【摘要】：針對(duì)一類分形特征曲面Hausdorff維數(shù)較難求解的問(wèn)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(jìn)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(chǔ).針對(duì)研究靜摩擦因數(shù)側(cè)重于采用實(shí)驗(yàn)儀器進(jìn)行考查的現(xiàn)狀,因其未能夠揭示摩擦機(jī)理.依據(jù)分形理論,構(gòu)建了求解分形盒維數(shù)D的簡(jiǎn)便途徑和表示分形粗糙度尺度參數(shù)G的函數(shù)表達(dá)式,在現(xiàn)有運(yùn)用W-M函數(shù)刻畫粗糙面輪廓曲線的基礎(chǔ)上,根據(jù)分形插值理論對(duì)接觸粗糙面輪廓曲線進(jìn)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(dá)式.通過(guò)數(shù)值仿真模擬得出維數(shù)對(duì)靜摩擦因數(shù)μ的影響關(guān)系,為摩擦學(xué)的研究提供數(shù)學(xué)理論支持.對(duì)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(jìn)而建立改進(jìn)滑動(dòng)摩擦因數(shù)模型,與Savkoor滑動(dòng)摩擦因數(shù)對(duì)比,驗(yàn)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(duì)滑動(dòng)摩擦因數(shù)的影響規(guī)律.結(jié)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(duì)滑動(dòng)摩擦因數(shù)的作用規(guī)律,從而為研究較為復(fù)雜的摩擦系統(tǒng)提供數(shù)學(xué)理論基礎(chǔ).
[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(xué)位授予單位】：遼寧工程技術(shù)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O313.5;O189

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 馮志剛;黃艷麗;;基于分形插值函數(shù)的分形插值曲面的變差與計(jì)盒維數(shù)[J];工程數(shù)學(xué)學(xué)報(bào);2012年03期

2 杜玉坤;曾春燕;;關(guān)于測(cè)度的Hausdorff維數(shù)的局部化[J];純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué);2012年02期

3 熊瑛;奚李峰;;滿足開(kāi)集條件的自相似集的Lipschitz等價(jià)[J];數(shù)學(xué)年刊A輯(中文版);2012年01期

4 王宏勇;樊昭磊;;具有函數(shù)縱向尺度因子的分形插值函數(shù)的分析特性[J];數(shù)學(xué)學(xué)報(bào);2011年01期

5 王宏勇;馬麗;;基于縱向尺度因子變化的分形插值函數(shù)誤差分析[J];廈門大學(xué)學(xué)報(bào)(自然科學(xué)版);2009年05期

6 陳咸存;阮火軍;郭秋麗;;仿射分形插值函數(shù)與縱向尺度因子[J];高校應(yīng)用數(shù)學(xué)學(xué)報(bào)A輯;2007年02期

7 周長(zhǎng)江;唐進(jìn)元;鐘志華;吳長(zhǎng)德;;齒輪傳動(dòng)齒面摩擦因數(shù)計(jì)算方法的研究[J];潤(rùn)滑與密封;2006年10期

8 侯根良;蘇勛家;徐可為;喬小平;王延斌;;高載荷條件下的材料表面摩擦因數(shù)測(cè)量[J];潤(rùn)滑與密封;2006年07期

9 王順;胡元中;王文中;王慧;;潤(rùn)滑點(diǎn)接觸粗糙表面滑動(dòng)摩擦因數(shù)的實(shí)驗(yàn)研究[J];潤(rùn)滑與密封;2006年07期

10 朱華,葛世榮;摩擦力和摩擦振動(dòng)的分形行為研究[J];摩擦學(xué)學(xué)報(bào);2004年05期

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