Page 98 - Electric Drives and Electromechanical Systems

Chapter 3 Power transmission and sizing 91

a stationary linear track and a moving carriage. The carriage incorporates several wheels
that fit on to the track shaped to maintain alignment.

3.4.3 Friction in conventional bearings

Friction within a bearing is made up of the rolling and sliding friction in the rolling
contacts, in the contact areas between rolling elements and cage, as well as in the
guiding surfaces for the rolling elements or the cage, the properties of the lubricant and
the sliding friction of contact seals when applicable.
The friction in these bearing is either caused by the metal-to-metal contact of the
balls or rollers on the bearing cage, or by the presence of lubrication within the bearing.
The manufacturer will be able to supply complete data, but, as an indication, the friction
torque, T b ; for a roller bearing can be determined using the following generally accepted
relationship,
(3.30)
T b ¼ 0:5B l d m b
where d is the shaft diameter and B l is the bearing load computed from the radial load,
F r and the axial load, F a in the bearings, given by,

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
2
B l ¼ F þ F a (3.31)
R
The value of the coefficient of friction for the bearing, m , will be supplied by the
b
manufacturer; typical values are given in Table 3.3.
The friction due to the lubrication depends on the amount of the lubricant, its
viscosity, and on the speed of the shaft. At low speeds the friction is small, but it in-
creases as the speed increases. If a high-viscosity grease is used rather than an oil, the
lubrication friction will be higher and this can, in extreme cases, give rise to overheating
problems. The contribution of the lubricant to the total bearing friction can be computed
using standard equations.

3.4.4 Air bearings
Air bearings can either be of an aerostatic or an aerodynamic design. In practice
aerodynamic bearings are used in turbomachinery, where speeds of up to 36 000 rev
min 1 in high temperature environments are typically found, and provide the lift

Table 3.3 Typical coefficients of friction for roller bearings.
Coefficient of
Bearing types friction, m b
Deep grove 0.0015e0.003
Self-aligning 0.001e0.003
Needle 0.002
Cylindrical, thrust 0.004