Multi point traversal method for nonlinear vibration reliability analysis of gear mechanism

Gear mechanism is widely used in aviation, aerospace, machine tools and key infrastructure and other fields, and is usually the core component of various important mechanical and mechanical products. Due to the influence of many unavoidable factors, such as operating environment, machining and assembly errors, the complex nonlinear vibration of gear mechanism is very easy to occur, resulting in the rapid decline or even loss of its performance, which leads to product failure; Therefore, under the condition of considering the gear mechanism itself and its external factors, accurate and efficient nonlinear vibration reliability analysis plays an important role in improving the design ability of products and ensuring long-term stable operation of products.

Scholars at home and abroad have done a lot of research on gear nonlinear vibration. On the basis of considering the backlash and transmission error, Ahmet et al. Established the single degree of freedom gear transmission model by using the lumped mass method, and then carried out the basic research on the chaotic phenomenon in the nonlinear vibration of the gear mechanism; Velex et al. Established the nonlinear vibration model of 6-DOF gear transmission by using lumped mass method, and studied the influence of tooth profile error on the dynamic performance of gear mechanism; Xie Haidong et al. Carried out vibration experimental research on powder metallurgy helical gear transmission, and analyzed the vibration signal characteristics of helical gear based on LabVIEW. In addition, the research on chaos and bifurcation in the nonlinear vibration process of gear mechanism has gradually become a hot issue.

Since gear vibration will have a great impact on the overall performance and safety of products, the nonlinear vibration response analysis of gear considering various random factors has become a research hotspot in recent years. Wang et al. Studied the reliability and sensitivity analysis of gear transmission random vibration based on the first pass through method and Edgeworth series method; Sun Zhili et al. Studied the reliability problem of gear nonlinear vibration considering multiple random parameters. However, the above research has not carried on the comprehensive analysis to the multi class response of gear nonlinear vibration, and lacks certain systematicness.

In this paper, firstly, a more reasonable and systematic definition of nonlinear vibration reliability of gear mechanism is given; secondly, combined with the series system model, the analytical method and multi-point traversal numerical simulation method of gear nonlinear vibration reliability analysis are proposed; finally, the rationality of the proposed method is illustrated by case analysis.

Based on the first passage theory and Monte Carlo simulation technology, a multi-point traversal method for nonlinear vibration reliability analysis of gear mechanism is proposed. Firstly, the systematic definition of gear nonlinear vibration reliability is given, and the analysis framework of gear nonlinear vibration reliability is given. Then, the analytical method and the multi-point traversal Monte Carlo simulation method for the reliability analysis of gear nonlinear vibration are proposed. The simulation method avoids the assumption that the nonlinear vibration response must obey the steady-state Gaussian random process. The case analysis shows that the reliability analysis results of gear nonlinear vibration equation with explicit dynamic expression can be stabilized after 20 000 simulation times, which proves the effectiveness of multi-point traversal Monte Carlo simulation method. The following research will combine the finite element analysis and multi-body dynamics analysis, and apply the response surface method to study the implicit reliability problem.

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