Vibration response-based time-variant reliability and sensitivity analysis of rolling bearings using the first-passage method

The vibration response of rolling bearings exhibits random and uncertain characteristics due to factors such as random process loads, material property degradation, and uncertain dimensional parameters. The time-variant reliability of rolling bearings obtained based on such vibration response is more realistic and accurate. In this paper, a novel vibration response-based time-variant reliability and sensitivity analysis model of rolling bearings is proposed. First, the forces on the rolling bearing are analyzed and the stress distribution is derived. Then, the equivalent stiffness and damping in the bearing vibration equation are obtained based on the ball-raceway contact model. To approximate the real degradation process, the vibration equation considering the impact load is proposed, and the statistical characteristics of the impact load with time are obtained from degradation data of the conducted bearing tests. Subsequently, the first-passage method is adopted to efficiently evaluate the time-variant reliability of rolling bearings based on the vibration response. In addition, reliability sensitivity index is derived to analyze the influence of input parameters on the reliability of rolling bearings, which improves design efficiency and provides references for further structural optimization. The accuracy and validity of the proposed model and method are verified by two cases of different bearing types.