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Fretting phenomena exist widely in structural engineering. In recent years, it has attracted more attention from scientists and technicians. In order to study the fretting wear in depth, we establish a new method of calculating the wear rate of material in vibratory environment. Firstly, according to the characteristics of friction pair and fretting wear process in fretting friction system, the asymmetric double potential well model is proposed and the potential energy function of the model is given. The transfer of particles between the two kinds of materials during the fretting is regarded as the motion of the particles in the two potential wells which are asymmetrical, and the particle motion equation in the potential well is established. Furthermore, considering the characteristics of the randomness, time-varying and irreversibility of particle motion in fretting friction system, a theoretical model is established by using the non-equilibrium statistical theory, which is based on the particle equation motion, combined with the Langevin equation in random theory and the Foker-Planck equation in the non-equilibrium statistical theory. The probability density distribution function of particles moving from the interior of the material to the material surface at any time is obtained. A method of calculating the wear rate is proposed by integrating the probability density distribution function. Secondly, by calculating the wear rate of the friction pair which consists of metal materials Mg and Fe, we obtain the potential energy function of the asymmetric double potential well model as the different surface energies of both materials. Furthermore, the probability density distribution function of particles moving in this friction pair is calculated. Then, the change of wear rate with wear time and width of potential well is derived, and the effect of normal force on wear rate is further analyzed. The results of calculation and analysis show that the wear rate of material decreases with the decrease of the width of the potential well in the friction pair system, decreases with the increase of wear time and increases with the increase of the normal force of the load, and the surface of the relatively soft material in the friction pair system is more likely to wear off. Finally, the conclusions of the theoretical model accord with the experimental results, illustrating the applicability of the theoretical model.
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Keywords:
- fretting wear /
- asymmetrical potential well /
- nonequilibrium statistical theory /
- wear rate
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[2] Hao H W, Yang M S, Sun S Q, Wang Y J, Zhang Z H 2016 Iron. Steel. 28 61 (in Chinese) [郝宏伟, 杨卯生, 孙世清, 王艳江, 张志慧 2016 钢铁研究学报 28 61]
[3] Wang Z, Cai Z B, Sun Y, Wu S B, Peng J F, Zhu M H 2017 Die. Mould Ind. 37 225 (in Chinese) [王璋, 蔡振兵, 孙阳, 吴松波, 彭金方, 朱旻昊 2017 摩擦学学报 37 225]
[4] Ding Y, Liang J, Deng K, Bo L, Dai Z D 2017 Chin. J. Nonferrous Met. 27 532 (in Chinese) [丁燕, 梁军, 邓凯, 柏林, 戴振东 2017 中国有色金属学报 27 532]
[5] Zhang D K, Ge S R, Zhu Z C 2002 J. Chin. Univ. Min. Technol. 31 367 (in Chinese) [张德坤, 葛世荣, 朱真才 2002 中国矿业大学学报 31 367]
[6] Zhu Z M, Jiang H 2017 Die. Mould Ind. 37 558 (in Chinese) [朱忠猛, 蒋晗 2017 摩擦学学报 37 558]
[7] Xiao J J 2013 High Energy Material Molecular Dynamics (1st Ed.) (Beijing: Science Press) pp7-13 (in Chinese) [肖继军 2013高能材料分子动力学(第一版) (北京: 科学出版社) 第713页]
[8] Wang Z G, Zhang P, Chen J X, Bai Q S, Liang Y C 2015 Acta Phys. Sin. 64 198104 (in Chinese) [王治国, 张鹏, 陈家轩, 白清顺, 梁迎春 2015 64 198104]
[9] Johnson K L 1986 Die. Mould Ind. 108 464
[10] Lu H 2008 M. S. Thesis (Beijing: Beijing Institute of Technology) (in Chinese) [卢宏 2008 硕士学位论文 (北京:北京理工大学)]
[11] Li R S 1995 Balanced and Non-equilibrium Statistical Mechanics (1st Ed.) (Beijing: Tsinghua University Press) pp4-6 (in Chinese) [李如生 1995 平衡和非平衡统计力学(第一版) (北京: 清华大学出版社)第46页]
[12] Xing X S 1986 Sci. China: Ser. A 29 501 (in Chines) [邢修三 1986 中国科学A辑 29 501]
[13] Bao J D 2009 Classical and Stochastic Simulation (1st Ed.) (Beijing: Science Press) p107 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (第一版) (北京: 科学出版社)第107页]
[14] Xing X S 1991 Chin. J. Mater. Res. 5 22 (in Chinese) [邢修三 1991 材料研究学报 5 22]
[15] Hu G, Hao B L 1994 Stochastic Force and Nonlinear System (1st Ed.) (Shanghai: Shanghai Science and Technology Education Press) p127 (in Chinese) [胡岗, 赫柏林 1994 随机力与非线性系统 (第一版) (上海: 上海科技教育出版社) 第127页]
[16] Xu Z M, Huang P 16 2006 Die. Mould Ind. 26 159 (in Chinese) [许中明, 黄平 2006 摩擦学学报 26 159]
[17] RiedoE, GneccoE, Bennewitz R, Meyer E 2003 Phys. Rev. Lett. 91 084502
[18] Jiang L R 2015 M. S. Thesis (Chengdu: Southwest Jiaotong University) (in Chinese) [蒋利荣 2015 硕士学位论文 (成都: 西南交通大学)]
[19] Li Z J, Zhang D T, Shao M 2009 Lubricat. Oil. 34 61 (in Chinese) [李助军, 张大童, 邵明 2009 润滑与密封 34 61]
[20] Wang K S, Liu Q K, Zhang D Y 2009 Acta Phys. Sin. 58 89 (in Chinese) [王可胜, 刘全坤, 张德元 2009 58 89]
[21] Ma L 2009 M. S. Thesis (Chengdu: Southwest Jiaotong University) (in Chinese) [马磊 2009 硕士学位论文 (成都: 西南交通大学)]
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[1] Zhou Z R, Vincent L 2002 Fretting Wear (1st Ed.) (Beijing: Science Press) pp30-32 (in Chinese) [周仲荣, Leo Vincent 2002微动磨损(第一版) (北京:科学出版社) 第3032页]
[2] Hao H W, Yang M S, Sun S Q, Wang Y J, Zhang Z H 2016 Iron. Steel. 28 61 (in Chinese) [郝宏伟, 杨卯生, 孙世清, 王艳江, 张志慧 2016 钢铁研究学报 28 61]
[3] Wang Z, Cai Z B, Sun Y, Wu S B, Peng J F, Zhu M H 2017 Die. Mould Ind. 37 225 (in Chinese) [王璋, 蔡振兵, 孙阳, 吴松波, 彭金方, 朱旻昊 2017 摩擦学学报 37 225]
[4] Ding Y, Liang J, Deng K, Bo L, Dai Z D 2017 Chin. J. Nonferrous Met. 27 532 (in Chinese) [丁燕, 梁军, 邓凯, 柏林, 戴振东 2017 中国有色金属学报 27 532]
[5] Zhang D K, Ge S R, Zhu Z C 2002 J. Chin. Univ. Min. Technol. 31 367 (in Chinese) [张德坤, 葛世荣, 朱真才 2002 中国矿业大学学报 31 367]
[6] Zhu Z M, Jiang H 2017 Die. Mould Ind. 37 558 (in Chinese) [朱忠猛, 蒋晗 2017 摩擦学学报 37 558]
[7] Xiao J J 2013 High Energy Material Molecular Dynamics (1st Ed.) (Beijing: Science Press) pp7-13 (in Chinese) [肖继军 2013高能材料分子动力学(第一版) (北京: 科学出版社) 第713页]
[8] Wang Z G, Zhang P, Chen J X, Bai Q S, Liang Y C 2015 Acta Phys. Sin. 64 198104 (in Chinese) [王治国, 张鹏, 陈家轩, 白清顺, 梁迎春 2015 64 198104]
[9] Johnson K L 1986 Die. Mould Ind. 108 464
[10] Lu H 2008 M. S. Thesis (Beijing: Beijing Institute of Technology) (in Chinese) [卢宏 2008 硕士学位论文 (北京:北京理工大学)]
[11] Li R S 1995 Balanced and Non-equilibrium Statistical Mechanics (1st Ed.) (Beijing: Tsinghua University Press) pp4-6 (in Chinese) [李如生 1995 平衡和非平衡统计力学(第一版) (北京: 清华大学出版社)第46页]
[12] Xing X S 1986 Sci. China: Ser. A 29 501 (in Chines) [邢修三 1986 中国科学A辑 29 501]
[13] Bao J D 2009 Classical and Stochastic Simulation (1st Ed.) (Beijing: Science Press) p107 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (第一版) (北京: 科学出版社)第107页]
[14] Xing X S 1991 Chin. J. Mater. Res. 5 22 (in Chinese) [邢修三 1991 材料研究学报 5 22]
[15] Hu G, Hao B L 1994 Stochastic Force and Nonlinear System (1st Ed.) (Shanghai: Shanghai Science and Technology Education Press) p127 (in Chinese) [胡岗, 赫柏林 1994 随机力与非线性系统 (第一版) (上海: 上海科技教育出版社) 第127页]
[16] Xu Z M, Huang P 16 2006 Die. Mould Ind. 26 159 (in Chinese) [许中明, 黄平 2006 摩擦学学报 26 159]
[17] RiedoE, GneccoE, Bennewitz R, Meyer E 2003 Phys. Rev. Lett. 91 084502
[18] Jiang L R 2015 M. S. Thesis (Chengdu: Southwest Jiaotong University) (in Chinese) [蒋利荣 2015 硕士学位论文 (成都: 西南交通大学)]
[19] Li Z J, Zhang D T, Shao M 2009 Lubricat. Oil. 34 61 (in Chinese) [李助军, 张大童, 邵明 2009 润滑与密封 34 61]
[20] Wang K S, Liu Q K, Zhang D Y 2009 Acta Phys. Sin. 58 89 (in Chinese) [王可胜, 刘全坤, 张德元 2009 58 89]
[21] Ma L 2009 M. S. Thesis (Chengdu: Southwest Jiaotong University) (in Chinese) [马磊 2009 硕士学位论文 (成都: 西南交通大学)]
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