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### Bearing Design for Life and Selection Formulae and Calculator

Bearing Design for Life and Selection Calculator

The load on a rolling contact bearing is exerted on a very small area as illustrated in Figure 1. Should the resulting contact stresses are very high and of the order of 2000 MPa. Despite very strong steels (e.g. BS 970 534 A99, AISI 52100) all bearings have a finite life and will eventually fail due to fatigue. For two groups of apparently identical bearings tested under loads P1 and P2, the respective lives L1 and L2 are related by the life equation given in Eq. 1 Contact area for a ball bearing.

Eq. 1
$\frac{{L}_{1}}{{L}_{2}}={\left(\frac{{P}_{2}}{{P}_{1}}\right)}^{k}$

where

L1 = life at load P1 (number of revolutions),
L2 = life at load P2 (number of revolutions),
k ≈ 3 for ball bearings,
k ≈ 3.33 for cylindrical roller bearings.

The dimensions for rolling element bearings have been standardized and can be purchased as stock items from specialist manufacturers and suppliers. The selection of a bearing from a manufacturer's catalog involves consideration of the bearing load carrying capacity and the bearing geometry. For a given bearing, the load carrying capacity is given in terms of the basic dynamic load rating and the basic static load rating.

The basic dynamic load rating, C, is the constant radial load which a bearing can endure for 1 x 106 revolutions without evidence of the development of fatigue in any of the bearing components.

The life of a ball bearing, L, is the number of revolutions (or hours at some constant speed), which the bearing runs before the development of fatigue in any of the bearing components.

Fatigue occurs over a large number of cycles of loading. For a bearing, this would mean a large number of revolutions. Fatigue is a statistical phenomenon with considerable spread of the actual life of a group of bearings of a given design. The rated life is the standard means of reporting the results of many tests of bearings. It represents the life that 90% of the bearings would achieve successfully at a rated load. The rated life is referred to as the L10 life at the rated load. The rated life, L10, of a group of apparently identical bearings is defined as the number of revolutions (or hours at some constant speed) that 90% of the group of bearings will complete before the first evidence of fatigue develops.

If in Eq. 1, P2 = C and the corresponding life L2 = 1 x 106 , then the life of a bearing L, with basic dynamic load rating C with a load P, is given by

Eq. 2
$L={\left(\frac{C}{P}\right)}^{k}$

where

L = life (millions of revolutions),
C = basic dynamic load rating (N),
$C=P{\left(\frac{L}{{10}^{6}}\right)}^{⟮1/k⟯}$