采用Copula的齿轮多失效模式可靠性分析

Reliability Study on Multiple Failure Modes of Gear Based on Copula

首先,建立了齿面接触疲劳和齿根弯曲断裂两种失效模式的失效功能函数,并确定了两种失效模式中具有共同的影响因素。然后,利用Copula函数建立了考虑失效模式相关时的系统失效概率模型。最后,利用不同Copula模型对某齿轮箱的一对齿轮进行多失效模式下的可靠性分析,并与大样本下的蒙特卡洛(Monte Carlo,MC)法进行对比。结果表明,样本量对Copula计算结果的稳定性和精度有重要影响,随着样本量的增加计算结果的稳定性和精度随之提高,但计算效率有所下降,且t-Copula最适用于本实例齿轮箱的多失效模式可靠性分析。

Firstly,the failure function of these two failure modes are established,and the common influencing factors in these two failure modes are determined.Then,the system failure probability model considering failure correlation is estab⁃lished by using Copula function.Finally,the reliability of a pair of gears in a gearbox with multiple failure modes is analyzed using different Copula models,and the results are compared with those of Monte Carlo method under large samples.The re⁃sults show that the sample size has an important influence on the stability and accuracy of the Copula calculation results.With the increase of the sample size,the stability and accuracy of the calculation results increase,but the calculation efficien⁃cy decreases,and the t-Copula is most suitable for the reliability analysis of the gearbox in this example.