Reliability and sensitivity analysis for bearings considering the correlation of multiple failure modes by mixed Copula function

Abstract

The correlation between contact fatigue failure and wear failure of rolling bearing is analyzed, and the reliability model of rolling bearing based on multi-correlation failure mode is established. Based on the improved linear fatigue cumulative damage theory and wear theory, the limit state equations of two failure modes are established, and the correlation of state functions of contact fatigue and wear failure modes is described by the mixed Copula function. The random sample data are generated by Monte Carlo method, and the unknown parameters are estimated by genetic algorithm based on the minimum deviation square criterion, then the dynamic reliability model of rolling bearing is established. The quadratic polynomial without cross-term is used as the implicit functional proxy model, then the Latin hypercube sampling method and least squares theory are employed to estimate parameters of mixed Copula function and finally, the reliability sensitivity analysis of multi-failure modes of bearing is presented by fourth-order moment estimation method. Taking a certain type of spherical roller bearing as an example, the bearing reliability analysis considering the correlation of failure modes is carried out. The results show that compared with the bearing reliability model based on the assumption of independent failure modes and the weakest link theory, the bearing reliability model based on multi-correlation failure is more consistent with the practical application.