平行轴圆柱副接触分析

Contact Analysis of Cylindrical Pair with Parallel Axes

将古典赫兹理论与现代Majumdar-Bhushan模型相结合,建立了两圆柱分形接触模型。考虑结合部虚拟材料厚度,以及引入圆柱接触面积比,对两圆柱线高副矩形接触面进行了受力分析。数值仿真表明:圆柱接触面积比不大于1;外接触时圆柱接触面积比小于内接触时;增加总载荷或减小结合部虚拟材料厚度都将增大圆柱接触面积比;外接触时实际接触面积小于内接触时;实际接触面积随着分形粗糙度、材料硬度或结合部虚拟材料厚度的增加而减小;随着分形粗糙度的增加,产生特定实际接触面积所需要的总载荷增加,微凸体变形量增大;对于给定总载荷,当分形维数从1.4增加到1.5时,实际接触面积相应增大,但当分形维数从1.5增加到1.9时,实际接触面积转而减小;内接触时的赫兹应力小于外接触时的赫兹应力。该研究结果可为进一步研究圆柱齿轮传动的齿面接触疲劳强度计算提供参考。

A fractal contact model between two cylinders was set up through combining classic Hertzian theory and modern Majumdar-Bhushan model.The force acting on the linear higher pair rectangular contact plane of two cylinders was analyzed considering the virtual material thickness of joint interface and introducing the cylindrical contact area ratio.Numerical simulation shows that the cylindrical contact area ratio is not greater than one,and the ratio of outer contact is less than that of inner contact.This cylindrical contact area ratio can be increased by increasing the total load or reducing the virtual material thickness of joint interface.The real contact area in exterior contact is less than that in interior contact.As the fractal roughness,material hardness or virtual material thickness of joint interface increases,the real contact area decreases.When the fractal roughness is increased,the total load required to produce a particular real contact area also increases,which results from the fact that an increase in fractal roughness implies an increase in asperity deformation,hence a higher load is required.As the fractal dimension is increased from1.4to 1.5,the real contact area first increases under a given total load.However,if the value of fractal dimension is increased from 1.5to 1.9,the real contact area decreases.The Hertzian stress in internal contact is less than that in external contact.These results may provide a basisfor the fatigue strength computation of gear surface contact in cylindrical gear transmission.