Relation between Hertz Stress-Life Exponent, Ball-Race Conformity, and Ball Bearing Life

Abstract

ANSI/ABMA and ISO standards based on the Lundberg-Palmgren bearing life theory are normalized for ball bearings having inner- and outer-race conformities of 52% (0.52) and made from pre-1940 bearing steel. The Lundberg-Palmgren theory incorporates an inverse 9th power relation between the Hertz stress and fatigue life for ball bearings. The effect of race conformity on the ball set life independent of the race life is not incorporated into the Lundberg-Palmgren theory. In addition, the post-1960 vacuum-processed bearing steel exhibits a 12th power relation between the Hertz stress and life. The work reported extends the previous work of Zaretsky, Poplawski, and Root to calculate the changes in bearing life—that includes the life of the ball set—caused by race conformity, the Hertz stress-life exponent, the ball bearing type, and the bearing series. The bearing fatigue life in actual application will usually be equal to or greater than that calculated using the ANSI/ABMA and ISO standards that incorporate the Lundberg-Palmgren theory. The relative fatigue life of an individual race is more sensitive to the changes in race conformity for the Hertz stress-life exponent n of 12 than where n = 9. However, when the effects are combined to predict the actual bearing life for a specified set of conditions and bearing geometry, the predicted life of the bearing will be greater for a value of n = 12 than n = 9.

KEY WORDS:

• Rolling-Element Bearings
• Bearing Life
• Race Conformity
• Bearing Geometry
• Stress-Life Exponent

Acknowledgments

Presented at the STLE Annual Meeting in Calgary, Alberta, Canada May 7-11, 2006

Review led by Mike Hoeprich

Notes

^a All values of LF _i and LF _o are normalized to 1.00 for conformity f of 0.520.

¹All life factors are benchmarked to L ₁₀ = (C _D /P _eq)³ and inner-and outer-race conformities of 0.52.

²For deep-groove and angular-contact ball bearings.