Research on Fractal Contact Model for Contact Carrying Capacity of Two Cylinders’ Surfaces Considering Friction Factors

doi:10.3901/JME.2016.07.114

Abstract

Abstract: In order to establish more accurate fractal contact model for analyzing contact carrying capacity of two cylinder’s surfaces, the process of creating a new fractal contact model considering the friction factors is presented. This model is derived by substituting the theory of calculating critical contact area of elastoplastic deformation with friction, and the equation of contact area distribution for cylinder surfaces into M-B model. Through the prediction analysis of the model affected by the main parameters in the Matlab, it is concluded that decreasing the friction coefficient, reducing the roughness amplitude and increasing material propertied parameters is helpful to improve the contact carrying capacity and ameliorate the mechanical characteristics of two contact bodies; the effects of fractal dimension on contact carrying capacity can’t be described as a simple linear relations and there is an optimal value of fractal dimension for the maximal contact carrying capacity. The research of the model helps to provide a new theory conference for analyzing the contact carrying capacity of gears and the other related products.

Key words: contact carrying capacity, cylinders, fractal theory, friction

CLC Number:

TH114

CHEN Qi, HUANG Shouwu, ZHANG Zhen, QIU Mingming. Research on Fractal Contact Model for Contact Carrying Capacity of Two Cylinders’ Surfaces Considering Friction Factors[J]. Journal of Mechanical Engineering, 2016, 52(7): 114-121.

References

[1] MAJUMDAR A,BHUSHAN B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces [J]. Journal of Tribology,1990,112(2)：205-216.
[2] MAJUMDAR A,BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces [J]. Journal of Tribology,1991,113(1)：1-11.
[3] BHUSHAN B,MAJUMDAR A. Elastic-plastic contact model for bifractal surfaces[J]. Wear,1992,153(1)：53-64.
[4] 陈奇,黄康,张彦,等. 两任意轮廓弹性体接触应力计算的分形模型研究[J]. 机械强度,2012,34(4)：557-561.
CHEN Qi,HUANG Kang,ZHANG Yan,et al. Research on fractal model of calculating the contact stress about two elastic body with arbitrary profile[J]. Journal of Mechanical Strength,2012,34(4)：557-561.
[5] ZHAO Han,CHEN Qi,HUANG Kang. Analysis of two ball's surface contact stress based on fractal theory[J]. Materials Science Forum,2011(675-677)：619-627.
[6] 黄康,赵韩,陈奇. 两圆柱体表面接触承载能力的分形模型研究[J]. 摩擦学学报,2008,28(6)：529-533.
HUANG Kang,ZHAO Han,CHEN Qi. Research of fractal contact model on contact carrying capacity of two cylinders' surface [J]. Tribology,2008,28(6)：529-533
[7] 陈奇,黄康,张彦,等. 基于分形接触模型的齿轮接触强度影响参数分析[J]. 中国机械工程,2013,16(016)： 2208-2211.
CHEN Qi,HUANG Kang,ZHANG Yan,et al. Analysis of influence parameters on gear’s contact strength based on fractal contact model[J]. China Mechanical Engineering,2013,16(016)：2208-2211.
[8] 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(2)：210-213.
LI Xiaopeng,GUO Hao,LIU Jingnian,et al. Fractal model and simulation of normal contact stiffness considering the friction between joint surfaces[J]. Journal of Vibration,Measurement & Diagnosis,2013(2)：210-213.
[9] 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 for tangential contact stiffness of joint surface considering friction factors and its simulation analysis[J]. Tribology,2013,33(5)：463-468.
[10] 李小彭,王伟,赵米鹊,等. 考虑摩擦因素影响的结合面切向接触阻尼分形预估模型及其仿真[J]. 机械工程学报,2013,48(23)：46-50.
LI Xiaopeng,WANG Wei,ZHAO Mique,et al. Fractal prediction model for tangential contact damping of joint surface considering friction factors and its simulation[J]. Journal of Mechanical Engineering,2013,48(23)：46-50.
[11] 魏龙,刘其和,张鹏高. 基于分形理论的滑动摩擦表面接触力学模型[J]. 机械工程学报,2012,48(17)：106-113.
WEI Long,LIU Qihe,ZHANG Penggao. Sliding friction surface contact mechanics model based on fractal theory[J]. Journal of Mechanical Engineering,2012,48(17)：106-113.
[12] GOEDECKE A,MOCK R. A new fractal model for dynamic contact phenomena including friction[C/CD]// Proceedings of the European COMSOL Conference,2008.
[13] 兰国生,张学良,丁红钦. 基于分形理论的结合面静摩擦因数改进模型[J]. 农业机械学报,2012,43(1)：213-218.
LAN Guosheng,ZHANG Xueliang,DING Hongqin,et al. Modified model of static friction coefficient of joint interfaces based on fractal theory[J]. Transactions of the Chinese Society for Agricultural Machinery,2012,43(1)： 213-218.
[14] 田红亮,朱大林,秦红玲. 结合面静摩擦因数分形模型[J]. 应用力学学报,2011,28(2)：158-162.
TIAN Hongliang,ZHU Dalin,QIN Hongling. Fractal model of static friction coefficient of joint interface and its simulation[J]. Chinese Journal of Applied Mechanics,2011,28(2)：158-162.
[15] YOU J,CHEN T. A static friction model for the contact of fractal surfaces[C]// Proceedings of the Institution of Mechanical Engineers,Part J： Journal of Engineering Tribology,2010,224(5)：513-518.
[16] HANAOR D A,GAN Y,EINAV I. Effects of surface structure deformation on static friction at fractal interfaces[J]. Géotechnique Letters,2013(3)：52-58.
[17] MAJUMDAR A,BHUSHAN B. Elastic-plastic contact model for bifractal surfaces[J]. Wear,1992,153：53-64.
[18] 葛世荣,朱华. 摩擦学的分形[M]. 北京：机械工业出版社,2005.
GE Shirong,ZHU Hua. Fractal tribology[M]. Beijing： China Machine Press,2005.
[19] MAJUMDAR A,BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces[J]. ASME Journal of Tribology,1991,113：1-11.
[20] 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.
CHEN Qi. Research on gear contact strength analysis of automobile gearbox by fractal theory[D]. Hefei：Hefei University of Technology,2010.
[21] 陈奇,赵韩,黄康,等. 分形理论在齿轮接触应力分析中的应用研究[J]. 中国机械工程,2010,21(9)：1014-1017,1057.
CHEN Qi,ZHAO Han,HUANG Kang,et al. Application research on gear contact stress analysis by fractal theory[J]. China Mechanical Engineering,2010,21(9)：1014-1017,1057.
[22] 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 cylinders’ joint interfaces [J]. Journal of Mechanical Engineering,2011,47(7)：53-58.
[23] 肖乾,王成国,周新建,等. 不同擦系数条件下的轮轨滚动接触特性分析[J]. 中国铁道科学,2011(4)： 66-71.
XIAO Qian,WANG Chengguo,ZHOU Xinjian,et al. Analysis on the characteristics of wheel/rail rolling contact under different friction coefficient[J]. China Railway Science,2011(4)：66-71.
[24] 夏延秋,丁津原,马先贵,等. 摩擦系数对齿轮接触疲劳寿命的影响[J]. 机械传动,2002(1)：48-49.
XIA Yanqiu,DING Jinyuan,MA Xiangui,et al. The Influence of friction coefficient on the contact fatigue life of gear[J]. Journal of Mechanical Transmission,2002 (1)：48-49.
[25] FEDER J. Fractals[M]. New York：Plenum,1988.
[26] 葛世荣,TONDER K. 粗糙表面的分形特征与分形表达研究[J]. 摩擦学学报,1997,17(1)：73-80.
GE Shirong,TONDER K. The fractal behavior and fractal characterization of rough surfaces[J]. Tribology,1997,17(1)：73-80.