Prediction of Ball Bearing Assembly Life from the Two-Parameter Weibull Life Distributions of the Components

This paper presents a method for predicting the life of a ball bearing assembly from the lives of its components. An important application of this method is the prediction of the improvement in bearing assembly life which would be obtained by improvement of one or more of the components. Bearing fatigue life experiments have shown that the cumulative distribution functions, i.e. the cumulative percent failed versus life relationships, for the bearing components, as well as the bearing assembly, can be approximated by two-parameter Weibull distributions. The components of a ball bearing assembly, i.e. the inner race, the ball complement and the outer race, are arranged in series. Survival of the assembly requires survival of all of the components. The approach employed in this paper is based on the theorem that the probability of survival of the assembly is given by the product of the survival probabilities of the components. The survival function method is not new, but it is believed that this paper presents a novel application of this method to ball bearings for predicting the assembly life. By this method the cumulative distribution function for the assembly was computed from survival functions of the components obtained from experimental data. This computed result was compared to the cumulative distribution function plotted from experimental data for the assembly. The Weibull hypothesis test method of Dubey was employed for this comparison and it was concluded that the computed result estimates the assembly life with sufficient accuracy. It was further concluded that the cumulative distribution function for the assembly can be approximated in the computation with a two-parameter Weibull distribution. Formulas are derived which allow the Weibull parameters for the assembly to be calculated directly from the Weibull parameters of the components. This provides a simple and sufficiently accurate method for predicting the performance of a ball bearing assembly as a function of the performance of the bearing components provided the component survival probabilities are independent.