考虑摩擦的球面切向接触刚度分形模型研究
|
摘要
为准确且方便地计算两球面的切向接触刚度(TCS),在前期对两球面接触分形模型研究的基础上,通过引入考虑摩擦因素的弹塑性变形临界面积计算公式,并基于接触面切向刚度基本理论,建立了考虑摩擦因素的两球面切向接触刚度的分形模型。对模型进行了仿真分析,结果表明:切向接触刚度与法向载荷成正比关系;摩擦因数与切向接触刚度的关系因分形维数的变化而呈现出不同的规律;受到分形维数变化的影响,切向接触刚度随接触面材料特性参数和分形粗糙度幅值的增大而增大;在一定工况下,切向接触刚度在分形维数取1.5时达到最大,且当分形维数在1.5左右时,其值增大最快;球面内接触比外接触时的切向刚度大;随着曲率半径的增大,切向刚度增大。研究结果为后续开展高副结合面(如轴承等)润滑及动力学分析提供了理论基础。
In order to precisely calculate TCS between spherical surfaces,this paper presented the establishment of fractal model for TCS calculations between spheres considering friction factors.This model was obtained by introducing the equation of critical contact area of elasto-plastic deformation with friction and employing the basic theory of TCS,and based on the fractal contact model of two spherical surfaces.The numerical results show that:the TCS increases with normal loads;the relationship between TCS and friction coefficient is vary as the fractal dimension changes.It is efficient to improve the TCS by adding material propertied parameters and fractal roughness amplitude.The maximum value appears in TCS when the fractal dimension is 1.5and the TCS increases significantly when the fractal dimension is about 1.5.Furthermore,TCS of inner contact is bigger than that of outer contact;TCS increases with curvature radius of cylinders.The theory herein helps to analyze the lubrication and dynamic characteristics between high-pairs joint surfaces(like bearings)in the future.
In order to precisely calculate TCS between spherical surfaces,this paper presented the establishment of fractal model for TCS calculations between spheres considering friction factors.This model was obtained by introducing the equation of critical contact area of elasto-plastic deformation with friction and employing the basic theory of TCS,and based on the fractal contact model of two spherical surfaces.The numerical results show that:the TCS increases with normal loads;the relationship between TCS and friction coefficient is vary as the fractal dimension changes.It is efficient to improve the TCS by adding material propertied parameters and fractal roughness amplitude.The maximum value appears in TCS when the fractal dimension is 1.5and the TCS increases significantly when the fractal dimension is about 1.5.Furthermore,TCS of inner contact is bigger than that of outer contact;TCS increases with curvature radius of cylinders.The theory herein helps to analyze the lubrication and dynamic characteristics between high-pairs joint surfaces(like bearings)in the future.
引文
[1]张学良,温淑花.基于接触分形理论的结合面切向接触刚度分形模型[J].农业机械学报,2002,33(3):91-93.Zhang Xueliang,Wen Shuhua.A Fractal Model of Tangential Contact Stiffness of Joint Surfaces Based on the Contact Fractal Theory[J].Transactions of the Chinese Society for Agricultural Machinery,2002,33(3):91-93.
[2]田红亮,赵春华,方子帆,等.基于各向异性分形理论的结合面切向刚度改进模型[J].农业机械学报,2013,44(3):257-266.Tian Hongliang,Zhao Chunhua,Fang Zifan,et al.Improved Model of Tangential Contact Siffness for Joint Interface Using Anisotropic Fractal Theory[J].Transactions of the Chinese Society of Agricultural Machinery,2013,44(3):257-266.
[3]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 Xian Jiaotong University,2014,48(7):46-52.
[4]李小彭,鞠行,赵光辉,等.考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析[J].摩擦学学报,2013,33(5):463-468.Li Xiaopeng,Ju Xing,Zhao Guanghui,et al.Fractal Prediction Model of Tangential Contact Stiffness of Joint Surface Considering Friction Factors and Its Simulation Analysis[J].Tribology,2013,33(5):463-468.
[5]赵韩,陈奇,黄康.两圆柱体结合面的法向接触刚度分形模型研究[J].机械工程学报,2011,47(7):53-58.Zhao Han,Chen Qi,Huang Kang.Fractal Model of Normal Contact Stiffness between Two CylindersJoint Interfaces[J].Journal of Mechanical Engineering,2011,47(7):53-58.
[6]陈奇,赵韩,黄康.齿轮结合面切向接触刚度分形计算模型研究[J].农业机械学报,2011,42(2):203-206.Chen Qi,Zhao Han,Huang Kang.Fractal Model of Tangential Contact Stiffness between Gearss Joint Surfaces[J].Transactions of the Chinese Society of Agricultural Machinery,2011,42(2):203-206.
[7]Chen Q,Huang K,Zhao H,et al.Simulation and Analysis of the Model of Calculating Contact Tangential Stiffness between CylindersJoint Interfaces by MATLAB[J].Applied Mechanics and Materials,2012,190:177-181.
[8]Shi J,Cao X,Zhu H.Tangential Contact Stiffness of Rough Cylindrical Faying Surfaces Based on the Fractal Theory[J].Journal of Tribology,2014,136(4):041401.
[9]Majumdar A,Bhushan B.Fractal Model of Elasticplastic Contact between Rough Surfaces[J].Journal of Tribology,1991,113(1):1-11.
[10]葛世荣,朱华.摩擦学的分形[M].北京:机械工业出版社,2005.
[11]陈奇.基于分形理论的汽车变速箱齿轮接触强度研究[D].合肥:合肥工业大学,2010.
[12]GB/T308-2002滚动轴承-钢球[S].北京:中国标准出版社,2002.
[13]郭明月.深沟球轴承结构参数对振动规律影响的仿真与试验研究[D].杭州:中国计量学院,2014.
[14]成大先.机械设计手册(第五版)[M].北京:化学工业出版社,2010.
[15]王薇.分形理论在表面粗糙度非接触测量中的应用[D].长春:吉林大学,2006.
[16]GB/T 18254-2002高碳铬轴承钢[S].北京:中国标准出版社,2002.
[2]田红亮,赵春华,方子帆,等.基于各向异性分形理论的结合面切向刚度改进模型[J].农业机械学报,2013,44(3):257-266.Tian Hongliang,Zhao Chunhua,Fang Zifan,et al.Improved Model of Tangential Contact Siffness for Joint Interface Using Anisotropic Fractal Theory[J].Transactions of the Chinese Society of Agricultural Machinery,2013,44(3):257-266.
[3]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 Xian Jiaotong University,2014,48(7):46-52.
[4]李小彭,鞠行,赵光辉,等.考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析[J].摩擦学学报,2013,33(5):463-468.Li Xiaopeng,Ju Xing,Zhao Guanghui,et al.Fractal Prediction Model of Tangential Contact Stiffness of Joint Surface Considering Friction Factors and Its Simulation Analysis[J].Tribology,2013,33(5):463-468.
[5]赵韩,陈奇,黄康.两圆柱体结合面的法向接触刚度分形模型研究[J].机械工程学报,2011,47(7):53-58.Zhao Han,Chen Qi,Huang Kang.Fractal Model of Normal Contact Stiffness between Two CylindersJoint Interfaces[J].Journal of Mechanical Engineering,2011,47(7):53-58.
[6]陈奇,赵韩,黄康.齿轮结合面切向接触刚度分形计算模型研究[J].农业机械学报,2011,42(2):203-206.Chen Qi,Zhao Han,Huang Kang.Fractal Model of Tangential Contact Stiffness between Gearss Joint Surfaces[J].Transactions of the Chinese Society of Agricultural Machinery,2011,42(2):203-206.
[7]Chen Q,Huang K,Zhao H,et al.Simulation and Analysis of the Model of Calculating Contact Tangential Stiffness between CylindersJoint Interfaces by MATLAB[J].Applied Mechanics and Materials,2012,190:177-181.
[8]Shi J,Cao X,Zhu H.Tangential Contact Stiffness of Rough Cylindrical Faying Surfaces Based on the Fractal Theory[J].Journal of Tribology,2014,136(4):041401.
[9]Majumdar A,Bhushan B.Fractal Model of Elasticplastic Contact between Rough Surfaces[J].Journal of Tribology,1991,113(1):1-11.
[10]葛世荣,朱华.摩擦学的分形[M].北京:机械工业出版社,2005.
[11]陈奇.基于分形理论的汽车变速箱齿轮接触强度研究[D].合肥:合肥工业大学,2010.
[12]GB/T308-2002滚动轴承-钢球[S].北京:中国标准出版社,2002.
[13]郭明月.深沟球轴承结构参数对振动规律影响的仿真与试验研究[D].杭州:中国计量学院,2014.
[14]成大先.机械设计手册(第五版)[M].北京:化学工业出版社,2010.
[15]王薇.分形理论在表面粗糙度非接触测量中的应用[D].长春:吉林大学,2006.
[16]GB/T 18254-2002高碳铬轴承钢[S].北京:中国标准出版社,2002.