三维分形表面的接触性能研究

发布时间：2018-06-17 05:24

本文选题：粗糙表面 + 分形几何理论　；参考：《西安理工大学》2017年硕士论文

【摘要】：接触问题广泛的存在于工程领域中,所有的微接触表面都不是绝对光滑的,而是由许多几何尺寸不同的微凸体间的接触,接触体之间的真实接触面积远小于宏观设计的名义接触面积,使得较小的真实接触面积承担较大的接触载荷,导致接触体表面的加速失效。为了提高接触元件表面的承载能力和工作的疲劳寿命,本文通过分形几何理论与接触力学相结合的方法,考虑了微凸体的等级范围的影响,对粗糙表面接触特性进行研究。本文以粗糙表面弹塑性接触为主要研究对象。首先基于Weierstrass-Mandelbrot分形函数,对二维和三维分形粗糙表面进行模拟仿真,获得了表面分形维数D越大,粗糙表面形貌越精细;轮廓特征尺度参数G越大,粗糙表面轮廓曲线的高度越大,但轮廓曲线的形状几乎不发生变化。其次,使用双变量的W-M函数来表征三维粗糙表面形貌信息,推导了各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件,结合每一等级微凸体的面积分布密度函数,建立了尺度相关的弹塑性接触模型,获得了三维粗糙表面真实接触面积、法向接触刚度和总的接触载荷之间的关系式。仿真结果表明:粗糙表面的力学性能仅与最小等级及后续的六个等级微凸体相关,其余微凸体对整个粗糙表面的力学性能影响很小。当最小等级及后续的六个等级处于弹性临界等级内,整个粗糙表面表现出近似弹性的力学性能;当最小等级及后续的六个等级微凸体的等级大于第二弹塑性临界等级,整个粗糙表面表现出近似非弹性的力学性能。随后,基于双变量的W-M函数,获得了叠加微凸体的参数,结合海洋岛屿面积分布函数,建立了三维分形粗糙表面弹塑性叠加接触模型,获得了真实接触面积与接触载荷之间的表达式。计算结果表明:叠加微凸体的临界接触面积与微凸体叠加的个数有关,随着微凸体叠加个数的增大,微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与经典的赫兹模型保持一致。当微凸体叠加的个数较多时,粗糙表面近似表现为塑性的力学性能;当微凸体叠加的个数较少时,粗糙表面近似表现为弹性的力学性能,从而解释了以往接触模型中粗糙表面先发生塑性变形再发生弹性变形的原因。最后,使用Leica DCM 3D测量粗糙表面的形貌信息和设计了粗糙表面接触性能试验台,并将试验结果与本文模型的计算结果进行了对比,验证了本模型的合理性与正确性。
[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.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH11

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