基于改进一次二阶矩法的渐开线齿轮多失效模式可靠性分析

Reliability analysis of involute gear with multiple failure modes based on improved first-order second-moment method

常规齿轮传动设计中,采用安全系数法判断齿轮是否安全,由于未考虑设计变量的非确定性因素,设计结果往往与实际脱节.为了准确地计算渐开线齿轮传动的可靠度,以带式输送机中的一级斜齿轮传动为研究对象,基于应力-强度干涉理论建立了齿面疲劳点蚀、齿根弯曲疲劳折断等多失效模式下渐开线斜齿轮传动的可靠度模型,并采用改进一次二阶矩法对各随机设计变量服从正态分布的可靠度进行了计算与分析.结果表明,考虑设计变量的离散性后计算多失效模式下的齿轮可靠度为93.16%,低于安全系数法99%的可靠度,更能反映实际情况,计算的可靠度更准确.采用改进的一次二阶矩法,在齿轮极限工作应力与材料强度分布规律未知的情况下,即可较准确、简便地计算齿轮传动的可靠度.为渐开线齿轮传动的可靠性设计和结构改进提供方法参考.

In the conventional gear transmission design,the safety factor method is used to judge whether the gear is safe or not.Since the non-deterministic factors of the design variables are not considered,the design results are often out of touch with the actual situation.In order to accurately calculate the reliability of the involute gear transmission,this paper takes the first-stage helical gear transmission in the belt conveyor as the research object.Based on the stress-strength interference theory,a reliability model of involute helical gear transmission is established under multiple failure modes,such as fatigue pitting of tooth surface and bending fatigue fracture of tooth root.Subsequently,the reliability of random design variables obeying normal distribution is calculated and analyzed by using the improved first-order second-moment method.The results indicate that the reliability of involute gear transmission under multiple failure modes is 93.16%,which is lower than the reliability of 99%by the safety factor method and can better reflect the actual situation.With this improved first-order second-moment method,the reliability of involute gear transmission can be calculated accurately and simply,thus providing a method reference for reliability design and structural improvement of involute gear transmission.