Statistical Distribution of Tapered Roller Bearing Fatigue Lives at High Levels of Reliability

Abstract

The original two-parameter Weibull distribution used for rolling element fatigue tends to under-estimate life at high levels of reliability. This is due to the fact that a finite life value for which 100% of the population will survive cannot be considered with this method. However, empirical evidence of a minimum life at 100% reliability has been shown for through hardened ball and spherical roller bearings, linear ball bearings, and tapered roller bearings (TRB), however, for TRB’s there is no mention as to the heat treatment nor is there a method put forth to approximate the data. Therefore, an experimental data set of 9702 TRB’s, 98% case carburized (CC), and another data set of 280 through hardened (TH) TRB’s were collected and utilized to provide evidence of a finite life at 100% reliability. The current data for both heat treatments appeared to follow that previously published for TRB’s, however, varied from published work on other bearing types. Next, a three-parameter Weibull distribution was fit to the CC data and found to be equally applicable to the TH data set. Use of this three-parameter Weibull distribution reduced the overall root-mean square (RMS) error over both data sets by at least half, and at very high reliability levels by at least one-third compared to the two-parameter Weibull, both conservatively underestimating. However, as there is still some error in the three-parameter Weibull fit and differences in the results based upon bearing type and date of study, more investigation should be conducted in this area to identify the proper variables and the true statistical distribution for all rolling bearing constructions.