基于泛形理论机械结合面法向接触刚度的表征

Study on representation of contact stiffness based on mechanical junction surface of ubiquitiform theory

泛形理论是继混沌理论、分形理论及孤立子理论之后新发展出来的一种非线性理论方法。依据激光共聚焦显微镜测试得到的粗糙表面的轮廓形貌,应用计盒法计算了粗糙表面轮廓形貌的泛形复杂度;根据所得结果绘制了度量尺码与测度在双对数坐标下的规律变化图,取线性拟合度最好区域为微凸体尺度自相似区间;最后基于微凸体尺度的上下限参数建立了粗糙表面形貌表征的接触刚度模型。研究表明:在泛形复杂度一定的情况下,结合面法向接触刚度随着法向载荷的增大而增大,二者表现为非线性关系;泛形复杂度越大,结合面法向接触刚度越大。研究结果可为现代高精度机床设计提供理论参考。

Succeeding chaos theory,fractal theory and soliton theory,ubiquitiform theory is a new nonlinear theoretical method.According to the rough surface profile measured by laser confocal microscope,the generalized complexity of rough surface profile was calculated by box counting method.According to the obtained results,the regular variation diagrams of measurement and measure in logarithmic coordinates were drawn,and the best region of linear fitting degree was the self-similarity region of micro-convex body scale.Finally,the contact stiffness model of rough surface was established based on the upper and lower limits of ubiquitiform scale parameters.The results show that the normal contact stiffness of the interface increases with the increase of the normal load when the complexity of the ubiquitiform is constant,and the relationship between them is nonlinear.The greater the complexity of the ubiquitiform,the greater the normal contact stiffness of the interface.The conclusion of this paper can provide theoretical reference for design of modern high-precision machine too.