Rolling-Contact Bearing Selection

Concept

Rolling-contact bearings (ball and roller bearings) are designed to support rotating shafts with minimal friction. Because the rolling elements are subjected to cyclic contact stresses, the ultimate failure mode is typically surface fatigue (spalling or pitting). Bearing selection is based on the statistical probability of surviving a certain duration under a given load. The primary metric is the $L_{10}$ life (or rating life), which represents the life in hours or revolutions that 90% of a group of identical bearings will achieve or exceed before the first evidence of fatigue develops.

Formula & Method

The relationship between the applied equivalent radial load ($P$), the basic dynamic load rating ($C_{10}$), and the life ($L$) in millions of revolutions is:

To convert life in hours ($L_h$) at a given rotational speed ($n$ in rpm) to life in millions of revolutions ($L$):

Therefore, to select a bearing from a manufacturer's catalog based on a design life ($L_D$) and design load ($P_D$), calculate the required catalog rating:

Worked Example

A detailed calculation example for bearing selection and dynamic load rating with an interactive system can be found at Calculation Example: Bearing Selection and Dynamic Load Rating

Engineering Meaning

The dynamic load rating ($C_{10}$) is a theoretical constant provided by the manufacturer, representing the load a bearing can withstand for exactly one million revolutions. The load-life relationship is highly non-linear ($a=3$ or $a=10/3$), meaning that a small reduction in applied load dramatically increases bearing life, while a slight overload will cause premature failure.

Engineering Check

Ensure that the equivalent radial load ($P$) correctly accounts for both radial and axial (thrust) forces acting on the bearing. Also, check the specific manufacturer's testing standards, as some base their ratings on $L_{10}$ life, while others may use different reliability metrics or modify the basic equation with application factors.

Explicit Exclusions

This fundamental article does not cover the calculation of the equivalent dynamic bearing load from combined radial and axial forces ($X$ and $Y$ factors). It also excludes reliability models beyond the 90% survival rate (Weibull distribution) and hydrodynamic journal bearings.