Rolling-Contact Bearing Selection

Concept

Rolling-contact bearings (ball and roller bearings) are designed to support rotating shafts with minimal friction. Because rolling elements undergo cyclic contact stresses, their ultimate failure mode is typically surface fatigue (spalling or pitting). Bearing selection is based on the statistical probability of survival for a given period under specific loads. The fundamental metric is the $L_{10}$ life (or rating life), defined as the life in hours or revolutions that 90% of a group of identical bearings will complete 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:

$L = \left( \frac{C_{10}}{P} \right)^a$

Where the exponent $a$ is:

• $a = 3$ for ball bearings
• $a = 10/3$ for roller bearings

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

$L = \frac{60 \times n \times L_h}{10^6}$

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

$C_{req} = P_D (L_D)^{1/a}$

Variables & Units

• $L$ = Life in millions of revolutions.
• $L_h$ = Life in hours.
• $n$ = Rotational speed in revolutions per minute (rpm).
• $P$ = Equivalent radial load, in Newtons (N) or lbf.
• $C_{10}$ = Basic dynamic load rating, in Newtons (N) or lbf.
• $a$ = Exponent based on bearing type.

Worked Example

A detailed interactive calculation example for bearing selection can be found at Worked Example: Rolling-Contact Bearing Selection.

Engineering Meaning

The dynamic load rating ($C_{10}$) is a theoretical constant provided by manufacturers representing the load that a bearing could endure for exactly one million revolutions. The load-life relationship is highly non-linear ($a=3$ or $a=10/3$). This means that a small reduction in the applied load can drastically increase the bearing's lifespan, while a small 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, verify the manufacturer's specific testing standard, as some manufacturers 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 foundational article excludes the calculation of equivalent dynamic bearing loads from combined radial and axial forces (the $X$ and $Y$ factors). It also excludes reliability models beyond 90% survival (Weibull distributions) and hydrodynamic journal bearings.