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
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摘要
提出一种新的基于低阶椭圆曲线方程的微凸体法向弹塑性接触刚度模型。进一步基于粗糙表面形貌的Greenwood-Williamson统计模型和微凸体高度分布概率密度函数,推导整个粗糙界面接触刚度和接触载荷表达式,建立粗糙界面接触的总刚度模型,并将模型计算结果与实验测量结果进行对比分析。研究结果表明:该模型考虑粗糙界面的弹性变形、弹塑性变形和完全塑性变形接触状态,且同时满足不同接触状态之间微凸体的接触刚度、接触载荷和接触面积均连续、单调且光滑变化的条件,克服了以往模型存在的接触刚度非连续、非单调的缺点;本文建立的粗糙界面接触刚度模型有效。
A new elastoplastic contact stiffness model based on the low order elliptic curve was proposed for single asperity contact. The Greenwood-Williamson model was used for surface topography description and the whole contact stiffness for the rough surface was further derived based on the height distribution density function for asperities, and the whole contact stiffness model was established for the rough interface contact. The model predictions were compared with the experimental results. The results show that the proposed model can be used to describe the different contact status of elastic, elstoplastic and fully plastic contact and make the contact parameters of stiffness, force and area all continuous,monotonous and smooth between different contact status, which overcomes the shortcomings of non-continuous and non-monotonous in previous models, the proposed model has validity.
A new elastoplastic contact stiffness model based on the low order elliptic curve was proposed for single asperity contact. The Greenwood-Williamson model was used for surface topography description and the whole contact stiffness for the rough surface was further derived based on the height distribution density function for asperities, and the whole contact stiffness model was established for the rough interface contact. The model predictions were compared with the experimental results. The results show that the proposed model can be used to describe the different contact status of elastic, elstoplastic and fully plastic contact and make the contact parameters of stiffness, force and area all continuous,monotonous and smooth between different contact status, which overcomes the shortcomings of non-continuous and non-monotonous in previous models, the proposed model has validity.
引文
[1]SAXENA A,PAREY A,CHOUKSEY M.Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects[J].Engineering Failure Analysis,2016,70:200-211.
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[14]徐超,王东.一种改进的粗糙表面法向弹塑性接触解析模型[J].西安交通大学学报,2014,48(11):115-121.XU Chao,WANG Dong.An improved analytical model for normal elastic-plastic contact of rough surfaces[J].Journal of Xi’an JiaoTong University,2014,48(11):115-121.
[15]SOJOUDI H,KHONSARI M M.On the modeling of quasi-steady and unsteady dynamic friction in sliding lubricated line contact[J].Journal of Tribology,2010,132(1):012101.
[16]LIOU J L,LIN J F.A modified fractal microcontact model developed for asperity heights with variable morphology parameters[J].Wear,2010,268(1/2):133-144.
[17]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.
[18]GREENWOOD J A,WILLIAMSON J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London,Series A,1966,295:300-319.
[19]MULVIHILL D M,BRUNSKILL H,KARTAL M E,et al.Acomparison of contact stiffness measurements obtained by the digital image correlation and ultrasound techniques[J].Experimental Mechanics,2013,53(7):1245-1263.
[20]BEHESHTI A,KHONSARI M M.Asperity micro-contact models as applied to the deformation of rough line contact[J].Tribology International,2012,52:61-74.
[2]LIU Jing,SHAO Yimin.Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges[J].Journal of Sound and Vibration,2017,398:84-102.
[3]XIAO Huifang,SHAO Yimin,XU Jinwu.Investigation into the energy dissipation of a lap joint using the one-dimensional microslip friction model[J].European Journal of Mechanics A:Solids,2014,43:1-8.
[4]LUNDBERG O E,NORDBORG A,LOPEI ARTEAGA I.The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction[J].Journal of Sound and Vibration,2016,366:429-446.
[5]CARRELLA A,BRENNAN M J,WATERS T P,et al.Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness[J].International Journal of Mechanical Sciences,2012,55(1):22-29.
[6]ZOU H T,WANG B L.Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation[J].Tribology International,2015,92:472-484.
[7]李小彭,潘五九,高建卓,等.结合面形貌特性对模态耦合不稳定系统的影响[J].机械工程学报,2017,53(5):116-127.LI Xiaopeng,PAN Wujiu,GAO Jianzhuo,et al.Influence of surface topography characteristics on mode coupling instability system[J].Journal of Mechanical Engineering,2017,53(5):116-127.
[8]JOHNSON K L.Contact mechanics[M].Cambridge:Cambridge University Press,1985.
[9]LIU Peng,ZHAO Han,HUANG Kang,et al.Research on normal contact stiffness of rough surface considering friction based on fractal theory[J].Applied Surface Science,2015,349:43-48.
[10]ZHAO Y W,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]CHANG W R,ETSION I,BOGY D B.An elastic-plastic model for the contact of rough surfaces[J].ASME Journal of Tribology,1987,109(2):257-263.
[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,LüYanming,JIANG Jianzhong.New elastic-plastic model for the contact of rough surfaces[J].Journal of Mechanical Engineering,2007,43(3):95-101.
[13]BRAKE M R.An analytical elastic-perfectly plastic contact model[J].International Journal of Solids and Structures,2012,49(22):3129-3141.
[14]徐超,王东.一种改进的粗糙表面法向弹塑性接触解析模型[J].西安交通大学学报,2014,48(11):115-121.XU Chao,WANG Dong.An improved analytical model for normal elastic-plastic contact of rough surfaces[J].Journal of Xi’an JiaoTong University,2014,48(11):115-121.
[15]SOJOUDI H,KHONSARI M M.On the modeling of quasi-steady and unsteady dynamic friction in sliding lubricated line contact[J].Journal of Tribology,2010,132(1):012101.
[16]LIOU J L,LIN J F.A modified fractal microcontact model developed for asperity heights with variable morphology parameters[J].Wear,2010,268(1/2):133-144.
[17]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.
[18]GREENWOOD J A,WILLIAMSON J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London,Series A,1966,295:300-319.
[19]MULVIHILL D M,BRUNSKILL H,KARTAL M E,et al.Acomparison of contact stiffness measurements obtained by the digital image correlation and ultrasound techniques[J].Experimental Mechanics,2013,53(7):1245-1263.
[20]BEHESHTI A,KHONSARI M M.Asperity micro-contact models as applied to the deformation of rough line contact[J].Tribology International,2012,52:61-74.
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