双粗糙平面法向接触建模方法的有限元对比分析
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摘要
基于统计学方法,Greenwood和Tripp(GT模型)提出双粗糙平面法向接触(双粗模型)可以等效为单粗糙平面与刚性平板之间的接触(单粗模型),但这种等效处理缺乏对接触应力场分析以及材料硬化的考虑。为进一步研究GT模型,基于高斯粗糙表面数字化表征,通过控制自相关长度和滤波方法,得到双粗糙平面及其等效单粗糙平面;借助有限元软件ABAQUS对2组模型法向接触进行建模及分析。结果表明:2组模型预测的接触刚度和接触面积符合较好,但接触压力与接触面积关系存在差异;2组模型预测的等效应力和接触压强的应力幅值以及云图的分布区域大致相近,但双粗模型由于存在大量微凸体侧接触,弱化接触状态以及材料硬化,因而应力幅值偏低。
Based on statistics model,Greenwood and Tripp( GT model) have proposed that the normal contact between two rough surfaces( two-rough-surface model) could be equivalent as a single rough surface in contact with a rigid flat( single-rough-surface model). However,this equivalence treatment lacks the analysis of contact stress field as well as the consideration of material hardening. In order to further elaborate the GT model by means of Gaussian rough surface,by means of autocorrelation length and filter approach,the rough surface in the two-rough-surface model and the equivalent rough surface in single-rough-surface model were all obtained perfectly. By virtue of finite element method( FEM),the two-rough-surface model and the equivalent single-rough-surface model were developed and analyzed. The results show that the predicted contact stiffness and contact area by the two models have great agreements with each other,but the relationship between contact force and contact area is different. The distribution of equivalent stress and contact pressure predicted by the two models are roughly the same,but their amplitudes in two-rough-surface model are slightly lower than those in single-rough-surface model due to the effect of shoulder-to-shoulder contact,which weakens the contact status and material hardening.
Based on statistics model,Greenwood and Tripp( GT model) have proposed that the normal contact between two rough surfaces( two-rough-surface model) could be equivalent as a single rough surface in contact with a rigid flat( single-rough-surface model). However,this equivalence treatment lacks the analysis of contact stress field as well as the consideration of material hardening. In order to further elaborate the GT model by means of Gaussian rough surface,by means of autocorrelation length and filter approach,the rough surface in the two-rough-surface model and the equivalent rough surface in single-rough-surface model were all obtained perfectly. By virtue of finite element method( FEM),the two-rough-surface model and the equivalent single-rough-surface model were developed and analyzed. The results show that the predicted contact stiffness and contact area by the two models have great agreements with each other,but the relationship between contact force and contact area is different. The distribution of equivalent stress and contact pressure predicted by the two models are roughly the same,but their amplitudes in two-rough-surface model are slightly lower than those in single-rough-surface model due to the effect of shoulder-to-shoulder contact,which weakens the contact status and material hardening.
引文
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[2]GREENWOOD J A,WILLIAMSON J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London.Series A,Mathematical and Physical Sciences,1966,295:300-319.
[3]GREENWOOD J A,TRIPP J H.The contact of two nominally flat rough surfaces[J].Proceedings of the Institution of Me chanical Engineers,1970,185:496-502.
[4]CHANG W R,ETSION I,BOGY D B.An elastic-plastic model for the contact of rough surfaces[J].Journal of Tribology,1987,109(2):257-263.
[5]BRIZMER V,KLIGERMAN Y,ETSION I.Elastic-plastic spherical contact under combined normal and tangential loading in full stick[J].Tribology Letter,2007,25(1):61-70.
[6]KOGUT L,ETSION I.A finite element based elastic-plastic model for the contact of rough surfaces[J].Tribology Transaction,2003,46(3):383-390.
[7]KOGUT L,ETSION I.A static friction model for elastic-plastic contacting rough surfaces[J].Journal of Tribology,2004,126(1):34-40.
[8]JACKSON R L,GREEN I.A statistical model of elasto-plastic asperity contact between rough surfaces[J].Tribology International,2006,39(9):906-914.
[9]JACKSON R L,STREATOR J L.A multi-scale model for contact between rough surfaces[J].Wear,2006,261(11/12):1337-1347.
[10]ZHAO B,ZHANG S,MAN J,et al.A modified normal contact stiffness model considering effect of surface topography[J].Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2014,229(6):677-688.
[11]SAHOO P,GHOSH N.Finite element contact analysis of fractal surfaces[J].Journal of Physics D:Applied Physics,2007,40(14):4245-4252.
[12]杨国庆,熊美华,洪军,等.3D粗糙表面的数字化表征与接触特性分析[J].西安交通大学学报,2012,46(11):58-63.YANG G Q,XIONG M H,HONG J,et al.Numerical characterization and contact performance for 3D rough surfaces[J].Journal of Xi’an Jiaotong University,2012,46(11):58-63.
[13]陈辉,胡元中,王慧,等.粗糙表面计算机模拟[J].润滑与密封,2006,31(10):52-56.CHEN H,HU Y Z,WANG H,et al.Computer simulation of rough surface[J].Lubrication Engineering,2006,31(10):52-56.
[14]BOTTIGLIONE F,CARBONE G MANTRIOTA G.Fluid leakage in seals:an approach based on percolation theory[J].Tribology International,2009,42(5):731-737.
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