Reevaluation of Rolling Element Bearing Load-Life Equation Based on Fatigue Endurance Data

Abstract

The load-life exponents used in the modified life rating equation for rolling element bearings were determined by statistical analysis of the experimental data generated in the 1940s, following Lundberg and Palmgren's seminal work. Based on fracture mechanics arguments, the fatigue life is known to be inversely proportional to the square root of the size of the nonmetallic inclusions. However, modern high-performance vacuum induction melt–vacuum arc remelt (VIMVAR) bearing steels are clean and nonmetallic inclusions are no longer the weak link. Fatigue life predictions (L₁₀ life) for modern bearings using the modified load-life relations greatly underpredict observed life. Hence, there is a need to update parameters of these equations using more recent life data. Based on the endurance data reported in Harris and McCool (1), validation analysis of the modified life rating equation was performed to reevaluate the values of load-life exponent for both ball and cylindrical roller bearings. The results from this study indicate that the load-life exponent for ball bearings should be 4.1, instead of 3, and for roller bearings it should be 5.5, instead of 3.33. Bearing L₁₀ life calculated using the corrected load-life exponents values shows better agreement with observed life. Details of the sampling technique used for reducing epistemic uncertainty in experimental data and the process of statistical reevaluation using Bayesian updating are discussed in detail. The accuracy of reevaluated results is presented using logarithmic plots of the ratio of predicted to actual fatigue lives for all data samples.

KEY WORDS:

• Ball Bearing
• Rolling Contact Fatigue
• Bearing L₁₀ Life
• Load-Life Exponent
• Validation
• Statistical Reevaluation
• Epistemic Uncertainty
• Weibull Parameters
• Bayesian Updating

FUNDING

This research work was partially supported by NSF GOALI Grant No: 1434708.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the feedback from reviewers. The feedback regarding consideration of the number of failures in each data set was found to be very important and it certainly enhanced the scientific relevance and quality of work presented in this article. In addition, the suggestion to include confidence intervals around each data point in Figs. 9 and 10 helped to improve readability of the results.