutes with which hand reamers should be
provided. It will be noticed that even the smallest sizes
are provided with six flutes. It is not considered good
practice to make hand reamers with a smaller number of
flutes if good results are expected from the use of the tool.
Size of Reamer.
Number of Flutes.
From i to i inch
6
8
10
12
14
16
From JJ to 1^ inches
From 1^ to If inches
From 1 §1 to 2f inches
From 2^ to 2} inches
From 2§| to 3 inches
416 SMALL TOOLS
From this table it will be seen that the pitch of the
teeth, or the distance from cutting edge to cutting edge
around the circumference of the reamer, increases from
about one-eighth inch for a one-quarter-inch reamer to
about nine-sixteenths for a three-inch reamer. The pitch of
the cutting edges for a one-inch reamer is about three-
eighths inch and for a two-inch reamer slightly more than
one-half inch.
Fluting Cutters for Reamers, — Often the same kind of
fluting cutters as are used for hand taps are employed
for reamers also. The reamer, however, does not remove
the same amount of metal as does the tap, and conse-
quently there is no need for the same amount of chip
room. The radius in the bottom of the flute is made
smaller, because the flute, being made shallower, does
not take away so much of the strength of the reamer,
and consequently the reenforcement in the form of a liberal
roimd in the bottom of the flute is not necessary.
Besides, the flutes on very small reamers are so shallow
that a comparatively large radius on the fluting cutter
would give a too great negative front rake to the
teeth.
Figs. 225 and 226 give the usual forms of reamer fluting
cutters. Fig. 225 shows a cutter of the same kind as used
for taps, but with a smaller radius, D. This class of
cutter is used for smaller size reamers, say up to If inches
diameter inclusive, while the cutter Fig. 226 is used for
larger sizes. The inclusive angle between the cutting
faces of the cutters is 85 degrees in both cases, the same
as for tap fluting cutters, but while the cutter Fig. 225
has one face making 55 and the other 30 degrees with a
line perpendicular to the axis of the cutter, in the cutter
Fig. 226 these angles are 15 and 70 degrees respectively.
In Table CV are given the dimensions commonly
REAMERS
417
employed for these cutters and the corresponding sizes
of reamers for which they are used,
TABLE CV.
FLUTING CUTTERS FOR REAMERS.
-B ^
A,
1
c
r
c
1
-16K-^
Fig. 226
Fig. 226
Diameter of
Reamer.
Diameter of
Fluting
Cutter.
Thiclsness of
Fluting
Cutter.
Diameter of
Hole in
Cutter.
Radius
between
Cutting Faces
of Cutter.
A
B
C
D
i
A
i
i
1
li
li
U
2
2i
2J
2}
3
If
H
If
2
2
2
2
2i
21
2i
2i
^
2i
2i
2J
2i
A
A
A
i
i
A
B
7
1
i
!
1
i
f
( sharp corner,
1 no radius.
( sharp corner,
( no radius.
1
A
418
SMALL TOOLS
Setting the Cutter for Fluting. — When setting the
cutter for fluting hand reamers, it should be set so that
the tooth gets a^Iight nega-
tive rake, that is, the cutter
should be set "ahead" of
the center as shown in Fig.
227. The amount to set
the cutter ahead should be
so selected that the angle
included between the front
face of the tooth and the
tangent to the circumfer-
ence of the reamer at the
point representing the cut-
ting edge will be 95 degrees.
(See Fig. 227.) A reamer
will cut more smoothly if
the cutting edge of the tooth
has a negative rake than
it will if the front face of the tooth is radial, that is,
running to the center.
Fig. 227. Setting the Cutter for
Fluting Reamers
TABLE CVI.
AMOUNT TO SET CUTTER AHEAD OF RADIAL LINE (see Fig. 227)
TO OBTAIN NEGATIVE FRONT RAKE.
Size of
Size of
Reamer.
a
Reamer.
a
0.011
li
0.066
1
0.016
u
0.076
h
0.022
2
0.087
0.027
2i
0.098
■
0.033
^
0.109
0.038
2}
0.120
1
0.044
3
0.131
li
0.055
REAMERS 419
In Table CVI the dimension a, Fig. 227, or the amount
to set the fluting cutter ahead of the radial line, is given.
The figures in this table give the angle ABG approxi-
mately 95 degrees as mentioned.
There may be objections raised to setting the fluting
cutter as much as one-eighth inch ahead of the radial line
for three-inch reamers, but inasmuch as the angle of nega-
tive rake remains the same as for smaller sizes, there is no
good reason why this amount should be made any smaller
than given in the table.
The depth of the flute should be such that the width of
the land of the tooth is about one-fifth of the average
distance from the face of one tooth to that of the next.
Should it not be as deep, there will not be room in the
grooves to hold the chips; should it be deeper, the teeth
will not be suflSciently strong, and will spring out into the
stock being cut, producing a very unsatisfactory hole which
will in all probability be larger than the reamer. The
width of the land will, of course, vary somewhat, due to the
breaking up of the flutes, which makes some of the lands
wider than the others.
Special Reamer Flitting CvMer, — The difficulties encoun-
tered in milling the flutes on unequal distances, or break-
ing up the flutes, . as it is commonly termed, are, as
mentioned, that if all the grooves are milled to the same
depth the remaining land will evidently be wider in the
case where the distance from cutting edge to cutting edge
is larger than it will be in the case where this distance is
smaller. To overcome this it would, of course, be possible
to mill the flutes deeper between the cutting edges, which
are further apart to insure that the width of the land would
be equal in all cases. That this is impracticable when
fluting reamers in large quantities is easily apprehended,
as it would necessitate raising or lowering the milling-
420
SMALL TOOLS
machine table for each flute being cut. Li Fig. 228 is
shown a method employed by the large machine-tool firm
of Ludwig Loewe & Co., Berlin, Germany. The principle
of this method is clearly shown in the cut. A formed
cutter, eccentrically relieved, is employed, which instead
of forming only the flutes, fonns the actual land of the
reamer, thus insuring that every land will be equally
wide with the others. The depth of the flute is deter-
mined by the depth of the portion of the cutter in front of
the cutting edge of the reamer, and it is easily seen that all
the flutes will be equally deep.
Fig. 228. Special Formed Reamer Fluting Cutter
That this method will be more expensive than the one
commonly employed, in which the lands are permitted to
become wide or narrow according to the amount the flutes
are broken up, is evident, but it cannot be disputed that
the general appearance of the reamer will be greatly
improved. The greater expense in making reamers in this
manner will depend on two factors. Li the first place,
the eccentrically relieved cutter will cost more to produce
than the ordinary fluting cutter. Li the second place, the
cutting speed cannot be as high with a cutter of this descrip-
tion as it can be with an ordinary milling cutter. On
the other hand, it is possible not only to gain the advan-
BEAMERS 421
tages mentioned above in regard to width of land and
depth of flute, but incidentally there is also gained the
possibility of giving to the flute a more accurate form to
answer the requirements of strength as well as chip room,
which are often by necessity overlooked on account of the
straight sides forming the flutes which must be adopted
when using the ordinary straight-sided fluting cutter,
with milling cutter teeth of the common shape. While it
cannot be expected that this method will be used to any
great extent on account of its drawbacks from a commercial
point of view, it is ingenious and well worth attention. In
Fig. 228 the fluting of a shell reamer is shown, but what has
been said applies, of course, equally as well to hand reamers.
Precautions in Hardening Reamers.
If the reamers to be hardened are larger than three-
quarters inch in diameter they should be held over the fire
immediately after being taken from the hardening bath, in
order to remove as much as possible the strains caused by
the hardening process. Another method is to remove the
reamer from the water bath as soon as it stops "singing'*
and plunge it immediately into an oil bath, allowing the
tool to stay in the oil until its temperature has been reduced
to that of the oil. The temper should be drawn to 370° F.
If reamers spring in hardening they are heated slightly and
pressure is applied to the convex side, the reamer being held
between centers in the same manner as in a lathe. This
same method is applied to long taps and to counterbores and
drills.
Principles of Grinding Reamers*
When grinding reamers, whether they be given an
eccentric or a flat relief, it is necessary to rest the face of
the tooth being ground against a guide finger which can
422 SMALL TOOLS
be adjusted to ^ve any desired amount of clearance.
Fig. 229 shows an end view of a reamer being ground.
A represents the emery wheel, which should run in the
direction of the arrow, so that the tooth of the reamer
may be pressed down on the finger JB. If the wheel were
running in the opposite direction, it would have a ten-
dency to pull the tooth of the reamer away from the guide
finger; the cutting edge of the tooth would then be groimd
away, and the reamer would be spoiled. It is claimed
that when using a dry grinder, that is, one where water is
not used on the emery wheel, the danger of heating the
Fig. 229 Fig. 280
tooth and drawing the temper is greater when the wheel
is run in the direction shown in Fig. 229; but if the face of
the wheel is kept free from glaze, and ordinary care is
exercised, there is little danger of drawing the temper,
provided a cutting wheel that is not too fine is used. In
order to give the tooth the proper clearance, the guide finger
is adjusted to bring the cutting edge below the center line.
It should not be attempted to remove too great an amount
of stock at one cut; it is better to take a number of suc-
cessive cuts, going around the reamer several times.
When grinding reamers it is absolutely necessary to
rest the face of the tooth being ground on the guide finger,
otherwise the teeth, particularly when irregularly spaced,
REAMERS 423
would not be ground with an equal amount of clearance,
nor would all the cutting edges be at an equal distance
from the center line of the reamer, and some of the teeth,
consequently, would not cut when such reamers were used.
Figs. 229 and 230 show, respectively, the correct and in-
correct ways of applying the guide finger, it being in
Fig. 230 applied to the tooth below the cutting edge
being ground.
Care should be taken not to give the cutting edge of a
reamer any more clearance than is necessary to permit
I
L jr. J
1>
Fig. 231. Fluted Chucking Reamer with Straight Shank
Fig. 282. Fluted Chucking Beamer with Taper Shank
it to cut freely. Too much clearance produces a weak
edge which is liable to chatter, and the reamer soon loses
its size.
Fluted Chucking Reamers.
Fluted chucking reamers are used in machines for en-
larging holes and finishing them smooth and true to
size. They are usually provided with either straight
or standard taper shank as shown in Figs. 231 and 232.
They are not intended for removing any large amoimt of
stock, 0.005 to 0.010 inch being aU that should be
424 SMALL TOOLS
required. The cutting edges are along the lines ah, and
at the front end there is a slight round, as shown at 6.
In cases where a very accurate hole is desired it must
be remembered that reamers held rigidly at the end of
the shank are liable to cut holes somewhat larger than
their own size. In such cases the reamers used for
chucking purposes should be somewhat smaller than the
final size of the hole to be reamed, and after having
reamed the hole by the chucking reamer it should be
finished by a hand reamer.
Number of Flutes. — The number of flutes with which
fluted chucking reamers should be provided is given in
the following table. It will be noticed that the pitch of
the cutting edges, or the distance from cutting edge to
cutting edge around the circumference of the reamer, is in
some cases a trifle smaller than in the case of hand
reamers. The same fluting cutters as are used for hand
reamers are used for fluted chucking reamers also.
Size of Reamer.
Number of Flutes.
From J to J inch .
6
8
10
12
14
16
From §j to 1 inch
From JW to Ht inches
From l|^ to 2 inches
From 2 JW to 2^^ inches
From 2i* to 3 inches
The slight rounded comers at the end of the flutes 6,
Figs. 231 and 232, should have a radius of one-thirty-second
inch for sizes up to and including three-quarters inch, and
one-sixteenth inch for larger sizes.
Dimensionlk. — The only two dimensions of conse-
quence are the over-all length and the length of the cut,
denoted 0 and D, respectively, in Fi^. 231 and 232.
REAMERS 426
The over-all length of the straight^hank and the taper-
shank chucking reamer are usually the same. The taper-
shank is nearly always a Morse standard taper. The
■size of reamer and the corresponding Morse taper shank
with which this reamer is provided are as follows :
Size of Reamer.
Number of Morse
Taper.
From J to i inch
1
2
3
4
5
From J^ to J inch
From JJ to 1 J inches
From 1 A to 1} inches
From l|| to 3 inches
The length of the cut, C, and the total length, D, Figs.
231 and 232, may be determined from the formulas:
C=E + finch and
D = 4:E + 5 inches,
in which formula E denotes the diameter of the reamer.
Dimensions figured from these formulas will be found in
Table CVII.
The diameter of the neck between the fluted part of the
reamer and the taper shank, Fig. 232, should be about one-
thirty-second inch smaller than either the diameter of the
reamer or the diameter at the large end of the shank,
depending upon which of these two diameters is the
smaller, so that the grinding wheel will clear the necked
portion when both the reamer part and the shank part
are ground.
The diameter of the straight shank should be from one-
sixteenth to one-quarter inch below the size of the reamer
for sizes up to one and one-half inches diameter. For
larger sizes the shank may be proportionally smaller, so
426
SMALL TOOLS
that the shank for a two-inch reamer is one and one-half
inches and for a three-inch reamer one and three-quarters
inches.
TABLE evil.
DIMENSIONS OF FLUTED CHUCKING REAMERS.
(See Figs. 231 and 232.)
Diameter
of
Reamer.
Length
of
Flute.
Total
Length.
Diameter
of
Reamer.
Length
of
Flute.
Total
Length.
E
C
D
E
C
D
i
6
11
2i
101
A
lA
61
1
2
11
1
H
6i
2
111
A
lA
6f
2
12
1
7
1
2
121
A
\t
7i
7i
2
2i
2J
13
131
i
lA
7}
2
3
14
8
2
3i
• 141
•
IJ
8}
2
3i
15
1
1}
9
2-
3i
16
IJ
li
9i
3
3f
17
u
2
10
Rose Chucking Reamers.
The rose chucking reamer is used for enlarging cored
holes, and is so constructed as to be able to remove a con-
siderable amount of stock. As shown in Fig. 233, the
cutting edges are on a 45-degree bevel on the end of the
reamer. At every other cutting tooth there is a groove
cut the full length of the reamer body. This groove serves
the purpose of providing a way for the chips to escape, and
forms a channel for lubricants to reach the cutting edges,
but does not have any cutting edge itself. Rose reamers
were formerly made without the grooves. The body of the
REAMERS
427
reamer was solid, with the exception of the cuts made to
form the teeth at the end, and for this reason they caused a
vast amomit of trouble, which has been done away with,
however, by cutting grooves for every other tooth as
mentioned. In fact, there is no reason why this groove
should not be cut for every tooth, excepting that it
would increase the expense of making the tool, and not
being imperative, this expense is, of course, properly
avoided.
Rose chucking reamers are slightly back tapered on the
Fig. 233. Rose Chucking Reamer
cylindrical body, that is, the diameter at the point with
the beveled cutting edges is slightly larger than the body
where it joins the shank. This provision also aids to pre-
vent the tool from binding in the hole being reamed. The
back taper ought properly not to exceed 0.0005 inch per
one inch, although it is usual in the manufacture of these
reamers to make this taper as much as 0.001 inch per one
inch.
The length of the beveled edge, F, Fig. 233, should in-
crease with the size of the reamers. The length for various
sizes should be as follows:
428
SMALL TOOLS
Size of Reamers.
Length of Beveled
Cutting Edge, F,
Fig. 233.
From T to # inch
A
From ^ to # inch
From -li- to i inch
From 4f to 14 inches
From IJL to 14 inches
From liA to 1ft inches
From liH- to 2 inches
From 2 Jlc to 2^ inches
From 2Ja to 24 inches
From 2^ to 34 inches
From 3JW to 34 inches
From 3m to 4 inches
This forai of reamer will usually produce holes slightly
larger than the size, and should always be made from
0.005 to 0.010 inch smaller than the finished size, and be
followed by a fluted reamer for finisliing. In cored holes
these reamers, however, are of great advantage, firstly, be-
cause they can take a heavy cut, and secondly, because
they will cut a hole that is nearer parallel than will a fluted
reamer if there are blowholes or hard spots in the walls
of the surface being worked upon.
Fluting Rose Reamers. — The grooves with which rose
reamers are provided along their cylindrical surface, not
being intended to produce cutting edges, are not of the
same shape as those cut in fluted reamers. A convex
cutter, having a width equal to from one-fifth to one-
fourth the diameter of the rose reamer itself, should be
used for cutting the groove. The depth of the groove
should be from one-eighth to one-sixth the diameter of
the reamer. The cylindrical part of the reamer between
the grooves should not be relieved but should be left
circular.
Rose reamers smaller than one-quarter inch in diameter
may be made without grooves, but in such a case they
REAMEES 429
should have only three teeth on the end, and fairly deep
cuts between the teeth to take care of the chips. The
best practice is, however, to provide rose reamers of all
sizes with grooves on the cylindrical part.
The number of cutting edges on the 45-degree beveled
end of the reamer is as follows:
Size of Reamer.
Number of Cutting
Edges.
From i to J inch
6
8
10
12
14
16
From U to 1 inch
From 1-JW to W incbeff r - „
From 1^ to 2 inches
From 2 A to 2^ inches
From 20 to 3 inchfta
The number of grooves is evidently equal to half the
number of cutting edges, there being one groove on the
cylindrical part for every second cut at the end. The
cuts at the end are milled with a 75Kiegree angular cutter.
The width of the land at the cutting edge should be
about one-fifth the distance from tooth to tooth. If
an angular cutter is preferred rather than a convex for
cutting the grooves on the cylindrical surface because
of the higher cutting speed permissible when milling the
grooves, an 80-degree angular cutter with a slight round
at the point may be used.
Dimensions. — Rose chucking reamers, like fluted chuck-
ing reamers, are made with both straight and taper
shank. The same dimensions for the total length as were
^ven for the fluted reamers apply to the rose reamers also,
but the length of the grooved portion of the reamer, or the
body, is longer. If E is the diameter of the reamer and C
the length of the grooved part (see Fig. 233), then
0 = -^ 4- IJ inches.
480
SMALL TOOLS
In Table CVIII aie given the dimenaons for rose
chucking reamers in accordance with this formula. What
was said in regard to the straight and taper shank of these
reamers, and the diameter of the neck in the latter class, in
connection with fluted chucking reamers applies to rose
reamers also.
TABLE CVIII.
DIMENSIONS OF ROSE CHUCKING REAMERS.
(See Fig. 233.)
Diameter
of
Reamer.
Length
of
Body.
Total
Length.
Diameter
of
Reamer.
Length
of
Body.
Total
Length.
B
C
D
E
C
D
i
6
U
3A
lOJ
t
6i
U
31
11
iH
61
1|
3A
Hi
A
6}
U
3v
12
i
ll
7
U
1!*
12i
A
2
n
2
13
tt
2A
2i
n
2
4^
V
13i
n
2
4
14
2
8
2
4^
i
14i
2A
8i
2
4^
15
1
2f
9
2
6J
16
U
2}f
9i
3
6
17
li
3
10
Jobbers' Reamers.
The jobbers' reamer, Fig. 234, constitutes, a class of
reamers by itself. It is provided with a long fluted body
and taper shank for use in machine. The comers at the
point of the reamer are slightly rounded as shown at a.
The radius for this rounded part should be about one-
thirty-second inch for reamers smaller than three-quarters
inch in diameter, and one-sixteenth inch for lai^r
sizes.
REAMERS
431
Between the fluted portion and the shank a neck is pro-
vided in order to permit the shank and the cutting edges
to be ground. The length of this neck varies according to
the size of the reamer. It is customary to make it about
one-half inch long for quarter-inch reamer, 1 inch for a
1-inch, 2 inches long for a 2-inch, and 3 inches long for a
3-inch reamer. The shank is nearly always a Morse stand-
Fig. 234. Jobbers' Beamer
ard taper shank. The sizes of shanks to use for various
sizes of reamers are as follows:
Size of Reamer.
Number of Morse
Taper Shank.
From 4- to i inch
1
2
3
4
5
From i^ to f inch
From If to IJ inches
From 1-A to ll- inches
From Iww to 3 inches . .
Jobbers' reamers are fluted with the same kind of cutters
as hand reamers. The number of flutes is also the same
as given for hand reamers.
Dimensions. — The length of the neck having already
been given, and the number of Morse taper shank deter-
mining the length of the shank part of the reamer, the only
additional dimensions necessary are the length of the flute
and the diameter of the neck. The latter should be about
one-thirty-second inch smaller in diameter than either the
reamer itself or the largest diameter of the taper shank,
depending upon which of these dimensions is the smaller,
432
SMALL TOOLS
go that the grindiiig wheel will clear the neck when grinding
the teeth as well as the shank.
The length of the flute may be determined from the
formula
A = 4D + 1 inch
for sizes up to and including 1| inches, and from the formula
A = -— + 4^ inches
for larger sizes. In these formulas A = length of cut and
D = diameter of the reamer. Dimensions for the length
of the flutes, approximately figured from these formulas,
are given in Table CIX.
TABLE CIX.
DIMENSIONS FOR THE LENGTH OF FLUTES OF JOBBERS' REAMERS.
(See Fig. 234.)
Diameter
Length
Diameter
Length
Diameter
Length
of
of
of
of
of
Of
Reamer.
Flute.
Reamer.
Flute.
Reamer.
Flute.
D
A
D
A
^
A
i
2
a
4i
U
6tt
2i ;
^
U
ej
i
4*
2
^
2}
5 i
2
7i
i
3
IJ
5i
2
7A
ft
3i
1
6
2
I
3i
1 '■
61 i
2
3i
1 :
61 1
2
7*
i
4
6i i
3
Si
Shell Reamers.
In order to save the amount of stock which goes into the
shank, shell reamers, having a hole through the center by-
means of which they are mounted on arbors, are quite
REAMERS
488
largely used. As one arbor can be used for a number of
reamers the saving is quite considerable. An ordinary
fluted shell reamer is shown in Fig. 235. The arbor on
which it is used is shown in Fig. 236. The reamer has a
key-way A which fits the key B on the arbor freely; the
reamer, when at work, is rotated by means of this key and
key-way. The hole through the reamer tapers, the taper
being one-eighth inch per foot. Manufacturers of reamers
have adopted certain standard sizes of arbors, and each
arbor corresponds to a certain number of different sizes of
reamers. Thus several sizes of reamers are provided with
Fig. 236. Fluted Shell Beamer
the same size hole through them, and can be used with the
same arbor. The arbor as well as the hole in the reamer
must be ground after hardening to insure that the reamer
will run true. When hardening, if the reamer is larger
than \\ inches in diameter, it should be removed from the
hardening bath, the same as large hand reamers, when it
ceases "singing," and be plunged into a tank of oil, where
it should remain imtil cool. When the tool is removed
from the oil bath, or, in the case of smaller reamers, from
the water bath, it should be held over a fire and slowly
revolved until at least partly relieved of the internal
stresses, tending to crack the tool, which are due to the
hardening process.
484
SMALL TOOLS
The outside of the reamer is provided with flutes and
cutting edges for the greater part of the length of the
reamer. A short distance at the end provided with the
key-way is turned down below the diameter of the cutting
edges. This is done in order to prevent any burr which
.- C--
^aper H per foot
e^L-
F ^
[
1 1
iV
1
1
M
n ■ ■ ■
'l
Fig. 236. Arbor for Shell Reamers
may be set up by the driving key on the arbor from inter-
fering with the hole reamed or spoiling the cutting edges
of the reamer. Besides, this turned-down portion pro-
vides space for marking the reamer with its size, and
gives a finished appearance to the tool.
Fig. 237. Rose Shell Reamer
Pig. 237 shows a shell reamer fluted in the same manner
as the rose chucking reamer. This reamer is termed
a rose shell reamer. The cutting edges, fluting, and back
taper are the same as described before under rose chuck-
ing reamers, but in all other particulars the tool is the
same as an ordinary shell reamer.
REAMERS
485
Arbors for Shell Reamers, — The arbor used for driving
shell reamers when at work consists of a stem or arbor
proper, C, Fig. 236, provided with a collar D which is
fastened to the arbor by means of a taper pin. On the
end of this collar is milled a tongue B so as to provide
for a key to fit the key-way in the reamer, as mentioned.
Precaution must be taken in milling -this tongue so that
it will be exactly in the center of the collar. The same care
must, of course, be used in milling the key-way in the
reamer which must be exactly in the center. When
grinding the outside of the reamer to size it should be
ground on an arbor similar to that on which it is to be
used, and the edge at the front end slightly rounded as
at 6, Fig. 235.
TABLE ex.
DIMENSIONS OF SHELL REAMER ARBORS.
(See Fig. 230 for dimensions denoted by letters.)
Diameter
at Size
Line.
Length
from Size
Line to
End of
Arbor.
' Total
Length.
Diameter
at Size
Line.
Length
from Size
Line to
End of
Arbor.
Total
Length.
E
F
H
E
•
F
H
1
1}
2
2i
2i
2|
3
6
7
8
9
9i
10
11
1
li
H
U
2
2i
2J
3i
3}
4
4i
5
5i
6
12
13
14
15
16
17
18
Arbors as well as driving collars should preferably be
made out of tool steel. The collars should be hardened.
The arbors, as manufactured, are made in 14 sizes, the
diameter of each being measured at E, halfway between
the end of the key and the solid part of the body of the
436 SMALL TOOLS
collar D. The arbor is provided with a flat milled on the
shank for the set screws by which it is clamped when
held in position for work. In Table CX are given the
most important dimensions for these arbors.
Fluting Shell Reamers. — The cutters used for fluting
regular shell reamers are the same as for hand reamers.
Rose shell reamers are fluted with the same kind of cut-
ters as rose chucking reamers. The number of flutes in
shell reamers must necessarily be greater in the smaller
sizes than in corresponding sizes of solid reamers, because
the flute cannot be cut so deep owing to the thin walls
of the shell. The numbers of flutes for regular shell
reamers are as follows:
Size of Reamer.
Number of Flutes.
From i to f inch
6
8
10
12
14
16
18
From JJ to f inch
From ^\ to IJ inches
From 1^ to 2\ inches
From 2 JC to 2# inches
From 2|4 to 4 inches
From 4WW to 5 inches
The number of cutting edges on the beveled end of rose
shell reamers is equal to the number of flutes in the regu-
larly fluted kind. The number of grooves on the cylindri-
cal part of the rose reamer is, of course, half that of the
number of cutting edges, there being one groove for every
second cutting edge.
Dimensions of Shell Reamers. — The over-all length of
the shell reamer must evidently be the same as the length
F on the arbor (Fig. 236) from the size line to the extreme
end. As the same arbor is used for a number of different
sizes of reamers, these arrange themselves in certain groups
with the same total length. The length of the fluted
REAMERS
437
portion in each such group is, of course, also the same,
as well as the dimensions for the key-way. The only
dimension which varies in each group besides the size of
the reamer itself is the diameter of the turned-down neck.
This dimension should be as much less than the diameter
of the reamer as stated below.
Diameter of Reamer.
Amount Diameter of
Recess should be Less
than Diameter of Reamer.
\-i inch
A-| inch
||-1 inch
lA-H inches
1 ^ inches and upward
0.006 inch
A inch
A inch
^ inch
i inch
In Table CXI are given the dimensions for the various
groups of shell reamers corresponding to the different
arbors.
TABLE CXI.
DIMENSIONS OF SHELL REAMERS.
(See Fig. 235.)
Diameter
of
Reamer.
Diameter
of Hole,
LjiTKe End.
Total
Length
of Turned-
Lengtli
Width of
Depth of
Leiwth.
down
Portion.
of Flutes.
Key-way.
Key-way.
I
K
L
M
A^
0
P
^A
i
H
H
A
i
A
If
1*
i
i3^A
2
■
H
Jt
ij-}
:
2i
If
A
A
M-i
1
2i
1 •
2
■,i
i
'i-H
2f
•
2i
i
1
3
■
2f
A
I!i-2
1
3i
2i
A
2A-2i
H
3f
3
A
2^-3
H
4
H
A
'
33V-3i
H
^
1
3i
A
3iJ-*
2
5
1
4
A
tt^
2i
5i
1
^
A
2i
6
1
5
A
438 • SMALL TOOLS
Taper Reamers.
Taper reamers are used for reaming holes for standard
taper pins and for taper sockets. A special kind of taper
reamer is made for locomotive work. The reamers for
standard taper-pin holes are usually always finishing
reamers, whereas for reaming taper sockets or other
work with large tapered holes usually both a roughing
and a finishing reamer are employed. The roughing
reamer is simply intended to remove enough stock so
that the finishing reamer can produce a smooth hole
true to size, without being exposed to excessive wear,
and thus retain its correct size so much the longer.
Roughing Taper Reamers. — Roughing taper reamers,
Fig. 238. Roughing Taper Reamer.
such as are used for reaming Morse and Brown and Sharpe
standard taper sockets, are made exactly like the finish-
ing reamers, except that they are made about 0.010 inch
smaller in diameter, and are provided with a spiral groove
cut like a thread all arornid the cutting edges, as shown
in Fig. 238. This thread or groove breaks up the chips in
the same manner as the nicks in the cutting edges of plain
milling cutters. The thread is cut left-hand, with a tool
similar to a square-thread tool but with the comers
slightly rounded. The width of the tool should vary
from about one-thirty-second inch for the smallest size
reamer for Morse taper sockets to three-thirty-seconds
inch for the largest sizes. The depth of the groove should
be slightly more than one-half of the width of the tool.
REAMERS 489
After being hardened and drawn to a temperature of
about 370° F., the roughing reamer should be ground
with a somewhat greater clearance than the finishing
reamer.
The pitch of the thread should be one-fifth inch for
the smallest sizes of roughing taper reamers up to one-
third inch for the largest sizes; that is, there will be from
three to five threads per inch, according to size, along the
cutting edge.
The cutting edges of roughing taper reamers are some-
times cut spiral. The spiral may be a right-hand one in
this case, as there is no danger of the reamer drawing into
the work too suddenly on account of the taper. How-
ever, most manufacturers make both roughing and finish-
ing reamers with straight flutes whenever there is not an
exceptionally steep taper or a long tapered -hole to be
reamed. In such a case the roughing reamers are con-
structed upon a different principle from the one just
described. The reamer is turned somewhat over-size,
and ground to the correct diameter desired before being
fluted. It is then returned to the lathe and a thread cut
on the surface with a square-nosed tool one-quarter inch
wide. The pitch of the thread is one-quarter inch, and
the depth such tliat the ground surface at the end of the
cut nearest the point of the reamer is barely touched, as
shown in Fig. 239. In the cut the dash-dotted lines indi-
cate the ground tool blank before the thread is cut, and
the full lines the appearance of the blank with its thread.
This latter is left-handed, and each step is slightly back
tapered, say 0.002 inch in the distance of one-quarter
inch; that is, the point a of each step is 0.002 inch further
away from the axis of the reamer than the point b. After
threading, the reamer is fluted with left-hand spiral flutes,
the spiral being so selected that the angle which the cut-
440
SMALL TOOLS
ting edges make with a plane through the axis of the
reamer is 15 degrees. Some tool-makers also advocate an
odd number of flutes for these reamers, but as long as
the reamer is provided with spiral flutes there seems to
Fig. 239. Method of Making Steep Taper Roughing Reamer
be no valid reason why an odd number of flutes should add
any advantages.
Fig. 240 shows another form of roughing taper reamer
for steep tapers. This form is known as a step reamer.
In fact, this tool is a kind of multiple counterbore;
Fig. 240. Step Reamer
each step together with the previous one forms a com-
plete cotmterbore, the smaller step being the guide, the
larger the body. All the cutting is done at the front
end of each step. The cylindrical portion of the step
should not be relieved, but it is preferable to slightly back
taper these portions the same as in the case of the threaded
REAMERS 441
taper reamer. The flutes may be straight or spiral; if
the latter, the same angle of spiral as mentioned previ-
ously should be selected. The number of flutes for this
kind of reamer is usually four.
Finishing Taper Reamers, — Finishing taper reamers,
as shown in Fig. 241, are similar to ordinary hand ream-
ers, except that the cutting edges taper. The flutes are
almost always cut straight, but spiral flutes are of advan-
tage in porous metal or in work pierced crosswise by other
holes or openings. The spiral should be right-handed,
there being no tendency to draw the reamer into the
hole on account of the taper of the hole.
Fig. 241. Finishing Taper Keamer
Taper-pin Reamers. — Taper-pin reamers, as mentioned,
are intended for reaming holes for standard taper pins.
The taper is one-quarter inch per foot. The diameter of
the small end of the reamer should be such that the reamer
will project at least one-sixteenth inch, or, on larger
sizes, one-eighth inch, through the hole reamed for the
longest standard taper pin of the size in question. The
cutting edges should be enough longer than the long-
est pin to permit the reamer to be ground a number
of times without being too 'small in diameter at the
upper end of the flutes for the size pin for which it is
intended.
In Table CXII are given the standard dimensions for
taper pins as adopted by the Pratt and Whitney Company,
and in Table CXIII the dimensions for corresponding sizes
of taper-pin reamers. These reamers are provided with a
442
SMALL TOOLS
square on the end of the shank for a tap wrench. The
length of the square should be about one and one-half
times the diameter of the shank. The size of the square
should be three-quarters the diameter of the shank.
TABLE CXII.
STANDARD TAPER PINS.
Diam.
Approx.
Frac-
Length
of
Diam.
Approx.
Frac-
Length
of
No. of
at
tional
No. of
at
tional
Taper-
Large
Size at
Longest
Pin of
this
Size.
Taper
Large
Size at
Longest
Pin of
this
Size.
pin.
End of
Large
Pin.
End of
Large
Pin.
End of
Pin.
Pin.
End of
Pin.
000000
0.0715
^
3
0.219
t
If
00000
0.092
&
4
0.250
2
0000
0.108
«
5
0.289
II
2i
000
0.125
J
.
6
0.341
3i
00
0.147
A
1
7
0.409
M
3}
0
0.156
ft
1
8
0.492
i
^
1
0.172
u
9
0.591
5i
2
0.193
A
li
10
0.706
M
6
TABLE CXIII.
DIMENSIONS OF TAPER-PIN REAMERS.
Xo. of
piQ
Reanier
Toial
Len^h
Reamer
Length
Edges.
length
of
Shank.
Diam.
Hi
End of
keiiraer
No. of
Tiiper-
pfii
Heamer
Total
Len^b
of
Reamer
Length
of
Cutlme
Ed^es,
Length
of
Shank.
Diam.
At
Smari
End of
Reamer
000000
H
J
h
0.057,
3
H
2i
0.1S2
00000
It
1
4
0.078
4
3i
n
1:
0.205
0000
1
n
0.09]
5
^i
3
12
0.239
000
li
H
0.108
6
4
0.270
00
2-
iVfi
f
0.125
7
6|
4r
0.32a
0
2
li
0.134
8
7^
5i
2
0.395
1
2
H
1
0.145
9
8i
€■:
2i
B.m
2
3
2
1
0.161
10
9* ,
7
2i
0,678
REAMERS
443
The number of flutes in taper-pin reamers should be
chosen as follows:
Number of Taper-pin
Reamer.
Number of Flutes.
000000-00
0-7
8-10
4
6
8
Taper Reamers for Morse Standard Taper Sockets. —
For reaming Morse standard taper sockets two reamers
are used, one roughing and one finishing. The construction
of the former has already been described. The finishing
reamer is made like the taper-pin reamer, with the excep-
tion, of course, that the taper is according to the Morse
standard taper gauges. This taper is different for the
different sizes or numbers of Morse tapers, but is approx-
imately five-eighths inch per foot. The exact figures for
the taper are given in Table CXIV.
These reamers are provided with a square, the length
of which should be about equal to the diameter of the
shank. The size of the square should be three-quarters
the diameter of the shank. This leaves a small round on
the comers of the square which is desirable for the appear-
ance of the tool as well as for the convenience of handling
a tool without sharp comers.
In Table CXIV are given all essential dimensions for
these reamers, and in Table CXV the dimensions for
Morse standard taper shanks. These taper shanks are
the ones most extensively used of all standard taper
shanks. It is practical/y the only taper shank ever used
on drills and reamers.
444
SMALL TOOLS
The number of flutes in roughing as well as finishing
reamers should be as follows :
Reamer for Morse Taper
Sockets No.
Number of Flutes.
0-1
2-4
5
6
7
6
8
10
14
16
TABLE CXIV.
DIMENSIONS OF REAMERS FOR MORSE STANDARD TAPERS.
Diameter
Diameter
No. of
Morse
Standard
Taper.
Total
Length
of
Reamer.
Length
of
Cutting
Edges.
Length
of
Shank.
at Small
End,
Finishing
Reamer.
at Small
End,
Roughing
Reamer.
Taper
per
Foot.
0
4
^
H
0.252
0.242
0.625
1
4f
2*
ij
0.369
0.359
0.600
2
5i
3i
21
0.572
0.562
0.602
3
6f
4
2f
0.778
0.768
0.602
4
8
5
3
1.020
1.010
0.623
5
9i
6i
3^
1.475
1.465
0.630
6
12
8i
3f
2.116
2.106
0.626
7
15
11
4
2.750
2.740
0.625
REAMERS
446
TABLE CXV.
DIMENSIONS OF MORSE STANDARD TAPERS.
Fig. 242
i
11
1-
'2
■s
Q
1
^
1
1
.^
1
N
fe 1
^ .
s -
E
^ >,
P
H
1^
^
^
^«
^^
1
in
1^1
■3
^?
'i
■s
%
^
A
1
1
as
3
fl
3
•3
f
^
^
^
Z)
A
/"
il
H
a:
/.
T
( '
,S"
0
0.252
0.356
2
2M
2A
m
A
i
A
0.160
2A
0.625
!
0.369
0.475
^
2A
2l^<^
2|^
i
A
iif
0.213
2!
0.600
2
0.572
0.700
2A
3A
24
2i
I
0.200
Si
0.602
3
0.778
0,938
3A
3f
3i
3l^
lA
A
A
0.322,
3ffi
0.602
4
1.020
1.231
4A
4!
*i
3
1 ;
iS
0.478
4-i
0.623
5
1.475
1.74g
5tk
6
Si
4 1
1
ft
0.635
5
0.630
6
2.116
2.404
71
111
7i
7 1
1
0,760;
8
0.626
7
2.750
3.270
10
104
91
2|
1|
n
1.135
Hi
0,625
Taper Reamers for Brown and Sharpe Standard Taper
Sockets. — Roughing and finishing reamers are used the
same as for the Morse taper sockets. The taper is one-
446
SMALL TOOLS
half inch per foot, except taper No. 10, which is 0.5161
inch per foot. In Table CXVI are given all the essential
dimensions for the reamers, and in Table CXVII the
dimensions for the taper shanks. It will be noticed
that in certain cases there are a number of different
lengths corresponding to the same nmnber of taper, all
being of the same diameter at the small end. While the
lengths of the shanks are different, the reamers can all
be made the same for the same number of taper, inas-
much as the diameter at the small end is the same, and
the only thing to consider is to make the length of the
cutting edges of the reamers long enough for the longest
or deepest taper socket of a particular size, in which case
they, of course, will be sufficient for the shorter lengths.
TABLE CXVI.
DIMENSIONS OF REAMERS FOR BROWN AND SHARPE STANDARD
TAPERS.
No. of
Taper.
Total
Length
of
Reamer.
Length
of
Cutting
Edges.
Length
of
Shank.
Diameter
at Small
End,
Finishing
Reamer.
Diameter
at Small
End,
Roughing
Reamer.
Taper
per Foot.
1
2
u
a
0.197
0.187
0.500
2
2f
If
li
0.247
0.237
0.500
3
4
2i
H
0.309
0.299
0.500
4
4
21
11
0.347
0.337
0.500
5
4}
2i
IJ
0.447
0.437
0.500
6
61
4
2}
0.497
0.487
0.500
7
7i
4}
21
0.597
0.587
0.500
8
7i
4f
21
0.747
0.737
0.500
9
7f
5
2i
0.897
0.887
0.500
10
lOi
7i
31
1.042
1.032
0.516
11
11
7f
8i
3i
1.247
1.237
0.500
12
Hi
3i
1.497
1.487
0.500
13
12i
8f
31
1.747
1.737
0.500
14
13
H
3f
1.997
1.987
0.500
15
131
9i
3i
2.247
2.237
0.500
16
14
10}
3f
2.497
2.487
0.500
17
15
11
4
2.747
2.737
0.500
18
15i
Hi
4
2.997
2.987
0.500
TABLE CXVII.
DIMENSIONS OF BROWN AND SHARPE TAPER SHANKS.
fi^—S
1
1
1
1
1
I
'4
i
c
K^
L.
^
.:*_..
:sig.
243
•5
Mi
^1
^5
5^
1
55
^ -6
II!
1.
If
1^
III
"H .
0
^
H
1,^
fl
E
F"
G
7;
f 1
K
L
M
1
0.239
0.200
?{j
1-4
i4
ft
0.135
fk
h
2
0.2&9
li!
1
0.250
lA
1ft
0,106
1
A
a
0.375
1:
0.312
H
H
llr
0.197
A
h
3
0.3S5
2-A
2i
0.312
If
l«
0.197
li
3
0.395
2^5
2l-
0.312
2
2,
0.197
^
t
4
0.402
13
1^
0.350
li
1
'i
0.228
4
0.420
2t^
2*
0.350
ll*
lit
i
0.22s
' ik
A
5
0.523
2*
2^,
0.450
li
li
Ir ;
0.200
■;
■
S
0.533
11'
2A
0.450
2
2
1^^
'
o.2ao
■'
5
0.53&
2^fl
0.450
2*
2
2A
2|f
3i
^ •
0,260
■
',
e 1
O.SOfl
2?^
2:-
0.500
2|
2i
■
0.291
i
iSr
6
0.635
3?M
3i
0.500
H
3-
0.291
^V
7 '
0.704
^1^
3^0.600
2v
2[
2
2 1
^i
0.322
if
A
7
0.720
H
3i
0.600
2:
3
f!
0.322
^1
1^
7
0.725
3f
3 ]
0.600
3
3
2 ^
i
0.322
1^1
7
0.767
4^
4;.?
0.600
4
*i
3^
\i
0 322
^
flr
8
0.898
^
4k
0.750
^^
3*
3*
0.353
S
8
0.917
4^
4*fl
0.750
4
^k
S^I
0.353
§
9
1.067'
4|
4
0.900
4
4
3;
0.385
^
1J
1 077
5
4
0.900
4i
4:
4ji
0.385
T^
10
1 260
Si
1.0446
5
5
4^
Ifk
0.447
T^
10
1 289
1.0446
5H
5i
5Vl
If^
0.447
P
^
10
1.312
7A
0^
1.0446
6^
6 4
6A
^ A
0.447
T¥
11
1.498
ep
1.250
S|^
^^
6:
ift
0.447
T
A
11
1. 531
71JI
7. .|
1.250
6|
6
67
lA
0.447
A
12
1.797
SA
7 J
1.500
n
7
6^
0.510
■
13
2.073
aft
1.750
7
8-
71
7^
0.510
■
14
2.344
2S
9A
9|^
2.000
8
BA
1
0,572
f"
^
15
3.615
2,250
S-.
8
m
0.572
.
J?!
16
2.gfi5
10
lOi
2.500
&
9
9
Ir
0.635
«
17
% ^fifS
2 750
91
10^
9|
lOf
IS
3.427
....
....
3^000
......
448
SMALL TOOLS
The Brown and Sharpe taper ehanks are used mostly
on shank end mills and T-slot cutters.
The number of flutes in roughing as well as finishing
reamers should be as follows :
Reamer for Brown and
Sharpe Taper Sockets No.
Number of Flutes.
1-5
^10
11-12
13
14^15
16-18
6
8
10
12
14
16
Jamo Taper Reamers, — The Jamo taper was proposed
several years ago by Mr. Oscar J. Beale of the Brown and
Sharpe Company. The taper per foot of all the Jamo
taper sizes is 0.600 inch on the diameter. The Jamo taper
has the advantage over the other two standard tapers
previously mentioned, the Morse and the Brown and Sharpe,
in that there is an exact relationship between the diameter
of the large end, the diameter of the small end, and the
length between the places where these diameters are
measured, and this relationship can be expressed by simple
formulas. The sizes of the Jamo tapers are known by
numbers from 2 and upwards, and by simply designating
the number of the taper all other necessary dimensions
can be determined by means of the formulas.
Let N = the number of Jamo taper,
D = the diameter of the large. end,
d = the diameter of the small end, and
L = the length of the taper.
N
Then D =
8
^=10'
-!•
REAMERS
449
If, for instance, we want to determine the size of a No. 7
Jamo taper, we find from our formulas that the diameter
of the large end is seven-eighths, the diameter of the small
end 0.700, and the length 3i inches. If we figure the taper,
we will find it to be 0.600 inch per foot, as stated before.
There is no table given for these taper shanks, because, on
account of the simplicity of figuring the dimensions for the
taper, no table is actually required. This taper, although
it has some very decided merits on account of being, one
might well say, the only system of standard tapers founded
on a scientific method, has not been used to any great
extent. The Pratt and Whitney Company have commenced
to use it of late for several of their new designs of machines,
particularly profiling machines, but it is safe to say that
the old standard tapers, the Morse and the Brown and
Sharpe still hold their own in almost all ordinary machine-
shop practice.
TABLE CXVIII.
REAMERS FOR JARNO TAPERS.
No. of
Jarno
Taper.
Total
Length
of
Reamer.
Length
of Cutting
Edge.
Length
of
Shank.
Diameter at
Small End,
Finishing
Reamer.
Diameter at
Small End,
Roughing
Reamer.
2
2|
If
li
0.200
0.190
3
H
2
H
0.300
0.290
4
H
2i
U
0.400
0.390
5
H
31
2
0.500
0.490
6
5i
3}
2i
0.600
0.590
7
^
4}
2i
0.700
0.690
8
7}
4}
2i
0.800
0.790
9
8i
H
2f
0.900
0.890
10
8}
6
2J
1.000
0.990
11
9i
lOi
6i
3
1.100
1.090
12
7
3i
1.200
1.190
13
lOf
7J
3
1.300
1.290
14
HI
8
3
1.400
1.390
15
12
8J
3
1.500
1.490
16
12f
9
3
1.600-
1.590
17
13|
. 9f
3
1.700
1.690
18
14
lOJ
3
1.800
1.790
19
Hf
lOf
4
1.900
1.890
20
151
Hi
4*
2.000
1.990
450
SMALL TOOLS
In Table CXVIII are given the principal dimensions for
reamers used to ream out Jamo taper sockets.
The number of flutes in Jamo taper reamers should be as
follows:
Number of Jarno
Number of
Taper.
Flutes.
2
4
3-4
6
5-10
8
11-15
10
16-18
12
19-20
14
Locomotive Taper Reamers. — Taper reamers for loco-
motive work are generally made in two styjes, with squared
Figs. 244 and 245. Locomotive Taper Reamers
and with taper shanks, as shown in Figs. 244 and 245. While
there are a great many various standards in use in dif-
ferent railroad shops, the commonly accepted standard
taper for locomotive taper reamers is one-sixteenth inch
per foot.
In Table CXIX are given the principal dimensions for
locomotive taper reamers with squared shanks as com-
monly made. The dimensions for the fluted part of those
with taper shank, generally Morse taper, are exactly the
same, the only difference being the over-all length, which,
REAMERS
451
of course, is dependent upon the number of Morse taper
shank used. The common practice is to use the following
numbers of Morse taper shanks for the sizes given below:
Sizes of Reamers.
Number of
Morse Taper
Shank.
From i to A inch
1
2
3
4
5
From 1 to } inch
From a to 1^ inches
From 11 to li| inches
From If to 2 inches
TABLE CXIX.
DIMENSIONS OF LOCOMOTIVE TAPER REAMERS WITH
SQUARED SHANK.
(See Fig
. 245.)
Diam.
at
Total
Length
Length
Length
Length
Diam.
Size
Small
of
of
of
of
of
of
End of
Flutes.
Neck.
Collar.
Square.
Collar.
Square.
Reamer
A
B
C
D
E
F
O
H
i
5
4
i
i
i
A
\
A
5}
4*
^
A
4
1
A
i
64
5
A
•
A
A
P
A
7i
54
"
i
i
*
8
6
■i
A
A
^
^
8}
64
i
1
U
4
9*
7
• ■
r
i
A
i
10
74
«
*
J*
. I
m
8
if
i
*
11}
9
i
lA
12}
10
]■
; •
1:
*
1 .
14
11
*
lA
«
1
15J
12
: ■
1
1
1
16i
13
lA
lA
1 •
^t
H
17*
14
u
lA
19i
15
1*
!■
1
lA
i|
16
■ ■
ll
1-
J.
20}
17
■ ■
2
1
2
21}
18
li
i
24
lA
452
SMALL TOOLS
The length of the neck between the taper shank and the
cutting portion of the reamer should be from three-eighths
inch on the quarter-inch size to one inch on a two-inch
reamer. The size of these reamers is measured at the ex-
treme small end of the fluted portion.
The number of flutes should be as follows:
Sizes of Reamers.
Number of
Flutes.
From i to J inch
6
8
10
12
From A to IJ inches
From 1^ to If inches
From l|| to 2 inches
Pipe Reamers. — Pipe reamers, Fig. 246, are used to
precede pipe taps. They are made of the same sizes as
pipe taps, excepting that the dimensions of the pipe reamer
correspond to the root diameters of the thread of pipe taps.
The taper of pipe reamers is three-quarters inch per foot.
They are fluted with the same kind of cutters as hand
reamers of sizes corresponding to the diameter at the small
end of the pipe reamers. Finishing reamers only are used.
The number of flutes for different pipe sizes is as follows:
Pipe Size.
From i to I .
From i to I .
From 1 to H
From H to 2
From 2i to 3
3i
4
Number of
Flutes in
Reamer.
6
8
10
12
14
16
18
The small end of pipe reamers is slightly chamfered, as
shown in Fig. 246, in order to facilitate the entering of the
reamer in holes which are of about the same size as the
REAMERS
453
small diameter of the reamer. Dimensions for pipe reamers
are given in Table CXX.
Pipe reamers are gauged in the same way as pipe taps,
previously described, and the same limits of error are
permissible.
TABLE CXX.
DIMENSIONS OF PIPE REAMERS.
rig.246
Dis-
Pipe
Size.
Diameter
at Size
Line.
tance
from
Size
Line to
Diam.
of
Shank.
Length
of
Fluted
Part.
Length
of
Shank.
Total
Length.
Length
of
Square.
Size of
Square.
Small
End.
A
B
C
D
E
F
0
h
0.343
a
ii
1
1«
2J
4
i
■■
0.447
A
A
u
If
2
A
■
0.582
A
A
li
1»
3 :
'
0.721
1}
2
3
i
A
1
0.931
1.170
s
If
1}
2i
24
3i
4i
«
8
H
1.515
lA
It
2
4
1
li
1.755
1
!•
2
3
5
1
1
2
2.230
1
1
2
3*
5
1
i«
2i
2.667
li
2
2
4
6
1*
3
3.292
lA
2
3
4i
7
1*
1*
3i
3.792
1
2«
3
4A
8A
2
2
4
4.292
iH
3
3f
4t
H
21
2}
464
SMALL TOOLS
Taper Reamers far Bridge Builders. — Taper reamers
for bridge builders, commonly called bridge reamers, are
made with Morse taper shank or straight squared shank,
as shown in Figs. 247 and 248. The fluted portion is
tapered for a distance 2), Fig. 248, and the remaining
part of the flutes, E, is straight. These reamers are
used for rough structural construction work and are not
required to be finished with the same degree of care as
reamers for machine construction. After hardening, the
flutes are usually left unpolished. These reamers are
T f
i ^1
Figs. 247 and 248. Taper Reamers for Bridge Builders
made in sizes from one-half to \\ inches. The taper per
foot of the tapered portion at the end of the reamer, as
usually made, is given in Table CXXI, together with the
essential dimensions of the straight-shank type of reamer.
The dimensions for the fluted portion of those with
Morse taper shank are exactly the same, the only differ-
ence being the total length, which, of course, is dependent
upon the size of Morse taper shank used. The common
practice is to provide the one-half up to five-eighths inch
sizes with No. 2, and all sizes eleven-sixteenths inch and
larger in diameter with No. 3 Morse taper shank. The
size of the reamer is measured on the straight part of the
flutes. In the case where an odd number of flutes is
REAMERS
456
employed, the size must be determined by a ring gauge.
The number of flutes is made five in all sizes below and
including seven-eights inch diameter, and six for larger
sizes.
TABLE CXXI.
DIMENSIONS OF REAMERS FOR BRIDGE BUILDERS.
Diameter of
Straight Part
of Reamer.
Diameter at
Point ot
Reamer.
Taper per Foo
of Tapered
Portion.
h
c
Length of
Tapered
Part.
S 00
•s 1
CO
A
B
D-
F
0
H
/
4
K
h
1
8*
3
5i
2}
A
A
A
A
1
8t
3
5*
2
i
A
i
4
li
8f
3
5i
2
A
^
\
U
H
3
6
2
4
A
U
H
3
6
2
*
4
K
■r
U
9|
3
6
2
*
A
:
A
U
9f
3
6
2
*
• •
J
«
U
9i
3
M
2*
*
f ;
1
\
U
10*
3
7;
3
1
iiV
U
If
lOi
3
7
3
*
iiV
1*
14
10*
3
r-
3
1
li
lA
»
14
m
3
r
3
lA
itV
*
li
14
lOf
3
71
3
li
11
: •
Table of Amount of Taper in Certain Lengths. — Table
CXXII . is given in order to facilitate the figuring of
the diameter at a certain place of a tapered tool when
the diameter at another place and the taper per foot are
given. Suppose, for instance, that the diameter at the
small end of a reamer is three-quarters inch, the taper is
three-thirty-seconds inch per foot (the common taper for
locomotive reamers in many railroad shops), and the diam-
eter at the large end of the flutes is desired. The length of
the flutes is 9| inches. By the use of Table CXXII we
find:
466
SMALL TOOLS
A taper per foot in 9 inches 0. 0703
A taper per foot in } inch 0.0059
This added to diameter at small end 0. 7500
Equals diameter at large end 0.8262
Grooved Chucking Reamers.
This tool, shown in Fig. 249, is partly a reamer and partly
a twist drill.' The cutting is performed by the beveled
edges Ay which form an angle of 60 degrees with the axis of
lig. 249. Grooved Chucking Reamer
the tool. The reamer is provided with three larger semi-
circular flutes, which are cut on a right-hand spiral, and
with three smaller grooves between these. The larger
grooves form passages through which the chips pass away;
the smaller grooves convey the lubricant to the cutting
edges. This form of reamer is extensively used in screw
machines for enlarging cored holes, and also in drill presses
for enlarging drilled holes, it being easier to enlarge a
drilled hole to size by a grooved chucking reamer than to
try to drill the hole to size by an ordinary twist drill.
This reamer is commonly provided with both straight
and Morse taper shank. When provided with Morse taper
shank the following numbers of taper shanks should be
used for the various sizes of grooved reamers:
Diameter of Reamer.
No. of Morse
Taper Shank.
From i to 4 inch
1
2
3
4
5
From A to f inch
From tf to 14- inches
From 1 A to \\ inches
From l|} to 3 inches
REAMERS
467
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458
SMALL TOOLS
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REAMERS
459
The length of the fluted part is given in Table CXXIII.
The total length of the reamer is dependent upon the length
of the Morse taper shank used. When made with straight
shank, this latter may be selected of such length that the
total length of the tool is the same as when a Morse taper
shank is used.
The diameter at the point of this reamer is larger than at
the shank end of the flutes, the amount of back taper being
0.003 inch per foot. This prevents the tool from binding
in the hole chucked.
The spiral of the -flutes should be so selected that the
edges of the flutes make an angle of between 25 and 20
degrees with a plane through the axis of the reamer. This
corresponds to a lead of the spiral equal to from about 7 to
8.5 times the diameter of the reamer. This is practically
the same amount of spiral as is used on twist drills.
TABLE CXXIII.
LENGTH OF FLtJTED PORTION OF GROOVED CHUCKING REAMERS.
Diameter
Length of
Diameter
Length of
Diameter
Length of
of
Fluted
of
Fluted
of
Fluted.
Reamer.
Portion.
Reamer.
Portion.
Reamer.
Portion.
i
4
i
8i
2
^f
A
^
a
8i
2
.2*
i
5
8i
2
10
• A
5h
H
81
2
101
A
6
6i
9
2^
2fi
101
10}
7
9i
2
10
H
^
9i
2
10
8
n
3
101
H
8i
9f
Center Reamers.
Center reamers are used for forming the centers on which
work is to revolve in lathes or grinding machines. They
460
SMALL TOOLS
are made in two different styles. The older one, Rg. 250,
has only one cutting edge, formed by cutting away the
metal down to the center of the tool and relieving the
beveled portion of the remaining half so that a cutting edge
is produced. The second and later style is that shown in
Fig. 251, which has four flutes or cuts. These cuts are
straight, and the lands between the cuts are relieved on the
beveled part. The inclusive angle of the point of the tool
must, of course, be that used for lathe centers, or 60 degrees.
' 1 1
K^
t \
--C — M*--0--^« -E >i
Fig. 260. Old Style Center
Beamer
Tig. 261. New Style Center
Beamer
These reamers are made with a straight shank. The
dimensions of both styles are the same and are given in
Table CXXIV.
TABLE CXXIV.
DIMENSIONS OF CENTER REAMERS.
(See Figs. 250 and 251.)
Full Di-
ameter of
Reamer.
Total
Length.
Length of
Beveled
Portion,
Approx.
Length of
Straight
Portion.
Length of
Shank.
Diameter
of Shank,
A
B
C
D
E
F
{
1
!!
2
2t
2t
2}
3i
i
1
H
REAMERS
461-
Flat-sided Reamers.
Very small reamers are sometimes provided with flats
instead of actual flutes, the sharp intersection or comer
between two flats acting as a cutting edge. These reamers
are used for small dowel and taper-pin holes, etc. The
diameter of the reamer is, of course, measured over the
sharp comers. If the reamer tapers, the taper of the flats
will evidently, not be the same as the taper of the reamer
itself, and the milling-machine head used when milling the
flats must be set to a different angle from that which the
Fig. 262. Determining the Angle to which to set the Index Head for
Milling Flat-sided Reamers
cutting edge makes with the center line. A simple formula
can be given expressing the relation between the taper per
foot, the number of flat sides in the reamer, and the angle
to which to set the milling-machine head. ,
Referring to Fig. 252, if
a = one-half included angle of cone,
ai = angle made by flat with the axis or center line,
N = number of sides,
T = taper per foot,
then
^ =
360^
2N'
462 SMALL TOOLS
The formula for the angle deared is
GEX cos 0 kT ^ 360°
**'^«'= HE =12^^I1V-
Expressed in words, the formula reads:
Tangent angular setting = ^ — ^ ^ — ^ x
cosine
360 degrees
2 X number of sides
For example, what would be the proper setting for the
milling-machine head when making four-sided reamers for
standard taper pins one-quarter inch taper per foot? We
find this if we divide one-half the taper per foot by 12, and
multiply the quotient by the cosine of 360 divided by 2
times the number of sides. The result is the tangent of
the required setting of the index head.
tan «! = -p5 X cos 45°
= ^ — -r — = 0.00736, the tangent of the required angle.
Reference to a table of tangents shows that the angle is
25 minutes.
Adjustable Reamers.
In order to permit the diameter of the hole reamed to
be slightly varied from the standard size, adjustable
reamers are used. These may be of two classes, those
which are adjusted but still have the cutting edges an
integral part of the reamer, as shown in Fig. 253, and
those which have inserted blades. The former are
usually employed in smaller sizes only, while the latter
are commonly used in sizes from 1\ inches up to 5 inches
diameter. On account of the construction of the class of
REAMERS 468
reamers shown in Fig. 253, the reamer cannot expand
uniformly its entire length; when that is desired, the
reamer with inserted blades must be selected.
Adjustable reamers are often called expansion reamers,
and there is no real difference between the two kinds.
If any distinction should be made, it would be advisable
to call reamers of the type shown in Fig. 253 expansion
reamers, as the change in diameter is actually effected by
expanding the tool itself, while inserted-blade reamers
should be called adjustable reamers.
Expansion Reamers. — Referring to Fig. 253, the reamer
shown is originally an ordinary hand reamer provided
with guide. The distance C represents this guide; D, a
"Fig. 258. Expansion Reamer
small neck or groove between the guide and the reamer
body; Ej the cutting edges; F, the neck between the
cutting edges and the shank; and (?, the shank. At
the forward end of the cutting edges there is a small
taper at P, the same as in ordinary hand reamers, and the
diameter of the guide, which is not fluted, is in the same
proportion to the full diameter of the reamer as for hand
reamers.
The body of the reamer is hollow and three slits are cut
with a one-thirty-second-inch saw from the outside to the
hole in the center. One of these slits is shown in the cut
at 0. The inside hole is tapered at /?, and a tapered plug
S, provided with a threaded part, serves as expander.
The thread engages a threaded portion in the reamer
guide, and, when the expander is turned so that the plug
464
SMALL TOOLS
moves inward, the cutting edges of the reamer are forced
outward on account of the taper at B, a slight spring
action being possible because of the slits cut through
the reamer body. The slits should extend into the
neck and end at the upper end of the guide, as shown.
They should be cut in the bottom of a flute, so as not to
impair the cutting edges.
Reamers of this type cannot be recommended for
accurate work. It is evident that the expansion takes
place opposite the tapered part /2, and that the cutting
edge is sprung up in an arc. The reamer will have no
parallel cutting edges, and, unless the guide fits the
original hole closely, will hardly be able to ream straight.
Fig. 254. Adjustable Hand Beamer with Inserted Blades'
For cheaper grades of work, however, the feature of a
simple means of expansion may be deemed valuable.
Adjustable Reamers with Inserted Blades, — There is a *
great number of designs possible for making an inserted-
blade reamer adjustable. One of the best of these designs
is shown in Fig. 254. The body and shank are made of
ordinary machine steel, while the blades and the binders
are made of tool steel. There has been a number of various
designs of inserted-blade reamers on the market, but there
are few which fill the requirements in all respects as well
as the one presented here.
As seen from Fig. 254, the reamer consists of a body C,
which has one end turned down to fit into a hole in the
shank, six blades, and six binders A, and finally a binding
REAMERS 466
nut D ai^td a check nut E, which are mounted on the threaded
part of the body. The end of the body, which is turned
down to fit the hole in the shank, is driven into place and
is secured by means of a taper pin. The body is slotted
longitudinally to receive the blades and has a circular groove
all around to receive the binders. The latter are held
firmly to the shoulder B on the blades (see Fig. 256) by
means of screws which are threaded into the body. The
hole F shown extending in the center of the reamer a trifle
beyond the center lines of the binding screws is for the pur-
pose of providing clearance for the tap when tapping the
screw holes. The blade is beveled off at an angle of 45 de-
Fig. 266. Adjustable Shell Reamer with Inserted blades
grees at its upper end, and the binding nut is chamfered on
the inside to correspond. This arrangement provides for a
strong grip of the nut on the blades. The binders are made
from a solid ring, being turned, chucked, reamed, and the
screw holes drilled and counterbored before the ring is cut
into pieces. The blades are ground cylindrical for a certain
distance towards the point of the reamer. This cylindrical
part serves as a guide in starting to ream. The remaining
part of the blade from the neck G upwards is ground and
relieved like an ordinary hand reamer.
In Fig. 255 a shell reamer of the same design is shown.
The hole is intended to receive a regular shell reamer arbor,
and the reamer is driven by means of the key-way H. The
466
SMALL TOOLS
blades of this reamer are shorter, are provided with a radius
at the point like regular shell reamers, and are relieved all
the way up and slightly back tapered. This back taper is
equal to 0.012 inch per foot. The radius R at the end of the
blade should be about one-sixteenth inch for sizes up to
four inches diameter and one-eighth inch for larger sizes.
Requirements for an Inserted-hlade Reamer, — The
requirements for a good inserted-blade reamer are that
the blades when bound in place shall be practically solid
with the body, that the design shall permit a liberal adjust-
Fig. 256. Method of Securing Blades in Reamers shown in
Figs. 264 and 266
ment in regard to size, that this adjustment shall be easily
accomplished, and that the means employed for binding
and adjusting the blades shall not be of such a kind as to
prevent the use of the reamer in any case where a solid
reamer could have been used. The design shown in the
cuts fills all these requirements. When the binders A are
tightened down against the shoulder B in the blade, and
the nuts are screwed tightly up against the end of the
blade, there is very little chance for the blade to move.
The tapered bottom of the slots in the body of the reamer
REAMERS
467
TABLE CXXV.
ADJUSTABLE HAND REAMERS.
Diam.
of
Reamer
Length
of
Cutting
Eiige.
Thick-
ness of
Blade.
No. of
BJadea.
Total
LfcTi^h
of
Reamer
of
Reamer
of
Cutting
Edge.
Thick-
ness of
Blade.
No, of
Blades.
Total
Length
of
Reamer
ji
2}
^
6
9
2h
4
i
6
12+
1|
2J
A
6
n
2i
4:
i
6
13
1^
3
6
9i
3
4.
i
8
13*
3
A
6
lOi
3i
4
A
8
14
1-
3:
^
6
m
3*
4
tk
8
m
1]
3
^
6
m
3|
4
A
8
16
2
3
&
6
Hi
4
5
T%
8
15i
2i
3i
}
6
12
TABLE CXXVI.
ADJUSTABLE SHELL REAMERS.
Diam.
Length
of
Thick-
No. of
Diam.
Length
of
Thick-
No. of
of
Reamer
Cutting
Edge.
ness of
Blade.
Blades.
of
Reamer
Cutting
Edge.
ness of
Blade.
Blades.
ji
li
T^
6
3
3i
i
8
If
A
6
3i
3*
^
8
1
H
6
3r
3i
8
1
2
^
6
3^
4
A
8
2 ■
A
6
4
4i
"fs
8
1-
2
^
6
4i
4i
"h
10
2
2
A
6
4*
4f
rf^
10
2i
2
^
6
4}
4i
}
10
2i
2
i
6
5
5
*
10
2}
3
i
6
into which the blades are fitted provides for the adjustment.
When the reamer is worn, the binders are loosened and the
nuts at the upper end of the blades screwed back. The
blades can then be moved upward as far as is necessary
for recovering the original size, the nuts and the binders are
again tightened, and the reamer may be ground to the
468 SMALL TOOLS
exa^t diameter required. The ease of accomplishing this
adjustment is apparent. No details used either for binding
or adjustment project outside of the reamer either at the
end or at any place on the diameter of the body. The
reamer cannot only pass entirely through a hole, but it can
ream down to the bottom of a hole, and even to a certain
width face the bottom if necessary. Very few reamers of
the ordinary adjustable or expansion type fill all the
requirements so well.
This must not be construed to mean that this is the only
adjustable reamer possible which will fill the requirements
outlined. There can, of course, be a great deal of variation
in the design, but the one in question, although patented
in one important detail, is chosen as an example because
of embodying all the features which are of importance. It
is manufactured by the Pratt and Whitney Company, Hart-
ford, Conn.
Dimensions. — In order to give a general idea of the
dimensions which should be followed in laying out any type
of inserted-blade reamer Tables CXXV and CXXVI are
appended. The dimensions given in these tables are
not, of course, intended to be followed too strictly, as
varying designs may require modifications. They will,
however, serve as a guide in lajdng out adjustable reamers
when occasionally required to be designed, and give an
idea of the general proportions. The shank of inserted-
blade hand reamers should be ground 0.002 inch smaller in
diameter than the minimum size for which the reamer is
intended.
CHAPTER XI.
DRILLS. —COUNTERBORES. — HOLLOW MILLS. —LATHE
ARBORS.
Twist Drills.
While the varieties of drills used in shop work are
many, at the present time the twist drill has so com-
pletely covered the field that it seems unnecessary to
deal with any other class of drills for ordinary drilling.
For deep-hole drilling, another kind of drills is, of course,
required. Drills for this class of work will be treated
later.
Twist drills one-quarter inch and larger are made with
either straight or taper shanks, the latter being by far
the more common. The taper of the shank is almost
exclusively Morse standard. A short neck is provided
between the fluted portion and the shank. The smaller
sizes of drills, the wire-gauge sizes, are made with straight
shank only, and have no neck. The shank and the body
are of the same diameter, so that, in fact, on these small
sizes the only difference between shank and body is the
fluting of the latter. Drawn wire (drill rod) is used for
all the wire-gauge sizes of drills, and no further finishing
process is necessary for the outside. The small sizes are
not ground nor are they backed off or relieved on the
cylindrical portion, the only operations on them being the
fluting, and the grinding and relieving of the cutting edges
at the end.
460
470 SMALL TOOLS
Fluting.
Number of Flutes or Grooves. — It is a well-known fact
that at present all twist drills are made with two flutes,
but twist drills having three or more flutes have been de-
vised, made, and tried. The advantage gained by adding to
the number of cutting edges has, however, not been great
enough to justify the increased cost of manufacture.
When there is added to this the weakness caused by the
increased number of grooves, and the complicated oper-
ation of correctly grinding such drills, it is clear why drills
having only two flutes have been and should be adopted.
' Lead of Helix or Spiral. — The lead of the helix of
the groove or flute is usually made about 7 X diameter
of drill. When this lead is used, the cutters for twist-
drill fluting as ordinarily manufactured will produce a
straight cutting edge when the inclusive angle of the
cutting point is 118 degrees, that is, when the cutting
edge makes an angle of 59 degrees with the drill axis.
With the advent of high-^peed steel and higher cutting
speeds it has been thought desirable to increase the lead
somewhat, as the higher speed would tend to more
speedily carry away the chips even if the helix, or spiral,
as it is commonly called, is not of so acute an angle with
the plane at right angles to the axis. But on the other
hand the higher speed and, with high speed steel drills, the
coarser feed would produce all the more chips to be
carried away, that there is reasonable doubt whether
the common angle of spiral is not the best one for all
purposes. If, however, for some reason special drills are
made for exceptionally slow speed, it is to be recom-
mended that the lead be made only five or six times the
diameter of the drill, so as to permit the chips to pass
along faster in spite of the slow cutting speed.
DRILLS — COUNTERBORES, ETC.
471
Fig. 267. Ap-
proximate Form
of Drill Fluting
Cutter
Flviing Cutters. — Fluting cutters for twist drills are
made of such a shape that the cutting edge of the drill
becomes practically a straight line. In other words, the
form of the cutter must be such that the
intersection between the flute and a plane
making a 59-degree angle with the axis of
the drill, the angle to which twist drills
are ground, will be a straight line. The
cutter form is laid out approximately, a3
shown in Fig. 257. In the formulas in
the cut, d signifies the diameter of the drill
to be grooved. The width of the cutter
is given in Table CXXVII. All other,
general dimensions of drill fluting cutters
are also given in Table CXXVII for various
diameters of drills. These cutters are usually made with
eccentric relief, but may also be made with ordinary
milling cutter teeth and ground by means of standard
forms.
Increased Twist. — In order that a drill may have
sufficient strength to resist the torsional strain to which it
is subjected when in use, without being at the same time
so thick at the point as to require a greater force than
necessary to penetrate the work, it has long been customary,
in shops where drills are manufactured, to make the grooves
with gradually decreasing depth from the point to the
shank. It is evident that simply receding with the cutter
from the axis of the drill, in order to increase the thickness
of the central portion, must produce grooves of a smaller
area near the shank than the sectional area of the grooves
at the point. If no means are employed to overcome this
difficulty, there will be a tendency for the chips to clog in
the grooves, which may result in injury to the work being
done as well as to the drill.
472
SMALL TOOLS
TABLE CXXVII.
DIMENSIONS OF FLUTING CUTTERS FOR TWIST DRILLS.
Fig.
268
Diam.
Diam.
of
A
B
C
of
A
B
C
Drill.
Drill.
i
2A
0.286
H
U
2i
0.850
A
2
0.350
*
3
0.933
i
2
0.396
1
3
1.036
t
2
0.428
1
3
1.135
2
0.476
1 •
3i
1.229
*
2
0.617
1
3
1.320
2
0.585
1
3
1.402
»
2
0.615
2
3
1.508
2
0.667
2i
4:
1.701
*
2
0.704
2*
4
1.888
1 .
1
2}
0.770
2i
4i
2.070
1 '
In order to overcome this difficulty the Morse Twist Drill
Company employs a method called "increased twist," in
which the spiral angle of the groove gradually increases
toward the shank end of the drill. This increase is
obtained by changing the rate of forward traverse of the
drill when grooving, meanwhile retaining the same amount
of rotary motion of the drill. This, of course, will change
the lead of the spiral, and the chips will move with a greater
DRILLS — COUNTERBORES, ETC. 473
speed as they pass into the part of the groove which has a
greater spiral angle than the angle at the point. This
greater speed of the chips will eliminate the difficulty due
to the smaller cross-sectional area of the groove.
Another method of overcoming the same difficulty is to
gradually turn the cutter in relation to the axis of the drill
when milling the grooves, the angle of spiral meanwhile
remaining constant. This turning of the cutter causes a
variation in the width of the groove, so that it is enough
wider at the shank end to compensate for the loss in depth
due to increasing the thickness of the central web. The
same object may be obtained by milling the groove twice,
the second time with a slightly different spiral, so that the
cutter in the second cut slightly widens the groove milled
in the first cut.
Fig. 269. Projection for Center at Pointed End of Twist Drills
The latter methods are preferable to the one of increased
twist, because the cutting lip of the drill will not be impaired
at any portion on the drill by changing the lead of the
groove.
To obtain the necessary variation in depth of the groove,
the spindle of the spiral head is slightly elevated, depending
on the length of the flute to be milled. The elevation
should be from one-half to 1 degree, the smaller value being
used for flutes say 3 inches long, and the larger for flutes
12 to 15 inches long. The cutters for milling the grooves are
right or left handed according to whether the milling is
started at the point or at the shank end of the fluted
portion.
In order to provide for a center in the pointed end of
the drill, this end is made with a projection as shown in
474 SMALL TOOLS
Pig. 259. This projection is left until after the grinding
operation. After the flutes have been cut and the drill
ground to desired size, the projection may be ground ofiF
and the cutting lips ground to the proper shape.
Thickness of Web.
The thickness of the web or central portion of a twist
drill is one of the most important features in the con-
struction of these tools. Mr. Fairfield, of the Worcester
Pol)rtechnic Institute, during experiments which he has
conducted for determining the thrust necessary to push a
drill through a piece of metal in drilling, found that there
was a great variation of the thrusts obtained from drills
of the same diameter working apparently under the same
conditions. This variation he found to depend upon the
fact that the thickness of the web of the drills varied quite
widely for the same diameter, even in drills manufactured
by the same maker.
There is no reason, however, why there could not be
given a common rule or formula for the thickness of the
web. If we begin with a drill of 0 diameter and estimate
a thickness of web of one-sixty-fourth inch for this
imaginary size of drill, then the thickness of the web
should increase one-sixty-fourth inch for every increase
of one-eighth inch in the diameter of the drill.
Expressing this in a formula: If D is the diameter of
the drill and W the thickness of the web, then
F=|+ Ainch.
The thickness of web of ordinary sizes of twist
drills figured from this formula is given in Table
CXXVIII.
DRILLS— COUNTERBORES, ETC.
476
TABLE CXXVra.
THICKNESS OF WEB AT POINT OF TWIST DRILLS.
Diam.
of
Drill.
Thickness of
Diam.
of
Drill.
Thickness of
Diam.
of
Drill.
Thickness of
Web.
Web.
Web.
J
0.031
A
0.126
U
0.234
A
0.039
»
0.133
U
0.250
1
0.046
1
0.140
2
0.266
A
0.054
lA
0.148
n
0.281
{
0.062
ij
0.156
2i
\
0.297
A
0.070
lA
0.164
2|
0.312
}
0.078
u
0.171
2}
0.328
t
0.086
ift
0.179
2{
0.343
0.093
If
0.187
2
0.359
a
0.101
lA
0.195
2
0.375
1
0.109
li
0.203
3
0.390
u
0.117
ij
0.219
It is obvious that it is almost impossible, or at least
very difficult, to measure the thickness of the web with an
ordinary micrometer, owing to the circular form in the
bottom of the grooves of the drill. For this reason a
micrometer with the anvil as well as the point of the
measuring screw rounded, as shown in Fig. 260, is
employed. This micrometer may be made from a regular
micrometer simply by removing the anvil and replacing
it by one made as shown, and rounding the end of the
measuring screw. As this micrometer will seldom be
required to measure any more than say one-half inch,
the point of the measuring screw, when rounded, can also
be shortened enough so that when the two points A and B
just touch one another the micrometer reading will be zero.
This will save any figuring or subtraction when using the
• tool which would be necessary if, owing to the increased
height of the anvil, the micrometer was not adjusted to
the zero line when the point of the measuring screw was
bearing on the point of the anviL
476 SMALL TOOLS
Relieving the Land of Twist Drills.
Li order to decrease the frictional resistance and pre-
vent clogging of . the chips the lands of the drill are
relieved. This relief may be of two kinds, according to
Fig. 260. Micrometer for Measuring Thickness of Web of Twist Drills
the method employed for canying out the operation.
The ordinary relief is shown in the end view, Fig. 261, and
may be termed eccentric relief. The other kind leaves a
Fig. '261. Eccentric Relief of
Drills
Fig. 262. Uniform Relief of
Drills
short portion of the land intact, and the remaining part is
milled down to a uniform depth as shown in Fig. 262.
Eccentric Relief. — In Fig. 263 is shown the method
used for producing the first kind of relief referred to. In
this method the relief is produced by the end of an ordi-
DRILLS— COUNTERBORES, ETC.
47T
nary end milling cutter. The milling-machine table is
turned to an angle of say one-half to one degree, as for
cutting a right-hand spiral; but as the angle depends
on several conditions it will be necessary to determine
what the effect will be under different circumstances. A
study of Fig. 263 will be sufficient for this, by assum-
ing the effect of different angles, mills, and pitches of
spirals. The object of placing the bed at an angle is to
cause the mill F to cut into the lip at C and have it just
touch it at E\ The line R being parallel with the face of
the mill, the effect of the angular deviation of the bed is
clearly shown at A.
Fig. 263. Producing Eccentric Relief on Drills
While the drill has a positive traversing and relative
movement, the edge of the mill at E' must always touch
the lip a given distance from the front edge, this being
the vanishing point. The other surface, forming the real
diameter of the drill, is beyond the reach of the cutter,
and is left to guide and steady it while in use. The point
E^, Fig. 263, shows where the cutting commences and its
increase until it reaches a maximum depth at C, where
it may be increased or diminished according to the angle
employed in the operation.
Uniform Relief, — The class of relief referred to as
uniform relief is produced as shown in Fig. 264. An angu-
lar cutter, is mounted on an arbor in a universal milling
478 SMALL TOOLS
attachment, and as the drill moves forward and along its
spiral path the cutter produces the relief shown in Fig. 262.
The face of the cutter is parallel with the axis of the drill.
Hardening Twist Drills.
While the operation of hardening is, as has been pre-
viously mentioned, one which depends greatly upon the
individual skill of the man performing the operation, it
may be well to call attention to the principles involved in
hardening a twist drill.
Fig. 264. Producing Uniform Relief on Twist Drills
The drill must be uniformly heated to the lowest
temperature consistent with results desired. The various
portions of the twist drill are of such unequal thickness
that it is necessary to heat slowly or the lighter portions
will be overheated before the heavier parts are suf-
ficiently hot. Twist drills are subjected to great strains
and should be as strong as possible; for this reason the
heats should be the lowest possible. The shape of the lands
of the drill is such that the steam formed by the con-
tact of water with the red-hot steel prevents the water
from getting into the flutes and properly hardening the
DRILLS— CXDUNTERBORES, ETC.
479
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ym'//MM//m
portion at the bottom, and as this portion forms the point
of the drill as it is ground back, it is necessary that it be
hard. To overcome the tendency of the steam to force the
water from the grooves a bath should be used which will
insure the water reaching the bottom of the flutes. Such
a bath is shown in Fig. 265.
It has a jet of water coming
up from the bottom, and
also has perforated pipes
coming up on the sides by
means of which water is
projected against all sides
of the drill and to the bot-
toms of the grooves, thus
insuring their hardening.
The drill should be heated
in a tube to prevent the
fire coming in contact with
the steel, unless we are
using a muffle furnace or
some form where the steel is not exposed to the action of
the fii'e or the air. A crucible with red-hot lead furnishes
a satisfactory means of heating drills, provided precaution
is used to prevent the lead sticking to the drill. The
foUowing solution not only prevents the lead sticking,
but as it is of a carbonaceous nature it increases, in a
measure, the surface hardness :
Pulverized charred leather 1 pound
Fine flour 1 J pounds
Fine table salt 2 pounds
The charred leather should be pulverized very fine; in
fact it should be sifted through a No. 45 sieve. The three
ingredients should be thoroughly mixed while in the dry
state, then water should be added slowly to prevent lumps,
Fig. 266. Hardening Bath for
Twist Drills
480 SMALL TOOLS
euough water being used to bring the mixture to the con-
sistency of varnish.
The drill may be dipped in the mixture and set in a warm
place to dry, as it is never safe to immerse anything that is
damp in red-hot lead, the presence of moisture causing the
lead to fly, endangering the eyes of the operator.
When the drill is uniformly heated it is. immersed in the
hardening bath and after hardening the temper may be
drawn. The amount necessary to draw the temper depends
on the heat given the steel when it was hardened and the
use to which the drill is to be put, although for most work
the temper should be drawn to 430° F.
Grinding.
The cylindrical surface of twist drills is ground with a
back taper of 0.005 inch per foot, that is, the point of the
drill is larger in diameter than the body back of it. This
prevents binding in the drilled hole. The cutting edges
are ground to an angle of 59 degrees with the center line of
the drill, as shown in Fig. 266, when standard fluting cutters
Fig. 266. Gauging Angle of Cutting Edges of Twist Drills
are used for grooving. This angle, however, is not neces-
sarily the best one for the point of the drill, as Mr. Fairfield
in his tests with several angles, varying from 37J to 70
DRILLS — CX)UNTERBORES, ETC. 481
degrees, shows that the 59-degree angle is not the most
desirable one. In fact, with different angles of the lip with
the center line the thrust necessary to push the drill through
a piece of metal decreases from 70 degrees all the way to
45 degrees, and then increases for any further decrease in
the angle. From this it appears that a 45-degree angle
would give the best results for practical machine-shop
work. There is, however, perhaps only one firm in the
country which gives the 45-degree angle the preference over
the common angle of 59 degrees, and that is the William
Sellers Company, Philadelphia, Pa.
It must be remembered, however, that a change in the
lip angle from 59 to 45 degrees would necessarily have to be
followed by a change in the form of standard fluting cutters,
as otherwise the cutting edge would not be straight but
hooked.
Factors Determining the Keenness and Dura-
BiLriY OF the Cutting Edge.
The keenness and durability of the cutting edge depend
upon three main factors, viz.: (1) the clearance given to
the cutting edge by grinding; (2) the angle of one cutting
edge to the other; and (3) the degree of twist of the groove,
i.e., the lead.
It is obvious that the speed of the various points of the
cutting edge is different according to the distance from the
center; hence the cutting point at the comer operates at
the highest rate of cutting speed and thus performs the
heaviest duty. Therefore the angle of clearance should be
^so selected that this comer is given the most desirable angle
for durability. The keenness of the comer also depends
upon the angle of the cutting edges with the center line,
which, as mentioned, while usually made 59 degrees, is by
482 SMALL TOOLS
actual tests proven to possess greater cutting ability if
made 45 degrees. For brass, in particular, an angle of
45 degrees is without any doubt far superior to the blunter
angle common for drills. The degree of twist or spiral of
the groove which has proven to best fill all requirements is,
as mentioned before, the one having a lead of 7 X the
diameter of drill.
Dimensions.
In Tables CXXIX and CXXX are given the essential
dimensions for twist drills. They are calculated to give
a uniform increase in dimensions for the increasing sizes
of drills. The dimensions given and for which formulas
are provided are the total length and the length of
the grooved portion. For the sake of uniformity in
regard to the total lengths, taper-shank and straight-shank
drills ought to have the same dimensions. As the length
of the taper shank must always be some "standard"
(usually and preferably Morse standard taper), formulas
are not given for the lengths of grooved parts on taper-
shank drills, as these lengths will, when the total length
is given, depend entirely upon the length of the standard
taper used. It is obvious that after the length of the
taper shank is deducted from the total length, the remain-
ing portion will be grooved as far up towards the taper-
shank as practicable. For straight-shank drills, however,
a formula is given which provides for well-proportioned
lengths of shank and grooved portion.
As the angle of helix of a twist drill is one of the most
important factors influencing its cutting qualities, the,
lead must be chosen so as to give a proper angle between
the direction of the groove and the center line of the
drill. This angle will be 24° Ky if the lead already stated
DRILLS — COUNTERBORES, ETC. 488
(7 X diameter of drill) is used. It is obvious that every
lead given in the table cannot be obtained on every uni-
versal milling machine, but in cases where this trouble is
met with it is preferable to use the nearest larger lead for
drills made of some kind of high-speed steel, and the
nearest lower lead for drills that are made of common
tool steel.
As Morse standard taper shanks are the most com-
monly used on drills, a column is given in the table show-
ing for what size drills different sizes of Morse tapers
should be used. Taper shanks are not used on any drills
smaller than one-quarter inch diameter.
Dimensions given in Tables CXXIX and CXXX are
figured from the formulas, and when the result is an
uneven fraction of an inch it is ^ven in the nearest six-
teenth.
L = total length.
G = length of grooved part.
D = diameter of drill.
S = lead.
For the total length:
1. Prom 3 inches diameter to 2Ar inches diameter,
L = 4 X D -h 9 inches.
2. From 2 inches diameter to J inch diameter.
L = 6 X D + 5 inches.
3. From No. 1 to No. 40 steel wire gauge,
L = 11 X D + li inches.
4. From No. 41 to No. 60 steel wire gauge,
L = 12 X D + 1 A inches.
484
SMALL TOOLS
TABLE CXXIX,
MAIN DIMENSIONS OF TWIST DRILLS.
Length of
No. of Morse
Diameter.
Total Length.
Groove on
Straight-
shank Drills.
Taper on
Morse Taper
Shank Drills.
Lead of
Grooves.
i
6^
H
1}
A
6J
H
2A
1
7i
4«
2f
A
7f
4}f
3A
i
8
5}
3i
\
"k
8f
5}
3«
8}
5if
2
4j
\
i
9f
6A
2
4«
9^
6f
2
5i
\
i
9i
6f
2
5}}
lOi
6if
2
6}
i
lOf
7A
3
6A
1
11
7}
3
7
lA
llf
7}
3
7A
H
llf
8A
3
7}
lA
12i
8f
3
SA
H
m
8f
3
8}
lA
12}
m
9A
9f
If
13i
9A
lA
13f
9}
lOA
H
14
9}
10}
lA
14i
lOA
10}f
If
14f
lOA
llf
itt
15J
lOf
ll}f
1}
15i
10}
12}
i«
151
iiA
12«
If
161
iiA
13}
m
16f
11}
13A
2
17
12
14
2A
m
12A
5
14A
2i
17i
121
5
1^
2A
17f
12A
5
ISA
2i
18
12}
5
^H
2A
18}
12if
5
\lt
2f
m
13}
5
2A
18}
13A
5
17A
2J
19
13}
5
17i
2A
19}
13}}
5
17tt
2f
19}
13}
5
18i
2H
19}
14A
5
18tt
2f
20
14}
5
19i
2H
20}
HA
5
19«
2}
20}
14f
5
20i
2if
20f
14«
6
20ft
3
21
15
5
21
DRILLS — COUNTERBORES, ETC.
For the length of grooved part:
1. From 3 inches diameter to 2^ inches diameter,
G = 3 X D + 6 inches.
2. From 2 inches diameter to J inch diameter,
(? = 4J X D + 3 inches.
3. From No. 1 to No. 40 steel wire gauge,
G = 11 X Z) + i inch.
4. From No. 41 to No. 60 steel wire gauge,
G = 10 X /> + i inch.
485
TABLE CXXX.
MAIN DIMENSIONS, WIRE GAUGE SIZES, TWIST DRILLS.
No. of Steel
Diameter in
Total Length.
Length of
Lead of
Wire Gauge.
Inches.
Groove.
Grooves.
1
.2280
4
2i
If
2
.2210
m
if
1ft
3
.2130
3}
4
.2090
m
2A
1^
5
.2055
3|
2i
lA
6
.2040
31
2J
ift
7
.2010
3f
n
ift
8
.1990
3H
2-!f
u
9
.1960
3tt
2-h
u
10
.1935
3t
^
u
11
.1910
3f
2f
1ft
12
.1890
3A
2ft
1ft
13
.1850
3A
2ft
1ft
14
.1820
3i
21
15
.1800
3i
2i
1
16
.1770
3A
2ft
1
•* 4
17
.1730
31
2i
1ft
18
.1695
31
2i
1ft
19
.1660
3A
2ft
1ft
20
.1610
3i
2
21
.1590
31
2
1
22
.1570
3i
2
23
.1540
3A
1«
1ft
24
.1520
3A
1«
1ft
25
.1495
3i
li
1ft
26
.1470
3i
1}
27
.1440
3A
iH
28
.1405
3A
iM
29
.1360
3
1}
\
486
SMALL TOOI£
TABLE
cxxx
. — Continued.
No. of Steel
Diameter in
Total Length.
Length of
Lead of
Wire Gauge.
Inches,
Groove.
GrooTe.
30
.1285
2«
m
31
.1200
2i|
ift
a
32
.1160
2}
HI
33
.1130
2
1
■ «
34
.1110
2i
35
.1100
2
^.
1^
36
.1065
2ti
is
37
.1040
2t
11
38
.1015
2f
If
ii
39
.0995
2A
a
40
.0980
2A
tl
41
.0960
21
ift
i
42
.0935
2ft
^ft
43
.0890
2i
ii
t
44
.0860
2}
ii
45
.0820
2ft
ift
A
46
.0810
2ft
ift
f,
47
.0785
H
Ift
A
48
.0760
2|
ft
49
.0730
2ft
1 '
50
.0700
2
f
51
.0670
2
i
i
52
.0635
1«
.
53
.0595
if
■
54
.0550
1}
i
1
55
.0520
m
{
56
.0465
H
ft
57
.0430
Itt
ft
58
.0420
m
ft
59
.0410
m
ft
60
.0400
IH
ft
The Drilling of Deep Holes.
Principles Involved in Deep-hole Drilling. — The diffi-
culties to be overcome in producing deep drilled holes
can be classified in three groups. In the first place, the
drill has a great tendency to run out, thus producing a
hole that is neither straight nor uniform in diameter; in
the second place, great difficulties are encountered in
trying to remove the chips in a satisfactory manner; and
in the third place, the heating of the cutting tool is diffi-
cult to prevent.
DRILLS — COUNTERBORES, ETC.
487
The principle involved in common drill presses where
the drill is given a rotary motion simultaneously with
the forward motion for feeding is the one least adapted to
produce a straight and true hole. Better results are
obtained by giving only a rotary motion to the drill and
feeding the work toward it. It has been found, however,
Fig. 267. Analysis of Action when Drill and when Work Revolves
that for drilling deep holes the reversal of this, that is,
imparting a rotary motion to the work and the feed
motion to the drill will answer the purpose still better. It
seems as if there coijld be no material difference between
the latter two methods. An analysis of the conditions
involved will show, however, that there is a decided differ-
ence in the action of the drill. If the driU rotates and
the work is fed forward as shown to the left in Fig. 267,
488 SMALL TOOLS
the drill when deviating from its true course will be
caused to continue to deviate still more by the wedge
action of the part By which tends to move in the direction
BA when the work is fed forward. In the case of the
work rotating and the drill being fed forward, as shown to
the right in the cut, the point of the drill when not run-
ning true will be carried around by the work in a circle
with the radius a, thus tending to bend the drill in various
directions. The drill is by this action forced back into the
course of "least resistance," as it is evident that the bend-
ing action being exerted on the drill in all directions will
tend to carry the point back to the axis of the work where
no bending action will appear. The chips, as is well
known, are carried off by forcing a fluid into the hole,
which upon its return carries the chips with it. This
fluid being oil will serve the double purpose of carrying
away the chips and lubricating the cutting tool, keeping
it at a normal temperature.
Example of Drill Used for Deep-hole Drilling. — The
drills used for deep-hole drilling are of entirely different
construction from ordinary drills. One drill which has
been developed by the liodge and Shipley Machine Tool
CJompany, Qncinnati, Ohio, is shown in Fig. 268. This
B 8.
-f^ — ^
Fig. 268. Lodge & Shipley Deep-Hole Drill
drill is manufactured by the Three Rivers Tool Company,
Three Rivers, Mich., and was described by Mr. Frank B.
Kleinhans in Machinery , January, 1904.
Referring to the cut. Fig. 268, the body of the drill B is
made of machine steel. The point P is made of tool steel
DRILLS — COUNTERBORES, ETC.
489
and held in position by the taper pin T. A hole H is
drilled in the shaiik, and from this hole the oil is led to slots
S, which are nulled along the outside. These slots run the
full length of the drill, and then shoot down at the ends as
indicated. F is a flat milled in the shank for the set screw
holding the drill when in use.
A longitudinal sectional view of this drill is shown in
Fig. 269, in which the construction of the passageway
for the oil is better seen. H is the inlet hole for the oil, as
mentioned, and the two smaller holes J, J, are drilled
to connect with hole H in the manner indicated. The
holes K, K, are drilled in a similar manner at the other
'K »j
Fig. 269. Section of Deep-Hole Drill shown in Fig. 268
end of the drill, and a piece of brass tube is bent to an arc
and the ends entered into the holes J and K. It is then
hammered down into place, and the joint is flushed with
solder. The slot P is milled with a convex cutter so as to
have a semicircular bottom, and the cutter of the drill is
fitted to this slot. The drill points should preferably be
made of high-speed steel, as they then stand up better
under high speed. They are made as shown in Fig. 270.
The hole H is reamed through the drill, while the cutter is
clamped firmly back against its seat at the end of the slot.
The angle A is made about 20 degrees. The cutting edge
is nicked at several places, as at N, in order to break up
the chips, this being done on the comer of an emery wheel.
After the drill is put into place it is ground up accurately
to the diameter, D.
Classes of Deep-hole Drills, — According to the manner
490
SMALL TOOLS
in which deep-hole drills perform their work, a differ-
ence is made between those which cut out all the metal of
the hole and those which only cut out a ring, leaving a core
in the center. When drilling with this latter class of drills
a great amount of energy is saved, inasmuch as there is less
metal removed; the method, however, is not generally
used for holes smaller than 3 inches in diameter. The
core which is cut out does not necessarily become scrap,
/
y^
o
3
Fig. 270. High Speed Steel Cutter used in the Drill in Fig. 268
as in most cases it can be used for various purposes. Several
cutting edges must be provided, and care must be taken
to see that they all take an equal cut, as otherwise there
will be a tendency for the drill to deviate from its true
course.
COUNTERBORES.
Counterbores are used for enlarging holes which are
already drilled, without changing their location. The tool
consists of a body part, the end of which performs the
cutting; a guide, which must accurately fit the hole already
DRILLS— COUNTERBORES, ETC. 491
drilled; and a straight or taper shank, by which the counter-
bore is held while in operation. The size of the body part
must be the same as the diameter of the enlarged hole
desired. The cutting edges are perpendicular to the axis
of the hole, so as to form a step with jlat bottom when the
counterboring operation is performed. When the cutting
edges form an angle with the axis, so as to give the enlarged
hole inclined or beveled sides, the tool is not termed a
counterbore but a countersink.
The ordinary form of counterbore is shown in Fig. 271.
Between the body and the shank there is a long necked-
down portion, permitting the tool to be used in deep holes.
Counterbores for screw holes are generally made in sets.
I
Fig. 271. Ordinaiy Form of Counterbore
Each set contains three counterbores: one with the body
the size of the screw head and the pilot the size of the hole
to admit the body of screw; one with body the size of head
of screw and the pilot the size of tap drill; and the third
with the body the size of body of screw and the pilot the
size of tap drill.
Fluting. — The making of counterbores presents but few
items which have not already been treated in connection
with other tools. They are usually provided with four
flutes, which as a rule are cut on a right-hand spiral. This
gives a certain amount of front rake to the cutting edge, and
is particularly preferable for all tools cutting steel. But
if the counterbore is to be used mostly for brass it is better
not to have any front rake, and the flutes are consequently
cut straight. When the tool is provided with spiral flutes
the angle of the flute with the center line of the counterbore
492 SMALL TOOLS
should be made about 15 degrees, which corresponds to a
lead of the flute equal to 12 X diameter of body of counter-
bore. While for most purposes counterbores are made
with four cutting edges, small counterbores are often made
with three, but unless the sizes are plainly stamped on
them it is diflicult to determine their size by measurement.
Counterbores fluted in this manner should be marked
before fluting.
The flutes should be cut deep enough to come below
the surface of the pilot, so that the body of the counter-
bore gets a perfect cutting edge for its full width of the
shoulder formed by turning down for the guide.
Relief. — The counterbore should be relieved on the
end of the body only and not on the cyKndrical surface,
as all cutting is done at the end. In order to facilitate
the relieving process, a small neck should be turned
between the guide and the body, immediately at the end
of the body. The relief is given to the cutting edges by
filing when only small quantities are made, but in manu-
facturing these tools special machines are used, rigged
up for relieving the cutting edges either by means of an
ordinary tool pulled back at regular intervals or by means
of a small milling cutter placed in a head on the carriage
of a lathe with a universal relieving attachment. The
amount of clearance given the cutting edges depends
somewhat on the nature of the work to be done, but for
general work an angle of 4 or 5 degrees will be found
satisfactory.
Grinding. — All tools which are held by their shanks
when used, must be ground after hardening in order to
insure that the body will run true with the shank. It is
customary to grind the shanks first, as placing a dog on
the finished ground surface of the cutting part of the tool
should as far as possible be avoided. Besides, if the shank
DRILLS — COUNTERBORES, ETC.
498
has sprung out of true in hardening, there is a better
opportunity when grinding so long a surface as that of
the shank, to set the machine so that it will grind the
whole tool true than there would be if one tried to set it
to grind correct from the body or pilot.
Straightening Counterbores. — When counterbores and
similar tools, such as taps and reamers, spring in harden-
ing it is possible to straighten them by applying pres-
sure on the convex side, the tool having been previously
slightly heated. The pressure may be applied, as shown
in Pig. 272, by a tool or piece of steel held in the tool-post
Fig. 272. Method of Stmghtening Counterbores in Lathe
of a lathe and forced against the work by means of the
cross-feed screw. The piece must be forced a trifle
beyond the straight line, as it will spring back when the
pressure ceases to be applied.
In the manufacture of tools where a great number of
pieces are to be straightened special "straightening lathes"
are employed, in which the pressure comes from below,
getting its support on the lathe bed. The principle, how-
ever, remains the same as the one shown in Pig. 272.
Dimensions of Gounterbores. — In Table CXXXI are
given the dimensions for counterbores. Referring to
Fig. 273, the dimensions have been given in relation to the
4
94
SMALL TOOLS
TABLE CXXXI.
|-
DIMENSIONS OF COUNTERBORES.
■
^ f ^
III
1
a f i
i
r
1
1
1
— B— ^ j«— — -D —
4« _
^
:fc
j<. ^
1
-
Fig. 273
-
A
B
C
D
E
F
G
i
ii
A
2J
1
^j
H
A
^
il
2A
A
ii
5A
1
1
A
2f
i
*-
5}
A
A
21
i
^?
.*
i
Sf
k
=1
21i
A
|i
7A
j
^a
2}
71
i
1
n
m
«
it
7«
1
vk
3
y
8i
■«
liSf
II
3A
1
t^
8«
\
life
5*
3i
§T
9i
a
1
i
3A
3i
1
8
9«
lOi
lA
m
^■•1
3A
lA
i^
lOA
li
H
il
3f
li
I. A
11
lA
m
^i
3A
lA
13^
iiA
H
m
U,
3i
li
lA
lit
lA
1}
Si
3A
lA
12A
li
m
3f
11
i|^
12}
lA
m
^A
m
lA
iM
13A
1
2
1 J
3}
li
ItV
13i
1
2^
iJ^T
m
4}
m
14^
13
1
^4
1 \
llf
ly
14|
1
^M
4A
If
Ii't
14
2
2}
1
4i
'If
m
14
2i
2I
4ii
Hi
1 i
15
2
1 j^
*i
1}
IH
15
2}
2§i
i||
5A
'ft
1 1^3
16
2i
2*,
ill
'IS
16}
2f
2U
If*
5A
1}
Ml
16}
2|
2h
5f
i§f
'n
17|
21
3^
2A
5^
M
i«l
17i
3
3i
2i
6
2
us
17}
DRILLS — COUNTERBORES, ETC.
495
diameter of the body of the counterbore A, As counter-
bores are used with straight shanks as well as with taper
shanks, the simplest and most universal way of making
up formulas as well as table will be to do so with refer-
ence to straight-shank counterbores only; but as there is
no reason for making the total lengths different for counter-
bores with straight or taper shanks, the formulas will also
hold good for counterbores with taper shanks of reason-
able proportions, as will also the dimensions for B and C.
As the Morse standard taper shanks are more used than
any other standard taper shanks, below is given an aux-
iUary table giving the numbers of Morse taper shanks that
ought to be used with certain size counterbores.
Diameter of Body, Inches.
No. of Morse
Taper.
A-l
1
aZi
2
frlf ...
3
1^2 ♦.
4
2^3
5
In the f 0
llowing formulas,
A = diameter of body, E = diameter of shank,
B = length of body, F = diameter of neck.
C = length of guide, G = total length.
D = length of shank.
For counterbores from one-quarber to 1 A inches the fol-
lowing formulas should be used:
J5=^. E^A.
4
L
)=A + 2i. (?=7.
4+3i.
496
SMALL TOOLS
For counterbores from IJ to 3 inches the following for-
mulas should be used :
B=^ + i.
C =
3A
D=^+lh
G =3A +8|.
Counterbores with Inserted Pilots.
The range of work possible with a counterboi-e is some-
times greatly increased by having pilots of various sizes
which may be inserted as occasion requires. In Fig. 274 is
Fig. 274. Inserted Pilot Counterbore
shown a counterbore designed to take pilots of different
sizes. This form of counterbore is oftentimes used where
it is necessary to sharpen quite often, as the pilot may be
removed and the teeth ground on their ends. If the teeth
are ground on a universal grinding machine they can be
kept very straight and square. After grinding, the pilot
may be again inserted, and the tool is ready for use.
The teeth in this class of counterbores are usually cut
as indicated in Fig. 274, that is, the body is not provided
with flutes the full length, but cut on the end only. This
is necessary in order to strengthen the tool as much as
possible. It is evident that being provided with a hole for
the pilot the strength of the tool would be seriously impaired
if it had flutes running the full length of the body.
DRILLS — COUNTERBORES, ETC. 497
counterbores with interchangeable bodies and
Guides.
Object of BuiU-up Tools. — The efforts constantly made
by progressive manufacturers to decrease the cost of tools
without impairing their efficiency have resulted in the
design of a number of holders for cutting tools which
permit a cheaper grade of material to be used in the holder
proper, while the best-quality steel can be used for the cut-
ting tool itself. A further impetus to these efforts has been
given by the extensive use of high-speed steel, the price of
which is so high as to make its use for many purposes pro-
hibitive if the whole tool should be manufactured through-
out of this material. Many tools which only a few years
ago were almost invariably made solid are therefore to-day
made up in several parts, the portion which performs the
cutting being the only one made out of high-grade material.
Incidentally another advantage is also gained. Inasmuch
as the cutting portion of a tool is the only one which, in
general, when worn, has caused the tool to be discarded, it
is now possible to retain all the other parts and replace the
cutting portion only.
Examples of Built-up Caunterbores, — The accompany-
ing cuts show a number of counterbores with interchange-
able bodies and guides. In the case of counterbores the
interchangeability is even of greater advantage than in
many other tools, inasmuch as here a number of guides can
be used with the same body, and vice versa, thus making it
possible to replace a very large collection of solid counter-
bores with a single holder and a few bodies and guides.
Fig. 275 shows a counterbore where the body consists
simply of a blade A inserted in a slot B in the holder. The
blade rests upon a hardened tool steel collar C, which is
driven into place. A slot is milled across the blade in the
498
SMALL TOOLS
center at D, and a set screw E serves the double purpose of
binding the blade against the collar C and holding it
central. The guide bushing F is provided with a small
slot fitting over the blade to prevent it from turning, and
is kept in place by the head of the screw E. There is,
fF^— -
Fig. 276.
Counterbore with Interchangeable Blades and
Guide Bushings
however, a slight allowance for play between the guide
bushing and the head of the screw, in order to insure that
the screw will bind the blade in the slot D and not tighten
down upon the bushing before binding the blade. By
simply removing the screw the counterbore can be pro-
vided with any size blade and guide within certain limits.
Fig. 276. Interchangeable Body and Guide Counterbore
Pig. 276 shows a counterbore of a different type. The
collar B is keyed to the holder, and is provided with a step
as shown in the cut by means of which the counterbore
body C is driven. The collar is movable in the longi-
tudinal direction of the holder, being pressed down toward
DRILLS— COUNTERBORES, ETC. 499
the counterbore by means of the nut A. The thrust when
binding is taken by the guide bushing D, which is provided
with a pin sliding in a slot in the guide pin E. This slot
is milled in the longitudinal direction of the holder about
one-half of the length of the guide pin, and is then milled
in form of a circular groove about one-quarter of a revolu-
tion. When the guide bushing with its pin is pushed over
the guide pin and given a quarter of a turn, the nut A can
be screwed down until it holds the body of the counter-
bore firmly in place. The advantage of this type is that
the bushing and body can be very quickly changed and
are simple to duplicate.
Pig. 277 shows a counterbore of a somewhat similar
Fig. 277. Another Desigu of Interchangeable Body and
Guide Counterbore
type. Here the driving collar A is fastened to the holder
by a taper pin, and provided with a key freely fitting a slot
in the body B. The guide C is screwed into the holder,
and binds the counterbore body against the driving collar.
The guide is provided with a screw slot to facilitate its being
screwed in and out. A portion D on the stem of the guide
should be plain and a good fit in a plain hole in the holder,
in order to insure that the guide will be concentric with
the body of the counterbore. The thread must, of course,
in such a case fit very freely.
The variations possible are evidently many, but the
types represented involve the principles upon which inter-
500
SMALL TOOLS
changeable body and guide counterbores are designed.
The body and the guide should be easy to duplicate, there
should be means insuring that they will always remain
concentric in relation to one another, and all details need-
ing fitting when made should be contained in the holder
itself in order to prevent difficulties arising when placing
new bodies or guides on old holders.
Hollow Mills.
The hollow mill, if the action of the tool is analyzed,
may be classed as a combination of end mill and counter-
bore. It is used most commonly in connection with spring
screw threading dies, taking a cut preceding the die.
Hollow mills are usually made adjustable, as shown in
Fig. 278. Adjustable Hollow Mill Fig. 279. Solid Hollow MUl
Fig. 278. The adjustment is produced by the same means
as in spring screw threading dies, that is, with a clamp
collar. In Fig. 279 is shown another class of hollow mills,
less commonly used, termed solid hollow mills. The teeth
in the latter are cut so shallow that the prongs are stiff
and cannot be adjusted for size by bending inward as in
the case of adjustable hollow mills.
In order to produce clearance and prevent the tool from
binding when cutting, the hole is back tapered so that the
DRILLS — COUNTERBORES, ETC. 601
size to be cut is at the end where the cutting is done, but
the diameter of the hole is gradually increasing toward
the rear portion of the mill. The amount of this back
taper is generally made dififerent for steel and for brass.
For steel the taper should be one-quarter inch per foot,
for brass three-eighths inch per foot. The hole at the
extreme cutting end should be chamfered slightly so that
the piece to be cut can be brought into a central position
by the mill.
Adjustable hollow mills are always provided with three
flutes. These flutes are cut straight if the mill is to be
used for brass, but on an angle, so as to produce front
rake, if the tool is to be used for steel. The angle is effected
simply by turning the milling-machine table over the
desired amount, and should not exceed 10 degrees.
The cutters used for cutting the flutes are 55-degree
double angle cutters, 12 degrees on one side and 43
degrees on the other. As the land of a mill with only
three flutes becomes too wide when milled with this
class of cutters, it must be made narrower either by milling
once more or by filing. The length of the fluted part
should be about six-tenths of the whole length of the mill.
The outside of hollow mills ought to be ground the
same as spring screw threading dies, and for the same
reasons. The front part of the mill should preferably be
tapered on the outside, and solid clamp collars with
tapered holes be used for adjustment. The object and
advantage of this, as well as the various forms of clamp
collars, was all completely dealt with in connection with
spring screw dies.
On small sizes the hole of the mill is enlarged toward the
rear end as shown in Fig. 280. This precludes the necessity
of tapering the hole all the way back. The cutting edge on
hollow mills is relieved 5 degrees as shown in Fig. 278.
502
SMALL TOOLS
In Table CXXXII are given dimensions for hollow mills,
corresponding to the dimensions already given for spring
screw dies. It is evident that these dimensions are not
Oolting end
/ofmlU
Fig. 280. Small Size Hollow Mill with Clearance Hole
necessarily the only ones possible. They are ^ven only
for guidance in laying out this class of tools. They cor-
respond, however, to the practice of prominent small-tool
manufacturers.
TABLE GXXXII.
DIMENSIONS OF HOLLOW MILLS.
Diameter
Outside
Total
Diameter
Outside
Total
of Cut.
Diameter.
Length.
of Cut.
Diameter.
Length.
i
i
H
J
11
2i
A
i
}
2
3
i
i
1 ^
i
2
3
i
i
1 t
1
2
3
A
i
1
li
2
3
fv
i
1-
li
2
3
i
2
It
2i
31
A
2
li
2i
31
}
2
ij
2i
31
}
2J
li
3i
4
A
1
2i
2
3i
4
1
2i
2i
3i
4
Solid Lathe Arbors.
Lathe arbors are usually manufactured by the makers
of small cutting tools, and while not directly pertaining to
the subject treated in this volume, it has been considered
DRILLS — COUNTERBORES, ETC. 603
advisable to include a few remarks regarding them. Lathe
arbors are used for holding in the lathe pieces which have
holes passing through them so that they cannot be placed
directly on the lathe centers. The arbor then serves as
the medium by means of which the piece to be turned in a
lathe may be supported while turning.
In Table CXXXIII are given the general dimensions for
solid lathe arbors. In Table CXXXIV are given the
dimensions for the flat for dogs and for counterbores and
centers in the ends of the arbors. The diameter of the
drill for the centers has been given according to Stub's
steel wire gauge. For arbors with very heavy duty the
centers may be made somewhat larger than those given in
the table.
The notations of the letters given in the tables are as
follows:
A = total length of arbor,
B = length of actual arbor,
C = length of end turned down for dog,
D = diameter of arbor,
E = diameter of end turned down for dog,
F = distance of size line from small end,
G = diameter of center drill,
H = depth of drilled hole,
/ = diameter of countersunk center,
K = diameter of counterbore,
L = depth of counterbore, and
M = width of flat for dog.
In Table CXXXIII it will be noticed that a dimension
F has been given for the distance of diameter D from the
small end of the actual arbor. This obviously implies
that the arbor is slightly tapered. The purpose of this
taper is to permit the arbor to find its way straight into
504
SMALL TOOLS
TABLE CXXXIII.
DIMENSIONS OF SOLID LATHE ARBORS.
^
-F — H
A
-e— ^
A-
Fig. 281
D
A
B
C
«
¥
\
4
2f
H
A
5
A
4i
2A
M
A
a
f
4i
2:
^
«
A
4f
5
2if
3i
ji
ft
\
\
5i
3
A
9
f
6
3
lA
i
i
6i
4
H
33'
^A
1
7
4
1ft
^A
li
7i
5
li
i^tf
U
8
5
ift
ll
1
If
8*
5
It
If
4
9
6
ift
lA
lA
If
9i
ft
Iv
1^
If
U
10
6
/k
lii
If
m
7
Igi"
Iff
2
11
7-
i
1:
1*
2;
11
7
1
If
2
2
11
8 '
«
2A
2
12
8f
sf
1:
2i&
2f
2
12i
It
t
2A
2A
2
12;
8
2
2A
2i
2
13
9
2ft
^
2A
2i
13
9
2i
2-1
2f
3
14
9
2ft
2
2A
2A
3i
14f
lOf
lOf
2ft
23^
3i
15i
3^
2
3f
16i
11
2ft
2
4
17
llf
2H
3i
2it
DRILLS — COUNTERBORES, ETC.
TABLE CXXXIV.
505
DIMENSIONS OF CENTERS AND FLATS FOR DOG, SOLID LATHE
ARBORS.
Fig. 282
(See also Notation on page 503.)
G
H
M
A
i
2
2i
2i
2f
^t
21
2i
3
3i
3i
34
4
0.046
0.052
0.055
0.059
0.063
0.073
0.079
0.089
0.096
0.104
0.110
0.120
0.128
0.136
0.144
0.152
0.157
0.166
0.172
0.180
0.189
0.196
0.204
0.213
0.221
0.234
0.250
0.266
0.281
J
A
i
A
i
A
f
}
lb
lb
it
I
t
I
A
A
A
A
A
A
A
606 SMALL TOOLS
the hole in the piece it is intended to support, and to
allow for possible variations in the diameters of the holes.
This taper is made very slight, usually 0.006 inch per foot.
As far as the hardening of arbors is concerned the practice
at the present time among manufacturers is to harden
them all over. That this practice has been universally
adopted has probably been due to the increased demands
placed on tools in regard to strength and durability, which
has followed the changed commercial conditions of recent
years. It can by no means be said, however, that an
arbor hardened all over will in the long run produce as
accurate results as would an arbor hardened only at the
ends, the central portion, or the actual arbor, being left
soft. The reason for this is very obvious. When hard-
ening the arbor all over, severe internal stresses will
occur, and after having been used for some time, and
hammered upon more or less when driving on and off
pieces, these internal stresses will cause the arbor to
spring and get out of true. This will not happen with a
soft arbor, hardened only at the ends, as no internal
stresses of any amount have to be considered. To keep
a soft arbor in good cdndition, and to keep it true, it is
only necessary to use it with care. When really accurate
work is desired, arbors hardened at the ends only should
therefore always be used.
It is true that if hardened arbors are considered desir-
able for any specific reason if they are "seasoned" before
finish grinding, the same as plug gauges, etc., the internal
stresses are greatly relieved, and the probabilities of spring-
ing while in use are largely reduced. But it is impossible
to fully eliminate these stresses, and no matter how care-
fully the hardening process has been attended to, and
how long the arbor has been seasoned, the soft arbor
will remain superior for many jobs of extreme accuracy.
INDEX.
PAGB
Acme screw thread 29
Acme thread taps, dimensions of 192, 195
general construction of 155
made in sets 149, 153
inserted chaser 313
Adjustable dies, round split 303
Adjustable reamers, expansion 463
with inserted blades 464
Adjustable taps, Pratt and Whitney Company's 271
purpose and kind of 268
Angular cutters, general 367
fixture for grinding 369
Arbors, lathe 502
shell end mill 366
shell reamer 435
Blacksmiths' taper taps 257
Boiler taps, straight 263
taper 253
Bridge builders' reamer 454
Briggs pipe reamers ' 452
Briggs pipe taps 245
Briggs standard pipe thread 25
British Association standard thread 22
British standard fine screw thread 20
Brown and Sharpe standard tapers 447
Burritt's tap 276
Center cut end mills 365
Center reamers 459
Change gearing for thread cutting 51
Chasers 106
Chucking reamers, fluted 423
rose 426
three-grooved 456
507
508 INDEX
PAGS
Ck>IlaFB, clamp, for spring screw dies 285
table of 292
Comparators for lead of taps and screws 95
Compound gearing for thread cutting 55
Concave forming tool, making a 387
Concave milling cutters 378
Convex milling cutters 379
Comer-rounding cutters 377
Counterbores, inserted pilot 496
interchangeable body and guide 497
solid 490
Cutters, angular 367
concave 378
convex 379
comer-rounding 377
eccentrically relieved 371
end milling 360
fluting, for hand taps 161
for machine taps 221
for reamers 416
grinding of 166
for fluting spiral-teeth milling cutters 368
formed 371
grinding 339
hardening 337
inserted-blade 393
interlocked 351
key-ways for 337, 338
metal slitting 392
plain milling 320
screw slotting 392
shell end milling 366
side milling 343
single-point 104
steel used for 355
special form of 399
straddle milling 343
T-slot 389
Die holders, for spring screw dies 310
ordinary lathe 308
Die taps, constmction of 230
table of 233
INDEX 509
PAGS
Dies, adjustable inserted chaser 313
adjustable round split 303
cutting taps with 157
grinding 315
inserted chaser 312
pipe 302
requirements of 279
self-opening 317
solid 298
spring screw 278
square bolt 301
Woodbridge 314
Drilling deep holes 486
Drill, construction of a deep-hole 488
Drills, twist, see Twist drills.
Eccentrically relieved cutters 371
Eccentrically relieved reamers 408
Echols thread 218
End milling cutters, center cut ' 365
milling teeth on end of 363
sheU 366
taper shank 360
English taper pipe taps 247
Plat relief of reamers 408
Flatnsided reamers. 461
Fluted chucking reamers 423
Fluted shell reamers 433
Fluting cutters, for hand taps 161
for machine taps 221
for reamers 416
grinding of 166
special reamer 419
Fluting counterbores 491
hand reamers 415
hand taps 159
machine taps 218
plain milling cutters 332
reamers 416
tapper taps 211
twist drills 470
Fonning tools, circular 384
fl»t 381
510 INDEX
PAOB
Forming tools, making convex and concave 387
Fractional threads, change gears for cutting 57
French standard thread 31
Gas-fixture thread 36
Gauges for testing lead of taps and screws 93
Gearing a lathe for thread cutting 51
Grinding angular cutters 369
fluting cutters 166
milling cutters 339
threading dies 315
Grooved chucking reamers 456
Hand reamers, breaking up the flutes 411
dimensions of 414
helical flutes in 409
number of flutes in 415
relief of 407
requirements placed on a 404
threaded end ^ 410
Hand taps, change of pitch in hardening of 178
construction of 142
definition of 138
dimensions of 190
fluting cutters for 161
fluting of 159
made in sets 142
nimiber of flutes in .... : • 164
relief of 176
Hardening, change of pitch of taps in 178
dies 287
milling cutters 337
pack 188
reamers 421
swelling of taps in 182
taps 187
Highnspeed steel for cutters 355
for taps 276
Hob taps 228
Hobs, pipe , 250
SeUere 228
Holders, die 308, 310
thread tool 102, 136
Hollow mills 500
INDEX 511
PAGX
Instrument and watch makers' thread 35
Interlocked milling cutters 351
International standard thread 31
Inserted blade counterbore 498
milling cutters 393
reamers, adjustable 462
requirements of 466
taps 271
Inserted chaser dies, adjustable 313
solid 312
Interchangeable body and guide counterbores 497
Jamo taper reamers 448
Jobbers' reamers 430
Key-ways for milling cutters 337, 338
Lag screw thread 35
Lead and pitch of screw threads 3
Lead of taps and screws, testing 91
Lead of taps, change of, in hardening 178
Lead screw for cutting taps long in lead 180
Machine screw taps, general 194
tables of 198, 201, 204, 206
Machine screws, tables of A. S. M. E. standard thread for 203-206
threads for 16, 38
Machine taps, definition and general appearance 215
dimensions of 222
fluting cutters for 220
fluting of 218
relief of 222
table of 224
Measuring lead of screw threads 92
Measuring screw thread diameters 69
Measuring threads by three-wire system 76
Metal slitting cutters 392
Metric lead screw, cutting English threads with 61
Metric reduction table 34
Metric threads, cutting, with English lead screw 68
Micrometer, ball-point 72
Brown and Sharpe screw thread 70
for measuring width of flat of United States standard
thread tools Ill
Micrometer attachment, sensitive 91
512 INDEX
PAGES
MillimeterB into inches 34
Milling cutters, see Cutters
Mills, hollow 500
Mills, see Cutters
Morse taper reamers 443
taper shanks 445
Mud and wash-out taps 256
P&tch-bolt taps 255
Pin reamers, standard taper 441
Pins, standard taper 442
Pipe dies 302
hobs 250
reamers 452
sizes 25
taps, Briggs 245
English 247, 267
straight 265
taps and drills combined 258
threads 25, 27
Pitch and lead of screw threads 3
Pitch, change of, in hardening 178
Plain milling cutters, general 320
hardening 337
number of teeth of 325
spiral of teeth of 330
with nicked teeth 331
Pulley taps 207
Reamers, adjustable 462
bridge 454
Briggs pipe 452
Brown and Sharpe taper 446
center 459
chucking, fluted 423
chucking, three-grooved 456
eccentric relief of 408
expansion 463
flat relief of . 408
flatHsided 461
fluted chucking 423
fluting of 415
grinding 421
grooved chucking 456
hand 403
INDEX 513
PAGE
Reamers, hardening 421
Jamo taper 448
jobbers' 430
locomotive taper 450
Morse taper 443
pipe 452
rose chucking 426
rose shell 434
shell 432
taper 438
taper pin 441
Relief of hand tape 176
machine taps 222
milling cutters 339
reamers 407
taper taps 241
tapper taps 212
Rolling threads 46
Rose chucking reamers 426
shell reamers 434
Round split dies 303
Screw machine taps 225
Screw thread micrometer, Brown and Sharpe 70
Screw thread systems, Acme 29
Briggs pipe 25
British Association standard 22
British standard fine 20
French standard 31
gas-fixture thread 36
instrument and watch makers' 35
international standard 31
lag screw 35
machine screw 38
sharp V - 9
square 28
United States standard 2
Whitworth standard 16
Whitworth standard for gas and water piping 27
Whitworth standard for instrument and watch makers . 35
Screw threads, drunken 238
' lead and pitch of 3
measuring 69
514 INDEX
PAGB
Screw threads, multiple 67
principal requirements of 8
produced by rolling 46
Self-opening dies 317
Sellers hobs 228
Sellers screw thread system 6
Shell end mills, arbors for 366
dimensions of 366
Shell reamers, adjustable 465
arbors for 435
fluted 433
rose 434
Side milling cutters, general 343
number of teeth in 348
relief of 349
Simple gearing for thread cutting 52
Single-point cutters ! 104
Solid dies 298
Spindle stay-bolt taps 262
Split adjustable dies 303
Spring screw threading dies, chamfering 289
clamp collars for 285, 291
fluting of 287
hardening 287
hobs for 290
preferable method of making 281
roughing and finishing 293
table of 291
Square bolt dies 301
Square thread 28
Square thread taps, dimensions of 192
general construction of 156
made in sets 151, 153
Square thread tools, diagram of clearance of 135
general construction 132
simplest form of 100
table of 134
Stay-bolt taps, radial 259
spindle 262
Steel used for taps 276
for cutters 355
Straddle milling cutters 343
Swelling of taps in hardening ^ 182
INDEX 515
PAGB
Tnslot cutters 380
TailHstock, effect of setting over in taper threading 237
Taper in certain lengths, table of 457
Taper pins, and reamers for 442
Taper leamers, bridge 454
Brown and Sharpe « 446
finishing 441
Jamo 448
locomotive 450
Morse 443
roughing 438
Taper shanks, Brown and Sharpe 447
Jamo 448
Morse 445
Taper taps, blacksmiths' 257
boiler 253
definition of 140
effect of setting over tail-stock when threading 237
general 236
relief of 241
testing lead of •. . 243
threading tools for 124
Tapper taps, definition and general appearance 210
'dimensions of 212
fluting of 211
relief of 212
table of 214
Taps, Acme thread 149, 153, 192
adjustable 268
blacksmiths' taper 257
boiler, straight 263
boiler, tap^r 253
Briggs pipe 245
Burritt's 276
definitions of different kinds of 138
die 230
' hand 142
hardening of 187
hob 228
inserted-blade 271
machine 215
machine screw 194
mud or wash-out 256
616 INDEX
PAGB
Taps, patch-bolt 255
pipe 245
pipe, and drill combined 258
pipe, EngliHh 247, 267
pipe hobs 250
pipe, straight 265
pulley 207
requirements for correctly threaded 158
screw machine 225
spindle stay-bolt 262
square thread 151, 153
stay-bolt, radial 257
spindle 262
steel used for 276
straight boiler 263
straight pipe 265
swelling of, in hardening 182
taper 236
taper boiler 253
tapper 210
testing lead of 92
Testing lead of taps and screws 92
Thread-cutting, change gears for 50
general principles of 66
review of methods in use 43
Thread milling machine, cutting threads in 45
influence of, on threading tools 129
Thread rolling ' 46
Thread systems, see Screw thread systems
Thread tool holder, Pratt and Whitney 102
special spring 136
Threading dies, see Dies
Threading tools, for square thread 100, 132
for taper taps 124
measuring width of flat of United States standard. . 109
simple form of • . . . 99
United States standard 106
Whitworth standard 116
with side clearance 121
Threads, see Screw threads
Twist drills, dimensions of 484
fluting 470
grinding 480
INDEX 517
PAGE
Twist drills, hardening 478
increased twist of 471
lead of helix of grooves in 470
relieving the lands of 476
thickness of web of 474
United States standard thread 2
United States standard thread tools 106
V-thread, sharp 9
Whitworth pipe taps 248
Whitworth thread 16
advantages and disadvantages of 20
for gas and water piping 27
for watch and mathematical instrument makers ... 35
Whitworth thread tools, the making of 116
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Merrill's Non-metallic Minerals: Their Occurrence and Uses Svo, 4 00
Stones for Building and Decoration. 8vo» 5 00
Monckton's Stair-building. 4to, 4 00
Patton's Practical Treatise on Foundations. 8vo, 5 00
Peabody's Naval Architecture 8vo, 7 50
Rice's Concrete-block Manufacture Svo, a 00
Richey's Handbook for Superintendents of Construction. z6mo, mor. 4 00
* Building Mechanics' Ready Reference Book:
* Building Foreman's Pocket Book and Ready Reference. (In
Press.)
* Carpenters' and Woodworkers' Edition i6mo, mor. z 50
* Cement Workers and Plasterer's Edition i6mo, mor. z 50
* Plumbers', Steam-Filters', and Tinners' Edition i6mo, mor. z 50
* Stone- and Brick-masons' Edition i6mo, mor. z 50
Sabin's House Painting i2mo, z 00
Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00
Siebert and Biggin's Modem Stone-cutting and Masonry. 8to, z 50
Snow's Principal Species of Wood 8vo, 3 5©
Towne's Locks and Builders' Hardware i8mo, mor. 3 00
Waifs Engineering and Architectural Jurisprudence 8vo, 6 00
Sheep, 6 50
Law of Contracts 8vo, 3 00
Law of Operations Preliminary to Construction in Engineering and Archi-
tecture. > 8vo, 5 00
Sheep, 5 50
Wilson's Air Conditioning i2mo, z 50
Worcester and Atkinson's Small Hospitals, Establishment and Maintenance.
Suggestions for Hospital Architecture, with Plans for a Small Hospital.
x2mo, z 25
ARMY AND NAVY.
Bemadou's Smokeless Powder, Nitro-cellulose, and the Theory of the Cellulose
Molecule i2mo, 2 50
Chase's Art of Pattern Making i2mo, a 50
Screw Propellers and Marine Propulsion 8vo, 3 00
* Cloke's Enlisted Specialist's Examiner 8vo, 2 00
Gunner's Examiner 8vo, 1 50
Craig's Azimuth 4to, 3 50
Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 00
* Davis's Elements of Law 8vo, 2 50
* Treatise on the Military Law of United States 8vo, 7 00
Sheep; 7 50
De Brack's Cavalry Outpost Duties. (Carr) 24mo, mor. 2 00
* Dudley's Military Law and the Procedure of Courts-martial. . . Large z2mo, 3 50
Purand's Resistance and Propulsion of Ships. 8vo, 5 00
2
* Dyer's Handbook of Light Artiltery. Z2mo, 3 00
Sissler's Modern High Explosives : 8vo, 4 00
* Flebeger's Text-book on Field Fortification Large xamo, 2 00
Hamilton and Bond's The Gunner's Catechism i8mo, z 00
* HofiTs Elementary Naval Tactics. 8vo, z 50
Ingalls's Handbook of Problems in Direct Fire. 8vo, 4 00
'*' Lissak's Ordnance and Gtumeiy 8vo, 6 00
* Ludlow's Logarithmic and Trigonometric Tables 8vo, z 00
* Lyontf's Treatise on Electromagnetic Phenomena. Vols. I. and II.. 8vo, each, 6 do
* Mahan's Permanent Fortifications. (Mercur) 8vo, half mor. 7 50
Manual for Courts-martial i6mo, mor. z 50
4* Mercur's Attack of Fortified Places Z2mo, 2 00
* Elements of the Art of War 8vo, 4 00
Metcalf's Cost of Manufactures — ^And the Administration of Workshoiw. .8vo, 5 00
ITixon's Adjutants' ManuaL 34mo, z 00
Peabody's Naval Architecture 8vo, 7 50
* Phelps's Practical Marine Survejring 8vo, 2 50
Putnam's Nautical Charts 8vo, 3 00
Sharpe's Art of Subsisting Armies in War. z8mo, mor. z 50
* Tupes and Poole*s Manual of Bayonet Exercises and Musketry Fencing.
24mo, leather, 50
* Weaver's Military Explosives 8vo, 3 00
Woodhull's Notes on Military Hygiene z6mo, z 50
ASSAYING.
Betts's Lead Refining by Electrolysis 8vo, 4 00
Fletcher's Practical Instructions in Quantitative Assaying with the Blowpipe.
x6mo, mor. z 50
Furman's Manual of Practical Assaying 8vo, 3 00
Lodge's Notes on Assaying and Metallurgical Laboratory Experiments 8vo, 3 00
Low's Technical Methods of Ore Analysis 8vo, 3 00
Miller's Cyanide Process i2mo, z 00
Manual of Assaying z2mo, z 00
Minet's Production of Aluminum and its Industrial Use. (Waldo )..\ ... i2mo, 2 50
O'DriscoU's Notes on the Treatment of Gold Ores 8vo, 2 00
Ricketts and Miller's Notes on Assaying. 8vo, 3 00
Robine and Lenglen's Cyanide Industry. (Le Clerc) 8vo, 4 00
Ulke's Modem Electrolytic Copper Refining 8vo, 3 00
Wilson's Chlnrination Process , Z2mo, z 50
Cyanide Processes. Z2ma i 50
ASTRONOMY.
Comstock's Field Astronomy for Engineers 8vo, a 50
Craig's Azimuth 4to, 3 50
Crandall's Text-book on Geodesy and Least Squares Svo. 3 00
Doolittle's Treatise on Practical Astronomy. 8vo, 4 00
Gore's Elements of Geodesy 8vo, 2 50
Hayford's Text-book of Geodetic Astronomy. 8vo» 3 00
Merriman's Elements of Precise Surveying and Geodesy. 8vo, 2 50
* Michie and Harlow's Practical Astronomy. 8vo, 3 00
Rust's Ex-meridian Altitude, Azimuth and Star-Finding Tables. 8vo, 5 00
* White's Elements of Theoretical and Descriptive Astronomy Z2mo» a 00
8
CHEinSTRY.
* Abderhalden't Phyiiological Chtmistry in Thirty Lectures. (Hall and Defren)
8to, 5 oo
* Aben'* Theory of Electrolytic Dissociation, (von Ende) i2mo, i 25
Alexeyeff's General Principles of Organic Syntheses. (Matthews) 8vo» 3 00
Allen's Tables for Iron Analysis Svo, 3 00
Arnold's Compendium of Chemistry. (Mandel) Large i2mo, 3 50
Aasodation of State and National Food and Dairy Departments, Hartford,
Meeting, Z906 Svo, 300
Jamestown Meeting, 1907 8vo, 3 00
Austen's Notes for Chemical Students lamo* z 50
Baskerville's Chemical EJements. (In Preparation.)
Bemadou's Smokeless Powder.— Nitro-cellulose, and Theory of the Cellulose
Molecule i2mo9 2 50
Bilts's Chemical Preparations. (Hall and Blanchard). (In Press.)
^Blanchard's Synthetic Inorgai^c Chemistry. .'i2mo, x 00
* Browning's Introduction to the Rarer Elements 8vo, i 50
Brush and Penfield's Manual of Determinative Mineralogy 8vo, 4 00
* Claassen's Beet-sugar Manufacture. (Hail and Rolfe) 8vo, 3 00
Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood).. .8vo, 3 00
Cohn's Indicators and Test-papers i2mo, 2 00
Tests and Reagents 8vo, 3 00
* Danneel's Electrochemistry. (Merriam) i2mo, z 25
Dannerth's Methods of Textile Chemistry i2mo, 3 00
Duhem's Thermodynamics and Chemistry. (Burgess) 8vo« 4 00
Ealde's Mineral Tables for the Determination of Minerals by their Physical
Properties 8vo, z 25
Eissler's Modern High Explosives 8vo, 4 00
Effront's Enzymes and their Applications. (Prescott) 8vo, 3 00
Erdmann's Introduction to Chemical Preparations. (Dunlap) i2mo, z 25
* Fischer's Physiology of Alimentation Large x2mo, 3 00
Fletcher's Practical Instructions in (^antitative Assaying with the Blowpipe.
i2mo, mor. i 50
Fowler's Sewage Works Analyses i2mo, 2 00
Fresenius's Manual of Qualitative Chemical Analysis. (Wells) 8vo, 5 00
Manual of Qualitative Chemical Analysis. Part I. Descriptive. (Wells) 8vo, 3 00
Quantitative Chemical Analirsis. (Cohn) 2 vols Svo. 12 50
When Sold Separately, VoL I, $6. Vol. II, |8.
Fuertes's Water and Public Health i2mo, z 50
Furman's Manual of Practical Assaying 8vo, 3 00
* Getman's Exercises in Physical Chemistry i2mo, 2 00
Gill's Gas and Fuel Analysis for Engineers i2mo, z 25
* Gooch and Browning's Outlines of Qualitative Chemical Analysis.
Large i2mo, z 25
Grotenfelt's Principles of Modem Dairy Practice. (WoU) x2mo, 2 00
Groth's Introduction to Chem'^*^] Crystallography (Marshall) i2mo, z 25
Hammarsten's Text-book of Physiological Chemistry. (Mandel) Svo, 4 00
Hanausek's Microscopy of Technical Products. (Winton) Svo, 5 00
♦Haskins and Macleod's Organic Chemistry z2iiio, 2 00
Hehn's Principles of Mathematical Chemistry. (Morgan) z2mo, i 50
Hering's Ready Reference Tables (Conversion Factors) z6mo, mor. 2 50
* Herrick's Denatured or Industrial Alcohol . • Svo, 4 00
Hinds's Inorganic Chemistry 8vo, 3 00
* Laboratory Manual for Students z2mo, z 00
* Holleman's Laboratory Manual of Organic Chemistry for Beginners.
(Walker^ i^mo* » «>
Text-book of Inorganic Chemistry. (Cooper) 8vo, 2 50
Text-book of Organic Chemistry. (Walker and Mott) , Svo, a 50
4
olley and Ladd's Analysis of Hixed Paints, Color Pigments, and Vaniishes.
Large x2mo, 2 50
Hopkins's Oil-chemists' Handbook. 8vo, 3 00
Iddings's Rock Minerals 8vo, 5 00
Jackson's Directions for Laboratory Work in Physiological Chemistry. .8vo, 1 25
Johannsen's Detennination of Rock-fonning Minerals in Thin Sections . .8vo, 4 00
Johnson's Chemical Analysis of Special Steel. Steel-making. (Alloys and
Graphite.) (In Presi.)
Keep's Cast Iron 8vo, 2 50
Ladd's Manual of Quantitative Chemical Analysis i2mo, i 00
lAndauer's Spectrum Anal3rsis. (Tingle) 8vo, 3 00
* Langwurtny and Austen's Occurrence of Aluminium in Vegetable Prod-
ucts, Animal Products, and Natural Waters 8yo, 2 00
Lassar-Cohn's Application of Some General Reactions to Investigations in
Organic Chemistry. (Tingle) i2mo, i 00
Leach's Inspection and Analysis of Food with Special Reference to State
ControL 8vo, 7 50
Lab's Electrochemistry of Organic Compounds. (Lorenz) 8vo, 3 00
Lodge's Notes on Assaying and Metallurgical Laboratory Experiments. .. .8vo, 3 00
Low's Technical Method of Ore Analysis 8vo, 3 00
Lunge's Techno-chemical Anal]rsis. (Cohn)./ i2mo, z 00
* McKay and Larsen's Principles and Practice of Butter-making 8vo, i 50
Maiie's Modem Pigments and their Vehicles i2mo, 2 00
Mandel's Handbook for Bio-chemical Laboratory i2mo, i 50
* Martin's Laboratory Guide to Qtialitative Analysis with the Blowpipe . . i2mo, 60
Mason's Examination of Water. (Chemical and Bacteriological.). . ..i2mo, i 25
Water-supply. (Considered Principally from a Sanitary Standpoint.
8vo, 4 00
Mathewson's Chemical Theory for First Year College Students. (In Press).
Matthews's Textile Fibres. 2d Edition, Rewritten 8vo, 4 00
* Meyer's Determination of Radicles in Carbon Compounds. (Tingle).. i2mo, 125
Miller's Cyanide Process i2mo, i 00
Manual of Assajring i2mo, i 00
Minet's Production of Aluminum and its Industrial Use. (Waldo) i2mo, 2 50
Mixter's Elementary Text-book of Chemistry i2mo, i 50
Morgan's Elements of Phjrsical Chemistry i2mo, 3 00
Outline of the Theory of Solutions and its Results i2mo, i 00
'*' Physical Chemistry for Electrical Engineers i2mo, z 50
Morse's Calculations used in Cane-sugar Factories i6mo, mor. z 50
* Mulr's History of Chemical Theories and Laws 8vo, 4 00
Mulliken's General Method for the Identification of Pure Organic Compounds.
VoL I Large 8vo, 5 00
O'Driscoll's Notes on the Treatment of Gold Ores '. . . .8vo, 2 00
Ostwald's Conversations on Chemistry. Part One. (Ramsey) i2mo, z 50
" " " •' Part Two. (TumbuU) z2mo, 2 00
* Palmer's Practical Test Book of Chemistry z2mo, z 00
* Pauli's Physical Chemistry in the Service of Medicine. (Fischer) z2mo, z 25
* Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests.
8vo, paper, 50
Tables of Minerals, Including the Use of Minerals and Statistics of
Domestic Production 8vo, z 00
Pictet's Alkaloids and their Chemical Constitution. (Biddle) 8vo, 5 00
Poole's Calorific Power of Fuels 8vo, 3 00
Prescott and Winslow's Elements of Water Bacteriology, with Special Refer-
ence to Sanitary Water Analysis z2mo, z 50
* Reisig's Guide to Piece-dyeing 8vo, 35 00
Richards and Woodman's Air, Water, and Food from a Sanitary Standpoint. .8 vo , 2 00
Rtcketts and Miller's Notes on Assaying 8vo, 3 00
Rideal's Disinfection and the Preservation of Food 8vo, 4 00
Sewage and the Bacterial Purification of Sewage 8vo» 4 00
5
RiCKs't Elementary ManuAl for the Chemical Laboratory 8vo, i 35
Robine and Lenglen'a Cyanide Industry. (Le Clerc) 8to, 4 00
Rnddiman's Incompatibilities in Prescriptions. Svo, 2 00
Whys in Pharmacy lamo, i 00
Ruer's Elements of Metallography. (Mathewson) (In Preparation.)
Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00
Salkowski's Physiological and Pathological Chemistry. (Omdorff) 8vo, a 50
Schimpf s Essentials of Volumetric Analysis i2mo, z as
* Qualitatiye Chemical Analysis 8vo, i 35
Text-book of Volumetric Analysis. zamo, a 50
Smith's Lecture Notes on Chemistry for Dental Students 8vo, a 50
Spencer's Handbook for Cane Sugar Manufacturers i6mo, mor. 3 00
Handbook for Chemists of Beet-sugar Houses i6mo'p mor. 3 00
Stockbridge's Rocks and Soils 8vo, 2 50
* Tillman's Descriptive General Chemistry. 8vo, 3 00
* Elementary Lessons in Heat 8vo, z 50
Treadwell's Qualitative Analysis. (Hall) 8vo, 3 00
Quantitative Analysis. (Hall) 8vo, 4 00
Turneaure and RuSsell's Public Water-supplies 8vo, 5 00
Van Deventer's Physical Chemistry for Begizmers. (Boltwood) lamo, z 50
Venable's Methods and Devices for Bacterial Treatment of Sewage Svo, 3 00
Ward and Whipple's Freshwater Biology. (In Press.)
Ware's Beet-sugar Manufacture and Refining. Vol. I Small 8vo, 4 00
Vol.11 SmallSvo,' 500
Washington's Manual of the Chemical Analysis of Rocks 8vo, 2 00
* Weaver's Military Explosives 8vo, 3 00
Wells's Laboratory Guide in Qualitative Chemical Analysis 8vo, z 50
Short Course in Inorganic Qualitative Chemical Anal3rsis for Engineering
Students i2mo, z 50
Text-book of Chemical Arithmetic Z2mo, z 25
Whipple's Microscopy of Drinking-water Bvo, 3 50
Wilson's Chlorination Process z2mo, z 53
Cyanide Processes i2mo, z 50
Winton's Microscopy of Vegetable Foods 8vo, 7 50
CIVIL ENGINEERING.
BRIDGES AND ROOFS. HYDR.\ULIC3. MATERIALS OF ENGINEER-
ING. RAILWAY ENGINEERING.
Baker's Engineers' Surveying Instruments z2mo, 3 00
Bixby's Graphical Computing Table Paper 10^ v 24! inches. 25
Breed and Hosmer's Princioles and Practice of Surveying. 2 Volumes.
Vol. I. Elementary Surveying 8vo, 3 00
VoL IL Higher Surveying 8vo, 2 50
* Burr's Ancient and Modern Engineering and the Isthmian Canal 8vo, 3 50
Comstock's Field Astronomy for Engineers 8vo, 2 50
* Corthell'9 Allowable Pressures on Deep Foundations z2mo, z 25
Crandall's Text-book on Geodesy and Least Squares 8vo, 3 00
Davis's Elevation and Stadia Tables 8vo, z 00
Elliott's Engineering for Land Drainage z2mo, z 50
Practical Farm Drainage Z2mo, i 00
*Fiebeger*s Treatise on Civil Engineering 8vo, 5 00
Flemer's Phototopographic Methods and Instruments. 8vo, 5 00
Folwell's Sewerage. (Designing and Maintenance.) 8vo, 3 00
Freitag's Architectural Engineering 8vo, 3 50
French and Ives's Stereotomy 8vo, a 50
Goodhue's Municipal Improvements zamo, z 50
Gore's Elements of Geodesy 8vo, a 50
* Hauch's and Rice's Tables of Quantities for Preliminary Estimates , . zamo, x 25
6
Bayford'8 Text-book of Geodetic Astronomy. Sw, 3 00
Eexinc's Ready Reference Tables. (Conversion Factors) z6mo, mor. 2 50
Howe's Retaining Walls for Earth. zamo» z as
* Ives's Adjustments of the Engineer's Transit and Level z6mo, Bds. as
Ives and Hilts's Problems in Surveying i6mo, mor. z so
Johnson's (J. B.) Theory and Practice of Surveying Small Svo, 4 00
Johnson's (L. J.) Statics by Algebraic and Graphic Methods. 8vo, a 00
Kinnicutt, Winslow and Pratt's Purification of Sewage. (In Preparation.)
Laplace's Philosophical Essay on Probabilities. (Truscott and Emory)
xamo, a 00
ICahan's Descriptive Creometry. 8vo, z so
Treatise on Civil Engineering. (1873.) (Wood) 8vo, s 00
Merriman's Elements of Precise Surveying and Geodesy. 8vo« a 50
Merriman and Brooks's Handbook for Surveyors x6mo, mor. a 00
Nugent's Plane Surveying 8vo» 3 so
Ogden's Sewer Construction 8vo, 3 00
Sewer Design lamo, a 00
Parsons's Disposal of Municipal Refuse 8vo, a 00
Patton's Treatise on Civil Engineering 8vO| half leather, 7 50
Reed's Topographical Drawing and Sketching 4to, 5 00
Rideal's Sewage and the Bacterial Purification of Sewage 8vo, 4 00
Riemer's Shaft-sinking under Difftcult (Auditions. (Coming and Peele). . . 8vo, 3 00
Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, z 50
Smith's Manual of Topographical Drawing. (McMillan) 8vo, a 50
Soper's Air and Ventilation of Subways Large lamo, 2 50
Tracy's Plane Survesdng i6mo, mor. 3 00
♦ Trautwine's Civil Engineer's Pocket-book z6mo, mor. 5 00
Venable's Garbage Crematories in America 8vo, 2 00
Methods and Devices for Bacterial Treatment of Sewage 8vo, 3 00
Wait's Engineering and Architectural Jurisprudence 8vo, 6 00
Sheep, 6 50
Law of Contracts 8vo, 3 00
Law of Operations Preliminary to Construction in Engineering and Archi-
tecture 8vo, 5 00
Sheep, 5 so
Warren's Stcreotomy — ^Problems in Stone-cutting 8vo, a 50
•Waterbury's Vest-Pocket Hand-book of Mathematics for Engineers.
aiXst inches, mor. i 00
Webb's Problems in the Use and Adjustment of Engineering Instruments.
i6mo, mor. i as
Wilson's (H. N.) Topographic Surveying 8vo, 3 50
Wilson's (W. L.) Elements of Railroad Track and Construction lamo, a 00
BRIDGES AND ROOFS.
Boner's Practical Treatise on the Construction of Iron Highway Bridges . . 8vo, a 00
Burr and Falk's Design and Construction of Metallic Bridges 8vc, 5 00
Influence Lines for Bridge and Roof Computations 8vo, 3 00
Du Bois's Mechanics of Engineering. VoL H. Small 4to, 10 00
Foster's Treatise on Wooden Trestle Bridges 4to, 5 00
Fowler's Ordinary Foundations 8vo, 3 50
French and Ives's Stereotomy 8vo, a se
Greene's Arches in Wood, Iron, and Stone 8vo, a so
Bridge Trusses 8vo, 2 50
Roof Trusses 8vo, i as
Grimm's Secondary Stresses in Bridge Trusses 8vo, a 50
HeDer's Stresses in Structures and the Accompanying Deformations 8vo, 3 00
Howe's Design of Simple Roof-trusses in Wood and SteeL 8va. a 00
Symmetrical Masonry Arches 8vo, a 50
Treatise on Arches. ...» 8vo, 4 oc
7
Johnson, Bryan, and Tumeaure's Theory and Practice in the I>esl8mng of
Modem Framed Structures. SmaU 4to, lo oo
Merriman and Jacoby's Text-book on Roofs and Bridges:
Part I. Stresses in Simple Trusses 8vo, 2 50
Part n. Grapiiic Statics. 8vo, 3 50
Part in. Bridge Design 8vo, 2 50
Part IV. Higher Structures 8vo, 2 50
Morison's Memphis Bridge Oblong 4to, 10 00
Sondericker's Graphic Statics, with Applications to Trusses, Beams, and Arches.
8vo, 2 00
Waddell's De Pontibus, Pocket-book for Bridge Engineers i6mo. mor, 2 00
* Specifications for Steel Bridges « . . i2mo, 50
Waddelland Harrington's Bridge Engineering. (In Preparation.)
Wright's Designing of Draw-spans. Two parts in one volume 8to, a 50
HYDRAULICS.
Barnes's Ice Formation. 8yo, 3 00
Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from
on Orifice. (Trautwine) 8vo, 2 00
Bovey's Treatise on Hydraulics. 8vo, 5 00
Church's Diagrams of Mean Velocity of Water in Open Channels.
Oblong 4to. paper, i 50
Hydraulic Motors 8vo, 2 00
Mechanics of Engineering. 8vo, 6 00
Coffin's Graphical Solution of Hydraulic Problems i6mo, mor. 2 50
Flather's Dynamometers, and the Measurement of Power i2mo, 3 00
Folwell's Water-supply Engineering. 8vo, 4 00
Frizell's Water-power. . ., 8vo, 5 00
Fuertes's Water and Public Health. i2mo, z 50
Water-filtration Works i2mo, 2 50
Ganguillet and Kutter's General Formula for the Uniform Flow of Water in
Rivers and Other Channels. (Hering and Trautwine) 8vo, 4 00
Hazen's Clean Water and How to Get It Large i2mo, x 50
Filtration of Public Water-supplies 8vo, 3 00
Hazlehurst's Towers and Tanks for Water-works 8vo, 2 50
Herschel's 115 Experiments on the Carrying Capacity of Large, Riveted, Metal
Conduits 8vo, 2 00
Hoyt and Grover's River Discharge 8vo, 2 00
Hubbaid and Kiersted's Water-works Management and Maintenance 8vo, 4 00
* Lyndon's Development and Electrical Distribution of Water Power 8vo, 3 00
Mason's Water-supply. (Considered Principally from a Sanitary Standpoint)
8vo, 4 00
Merriman's Treatise on Hydraulics 8vo, 5 00
* Michie's Elements of Anal3rtical Mechanics 8vo, 4 00
* Molitor's Hydraulics of Rivers, Weirs and Sluices 8vo, 2 00
Richards's Laboratory Notes on Industrial Water Analysis. (In Press),
Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water-
supply Large 8vo, 5 00
* Thoma-! and Watt's Improvement of Rivers 4to, 6 00
Tumeaure and Russell's Public Water-supplies 8vo, 5 00
Wegmann's Design and Construction of Dams. 5tb Ed., enlarged 4to, 6 00
Water-supply of the City of New York from 1658 to 1895 4to, xo 00
Whipple's Value of Pure Water .Large i2mo, x 00
Williams and Hazen's Hydraulic Tables 8vo, z 50
Wilson's Irrtjfat'on Engineering Small 8vo, 4 00
Wolfif's Windmill as a Prime Mover 8vo, 3 00
Wood's Elements of Analytical Mechanics .8vo, 3 00
Turbines. 8vo, 2 50
8
MATERIALS OF ENGINEERING.
Baker's Roads and Pavements 8vo, 5 00
Treatise on Masonry Construction .8yo, 5 00
Birkmire'« Architectural Iron and Steel 8vo, 3 50
Compound Riveted Girders as Applied in Buildings 8vo, 2 00
Black's United States PubUc Works Oblong 4to. 5 00
Bleininger's Manufacture of Hydraulic Cement. (In Preparation.)
♦ Bovey's Strength of Materials and Theory of Structures 8vo, 7 50
Burr's Elasticity and Resistance of the Materials of Engineering 8'vo, 7 50
Byrne's Highway Construction. 8vo, 5 00
Inspection of the Materials and Workmanship Employed in Construction.
i6mo* 3 00
Church's Mechanics of Engineering 8vo, 6 00
Du Bois's Mechanics of Engineering.
VoL I. Kinematics, Statics, Kinetics Small 4to, 7 5©
VoL II. 'ihe Stresses in Framed Stractures, Strength of Materials and
Theory of Flexures. Small 4to, 10 00
^Bckel's Cements, Limes, and Plasters 8vo, 6 00
Stone and Clay Products used in Engineering. (In Preparation.)
Fowler's Ordinary Foundations 8vo, 3 50
Graves's Forest Mensuration 8vo, 4 00
Green's Principles of Americau Forestry i2mo, i 50
♦ Greene's Structural Mechanics 8vo, 2 50
Holly and Ladd's Analysis of Mixed Paints, Color Pigments and Varnishes
Large i2mo, 2 50
Johnson's (C. M.) Chemical Analysis of Special Steels. (In Preparation.)
Johnson's (J. B.) Materials of Construction '. L&rge 8vo, 6 00
Keep's Cast Iron 8vo, 2 50
Kidder's Architects and Builders' Pocket-book i6mo, 5 00
Lanza's Applied Mechanics 8vo, 7 5o
Maire's Modern Pigments and their Vehicles i2mo, 2 00
Martens's Handbook on Testing Materials. (Henning) 2 vols 8vo, 7 5©
Maurer's Technical Mechanics 8vo, 4 00
Merrill's Stones for Building and Decoration 8vo, 5 00
Merriman's Mechanics of Materials 8vo, 5 00
♦ Strength of Materials lamo, i 00
MetcalTs SteeL A Manual for Steel-users i2mo, 2 00
Morrison's Highway Engineering 8vo, 2 50
Patton's Practical Treatise on Foundations 8vo, s 00
Rice's Concrete Block Manufacture 8vo, 2 o©
Richardson's Modem Asphalt Pavements 8vo. 3 00
Richey's Handbook for Superintendents of Construction i6mo, mor. 4 00
♦ Ries's Clays: Their Occurrence, Properties, and Uses 8vo, 5 00
Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00
*Schwarz'sLonj?1eaf Pine in Virgin Forest "mo, i 25
Snow's Principal vSpecies of Wood 8vo, 3 5o
Spalding's Hydraulic Cement "°^^» ^ ^
Text-book on Roads and Pavements i2mo, 2 00
Taylor and Thompson»s Treatise on Concrete, Plain and Reinforced 8vo, 5 00
Thurston's Materials of Engineering. In Three Parts 8vo, 8 00
Part L Non-metallic Materials of Engineering and Metallurgy 8vo, 2 00
Part n. Iron and Steel 8^?» 3 5©
Part in. A Treatise on Brasses, Bronzes, and Other AUoys and their
Constituents |^°' ^ 5©
TiUson's Street Pavements and Paving Materials 8vo, 4 ©©
Tumeaure and Maurer's Principles of Reinforced Concrete Construction.. .8vo, 3 ©©
Waterbury's Cement Laboratory Manual 12m©, i ©o
0
' RAILWAY ENGDfEERIirG.
AndfcwB'f Handbook for Street Railway Encineeri 3x5 inchet, mor. i 2$
Berc** BuUdiacB and Structures of American Railroads 4to, 5 00
Brooks's Handbook of Street Railroad Location. i6mo, mor. i so
Butfs Civil Engineer's Field-book. i6mo, mor. 2 50
CrandaU's Railway and Other Earthwork Tables. 8vo, i 50
Transition Curve idmo, mor. i 50
* Crockett's Methods for Baithwork Compiitatioiis 8vo, x 50
Dawson's "Engineering" and Electric Traction Pocket-book x6mo. mor. 5 00
Dredge's History of the Pennsylvania Raikoad: (1879) Paper, 5 00
Fisher's Table of Cubic Yards Cardboard, 25
Godwin's Railroad Engineers' Field-book and Explorers' Guide. . . x6mo, mor. 2 50
Hudson's Tables for Calculating the Cubic Contents of Excavations and Em-
bankments. 8vo, z 00
Ives and Hilts'o Problems in Surveying, Railroad Surveying and Geodesy
i6mo, mor. z 50
Molitor and Beard's Manual for Resident Engineers x6mo, z 00
Nagle's Field Manual for Raikoad Engineers. i6mo, mor. 3 00
Philbrick's Field Manual for Engineers i6mo, mor. 3 00
Raymond's Railroad Engineering. 3 vcflumes.
VoL I. Railroad Field Geometry. (In Preparation.)
VoL II. Elements of Railroad Engineering 8vo, 3 50
Vol III. Raikoad Engineer's Field Book. (In Preparation.)
Searles's Field Engineering i6mo, mor. 3 00
Raikoad SpiraL i6mo, mor. z 50
Taylor's Prismoidal FormuleB and Earthwork 8vo, z 50
*Trautwine'8 Field Practice of Laying Out Circular Curves for Raikoads.
zamo. mor, a 50
* Method of Calculating the Cubic Contents of Excavatiops and Embank-
ments by the Aid of Diagrams 8vo, 2 00
Webb's Economics of Raikoad Construction Large lamo, 2 50
Raikoad Construction. z6mo, mor. 5 00
Wellington's Economic Theory of the Location of Railways Small 8vo, s 00
DRAWING.
Ban's Kinematics of Machinery 8vo, 2 50
* Bartlett's Mechanical Drawing 8vo, 3 00
* " " " Abridged Ed 8vo, z 50
Coolidge's Manual of Drawing 8vo, paper, z 00
Coolidge and Freeman's Elements of General Drafting for Mechanical Engi-
. neers Oblong 4to, 2 50
Durley's Kinematics of Machines 8vo, 4 00
Emch's Introduction to Projective Geometry and its Applications. 8vo, 2 50
Hill's Text-book on Shades and Shadows, and Perspective. . ..• 8vo, 2 00
Jamison's Advanced Mechanical Drawing Svo, 2 00
Elements of Mechanical Drawing Svo, 2 50
Jones's BSachine Design:
Part I. Kinematics of Machinery. Svo, z 50
Part n. Form, Strength, and Proportions of Parts Svo, 3 00
MacCord's Elements of Descriptive Geometry. Svo, 3 oo
Kinematics; or, Practical Mechanism. Svo, 5 00
Mechanical Drawing. 4to, 4 00
Velocity Diagrams Svo, z 50
McLeod's Descriptive (reometry Large Z2mo, z 50
* Mahan's Descriptive (jeometry and Stone-cutting. Svo, z 50
Industrial Drawing. (Thompson.) Svo, 350
10
McLeod's Descriptiye Geometry Large xamo, z $•
* Mohan's Descriptive Geometry and Stone-cutting. Sto, z $•
Industrial Drawing. (Thompson) Svo, 3 50
Moyer's Descriptive Geometry. 8vo, 2 00
Seed's Topographical Drawing and Sketching. • , , 4to, 5 00
Reid's Course in Mechanical Drawing. 8vo, 2 00
Text-book of Mechanical Drawing and Elementary Macliine Design. 8yo» 3 00
Robinson's Principles of Mechanism. 8vo, 3 00
Schwamb and Merrill's Elements of Mechanism. 8vo, 3 00
Smith's (R. S.) Manual of Topographical Drawing. (McMillan) 8vob 2 50
Smith (A. W.) and Marx's Machine Design 8vo, 3 00
* Titsworth's Elements of Mechanical Drawing Oblong 8vo, i 35
Warren's Drafting: Instruments and Operations lamo, i 35
Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50
Elements of Machine Construction and Drawing 8vo, 7 50
Elements of Plane and Solid Free-hand Geometrical Drawing ismo, z 00
General Problems of Shades and Shadows 8vo, a 00
Manual of Elementary Problems in the Linear Perspective of Form and
Shadow i3mo, z 00
Manual of Elementary Projection Drawing. , zamo. z 50
Plane Problems in Elementary Creometry zsmo, z 25
Problems, Theorems, and Examples in Descriptive Geometry 8vo, 3 50
Weisbach's Kinematics and Power of Transmission. (Hermann and
Klein) 8vo, 5 00
Wilson's (H. M.) Topographic Surveying 8vo, 3 50
Wilson's (V. T.) Free-hand Lettering 8vo, z 00
Free-hand Perspective 8vo, 2 50
WoolTs Elementary Course in Descriptive Geometry^ Large 8vo» 3 00
ELECTRICITY AND PHYSICS.
* Abegg's Theory of Electrol3rtic Dissociation, (von Ende). . . • z2mo. z 25
Andrews's Hand-Book for Street Railway Engineering 3X5 inches, mor. z 25
Anthony and Brackett's Text-book of Physics. (Magie) Large i2mo, 3 00
Anthony's Theory of Electrical Measurements. (Ball) x2mo, z 00
Benjamin's History of Electricity 8vo, 3 00
Voltaic Cell 8vo, 3 00
Betts's Lead Refining and Electrolysis 8vo, 4 00
Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood)..8vo, 3 00
* Collins's Manual of Wireless Telegraphy z2mo, z 50
Mor. 3 00
Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 00
* Danneel's Electrochemistry. (Merriam) x2mo, z 25
Dawson's "Engineering'' and Electric Traction Pocket-book .... z6mo, mor. 5 00
Dolezalek's Theory of the Lead Accumulator (Storage Battery), (von Ende)
z2mo, 2 50
Duhem's Thermodynamics and Chemistry. (Burgess) 8vo, 4 00
Flather's Dynamometers, and the Measurement of Power z2mo, 3 00
Gilbert's De Magnete. (Mottelay) 8vo, 2 50
* Hanchett's Alternating Currents z2mo, z 00
Hering's Ready Reference Tables (Conversion Factors) z6mo, mor. 2 so
* Hobart and Ellis's High-speed Dynamo Electric Machinery 8vo, 6 00
Hohnan's Precision of Measurements 8vo, 2 00
Telescopic Mirror-scale Method, Adjustments, and Tests. . . .Large 8vo, 75
* Eaiapetoff's Experimental Electrical Engineering 8vo, 6 00
Kinzbrunner's Testing of Continuous-current Machines 8vo, 2 00
Landauer's Spectrum Analysis. (Tingle). , » 8vo, 3 00
Le Chatelier's High-temperature Measurements. (Boudouard— Burgess).. z2mo, 3 00
LSb'ft Electrochemistry of Organic Compounds. (Lorenz) 8vo, 3 00
* Lyndon's Development and Electrical Distribution of Water Fower 8vo, 3 00
11
* Lyon's Treattse on Electromacnetic Phenomena. Vols. L and n. 8vo, each 6 oo
* Michie's Elements of Wave Motion RelatinK to Sound and Light 8vo, 4 00
Morgan's Outline of the Theory of Solution and its Results zamo, z 00
* Physical Chemistry for Electrical Engineers zamo, z 50
Siandet's Elementary Treatise on Electric Batteries. (Fishback) zamo, a 50
* Norris's Introduction to the Study of Electrical Engineering 8vo, a 50
* Parshall and Hobarf s Electric Machine Design 4to, half mor. la 50
Reagan's Locomotives: Simple, Compound, and Electric. New Edition.
Large zamo, 3 so
* Rosenberg's Electrical Engineering. (Haldane Gee — Kinzbrunner) . . .8vo, a 00
Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, a So
Schapper's Laboratory Guide for Students in Physical Chemistry zamo, z 00
* Tillman's Elementary Lessons in Heat 8vo, z so
Tory and Pitcher's Manual of Laboratory Physics Large zamo, a 00
Hike's Modem Electrolytic Copper Refining 8vo, 3_oo
LAW.
Brennan's Handbook: A Compendium of Useful Legal Information for
Business Men z6mo, mor. 5 00
* Davis's Elements of Law 8vo. a so
* Treatise on the Military Law of United States .• .8vo, 7 00
* Sheep, 7 so
* Dudley's Military Law and the Procedure of Courts-martial . . .Large zamo, a so
Manual for Courts-martial z6mo, mor. z so
Wait's Engineering and Architectural Jurisprudence 8vo, 6 00
Sheep, 6 So
Law of Contracts 8vo, 3 00
Law of Operations Preliminary to Construction in Engineering and Archi-
tecture ; 8vo, s 00
Sheep, s 5o
MATHEMATICS.
Baker's Elliptic Functions 8vo, t So
Briggs's Elements of Plane Analytic Geometry. (Bdcher) zamo, z 00
* Buchanan's Plane and Spherical Trigonometry 8vo, 1 00
Byerley's Harmonic Functions 8vo, z 00
Chandler's Elements of the Infinitesimal Calculus zamo, a 00
Coffin's Vector Analysis. (In Press.)
Compton's Manual of Logarithmic Computations zamo, i so
* Dickson's College Algebra Large zamo, i 50
* Introduction to the Theory of Algebraic Equations Large zamo, z aS
Emch's Introduction to Projective Geometry and its Applications 8vo, a So
Fiske's Functions of a Complex Variable 8vo, z 00
Halsted's Elementary Synthetic Geometry 8vo, z So
^ Elements of Geometry 8vo, i 7S
* Rational Geometry zamo, i so
Hyde's Grassmann's Space Analysis 8vo, i 00
* Johnson's (J. B.) Three-place Logarithmic Tables: Vest-pocket size, paper, zs
zoo copies, s 00
* Mounted on heavy cardboard, 8 X zo inches, as
zo copies, a 00
Johnson's (W. W.) Abridged Editions of Differential and Integral Calculus
Large zamo, z vol. a 8^
Curve Tracing in Cartesian Co-ordinates zamo, i 00
Differential Equations 8vo, z 00
Elementary Treatise on Differential Calculus Large zamo, z 50
Elementary Treatise on the Integral Calculus Large zamo, z So
Theoretical Mechanics zamo, 3 00
Theory of Errors and the Method of Least Squares zamo, i 30
Treatise on Differential Calculus Large zamo, 3 00
' 12
Johnson's Treatise on tbe Intecral Calculus. Laree lamo, 3 oo-
Treatise on Ordinary and Partial Differential Equations.. Lar^e x2nio» 3 50
Sarapetoffs Engineering Applications of Higher Mathematics. (In Pre-
paration.)
Laplace's Philosophical Essay on Probabilities. (Truscott and Emory)..i2mo, 2 00
* Ludlow and Bass's Elements of Trigonometry and Logarithmic and Other
Tables 8vo, j 00
Trigonometry and Tables published separately Each, 2 00
* Ludlow's Logarithmic and Trigonometric Tables 8vo, i 00
Macfarlane*s Vector Analysis and Quaternions 8vo, z 00
McManon's Hyperbolic Functions Bvo, z 00
Manning's Irrational IV umbers and their Representation by Sequences and
Series z2mo, z 25
Mathematical Monographs. Edited by Mansfield Merriman and Robert
S. Woodward , Octavo, each z 00
No. z. History of Modern Mathematics, by David Eugene Smith.
No. 2. Synthetic Projective Geometry, by George Bruce Halsted.
No. 3. Determinants, by Laenas Gifiord Weld. No. 4. Hyper-
bolic Functions, by James McMahon. No. 5. Harmonic Func-
tions, by William E. Byerly. No. 6. Grassmann's Space Analysis,
by Edward W. Hyde. No. 7. Probability and Theory of Errors,
ty Robert S. Woodward. No. 8. Vector Analysis and Quaternions,
by Alexander Macfarlane. No. 9. Differential Equations, by
William Woolsey Johnson. No. zo. The Solution of Equations,
by Mansfield Merriman. No. zx. Functions of a Complex Variable,
by Thomas S. Fiske.
Maurer's Technical Mechanics 8vo, 4 00
Merriman's Method of Least Squares 8vo, 2 00
Solution of Equations 8vo, I 00
Rice and JohnsoD's Differential and Integral Calculus. 2 vols, in one.
Large z2mo, i 50
Elementary Treatise on the Differential Calculus Large z2mo, 3 00
Smith's History of Modern Mathematics 8vo, z 00
* Veblen and Lennes's Introduction to the Real Infinitesimal Analysis of Ode
Variable 8vo, 2 00
* Waterbury's Vest Pocket Hand-Book of Mathematics for Engineers.
2^X5t inches, mor. 100
Weld's Determinations ; 8vo, z 00
Wood's Elements of Co-ordinate Geometry 8vo, 2 00
Woodward's Probability aid Theory of Errors .8vo, z 00
MECHANICAL ENGINEERING.
MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS.
Bacon's Porge Practice Z2mo, z 50
Baldwin's Steam Heating for Buildings z2mo, 2 50
Baxr's Kinematics of Machinery 8vo, 2 50
* Bartlett's Mechanical Drawing 8vo, 3 00
* " " " Abridged Ed 8vo, z 50
Benjamin's Wrinkles and Recipes z2mo, 2 00
* Burr's Arci^nt and Modem Engineering and the Isthmian Canal 8vo, 3 50
Carpenter's Experimental Engineering 8vo, 6 00
Heating and Ventilating Buildings 8vo, 4 00
Clerk's Gas and Oil Engine Large z2mo, 4 00
Compton's First Lessons in Metal Working z2mo, z 50
Compton and De Groodt's Speed Lathe. z2mo, i 50
Coolidge's Manual of Drawing 8vo, paper, z 00
Coolidge and Freeman's Elements of General Drafting for Mechanical En-
gineers Oblong 4to, 2 50
13
so
50
00
00
00
as
00
50
00
00
00
50
50
00
00
00
00
00
00
00
50
50
50
CromwelPt TrefttiBe on Bells and Pulleys lamo*
Tteatiae on Toothed Gearing. zamo,
Dnrley's Kinematics of Machines 8vo»
Flatlier's Dynamometers and the Measurement of Power. zamo.
Rope Driving. lamo.
Gill's Gas and Fuel Analysis for Engineers. zamo.
Goss's Locomotive Sparks 8to»
Greene's Pumping Machinery. (In Preparation.)
Bering's Ready Reference Tables (Conversion Factors). x6mo, mor.
* Hobart and Ellis's High Speed Dynamo Electric Machinery 8vo»
Button's Gas Engine 8vo,
Jamison's Advanced Mechanical Drawing 8vo,
Elements of Mechanical Drawing 8vo,
Jones's Gas Engine. (In Press.)
Machine Design:
Part I. Kinematics of Machinery. 8vo,
Part n. Form, Strength, and Proportions of Parts 8vo,
Kent* 8 Mechanical Engineers* Pocket-book. i6mo, mor.
Kerr's Power and Power Transmission 8vo,
Leonard's Machine Shop Tools and Methods 8vo,
* Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean) . . . 8vo,
MacCord's Kinematics; or. Practical Mechanism. 8vo,
Mechanical Drawing 4to,
Velocity Diagrams 8vo,
MacFariand's Standard Reduction Factors for Gases 8vo,
Mahan's Industrial Drawing. (Thompson) 8vo,
Oberg's Screw Thread Systems, Taps, Dies, Cutters, and Reamers. (In
Press.)
* Parshall and Hobart's Electric Machine Design Small 4to, half leather, za 50
Peele's Compressed Air Plant for Mines 8vo, ■ 3 00
Poole's Calorific Power of Fuels 8vo, 3 00
* Porter's Engineering Reminiscences, 1855 to 1882 8vo, 3 00
Reid's Course in Mechanical Drawing 8vo, 2 00
Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 00
Richard's Compressed Air lamo, i 50
Robinson's Principles of Mechanism 8vo, 3 00
Schwamb and Merrill's Elements of Mechanism 8vo, 3 00
Smith's (O.) Press-working of Metals 8vo, 3 00
Smith (A. W.) and Marx's Machine Design. 8vo, 3 00
SoTd's Carbureting and Combustion in Alcohol Engines. (Woodward and Preston).
Large lamo^ 3 00
Thurston's Animal as a Machine and Prime Motor, and the Laws of Energetics.
lamo* z 00
Treatise on Friction and Lost Work in Machinery and Mill Work... 8vo, 3 00
Tillson's Complete Automobile Instructor i6mo» z 50
mor. a 00
Titsworth's Elements of Mechanical Drawing. Oblong 8vo» z 25
Warren's Elements of Machine Construction and Drawing. 8vo, 7 50
* Waterbury's Vest Pocket Hand Book of Mathematics for Engineers.
2^X5} inches, mor. . z 00
Weisbach's Kinematics and the Power of Transmission. (Herrmann —
Klein) 8vo, 5 00
Machinery of Transmission and Governors. (Herrmann — Klein).. .8vo, 5 00
Wood's Turbines 8vo, a 50
MATERIALS OF ENGINEERING
* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50
Burr's Elasticity and Resistance of the Materials of Engineering 8vo, 7 50
Church's Mechanics of Engineering 8vot 6 00
* Greene's Structural Mechanics 8vo, a so
14
Holley and Ladd't AnalFtit of Mixed Paints, Color Pigments, and Varnishes.
Large zamo, a 50
Johnson's Materials of Construction. 8to, 6 00
Keep's Cast Iron. 8vo, a 50
Lanza's Applied Mechanics. 8vo, 7 5o
Hidre's Modem Pigments and their Vehicles xamo, a 00
Martens's Handbook on Testing Materials. (Henning) Svo, 7 50
Maurer's Technical Mechanics. Svo, 4 00
Merriman's Mechanics of Materials Svo, 5 00
* Strength of Materials : lamo, z 00
MetcalTs SteeL A Manual for Steel-users. zamo, a 00
Sabin's Industrial and Artistic Technology of Paints and Varnish. Svo, 3 00
Smith's Materials of Machines zamo, z 00
Thurston's Materials of Engineering 3 vols.» Svo, 8 00
Part I. Non-metallic Materials of Engineering and Metallurgy . . . Svo, a 00
Part n. Iron and SteeL Svo, 3 50
Part m. A Treatise on Brasses, Bronzes, and Other Alloys and their
Constituents Svo, a 50
Wood's (De V.) Elements of Analytical Mechanics Svo, 3 00
Treatise on the Resistance of Materials and an Appendix on the
Preservation of Timber Svo, a 00
Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and
Steel Svo, 4 00
STEAM-ENGINES AND BOILERS.
Berry's Temperature-entropy Diagram. zamo, z as
Camot's Reflections on the Motive Power of Heat. (Thurston) zamo, z 50
Chase's Art of Pattern Making lamo, a 50
Creighton's Ste I m-engine and other Heat-motors. Svo, 500
Pawson's " Engineering" and Electric Traction Pocket-book z6mo, mor. 5 00
Ford's Boiler Making for Boiler Makers iSmo, i 00
• Gebhardt's Steam Power Plant Engineering Svo, 6 00
Goss's Locomotive Performance Svo, 5 00
Hemenway's Indicator Practice and Steam-engine Economy zamo, a 00
Button's Heat and Heat-engines Svo. 5 00
Mechanical Engineering of Power Plants Svo, 5 00
Kent's Steam boiler Economy Svo, 4 00
Kneass's Practice and Theory of the Injector Svo, z 50
MacCord's Slide-valves Svo, a 00
Meyer's Modem Locomotive Construction 4to, zo 00
Mover's Steam Turbines. (Tn Press.)
Peabody's Manual of the Steam-engine Indicator zamo. z 50
Tables of the Properties of Saturated Steam and Other Vapors Svo, z 00
Thermodynamics of the Steam-engine and Other Heat-engines Svo, 5 00
Valve-gears for Steam-engines Svo, a 50
Peabody and Miller's Steam-boilers Svo, 4 00
Pray's Twenty Years with the Indicator Large Svo, a 50
Pupin's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors.
(Osterbergl zamo, z 35
Reagan's Locomotives. Simple, Compound, and Electric. New Edition.
Large zamo, 3 50
Sinclair's Locomotive Engine Running and Management zamo, a 00
Smart's Handbook of Engineering Laboratory Practice zamo, a 50
Snow's Steam-boiler Practice Svo, 3 00
Spangler's Notes on Thermodynamics zamo, z 00
Vahre-gears Svo, a 50
Spangler, Greene, and Marshall's Elements of Steam-engineering Svo, 3 00
Thomas's Steam-turbines Svo, 4 00
15
Thnnton'g Handbook of Engine and Boiler Trials, and the Um of the Indi-
cator and the Prony Brake 8vo, 5 00
Handy Tables. 8yo, i 50
Manual of Steam-boUers, their resigns. Construction, and Operation..8vo, 5 00
Thurston's Manual of the Steam-engine 2 vols., 8to, 10 00
Part L* History. Structure, and Theory Sv>, 6 00
Part IL Design, Constrzction, and Operation. 8to, 6 00
Steam-boiler Explosions in Theory and in Practice i2mo, z 50
Wehrenf enning's Analysis and Softening of Boiler Feed-water (Patterson) 8vo, 4 00
Weisbach's Heat, Steam, and Steam-engines. (Du Bois) 8to, 5 00
Whitham's Steam-engine Design Svo, 5 00
Wood's Thermodynamicst Heat Motors, and Refrigerating Machines. . .8vo, 4 00
MECHANICS PURE AND APPLIED.
Church's Mechanics of Engineering. 8vo, 6 00
Notes and Examples in Mechanics. 8yo, a 00
Dana's Text-book of Elementary Mechanics for Colleges and Schools, .zamo* z 50
Dtt Bois's Elementary Principles of Mechanics:
VoL L Kinematics 8vo, 350
VoL n. Statics 8vo, 4 00
Mechanics of Engineering. Vol. I Small 4to, 7 50
VoL n. *. Small 4to, zo 00
* Greene's Structural Mechanics. 8vo, 2 50
James's Kinematics of a Point and the Rational Mechanics of a Particle.
Large zamo, a 00
* Johnson's (W. W.) Theoretical Mechanics. xamo. 3 00
Lanza's Applied Mechanics 8vo, 7 50
* Martin's Text Book on Mechanics, VoL I, Statics xamo, z as
* V<d. 2, Kinematics and Kinetics . .zamo, 1 50
Maurer's Technical Mechanics 8to, 4 00
* Merriman's Elements of Mechanics zamo, z 00
Mechanics of Materials 8vo, 5 00
* liichie's Elements of Analytical Mechanics 8yo, 4 00
Robinson's Principles of Mechanism. 8to, 3 00
Sanborn's Mechanics Problems Large zamo, z 50
Schwamb and Merrill's Elements of Mechanism 8vo, 3 00
Wood's Elements of Analytical Mechanics Qvo, 3 00
Principles of Elementary Mechanics zamo, z as
MEDICAL.
* Abderhalden's Physiological Chemistry in Thirty Lectures. (Hall and Defren)
8vo, 5 00
von Behring's Suppression of Tuberculosis. (Bolduan) xamo, z 00
* Bolduan's Immune Sera xamo, z 50
Bordet's Contribution to Immunity. (Gay). (In Preparation.)
Davenport's Statis::ical Methods with Special Reference to Biological Varia-
tions i6mo, mor. z 50
Ehrlich's Collected Studies on Immunity. (Bolduan) 8vo, 6 00
* Fischer's Physiology of Alimentation Large zamo, doth, a 00
de Fursac's Manual of Psychiatry. (Rosanofif and Collins) Large zamo, a so
Hammarsten's Text-book on Physiological Chemistry. (Mandel). 8vo, 4 00
Jackson's Directions for Laboratory Work in Physiological Chemistry . . .8vo, z as
Lassar-Cohn's Practical Urinary Analysis. (Lorenz) zamo, z 00
Mandel's Hand Book for the Bir-Chemical Laboratory zamo, z 50
* Pauli's Physical Chemistry in the Service of Medicine. (Fischer), i . . . zamo, z as
* Pozzi-Escot's Toxins and Venoms and their Antibodies. (Cohn) zamo. z 00
Rostoski's Serum Diagnosis. (Bolduan) xamo, x 00
Ruddiman's Incompatibilities in Prescriptions 8vo, a 00
Whys in Pharmacy »^«0' ' «>
16
Salkowski's Physiological and Pathological Chemistry. (Omdorff^ 8vo» 2 50
* Satterlee's Outlines of Human Embryology i2mo. 1 25
Smith's Lecture Notes on Chemistry for Dental Students 8vo, 2 50
Steel's Treatise on the Diseases of the Dog . . 8vo, 3 50
* Whipple's Typhoid Fever Large i2mo, 3 00
Woodhull's Notes on Military Hygiene i6mo, i 50
* Personal Hysriene i2mo, i 00
Worcester and Atkinson's Small Hospitals Establishment and Maintenance,
and S ggestions for Hospital Architecture, with Plans for a Small
Hospital lamo, z 25
METALLURGY.
Betts's Lead Refining by Electrolysis Svo, 4 00
BoUand's Encyclopedia of Founding and Dictionary of Foundry Terms Used
in the Practice of Moulding i2mo, 3 00
Iron Founder i2mo, 2 50
" " Supplement i2mo, 2 50
Douglas's Untechnical Addresses on Technical Subjects i2mo, z 00
Goesel's Minerals and Metals: A Reference Book i6mo, mor. 3 oe
* Iles's Lead-smelting i2mo, 2 5c
Keep's Cast Iron 8vo, 2 50
Le Chatelier's High-temperature Measurements. (Boudouard — ^Burgess) i2mo, 3 00
Metcalf s Steel. A Manual for Steel-users i2mo, 2 00
Miller's Cyanide Process i2mo, z 00
Minefs Production of Aluminium and its Industrial Use. (Waldo) . . .i2mo, 2 50
Robine and Lenglen's Cyanide Industry. (Le Clerc) 8vo, 4 00
Ruer's Elements of Metallography. (Mathewson) (In Press.)
Smith's Materials of Machines i2mo, z 00
Tate and Stone's Foundry Practice. (In Press.)
Thurston's Materials of Engineering. In Three Parts . « 8vo, 8 00
Part I. Non-metallic Materials of Engineering and Metallurgy . . . 8vo, 2 00
Part H. Iron and Steel. 8vo, 3 50
Part nL A Treatise on Brasses, Bronzes, and Other Alloys and their
Constituents 8vo, 2 50
Hike's Modem Electrolytic Copper Refining 8vo, 3 00
Wesf s American Foundry Practice z2mo, 2 50
Moulder's Text Book i2mo, 2 50
Wilson's Chlorination Process Z2mo, z 50
Cyanide Processes z2mo, z 50
MINERALOGY.
Barringer's Description of Minerals of Commercial Value Oblong, mor. 2 50
Boyd's Resources of Southwest Virginia 8vo, 3 00
Boyd's Map of Southwest Virginia. Pocket-book form. 2 00
* Browning's Introduction to the Rarer Elements 8vo, z 50
Brush's Manual of Determinative Mineralogy. (Penfield) Svo, 4 00
Butter's Pocket Hand-Book of Minerals z6mo, mor. 3 00
Chester's Catalogue of Minerals Svo, paper, z 00
Cloth, z 25
♦Crane's Gold and Silver Svo, 5 00
Dana's First Appendix to Dana's New " System of Mineralogy. ." . . Large Svo, z 00
Manual of Mineralogy and Petrography x2mo 2 00
Minerals and How to Study Them Z2mo, r 50
System of Mineralogy Large Svo, half leather, Z2 50
Text-book of Mineralogy Svo, 4 00
Douglas's Untechnical Addresses on Technical Subjects z2mo, z 00
Eakle's Mineral Tables 8vo, z 25
Stone and Clay Froducts Used in Engineering. (In Preparation.)
17
Egleston's Catalogue of Minerals and Synonyms. 8vo»
Goesel's Minerals and Metals: A Reference Book x6mo mor.
Oroth's Introduction to Chemical Crystallography (Marshall) .- zamo,
*lddlngs*i Rock Minerals 8yo,
Johannaeii'a Determination of Rock-fonniiig Mineials in Thin Sections &▼•,
* Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe, lamo,
Merrill's Ron-metallic Minerals: Their Occurrence and Uses 8to,
Stones for Building and Decoration 8vo,
* Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests.
8vo. paper,
Tahies of Minerals, Including the Use of Mmerals and Statistics of
Domestic Production 8vo,
* Pinson's Rocks and Rock Minersls iimo,
* Richards's Synopsis of Mineral Characters. zamo. mor.
* Ries's Clays: Their Occurrence, Properties, and Uses. 8vo,
* Tillman's Text-book of Important Minerals and Rocks 8vo,
MINIlfG.
* Beaid's Mine Gases and Rxptosions Large zamo,
Boyd's Map of Southwest Viiginia Pocket-book lorm,
Resources of Southwest Virginia ; 8vo,
* Crsne's Gold and Silver 8vO»
Douglas's Untechnical Addresses on Technical Subjects lamo.
Eissler's Modem High Explosives. 8vo,
Goesel's Minerals and Metals : A Reference Book z6mo, mor.
Ihlseng's Manual of Mining Svo,
* nes's Lead-smelting zamo.
Miller's Cyanide Process zamo,
O'DriscoU's Notes on the Treatment of Gold Ores. 8vo,
Peele's Compressed Air Plant for Mines 8vo,
Riemer's Shaft Sinking Under Difflcult Conditions. (Coming and Peele) . . . 8vo,
Robine and Lenglen's Cyanide Industry. (Le Clerc) 8vo,
* Weaver's Military Explosives 8vo,
Wilson's Chlorination Process zamo,
Cyanide Processes .* zamo,
Hydraulic and Placer Mining, ad edition, rewritten zamo.
Treatise on Practical and Theoretical Mine Ventilation lamo,
SANITARY SCIENCE.
Association of State and National Food and Dairy Departments, Hartford Meeting,
Z906 8vo, 3 00
Jamestown Meeting, 1907 8vo, 3 00
* Bashore's Outlines of Practical Sanitation zamo, z as
Sanitation of a Country House zamo, z 00
Sanitation of Recreation Camps and Parks zamo, z 00
Folwell's Sewerage. (Designing, Construction, and Maintenance) 8vo, 3 00
Water-supply Engineering 8vo, 4 00
Fowler's Sewage Works Analyses zamo, a 00
Fuertes's Water-filtration Works zamo, a 50
Water and Public Health zamo, z 50
Gerhard's Guide to Sanitary House-inspection z6mo, i oo
* Modem Baths and Bath Houses 8vo, 300
Sanitation of Public Buildings • zamo, z 50
Hkzen's Clean Water and How to Get It Large zamo, i 50
Filtration of Public Water-supplies. Svo, 3 00
Kinnicut, Winslow and Pratf s Purification of Sewage. (In Press.)
Leach's Inspection and Analysis of Food with Special Reference to State
Control 8vo^ 7 00
18
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35
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60
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5
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Mason's ExamixiAtion of Water. (Chemical and Bacteriological) lamo, z 35
Water-supply. (Considered Principally from a Sanitary Standpoint) . . Svo, 4 00
* Meniman's Elements of Sanitary Engineering 8to, a 00
Ogden's Sewer Design. i2mo, a 00
PaiBODs's Disposal of Municipal Refuse 8to, a 00
Prescott and Winslow's Elements of Water Bacteriology, with Special Refer-
ence to Sanitary Water Analysis. lamo, z 50
* Price's Handbook on Sanitation lamo, i 50
Richards's Cost of Cleanness. A Twentieth Century Problem lamo, i 00
Cost of Food. A Study in Dietaries lamo, z 00
Cost of Liring as Modified by Sanitary Science Z2mo, z 00
Coist of Shelter. A Study in Economics lamo, z 00
* Richards and Williams's Dietfur Computer 8vo, z 50
Richards and Woodman's Air, Water, and Food from a Sanitary Stand-
point 8vo, a 00
Rideal's Disinfection and the Preservation of Food 8vo, 4 00
Sewage and Bacterial Purification of Sewage 8vo, 4 00
Sopei's Air and Ventilation of Subways Large lamo, a 50
Tumeaure and Russell's Public Water-supplies 8vo, 5 00
Yenable'8 Garbage Crematories in America 8to, a 00
Method and Devices for Bacterial Treatment of Sewage 8vo, 3 00
Ward and Whipple's Freshwater Biology xamo, a 50
Whipple's Microscopy of Drinldng-water 8vo, 3 50
* Typhod Fever. Large lamo, 3 00
Value of Pure Water Large lamo, z 00
Winslow's Bacterial Classification lamo, a 50
Winton's Microscopy of Vegetable Foods. 8vo, 7 50
MISCELLANEOUS.
Emmons's Geological Guide-book of the Roclry Mountain Excursion of the
International Congress of Geologists Large 8vo, z 50
Ferrel's Popular Treatise on the Winds. 8vo, 4 00
Fitzgerald's Boston Machinist z8mo, z 00
Gannett's Statistical Abstract of the World a4mo, 75
Haines's American Railway Management lamo, a 50
* Hanusek's The Microscopy of Technical Products. (Winton) 8vo, 5 00
Owen's The Dyeing and Cleaning of Textile Fabrics. (Standage). (In Press.)
Ricketts's History of Rensselaer Polytechnic Institute X824-1894.
Large lamo, 3 00
Rotfaerham's Emphasized New Testament Large 8vo, a 00
Standage'8 Decoration of Wood, Glass, Metal, etc zamo, a 00
Thome's Structiual and Physiological Botany. (Bennett) z6mo, a as
Westermaier's Compendium of General Botany. (Schneider) 8vo, a 00
Winslow's Elements of Applied Microscopy zamo, z 50
HEBREW Am) CHALDEE TEXT-BOOKS.
Green's Elementary Hebrew Grammar zamo, z as
Gesenius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures.
(Tregelles) Small 4to» half mor. s 00
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