Contact Problem Between Two Spheres Considering Surface Roughness and Geometrical Curvature

doi:10.7652/xjtuxb201603001

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Contact Problem Between Two Spheres Considering Surface Roughness and Geometrical Curvature

更新时间：2025-07-09

- Contact Problem Between Two Spheres Considering Surface Roughness and Geometrical Curvature
- Vol. 50, Issue 3, Pages: 1-7+44(2016)
- 作者机构：
  
  三峡大学机械与动力学院,湖北,宜昌,443002
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201603001
  CLC： TH113.1
- Online First：10 March 2016，
  
  Published：2016
- 稿件说明：
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Contact Problem Between Two Spheres Considering Surface Roughness and Geometrical Curvature[J]. 2016, 50(3): 1-7+44.
DOI：

Contact Problem Between Two Spheres Considering Surface Roughness and Geometrical Curvature[J]. 2016, 50(3): 1-7+44. DOI： 10.7652/xjtuxb201603001.

摘要

为探讨曲面结合面的接触机理

研究了两球体的法向接触问题。计入结合面虚拟材料厚度

对两球体点高副接触时形成的圆形接触区域进行了受力分析

在分析过程中尝试联合Majumdar-Bhushan平面模型和经典赫兹理论; 采用Hardy在任一点处处不可求导的条件

严格证明了二维Weierstrass-Mandelbrot分形函数中分形维数D的整个取值范围为1≤D<2。数值模拟表明:球体广义接触面积比不大于1; 内接触时的球体广义接触面积比大于外接触时的

增加压紧力或减小结合面虚拟材料厚度均会增大球体广义接触面积比; 内接触时的真实接触面积大于外接触时的

真实接触面积随着分形粗糙度、材料硬度或结合面虚拟材料厚度的增加而减小; 随着分形粗糙度的增加

产生指定真实接触面积所需要的压紧力增加; 当分形粗糙度增加时

微凸体的法向变形量和压紧力增大; 对于给定的压紧力

当分形维数从1.4增加至1.5时

狭义接触面积比随之增加

当分形维数从1.5增加至1.9时

狭义接触面积比逐渐减小; 内接触时的赫兹应力小于外接触时的。此项研究可为深入研究滚动轴承中球轴承的接触强度计算提供基础

所建立的球体接触分形模型具备通用性与实用性

可望丰富机械设计中机械零件接触强度的理论。

Abstract

The normal contact problem of two spheres was studied to investigate the contact regime of curvature joint interface. The force applied to the circular contact region formed by the point higher pair contact of two spheres was analyzed through utilizing the virtual material thickness of joint interface. The Majumdar-Bhushan plane model and classic Hertz theory were combined in the analysis. It was demonstrated that the entire definite range of fractal dimension satisfies 1≤D<2 in the two-dimensional Weierstrass-Mandelbrot fractal function by adopting Hardy's non-differentiable condition at a point anywhere. Numerical simulation exhibits that the spherical generalized contact area ratio is not greater than one. The spherical generalized contact area ratio in inner contact is larger than that of outer contact. The spherical generalized contact area ratio may increase by increasing the compressive force or reducing the virtual material thickness of joint interface. The true contact area in internal contact is higher than it in external contact. As the fractal roughness

material hardness or virtual material thickness of joint interface increases

the true contact area decreases. As the fractal roughness increases

the compressive force required to produce a specified true contact area increases. This accounts for the fact that an increase in the fractal roughness implies an increase in microcontact's normal deformation

which therefore requires a higher compressive force. As the value of fractal dimension increases from 1.4 to 1.5

the actual contact area first increases for a given compressive force. As the value of fractal dimension increases from 1.5 to 1.9

the true contact area decreases. The Hertz stress in internal contact is smaller than that in external contact. These research findings may provide a basis for further research on the contact strength calculation of spherical bearing. The spherical contact fractal model possesses the universality and practicality to expand the mechanical part contact strength theory in machine design.

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references

HERTZ H. Über die berührung fester elastischer körper [J]. J Reine und Angewandte Mathematik, 1882, 92: 156-171.

GREENWOOD J A, WILLIAMSON J B P. Contact of nominally flat surfaces [J]. Proceedings of the Royal Society of London: Series A Mathematical and Physical Sciences, 1966, 295(1442): 300-319.

CHANG W R, ETSION I, BOGY D B. An elastic-plastic model for the contact of rough surfaces [J]. ASME Journal of Tribology, 1987, 109(2): 257-263.

CHANG W R, ETSION I, BOGY D B. Adhesion model for metallic rough surfaces [J]. ASME Journal of Tribology, 1988, 110(1): 50-56.

CHANG W R, ETSION I, BOGY D B. Static friction coefficient model for metallic rough surfaces [J]. ASME Journal of Tribology, 1988, 110(1): 57-63.

MAJUMDAR A, BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces [J]. ASME Journal of Tribology, 1991, 113(1): 1-11.

ZHAO Yongwu, MAIETTA D M, CHANG L. An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow [J]. ASME Journal of Tribology, 2000, 122(1): 86-93.

YANG J, KOMVOPOULOS K. A mechanics approach to static friction of elastic-plastic fractal surfaces [J]. ASME Journal of Tribology, 2005, 127(2): 315-324.

JIANG Shuyun, ZHENG Yunjian, ZHU Hua. A contact stiffness model of machined plane joint based on fractal theory [J]. ASME Journal of Tribology, 2010, 132(1): 011401.

ZHANG Xueliang, WANG Nanshan, LAN Guosheng, et al. Tangential damping and its dissipation factor models of joint interfaces based on fractal theory with simulations [J]. ASME Journal of Tribology, 2014, 136(1): 011704.

尤晋闽, 陈天宁. 悬臂梁平面结合面参数的识别技术研究 [J]. 西安交通大学学报, 2008, 42(11): 1323-1326.

YOU Jinmin, CHEN Tianning. Parameters identification for joint surfaces of cantilever beam [J]. Journal of Xi'an Jiaotong University, 2008, 42(11): 1323-1326.

张学良, 温淑花, 兰国生, 等. 平面结合面切向接触阻尼分形模型及其仿真 [J]. 西安交通大学学报, 2011, 45(5): 74-77, 136.

ZHANG Xueliang, WEN Shuhua, LAN Guosheng, et al. Fractal model for tangential contact damping of plane joint interfaces with simulation [J]. Journal of Xi'an Jiaotong University, 2011, 45(5): 74-77, 136.

黄康, 赵韩, 陈奇. 两圆柱体表面接触承载能力的分形模型研究 [J]. 摩擦学学报, 2008, 28(6): 529-533.

HUANG Kang, ZHAO Han, CHEN Qi. Research of fractal contact model on contact carrying capacity of two cylinders' surface [J]. Tribology, 2008, 28(6): 529-533.

陈奇, 黄康, 张彦, 等. 两任意轮廓弹性体接触应力计算的分形模型研究 [J]. 机械强度, 2012, 34(4): 557-561.

CHEN Qi, HUANG Kang, ZHANG Yan, et al. Research on fractal model of calculating the contact stress about two elastic body with arbitrary profile [J]. Journal of Mechanical Strength, 2012, 34(4): 557-561.

田红亮, 刘芙蓉, 方子帆, 等. 引入各向同性虚拟材料的固定结合部模型 [J]. 振动工程学报, 2013, 26(4): 561-573.

TIAN Hongliang, LIU Furong, FANG Zifan, et al. Immovable joint surface's model using isotropic virtual material [J]. Journal of Vibration Engineering, 2013, 26(4): 561-573.

TIAN Hongliang, LI Bin, LIU Hongqi, et al. A new method of virtual material hypothesis-based dynamic modeling on fixed joint interface in machine tools [J]. Elsevier International Journal of Machine Tools Manufacture, 2011, 51(3): 239-249.

HARDY G H. Weierstrass's non-differentiable function [J]. Transactions of the American Mathematical Society, 1916, 17(3): 301-325.

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Related Institution

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