Page 265 - Tribology in Machine Design

250 Tribology in machine design

during the rolling of the ball along the surface of the inner and outer races
respectively, / ;, / 0 are the distances moved in unit time by the point of contact
of the ball with the inner and outer races respectively and z is the number of
balls. The distances moved in unit time are given by the formulae

where n is the rotational velocity of the inner race, n b is the rotational
velocity of the ball, d b is the diameter of the ball, D 0 is the diameter of the
pitch circle, R t., R lo are the radii of curvature of the roller groove of the inner
and outer races respectively and a is the contact angle.
Equation (7.2) is valid for the case where the inner race rotates and the
outer one is stationary. The friction torque due to differential sliding is
given by

or after expansion

where/is the coefficient of sliding friction, B {, B 0 are the factors determined
by the geometric conditions of deformations and r {, r 0 are the respective
radii of deformed raceway surfaces of the inner and outer rings.

7.2.2. Friction torque due to gyroscopic spin
Friction torque arising from gyroscopic spin appears in the presence of the
contact angle a. To find M gr it is necessary to determine the moment of
inertia of the ball, /, obtained from the expression

3
where y = 7.8 gm cm is the density of the steel ball. Friction torque due to
gyroscopic spin equals

where n sh denotes the rotational speed of the shaft supported by the bearing.