混合润滑状态下粗糙分形界面的接触载荷与油膜厚度研究

doi:10.3901/JME.2025.11.231

摘要/Abstract

摘要： 粗糙分形界面的混合润滑接触现象广泛存在于晶圆减薄、齿轮传动、圆柱滚子轴承等机械系统，混合润滑状态下等效油膜厚度的准确计算至关重要。目前基于分形理论接触力学模型采用离散基准尺度的计算方法，膜厚计算忽略了外载荷的动态影响，且等效油膜厚度依赖数值方法导致缺乏显式表达。鉴于此，首先将接触面积和基准长度作为二重积分区域，修正了现有接触力学模型基准长度不连续的问题，再根据外载荷与最大微凸体变形量的函数关系，推导了等效油膜厚度的解析式，实现了粗糙界面混合润滑状态下固液载荷的解耦，最后与文献中的膜厚实验数据对比，验证了该方法的有效性。研究表明：等效油膜厚度与外载荷、弹性模量负相关，而与柱体半径、润滑油黏度及黏压指数正相关；粗糙接触界面从混合润滑进入全膜润滑状态所需的临界速度与外载荷正相关，固体载荷分配系数与外载荷、表面粗糙度正相关；增大接触面的分形维数或减小分形粗糙度，均可提高润滑油的接触占比，为减少微凸体接触引发的表面摩擦磨损及提高零部件使用寿命提供依据。

关键词: 机械结合面, 分形粗糙表面, 混合润滑, 微凸体接触, 油膜厚度

Abstract: The mixed lubrication contact phenomenon of rough fractal interfaces widely exists in mechanical systems such as wafer thinning, gear transmission, and cylindrical roller bearings. The accurate calculation of the equivalent oil film thickness in the mixed lubrication state is crucial. Currently, based on the fractal theory and contact mechanics model, the calculation method using discrete reference scales is adopted. The film thickness calculation ignores the dynamic influence of external loads, and the equivalent oil film thickness relies on numerical methods, leading to a lack of explicit expression. In view of this, this article first uses the contact area and reference length as a two-dimensional integral region to correct the problem of discontinuity in the reference length of the existing contact mechanics model. Then, based on the function relationship between external loads and the maximum micro-protrusion deformation, it deduces the analytical formula for the equivalent oil film thickness, realizing the decoupling of solid-liquid loads under mixed lubrication conditions with rough fractal interfaces. Finally, it compares with experimental data of film thickness in the literature to verify the effectiveness of this method. The research shows that the equivalent oil film thickness is negatively correlated with external loads and elastic modulus, while positively correlated with cylinder radius, lubricating oil viscosity, and viscoelastic index. The critical velocity required for the rough contact interface to enter the full film lubrication state from mixed lubrication is positively correlated with external loads, and the solid load distribution coefficient is positively correlated with external loads and surface roughness. Increasing the fractal dimension of the contact surface or reducing the fractal roughness can both increase the proportion of lubricating oil in contact, providing a basis for reducing surface friction and wear caused by micro-protrusion contact and improving component service life.

Key words: contact interface, fractal rough surface, mixed lubrication, asperity contact, oil film thickness

中图分类号:

TH117

孙韵韵, 余欣, 巫世晶, 刘胜. 混合润滑状态下粗糙分形界面的接触载荷与油膜厚度研究[J]. 机械工程学报, 2025, 61(11): 231-243.

SUN Yunyun, YU Xin, WU Shijing, LIU Sheng. Study on the Contact Load and Oil Film Thickness of Rough Fractal Interface under Mixed Lubrication[J]. Journal of Mechanical Engineering, 2025, 61(11): 231-243.

参考文献

[1] GONZALEZ-VALADZ M，DWYER-JOYCE R S，LEWIS R. Ultrasonic reflection from mixed liquid-solid contacts and the determination of interface stiffness[J]. Tribology and Interface Engineering Series，2005(48)： 313-320.
[2] 李猛，田桂斌，刘意，等，圆柱滚子轴承混合润滑状态下的超声法膜厚测量[J]. 振动与冲击，2020，39(10)：279-284. LI Meng，TIAN Guibin，LIU Yi，et al. Ultrasonic measurement of oil film thickness in cylindrical roller bearings under mixed lubrication[J]. Journal of Vibration and Shock，2020，39(10)：279-284.
[3] XIAO H F，SUN Y Y. An improved virtual material based acoustic model for contact stiffness measurement of rough interface using ultrasound technique[J]. International Journal of Solids and Structures，2018. 155：240-247.
[4] JOHNSON K L，GREENWOOD J A，POON S Y. A simple theory of asperity contact in elastohydro-dynamic lubrication[J]. Wear，1972，19(1)：91-108.
[5] JACKSON R L，GREEN I. A statistical model of elasto-plastic asperity contact between rough surfaces[J]. Tribology International，2006，39(9)：906-914.
[6] MAJUMDAR A，BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology-Transactions of the ASME，1991，113(1)：1-11.
[7] YU X，SUN Y Y，ZHAO D，et al. A revised contact stiffness model of rough curved surfaces based on the length scale[J]. Tribology International，2021，164：107206.
[8] 王志坚，陈晓阳，沈雪瑾，考虑粗糙峰弹塑性变形和润滑油性质的有限长线接触副混合润滑模型[J]. 上海交通大学学报，2018，52(5)：525-532. WANG Zhijian，CHEN Xiaoyang，SHEN Xuejin. A mixed EHL model of finite-length line contact considering asperity elasto-plastic deformation and the lubricant properties[J]. Journal of Shanghai Jiaotong University，2018，52(5)：525-532.
[9] 冯彦，邱卓一，史修江，等. 考虑真实粗糙表面的燃机球轴承磨损与混合润滑耦合机理[J]. 机械工程学报，2023，59(21)：330-340. FENG Yan，QIU Zhuoyi，SHI Xiujiang，et al. The coupling mechanism of wear and mixed lubrication for gas turbine ball bearing considering real rough surfaces[J]. Journal of Mechanical Engineering，2023，2023，59(21)：330-340.
[10] 王旭，梁鹤，王文中，点接触混合润滑中两种求解模型的比较[J]. 润滑与密封，2022，47(2)：88-95. WANG Xu，LIANG He，WANG Wenzhong. Comparison of two solution models in point contact mixed lubrication[J]. Lubrication Engineering，2022，47(2)：88-95.
[11] MASJEDI M，KHONSARI M M. Film thickness and asperity load formulas for line-contact elastohydrodynamic lubrication with provision for surface roughness[J]. Journal of Tribology-Transactions of the ASME，2012，134(1)：011503.
[12] PEI J X，HAN X，TAO Y R，et al. Mixed elastohydrodynamic lubrication analysis of line contact with Non-Gaussian surface roughness[J]. Tribology International，2020，151：106449.
[13] PEI J X，HAN X，TAO Y R. An improved stiffness model for line contact elastohydrodynamic lubrication and its application in gear pairs[J]. Industrial Lubrication and Tribology，2020，72(5)：703-708.
[14] KOGUT L，ETSION I. Elastic-plastic contact analysis of a sphere and a rigid flat[J]. Journal of Applied Mechanics-Transactions of the ASME，2002，69(5)：657-662.
[15] 吴正海，徐颖强，刘楷安，等，脂润滑点接触副混合润滑模型研究[J]. 机械工程学报，2022，58(1)：145-153. WU Zhenghai，XU Yingqiang，LIU Kaian，et al. The study on grease mixed-lubrication model of point contact pair[J]. Journal of Mechanical Engineering，2022，58(1)：145-153.
[16] 肖会芳，孙韵韵，徐金梧，等，混合润滑状态下粗糙界面法向接触刚度计算模型与特性研究[J]. 振动与冲击，2018，37(24)：106-114，147. XIAO Huifang，SUN Yunyun，XU Jinwu，et al. A calculation model for the normal contact stiffness of rough surface in mixed lubrication[J]. Journal of Vibration and Shock，2018，37(24)：106-114，147.
[17] LU X B，KHONSARI M M，GELINCK E R M. The Stribeck curve：Experimental results and theoretical prediction[J]. ASME Journal of Tribology，2006，128(4)：789-794.
[18] 毕浩程，郝木明，任宝杰，等，接触式机械密封混合润滑状态摩擦演化规律研究[J]. 摩擦学学报，2023，43(11)：1241-1253. BI Haocheng，HAO Muming，REN Baojie，et al. Frictional evolution of contact mechanical seals with hybrid lubrication[J]. Tribology，2023，43(11)：1241-1253.
[19] 高志强，王双琦，席云鹏，等，介观双粗糙弹塑性流体动力润滑界面法向接触刚度模型[J]. 摩擦学学报，2022，42(4)：657-668. GAO Zhiqiang，WANG Shuangqi，XI Yunpeng，et al. Model of normal contact stiffness of mesoscopic double rough elastoplastic hydrodynamic lubrication interface[J]. Tribology，2022，42(4)：657-668.
[20] 高志强，席云鹏，彭丽霞，等，混合润滑状态下非高斯表面法向接触刚度研究[J]. 机械科学与技术，2024(8)：1386-1393. GAO Zhiqiang，XI Yunpeng，PENG Lixia，et al. Study on normal contact stiffness of non-Gaussian surface under mixed lubrication[J]. Mechanical Science and Technology for Aerospace Engineering，2024(8)：1386-1393.
[21] BUZIO R，BORAGNO C，BISCARINI F，et al. The contact mechanics of fractal surfaces[J]. Nature Materials，2003，2(4)：233-236.
[22] SUN Y Y，XIAO H F，YU W N，et al. Study on the normal contact stiffness of the fractal rough surface in mixed lubrication[J]. Proceedings of the Institution of Mechanical Engineers，Part J：Journal of Engineering Tribology，2018，232(12)：1604-1617.
[23] 李玲，云强强，李治强，等，考虑基体变形的混合润滑结合面接触特性[J]. 振动.测试与诊断，2019，39(5)：953-959，1128-1129. LI Ling，YUN Qiangqiang，LI Zhiqiang，et al. Contact characteristics of joint surfaces considering bulk substrate deformation in mixed lubrication [J]. Journal of Vibration，Measurement & Diagnosis，2019，39(5)：953-959，1128-1129.
[24] 李玲，裴喜永，史小辉，等，混合润滑状态下结合面的法向接触刚度研究[J]. 振动与冲击，2020，39(3)：16-23. LI Ling，PEI Xiyong，SHI Xiaohui，et al. Normal contact stiffness of machine joint surfaces under mixed lubrication state[J]. Journal of Vibration and Shock，2020，39(3)：16-23.
[25] 李玲，裴喜永，史小辉，等，混合润滑状态下结合面法向动态接触刚度与阻尼模型[J]. 振动工程学报，2021，34(2)：243-252. LI Ling，PEI Xiyong，SHI Xiaohui，et al. Normal dynamic contact stiffness and damping model of joint surfaces in mixed lubrication[J]. Journal of Vibration Engineering，2021，34(2)：243-252.
[26] 兰国生，冀成龙，李祥，等，混合润滑结合面法向接触刚度模型研究[J]. 振动与冲击，2023，42(17)：220-227. LAN Guosheng，JI Chenglong，LI Xiang，et al. Normal contact stiffness model of mixed lubrication joint surface[J]. Journal of Vibration and Shock，2023，42(17)：220-227.
[27] 王世军，刘鑫，吴敬伟，等，基于混合润滑的结合面法向接触刚度建模[J]. 西安理工大学学报，2023，39(1)：47-59. WANG Shijun，LIU Xin，WU Jingwei，et al. Modeling on normal contact stiffness of inter- faces based on mixed lubrication[J]. Journal of Xi’an University of Technology，2023，39(1)：47-59.
[28] CHENG G，XIAO K，WANG J X，et al. Calculation of gear meshing stiffness considering lubrication[J]. ASME Journal of Tribology，2019，142(3)：031602.
[29] SOJOUDI H，KHONSARI M. On the behavior of friction in lubricated point contact with provision for surface roughness[J]. ASME Journal of Tribology，2009，132(1)：012102.
[30] XIANG G，HAN Y F，WANG J X，et al. Coupling transient mixed lubrication and wear for journal bearing modeling[J]. Tribology International，2019，138：1-15.
[31] MORAG Y，ETSION I. Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces[J]. Wear，2007. 262(5-6)：624-629.
[32] 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.
[33] YU X，SUN Y Y，WU S J. Multi-stage contact model between fractal rough surfaces based on multi-scale asperity deformation[J]. Applied Mathematical Modelling，2022，109：229-250.
[34] YU X，SUN Y Y，WU S J. Analytically decoupling of friction coefficient between mixed lubricated fractal surfaces[J]. International Journal of Mechanical Sciences，2023，255：108465.
[35] PAN P，HAMROCK B J. Simple formulas for performance parameters used in elastohydrodynamically lubricated line contacts[J]. ASME Journal of Tribology，1989，111(2)：246-251.
[36] DWYER-JOYCE R S，REDDYHOFF T，ZHU J. Ultrasonic measurement for film thickness and solid contact in elastohydrodynamic lubrication[J]. Journal of Tribology-Transactions of the ASME，2011，133(3)：031501.