新的柔性结合部法向接触刚度和接触阻尼方程  

New Equations of Normal Contact Stiffness and Damping for Flexible Joint Interface

作　　者：田红亮[1] 赵美云[2] 郑金华[1] 赵春华[1] 赵新泽[1] 方子帆[1] 朱大林[1] 

机构地区：[1]三峡大学机械与动力学院,湖北宜昌443002 [2]三峡大学水电机械设备设计与维护湖北省重点实验室,湖北宜昌443002

出　　处：《西安交通大学学报》2015年第1期118-126,共9页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51275273);三峡大学水电机械设备设计与维护湖北省重点实验室开放基金资助项目(2012KJX02);三峡大学博士科研启动基金资助项目(KJ2012B013)

摘　　要：以修正分形几何学理论和赫兹法向接触力学方程为基础,推导出了柔性结合部法向接触刚度与阻尼方程。假设峰元顶端的曲率半径为变量,提出了一种全新的求导函数而非偏导函数的求解方法,建立了单峰元与平面接触的法向接触刚度方程。数值模拟表明:峰元承担的法向弹性载荷与其顶端的变形量之间符合非线性幂函数凹弧关系;降低表面粗糙度或增加法向接触载荷都将增大实际接触面积;当表面粗糙轮廓分形维数在较小范围内时,实际接触面积随着表面粗糙轮廓分形维数的增加而增大,而当表面粗糙轮廓分形维数在较大范围内时,实际接触面积随着表面粗糙轮廓分形维数的增加而变小;降低表面粗糙度或增加表面粗糙轮廓分形维数与法向接触载荷皆将增加法向接触刚度;法向接触阻尼随着表面粗糙轮廓分形维数的增加先减小后增大;当表面粗糙轮廓分形维数小于临界值时,法向接触阻尼随着分形粗糙度的增大而增大,而当表面粗糙轮廓分形维数超过转折点时,法向接触阻尼随着分形粗糙度的增大而减小;当法向接触载荷增大时,法向接触阻尼略微减小。Equations of normal contact stiffness and damping for flexible joint interface were built up following the modified fractal geometry theory and Hertz normal contact mechanics expression. Supposing the curvature radius at the tip of the asperity is a variable, a completely new calculating method of differential function, not partial differentiable function, was established to solve the normal contact stiffness equation when an asperity contacted a plane. The digital simulation reveals that there is a nonlinear power function concave arc relationship between asperity＇s normal elastic load and its tip deformation. The real contact area may increase by reducing the surface roughness or increasing the normal contact load. The real contact area increases with the fractal dimension of a surface in the smaller fractal dimension of a surface rough profile, while decreases with the fractal dimension of a surface in the larger fractal dimension of a surface rough profile. The normal contact stiffness will increase by reducing the surface roughness or increasing the fractal dimension of a surface rough profile and the normal contact load. The normal contact damping decreases at first and then increases with the increase of the fractal dimension of a surface rough profile. When the fractal dimension of a surface rough profile is less than the critical value, the normal contact damping increases with the fractal roughness. When the fractal dimension of a surface rough profile exceeds the turning point, the normal contact damping will decrease with the fractal roughness. As the normal contact load increases, the normal contact damping decreases slightly.

关 键 词：柔性结合部 法向接触刚度 法向接触阻尼 分形几何学理论 

分 类 号：TH113.1[机械工程—机械设计及理论]