Page 267 - Tribology in Machine Design
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252 Tribology in machine design
and is usually determined from tables contained in the textbooks on
elasticity. The expression for the loss caused by elastic hysteresis can be
written as
where p { is the load on the ith ball. Hysteresis losses are practically
independent of the shape of the raceway.
7.2.4. Friction torque due to geometric errors
The main cause of changes in the friction torque are errors in the geometric
shape of the bearing elements. The process leading to the formation of the
friction torque is shown in Fig. 7.6. The line of action is formed at every
given instant. In an ideal bearing this line passes through the centre of the
loaded ball. In a real bearing the line of action does not coincide with the
Figure 7.6 direction of the theoretical line of action.
In a real radial bearing, centre 0 of the raceway circle of the moving inner
ring does not coincide with the theoretical centre 0 (see Fig. 7.7). Total
errors Azj and Az 2 arise due to geometric imperfections. While determining
the centre 0 { it is assumed that the radial bearing is loaded purely by radial
load R applied at the point 0 {. Here the radial load is taken by two balls
which roll without slip. Then
where d { is the diameter of the inner ring raceway and k is the turning angle
Figure 7.7 of the moving ring of the bearing, relative to the stationary one.
7.2.5. Friction torque due to the effect of the raceway
If it is assumed that the inner ring of the bearing rotates about a vertical axis
and the raceway under the action of its own weight touches the ball only at
one point, then the friction torque due to the contact of the rolling elements
with the raceway housing is expressed in the form
where G c is the raceway housing mass, R T is the radius of the raceway of the
inner ring and/ c is the friction coefficient between the rolling elements and
the raceway housing.
7.2.6. Friction torque due to shearing of the lubricant
The presence of a lubricant between the rolling bodies in a bearing leads to
