Fuzzy chaos method for evaluation of nonlinearly evolutionary process of rolling bearing performance

The failure of a rolling bearing in running usually has an early sign along with a time history, in which a time series of its performance performs abnormally. There should be a mutant gene driving the time series change according to genetics point of view, but so far it has not been found, having difficulty in mathematical revealing the inherent mechanism of variation of the rolling bearing performance. For this reason, fusing the fuzzy set theory and the chaos theory, a fuzzy chaos method is proposed to evaluate the nonlinearly evolutionary process of the rolling bearing performance as a time series. The fuzzy equivalence relation based on a phase space is employed to represent the mutant gene and the optimum measure for fuzzy equivalence relation is advanced to uncover the essence of variation of the rolling bearing performance. The experimental investigation on the vibration acceleration of the small size bearing and the friction torque of the large size bearing shows that the fuzzy chaos method is correct and effective.

► We propose a new method to evaluate evolution of rolling bearing performances.
► We study the nonlinearly evolutionary process of rolling bearing performances.
► We develop the fuzzy equivalence relation using the chaos theory.
► We find a mutant gene of driving the rolling bearing performance change.