表面张力是物质表面层分子间存在的力，它对机械结合面的接触特性有着重要的影响。为此，采用Nayak随机过程模型表征各向同性表面上微凸体的高度与曲率分布，建立考虑表面张力的单个微凸体接触模型，通过高斯-切比雪夫求积公式求解验证了模型的正确性；基于统计学理论将单个微凸体的计算模型扩展到整个粗糙表面上，建立了新的结合面接触模型，揭示了表面张力对结合面接触载荷、真实接触面积以及接触刚度的影响规律。结果表明：当两表面间平均距离相同时，与传统不考虑表面张力的模型相比，新模型具有较大的接触载荷和接触刚度，较小的真实接触面积；当接触载荷增大时，真实接触面积增大的速率随着表面张力的增大而减小；接触刚度随着接触载荷或真实接触面积的增大而增大，且表面张力越大，递增速率越快。
Abstract
Surface tension is a force existing among surface layer molecules of material and significantly affecting contact characteristics of mechanical interface. Here, Nayak random process model was introduced to characterize height and curvature distribution of an asperity on an isotropic surface, and establish a contact model of a single asperity considering surface tension. Gauss-Chebyshev quadrature formula was used to verify the correctness of the model. Then, the calculation model of a single asperity was extended to a whole rough surface based on the statistics theory to build a new contact model of mechanical interface. Effect laws of surface tension on interface contact load, actual contact area, and contact stiffness were revealed. Results showed that when the mean distance between two surfaces keeps the same, compared with the traditional model not considering surface tension, the new model has larger contact load and contact stiffness, and smaller actual contact area; when contact load grows, actual contact area increasing rate drops with increase in surface tension; contact stiffness grows with increase in contact load or actual contact area, the greater the surface tension, the faster the contact stiffness increasing rate.
关键词
机械结合面 /
表面张力 /
接触特性建模 /
高斯-切比雪夫求积
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Key words
mechanical interface /
surface tension /
contact characteristics modeling /
Gauss-Chebyshev quadrature
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参考文献
[1] Greenwood J A, Williamson J B P. Contact of Nominally Flat Surfaces[J]. Proceedings of the Royal Society of London,1966,295(1442):300-319.
[2] Pullen J, Williamson J B P. On the Plastic Contact of Rough Surfaces[J]. Proceedings of the Royal Society of London,1972,327(1569):159-173.
[3] Chang W R, Etsion I, Bogy D B. An elastic-plastic model for the contact of rough surfaces[J]. Journal of tribology, 1987,109(2):257-263.
[4] 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.
[5] 李玲，李治强，蔡安江，等. 修正G-W模型研究结合面微观接触特性[J]. 振动与冲击，2017, 36(21):53-59.
LI Ling, LI Zhi-qiang, CAI An-jiang, et al. Analysis on the micro-contact characteristics of joint interfaces by using a modified G-W model[J]. Journal of Vibration and Shock, 2017, 36(21):53-59.
[6] 王南山，张学良，兰国生，等. 临界接触参数连续的粗糙表面法向接触刚度弹塑性分形模型[J]. 振动与冲击，2014, 33(9):72-77.
WANG Nan-shan, ZHANG Xue-liang, LAN Guo-sheng, et al. Elastoplastic fractal model for normal contact stiffness of rough surfaces with continuous critical contact parameters[J]. Journal of Vibration and Shock, 2014, 33(9):72-77.
[7] Majumdar A, Bhushan B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology, 1991,113(1):1-11.
[8] 孙见君，张凌峰，於秋萍，等. 基于粗糙表面分形表征新方法的结合面法向接触刚度模型[J]. 振动与冲击，2019, 38(7):212-217.
SUN Jian-jun, ZHANG Ling-feng, YU Qiu-ping, et al. A joint surface normal contact stiffness model based on a new rough surface fractal characterization method[J]. Journal of Vibration and Shock, 2019, 38(7):212-217.
[9] Hertz H. On the contact between elastic bodies[J]. Reine Angew Math,1882,92:156-171.
[10] Huang Z P, Sun L. Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis[J]. Acta Mechanica,2007,190(1-4):151-163.
[11] Zhu X, Xu W. Effect of surface tension on the behavior of adhesive contact based on Lennard–Jones potential law[J]. Journal of the Mechanics and Physics of Solids,2018,111:170-183.
[12] Ru C Q. Size effect of dissipative surface stress on quality factor of microbeams[J]. Applied Physics Letters, 2009,94(5):051905.
[13] Olsson P，Park H S. On the importance of surface elastic contributions to the flexural rigidity of nanowires[J]. Journal of the Mechanics & Physics of Solids,2012, 60(12):2064-2083.
[14] Hajji M A. Indentation of a Membrane on an Elastic Half Space[J]. Journal of Applied Mechanics,1978,45(2): 320-324.
[15] Huang G Y, Yu S W. Effect of surface elasticity on the interaction between steps[J]. Journal of Applied Mechanics,2007,74(4):821-823.
[16] He L H, Lim C W. Surface Green function for a soft elastic half-space: Influence of surface stress[J]. International Journal of Solids & Structures,2006,43(1): 132-143.
[17] Gao X, Hao F, Fang D, et al. Boussinesq problem with the surface effect and its application to contact mechanics at the nanoscale[J]. International Journal of Solids & Structures,2013,50(16-17):2620-2630.
[18] Xu X, Jagota A, Hui C Y. Effects of surface tension on the adhesive contact of a rigid sphere to a compliant substrate[J]. Soft Matter,2014,10(26):4625-4632.
[19] Nayak P R. Random process model of rough surfaces[J]. Journal of Lubrication Technology,1971,93(3):398-407.
[20] Longuet-Higgins M S. The Statistical Analysis of a Random, Moving Surface[J]. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences,1957,249(966):321-387.
[21] Greenwood J A. A simplified elliptic model of rough surface contact[J]. Wear,2006,261(2):191-200.
[22] Ding Y, Niu X R, Wang G F. Elastic compression of nanoparticles with surface energy[J]. Journal of Physics D Applied Physics,2015,48(48):485303.
[23] Erdogan F, Gupta G D. On the numerical solution of singular integral equations[J]. Quarterly of Applied Mathematics,1972,29(4):525-534.
[24] Panda S, Panzade A, Sarangi M, et al. Spectral Approach on Multi-scale Roughness Characterization of Nominally Rough Surfaces[J]. Journal of Tribology,2017, 139(3):031402.
[25] Popov V L. Contact mechanics and friction[M]. Berlin: Springer Berlin Heidelberg, 2010.
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