Page 288 - Tribology in Machine Design

8 Lubrication and efficiency of
involute gears

8.1. Introduction Because it is assumed that the reader already has an understanding of the
kinematics, stress analysis and the design of gearing, no further presen-
tation of these topics will be given in this chapter. Instead, prominent
attention will be given to lubrication and wear problems, because the
successful operation of gears requires not only that the teeth will not break,
but also that they will keep their precise geometry for many hours, even
years of running. The second topic covered in this chapter is the efficiency of
gears. It is customary to express the efficiencies of many power transmitting
elements in terms of a coefficient of friction. A similar approach has been
adopted here. In order to arrive at sensible solutions a number of
simplifying assumptions are made. They are:
(i) perfectly shaped and equally spaced involute teeth;
(ii) a constant normal pressure at all times between the teeth in
engagement;
(hi) when two or more pairs of teeth carry the load simultaneously, the
normal pressure is shared equally between them.

8.2. Generalities of If two parallel curved surfaces, such as the profiles of meshing spur gear-
gear tribodesign teeth, made of a truly rigid material, were pressed together they would make
contact along a line, which implies that the area of contact would be zero,
and the pressure infinite. No materials are rigid, however, so deformation of
an elastic nature occurs, and a finite, though small area, carries the load.
The case of two cylinders of uniform radii RI and R 2 was solved by Hertz. If
we take the case of two steel cylinders for which v = 0.286 then the maximum
compressive stress is given by

where P is the compressive load per unit length of the cylinders and E is the
equivalent Young modulus. If the radius of relative curvature R of the
cylinders is defined as I//?! + 1/7? 2 then

It should be noted that this stress is one of the three compressive stresses,