齿轮参数对三维裂纹应力强度因子影响的研究

The research on the influence of gear parameters on the stress intensity factors of three-dimensional crack

建立了齿轮三维精确三齿模型,结合线弹性疲劳力学和边界元方法,运用专业断裂分析软件FRANC3D对齿轮齿根裂纹进行了数值分析,模拟求解了齿根椭圆形裂纹的裂尖三种类型的应力强度因子,并且探讨了三种应力强度因子随载荷、裂纹长度、模数、齿数、变位系数、裂纹角度等齿轮参数的变化规律。结果表明:I型、II型应力强度因子的数值在裂纹前缘呈近似于抛物线分布,而III型应力强度因子的数值在裂纹前缘呈近似于正弦曲线分布;应力强度因子随齿面载荷的变化呈线性规律;模数对裂纹两端的II型应力强度因子、裂纹中间的I型和III型应力强度因子影响较小,基本不变;齿数对应力强度因子影响较小,其在不同齿数下的最大差值仅为187 N.m-3/2;变位系数对其影响基本也呈线性变化;裂纹发生角度为60°时,I型应力强度因子比其它角度下的值都要大,因此应尽量避免产生此角度下的裂纹。本文研究为齿轮的断裂分析和寿命预测奠定了一定的基础。

The three dimensional three tooth model of gear is established.Based on linear elastic fatigue mechanics and boundary element method,by using the professional fracture analysis software FRANC3D,the tooth root crack of gear is studied by numerical analysis and the stress intensity factors(SIF) with three types on crack tip of an elliptical crack in tooth root are solved.Then the variation laws of factors with change of load,crack length,modulus,tooth number,modification coefficient and crack angle are discussed.Results obtained show that the distribution of SIF’s value of type I and type II in the crack front is similarly parabolic,while the distribution of SIF’s value of type III in the crack front is similarly sinusoidal.The variation law of SIF’s value with change of the tooth surface load is linear;the effect of tooth number on SIF is smaller;the variation law of SIF’s value with changing the modification coefficient also is similarly linear;When the crack initiation angle is 60°,the SIF’s value is larger than that of other angles,so the crack with 60° should be avoided as far as possible.These results lay a good foundation for fracture analysis and life prediction of gear.