结合面静摩擦因数尺度关联三维分形模型

doi:10.3901/JME.2021.09.127

摘要/Abstract

摘要： 针对现有结合面静摩擦因数分形模型的静摩擦因数随结合面法向接触载荷增大而增大，与试验研究结论及统计模型不一致的问题，基于尺度等级定义微凸体的大小，严格区分微凸体高度与变形，构建各尺度等级微凸体的法向接触载荷与接触面积之间关系及其发生弹性和弹塑性第一变形时所能承受的最大切向载荷即最大静摩擦力计算模型，进而建立结合面法向接触载荷与最大静摩擦力计算模型，在此基础上，依据结合面静摩擦因数定义，提出与微凸体尺度等级关联的考虑微凸体完全弹性、弹塑性和完全塑性三种变形机制的结合面静摩擦因数三维分形模型，数值仿真分析了结合面静摩擦因数与法向接触载荷和分形维数D等的关系，结果表明结合面静摩擦因数随着结合面法向接触载荷的增大而减小，随着分形维数的增大而增大，并试验实例验证了所建模型的正确性，解决了现有结合面静摩擦因数分形模型与统计模型和试验结果之间的不一致性。

关键词: 结合面, 静摩擦因数, 尺度关联, 分形模型

Abstract: In view of the fact that the static friction coefficient of the fractal model of the static friction coefficient of the existing interface increases with the increase of the normal contact load of the interface, which is inconsistent with the experimental results and the statistical model. The size of the micro convex body is defined based on the scale level, and the height and deformation of the micro convex body are strictly distinguished. The relationship between the normal contact load and the contact area of the micro convex body at each scale level and the calculation model of the maximum tangential load that the micro convex body can bear when the full elastic and the first elastic-plastic deformation occur are established. Finally, the calculation model of the relationship between the normal contact load and the maximum static friction force is established. On this basis, according to the definition of the static friction coefficient of the joint surface, a three-dimensional fractal model of the static friction coefficient of the joint surface is proposed, which is related to the scale level of the micro convex body and considers three deformation mechanisms of the micro convex body, i.e. complete elasticity, elastoplasticity and complete plasticity. The relationship between the static friction coefficient of the joint surface and the normal contact load and fractal dimension D is analyzed by numerical simulation. The results show that the static friction coefficient decreases with the increase of normal contact load and increases with the increase of fractal dimension. By comparing with the experiment, the correctness of the model is proved, and the inconsistency between the fractal model of static friction coefficient and the statistical model and the experimental results is solved.

Key words: joint interfaces, static friction factor, scale correlation, fractal model

中图分类号:

TH113

张学良, 张伟, 温淑花, 姚世生. 结合面静摩擦因数尺度关联三维分形模型[J]. 机械工程学报, 2021, 57(9): 127-138.

ZHANG Xueliang, ZHANG Wei, WEN Shuhua, YAO Shisheng. Three-dimensional Fractal Model with Scale Correlation for Static Friction Factor of Joint Interfaces[J]. Journal of Mechanical Engineering, 2021, 57(9): 127-138.

参考文献

[1] CHANG W R，ETSION I，BOGY D B. Static friction coefficient model for metallic rough surfaces[J]. Journal of Tribology，1988，110(1)：57-63.
[2] KOGUT L，ETSION I. A static friction model for elastic-plastic contacting rough[J]. Journal of Tribology，2004，126(1)：34-40.
[3] KOGUT L，ETSION I. A semi-analytical solution for the sliding inception of a spherical contact[J]. Journal of Tribology，2003，125(3)：499.
[4] YOU J M ，CHEN T N. A static friction model for the contact of fractal surfaces[J]. Proceedings of the Institution of Mechanical Engineers，Part J：Journal of Engineering Tribology，2010，224(5)：513-518.
[5] 尤晋闽，陈天宁. 结合面静摩擦系数的统计模型[J]. 振动与冲击，2010，29(12)：26-29. YOU Jinmin，CHEN Tianning. Statistical type of static friction coefficient of joint surface[J]. Journal of Vibration and Shock，2010，29(12)：26-29.
[6] 盛选禹，雒建斌，温诗铸. 基于分形接触的静摩擦系数预测[J]. 中国机械工程，1998，9(7)：16-18. SHENG Xuan，YAN Jianbin，WEN Shizhu. Prediction of static friction coefficient based on fractal contact[J]. China Mechanical Engineering，1998，9(7)：16-18.
[7] 田红亮，赵春华，方子帆，等. 金属材料表面静摩擦学特性的预测研究-理论模型[J]. 振动与冲击，2013，32(12)：40-44. TIAN Hongliang，ZHAO Chunhua，FANG Zifan，et al. Prediction study of surface static tribological properties of metallic materials-theoretical model[J]. Journal of Vibration and Shock，2013，32(12)：40-44.
[8] 田红亮，刘芙蓉，赵春华，等. 金属材料表面静摩擦学特性的预测研究——试验佐证[J]. 振动与冲击，2014，33(1)：209-220. TIAN Hongliang，LIU Furong，ZHAO Chunhua，et al. Prediction of surface static tribological properties of metallic materials——experimental support[J]. Journal of Vibration and Shock，2014，33(1)：209-220.
[9] DUNKIN J E，KIM D E. Measurement of static friction coefficient between flat surfaces[J]. Wear，1996，193(2)：186-192.
[10] IBRAHIM D R D，JACKSON R L ，FLOWERS G T. Measurements of the Static Friction Coefficient Between Tin Surfaces and Comparison to a Theoretical Model[J]. Journal of Tribology，2011，133(3)：031408.
[11] 张学良. 机械结合面动态特性及应用[M]. 北京：中国科技出版社，2002. ZHANG Xueliang. Dynamic characteristics and application of mechanical joint surface[M]. Beijing：China Science and Technology Press，2002.
[12] YAN W，KOMVOPOULOS K. Contact analysis of elastic-plastic fractal surfaces[J]. Journal of Applied Physics，1998，84(7)：3617-3624.
[13] 陈建江，原园，成雨，等. 尺度相关的分形结合面法向接触刚度模型[J]. 机械工程学报，2018，54(21)：127-137. CHEN Jianjiang，YUAN Yuan，CHENG Yu，et al. Scale-dependent fractal joint surface normal contact stiffness model[J]. Journal of Mechanical Engineering，2018，54(21)：127-137.
[14] KOGUT L，ETSION L. Elastic-plastic contact analysis of a sphere and rigid flat[J]. Journal of Applied Mechanics，2002，69：657-662.
[15] 成雨. 三维分形表面的接触性能研究[D]. 西安：西安理工大学，2017. CHENG Yu. Study on contact performance of three-dimensional fractal surface [D]. Xi'an：Xi'an University of Technology，2017.
[16] LIOU J L ，LIN J F ，LIOU J L ，et al. A modified fractal microcontact model developed for asperity heights with variable morphology parameters[J]. Wear，2010，268(1)：133-144.
[17] CHUL H L，ANDREAS A. Static friction experiments and verification of an improved elastic-plastic model including roughness effects[J]. Tribology，2007，129(4)：754-760
[18] 李玲，王晶晶，裴喜永，等. 机械结合面接触刚度建模新方法[J]. 机械工程学报，2020，56(9)：162-169. LI Ling，WANG Jingjing，PEI Xiyong，et al. A new method for modeling the contact stiffness of mechanical joints[J].Chinese Journal of Mechanical Engineering，2020，56(9)：162-169.
[19] ANDREAS A，POLYCARPOU I E. Comparison of the static friction subboundary lubrication model with experimental measurements on thin-film disks[J]. Tribology Transactions，1998，41(2).
[20] 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，2019，50(6)：1343-1350. XIAO Huifang，SUN Yunyun，XU Jinwu. Normal elastoplastic contact model of rough interface with continuous rigidity，monotonous and smooth variation[J].Journal of Central South University，2019，50(6)：1343-1350.
[21] GREENWOOD J A，TRIPP J H. The elastic contact of rough spheres[J]. J. Appl. Mech.，1967，34(1)：153-0.
[22] GREENWOOD J A，WILLIAMSON J B P. Contact of nominally flat surfaces [J].Proceedings of the royal society of. London，1966，295：300-319.
[23] 张伟，张学良，温淑花，等. 考虑微凸体基体变形和相互作用的结合面法向接触刚度模型[J]. 西安交通大学学报，2020，54(6)：115-121. ZHANG Wei，ZHANG Xueliang，WEN Shuhua，et al. The normal contact stiffness model of the joint surface considering the deformation and interaction of the asperity matrix[J]. Journal of Xi'an Jiaotong University，2020，54(6)：115-121.
[24] YUAN Y ，CHENG Y ，LIU K ，et al. A revised Majumdar and Bushan model of elastoplastic contact between rough surfaces[J]. Applied Surface Science，2017：S0169433217319499.
[25] YOU J M，CHEN T N. Statistical model for normal and tangential contact parameters of rough surfaces[J]. Proceedings of the Institution of Mechanical Engineers，2011，225(1)：1-15.
[26] 田小龙. 考虑微凸体相互作用的机械结合面接触刚度模型[D]. 西安：西安理工大学，2015. TIAN Xiaolong. Contact stiffness model of mechanical interface considering the interaction of micro convex bodies [D]. Xi'an：Xi'an University of Technology，2015.