Dynamic reliability analysis of gear transmission system based on sparse grid numerical integration and saddle‐point approximation method

Abstract

AbstractGear systems are widely used in various mechanical transmission systems. This paper aims to develop an effective and practical method for dynamic reliability analysis of gear transmission system. The proposed method can comprehensively evaluate the dynamic reliability of gear transmission system by adopting the fourth‐moment SPA method. First, a nonlinear dynamics model of a single‐stage spur gear transmission system is established, which simultaneously takes into account the nonlinear backlash, time‐varying meshing stiffness, and static transmission error. After that, a dynamic reliability model for the tooth surface contact fatigue failure of gear system is established with the uncertainty of the motion, structure, and material parameters using stress‐strength interference (SSI) theory. To be specific, the sparse grid numerical integration (SGNI) method is applied to solve the statistical characteristic parameters of the dynamic reliability of the system. The probability distribution of the performance function is obtained with the fourth‐moment SPA method. Test examples show that the results of the proposed method are consistent with the results obtained by the Monte Carlo simulation (MCS) and superior to the maximum entropy with fractional moments (ME‐FM) method, which verifies the effectiveness of this approach. Finally, the dynamic reliability of the gear transmission system with respect to load times is evaluated.