基于分形理论的圆弧齿轮滑动摩擦接触力学模型

Sliding Friction Contact Mechanics Model of the Involute Arc Cylindrical Gear Based on Fractal Theory

考虑到圆弧齿线圆柱齿轮传动接触之间的滑动摩擦与微凸体的连续性变形,结合分形理论和Hertz接触理论建立圆弧齿线圆柱齿轮的滑动摩擦接触力学模型,通过模型数值分析与ANSYS WORKBENCH分析的最大接触应力结果对比,证明该模型所反映圆弧齿线圆柱齿轮接触应力状态的正确性。该模型中,载荷与真实接触面积之间关系不仅与分形维数和特征尺度系数有关,还与齿轮节点曲率和齿轮齿线半径有关。同时,理论计算表明,分形维数一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着分形维数的增大先增大后减小,随着特征尺度系数的增大而减小;摩擦因数对真实接触面积的影响不大。该模型的建立为圆弧齿线圆柱齿轮工作状态的研究及强度分析提供了理论依据。

Considering the continuity of deformation and sliding friction between the contacts of involute arc cylindrical gear,a new sliding frictional fractal contact model of two involute arc cylindrical gears is set up through combining the fractal contact model and Hertz contact model.It proves that the frictional fractal contact model is correct by comparing ANSYS WORKBENCH results with the numerical analysis of fractal model.The model shows that relationship between the load and the real contact area is not only affected by the characteristic length scale and fractal dimension,but also by the contact radius and tooth line radius.Meanwhile,Theoretical calculation results show that real contact area increases with the increases of the load when the surface topography is affeeted constant.Contact area decreases with the increases of characteristic length scale,and increases at first and then decreases with the increases of fractal dimension when the load is constant.Friction factor has a little influence on real contact area.The contact mechanics model provides a foundation for study of the working style and strength analysis.