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### Ball and Roller Bearing Analysis Loading and Selection Formulas and Calculator

Bearing Application, Specifications and Engineering

Ball and Roller Bearing Analysis for Loading and Selection Formulas and Calculator

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The minimum required basic load rating (load for which 90% of the bearings from a given population will survive 1 million revolutions) is given by:

This is sometimes called the bearing life regression equation.

Eq. 1

*C = P L ^{( 1/a )}*

where

*C* = minimum required basic load rating

*P* = design radial load

*L* = design life (in millions of revolutions)

*a* = 3 for ball bearings; 3/10 for roller bearings

When a ball bearing is subjected to both radial and axial loads, an equivalent radial load must be used in the basic load rating equation. The equivalent radial load is

*Eq. 2
P _{eq} = X · V · F_{r} + Y · F_{a}*

where

*P _{eq}* = equivalent radial load

*F*= applied constant radial load

_{r}*F*= applied constant axial (thrust) load

_{a}For radial contact, deep-groove ball bearings:

*V = 1* if inner ring rotating, 1.2 if outer ring rotating

if *F _{a}* /

*( V · F*) > e, then X

_{r}*= 0.56*and

*Y = 0.840 ( F*

_{a}/ C_{o})^{-0.247}where:

*Eq. 3
e = 0.513 ( F _{a} / C_{o} )^{0.236}*

C_{o} = basic static load rating from bearing catalog

if *F _{a}* /

*( V · F*) ≤ e, then

_{r}*x = 1*and

*Y = 0*

*Eq. 4
F _{R}* =

*F*

_{D}( N_{D}/ N_{R})^{1/a}= F_{D}( L_{D}N_{D}/ ( L_{R}N_{R}) )^{1/a}where:

*F _{R}* = catalog radial rating (lb or kN)

*L*= catalog rated life (hr)

_{R}*N*= catalog rated speed (rev per min)

_{R}*F*= required radial design load (lb or kN)

_{D}*L*= required design life (hr)

_{D}*N*= required design speed (rev per min)

_{D}Source:

Budynas, Richard G., and J. Keith Nisbett, Shigley's Mechanical Engineering Design, 8th ed., New York: McGraw-Hill, 2008.

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