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

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

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
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
Peq = X · V · Fr + Y · Fa

where
Fa = applied constant axial (thrust) load

For radial contact, deep-groove ball bearings:

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

if Fa / ( V · Fr ) > e, then X = 0.56 and Y = 0.840 ( Fa / Co )-0.247

where:

Eq. 3
e = 0.513 ( Fa / Co )0.236

Co = basic static load rating from bearing catalog

if Fa / ( V · Fr ) ≤ e, then x = 1 and Y = 0

Eq. 4
FR
= FD ( ND / NR )1/a = FD ( LD ND / ( LR NR ) )1/a

where:

FR = catalog radial rating (lb or kN)
LR = catalog rated life (hr)
NR = catalog rated speed (rev per min)
FD = required radial design load (lb or kN)
LD = required design life (hr)
ND = required design speed (rev per min)

Source:

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

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