STP1542: A Universal Bivariate Weibull Model for Static and Dynamic Fatigue Reliability Forecasting

    Robinson, Ernest Y.
    The Aerospace Corporation, Altadena, CA

    The Aerospace Corporation, Altadena, CA

    Pages: 21    Published: Oct 2012


    Abstract

    A universal statistical model based on a bivariate Weibull distribution is presented to forecast the reliability of bearing rolling contact fatigue (RCF) life under various applied load levels. The model is derived from work done in the field of composite material static fatigue (also known as stress rupture), and a statistically significant database, including hundreds of observations, confirmed the model predictions. Although the detailed failure mechanisms in RCF (lubricant starvation, contamination, centrifugal forces, differential component growth, ball tracking, surface smoothness, etc.) that determine the RCF life of ball bearings are complex and the definition of failure rests on arbitrary test acceleration changes, the static fatigue model has attractive features that might be useful for RCF life data correlation and reliability forecasts, as illustrated in this article. Ultimately, the value of a forecast model rests on replicating experiments that confirm model predictions. There are two premises underlying the model. First, the fatigue life is represented by a Weibull distribution, characterized by the Weibull slope (shape factor), which is denoted here as b and which is normally assumed to be invariant with life. Second, the applied load parameter. for example, the median strength-normalized contact stress. also reflects a Weibull distribution at a hypothetical constant time. These assumptions lead to the convenient use of median-normalized variables for the life and load parameters and underlie what is here called the reliability forecast chart, giving a comprehensive overview of reliability for service life at a constant operating load or stress. We address details of this model with a graphical presentation of static and RCF data and data analyses that apply the form of the static fatigue model. In addition, a method of estimation of the two shape factors is addressed, as these underlie the trade, at constant reliability, between load and life (the so-called load-life exponent). Model variants that address progressive over-arching damage, such as corrosion, can also be drawn from the prior static fatigue model. For further development and application of the model, more data are required.

    Keywords:

    bivariate, Weibull, distribution, rolling, contact, fatigue, model


    Paper ID: STP104267

    Committee/Subcommittee: F34.01

    DOI: 10.1520/STP104267


    CrossRef ASTM International is a member of CrossRef.