DATA SHEETS
REVISED AND RE-ARRANGED IN LIBRARY FORM
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No. 7
Shafting, Keys and
Keyways
PRICE 25 CENTS
CONTENTS
Horsepower Transmitted by Shafting 4
Diagrams of Strength of Shafts for Different Fiber Stresses 8
Moment of Inertia and Section Modulus of Circular Sections 12
Shear Stresses Combined with Tension or Compression Stresses 13
Combined Bending and Torsional Moments 14
Tables of Diameters of Shafts for Combined Torsional and Bending
Stresses 18
Diagrams of Diameters of Shafts for Combined Torsional and Bending
Stresses 20
Weights and Areas of Cold Rolled Steel Shafting 25
Allowances and Tolerances for Running Fits 27
Allowances for Forcing, Driving and Running Fits ".28
Pressure Factors for Forcing Fits 29
Limits for Limit Gages 30
Woodruff Keys 32
United States Navy Standard Proportions of Keys 35
Table of Gib Keys 36
Table for Milling Keyways 37
Duplex Keys 38
The Industrial Press, 49-55 Lafayette Street, New York
Publishers of MACHINERY
COPYRIGHT, 1910, THE INDUSTRIAL PRESS, NEW YORK
MACHINERY'S DATA SHEET SERIES
COMPILED FROM MACHINERY'S MONTHLY DATA
SHEETS AND ARRANGED WITH
EXPLANATORY MATTER
No. 7
Shafting, Keys and
Key ways
CONTENTS
Horsepower Transmitted by Shafting 4
Diagrams of Strength of Shafts for Different Fiber Stresses 8
Moment of Inertia and Section Modulus of Circular Sections 12
Shear Stresses Combined with Tension or Compression Stresses 13
Combined Bending and Torsional Moments 14
Tables of Diameters of Shafts for Combined Torsional and Bending
Stresses 18
Diagrams of Diameters of Shafts for Combined Torsional and Bending
Stresses 20
Weights and Areas of Cold Rolled Steel Shafting 25
Allowances and Tolerances for Running Fits 27
Allowances for Forcing, Driving and Running Fits 28
Pressure Factors for Forcing Fits 29
Limits for Limit Gages 30
Woodruff Keys 32
United States Navy Standard Proportions of Keys 35
Table of Gib Keys i ^-.* :.. .; ; .\ • ', 1 36
Table for Milling Key ways '.«.•". ..'.'.* . X .' .V. .* 37
Duplex Keys. . . .38
Copyright, 1930, The Industrial Tress, Publishers of MACHINERY,
49-55 Lafayette Street, New York City
In the following pages are compiled a number of diagrams and con-
cise tables relating to shafting, keys and keyways, carefully selected
from MACHINERY'S monthly Data Sheets, issued as supplements to the
Engineering and Railway editions of MACHINERY since September, 1898.
A number of additional tables also are included which are published
here for the first time.
In order to enhance the value of the tables and diagrams, brief ex-
planatory notes have been provided wherever necessary. In these
notes references are made to articles which have appeared in MA-
CHINERY, and to matter published in MACHINERY'S Reference Series,
giving additional information on the subject. These references will
be of considerable value to readers who wish to make a more thorough
study of the subject. In a note at the foot of the tables reference is
made to the page on which the explanatory note relating to the table
appears.
•A •.,,"•;«?;
J «.•» i» «• •>.* % .
SHAFTING, KEYS AND KEYWAYS
Horsepower Transmitted by
Shafting
A question which often meets the ma-
chine designer is that of determining
the horsepower that may be safely trans-
mitted by a shaft of a given diameter at
a given number of revolutions per min-
ute. Quite as frequently the horsepower
and the speed are known, and it is re-
quired to find the diameter of the shaft
which will safely transmit the given
power. On page 4 a table is presented
giving working proportions for shafting
of medium steel; this table will be
found useful whenever either of the
above problems are met with.
Assume, for example, that it is re-
quired to find the diameter of a shaft
for transmitting 40 horsepower at a
speed of 250 revolutions per minute. The
shaft is not subjected to any bending
action except its own weight. Consult-
ing the table to the left on page 4 and
locating 40 in the body of the table, in
the column under 250 revolutions per
minute, we find in the extreme left-hand
column that the diameter of the re-
quired shaft should be two inches. The
table also gives the maximum permis-
sible distance between the shaft bear-
ings, which in this case is slightly more
than 14 feet.
When the exact horsepower given can-
not be found in the table, it is advisable
to take the nearest larger value listed
in the table, and find the diameter of
shaft required to transmit this horse-
power.
On page 5 a table is given for finding
the horsepower which can be safely
transmitted by cold rolled steel line
shafting. The body of the table gives
the horsepower. For example, assume
that a 3-inch shaft revolves at a speed
of 400 revolutions per minute. What
power can this shaft safely transmit?
By locating 3 inches in the left-hand
column, and 400 at the top of the verti-
cal columns at the head of the page,
and following the vertical column down-
ward until opposite 3 inches, we find
that under the given conditions 154
horsepower may be safely transmitted.
On pages 6 and 7 are given the horse-
power which may safely be transmitted
by turned steel line shafting. In this
case the diameters are carried up to 12
inches. The tables on pages 5, 6 and 7
are used by the transmission depart-
ment of the Jones & Laughlin Steel Co.
These tables are based on the assump-
tion that bearings are placed at inter-
vals of from 8 to 10 feet, and that all
pulleys are located near the bearings.
The reason why the table for cold-rolled
steel shafting is carried up only to 5
inches diameter, is that 5 inches is the
largest diameter cold rolled at the pres-
ent time.
Diagrams for Strength of
Bound Shafts
On pages 8 to 11, inclusive, are given
diagrams for determining the dimen-
sions of round shafts under different con-
ditions. The diagram on page 8 is
intended for finding the diameter of the
shaft when the twisting moment and
the fiber stress are known. Assume as
an example that a shaft is subjected to
a twisting moment of 100,000 inch-
pounds, and that the allowable fiber
stress is 8000 pounds per square inch.
The twisting moments, in thousands of
inch-pounds, are given on the scale
at the bottom of the table, and the fiber
stresses are represented by the diagonal
(Continued on page 16.)
347498
4 MACHINERY'S DATA SHEETS
No. 7
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No. 7 SHAFTING, KEYS AND KEY WAYS 5
HORSEPOWER TRANSMITTED BY COLD ROLLED STEEL LINE SHAFTING
Diameter
of Shaft
Number of Revolutions Per Minis fe
100
125
150
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Contributed by Frank Wackermann, Pittsburg. Pa. Explanatory note : 1'ajje 3.
6 MACHINERY'S DATA SHEETS No. 7
HORSEPOWER TRANSMITTED BY TURNED STEEL LINE SHAFTING
Diameter
of Shaft
Number of- Revolutions Per Minute
100
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Contributed by Frnnk Wackermann, Plttsburg, Pa. Explanatory note : Page 3.
No. 7 SHAFTING', KEYS AND KEY WAYS 1
HORSEPOWER TRANSMITTED BY TURNED STEEL LINE SHAFTING
Diameter
of Shaft
A/umber of Revolutions Per Minute
100
125
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722
813
903
994
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1444
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J805
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7
381
476
573
667
762
857
953
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502
603
702
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2005
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75
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646
776
904
1033
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1679
/808
2066
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2583
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545
682
820
957
IO9I
1227
/365
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2/82
2455
2728
3OOO
3273
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568
712
855
998
1138
1280
/423
1567
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/848
/99/
2275
2560
2844
3128
34/3
5 '5
593
742
892
1041
1/87
1335
1484
1634
1780
1928
2076
2373
2670
2966
3263
3560
<S'$
623
780
937
1094
1247
1402
1559
1717
1870
2025
2181
2493
2805
3/16
3428
5%
651
816
980
1/45
I3O5
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1632
1796
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2282
2606
2935
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3586
*«fe
681
853
1025
1197
1364
1533
1707
f879
2047
2216
2387
2728
3070
34/1
3751
15
7/3
892
1072
1252
/427
I6O5
1785
1964
2/40
23/8
2496
2855
32/0
3566
8%
744
931
II 19
1306
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1675
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20JO
2233
24/9
2603
2977
3350
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87'&
766
972
1167
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IS53
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1943
2139
2330
2523
27/8
3/06
3495
3863
9
809
1013
1217
1421
1620
/822
2027
2231
2430
2632
2834
3240
3645
9''8
844
1056
1269
1482
1689
1900
2//3
2325
2533
2744
2955
3377
3800
9''4
878
1099
1321
1542
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2198
2420
2637
2855
3075
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15
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1376
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2060
229f
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2747
2975
3204
3662
n
951
1191
/43I
I67f
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2142
2382
2622
2858
3094
3334
3808
g
989
1238
1488
1737
1980
2227
2477
2726
Z972
32/8
3464
3960
o
1029
f288
1548
1808
2000
23/7
2577
2837
309O
3346
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37#
1069
1338
1608
1878
2/40
2407
2677
2947
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3476
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/#
III 1
1388
1666
1944
2222
2500
2778
3055
3333
36/1
3888
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1/95
1497
1798
ZIOO
2393
2692
2994
3295
3590
3888
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1285
1608
1934
2258
2573
2895
3219
3543
3860
4I8O
/03s
1379
1726
2O74
2422
276O
3/05
3453
3800
4/40
4484
//
1477
1850
2223
2595
2958
3327
3700
4O73
4437
//''£
1688
ZII4.
2540
2966
3380
3802
4247
4654
5O7O
/2
1918
2402
2886
3369
3840
432O
4804
5288
5760
Contributed by Frank Wackermann, Pittsburg, Pa. Explanatory note : Page 3.
MACHINERY'S DATA SHEETS
No. 7
<
0
loo
200
800
500
1.
2
3
5
i
10
15
ST 25
f »
1 40
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350
400
450
600
600
Diameter of. bar in inches.
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No. 7
SHAFTING, KEYS AND KEYWAYS
0
200
300
500
1
3
5
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15
20
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10
MACHINERY'S DATA SHEETS
No. 7
o i 1
Bending moments in thousand inch pounds.
g g g g g§ & g y
coo
No. 7
SHAFTING, KEYS AND KEYWAYS
11
NEW DIAMETERS REQUIRED FOR SHAFTS.
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No. 3.
ain
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12 MACHINERY'S DATA SHEETS No. 7
MOMENT OF INERTIA AND SECTION MODULUS OF CIRCULAR SECTIONS
Moment of /nerfia I- "gff* Secf/on Moctu/us Z- ^5f~
O « Diameter in Inches. J~- Moment of /nerfia. Z - Sect/on Mocfis/e/s.
D
I
Z
0
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k
o.ooooot
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2 O.I 29
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4
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O.OO/S34
£ ^J
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4
27.725
//.374
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1.7328
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S
30.680
/2.272
%
O.OOO971
0.0 OS/ 77
zi
/.9/7S
/.5340
4
33.865
/3.2/S
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0.00/798
0.008221
*t
2.1 166
/.6S20
^
37.29/
14. 2O 6
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1.7758
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/ 5.24 5
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O.OI 74 73
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4
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3.3537
2.3330
4
58.479
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0.021393
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2.4885
6
63.6/3
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%
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2.6507
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22.559
%
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4.31 79
2.8/99
4
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2.9961
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8f. 076
2S.436
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0.0626
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4
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87.624
26.96/
4
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94.562
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30./93
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7
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Contributed by John S. Myers, MACHINERY'S Data Sheet No. 87. Explanatory note: Page 16.
No. 7 SHAFTING, KEYS AND KEYWAYS 13
SHEAR STRESSES COMBINED WITH TENSION OR COMPRESSION STRESSES
Let £ - Un/f Shear, t - Vn/f Tens/on or Compress /'on,
5m - Max /mum Combmed Vn/'f Shear,
fa - Maxfmt/m Comb/necf L/n/'f Tens /or? or Co/r>press/on .
w'ta-lr&f-Hi+i
/<**&*****
L
Tension *y-
Factor -*•
Shear ,/
Factor 3
1
Shear //
Factor "
Tens/o/7 -y-
Facfor ^
Q^Q£
/.0025
/0. 0499
o.os
/. 0003
20.5060
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S-.0990
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3. 48 O/
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7. /854
O.2O
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2.6926
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5-. 5-2 SO
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2. 23$ /
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4.53/2
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/. 9437
O.3O
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3. 8706
0.35
/. //03
/. 7438
O.35
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3.4000
O.4O \ /./4O3
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J.0/98
3.0495-
0.45 /./7Z7
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0.45
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2. 7773
O.SO /.207/
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O.SO
j.0308
2.5*0/0
C.SS /.2433
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2.3857
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O.00
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2. 240 /
0. 65 /. 32 O/
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2.//77
0. 70 /. 36O2
/. 2289
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2.0/35*
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0.9O
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O.9O
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0.95
/. 5735
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0.95
/. /07/
/. 6653
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LOS
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1. 0770
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A3937
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2. 03 3 &
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f.SC
Z.OQlf
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Contributed by John S. Myers, MACHINERY'S Data Sheet No. 87. Explanatory note : Page IT.
14
MACHINERY'S DATA SHEETS
No. 7
3enctmg Moments /n Incn Pounds — Av
No. 7
SHAFTING, KEYS AND KEYWAYS
15
Bencff'ng Momertte //? /nch Pounds —
SI
nil
8*
1
gw
So!
I.
l!
££
ir
^
!
16
MACHINERY'S DATA SHEETS
No. 7
lines. Locate, therefore, 100 on the
lower scale, and follow the line from
the point so located upward until inter-
secting the diagonal line marked 8000.
From the point of intersection follow
the horizontal line to the scale at the
left-hand side marked "Diameter of bar
in inches." It will be seen that a shaft 4
inches in diameter is required.
On page 9 is given a diagram of
transverse strength of round shafts for
different fiber stresses. Assume in this
case that a shaft is subjected to a bend-
ing moment of 80,000 inch-pounds and
that a fiber stress of 12,500 pounds per
square inch is allowable. The bending
moments in thousands of inch-pounds
are given on the scale at the bottom of
the diagram, and the fiber stresses are
represented by the diagonal lines, the
same as in the previous diagram; hence
by locating 80 on the lower scale and
following the vertical line from the
point so located until it intersects the
diagonal line marked 12,500, and from
the point of intersection following the
horizontal line to the left, we find that
the diameter of the required shaft is 4
inches.
On page 10 is given a diagram for
the strength of round shafts subjected
to a combined twisting and bending mo-
ment. This diagram is calculated for a
tensile strength of 7500, and a torsional
shearing strength of 6000 pounds per
square inch. The twisting moment in
thousands of inch-pounds is located on
the scale at the bottom of the diagram,
the bending moments are located on the
scale at the left-hand side, and the di-
ameter of the required shaft is deter-
mined by the curve which comes nearest
to the intersection between the vertical
line from the twisting moment and the
horizontal line from the bending mo-
ment. Assume, as an example, that a
shaft is subjected to a twisting mo-
ment of 175,000 inch-pounds and a bend-
ing moment of 90,000 inch-pounds. The
two lines corresponding to these values
are found to intersect very nearly on
the 6-inch curve. A shaft 6 inches in
diameter is thus required.
On page 11 an auxiliary diagram to
that on page 10 is given, from which
the required diameter of round shafts
may be found for other fiber stresses
than 7500 pounds per square inch, for
which the diagram on page 10 is made
up. When using this table, the diam-
eter for a fiber stress is 7500 pounds
per square inch is first found from page
10. This diameter is then located on
the lower scale in the diagram on page
11. The vertical line from the point
so located is followed until it intersects
the diagonal line representing the allow-
able fiber stress; from the point of in-
tersection a horizontal line is then fol-
lowed to the left-hand scale, where the
corrected diameter for the permissible
fiber stress is read off. For example,
if we have found from the diagram on
page 10 that for given conditions a six-
inch shaft is required at a fiber stress
of 7500 pounds per square inch, we
find from this diagram that if we in-
crease the stress to 12,500 pounds, a
shaft 5 inches in diameter would be
sufficient. [MACHINERY, September,
1905, Computing Hollow and Solid Shaft-
ing.]
Moment of Inertia and Section Modulus
of Circular Sections
When calculating the strength of shaft-
ing, tables of the moment of inertia and
section modulus of circular sections, for
diameters varying by small fractions of
an inch, are very convenient. On page
12 such a table is given. The values in
this table are used when the shaft is
subjected to bending moments only.
For torsional moments the polar mo-
ment of inertia and section modulus
should be used; but since these quanti-
ties are, in this specific case, exactly
double those given in the table, the tab-
ulated values may simply be multiplied
by 2 in cases where torsional moments
are dealt with.
The use of the table can be best illus-
No. 7
SHAFTING, KEYS AND KEYWAYS
17
trated by an actual problem. Assume
that the maximum combined bending
moments on a shaft are 52,900 inch-
pounds. Using a fiber stress not ex-
ceeding 10,000 pounds per square inch,
what size shaft would be required? The
section modulus in this case is
52,900
Z = = 5.29.
10,000
Referring now to the table on page 12
we find that the diameter corresponding
to this section modulus is 3 13/16
inches, approximately. This diameter
corresponds to a value of Z = 5.44, and
is thus on the side Of safety. [MACHIN-
ERY, May, 1908, Maximum Stresses.]
Shear Stresses Combined with Tension
or Compression Stresses
The question of shearing stresses com-
bined with tension or compression
stresses is one which always causes con-
siderable difficulty. On page 13 a table
of factors is given by means of which
the maximum combined unit shear and
the maximum combined unit tension or
compression may be determined when
the forces causing shear and tension or
compression are known. For example,
assume that 8 (see table on page 13) =
9000, and t = 12,000 pounds per square
8
inch; then — = 0.75, and from the table
t
we find that the tension (or compres-
sion) factor x then equals 1.40. This
means that if the shear is 75 per cent
of the tension, the maximum combined
tension will be 1.40 times what it would
have been if there had been no shear.
This table makes it possible to quickly
determine the maximum stresses in
shafts subjected to combined tension and
compression stresses, provided the sep-
arate unit stresses are known. [MA-
CHINERY, March and April, 1904, Notes
on Design; May, 1908, Maximum
Stresses; MACHINERY'S Reference Series
No. 12, Mathematics of Machine Design,
Chapter I: Machinery Shafting.]
Table of Combined. Bending- and
Torsional Moments
One of the most familiar examples of
combined stresses in shafting is that of
torsion and bending, the torsional
stresses being shearing stresses, and the
bending stresses being tension and com-
pression stresses. The maximum stress
may be found by calculating each separ-
ately, and combining them by the aid of
the table on page 13, as already men-
tioned. The tables on pages 14 and 15
also may be used for more directly com-
bining these stresses. If the bend-
ing and the torsional moments, both in
inch-pounds, are known, they are located
at the left-hand side and at the top of
the tables, as indicated. The body of
the tables then gives the maximum or
"ideal" torsional moment in the line
marked T to the left, and the maximum
or "ideal" bending moment in the lines
marked B. For example, a shaft 3^
inches in diameter is subjected to a tor-
sional moment of 36,000 inch-pounds and
a bending moment of 35,000 inch-pounds.
What is the combined shearing stress
and the combined tension and compres-
sion stress?
Referring to the table on page 15 and
remembering that all values may be mul-
tiplied by 10, we find, by locating the
torsional moment 3600 (instead of
36,000) at the top of the column, and
the bending moment 3500 (instead of
35,000) in the left-hand column, that the
maximum twisting moment, in this case,
is 50,210, and the maximum bending mo-
ment 85,210 inch-pounds. Having now
found the maximum moments, we can
find the maximum combined unit shear
and unit tension or compression; From
page 12 we find tkat the section modulus
Z for a 3M»-inch shaft is 4.209. The polar
section modulus being twice this, we
have Zp =8.418.
Using the notation,
Maximum combined unit shear = Sm,
Maximum combined unit tension or
compression =3 fm,
(Continued on page 24.)
18
MACHINERY'S DATA SHEETS
No.
51
U
H
U
5Jt
33
3*
^
p
J»
i
8i
Bending Moments in Thousands of /ncn Pounds.
fe^fe
&fcfe
!S
Qo
(N
!***
is
Ui
Ui
N)
Ui
U|
(M
Ui
Jo N f^
^ Q^N^lCi **"• ^ ^ ^ $Q ^ ^tN|
U|
Bending Moments tn Thousands of /nch Pounds.
"SI
3
re
i?
s
s
nc
Hi
Irf
1
ill
ss
nc
No. 7
SHAFTING, KEYS AND KEYWAYS
19
Bend/'ngf Women fs in Thousands of /nch Pounds.
00
to <* Si
*0
I
«
Qo
NKfcc-
Co
Co
^\VMQ^I
Qo
Co
CO
Co Qo
Qo
Co
CD
Oo
Qo
Qo
h)
Qo
Co
Co
Co
Co
Co
Qo
CD
CD
Co
Qo
Co
Qo
Qo
"»1 ^1 /N
^^ ^
Qo
Qo
Oo
Co
Co
Co
Qo
Co
Oo
Qo
r.
«fo^«W*<^
20
MACHINERY'S DATA SHEETS
No. 7
Momenfe />? Thousands of //7ch fot/nc/s -B.
No. 7
SHAFTING, KEYS AND KEY WAYS
Bending Moments in Ten Thousands of fncn Pounds.
22
MACHINERY'S DATA SHEETS
Bending Moments in Hundred Thousands of fnch Pounds.
S* toooo
I
1 I
i i i
I I
I I
II I I I I
/ I /
/ I I/
J I
7
A
No. 7
SHAFTING, KEYS AND KEY WAYS
23
Bending Moments in Mi //ions of /nch Pounds.
I
• =7SOO
I I
x
t
I 1
z
/G
J_
I I
T
«r
X
it-
j I
x
24
MACHINERY'S DATA SHEETS
No. 7
and proceeding to make use of the
values found in the table on page 15 we
find:
50,210
fi£ = =5970, and
8.418
85,210
tm =- - = 10,120.
8.418
These two values give the maximum
combined unit stresses.
It will be noted that in the tables on
pages 14 and 15 the values B of the
maximum or ideal bending moments are
always greater than the values T of the
maximum or ideal torsional moments.
Hence it is the combined tension or
compression stresses which determine
the size of the section to be used, and
the maximum torsional moment may be
entirely neglected. All authorities do
not agree on the subject of combined
torsion and bending. The tables given
agree with the formulas given by Ran-
kine. The formula given by Grashof
gives a torsional moment which has a
greater value than that obtained from
the Rankine formula. This latter, how-
ever, is commonly used, and shafting
designed from calculations based upon
this formula has proved satisfactory.
In this connection it is well to note
that in the case of shafting, the location
and direction of the tooth loads, belt
pulls, etc., which produce bending, re-
main fixed while the shaft rotates. The
bending stresses are thus constantly
varying in direction, and since a greater
factor of safety should be used for re-
versible stresses than for those which
are constant in direction, many design-
ers recommend that the allowable work-
ing stresses should vary according to
whether the torsional or bending mo-
ment predominates. Higher stresses
may be used when the torsional mo-
ment is greater; when the bending mo-
ment is greater the stresses ought to be
made proportionately less. On the
other hand the ultimate tensile stress is
approximately 25 per cent greater than
the ultimate shearing stress, and as the
determining stress is always the com-
bined tension or compression and not
the shear, and since the Rankine for-
mula is less liberal in recognizing the
torsional moment than is that of Gras-
hof, it is safe to say that when using
the Rankine formula, ample provision
is made for the fact that the bending
stresses are reversible, even when a con-
stant allowable safe stress is assumed.
[MACHINERY, July, 1908, Maximum
Stresses.]
Diameters of Shafts for Combined Tor-
sional and Bending- Stresses
On pages 18 and 19 are given tables
for the diameters of shafts subjected to
combined torsional and bending stresses.
The tables are arranged for fiber
stresses of 7500, 10,000 and 12,500
pound's per square inch. As an example,
find the diameter of a shaft to sustain
a bending moment of 80,000 inch-pounds
and a torsional moment of 100,000 inch-
pounds, if a fiber stress of 10,000
pounds per square inch is allowed. By
referring to the table on page 18, and
locating the torsional moment as given
in thousands of inch-pounds at the top,
and the oending moment as given at the
left-hand side, in the line and column
corresponding to a fiber stress of 10,000
pounds per square inch, and then locat-
ing in the body of the table the diameter
of the shaft corresponding to these mo-
ments, we find that the diameter re-
quired is 4% inches.
One difficulty with tables is the inter-
polation for immediate values. A dia-
gram or chart is much better in this
respect, and if drawn to a convenient
scale is often preferable. On pages 20
to 23, inclusive, are given diagrams for
finding the diameter of shaft required
for combined torsional and bending
stresses. The use of these diagrams is
very simple. The bending and torsional
moments in thousands, ten-thousands,
hundred-thousands, and millions of
(Contlnuod on page 26.)
No. 7
SHAFTING, KEYS AND KEYWAYS
25
WEIGHTS AND AREAS OF COLD ROLLED STEEL SHAFTING.
Diameter,
Inches.
Area, .
Square
Inches.
Circumference
Inches.
Weight per
Foot,
Pounds.
Diameter,
Inches.
Area,
Square
Inches.
Circumference,
Inches.
Weight per
Foot,
Pounds.
A
,0276
,5890
,095
2A
3.7583
6,8722
12,80
i
,0491
,7854
,167
n
3,9761
7,0686
13,52
A
,0767
,9817
,260
2A
4,2000
7,2649
14,35
I
,1104
1,1781
,375
n
4,4301
7,4613
15,07
A
,1503
1,3744
,511
2A
4,6664
7,6576
15,89
}
,1963
1,5708
,667
2^
4,9087
7,8540
16,70
T9*
,2485
1,7671
,845
lA
5,1572
8,0503
17,55
6
¥
,3068
1,9635
1,05
21
5,4119
8,2467
18,41
u
,3712
2,1598
1,26
2tt
5,6727
8,4430
19,31
!
,4418
2,3562
1,50
21
5,9396
8,6394
20,21
.it
,5185
2,5525
1,77
21!
6,2126
8,8357
21,15
?•
,6013
2,7489
2,05
21
6,4918
9,0321
22,09
«
,6903
2,9452
2,35
211
6,7771
9,2284
23,06
1
,7854
3,1416
2,68
3
7,0686
9,4248
24,05
1A
,8866
3,3379
3,02
3£
7,6699
9,8175
26,09
n
,9940
3,5343
3,38
Si"*
7,9798
10,014
27,16
1A
,1075
3,7306
3,77
31
8,2958
10,210
28,22
H
,2272
3,9270
4,17
31
8,9462
10,603
30,43
1A
,3530
4,1233
4,61
SA
9,2806
10,799
31,58
11
,4849
4,3197
5,05
31
9,6211
10,996
32,73
1iV
,6230
4,5160
5,52
31
10,321
11,388
35,20
H
,7671
4,7124
6,01
3H
10,680
11,585
36,40
1l9TT
,9175
4,9087
6,52
31
11,045
11,781
37,57
1 1
2,0739
5,1051
7,06
11
11,793
12,174
39,40
Itt
2,2365
5,3014
7,61
311
12,177
12,370
41,04
11
2,4053
5,4978
8,18
4
12,566
12,566
42,75
1«
2,5802
5,6941
8,78
4i
14,186
13,352
48,26
11
2,7612
5,8905
9,39
4T7*
15,466
13,941
52,62
HI
2,9483
6,0868
10,03
41
15,904
14,137
54,11
2
3,1416
6,2832
10,69
4!
17,728
14,923
60,88
2iV
3,3410
6,4795
11,35
411
19,147
15,512
65,50
2*
3,5466
6,6759
12,07
5
19,635
15,708
67,45
MACHINFRY'S Data Sheet No. 29. Explanatory note : Page 26.
26
MACHINERY'S DATA SHEETS
No. 7
inch-pounds, as the case may be, are lo-
cated at the left-hand side and at the
bottom of the diagram respectively; the
horizontal line from the bending mo-
ment and' the vertical line from the
torsional moment are followed until
they intersect as shown by the dotted
lines on page 20. The curve passing
exactly or approximately through the
point of intersection then indicates the
diameter of shaft required. In the ex-
ample shown on page 20 it will be seen
that the lines intersect between the
111/16- and 13/4-inch curves. It is
always better to make the shaft a trifle
stronger than necessary; in this case,
then, one of 1%-inch diameter would be
used. This shaft would be of the re-
quired size to transmit a torsional mo-
ment of 4000 inch-pounds, and could in
addition sustain a bending moment of
4000 inch-pounds, at a fiber stress of
10,000 pounds per square inch, these be-
ing the known requirements from which
the dotted lines in the diagram were
traced. [MACHINERY, July, 1908, Maxi-
mum Stresses.]
Weights and Areas of Cold-rolled
Steel Shafting
When calculating the stresses in shaft-
ing, the weight of the shafting itself
must be considered whenever the dis-
tance between the bearings is consider-
able. The table on page 25 will be
found convenient in such instances, as
it gives the weight per foot in pounds
of cold rolled steel shafting from 3/16
to 5 inches diameter; besides, the area
in square inches and the circumference
in inches are given. In calculating the
stresses caused by the weight of the
shaft itself, the total weight between the
bearings is, of course, considered as
uniformly distributed along the whole
shaft, the shaft being assumed to be sup-
ported freely at the bearings. The bend-
ing moments caused by pulleys, belting,
gears, etc., are then determined and
these are added to find the total bend-
ing moment.
Allowances and Tolerances for
Various Kinds of Fits
Running fits, as implied by the name,
are characterized by the condition that
of two machine members fitted together,
cne is free to revolve inside or about
the other, the fit, however, being other-
wise as close as possible. It is evident
that the member that fits inside of the
other must be a very small amount less
in diameter than the hole into which
it fits.
The term "forcing fit" is used when a
pin, axle, or other part, which is some-
what larger than the hole into which
it is inserted, is pressed into place by a
hydraulic press or by other means. The
crank-pins and axles for locoonotive driv-
ing wheels are usually inserted in this
way.
The term "shrinking fit" is applied
when a part which is to be held in po-
sition by being tightly fitted into a hole
is first turned a few thousandths of an
inch larger than the hole, and then the
diameter of the hole increased by heat-
ing it, after which the pin is inserted
in the heated part. When this part
cools down, the consequent contraction
of the metal causes it to grip the pin
with tremendous pressure. Locomotive
tires, for example, are attached to their
wheel centers by means of a shrinking
fit.
Allowances and tolerances for run-
ning fits recommended by the Engineer-
ing Standards Committee of Great Bri-
tain are given on page 27. The note
at the bottom of the page should be care-
fully read before using the table, in
order to avoid misunderstandings.
On page 28 a diagram is given of al-
lowances for forcing, driving and run-
ning fits as adopted by the Builders'
Iron Foundry, Providence, R. I. In the
diagram two heavy lines are drawn for
each kind of fit, the upper line indicat-
ing the maximum and the lower line
the minimum allowance for the respec-
tive diameter. For example, assume
(Continued on page 34.)
No. 7 SHAFTING, KEYS AND KEYWAYS
ALLOWANCES AND TOLERANCES FOR RUNNING FITS
27
Nominal
D/crmefer
<Shcrff
/41/owance
(Minimum
Difference
between Shaft
and Ho /e)
Ho/e-
Minimum
Diameter
Tolerance
CDifference)
Mcrximum
Diameter
Mr/imum
Diameter
To/erance
(Difference)
Maximum
D/'amefer
/nches
Inches
Inches
Inches
Inches
Inches
Inches
/nches
4
O.2495
o.ooos
0.2S
O.OOOS
O.2SOS
O. OO03
O.2S08
i
O.4993
0.0007
O.SO
O.0007
O.SO 07
O.OOO7
O.SO/4-
f
0. 7491
0.0009
0.7S
O.OOO8
0.7S08
O.OOO9
0. 7S/7
1
0.9990
Q.OO/0
I.OO
o.oo/o
I.OO/O
O.OO/O -
/.OO2O
4
1.4988
0.00/2
/.SO
O.OO/2
/.SO/ 2
O.OO/3
/.S02S
2*
/.993S
0.00/S
2.OO
o.oo/s
2.00/S
O.OO/S
2.003O
3
2.998Z
0.00 IB
3.OO
O.OO/8
3.OO/8
•0. 00/7
3.003S
4-
3.9930
0.002O
4.0O
0. 0020
4-. O02O
O.O020
4. OO4O
S
4.9980
0.0020
S.OO
0.0020
S. 0020
0.0020
S.0040
0
S.997S
O.OO2S
6.0O
0.0 OSS
6. 002S
0.002S
6.00SO
7
9.9975
O.OO2S
7.00
O.OO2S
7.O02S
O.002S
7.0OSO
8
7.997S
O.002S
8.0O
o.oozs
8JO2S
O.002S
8.00SO
9
8.9970
O.OO3O
9.OO
0.0030
9.OOJO
0.0030
9.00&O
10
9.997O
0.0030
10.00
0.003O
/O.OO3O
O.OO30
/O.OO&O
II
10.9970
O.003O
II.OO
O.O03O
//.OO30
O.O030
//.OO&O
12
//.997V
0. 003O
/2.00
0.0030
/2.O030
O.0030
/2.O060
Note-.- The crbore a/fowances and tolerances for running fits are
recommended by the Engineering Standards Committee of Great
Britain ', for first- class work. For second- and fhircf-c/ass work,
mu/fip/e/ the fo/erances by 2 and 3, respecf/'re/t/. /^orexfrcrf/he
aua//'ty of work, about 2/s Me abore af/otrances for f/'rsf-c/ass work
are recommended. The maximum cf/'amefer- of the snaff is f/?e
nominal diameter in a// grades of /rortf.
MACHINERY'S Data Sheet No. 78. Explanatory note: Page 26.
28
MACHINERY'S DATA SHEETS
No. 7
8888
h*
il'IS
Diameters.
LIMITS FOB STANDABD HOLES.
TH
z
z
z
0
-n
H
0)
ousXn
UNbE
NOHM/
D H8
R
II
TON
ou
/ER
5AN
N
DT
)M
^S
NA
OF
. D
AN
AM
IN
ETE
|S Si MAXIMUM
a |
•J
r
L
E
c»
^
S
I
Diameter - .00025
Diameter - .00025
Diameter — .0005
Diameter — .001
Minimum.
0
2
m
3]
Z
c
x
C
CO
&
- 2
z
0
z
2
C
Diameter + .00025
Diameter + .00075
Diameter + .001
Diameter -t- .001
Maximum.
r
n
M
1AMET
e>
m
XI
z
z
o
I
m
S
^5
:j-
0
m
-n
E
H
0)
»i
<i
<i
B
*-
No. 7
SHAFTING, KEYS AND KEYWAYS
29
PRESSURE FACTORS
30
MACHINERY'S DATA SHEETS
DIAGRAM FOR RUNNING FITS AND LIMIT GAGES
No. 7
ALLOWANCES FOR RUNNING FITS.
.03T.
.005
.004
.003
.002'
,001
0" 1" 2" 3" 4' 5" 6" 1" 8" 9" 10" 11" 12" 13" 14" 15" lliDia.
A = allowance in inches. D = nominal diameter of fit in inches.
0.31Z) + 0.5
For running fits, A =
1000
TABLE OF LIMITS FOR LIMIT GAGES.
.002
.0015
II
.001
.0005
0
.COOS'
.001
.002
2" 3' 4" 5" 6" 7"
total limit in inches. D = nominal diameter of fit in inches.
0.375 D + 0.6
1000
8"Dia.
ALLOWANCES FOB SHRINKING FITS ADOPTED BY THE AMERICAN MASTER
MECHANICS' ASSOCIATION.
Diameter of tire, in inches 38 44 50 56 62
Shrinkage allowance, in inches 040 .047 .053 .060 .066
.070
From a paper by Stanley H. Moore read before the American Society of Mechanical Engineers.
MACHINERY s Data Sheet No. 23. Explanatory notes: Pages 26 and 39.
No. 7
SHAFTING, KEYS AND KEY WAYS
FORCING, SHRINKING AND DRIVING FITS
31
4)16
ui .010
o
<.008
.007
.006
.005
.004
.003
.002
.001
E±
18'
13" 14' 15" l6Dia
A = allowance in inches.
= nominal diameter of fit in inches.
2 D + 0.5
For forcing fits, A =
For shrinking fits, A =
1000
1.06 D + 0.5
1000
For driving fits, A =
0.5 D + 0.5
1000
NOTE. — While the data given in the above table is the result of an investigation of the prac-
tice of a large number of shops, the allowances for the large diameters is considered excessive, as
they give results which require presses of more than ordinary power to make the fits. It is the
practice in a large number of shops to decrease the allowance per inch as the diameter increases.
The general rule of .001 inch per inch of diameter has been found very satisfactory for sizes
above 6 inches, while the allowances for the smaller sizes correspond more nearly to those given
above.
From a paper by Stanley H. Moore read before the American Society of Mechanical Engineers.
MACHINEUY'S Data Sheet No. 23. Explanatory note : Page 26.
32
MACHINERY'S DATA SHEETS
WOODRUFF KEYS— I
No. 7
i
Woodruff Jfcrncfcrrcf ffet/s
K <* -«|
Tlr .i x- — x.
/T
n c
<-"
'_ 4_
'•f
X---/ 1
V
vly
NO. Of
Key
Diam. of
Key
Thickness
of Key
£ty»/A «^
ffeytvay
Center of
stocK.frvm
which Hey
ismade.fo
fop of Key
NO Of
Key
Diam. of
Key
Thickness
of Key
Depth of
Heytray
Center of
stock, from
which key
is made, fo
top of key
ct
b
C
a
a
b
C
ct
1
t
l
.&
*
B
i
1
J
k
2
i
h
A
A
,*
4
4
32
£
3
i
*
^
b
f7
>i
£
*
£
4
s
A
&
&
»
&
k
1
4
*
*
i
1
k
C
''t
I
£
52
A
0
*
.3?
£
k
/9
'k
3
h
i
7
1
i
/i
T*
20
'k
£
k
4
8
*
>S
£
76
21
'k
k
i
A
9
f
4
A
k
0
4
1
&
£
10
&
j£
4
k
£
'k
I
1
£
II
Ir
i
32
re
22
'J
i
i
3
32
/£
1
/2
I
Te
23
/I
1
k
k
A
i
4
''e
k
'_
/I
1
4
J2
13
/
1
&
it
24
'.?
k
'-s
£
14
/
b
64
76
25
4
£
fz
£
,5
/
6
b
76
G
^
1
4
i
MACHINBKT'S Data Sheet No. 81. Explanatory note : Page 39.
No. 7
SHAFTING, KEYS AND KEYWAYS
WOODRUFF KEYS— II
33
yyooc/ruff Spec/af Xet/s
. A
KCf >J
)/
Ct
\ i !
( J
a
c
i X^— "X/ 1 /
\ t
1 J V
~*
\ e L
\~T /
No. of
Key
Dictm. of
Hey
Thickness
of Hey
Deptnof
Keyway
Centerof
stock, from
which key
is made, fo
top of key
W/dfn of
F/at
No. of
Hey
Diam. of
Hey
Thickness
of Key
Depfnof
Heyway
Centerof
sfockjrom
which key
ismacfejo
top of key
Mcff/t of
a
b
c
ct
e
a
b
C
c(
e
2<5
4
%
32.
/7
32
32
3f
f
T<5
h
f
}*
27
4
k
''8
&
k
32
4
i
k
f
T0
28
4
s
Te
32
'J
k
33
4
S
3Z
f
%
29
4
I
I
&
32
34
*
*
S
10
12
9
fe
30
4
*
T&
f
3
I
Standard Keys fo use w/ffy rar/ous cf/'amefer ^hcrfte
Diameter of
Shaft
Number of
Keys
D/amerer of
Sftcrff
Number of
D/amefer of
Sfiaff
Number of
Key*
•£ — 2
1
7 US
'8 ~ T0
6, 8, 10
'I -'I
14, 17, 2O
7 1
16 2
2,4
1
9, //, /3
4-4
J£, /e, 2/, 24
J0 ~ 8
3,5
4 - 4
4.4 «*
<%->$
J8, 2/f 24
- -\
s,*,r
//!
//^ /J, /^
#-2
21,2*
(3
0,8
4-4
/£", A?f /7, 20
4-^
2S
MACHINEUY'S Data Sheet No. 81. Explanatory note : Page 39.
MACHINERY'S DATA SHEETS
No. 7
that it is required to find the diameter
to which to turn a pin to be fitted by a
forcing fit into a standard 7-inch hole.
By locating 7 on the line marked
"Nominal diameter in inches," and fol-
lowing the vertical line from 7 until it
intersects the heavy lines for forcing
fits, it will be seen that the pin should
be from 0.009 to 0.010 inch above the
nominal diameter. If a running fit had
been required instead of a forcing fit, we
would have followed the line downward
from 7 until intersecting the heavy lines
representing the limits for running fits.
Assuming the hole to be standard size
as mentioned, the pin should thus have
been turned from 0.0025 to 0.004 inch
below the size of the hole. In the case
of running fits, however, it is almost
always the practice to make the diam-
eter of the shaft the standard or nomi-
nal size, and to provide for the allow-
ance in the hole. In such a case the
shaft would have been made 7 inches in
diameter while the hole would have
been made from 7.0025 to 7.004 inches
in diameter.
Whether parts should be assembled by
pressing them into place or by the
shrinking method depends somewhat
upon circumstances. To press a tire,
for example, over a wheel center, would
be a rather difficult job, owing to the
size and shape of the work. On the
other hand, a pin is easily forced into
place with a hydraulic press if such a
tool is available; otherwise the hole can
be heated and expanded sufficiently to
permit the insertion of the pin by sledg-
ing or even by hand. The hydraulic
press is more economical for most work,
and in addition there is an advantage
in its use in that the exact pressure or
tonnage required to force the part into
place is indicated by a gage, while there
is more or less uncertainty connected
with a shrinking fit. If the allowance
when turning a pin for a shrinking fit
were too great, the part into which the
pin is fitted might be broken when
cooled down, owing to the excessive
stresses produced. When using a press
this danger is largely eliminated, as the
approximate pressure required can be
calculated, and the pressure gage indi-
cates at every moment what the actual
pressure is. Tests have demonstrated,
however, that a shrinking fit is superior
to a forcing or press fit, as the assem-
bled parts are held more securely to-
gether.
The ultimate pressure finally required
to force the pin or other part into
place depends not only upon the allow-
ance for the fit, but also upon the length
of the bore or the area of the surface
of the fit. The pressure required for
forcing a pin with a given allowance
into a hole may be determined by the
formula given with the diagram on page
29, where the pressure factor PF is de-
termined from the diagram. This pres-
sure factor varies with the diameter of
the pin. For example, if the pin is 6
inches in diameter, then we find from
the diagram that the pressure factor is
75. To find this, we locate 6 on the
scale at the bottom of the diagram, and
follow the vertical line from the point
so located until it intersects the curve
drawn on the diagram; from the point
of intersection, we follow the horizontal
line to the scale at the left where the
pressure factor 75 is read off. The ex-
ample given in connection with the dia-
gram and formula indicates clearly their
use for practical calculations.
The diagrams for running, forcing,
shrinking and driving fits given on
pages 30 and 31 are compiled from a
paper read by Stanley H. Moore before
the American Society of Mechanical En-
gineers, and are the results of an inves-
tigation of the practice in a large num-
ber of shops. Before using these dia-
grams, however, the note at the bottom
of page 31 should be read and compari-
son made with the diagram on page 28.
The use of the diagrams on pages 30
and 31 is very simple. On the scale at
the bottom of the diagrams are given
(Continued on page 39.)
No. 7
SHAFTING, KEYS AND KEYWAYS
DIMENSIONS OF KEYS— I
35
PROPORTIONS OF KEYS.
(United States Navy Standard.)
D=0
r 8* 9" 10
InduatrinLPresa,. K. F.
w
W
f"
I"
1"
U"
H"
11"
H"
1!"
2"
21"
2f"
3'
31 '
31"
A"
H"
i"
A"
i"
8
6 "
B
-H"
A"
A"
sa
I"
I"
TV
A"
iV
i"
4"
41"
41"
5"
51"
5£"
6"
61"
7"
7i"
71"
71"
ir'
i"
1"
1iV
U"
1A"
1A"
1A"
1A"
\"
TV
A"
TV
I"
H"
11"
8"
8i"
81"
9'
9i"
9!"
10"
If"
11"
11"
H"
11"
2"
2"
i"
«"
ir
ir
1"
1"
MACHINERY'S Data Sheet No. 33. Explanatory note : Page 39.
36
MACHINERY'S DATA SHEETS
DIMENSIONS OF KEYS— II
No. 7
TABLE OF GIB KEYS. Computed by F. D. Buffum, Akron, O
Indu»trial frest, N^K.
Keys of proportions given below are weakest in shear.
The safe twisting moment per inch of length of keys = R B S
R = Radius of shaft.
B = Breadth of key.
S = Safe shearing strength of material in key.
B = ^ bore up to 6 inches. Then B = .211 bore. Taken to eighths.
G = B approximately.
H = £ bore up to 6 inches. Then H = £ bore.
h = Radius = £ bore taken to eighths. But minimum value = -ft inch.
L = Length of hub + | inch.
Taper -J- inch per foot.
Bore and Shaft
Diameter.
If to
1Ato
1ft to
IHto
m to
2ft to
2ft to
244 to
2Hto
3ft to
3ft to
3i4to
3H to . o
4ft to* 4!
4ft to 4!
51
to
-xo to
6ft to
14
II
It
11
2i
21
21
21
3!
31
31
4*
5!
61
61
71
71
81
8[lto 9*
Sit to 10 f
10if to 111
IHtto 121
7ft to
Width
of Key
1
I
I
I
*
T
2
21
24
24
Height
of Key
n.
ft
4
1
A
I
I
U
U
I
7
Depth
i
i
A
ft
1
1
A
A
ft
44
44
t
ft
ft
4
ft
h and
Bad.
A
A
i
1
I
I
I
f
f
t
t
I
4
1
1
14
11
11
11
Safe Twisting Moment on Key per inch
of Length for S =
5000
1
1
1
1
H
H
H
H
11
It
2
2
2
2
2
630
1170
1410
2190
2500
3520
3910
5160
5620
7110
7660
9380
10000
11950
12660
15620
18910
22500
24380
26250
30470
36090
46250
57660
70310
76560
7500
10000
940
1760
2110
3280
3750
5270
5860
7730
8420
10660
11480
14060
15000
17930
18980
23440
28360
33750
36560
39380
45700
54140
69380
86480
105470
114840
1250
2340
2810
4380
5000
7030
7810
10313
11250
14220
15310
18750
20000
23910
25310
31250
37810
450GO
48750
52500
60940
72190
92500
115320
140630
153130
MACHINERY'S Data Sheet Is7o. 14. Explanatory note: Page 3!».
No. 7
SHAFTING, KEYS AND KEYWAYS
TABLE FOR USE WHEN MILLING KEYWAYS
37
K~£-->j ,-A
O~~~x<\]^ T^SN""^ ^* va/ue$ in the body of the fab/e give the
"^'7^^^^^^^^^^^^\ dimension A, which shoufcf be added fo fhe
/"^oooooooJoo^oSoo^ov deplh C of the key way in order to f/'ncf the
/^^^V^^^S^A fofaldepfh from fhe oufs/de of 'the shaff
^^^^^^^^^^^^ to fhe boffom of fhe key way. When mi //ing
^^^^^^^^^^^^| key ways, fhe cuffer can fnen be fed down
V^\X^\\\\\\\xv\xx\xy this fofaf depfhf and no further measc/i — ;
\$oooo^ooo^$ooSo/ ing is necessary.
Stze
of
Shaft
Width of Key way B
Size
of
Shaft
Wictfh of Key way B
l/4
f*
%
7
/£
j_
i
%
%
re
Lz
i
0.0325
—
2%
0.0 OG8
0.0104
o.otss
O.0209
O.0274
%
0.0289
—
—
—
*4
0.0066
0.0102
O.OIS2
O.OZ02
O.O267
%
0.0254
O.O4I3
—
—
*fc
0.0064
O.OIOO
O.OI 49
O.OI 98
O.O26O
%
0.02 3 e
0.0379
—
—
z'-2
0.0063
O.0038
O.O/46
O.OI 94
0.02S3
%
0,0220
O.0346
O.OSII
—
z*',e
O.OO6I
O.OO94
0.0142
O.O/89
O.O247
\
0.0198
0.0314
O.046S
- —
2*
O.OO6O
O.OO9O
O.O/39
0.0/8S
0.0242
1
0.0/77
0.0283
O.042O
O.OS83
—
z"K
O.OOS9
O.O089
O.OI 36
O.O/&O
0.0236
\
o.oie4
0.0264
0.0392
O.OS44
—
,?$
O.OOS8
O.OO8&
O.OI33
O.OI 76
0.0230
i
0.0 1 S2
O.0246
O.036S
O.OS06
O.067O
2%
0.0051
O.0086
O.0129
O.OI72
O.O226
ihe
O.OI43
0.0228
0.0342
0.0476
0.062S
Z7'8
O.OOS6
O.O084
O.OI26
O.OI 68
0.0220
?i
O.OI36
O.02IO
0.03/9
O.0446
O.OS3I
^
O.OOS4
O.O083
O.OI 22
O.OI64
0.02/6
1%
0.0131
O.02O4
0.0304
0.042 /
O.OSSI
3
O.OOS3
O.008I
O.OI 19
0.0161
0.0211
/fe
0.0/27
O.OI 98
O.O29O
0.0397
0.0 S2 2
^
O.OOS2
O.OOSO
O.OI 16
O.O/S8
O.O2O7
/5
0.0/23
O.OI9I
O.O279
O.O38O
O.0499
^
O.OOS/
0.0078
O.OI 14
O.OfSS
0.0202
/^
0.0120
0.0 18S
0.0 268
O.0364
O.O477
3*,e
o.ooso
O.O076
O.O//2
O.OI £7
0.0198
75
0.0 1 14
0.0174
0.0 2 S4
0.0346
0.04S3
3k
O.OO49
0.007S
O.Ot 10
O.O/49
0.0/94
75
o.oi to
O.O/64
O.OZ4O
0.0328
O.0429
&*
0.0048
O.0074
O.OI 08
O.OI 46
0.0/91
75
0.01 Of
0.0 IS8
0.0231
O.O3O9
O.04/2
3%
O.0047
O.OO72
o.o/oe
O.O/43
0.0/87
5
0.01 OS
O.OI S3
O.OZ2I
O.029I
0.039S
3\
O.OO46
0.0071
0.0104
O.O/40
0.0/84
i"',e
0.0102
O.O/47
O.OZ/4
0.0282
O.0383
3''t
0.0 04S
O.007O
O.OIO2
0.0/36
O.O18O
1
O.0099
O.OI 42
O.02O7
O.0274
0.0371
3%
0.0044
O.O069
O.O/O/
O.O/3S
0.0/77
a
0.0 093
0.0/30
0.0198
O.026S
O.O3SS
3%
O.0043
O.OO67
O.OIOO
O.O/33
O.OI 74
/%
0. 0093
O.O13O
O.OI9O
O.O257
O.O339
3%
O.O042
O.O066
O.OO99
0.0131
O.O/7f
^
O.009O
0.0 / 27
0.0184
O.O2SO
0.0328
3\
O.0042
O.006S
O.O098
O.OI 28
0.0/68
2
O.OO88
O.OIZ4
0.0/79
O.OZ43
O.O3/7
3''*/6
O.004I
O.O064
0.0097
O.OI26
0.0166
ii
O.0083
O.OI 17
O.O/73
O.0236
O.O3O8
3\
O.004I
O.0063
O.0096
0.0124
0.0163
?5
O.OO78
O.OI 1 1
O.OI 68
O.OZZ9
0.0299
3$*
O.004I
O.OO62
O.OO9S
O.O/23
OjO/6/
Z*,6
O.0073
O.OI O9
O.OI63
0.0222
O.O29I
4
O.OO4O
o.ooet
O.OO94
0.0/2 /
O.OI6O
2k
O.OO7O
O.O/O7
O.OIS9
O.OZI6
0.0282
Contributed by James J. Loftus. Explanatory note: Page 39.
MACHINERY'S DATA SHEETS
DUPLEX KEYS
No. 7
A
B
Bore of
Hollow
Shaft
D
21
22
*%
23
24
2S
>*&
1
26
(f
m
27
28
30
'*$
31
I 0
32
/o
1 1
3%
33
II
12
13
14
4*4
34
35
36
9%
n?6
ff,
/z
No. 7
SHAFTING, KEYS AND
39
the diameters in inches, and on the
scale at the left-hand side the allow-
ances. Assume, for example, that we
want to find the allowance for a shrink-
ing fit for a 4-inch diameter pin. Re-
ferring to page 31, we find by following
the vertical line from 4 inches until it
intersects the diagonal line for shrink-
ing fits, and from the point of intersec-
tion following the horizontal line to the
left-hand scale, that an allowance of
nearly 0.005 inch is required.
Allowances for shrinking fits adopted
by the American Master Mechanics As-
sociation are given at the bottom of
page 30. These allowances refer direct-
ly to tires to be shrunk onto their
wheel centers. [MACHINERY, July, 1909,
Machine Shop Practice — Shrinking and
Forcing Pits.]
Diagram of Limits for Limit Gages
On page 30 a diagram is given show-
ing suitable maximum and minimum
limits for limit gages for ordinary work.
It will be understood that the upper
and lower diagonal lines in this dia-
gram indicate the maximum and mini-
mum limits corresponding to various
diameters. To find the limits for any
given diameter, say 6 inches, this di-
mension is first located on the bottom
scale, and the vertical line from 6 inches
is followed until it intersects the lower
diagonal line. From the point of inter-
section the horizontal line is followed
to the left, and the minimum limit read
off. This diagram is made up on the
principle that the maximum limit is as
much above standard size as the mini-
mum limit is below standard size, so that
when the minimum limit has been found
there is no need of locating the maximum
limit. For a 4-inch diameter shaft, for
example, the allowable limits would be
very slightly more than 0.001 inch above
or below the standard size.
Keys
On pages 32 and 33 are given tables
of Woodruff standard and special keys.
In the lower part of page 33 a table is
also given of Woodruff standard keys
to be used with various shaft diameters.
It will be seen that the designer's judg-
ment must be relied upon to a certain
extent, as a number of different sizes of
keys may be used for the same diam-
eters. For ordinary practice, when no
special considerations have to be taken
into account and where more than two
keys are given for the same diameters,
the medium size key is the most suit-
able.
On page 35 is given a diagram and
table of the United States Navy stand-
ard proportions of keys. The diagram
is shown only to indicate how the sizes
were determined by plotting the dimen-
sions from a curve supposed to give the
best theoretical dimensions. When us-
ing the information given on page 35,
no attention need be paid to the dia-
gram, but the table should be used di-
rectly, as all the required information is
contained therein.
On page 36 is given a table of gib
keys. In addition to the dimensions, it
will be seen that the safe twisting mo-
ments which the key will sustain for
each inch of length, at different shear-
ing stresses, are given. This informa-
tion will be of considerable value in
quickly calculating the strength of keys
when the twisting moment is known.
[MACHINERY, September, 1901, Notes on
Keys and Key ways; March, 1907, Keys
and Key ways; MACHINERY'S Reference
Series No. 22, Calculation of Elements
of Machine Design, Chapter VI, Keys
and Keyways.]
Table for Use when Milling
Keyways
The table given on page 37 will be
found very useful when milling keyways
to a given depth. The usual way of
measuring the depth of a keyway is to
mill off the top of the shaft until the
flat on the top is of the same width as
the cutter. Then the index is set to
zero and the cutter is fed down the re-
40
MACII/XERY'S DATA SHEETS
No. 7
quired depth C (see page 37). When
milling off the top of the shaft, difficulty
is experienced in measuring properly
the width of the flat. By means of the
table a more accurate measurement can
quickly be obtained. Bring the cutter
down so that it will just touch the work
on the top, and set the index to zero.
Then add the figures given in the body
of the table for the given size of shaft
and width of keyway, to the depth C
of the keyway. This gives the total
depth from the outside of the shaft to
the bottom of the keyway. For ex-
ample: If the size of the shaft is 3
inches and the width of the keyway one-
half inch, then, from the table, we find
that 0.0211 inch should be added to the
given depth C of the keyway — usually
made half the width B — in order to find
the total depth from the top of the shaft
to the bottom of the keyway. In this
case, then, this dimension would be
0.250 + 0.0211 = 0.2711 inch. [MA-
CHINERY, December, 1908, Keyway Gag
ing in Shafts and Hubs.]
AN INITIAL FINE i Ol ; » OM«
W,LU BE *«•»•» "^ES. TOE PENALTY
THIS BOOK ON T t*D*'™° ON THE FOURTH
O.Y
TU
UNIVERSITY OF CALIFORNIA LIBRARY
No. 16. Machine Tool Drives.— Sp
and Feeds of Machine Too; : or
Singh- Pulley Drives; Drives for High
Speed Cutting Tools.
No. 17. Strength of Cylinders -For
mulas, Charts, and Diagrams.
No. 18. Shop Arithmetic for the Ma
chinist. — Tapers; Cham Cutting
Speeds: Feeds; Ind. -ring for '
ting Spirals; Angi
No. 19. Use of Formulas in Mechanics.
— With numero! lions.
No. 20. Spiral Gearing*. — Rules, Formu-
las, and Diagrams,
No. 21. Measuring Tools. — History and
Development of Standard Measurements;
Special Calipers; Compasses; Micron;
Tools; Protractors, etc.
No. 22. Calculation of' Elements of
Machine Design. — Factor ..f Safety;
Strength of Bolts; Riveted Joints; K
and Key ways; Toggle-joints.
No. 23. Theory of Crane Design. — Jib
Cranes; Calculation of Shaft, Gears, and
Bearings; Force Required to Move Crane
Trolleys; Pillar Cranes.
No. 24. Examples of Calculating* De-
signs.— ("harts in Designing; Punch and
Riveter Frames; Shear Frames; Billet
and Bar Passes
No. 25. Deep Hole Drilling.— Methods
of Drilling; Construction of Drills.
No. 26. Modern Punch and Die Con-
struction.—Construction and I'se of Sub-
Modern Blanking Die Con-
struction; Drawing and Forming Dies.
No. 27. Locomotive Design, Part I. —
Boilers, Cylinders, Pipes and Pistons.
No. 28. Locomotive Design, Part II. —
Stephenson Valve Motion; Theory. Calcu-
lation and Design of Valve Motion; The
Walschaerta Valve Motion.
No. 29. locomotive Design, Part III.
lokehox; Fxhaust Pipe; Frames;
Cross-heads: Cuide .Bars; Connecting-rods;
('"rank-pins; Axles; Driving-wheels.
No. 30. Locomotive Design, Part IV. —
Springs. Trucks, Cab and Tender.
No. 31. Screw Thread Tools and Gages.
No. 32. Screw Thread Cutting.— I, a the
Chan Thread Tc.«ds; Kinks.
No. 33. Systems and Practice of the
Drafting-Room.
No. 34. Care and Repair of Dynamos
and Motors.
No. 35. Tables and Formulas for Shop
and Drafting-Room. — The I'se of Formu-
las; Solution of Triangles; Strength of
Materials; clearing: Screw Threads; Tap
Drills; Drill Sixes; Tapers; Keys: Jig
Bushings,
No. 36. Iron and Steel. — Principles of
Manufacture and Treatment.
Tooth Outlines; Strength and Dnrabi!
I >esign ; Methods of ' • et h.
No. 38. Grinding and Grinding Ma
chines.
No. 39. Fans, Ventilation and Heating.
ns; Heaters; Shop Heating.
No. 40. Ply-Wheels. — T h e i r Purp
Calculation and Design.
No. 41. Jigs and Fixtures, Part I.—
Principles of Jig and Fixture Design;
Drill and Boring Jig Bushings; Locating
Points; Clamping Devices.
No. 42. Jigs and Fixtures, Part II. —
Open and Closed Drill Jigs.
No. 43. Jigs and Fixtures, Part III. —
Boring and Milling Fixtures.
No. 44. Machine Blacksmi thing. — Sys-
tems, Tools and Machines used.
No. 45. Drop Forging. — Lay-out of
Plant; Methods of Drop Forging; Dies.
No. 46. Hardening" and Tempering. —
Hardening Plants: Treating High-Speed
Steel; Hardening Gages; Hardening
Kinks.
No. 47. Electric Overhead Cranes. —
Design and Calculation.
No. 48. Files and Filing.— Types of
Files; I'sing and Making Files.
No. 49. Girders for Electric Overhead
Cranes.
No. 50. Principles and Practice of As-
sembling Machine Tools, Part I.
No. 51. Principles and Practice of As-
sembling Machine Tools, I 'art 11.
No. 52. Advanced Shop Arithmetic for
the Machinist.
No. 53. Use of Logarithms and Logar-
ithmic Tables.
No. 54. Solution of Triangles, Part I.
— Methods, Rules and Kxamples.
No. 55. Solution of Triangles, Part II.
— Tables of Natural Functions.
No. 56. Ball Bearings.— Principles of
Design and Construction.
No. 57. Metal Spinning.— M a c h i n e s(
Tools and Methods
No. 58. Helical and Elliptic Springs.—
Calculation and Design.
No. 59. Machines, Tools and Methods
of Automobile Manufacture.
No. 60. Construction and Manufacture
of Automobiles.
No. 61. Blacksmith Shop Practice. —
Mode] Blacksmith Shop: \\Vlding; F
of Hooks and Chains; Miscellan
Appliances and Methods.
No. 62. Hardness and Durability Test-
ing of Metals.
No. 63. Heat Treatment of Steel. —
Hardening. Tempering and Case-Harden-
ing.
No. 64. Gage Making and Lapping.
No. 65. Formulas and Constants for
Gas Engine Design.
No. 37. Bevel Gearing. — Rules and
Formulas; Kxamples of Calculation;
M.\< HI.VKKY, the monthly mechanical journal, originator of the Reference and
Data Sheet Series, is published in four editions — the /<//<*;> Kdition. $1.00 a year;
the Eufjit' -:<lition, $2.00 a year; the Rnilirny Editi<.»i, $2.00 a year, and the
Kilit'um. $3.00 a year.
The Industrial Press, Publishers of MACHINERY,
49-55 Lafayette Street, New York City, U. S. A.
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