【摘要】：針對一類分形特征曲面Hausdorff維數(shù)較難求解的問題,利用自仿射迭代函數(shù)系統(tǒng)(IFS)的吸引子理論以及分形插值曲線的維數(shù)理論,得出局部與全局自相似和局部與局部自相似類分形曲面的Hausdorff維數(shù)求解方法,進而豐富了曲面的維數(shù)值求解研究思想且為其奠定理論基礎.針對研究靜摩擦因數(shù)側重于采用實驗儀器進行考查的現(xiàn)狀,因其未能夠揭示摩擦機理.依據分形理論,構建了求解分形盒維數(shù)D的簡便途徑和表示分形粗糙度尺度參數(shù)G的函數(shù)表達式,在現(xiàn)有運用W-M函數(shù)刻畫粗糙面輪廓曲線的基礎上,根據分形插值理論對接觸粗糙面輪廓曲線進行校正.由接觸面受力分析,得出靜摩擦因數(shù)影響因子μ*的表達式.通過數(shù)值仿真模擬得出維數(shù)對靜摩擦因數(shù)μ的影響關系,為摩擦學的研究提供數(shù)學理論支持.對路面分形特征和輪胎黏彈性分析,提出輪胎嚙合維數(shù)理論.進而建立改進滑動摩擦因數(shù)模型,與Savkoor滑動摩擦因數(shù)對比,驗證了模型可靠性.由數(shù)值仿真模擬分析了不同分形維數(shù)路況和不同特性的輪胎對滑動摩擦因數(shù)的影響規(guī)律.結果表明：模型可以較好地表現(xiàn)各種分形維數(shù)值路面與輪胎黏彈特性對滑動摩擦因數(shù)的作用規(guī)律,從而為研究較為復雜的摩擦系統(tǒng)提供數(shù)學理論基礎.
[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.
【學位授予單位】：遼寧工程技術大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O313.5;O189

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