基于分形几何重构与侧向接触力学模型的弹性微凸体分层次接触仿真方法

doi:10.3901/JME.2018.15.117

机械工程学报 ›› 2018, Vol. 54 ›› Issue (15): 117-124.doi: 10.3901/JME.2018.15.117

基于分形几何重构与侧向接触力学模型的弹性微凸体分层次接触仿真方法

陈鼎, 侯亮, 郭腾鹏

厦门大学机电工程系厦门 361000

收稿日期:2017-08-11 修回日期:2017-12-15 出版日期:2018-08-05 发布日期:2018-08-05
通讯作者: 侯亮(通信作者),男,1974年出生,博士,教授,博士研究生导师。主要研究方向为复杂机电装备产品的大批量定制与创新设计、振动与噪声控制、预测与健康管理。E-mail:hliang@xmu.edu.cn
作者简介:陈鼎,男,1985年出生,博士研究生。主要研究方向为粗糙界面接触、分形理论应用、车辆动力学。E-mail:dingcr8@163.com
基金资助:
厦门市“十三五”国家海洋经济创新发展区域示范（16CZB033SF14）和福建省高端装备制造协同创新中心资助项目。

Hierarchical Contact Simulation for Elastic Asperity Based on Fractal Geometry Reconstruction and Lateral Contact Model

CHEN Ding, HOU Liang, GUO Tengpeng

Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361000

Received:2017-08-11 Revised:2017-12-15 Online:2018-08-05 Published:2018-08-05

摘要/Abstract

摘要： 依据分形几何重构与弹性微凸体侧向接触的研究基础，提出两者相结合的分层次仿真方法，并用于确定弹性微凸体的法向载荷与接触面积，法向变形量与切向载荷之间的关系，以及进一步讨论并分析了不同分形维数对接触矢量角和侧向接触特性的影响。结果表明，分层次接触的仿真过程具有描述低层级中一对微凸体侧向接触数、接触矢量和接触面积向高层级粗糙面传递和累计的能力；随着高层级粗糙面载荷的变化，低层级中的一对微凸体展现出不同的接触面积与载荷区间，并具有向相应弹性极限值变化的趋势；随着粗糙面分形维数的增大，微凸体的侧向接触矢量角的幅值呈线性下降，但平均值呈非线性降低；当分形维数大于2.4时，极窄的幅值范围以及接近于π/2的接触矢量角使得微凸体间可以近似为完全法向接触。

关键词: 侧向接触, 弹性微凸体, 分层次仿真, 分形几何, 接触矢量角

Abstract: Based on the research foundation of fractal geometry reconstruction and elastic asperity lateral contact model, a hierarchical simulation method is established and used to determine the relationship between normal load and contact area, and the relationship between normal deformation and tangential load of the discrete asperities. On this basis, the influence of different fractal dimensions on the contact vector angle and the lateral contact characteristics of the asperity is further considered. The simulation results show that the hierarchical simulation has the ability to describe the transfer of contact number, contact vector and contact area between asperities from low-level region to a high-level rough surface. With the change of the high-level regional load, discrete asperities on the low-level exhibit different contact areas and load intervals, and have a tendency to change to the corresponding elastic critical value. With the increase of the fractal dimension of the rough surface, the amplitude of the lateral contact vector angle decreases linearly, and its mean value decreases nonlinearly. When the fractal dimension is greater than 2.4, the contact between asperities is approximated to complete normal contact due to the extremely narrow amplitude range and contact angle which is close to π/2.

Key words: elastic asperity, fractal geometry, hierarchical simulation, lateral contact, vector angle

中图分类号:

TH113

陈鼎, 侯亮, 郭腾鹏. 基于分形几何重构与侧向接触力学模型的弹性微凸体分层次接触仿真方法[J]. 机械工程学报, 2018, 54(15): 117-124.

CHEN Ding, HOU Liang, GUO Tengpeng. Hierarchical Contact Simulation for Elastic Asperity Based on Fractal Geometry Reconstruction and Lateral Contact Model[J]. Journal of Mechanical Engineering, 2018, 54(15): 117-124.

参考文献

[1] 李玲,蔡安江,蔡力钢,等. 螺栓结合面微观接触模型[J]. 机械工程学报,2016,52(7):205-212. LING Ling,CAI Aajiang,CAI Ligang,et al. Micro-contact model of bolted-joint interface[J]. Journal of Mechanical Engineering,2016,52(7):205-212.
[2] LEE Y,LIU Y,BARBER J R,et al. Thermal considerations during transient asperity contact[J]. Tribology International,2016,94:87-91.
[3] 胡琼,孙见君,马晨波,等. 基于微凸体侧接触模型的机械密封端面混合摩擦热理论预测[J]. 机械工程学报,2017,53(21):102-108. HU Qiong,SUN Jianjun,MA Chenbo,et al. Theoretical prediction of mixed frictional heat of mechanical seals based on shoulder-shoulder contact model of asperities[J]. Journal of Mechanical Engineering,2017,53(21):102-108.
[4] 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.
[5] STANLEY H M,KATO T. An FFT-besed method for rough surface contact[J]. Journal of Tribology,1997,119(3):481-485.
[6] ALMQVIST A,SAHLIN F,LARSSON R,et al. On the dry elasto-plastic contact of nominally flat surfaces[J]. Tribology International,2007,40(4):574-579.
[7] MAJUMDAR A,BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology,1991,113(1):1-11.
[8] BERRY M V,LEWIS Z V. On the Weierstrass- Mandelbrot fractal function[J]. Proceedings of the Royal Society of London,1980,370(1743):459-484.
[9] MANDELBROT B B. The fractal geometry of nature[M]. US:W.H. Freeman Co.,1983.
[10] AUSLOOS M,BERMAN D H. A Multivariate Weierstrass-Mandelbrot Function[J]. Proceedings of the Royal Society of London,1985,400(1819):331-350.
[11] YAN W,KOMVOPOULOS K. Contact analysis of elastic-plastic fractal surfaces[J]. Journal of Applied Physics,1998,84(7):3617-3624.
[12] KOGUT L,ETSION I. A semi-analytical solution for the sliding inception of a spherical contact[J]. Journal of Tribology,2003,125(3):499-506.
[13] BRIZMER V,KLIGERMAN Y,ETSION I. Elastic-plastic spherical contact under combined normal and tangential loading in full stick[J]. Tribology Letters,2007,25(1):61-70.
[14] SEPEHRI A,FARHANG K. On elastic interaction of nominally flat rough surfaces[J]. Journal of Tribology,2008,130(1):125-128.
[15] 赵永武,吕彦明,蒋建忠. 新的粗糙表面弹塑性接触力学模型[J]. 机械工程学报,2007,43(3):95-101. ZHAO Yongwu,LÜ Yanming,JIANG Jianzhong. New elastic-plastic model for the contact of rough surfaces[J]. Chinese Journal of Mechanical Engineering,2007,43(3):95-101.
[16] ZHAO Y,MAIETTA DM,CHANG L. An Asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow[J]. Journal of Tribology,2000, 122(1):86-93.
[17] 杨红平,傅卫平,王雯,等. 基于分形几何与接触力学理论的结合面法向接触刚度计算模型[J]. 机械工程学报,2013,49(1):102-107. YANG Hongping,FU Weiping,WANG Wen,et al. Calculation model of the normal contact stiffness of joints based on the fractal geometry and contact theory[J]. Journal of Mechanical Engineering,2013,49(1):102-107.
[18] JIANG Shuyun,ZHENG Yunjian,ZHU Hua. A contact stiffness model of machined plane joint based on fractal theory[J]. Journal of Tribology,2010,132(1):0114011-7.
[19] 高志强,傅卫平,王雯,等. 弹塑性微凸体侧向接触相互作用能耗[J]. 力学学报,2017,49(4):858-869. GAO Zhiqiang,FU Weiping, WANG Wen,et al. The contact energy dissipation of the lateral and interactional between the elastic-plastic asperities[J]. Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):858- 869.
[20] HANAOR D A H,GAN Y,EINAV I. Static friction at fractal interfaces[J]. Tribology International,2016,93:229-238.
[21] MORAG Y,ETSION I. Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces[J]. Wear,2007,262(5-6):624-629.
[22] KOGUT L,ETSION I. Elastic-plastic contact analysis of a sphere and a rigid flat[J]. ASME Journal of Applied Mechanics,2002,69(5):657-662.

基于分形几何重构与侧向接触力学模型的弹性微凸体分层次接触仿真方法

Hierarchical Contact Simulation for Elastic Asperity Based on Fractal Geometry Reconstruction and Lateral Contact Model

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

编辑推荐

Metrics

本文评价

[1]	周诗杰, 阿达依·谢尔亚孜旦. 摩擦副表面微观动压效应集成、传递及影响的研究[J]. 机械工程学报, 2018, 54(21): 120-126.
[2]	田红亮, 董元发, 余媛, 张屹, 陈甜敏, 郑金华. 机床地脚低速滑动界面法向刚度分形模型及试验验证[J]. 机械工程学报, 2017, 53(17): 172-184.
[3]	田红亮;钟先友;秦红玲;赵春华;方子帆;朱大林;陈保家;张发军. 依据各向异性分形几何理论的固定结合部法向接触力学模型[J]. , 2013, 49(21): 108-122.
[4]	杨红平;傅卫平;王雯;杨世强;李鹏阳;王伟. 基于分形几何与接触力学理论的结合面法向接触刚度计算模型[J]. , 2013, 49(1): 102-107.
[5]	周超;高诚辉. 基于离散傅里叶变换的分形粗糙表面轮廓合成与研究[J]. , 2011, 47(17): 99-103.
[6]	刘天雄;华宏星;李中付;陈兆能;朱继海. 基于分形几何状态监测方法的应用研究[J]. , 2001, 37(5): 100-104.
[7]	陈国安;葛世荣. 基于分形理论的磨合磨损预测模型[J]. , 2000, 36(2): 29-33.
[8]	李成贵;张国雄;袁长良. 三维表面粗糙度的等方性评定[J]. , 1999, 35(1): 15-19.