考虑失效模式相关性的正态分布随机载荷作用下的齿轮可靠性建模

摘要

Bending and contact fatigue failures are two main failure modes of gear and there is a certain correlation between them.A novel method is proposed to calculate the reliability of a gear under stochastic load with normal distribution.Assuming that a tangential load with normal distribution is imposed on an arbitrarily selected helical gear, the scattering spots diagram of limit state functions of failure modes will be obtained with Monte Carlo simulation method.By means of inspection on the distribution pattern of the scattering spots, a bivariate normal distribution model is proposed to be used to build up the joint distribution of these two failure modes.The mean of the limit state function is estimated through marginal distribution when considering that the marginal distribution of the bivariate normal distribution is two one-dimensional normal distributions.In addition, the covariance matrix is found with covariance function in software Matlab first and then the correlation coefficient of two sets of data is figured out.Finally, this model is applied to the solution of the reliability of the wind turbine gear.And its result indicates that this model is of high efficiency.%弯曲和接触疲劳失效是齿轮的两种主要失效模式,两种失效模式之间存在一定的相关性.假设齿轮受到正态分布随机载荷的作用,提出一种计算齿轮可靠度的新方法.任意选择一个标准斜齿轮, 在该齿轮上施加服从正态分布的切向载荷,采用Monte Carlo仿真的方法得到齿轮在两种失效模式下极限状态函数的散点图.通过观察散点的分布规律,提出采用二元正态分布模型建立两种失效模式的联合 分布.考虑到二元正态分布的边缘分布是两个一维正态分布,利用边缘分布得到极限状态函数值的均值的估计值.通过Matlab中协方差函数先求得协方差矩阵,再通过计算得到两组数据的相关系数值.最后, 将该模型应用于风电齿轮箱中齿轮的可靠度求解中,结果表明该模型具有高效性.