两弹塑性非赫兹接触粗糙表面温升的分形模型

Fractal Model of Temperature Rise Between Two Elastoplastic NonHertz Contact Rough Surfaces

针对赫兹接触理论存在的3个缺陷,考虑表面粗糙度和塑性变形,适当处理接触物体交界面处的摩擦,将赫兹接触理论以更符合实际的方式推广到滑动接触.采用球形微凸体的赫兹接触理论和MB修正模型,对微接触点的温升进行了分析,得到了低速滑动区域内的分形区域实际接触面积温升的补充累积概率分布函数的封闭形式表达式.分析结果表明:分形区域的最大温升随滑动速度增大而线性增大,非零域随滑动速度增大而扩展.对于固定的量纲一分形粗糙度参数,最大温升随分形维数增大而减小;对于固定的分形维数,最大温升随量纲一分形粗糙度参数增大而增大.温升的补充累积概率分布函数随滑动速度增大而增大,随分形维数增大或量纲一分形粗糙度参数减小而减小.平均温升为最大温升的0.402 3倍,温升的标准差为最大温升的0.24倍.

The Hertz contact theory has 3 shortcomings. Surface roughness and plastic deformation considered, a proper treatment of friction at the interface of bodies in contact has enabled the Hertz contact theory to be extended to slipping contact in a more realistic way. The microcontact temperature rises were analyzed in light of the Hertz contact theory for spherical asperity tips and MB modified model. A closed form expression for the complementary cumulative probability distribution function of the temperature rise at the real contact area of a fractal domain was deduced for the slow sliding region. The analytical results indicate that when the sliding speed increases, the maximum temperature rise of a fractal regime linearly increases; the nonzero domain expands as the sliding velocity increases. For fixed dimensionless fractal roughness parameter, when the fractal dimension increases the maximum temperature rise decreases; while for fixed fractal dimension, when the dimensionless fractal roughness parameter increases, it results in a higher maximum temperature rise. When the sliding speed increases, the complementary cumulative probability distribution function of the temperature rise increases; and when the fractal dimension increases, or the dimensionless fractal roughness parameter decreases, it decreases. The average value and standard deviation of the temperature rise are 0. 4023 and 0.24 times the maximum temperature rise, respectively.