考虑微凸体相互作用及硬度变化的加卸载接触分形模型
Fractal Model of Loading-Unloading Contact Considering Asperity Interaction and Hardness Changes
DOI: 10.12677/MOS.2023.121028, PDF,   
作者: 王嘉豪, 杨丽红：上海理工大学机械工程学院，上海
关键词: 粗糙表面；接触模型；相互作用；硬度；分形；Rough Surface； Contact Model； Interaction； Hardness； Fractal
摘要: 基于分形理论，建立了考虑微凸体的相互作用及硬度变化的加卸载接触模型。推导了单个微凸体在加卸载过程中接触面积、接触载荷、表面分离、变形量的关系式。根据接触面积的分布密度函数，推导粗糙表面的实际接触特性关系式，并通过数值计算分析了相关参数对接触特性的影响。结果表明：单个微凸体发生弹性变形时，卸载过程与加载过程完全一致；发生弹塑性变形时，随着微凸体加载结束时的变形量的增大，在相同接触载荷下，卸载时的接触面积越大，且不能完全回复；发生完全塑性变形时，微凸体在卸载过程中不回复。随着分形维度D的增大、尺度系数G的减小，粗糙表面越光滑，在相同接触载荷下，接触面积越大，表面分离减小。
Abstract: Based on fractal theory, a loading-unloading contact model considering the interaction of asperities and the change of hardness is established. The relationship between contact area, contact load, sur-face separation and deformation of a single asperity during loading and unloading is derived. Ac-cording to the distribution density function of the contact area, the actual contact characteristics of rough surfaces are derived, and the influence of relevant parameters on the contact characteristics is analyzed through numerical calculation. The results show that the unloading process is consistent with the loading process when a single asperity undergoes elastic deformation; when elastic-plastic deformation occurs, with the increase of deformation at the end of loading, the contact area at un-loading is larger under the same contact load, and cannot be fully recovered; when complete plastic deformation occurs, the asperities do not recover during unloading. With the increase of fractal di-mension D and fractal roughness G, the smoother the rough surface is, the larger the contact area is, and the smaller the surface separation is under the same contact load.
文章引用：王嘉豪, 杨丽红. 考虑微凸体相互作用及硬度变化的加卸载接触分形模型[J]. 建模与仿真, 2023, 12(1): 290-303. https://doi.org/10.12677/MOS.2023.121028

参考文献

[1] Hertz, H. (1882) Ueber die Berührung fester elastischer Körper. In: Band 92, Walter de Gruyter GmbH, Berlin, 156-171. [Google Scholar] [CrossRef] 
[2] Greenwood, J.A. and Williamson, J.B.P. (1966) Contact of Nominally Flat Surfaces. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 295, 300-319. [Google Scholar] [CrossRef] 
[3] Chang, W.R., Etsion, I. and Bogy, D.B. (1987) An Elastic-Plastic Model for the Contact of Rough Surfaces. Journal of Tribology, 109, 257-263. [Google Scholar] [CrossRef] 
[4] Zhao, Y., Maietta, D.M. and Chang, L. (2020) An Asperity Microcontact Model Incorporating the Transition from Elastic Deformation to Fully Plastic Flow. Journal of Tribology, 122, 86-93. [Google Scholar] [CrossRef] 
[5] Kogut, L. and Etsion, I. (2002) Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat. Journal of Applied Mechanics, 69, 657-662. [Google Scholar] [CrossRef] 
[6] Kogut, L. and Etsion, I. (2003) A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces. Tribology Transactions, 46, 383-390. [Google Scholar] [CrossRef] 
[7] 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(3): 95-101.
[8] 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]. 机械工程学报, 2013, 49(1): 102-107.
[9] 肖会芳, 孙韵韵, 徐金梧. 刚度连续、单调且光滑变化的粗糙界面法向弹塑性接触模型[J]. 中南大学学报(自然科学版), 2019, 50(6): 1343-1350.
[10] Majumdar, A. and Bhushan, B. (1991) Fractal Model of Elastic-Plastic Contact between Rough Surfaces. Journal of Tribology, 113, 1-11. [Google Scholar] [CrossRef] 
[11] Morag, Y. and Etsion, I. (2007) Resolving the Contradiction of Asperities Plastic to Elastic Mode Transition in Current Contact Models of Fractal Rough Surfaces. Wear, 262, 624-629. [Google Scholar] [CrossRef] 
[12] Wang, S. and Komvopou-los, K. (1994) A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part I—Elastic Contact and Heat Transfer Analysis. Journal of Tribology, 116, 812-823. [Google Scholar] [CrossRef] 
[13] 葛世荣, 索双富. 表面轮廓分形维数计算方法的研究[J]. 摩擦学学报, 1997(4): 66-74.
[14] 葛世荣, 陈国安. 磨合表面形貌变化的特征粗糙度参数表征[J]. 中国矿业大学学报, 1999(3): 4-7.
[15] 李小彭, 郭爽, 刘洋, 户丹丹. 考虑域扩展因子的结合面静摩擦系数模型[J]. 机械设计与制造, 2019(4): 256-259.
[16] 兰国生, 张学良, 丁红钦, 温淑花, 张宗阳, 卢青波. 基于分形理论的结合面静摩擦因数改进模型[J]. 农业机械学报, 2012, 43(1): 213-218.
[17] Zhao, Y. and Chang, L. (2001) A Model of Asperity Interactions in Elastic-Plastic Contact of Rough Surfaces. Journal of Tribology, 123, 857-864. [Google Scholar] [CrossRef] 
[18] 田红亮, 钟先友, 赵春华, 赵新泽, 方子帆, 刘芙蓉, 朱大林, 林卫共, 晏红. 计及弹塑性及硬度随表面深度变化的结合部单次加载模型[J]. 机械工程学报, 2015, 51(5): 90-104.
[19] Etsion, I., Kligerman, Y. and Kadin, Y. (2004) Unloading of an Elastic-Plastic Loaded Spherical Contact. International Journal of Solids and Structures, 42, 3716-3729. [Google Scholar] [CrossRef] 
[20] 陈建江, 原园, 徐颖强. 粗糙表面的加卸载分形接触解析模型[J]. 西安交通大学学报, 2018, 52(3): 98-110.
[21] Yan, W. and Komvopoulos, K. (1998) Contact Analysis of Elastic-Plastic Fractal Surfaces. Journal of Applied Physics, 84, 3617-3624. [Google Scholar] [CrossRef] 

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