基于鞍点逼近的机械零部件可靠性及其灵敏度分析

将鞍点逼近理论与灵敏度分析方法相结合，讨论具有随机参数的机械零部件可靠性及其灵敏度问题。在基本随机参数概率分布已知的前提下，应用鞍点逼近技术获得了外载荷作用下随机结构响应的概率密度函数和分布函数。在实例计算中，对螺栓、汽车前轴进行数值分析，将所提方法得出的数值分析结果与Monte-Carlo方法计算的结果进行对比验证，得出由鞍点逼近技术计算概率密度函数和分布函数具有计算结果准确度高、计算速率较快、尾部分布较好的优点。应用灵敏度分析方法，利用鞍点逼近技术计算的随机结构响应的概率密度函数，得到机械零部件随机参数可靠性灵敏度的变化规律，研究设计参数的改变对螺栓、汽车前轴可靠性的影响，为机械零部件的可靠性设计提供理论依据。

Analysis of Reliability and Reliability Sensitivity for Machine Components by Mean-value First Order Saddlepoint Approximation

Based on saddlepoint approximation method and sensitivity analysis method, reliability and reliability sensitivity of machine components with random parameters are studied. On the premise that the probability distribution of basic random parameters is known, probability density function and probability distribution function of stochastic structure response under the action of external loads are obtained by using saddlepoint approximation technique. In the calculation of practical example, numerical analysis of the bolt and automotive front axle is carried out, the result obtained by using the saddlepoint approximation method is compared with that of Monte-Carlo method, which shows that the former has the advantages of higher calculation accuracy and speed, and better tail distribution. The sensitivity analysis method and probability density function are employed to discuss the variation regularities of reliability sensitivity, and the effect of design parameters on reliability of the bolt and the automobile front axle is analyzed. This method provides the theoretical basis for reliability design of machine components.