考虑多尺度接触状态的新接触模型

doi:10.3901/JME.2019.09.080

摘要/Abstract

摘要： 提出了一种接触模型，模型的建立基于经典的Hertz接触力学理论和现有的分形接触模型。研究了单个微凸体接触状态随尺度序数n的变化规律，考虑了不同尺度序数n的影响而引入线性因子对模型进行修正，采用了与以往分布函数计算方法不同的思路，在此基础上对微凸体面积分布函数积分求和，获得了接触表面真实接触载荷与接触面积的关系。结果表明：单个微凸体的临界参数对接触参数有影响；微凸体的变形顺序为弹性，弹塑性，塑性变形，与传统的接触模型一致；线性因子与特征系数G，分形维数D有一定的关系；新的分布函数和线性因子的引入提高了接触参数的精度；考虑多尺度特性的新模型相比经典的GW模型，MB模型与Bhushan试验数据更接近，尤其在接触载荷较大时；与现有的考虑尺度因素的接触模型做比较，计算精度有了更进一步的提高。

关键词: 粗糙表面, 弹塑性, 多尺度, 接触模型, 微凸体

Abstract: A new elastic-plastic model for contact of rough surfaces is presented. The model based on the traditional contact theory of Hertz and the presented fractal contact models is developed. Research the regularity of the contact condition of micro-bulge, considered on the multi contact asperity in different fractal parameters in the first detail. Then, to modify the contact areas by considering the multi-scale levels and a new way use to calculate the distribution function. The model developed evaluates that the multi-scale parameter will influence the values of critical contact parameters, the deformation of contact area will be the conditions of elastic, elastic-plastic and plastic successively and the effect factor has relationship with G and D. Besides, by considering the effect factor and using new distribution function, the new model gains the more precise results than the model of GW and MB. It is show that the predict values from present model is fitting closer than the values from MB model and GW model to the results of Bhushan' experimental observation. The comparison results strongly indicate that the new model is more reasonable in describing the contact behavior between rough surfaces.

Key words: asperity, contact model, elastic-plastic, multi-scale levels, rough surfaces

中图分类号:

TH117

运睿德, 丁北. 考虑多尺度接触状态的新接触模型[J]. 机械工程学报, 2019, 55(9): 80-89.

YUN Ruide, DING Bei. New Fractal Contact Model Considered Multi-scale Levels[J]. Journal of Mechanical Engineering, 2019, 55(9): 80-89.

参考文献

[1] 陈奇,黄守武,张振,等. 考虑摩擦因素的两圆柱体表面接触承载能力的分形模型研究[J]. 机械工程学报,2016,52(7):114-121. CHEN Qi,HUANG Shouwu,ZHANG Zhen,et al. Research on fractal contact model for contact carrying capacity of two cylinder's surfaces considering friction factors[J]. Journal of Mechanical Engineering,2016,52(7):114-121.
[2] 魏龙,张鹏高,刘其和,等. 接触式机械密封端面摩擦系数影响因素分析与试验[J]. 摩擦学学报,2016,36(3):354-361. WEI Long,ZHANG Penggao,LIU Qihe,et al. Influencing factors analysis and experiments of friction coefficient between the end faces for contact mechanical seals[J]. Tribology,2016,36(3):354-361.
[3] 嵇正波,孙见君,陆建花,等. 基于逾渗理论的机械密封界面静态泄漏预测方法[J]. 摩擦学学报,2017,37(6):734-742. JI Zhengbo,SUN Jianjun,LU Jianhua,et al. Predicting method for static leakage of contacting mechanical seals interface based on percolation theory[J]. Tribology,2017,37(6):734-742.
[4] 田小龙,王雯,傅卫平,等. 考虑微凸体相互作用的机械结合面接触刚度模型[J]. 机械工程学报,2017,53(17):149-159. TIAN Xiaolong,WANG Wen,FU Weiping,et al. Contact stiffness model of mechanical joint surfaces considering the asperity interactions[J]. Journal of Mechanical Engineering,2017,53(17):149-159.
[5] GREENWOOD J A,WILLIAMSON J B P. Contact of nominally flat surfaces[J]. Proceedings of the Royal Society of London,1966,295(1442):300-319.
[6] WHITEHOUSE D J,ARCHARD J F. The properties of random surfaces of significance in their contact[J]. Proc. Roy. Soc. London,1970,316(1524):97-121.
[7] NAYAK P R. Random process model of rough surfaces in plastic contact[J]. Wear,1971,26(3):398.
[8] BUSH A W,GIBSON R D,THOMAS T R. The elastic contact of a rough surface[J]. Wear,1975,35(1):87-111.
[9] CIAVARELLA M,GREENWOOD J A,PAGGI M. Inclusion of "interaction" in the Greenwood and Williamson contact theory[J]. Wear,2008,265(5-6):729-734.
[10] ZHAO Y,MAIETTA D M,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.
[11] ZHAO Y,CHANG L. A Model of asperity interactions in elastic-plastic contact of rough surfaces[J]. Journal of Tribology,2001,123(4):857.
[12] 赵永武,吕彦明,蒋建忠. 新的粗糙表面弹塑性接触模型[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
[13] CHANG W R. An elastic-plastic model for the contact of rough surfaces[J]. Journal of Tribology,1987,109(2):257-263.
[14] MAJUMDAR A,BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology,1991,113(1):1-11.
[15] KOGUT L,ETSION I. Elastic-Plastic contact analysis of a sphere and a rigid flat[J]. Journal of Applied Mechanics,2002,69(5):657-662.
[16] 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.
[17] JACKSON R L,STREATOR J L. A multi-scale model for contact between rough surfaces[J]. Wear,2006,261(11-12):1337-1347.
[18] WRIGGERS P,NETTINGSMEIER J. Homogenization and multi-scale approaches for contact problems[M]. Vienna:Springer,2008.
[19] 孙伟,黄信,孙志勇,等. 实际结合面的法向接触刚度多尺度计算方法[J]. 机械设计与制造,2017(10):1-4. SUN Wei,HUANG Xin,SUN Zhiyong,et al. A multiscale calculation method of normal contact stiffness of actual interfaces[J]. Machinery Design and Manufacture,2017(10):1-4.
[20] 史建成,刘检华,丁晓宇,等. 基于确定性模型的金属表面多尺度接触行为研究[J]. 机械工程学报,2017,53(3):111-120. SHI Jianchen,LIU Jianhua,DING Xiaoyu,et al. On the multi-scale contact behavior of metal rough surface based on deterministic model[J]. Journal of Mechanical Engineering,2017,53(3):111-120.
[21] MIAO X,HUANG X. A complete contact model of a fractal rough surface[J]. Wear,2014,309(1-2):146-151.
[22] 丁雪兴,严如奇,贾永磊. 基于基底长度的粗糙表面分形接触模型的构建与分析[J]. 摩擦学学报,2014,34(4):341-347. DING Xuexing,YAN Ruqi,JIA Yonglei. Construction and analysis of fractal contact mechanics model for rough surface based on base length[J]. Tribology,2014,34(4):341-347.
[23] 成雨,原园,甘立,等. 尺度相关的分形粗糙表面弹塑性接触力学模型[J]. 西北工业大学学报,2016,34(3):485-492. CHENG Yu,YUAN Yuan,GAN Li,et al. The elastic-plastic contact mechanics model related scale of rough surface[J]. Journal of Northwestern Polytechnical University,2016,34(3):485-492.
[24] YUAN Y,CHENG Y,LIU K,et al. A revised Majumdar and Bhushan model of elastoplastic contact between rough surfaces[J]. Applied Surface Science,2017,425-432.
[25] 约翰逊K L. 接触力学[M]. 北京:高等教育出版社,1992. JOHNSON K L. Contact mechanics[M]. Beijing:Higher Education Press,1992.
[26] TABOR D. The hardness of metals[J]. Measurement Techniques,1951,5(4):281.
[27] KOMVOPOULOS K,YAN W. A fractal analysis of stiction in microelectromechanical systems[J]. Journal of Tribology,1997,119(3):391-400.
[28] MANDELBROT B B,WHEELER J A. The fractal geometry of nature[J]. American Journal of Physics,1983,51(4):468.
[29] BHARAT B. The real area of contact in polymeric magnetic media-part Ⅱ:Experimental data and analysis[J]. ASLE Transactions,1985,28(2):181-197.