Page 274 - Tribology in Machine Design

Rolling-contact bearings 259

The spin component of the ball relative to the inner race is then co s-i. In
most instances, oj s-i will be greater than co s-0 so that great care must be taken
in designing a ball-bearing for a high-speed application where heat
generation is critical.
The spinning moments given by eqn (7.39) can be calculated to determine
which race will have ball control. The heat generated because of ball spin
can be calculated by solving for the value of o> s in velocity diagrams similar
Figure 7.16 to those presented earlier.
A further cause of possible ball skidding in lightly loaded ball-bearings
that operate at high speed is the gyroscopic moment that acts on each ball.
If the contact angle a is other than zero, there will be a component of spin
about the axis through O normal to the plane of Fig. 7.12. A gyroscopic
couple will also develop. The magnitude of this moment is

where / is the moment of inertia of a ball about the axis through 0 and is
given by eqn (7.7).
Gyroscopic moment will tend to rotate the ball clockwise in the plane of
the figure. Rotation will be resisted by the friction forces at the inner- and
the outer-race contacts, which are /P; and fP 0, respectively. Whether slip
takes place depends on the magnitude of the bearing load. In lightly loaded
bearings that operate at high speeds, slippage is a possibility.

7.5. Lubrication of 7.5.1. Function of a lubricant
rolling-contact bearings ,,.._ , , . . . „ , , .
A liquid or a grease lubricant in a rolling-element bearing provides several
functions. One of the major functions is to separate the surfaces of the
raceways and the rolling elements with an elastohydrodynamic film. The
formation of the elastohydrodynamic film depends on the elastic deform-
ation of the contacting surfaces and the hydrodynamic properties of the
lubricant. The magnitude of the elastohydrodynamic film is dependent
mainly on the viscosity of the lubricant and the speed and load conditions
on the bearing. For normal bearing geometries, the magnitude of the
elastohydrodynamic film thickness is of the order of 0.1 to 1.0 jum. In many
applications, conditions are such that total separation of the surfaces is not
attained, which means that some contact of the asperities occurs. Since the
surfaces of the raceways are not ideally smooth and perfect, the existing
asperities may have greater height than the generated elastohydrodynamic
film and penetrate the film to contact the opposing surface. When this
happens, it is a second function of the lubricant to prevent or minimize
surface damage from this contact. Action of additives in the lubricants, aid
in protecting the surfaces by reacting with the surfaces and forming films
which prevent excessive damage. Contacts between the cage and the rolling
elements and the cage and guiding loads on the race may also be lubricated
by this means.
If the operating conditions are such that the asperity contacts are
frequent and sustained, significant surface damage can occur when the