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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
Peq = X · V · Fr + Y · Fa

where
Peq = equivalent radial load
Fr = applied constant radial load
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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