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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_r = applied constant radial load
F_a = 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 F_a / ( V · F_r ) > e, then X = 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_r ) ≤ e, then 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_R = catalog rated life (hr)
N_R = catalog rated speed (rev per min)
F_D = required radial design load (lb or kN)
L_D = required design life (hr)
N_D = 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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