基于粗糙表面分形表征新方法的结合面法向接触刚度模型

PDF(1613 KB)

振动与冲击 ›› 2019, Vol. 38 ›› Issue (7) : 212-217.

论文

孙见君，张凌峰，於秋萍，嵇正波，马晨波

作者信息 +

A joint surface normal contact stiffness model based on a new rough surface fractal characterization method

SUN Jianjun, ZHANG Lingfeng, YU Qiuping, JI Zhengbo, MA Chenbo

Author information +

文章历史 +

摘要

如何有效预测结合面的接触刚度，是机械结构设计研究的一个重要课题。结合面接触刚度模型主要分为基于统计学特征参数的和基于分形参数的两类。前者依赖于粗糙表面形貌的测量尺度，后者与测量尺度无关。然而，多数研究者在利用分形理论进行建模时，以对应于微凸体接触面积a的尺寸l=a1/2作为微凸体基底尺寸描述微凸体初始轮廓，给出了错误的微凸体变形机制和结合面接触刚度模型。本文提出了一种基于D、G和最大微凸体高度的粗糙表面轮廓分形表征新方法，探讨了微凸体接触变形机制，建立了与测量尺度无关的粗糙表面接触力学分形模型，揭示了接触刚度的变化规律。研究表明：接触载荷可用表达式Fc=F (E, D, G, h, aL)描述；当结合面上的接触压力小于其屈服强度时，无论微凸体发生何种变形，结合面均因存在有弹性变形的接触点而具有一定的法向接触刚度。

Abstract

It is an important topic in mechanical structure design study to effectively predict contact stiffness of a joint surface. Contact stiffness models of a joint surface are mainly divided into two types including one based on statistical characteristic parameters and the other based on fractal ones. The former depends on the measurement scale of rough surface topography and the latter is independent of measurement scale. When most of researchers used the fractal theory to model rough surface,the size l=a1/2,corresponding to the contact area of an asperity a,was taken as the base size of the asperity to describe the initial profile of asperities,and give incorrect asperities’ deformation mechanism and joint surface’s contact stiffness model. Here,a new rough surface fractal characterization method based on fractal dimension D,roughness parameter G and the maximum asperity height was proposed to explore asperities’ contact deformation mechanism,establish a rough surface contact mechanical fractal model independent of the measurement scale and reveal contact stiffness variation law. The study results showed that the contact load can be described with the expression Fc=F(E,D,G,h,aL); when the contact pressure on a joint surface is less than its yield strength,the joint surface has a certain normal contact stiffness due to the presence of contact points with elastic deformation,no matter what kind of deformation occurs in asperities.

导出引用

孙见君，张凌峰，於秋萍，嵇正波，马晨波. 基于粗糙表面分形表征新方法的结合面法向接触刚度模型[J]. 振动与冲击, 2019, 38(7): 212-217

SUN Jianjun, ZHANG Lingfeng, YU Qiuping, JI Zhengbo, MA Chenbo. A joint surface normal contact stiffness model based on a new rough surface fractal characterization method[J]. Journal of Vibration and Shock, 2019, 38(7): 212-217

参考文献

[1] Ren Y, Beards C F. Identification of effective linear joints using coupling and joint identification techniques [J]. ASME Journal of Vibration and Acoustics，1998, 120(2): 331-338.
[2] Shi J P，Ma K，Liu Z Q. Normal contact stiffness on unit area of a mechanical joint surface considering perfectly elastic elliptical asperities[J]. ASME Journal of Tribology，2012,134:0314021-6.
[3] Shi Xi, Polycarpou A A. Measurement and modeling of normal contact stiffness and contact damping at the meso scale[J]. ASME Journal of Vibration and Acoustics, 2005, 127(2):52-60.
[4] Zhai C, Gan Y, Hanaor D at el. The role of surface structure in normal contact stiffness[J]. Experimental Mechanics, 2016,56:359-368.
[5] 王雯, 吴洁蓓, 傅卫平等. 机械结合面法向动态接触刚度理论模型与试验研究[J]. 机械工程学报, 2016，52(13)：123-130.
WANG Wen, WU Jie-bei, FU Wei-ping, et al.. Theoretical model and experimental study on normal dynamic contact stiffness of mechanical interface [J]. Chinese Journal of Mechanical Engineering, 2016,52 (13): 123-130.
[6] Kogut L, Etsion I. A finite element based elastic-plastic model for the contact of rough surfaces[J]. Tribology Transactions, 200 3 ,46(3)：383-390.
[7] Zhao Bin, Zhang Song, Wang Peng, et al.. Loading–unloading normal stiffness model for power-law hardening surfaces considering actual surface topography[J]. Tribology International, 2015, 90:332-342.
[8] Majumdar A, Bhushan B. Fractal model of elastic-plastic contact retween rough surfaces[J]. ASME Journal of Tribology, 1991, 113(1):1-1.
[9] 何联格, 左正兴, 向建华. 考虑微凸体弹塑性过渡变形机制的结合面法向接触刚度分形模型[J]. 上海交通大学学报，2015, 49 (1): 116-121.
HE Liange, ZU Zhengxing, XIANG Jianhua. Fractal stiffness model of contact flection considering asperity-tolerance transition mechanism of asperity[J]. Journal of Shanghai Jiaotong University, 2015, 49 (1): 116-121.
[10] Pohrt R and Popov V L. Normal contact stiffness of elastic solids with fractal rough surfaces[J]. Physics Review Letters, 2012, 108:104301.
[11] 庄艳，李宝童，洪军, 等. 一种结合面法向接触刚度计算模型的构建[J]. 上海交通大学学报，2013, 47 (2): 180-186.
ZHUANG Yan, LI Baotong, HONG Jun, et al.. An approach to calculate the contact stiffness of normal direction[J]. Journal of Shanghai Jiaotong University, 2013, 47(2): 180-186.
[12] 温淑花, 张学良, 武美先, 等. 结合面法向接触刚度分形模型建立与仿真[J]. 农业机械学报, 2009, 40(11):197-202.
WEN Shuhua，ZHANG Xueliang，WU Meixian，et al．Fractal model of normal contact stiffness of joint interfaces and its simulation[J]. Transactions of the Chinese Society for Agricultural Machinery, 2009, 40(11):197-202.
[13] 王南山, 张学良, 兰国生,等. 临界接触参数连续的粗糙表面法向接触刚度弹塑性分形模型[J]. 振动与冲击, 2014, 33(9):72-77.
WANG Nanshan，ZHANG Xueliang，LAN Guosheng，et al. Elastoplastic fractal model for normal contact stiffness of rough surfaces with continuous critical contact parameters[J]. Journal of Vibration and Shock, 2014, 33(9): 72-77
[14] 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.
[15] Jiang S, Zheng Y, Zhu H. A Contact Stiffness Model of Machined Plane Joint Based on Fractal Theory[J]. ASME Journal of Tribology, 2010, 132(1): 114011-114017
[16] Buczkowski R, Kleiber M, Starzyński G. Normal contact stiffness of fractal rough surfaces[J]. Archives of Mechanics, 2014, 66(6):411-428.
[17] 田红亮, 钟先友, 秦红玲, 等. 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]. 机械工程学报，2013, 49(21): 108-122.
TIAN Hongliang, ZHONG Xianyou, QIN Hongling, et al.. Formal contact mechanics model of fixed joint based on anisotropic fractal theory [J]. Chinese Journal of Mechanical Engineering, 2013, 49 (21): 108-122.
[18] Liu P, Zhao H, Huang K, et al. Research on normal contact stiffness of rough surface considering friction based on fractal theory[J]. Applied Surface Science, 2015, 349:43-48.
[19] 张学良，黄玉美，傅卫平. 粗糙表面法向接触刚度的分形模型[J]. 应用力学学报，2000, 17(2)：31-35.
ZHANG Xueliang, HUANG Yumei, FU Weiping. Fractal normal fracture model of rough surfaces[J]. Chinese Journal of Applied Mechanics, 2000, 17 (2): 31-35.
[20] Morag Y, Etsion I. Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces. Wear, 2007,262(5/6): 624-629.
[21] Liou J L, Chi M T, Lin J F. A microcontact model developed for sphere- and cylinder-based fractal bodies in contact with a rigid flat surface. Wear, 2010, 268(3–4):431-442.
[22] Chen Q, Xu Fan, Liu Peng, et al. Research on fractal model of normal contact stiffness between two spheroidal joint surfaces considering friction factor[J]. Tribology Inter- national, 2016, 97:253-264.
[23] Berry M V and Lewis Z V. On the Weierstrass-Mandelbroot fractal function[J]. Proceedings of the Royal Society, 1980, Vol.A370:459-484.
[24] Mayer E. Mechanical Seals[M]. London:Newnes-Butterworth, 1997.
[25] Hertz H.Über die Berührung fester elastischer Körperü[J]. J. die reine und angewandte Mathematik ,1882,92, 156–171.
[26] Hill R. The mathematical theory of plasticity[M]. Oxford University Press, London, 1950.
[27] Zhao Y W, David D M, Chang L. An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow[J]. ASME Journal of Tribology, 2000,122:86-93.
[28] Wang S, Komvopoulosk K. A fractal theory of the interfacial temperature distribution in the slow sliding regime: part I elastic contact and heat transfer analysis[J]. ASME Journal of Tribology, 1994, 116(4): 812-823.
[29] 孙见君, 何小元, 徐建中,等. 机械密封端面形貌分形行为[J].石油化工设备，2007, 36(6): 15-18.
SUN Jianjun, HE Xiaoyuan, XU Jianzhong, et al. Study on fractal behaviors of surface topography of mechanical seals [J]. Petro-chemical Equipment, 2007, 36(6): 15-18.