Page 272 - Tribology in Machine Design
P. 272
Rolling-contact bearings 257
From the geometry shown in Fig. 7.11
where d is diameter of the ball. The velocity of the ball centre V 0 is
Substituting eqns (7.27) and (7.28) into eqn (7.31) gives
The angular velocity of the separator or ball set co c about the shaft axis is
Then
The speed of the separator when the outer race is fixed is
For a < 90°, the separator is always less than half the shaft speed. When
both races rotate, the speed of the inner race relative to the separator is
The speed of the outer race relative to the separator is
From eqns (7.36) and (7.37) the speed of the inner race relative to the
separator is always greater than that of the outer race relative to the
separator. A point on the inner-race ball track will receive a greater number
of stress cycles per unit time than will a point on the outer race. For ball-
bearings that operate at nominal speeds, the centrifugal force on the balls is
so negligible that the only forces that keep the ball in equilibrium are the
two contact forces. For such conditions, the contact forces are equal and
opposite, and the inner- and the outer-race contact angles are ap-
proximately equal. Even when the two contact angles are equal, true rolling
of the ball can occur at only one contact. As shown in Fig. 7.12, the ball is
Figure 7.12 rolling about axis OA, and true rolling occurs at the inner-race contact B
