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RESEARCH PAPERS

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

[+] Author and Article Information
Michael N. Kotzalas

 The Timken Company, 1835 Dueber Avenue, S.W. Canton, OH 44706-0930michael.kotzalas@timken.com

J. Tribol 127(4), 865-870 (May 26, 2005) (6 pages) doi:10.1115/1.2000981 History: Received July 15, 2004; Revised May 26, 2005

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.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Analysis of simulated data sets using the two-parameter Weibull distribution, showing ability of the analytical methods to detect zero life at high reliability

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Figure 2

Analysis of simulated data sets using the three-parameter Weibull distribution, showing ability of the analytical methods to detect a finite life at high reliability

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Figure 3

Three-parameter Weibull fit to case carburized tapered roller bearing standardized test data

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Figure 4

Case carburized three-parameter Weibull curve with through hardened tapered roller bearing standardized test data

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Figure 5

Comparison of current work with that of previous researchers

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