齿轮机构非线性振动可靠性分析的多点穿越方法研究

Multi-crossing method for nonlinear vibration reliability analysis of gear sets

齿轮机构的非线性振动是造成机械产品故障的主要原因之一。考虑多种随机因素的影响,定量分析齿轮非线性振动的可靠性具有较高的工程实用价值。首先,采用系统性观点给出齿轮非线性振动可靠性的定义,提出齿轮非线性振动可靠性分析的系统框架;然后,在假设齿轮非线性振动响应服从稳态随机过程的前提下,提出齿轮非线性振动可靠性分析的解析方法;结合首次穿越理论及蒙特卡罗仿真技术,提出多点穿越蒙特卡罗仿真分析方法,避免了解析方法中齿轮非线性振动响应服从稳态随机过程的假设;最后,通过案例分析说明所提仿真方法的合理性及工程适用性。

The nonlinear vibration of gear sets is one of the main causes of mechanical failure.Considering the influence of various random factors,the quantitative analysis of the nonlinear vibration reliability of gear sets has significant practical value in engineering.Firstly,the definition of gear nonlinear vibration reliability was given from a systematic point of view,and the system framework of gear nonlinear vibration reliability analysis was put forward.Then,on the premise that the gear nonlinear vibration response obeys the steady state random process,the analytical method of gear nonlinear vibration reliability analysis was proposed.Furthermore,combined with the first-passage theory and Monte Carlo simulation technology,a multi-crossing Monte Carlo simulation method was proposed to avoid the assumption that the gear nonlinear vibration response was subject to steady state random process in the analytical method.Finally,the rationality and engineering applicability of the proposed simulation method were illustrated by a case study.