机械结合面切向接触刚度的三维分形理论建模
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摘要
将微凸体的弹塑性变形区进一步划分,并考虑三维结合面形貌的W-M函数,推导了三维机械结合面切向分形接触刚度的理论模型。数值模拟了结合面的三维切向接触刚度随着分形维数D、分形尺度系数G、材料特征参数间的变化趋势,以及二维分形和三维分形间的对比分析。仿真结果显示:机械结合面的三维切向接触刚度与法向载荷和材料特征参数成单调递增关系,与分形尺度系数成单调递减关系;而其与分形维数之间以D=2.5为界,依次成递增与递减关系;三维分形下的结合面切向接触刚度大于二维分形下的结合面切向接触刚度。切向接触刚度模型的构建可为后续粗糙表面接触非线性动力学及整机动力学模型的建立提供基础。
Establishing the stiffness model of joint surfaces is one of the key problems to study the static and the dynamic characteristics of the mechanical systems.The elastic-plastic deformation zone of asperity is further divided and the modified W-M function of three-dimensional surface topography is considered,then the three-dimensional fractal tangential contact stiffness model of mechanical joint surfaces is established.Through numerical simulation the relationship between the tangential contact stiffness and the fractal dimension,the topothesy and the material characteristic parameters are studied.Comparative analysis between two dimensional fractal and three dimensional fractal is carried out.Results show:the tangential contact stiffness increases with the normal load and the characteristic parameters of material increase,and decreases with the topothesy increases;the relationship between fractal dimension and tangential contact stiffness is more complicated;the three-dimensional fractal tangential stiffness is greater than the two-dimensional case.The construction of the tangential contact stiffness model can provide the foundation for the establishment of the nonlinear dynamics of rough contact surface and the dynamic model of whole machine in future.
Establishing the stiffness model of joint surfaces is one of the key problems to study the static and the dynamic characteristics of the mechanical systems.The elastic-plastic deformation zone of asperity is further divided and the modified W-M function of three-dimensional surface topography is considered,then the three-dimensional fractal tangential contact stiffness model of mechanical joint surfaces is established.Through numerical simulation the relationship between the tangential contact stiffness and the fractal dimension,the topothesy and the material characteristic parameters are studied.Comparative analysis between two dimensional fractal and three dimensional fractal is carried out.Results show:the tangential contact stiffness increases with the normal load and the characteristic parameters of material increase,and decreases with the topothesy increases;the relationship between fractal dimension and tangential contact stiffness is more complicated;the three-dimensional fractal tangential stiffness is greater than the two-dimensional case.The construction of the tangential contact stiffness model can provide the foundation for the establishment of the nonlinear dynamics of rough contact surface and the dynamic model of whole machine in future.
引文
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[2]Mandelbort B B.The Fractal Geometry of Nature[M].New York:W H Freeman,1982.
[3]Bemporad A,Paggi M.Optimization algorithms for the solution of the frictionless normal contact between rough surfaces[J].International Journal of Solids&Structures,2015,S69-70(3):94—105.
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[11]李小彭,郭浩,刘井年,等.考虑摩擦的结合面法向刚度分形模型及仿真[J].振动、测试与诊断,2013,33(2):210—213.Li Xiaopeng,Guo Hao,Liu Jingnian,et al.Normal stiffness fractal model of joint surface considering friction factors and its simulation[J].Journal of Vibration,Measurement&Diagnosis,2013,33(2):210—213.
[12]Jiang S,Zheng Y,Zhu H.A contact stiffness model of machined plane joint based on fractal theory[J].Journal of Tribology,2010,132(1):011401-1-011401-7.
[13]You J M,Chen T N.Statistical model for normal and tangential contact parameters of rough surfaces[J].ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C:Journal of Mechanical Engineering Science,2010,1(1):1—15.
[14]Zhao Y,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.
[15]Chang W R,Etsion I,Bogy D B.Static friction coefficient model for metallic rough surfaces[J].ASME Journal of Tribology,1988,110(1):57—63.
[16]Yan W,Komvopoulos K.Contact analysis of elasticplastic fractal surfaces[J].Journal of Applied Physics,1998,84(7):3617—3624.
[17]Luen L J,Fin L J.A new microcontact model developed for variable fractal dimension,topothesy,density of asperity,and probability density function of asperity heights[J].Journal of Applied Mechanics,2007,74(4):603—613.
[18]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.
[19]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 Xuanyu,Luo Jianbin,Wen Shizhu.Prediction of static friction coefficient based on fractal contact[J].China Mechanical Engineering,1998,9(7):16—18.
[20]李小彭,梁亚敏,郭浩,等.结合面广义间隙的等效模型研究[J].振动工程学报,2014,27(1):25—32.Li Xiaopeng,Liang Yaming,GUO Hao,et al.Study on equivalent model of generalized clearance of joint surface[J].Journal of Vibration Engineering,2014,27(1):25—32.
[21]田红亮,刘芙蓉,方子帆,等.引入各向同性虚拟材料的固定结合部模型[J].振动工程学报,2013,26(4):561—573.Tian Hongliang,Liu Furong,Fang Zifang,et al.Immovable joint surface′s model using isotropic virtual material[J].Journal of Vibration Engineering,2013,26(4):561—573.
[22]Li X,Liang Y,Zhao G,et al.Dynamic characteristics of joint surface considering friction and vibration factors based on fractal theory[J].Journal of Vibroengineering,2013,15(2):872—883.
[23]李小彭,王雪,运海萌,等.三维分形固定结合面法向接触刚度的研究[J].华南理工大学学报(自然科学版),2016,44(1):114—122.Li Xiaopeng,Wang Xue,Yun Haimeng,et al.Investigation into normal contact stiffness of fixed joint surface with three-dimensional fractal[J].Journal of South China University of Technology(Natural Science Edition),2016,44(1):114—122.
[24]赵光辉.固定结合面接触刚度建模与广义间隙等效方法研究[D].沈阳:东北大学,2014.Zhao Guanghui.Study on contact stiffness modeling and equivalent method of generalized clearance of fixed joint surface[D].Shenyang:Northeastern University,2014.
[2]Mandelbort B B.The Fractal Geometry of Nature[M].New York:W H Freeman,1982.
[3]Bemporad A,Paggi M.Optimization algorithms for the solution of the frictionless normal contact between rough surfaces[J].International Journal of Solids&Structures,2015,S69-70(3):94—105.
[4]Pohrt R,Li Q.Complete boundary element formulation for normal and tangential contact problems[J].Physical Mesomechanics,2014,17(4):334—340.
[5]Jourani A.Effect of 3Dfractal dimension on contact area and asperity interactions in elastoplastic contact[J].Aip Advances,2016,6(5):5799—76.
[6]温淑花,张学良,文晓光,等.结合面切向接触刚度分形模型建立与仿真[J].农业机械学报,2009,40(12):223—227.Wen Shuhua,Zhang Xueliang,Wen Xiaoguang,et al.Fractal model of tangential contact stiffness of joint interfaces and its simulation[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(12):223—227.
[7]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 and simulation of normal contact stiffness of joint interfaces and its simulation[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(11):197—202.
[8]Majumdar A,Bhushan B.Fractal model of elasticplastic contact between rough surfaces[J].ASME Journal of Tribology,1991,113(1):1—11.
[9]田红亮,陈从平,方子帆,等.应用改进分形几何理论的结合部切向刚度模型[J].西安交通大学学报,2014,48(7):46—52.Tian Hongliang,Chen Congping,Fang Zifan,et al.Tangential stiffness model for joint interface adopting the revised fractal geometric theory[J].Journal of Xi′an Jiaotong University,2014,48(7):46—52.
[10]田红亮,赵春华,朱大林,等.金属材料结合部法切向刚度修正与实验验证[J].农业机械学报,2012,43(6):207—214.Tian Hongliang,Zhao Chunhua,Zhu Dalin,et al.Modification of normal and tangential stiffness for joint interface with metallic material and experimental validation[J].Transactions of the Chinese Society for Agricultural Machinery,2012,43(6):207—214.
[11]李小彭,郭浩,刘井年,等.考虑摩擦的结合面法向刚度分形模型及仿真[J].振动、测试与诊断,2013,33(2):210—213.Li Xiaopeng,Guo Hao,Liu Jingnian,et al.Normal stiffness fractal model of joint surface considering friction factors and its simulation[J].Journal of Vibration,Measurement&Diagnosis,2013,33(2):210—213.
[12]Jiang S,Zheng Y,Zhu H.A contact stiffness model of machined plane joint based on fractal theory[J].Journal of Tribology,2010,132(1):011401-1-011401-7.
[13]You J M,Chen T N.Statistical model for normal and tangential contact parameters of rough surfaces[J].ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C:Journal of Mechanical Engineering Science,2010,1(1):1—15.
[14]Zhao Y,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.
[15]Chang W R,Etsion I,Bogy D B.Static friction coefficient model for metallic rough surfaces[J].ASME Journal of Tribology,1988,110(1):57—63.
[16]Yan W,Komvopoulos K.Contact analysis of elasticplastic fractal surfaces[J].Journal of Applied Physics,1998,84(7):3617—3624.
[17]Luen L J,Fin L J.A new microcontact model developed for variable fractal dimension,topothesy,density of asperity,and probability density function of asperity heights[J].Journal of Applied Mechanics,2007,74(4):603—613.
[18]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.
[19]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 Xuanyu,Luo Jianbin,Wen Shizhu.Prediction of static friction coefficient based on fractal contact[J].China Mechanical Engineering,1998,9(7):16—18.
[20]李小彭,梁亚敏,郭浩,等.结合面广义间隙的等效模型研究[J].振动工程学报,2014,27(1):25—32.Li Xiaopeng,Liang Yaming,GUO Hao,et al.Study on equivalent model of generalized clearance of joint surface[J].Journal of Vibration Engineering,2014,27(1):25—32.
[21]田红亮,刘芙蓉,方子帆,等.引入各向同性虚拟材料的固定结合部模型[J].振动工程学报,2013,26(4):561—573.Tian Hongliang,Liu Furong,Fang Zifang,et al.Immovable joint surface′s model using isotropic virtual material[J].Journal of Vibration Engineering,2013,26(4):561—573.
[22]Li X,Liang Y,Zhao G,et al.Dynamic characteristics of joint surface considering friction and vibration factors based on fractal theory[J].Journal of Vibroengineering,2013,15(2):872—883.
[23]李小彭,王雪,运海萌,等.三维分形固定结合面法向接触刚度的研究[J].华南理工大学学报(自然科学版),2016,44(1):114—122.Li Xiaopeng,Wang Xue,Yun Haimeng,et al.Investigation into normal contact stiffness of fixed joint surface with three-dimensional fractal[J].Journal of South China University of Technology(Natural Science Edition),2016,44(1):114—122.
[24]赵光辉.固定结合面接触刚度建模与广义间隙等效方法研究[D].沈阳:东北大学,2014.Zhao Guanghui.Study on contact stiffness modeling and equivalent method of generalized clearance of fixed joint surface[D].Shenyang:Northeastern University,2014.