分形理论在摩擦学系统中的应用研究
发布时间：2018-11-28 20:23
【摘要】：针对一类分形特征曲面Hausdorff维数较难求解的问题,利用自仿射迭代函数系统(IFS)的吸引子理论以及分形插值曲线的维数理论,得出局部与全局自相似和局部与局部自相似类分形曲面的Hausdorff维数求解方法,进而丰富了曲面的维数值求解研究思想且为其奠定理论基础.针对研究静摩擦因数侧重于采用实验仪器进行考查的现状,因其未能够揭示摩擦机理.依据分形理论,构建了求解分形盒维数D的简便途径和表示分形粗糙度尺度参数G的函数表达式,在现有运用W-M函数刻画粗糙面轮廓曲线的基础上,根据分形插值理论对接触粗糙面轮廓曲线进行校正.由接触面受力分析,得出静摩擦因数影响因子μ*的表达式.通过数值仿真模拟得出维数对静摩擦因数μ的影响关系,为摩擦学的研究提供数学理论支持.对路面分形特征和轮胎黏弹性分析,提出轮胎啮合维数理论.进而建立改进滑动摩擦因数模型,与Savkoor滑动摩擦因数对比,验证了模型可靠性.由数值仿真模拟分析了不同分形维数路况和不同特性的轮胎对滑动摩擦因数的影响规律.结果表明：模型可以较好地表现各种分形维数值路面与轮胎黏弹特性对滑动摩擦因数的作用规律,从而为研究较为复杂的摩擦系统提供数学理论基础.
[Abstract]:Aiming at the problem that the Hausdorff dimension of a class of fractal characteristic surfaces is difficult to solve, the attractor theory of self-affine iterative function system (IFS) and the dimension theory of fractal interpolation curve are used. The Hausdorff dimension method of local and global self-similarity and local self-similar fractal surfaces is obtained, which enriches the research idea of dimensional numerical solution of surfaces and lays a theoretical foundation for them. In view of the present situation that the static friction coefficient is mainly studied by means of experimental instruments, it can not reveal the friction mechanism. Based on the fractal theory, a simple way to solve the fractal box dimension D and a functional expression to represent the fractal roughness parameter G are constructed. The W-M function is used to depict the rough surface contour curve. The contours of contact rough surface are corrected according to fractal interpolation theory. The expression of the influence factor 渭 * of the static friction coefficient is obtained from the analysis of the force on the contact surface. The influence of dimension on static friction coefficient 渭 is obtained by numerical simulation, which provides mathematical theory support for tribology research. The theory of meshing dimension of tire is put forward based on the fractal characteristics of pavement and the analysis of tire viscoelasticity. Then the improved sliding friction coefficient model is established and compared with the Savkoor sliding friction coefficient to verify the reliability of the model. The influence of different fractal dimension road conditions and different characteristics on sliding friction coefficient is analyzed by numerical simulation. The results show that the model can well represent the effect of the viscoelastic properties of various fractal dimensions of pavement and tire on the sliding friction coefficient, thus providing a mathematical theoretical basis for the study of more complex friction systems.
【学位授予单位】：辽宁工程技术大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O313.5;O189
本文编号：2364161
[Abstract]:Aiming at the problem that the Hausdorff dimension of a class of fractal characteristic surfaces is difficult to solve, the attractor theory of self-affine iterative function system (IFS) and the dimension theory of fractal interpolation curve are used. The Hausdorff dimension method of local and global self-similarity and local self-similar fractal surfaces is obtained, which enriches the research idea of dimensional numerical solution of surfaces and lays a theoretical foundation for them. In view of the present situation that the static friction coefficient is mainly studied by means of experimental instruments, it can not reveal the friction mechanism. Based on the fractal theory, a simple way to solve the fractal box dimension D and a functional expression to represent the fractal roughness parameter G are constructed. The W-M function is used to depict the rough surface contour curve. The contours of contact rough surface are corrected according to fractal interpolation theory. The expression of the influence factor 渭 * of the static friction coefficient is obtained from the analysis of the force on the contact surface. The influence of dimension on static friction coefficient 渭 is obtained by numerical simulation, which provides mathematical theory support for tribology research. The theory of meshing dimension of tire is put forward based on the fractal characteristics of pavement and the analysis of tire viscoelasticity. Then the improved sliding friction coefficient model is established and compared with the Savkoor sliding friction coefficient to verify the reliability of the model. The influence of different fractal dimension road conditions and different characteristics on sliding friction coefficient is analyzed by numerical simulation. The results show that the model can well represent the effect of the viscoelastic properties of various fractal dimensions of pavement and tire on the sliding friction coefficient, thus providing a mathematical theoretical basis for the study of more complex friction systems.
【学位授予单位】：辽宁工程技术大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O313.5;O189
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