失效相关的齿轮一次四阶矩可靠性分析

齿轮是机械传动的关键零件之一,为了分析其可靠性,在改进的验算点一次二阶矩可靠性方法基础上,应用Taylor级数展开和Hermite多项式近似等方法,推导了齿轮功能函数的验算点前四阶矩,分析了具有齿根断裂和齿面点蚀两种主要相关失效模式的齿轮传动可靠性,给出了其相关系数和齿轮的可靠度。另一方面,因影响齿轮失效的因素繁杂众多,计算齿轮的可靠度时,不管是用一次二阶矩可靠性方法还是四阶矩可靠性方法,其计算量均偏大,且容易出错。针对该问题,提出了一种分类变差系数验算点一次四阶矩可靠性分析方法,该方法对齿轮功能函数的不同基本随机变量进行分类综合,减少了设计变量,使计算量明显减小,解决了用矩方法分析结构可靠性时计算量偏大且易出错的难题。最后应用所提分类变差系数验算点一次四阶矩可靠性分析法估计了某车床主轴箱一对传动齿轮的可靠性,计算结果显示该对齿轮齿根弯曲疲劳强度和齿面接触疲劳强度有一定的相关性,所用一次四阶矩方法因包含偏度、峰度等更高阶的统计信息可进一步提高估计精度。

Reliability analysis for gear pairs with correlated failure modes using first-order fourth-moment method

Gears pair is one of key components of mechanical transmission. To analyze its reliability, based on the improved checking point first-order second-moment (IFOSM) reliability method, Taylor series expansion and Hermite polynomial approximation were used to derive gear performance function’s checking point first-order fourth-moment (FOFM) method, analyze gear transmission reliability with two major correlated failure modes of tooth root fracture and tooth surface corrosion, and give two modes’ correlation coefficient and gear reliability. On the other hand, due to many factors affecting gear failure, when either IFOSM reliability method or FOFM reliability one was used to estimate gear reliability, the computation amount was large and they were easy to make mistakes. Aiming at this problem, a classified variation difference coefficient checking point first-order fourth-moment reliability analysis method was proposed. This method was used to classify and integrate gear performance function’s basic random variables, significantly reduce design variables and computation amount, and solve the difficult problem mentioned above. Finally，the proposed method was used to estimate the reliability of a transmission gear pair in a certain lathe spindle box. The results showed that there is a certain correlation between tooth root bending fatigue strength and tooth surface contact fatigue strength of the gear pair; the proposed FOFM method can further improve estimation accuracy due to its containing higher order statistical information of skewness and kurtosis.