本文選題：粗糙表面 + 分形幾何理論��； 參考：《西安理工大學(xué)》2017年碩士論文

【摘要】：接觸問(wèn)題廣泛的存在于工程領(lǐng)域中,所有的微接觸表面都不是絕對(duì)光滑的,而是由許多幾何尺寸不同的微凸體間的接觸,接觸體之間的真實(shí)接觸面積遠(yuǎn)小于宏觀設(shè)計(jì)的名義接觸面積,使得較小的真實(shí)接觸面積承擔(dān)較大的接觸載荷,導(dǎo)致接觸體表面的加速失效。為了提高接觸元件表面的承載能力和工作的疲勞壽命,本文通過(guò)分形幾何理論與接觸力學(xué)相結(jié)合的方法,考慮了微凸體的等級(jí)范圍的影響,對(duì)粗糙表面接觸特性進(jìn)行研究。本文以粗糙表面彈塑性接觸為主要研究對(duì)象。首先基于Weierstrass-Mandelbrot分形函數(shù),對(duì)二維和三維分形粗糙表面進(jìn)行模擬仿真,獲得了表面分形維數(shù)D越大,粗糙表面形貌越精細(xì);輪廓特征尺度參數(shù)G越大,粗糙表面輪廓曲線的高度越大,但輪廓曲線的形狀幾乎不發(fā)生變化。其次,使用雙變量的W-M函數(shù)來(lái)表征三維粗糙表面形貌信息,推導(dǎo)了各等級(jí)微凸體發(fā)生彈性、彈塑性以及完全塑性變形的存在條件,結(jié)合每一等級(jí)微凸體的面積分布密度函數(shù),建立了尺度相關(guān)的彈塑性接觸模型,獲得了三維粗糙表面真實(shí)接觸面積、法向接觸剛度和總的接觸載荷之間的關(guān)系式。仿真結(jié)果表明:粗糙表面的力學(xué)性能僅與最小等級(jí)及后續(xù)的六個(gè)等級(jí)微凸體相關(guān),其余微凸體對(duì)整個(gè)粗糙表面的力學(xué)性能影響很小。當(dāng)最小等級(jí)及后續(xù)的六個(gè)等級(jí)處于彈性臨界等級(jí)內(nèi),整個(gè)粗糙表面表現(xiàn)出近似彈性的力學(xué)性能;當(dāng)最小等級(jí)及后續(xù)的六個(gè)等級(jí)微凸體的等級(jí)大于第二彈塑性臨界等級(jí),整個(gè)粗糙表面表現(xiàn)出近似非彈性的力學(xué)性能。隨后,基于雙變量的W-M函數(shù),獲得了疊加微凸體的參數(shù),結(jié)合海洋島嶼面積分布函數(shù),建立了三維分形粗糙表面彈塑性疊加接觸模型,獲得了真實(shí)接觸面積與接觸載荷之間的表達(dá)式。計(jì)算結(jié)果表明:疊加微凸體的臨界接觸面積與微凸體疊加的個(gè)數(shù)有關(guān),隨著微凸體疊加個(gè)數(shù)的增大,微凸體的高度和峰頂曲率半徑減小。微凸體的變形順序?yàn)閺椥宰冃�、彈塑性變形和完全塑性變�?與經(jīng)典的赫茲模型保持一致。當(dāng)微凸體疊加的個(gè)數(shù)較多時(shí),粗糙表面近似表現(xiàn)為塑性的力學(xué)性能;當(dāng)微凸體疊加的個(gè)數(shù)較少時(shí),粗糙表面近似表現(xiàn)為彈性的力學(xué)性能,從而解釋了以往接觸模型中粗糙表面先發(fā)生塑性變形再發(fā)生彈性變形的原因。最后,使用Leica DCM 3D測(cè)量粗糙表面的形貌信息和設(shè)計(jì)了粗糙表面接觸性能試驗(yàn)臺(tái),并將試驗(yàn)結(jié)果與本文模型的計(jì)算結(jié)果進(jìn)行了對(duì)比,驗(yàn)證了本模型的合理性與正確性。
[Abstract]:The contact problem exists widely in the engineering field. All microcontact surfaces are not absolutely smooth, but by the contact between many microconvex bodies of different geometric sizes. The actual contact area between the contact bodies is much smaller than the nominal contact area of the macroscopic design, which makes the smaller real contact area bear a larger contact load, resulting in the accelerated failure of the contact surface. In order to improve the bearing capacity and fatigue life of contact element surface, the contact characteristics of rough surface are studied by combining fractal geometry theory with contact mechanics and considering the influence of the grade range of micro-convex body. In this paper, the elastoplastic contact of rough surface is the main research object. Firstly, based on the Weierstrass-Mandelbrot fractal function, the 2D and 3D fractal rough surfaces are simulated and simulated. The height of rough surface contour curve is higher, but the shape of rough surface contour curve almost does not change. Secondly, the two-variable W-M function is used to characterize the 3D rough surface topography information, and the conditions for elastic, elastic-plastic and complete plastic deformation of each class of micro-convex bodies are derived, and the area distribution density function of each class of microconvex bodies is given. A scale dependent elastoplastic contact model is established, and the relationship among the true contact area, normal contact stiffness and total contact load of 3D rough surface is obtained. The simulation results show that the mechanical properties of the rough surface are only related to the minimum grade and the following six classes of microconvex bodies, while the other microconvex bodies have little effect on the mechanical properties of the whole rough surface. When the minimum grade and the following six grades are within the elastic critical grade, the whole rough surface shows the mechanical properties similar to elasticity, and when the minimum grade and the following six classes of micro-convex body are larger than the second critical grade of elastoplastic, The whole rough surface shows approximate inelastic mechanical properties. Then, based on the W-M function of two variables, the parameters of the superposed microconvex body are obtained. Combined with the area distribution function of the ocean islands, the elastic-plastic superposition contact model of three-dimensional fractal rough surface is established. The expression between the real contact area and the contact load is obtained. The results show that the critical contact area of the superimposed microconvex body is related to the number of the superimposed microconvex bodies. With the increase of the superposition number of the microconvex bodies, the height of the microconvex bodies and the radius of the peak curvature decrease. The deformation order of the microconvex body is elastic deformation, elastic-plastic deformation and complete plastic deformation, which is consistent with the classical Hertz model. When the number of microconvex superpositions is large, the rough surface approximately shows the mechanical properties of plasticity, and when the number of microconvex superpositions is small, the rough surface approximately shows the elastic mechanical properties. The reason of plastic deformation and then elastic deformation of rough surface in the previous contact model is explained. Finally, the topography information of rough surface was measured by Leica DCM 3D and the contact property test bench of rough surface was designed. The experimental results were compared with the calculated results of this model, and the rationality and correctness of the model were verified.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TH11

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