A SIMPLE PROBLEM IN FORCED LUBRICATION.
[Engineering, Dec. 14, 28, 1917*.]
THE important case of a shaft or journal running in bearings has been successfully treated by Reynolds, Sommerfeld and others. As Tower showed, the combination acts as a pump, and of itself maintains the layer of lubricant between the opposed solid surfacesf. There are other cases, and some of them are of practical importance, where the layer can be maintained only with the aid of special devices, such as Michell bearings, or by the forcible introduction of fluid from outside, in order to compensate inevitable escapes. Thus, Fig. 1,
when a shaft E with a flat end bears against a flat surface AB, the included oil tends to escape from the pressure, whether at G when the flat surface is continued, or at D when it is surmounted by a cylindrical cup. The permanence of the layer requires a continuous forcible feed, which may be through an axial perforation at F', for here, in contradistinction to the case of the journal, the rotation of the shaft does not avail. It is proposed to consider the problem thus presented, supposing in the first instance, that there is no cup. The small distance between the flat surfaces, i.e., the thickness of the oil layer, is denoted by h, and the angular velocity of the shaft by <w. The motion is referred to cylindrical coordinates r, 6, z, where z is measured parallel
* In the original statement there was an. error, pointed out by Mr W. Pettingill.
f As was noticed at an early "date by the present writer (President's address to British Association in 1884), this requires that the layer be thicker on the ingoing than on the outgoing side. [This collection, Vol. n. p. 344.]um of 1916* has its advantages. It would give the bearing with electric signals only, but requires further experimenting, which if desired could be arranged for at the National Physical Laboratory but perhaps not during the war.