基于权函数法的齿根裂纹应力强度因子求解

Solving the stress intensity factor of cracked dedendum based on the weight function method

计算齿轮齿根裂纹应力强度因子是预测裂纹齿轮剩余寿命及求解具有裂纹的齿轮传动系统动力学问题的基础。应用权函数法求解齿根裂纹应力强度因子,缺乏齿轮在简单参考载荷作用下齿根裂纹应力强度因子的理论解。文中以有限宽板条边缘裂纹在裂纹面均布载荷作用下的应力强度因子替代轮齿裂纹在参考载荷轮齿裂纹的应力强度因子,从而得到计算齿根裂纹应力强度因子的权函数,最后用权函数法求出了具有不同裂纹长度条件下齿轮从开始进入啮合到退出啮合整个过程的齿根裂纹应力强度因子。计算结果表明:齿根裂纹应力强度因子随裂纹长度的增加而呈现非线性增加,而轮齿啮合过程中齿根裂纹应力强度因子与法向力的大小及作用位置密切相关。

It is necessary to calculate the stress intensity factor of cracked dedendum for predicting the residual life of cracked gear and solving the dynamical problems of a geared system with cracked dedendum.No literature has been reported to the theoretical solutions of the stress intensity factor for cracked dedendum with the simple reference load.Therefore,it is difficult to solve the stress intensity factor of cracked dedendum by means of the weight function method.In this article,the stress intensity factor of cracked dedendum with the reference load is replaced with the stress intensity factor of a single edge crack on a finite width plate under the uniform crack-face pressure,so that the weight functions are identified in order to calculate the stress intensity factor.With the aid of the weight function method,the stress intensity factor of cracked dedendum with different crack lengths during the whole meshing process from beginning to end is worked out.The results show that the stress intensity factor of cracked dedendum increase non-linearly with the crack length and are closely related to the magnitude and position of the normal force during the whole meshing process.