Rolling bearings : common principles and data

The simplest bearing is probably the door hinge. When the load or speed of rotation is high, bearings are used, as they minimize friction torque and heat build-up when operating at high speeds.

Bearing calculation is generally left to the bearing manufacturers, or to the computer in large companies. However, a pre-dimensioning calculation of bearings by hand allows better selection of the most optimal bearing geometries, as it provides information on sensitive design parameters. This article is the first in a series of five dedicated to the hand calculation of ball, roller and needle bearings. A simplified approach is presented, applicable when the rotational speed is low or moderate, not exceeding 40% of the maximum permissible rotational speed given in the catalogs.

This static dimensioning approach is applicable to all bearing types and takes into account the most general load case that can be encountered on a bearing: axial load + radial load + moment. It consists of reducing the combined loading to an equivalent radial load, which can be compared with the static load capacity C_o given in the bearing catalogs, to check the bearings' resistance to Hertz pressures. The approach could also be used to calculate the service life of a rolling bearing, provided that the static load coefficients X_o and Y_o are replaced by the dynamic load coefficients X and Y, given in the bearing catalogs.

In the particular case of ball or roller thrust bearings, the combined load is reduced not to a radial load but to an equivalent axial load.

The assumptions used for this simplified calculation are as follows :

• the usual data given in bearing catalogs are available;

• the solids are considered to be dimensionally stable (bushings, shaft and hub);

• low or moderate rotation speed;

• for preloaded bearings, the contact angle is assumed to be constant. This assumption is valid because, in practice, the contact angle increases slightly (by less than 2 degrees) with axial load. It would increase sharply if a large axial load were exerted on a bearing with a small contact angle, but such a case would be a design fault.