考虑三维结合部形貌的静摩擦因数非线性分形模型

doi:10.12068/j.issn.1005-3026.2017.10.016

东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (10): 1447-1452.DOI: 10.12068/j.issn.1005-3026.2017.10.016

考虑三维结合部形貌的静摩擦因数非线性分形模型

潘五九，李小彭，王雪，李木岩

(东北大学机械工程与自动化学院，辽宁沈阳110819)

收稿日期:2016-05-09 修回日期:2016-05-09 出版日期:2017-10-15 发布日期:2017-10-13
通讯作者: 潘五九
作者简介:潘五九(1986-)，男，安徽当涂人，东北大学博士研究生; 李小彭(1976-)，男，江西宁都人，东北大学教授，博士生导师.
基金资助:
国家自然科学基金资助项目(51275079，51575091)；中央高校基本科研业务专项资金资助项目(N160306003).

Nonlinear Fractal Model for Static Friction Coefficient Considering Three-Dimensional Topography of Joint Surfaces

PAN Wu-jiu， LI Xiao-peng， WANG Xue， LI Mu-yan

School of Mechanical Engineering & Automation， Northeastern University， Shenyang 110819， China.

Received:2016-05-09 Revised:2016-05-09 Online:2017-10-15 Published:2017-10-13
Contact: LI Xiao-peng
About author:-
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摘要/Abstract

摘要： 考虑三维结合部形貌的W-M函数，推导了结合部静摩擦因数非线性分形理论模型.数值模拟了考虑三维形貌的结合部静摩擦因数与法向载荷P、分形维数D、分形尺度系数G的关系，以及在二维分形和三维分形模型中的差异.结果表明:结合部静摩擦因数与法向载荷成单调递增关系，与分形尺度系数成单调递减关系.当D小于2.5时，静摩擦因数随分形维数的增大而增大;当D大于2.5时，静摩擦因数随分形维数的增大而减小;三维分形下的静摩擦因数小于二维分形下的静摩擦因数.

关键词: 三维形貌, 结合部, 静摩擦因数, 分形理论, 非线性

Abstract: Considering three-dimensional topography W-M function of joint surfaces， a nonlinear fractal model for static friction coefficient considering three-dimensional topography of joint surfaces was established. Relations between the static friction coefficient considering three-dimensional topography of joint surfaces and normal load， the fractal dimension， fractal roughness were numerically simulated， as well as the difference between static friction coefficients in the two-dimensional fractal model and three dimensional fractal model. The results showed that the static friction coefficient increases monotonically with the increase of normal load， and decreases monotonically with the increase of topothesy. When D is less than 2.5， the static friction coefficient increases with the increase of fractal dimension; when the D is greater than 2.5， the static friction coefficient decreases with the increase of fractal dimension; the three-dimensional fractal static friction coefficient is smaller than that of the two-dimensional.

Key words: three-dimensional topography, joint surfaces, static friction coefficient, fractal theory, nonlinear

中图分类号:

TH113.1

潘五九，李小彭，王雪，李木岩. 考虑三维结合部形貌的静摩擦因数非线性分形模型[J]. 东北大学学报:自然科学版, 2017, 38(10): 1447-1452.

PAN Wu-jiu， LI Xiao-peng， WANG Xue， LI Mu-yan. Nonlinear Fractal Model for Static Friction Coefficient Considering Three-Dimensional Topography of Joint Surfaces[J]. Journal of Northeastern University Natural Science, 2017, 38(10): 1447-1452.

参考文献

[1]Ren Y，Beards C F.Identification of effective linear joints using coupling and joint identification techniques［J］.ASME Journal of Vibration and Acoustics，1998，120(2):331-338.
[2]Ibrahim R A，Pettit C L.Uncertainties and dynamic problems of bolted joints and other fasteners［J］.Journal of Sound and Vibration，2005，279(3/5):857-936.
[3]李小彭，梁友鉴，孙德华，等.系统参数对自激振动系统动力学稳定性的影响［J］.东北大学学报(自然科学版)，2015，36(5):690-694.(Li Xiao-peng，Liang You-jian，Sun De-hua，et al.Impact of the system parameters on self-excited vibration system dynamic stability［J］.Journal of Northeastern University(Natural Science)，2015，36(5):690-694.)
[4]Baramsky N，Seibel A，Schlattmann J.Modeling of friction-induced vibrations during tightening of bolted joints［J］.Proceedings in Applied Mathematics and Mechanics，2016，16(1):259-260.
[5]Iroz I，Hanss M，Eberhard P.Transient simulation of friction-induced vibrations using an elastic multibody approach［J］.Multibody System Dynamics，2017，39(1/2):37-49.
[6]田红亮，赵春华，方子帆，等.金属材料表面静摩擦学特性的预测研究——理论模型［J］.振动与冲击，2013，32(12):40-44.(Tian Hong-liang，Zhao Chun-hua，Fang Zi-fan，et al.Predication investigation on static tribological performance of metallic material surfaces—theoretical model ［J］.Journal of Vibration and Shock，2013，32(12):40-44.)
[7]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.
[8]兰国生，张学良，丁红钦，等.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 Guo-sheng，Zhang Xue-liang，Ding Hong-qin，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.)
[9]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.
[10]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.
[11]Yan W，Komvopoulos K.Contact analysis of elastic-plastic fractal surfaces［J］.Journal of Applied Physics，1998，84(7):3617-3624.
[12]Li X P，Yue B，Zhao G，et al.Fractal prediction model for normal contact damping of joint surfaces considering friction factors and its simulation［J］.Advances in Mechanical Engineering，2014，9(1):1-5.
[13]Hamilton G M.Explicit equations for the stresses beneath a sliding spherical contact［J］.Journal of Mechanical Engineering Science，1983，197(1):53-59.
[14]田红亮，刘芙蓉，赵春华，等.金属材料表面静摩擦学特性的预测研究——实验佐证［J］.振动与冲击，2014，33(1):209-220.(Tian Hong-liang，Liu Fu-rong，Zhao Chun-hua，et al.Prediction of static friction performance of metallic material surfaces with experimental proof［J］.Journal of Vibration and Shock，2014，33(1):209-220.)

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考虑三维结合部形貌的静摩擦因数非线性分形模型

Nonlinear Fractal Model for Static Friction Coefficient Considering Three-Dimensional Topography of Joint Surfaces

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