考虑失效相关的圆柱蜗杆传动四阶矩可靠性分析

为了评估圆柱蜗杆传动机构的可靠性,利用Taylor级数将蜗杆传动机构功能函数进行展开并得到其前四阶中心矩,以此作为约束条件,结合最大熵原理分别得到蜗轮齿面接触强度和齿根弯曲强度结构功能函数的概率密度函数,在此基础上,分析了蜗轮齿面接触和齿根弯曲两种失效模式的可靠性。另一方面,考虑蜗轮齿面接触和齿根弯曲两种失效模式之间的相关性,建立了其失效相关条件下的可靠性模型,给出了两种失效模式之间的相关系数和蜗轮总体可靠度。以某减速器蜗轮为例对所提方法通过蒙特卡洛仿真进行了验证。结果表明,基于四阶矩和最大熵原理的可靠性方法具有较高的精度,蜗轮两种失效模式之间存在一定的相关性。因此,考虑失效相关的蜗轮可靠性评估方法对于蜗杆传动的综合可靠性评估具有重要的意义。

Reliability Analysis of Cylindrical Worm Drive Using Fourth-moment Method Considering Failure Correlation

In order to evaluate the reliability of the cylindrical worm drive mechanism, the Taylor series expansion is used to expand the state function of the worm gear mechanism and the first four-order center moments of the structural state function are obtained. Regarded this as a constraint condition, the probability density functions of the worm gear tooth surface contact strength and tooth root bending strength structural state function are obtained by combining the maximum entropy principle. On the basis of the probability density functions, the reliability of the two failure modes of the worm gear is analyzed. On the other hand, considering the correlation between the two failure modes of worm gear tooth surface contact and tooth root bending, the reliability model under failure-related conditions is established, and the correlation coefficient between the two failure modes and the overall reliability of worm gear are given. Taking the worm gear of a reducer as an example, the proposed method was verified by Monte Carlo simulation. The results show that the reliability method based on the fourth moment and the maximum entropy principle has higher precision, and there is a certain correlation between the two failure modes of the worm wheel. Therefore, considering the failure-related worm wheel reliability assessment method is of great significance for the comprehensive reliability assessment of worm drive.