弹流润滑（Elastohydrodynamic lubrication, 简称EHL, 国内又称弹性流体动力润滑）是关于点或线接触的流体润滑如齿轮齿面润滑、滚动轴承润滑、凸轮与推杆间润滑等。这种润滑研究顺应了历史上机械工业的发展。

      早期，Grubin提出了一个预估线接触弹流润滑接触区膜厚的公式，给出了一种线接触弹流润滑的解析解[1]。其后，弹流润滑理论研究分成了数值解和解析解两个分支，前者得益于计算机的发展和普及。数值解的代表是英国的D. Dowson(利兹大学)和美国的华人学者H. S. Cheng（郑绪云，西北大学）。前者考虑牛顿流变模型，给出了线接触和点接触弹流润滑数值解[2-5], 并出版了一本书叫《弹性流体动力润滑》[6]。前者还推出了普适性的流体润滑雷诺方程[7], 可用于考虑热效应、非牛顿流体、非稳态和粗糙表面的弹流润滑分析。后者则分别给出了考虑热效应、非牛顿流变效应和粗糙表面效应的弹流润滑数值解[8-11]。同时，Greenwood[12]通过入口区分析，给出了考虑热效应的线接触弹流润滑解析解。

    弹流润滑实验研究也在同步进行。F. W. Smith[13]进行了线接触弹流润滑的摩擦力测试，发现实验中摩擦力实际上为有限值，提出了润滑剂剪切强度或极限剪应力概念。Johnson和Tavaarwerk[14]实验中发现弹流润滑中的流体实际上为非牛顿流体。Bair和Winer[15，16]进行了高剪切率下润滑油流变实验，提出弹流润滑中流体应具有极限剪应力。在他们的发现基础上，Hamrock等进行了考虑润滑剂极限剪应力的弹流润滑数值计算[17-19]，发现润滑剂极限剪应力效应（俗称粘塑性效应）可引起弹流润滑膜坍塌[20]。

   关于弹流润滑失效，国际上曾专门召开过会议探讨过这个问题，并开展了系列研究，出版了系统性技术报告[21-23]。

    弹流润滑数值计算的大幅改善则源于上世纪八十年代多重网格法的引入[24-27]。

   国内相关研究，一直处于跟踪状态，对于成果的表述，还是慎用“率先”、“首次”等字眼为好。这也是对同行尊重的需要。 

参考文献：

[1]Grubin, A. N.; Fundamentals of the hydrodynamic theory of lubrication of heavily loaded cylindrical surfaces. In: Ketovam Kh.F.(ed.) Central Scientific Research Institute for Technology and Mechanical Engineering, D.S.I.R, Vol.337, 115-166. London Translations, Wellington, 1949.

[2]Dowson, D. and Higginson, G. R., A Numerical Solution to the Elasto-Hydrodynamic Problem, Journal of Mechanical Engineering Science, Published June 1, 1959.

https://doi.org/10.1243/JMES_JOUR_1959_001_004_02

[3]Hamrock, B. J. and Dowson, D., Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 1—Theoretical Formulation.

Journal of Lubrication Technology, Vol. 98, 223-228, 1976.

https://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1463255

[4]Hamrock, B. J. and Dowson, D., Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part II—Ellipticity Parameter Results. Journal. of Lubrication Technology, Vol. 98, 375-381, 1976. https://tribology.asmedigitalcollection.asme.org/article.aspx?articleID=1463356

[5]Hamrock, B. J. and Dowson, D., Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III—Fully Flooded Results.

Journal of Lubrication Technology, Vol. 99, 264-275, 1977.

https://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1463691

[6]Dowson, D. and Higginson, G. R., Elastohydrodynamic Lubrication, Pergamon Press, New York, NY, 1966.

[7]Dowson, D., A generalized Reynolds equation for fluid-film lubrication. International Journal of Mechanical Sciences, Volume 4, Issue 2, 159-170, 1962.

https://www.sciencedirect.com/science/article/pii/S0020740362800381

[8]Cheng, H. S., A Refined Solution to the Thermal-Elastohydrodynamic Lubrication of Rolling and Sliding Cylinders, A S L E Transactions, Volume 8,397-410, 1965.

https://www.tandfonline.com/doi/abs/10.1080/05698196508972110

[9] Wang, K. L. and Cheng, H.S., Thermal elastohydrodynamic lubrication of spur gears, NASA technical report, 1980.

https://ntrs.nasa.gov/search.jsp?R=19800008077

[10]Trachman E. G. and Cheng, H. S., Rheological effects on friction in elastohydrodynamic lubrication,

NASA technical report, 1973.

https://ntrs.nasa.gov/search.jsp?R=19730012686

[11]Chow, L. S. H. and Cheng, H. S., Influence of surface roughness and waviness on film thickness and pressure distribution in elastohydrodynamic contacts, NASA technical report, 1976.

https://ntrs.nasa.gov/search.jsp?R=19760014469

[12]Greenwood, J. A. and Kauzlarich, J. J., Inlet Shear Heating in Elastohydrodynamic Lubrication. Journal of Lubrication Technology, Vol. 95, 417-423, 1973.

http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1462396

[13]Smith, F.W., Lubricant behavior in concentrated contacts-some rheological problems. ASLE Transactions, Vol.3,No.3, 18-25, 1960.

[14]Johnson, K. L. and Tevaarwerk, J. L., Shear behaviour of elastohydrodynamic oil films. Proceedings of the Royal Society of London, Vol.356, 215-236, 1977.

http://rspa.royalsocietypublishing.org/content/356/1685/215.short

[15] Bair, S. and Winer, W. O., A Rheological Model for Elastohydrodynamic Contacts Based on Primary Laboratory Data. Journal of Lubrication Technology, Vol.101, 258-264, 1979.

https://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1464190

[16]Bair, S. and Winer, W. O., Shear Strength Measurements of Lubricants at High Pressure.

Journal of Lubrication Technology, Vol.101, 251-257, 1979.

https://tribology.asmedigitalcollection.asme.org/article.aspx?articleID=1464185

[17]Jacobson, B. O. and Hamrock, B. J., Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication of Rectangular Contacts. Journal of Tribology, Vol.106, 275-282, 1984. http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1458363

[18]Lee, Rong-Tsong and Hamrock, B. J., A Circular Non-Newtonian Fluid Model: Part I—Used in Elastohydrodynamic Lubrication. Journal of Tribology, Vol. 112, 486-495, 1990.

http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1459710

[19]Hsiao, Hsing-Sen S. and Hamrock, B. J., A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model. Journal of Tribology, Vol..114, 540-551, 1992.

https://tribology.asmedigitalcollection.asme.org/article.aspx?articleID=1460160

[20]Shieh, Jinn-an and Hamrock, B. J., Film Collapse in EHL and Micro-EHL.

Journal of Tribology, Vol. 113, 372-377, 1991.

http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1459905

[21]Czichos, H., Failure criteria in thin film lubrication— the concept of a failure surface. Tribology, Vol.7, Issue 1,14-20, 1974.

https://www.sciencedirect.com/science/article/pii/0041267874900621

[22]Czichos, H. and Kirschke, K., Investigations into film failure (transition point) of lubricated concentrated contacts. Wear, Vol.22, 321-336, 1972.

https://www.sciencedirect.com/science/article/abs/pii/0043164872903924

[23]Czichos, H., Failure criteria in thin film lubrication: Investigation of the different stages of film failure. Wear, 13-17, 1976.

https://www.sciencedirect.com/science/article/abs/pii/0043164876901393

 [24]Lubrecht, A. A., ten Napel, W. E. and Bosma, R., Multigrid, an Alternative Method for Calculating Film Thickness and Pressure Profiles in Elastohydrodynamically Lubricated Line Contacts. Journal of Tribology, Vol.108, 551-556, 1986.

http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1458878

[25]Lubrecht, A. A., ten Napel, W. E. and Bosma, R., Multigrid, an Alternative Method of Solution for Two-Dimensional Elastohydrodynamically Lubricated Point Contact Calculations.

Journal of Tribology, Vol.109, 437-443, 1987.

http://tribology.asmedigitalcollection.asme.org/article.aspx?articleid=1459061

[26]Lubrecht, A. A., Venner, C. H., ten Napel, W. E. and Bosma, R., Film Thickness Calculations in Elastohydrodynamically Lubricated Circular Contacts, Using a Multigrid Method.

Journal of Tribology, Vol. 110, 503-507, 1988.

https://tribology.asmedigitalcollection.asme.org/article.aspx?articleID=1459305

[27]Lubrichet, A. A. et al., Solving Reynolds' equation for EHL line contacts by application of a multigrid method. The 13^th Leeds-Lyon Symposium on Tribology, 1987.