齿根三维粗糙表面的应力集中系数计算研究

考虑粗糙表面影响因素的齿轮齿根处应力集中系数计算是齿轮弯曲疲劳寿命精准预估的难题，以磨削喷丸后的直齿轮为研究对象，研究粗糙表面下的齿根应力与应力集中计算问题。采用白光干涉仪Wyko NT9100对磨削喷丸齿根粗糙表面进行测量，得到粗糙表面形貌数据，基于空间坐标变换原理，使用Python对有限元软件进行二次开发，通过调整齿根细化网格节点坐标实现了齿根表面粗糙形貌的添加工作，建立了齿根过渡曲面三维粗糙表面有限元模型并进行仿真分析。通过数值计算得到三维粗糙表面参数下的齿根应力分布与应力集中系数，对粗糙表面参数与应力集中系数的关联规律进行非线性回归分析，建立粗糙表面参数与应力集中系数的关联规律。结果表明，粗糙表面参数S_a、S_v、S_10z拟合应力集中系数得到拟合公式的相关系数分别为0.799，0.784，0.914，十点区域高度参数S_10z能较好地表征齿根表面的应力集中。

Stress Concentration Calculation Factor of Tooth Root with 3D Rough Profile

The calculation of the stress concentration factor in the tooth root of the gear considering the influence of the rough surface is a difficult problem in accurately predicting the bending fatigue life of the gear. The ground and shot peened spur gear as the research object to study the root stress and stress concentration under the rough surface of tooth root. The white light interferometer Wyko NT9100 is used to measure the rough surface of the ground and shot peened tooth root, and the rough surface topography data is obtained. Based on the principle of space coordinate transformation, the finite element software is redeveloped by using Python, adjusting the coordinates of the tooth root refined mesh nodes, the rough topography of the tooth root surface is added, and the 3D rough surface finite element model of the tooth root transition surface is established and simulated. Through numerical calculation, the root stress distribution and stress concentration factor under 3D rough surface parameters are obtained, and the correlation law between rough surface parameters and stress concentration factor is performed nonlinear regression analysis, and the correlation law between rough surface parameters and stress concentration factor is established. The results show that the correlation coefficients of the fitting formulas obtained by fitting the rough surface parameters S_a, S_v, S_10z and stress concentration coefficients are 0.799, 0.784, 0.914, respectively. The ten-point region height parameter can better characterize the stress concentration on the tooth root surface.