圆柱齿轮齿根三维裂纹扩展分析及寿命预测

Three-dimensional crack propagation simulation and life prediction in tooth root of cylindrical gear

基于线弹性断裂力学理论,建立含齿根初始裂纹的圆柱齿轮三维边界元模型,计算了裂纹前缘应力强度因子;对初始裂纹进行自动扩展分析,得到齿根裂纹的扩展轨迹及裂纹扩展寿命。在此基础上,研究了载荷大小、裂纹尺寸、裂纹位置及裂纹方向对裂纹扩展寿命的影响规律。结果表明,齿根裂纹以先慢后快的速率扩展,齿宽方向比齿厚方向易于扩展;随着载荷及初始裂纹尺寸的增大,裂纹扩展寿命逐渐减小,载荷对扩展寿命的影响很大,初始裂纹深度对扩展寿命的影响大于裂纹宽度;初始裂纹越靠近齿轮端面扩展寿命越长,初始裂纹方向为-30°左右时,裂纹扩展寿命最短。

Based on the theory of linear elastic fracture mechanics,a three-dimensional boundary element model of cylindrical gear with crack in tooth root is established and the stress intensity factor of crack tip is calculated.Then,through the automatic propagation analysis of initial crack,the growth trajectory and the propagation life of the crack at tooth root are obtained.Based on the obtained result,the influence of load magnitude,crack size,crack location and crack orientation on the crack propagation life is discussed.The results indicate that the tooth root crack expands slowly at first and then faster and faster;the crack propagates more easily along the tooth width than along the tooth thickness;the crack propagation life decreases with the increase of load magnitude or crack size,the effects of load magnitude on propagation life is significantly and the propagation life is more sensitive to initial crack depth than width;the propagation life is longer when crack is closer to the gear end-face and is shortest when crack has an initial direction about-30 degrees.