Research Papers: Elastohydrodynamic Lubrication

A Strongly Coupled Fluid Structure Interaction Solution for Transient Soft Elastohydrodynamic Lubrication Problems in Reciprocating Rod Seals Based on a Combined Moving Mesh Method

[+] Author and Article Information
Haiping Gao, Baoren Li, Xiaoyun Fu

School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China

Gang Yang

School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: ygxing_73@hust.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received September 20, 2014; final manuscript received March 2, 2015; published online April 29, 2015. Assoc. Editor: Min Zou.

J. Tribol 137(4), 041501 (Oct 01, 2015) (13 pages) Paper No: TRIB-14-1231; doi: 10.1115/1.4030022 History: Received September 20, 2014; Revised March 02, 2015; Online April 29, 2015

Soft elastohydrodynamic lubrication (EHL) problems widely exist in hydraulic reciprocating rod seals and pose great challenges because of high nonlinearity and strong coupling effects, especially when the EHL problems are of high dimensions. In this paper, a strongly coupled fluid structure interaction (FSI) model is proposed to solve the transient soft EHL problems in U-cup hydraulic reciprocating rod seals. The Navier–Stokes equations, rather than the Reynolds equation, are employed to govern the whole fluid field in the soft EHL problems, with the nonlinearity of the solid taken into consideration. The governing equations of the fluid and solid fields are combined into one equation system and solved monolithically. To determine the displacements of nodes of the fluid field, a new moving mesh method based on the combination of the Laplace equation and the leader–follower methods is put forward. At last, the proposed FSI model runs successfully with the moving mesh method, and the boundaries of the hydrodynamic lubrication zones and the hydrostatic zones are formed automatically and change dynamically during the coupling process. The results are as follows: The soft EHL problems show typical characteristics, like the constriction effects of the lubricating films, and the law of dynamic development of the lubricating films and the fluid pressures is revealed. The minimum stroke lengths needed to generate complete lubricating films vary with the rod speeds and movement directions, so the design of the rod seals should be paid close attention to, in particular the rod seals of short stroke lengths. Furthermore, along with the dynamic development processes of the fluid pressures during the instroke of U-cup seals, the lubricating film humps expand and locate between the fluid pressure abrupt points and the outlet zones. After the U-cup seals reach the steady-states, the fluid abrupt points disappear and no changes of the film humps are observed. Theoretically, the proposed method can be popularized to solve similar soft EHL problems.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Nikas, G., 2010, “Eighty Years of Research on Hydraulic Reciprocating Seals: Review of Tribological Studies and Related Topics Since the 1930s,” Proc. Inst. Mech. Eng., Part J, 224(1), pp. 1–23. [CrossRef]
Nau, B., 1987, “The State of the Art of Rubber-Seal Technology,” Rubber Chem. Technol., 60(3), pp. 381–416. [CrossRef]
Nau, B., 1999, “An Historical Review of Studies of Polymeric Seals in Reciprocating Hydraulic Systems,” Proc. Inst. Mech. Eng., Part J, 213(3), pp. 215–226. [CrossRef]
Kanters, A., Verest, J., and Visscher, M., 1990, “On Reciprocating Elastomeric Seals: Calculation of Film Thicknesses Using the Inverse Hydrodynamic Lubrication Theory,” Tribol. Trans., 33(3), pp. 301–306. [CrossRef]
Dowson, D., and Higginson, G., 1959, “A Numerical Solution to the Elasto-Hydrodynamic Problem,” J. Mech. Eng. Sci., 1(1), pp. 6–15. [CrossRef]
Stephenson, R. R., and Osterle, J. F., 1962, “A Direct Solution of the Elasto-Hydrodynamic Lubrication Problem,” ASLE Trans., 5(2), pp. 365–374. [CrossRef]
Thatte, A., and Salant, R. F., 2009, “Elastohydrodynamic Analysis of an Elastomeric Hydraulic Rod Seal During Fully Transient Operation,” ASME J. Tribol., 131(3), pp. 603–610. [CrossRef]
Yang, B., and Salant, R. F., 2008, “Numerical Model of a Tandem Reciprocating Hydraulic Rod Seal,” ASME J. Tribol., 130(3), p. 032201. [CrossRef]
Salant, R., Yang, B., and Thatte, A., 2010, “Simulation of Hydraulic Seals,” Proc. Inst. Mech. Eng., Part J, 224(9), pp. 865–876. [CrossRef]
Schmidt, T., André, M., and Poll, G., 2010, “A Transient 2D-Finite-Element Approach for the Simulation of Mixed Lubrication Effects of Reciprocating Hydraulic Rod Seals,” Tribol. Int., 43(10), pp. 1775–1785. [CrossRef]
Stupkiewicz, S., 2009, “Finite Element Treatment of Soft Elastohydrodynamic Lubrication Problems in the Finite Deformation Regime,” Comput. Mech., 44(5), pp. 605–619. [CrossRef]
Stupkiewicz, S., and Marciniszyn, A., 2009, “Elastohydrodynamic Lubrication and Finite Configuration Changes in Reciprocating Elastomeric Seals,” Tribol. Int., 42(5), pp. 615–627. [CrossRef]
Fatu, A., and Hajjam, M., 2011, “Numerical Modelling of Hydraulic Seals by Inverse Lubrication Theory,” Proc. Inst. Mech. Eng., Part J, 225(12), pp. 1159–1173. [CrossRef]
Ongün, Y., André, M., Bartel, D., and Deters, L., 2008, “An Axisymmetric Hydrodynamic Interface Element for Finite-Element Computations of Mixed Lubrication in Rubber Seals,” Proc. Inst. Mech. Eng., Part J, 222(3), pp. 471–481. [CrossRef]
Nikas, G. K., and Sayles, R. S., 2004, “Nonlinear Elasticity of Rectangular Elastomeric Seals and Its Effect on Elastohydrodynamic Numerical Analysis,” Tribol. Int., 37(8), pp. 651–660. [CrossRef]
Thatte, A., and Salant, R. F., 2009, “Transient EHL Analysis of an Elastomeric Hydraulic Seal,” Tribol. Int., 42(10), pp. 1424–1432. [CrossRef]
Habchi, W., Eyheramendy, D., Vergne, P., and Morales-Espejel, G., 2008, “A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem,” ASME J. Tribol., 130(2), p. 021501. [CrossRef]
Bruyere, V., Fillot, N., Morales-Espejel, G. E., and Vergne, P., 2012, “Computational Fluid Dynamics and Full Elasticity Model for Sliding Line Thermal Elastohydrodynamic Contacts,” Tribol. Int., 46(1), pp. 3–13. [CrossRef]
Liu, H., Xu, H., Ellison, P. J., and Jin, Z., 2010, “Application of Computational Fluid Dynamics and Fluid–Structure Interaction Method to the Lubrication Study of a Rotor–Bearing System,” Tribol. Lett., 38(3), pp. 325–336. [CrossRef]
Hong, Y. P., Chen, D. R., Kong, X. M., and Wang, J. D., 2002, “Model of Fluid–Structure Interaction and Its Application to Elastohydrodynamic Lubrication,” Comput. Methods Appl. Mech. Eng., 191(37–38), pp. 4231–4240. [CrossRef]
Hartinger, M., Dumont, M.-L., Ioannides, S., Gosman, D., and Spikes, H., 2008, “CFD Modeling of a Thermal and Shear-Thinning Elastohydrodynamic Line Contact,” ASME J. Tribol., 130(4), p. 041503. [CrossRef]
Liao, C., Huang, W., Wang, Y., Suo, S., and Liu, Y., 2013, “Fluid–Solid Interaction Model for Hydraulic Reciprocating O-Ring Seals,” Chin. J. Mech. Eng., 26(1), pp. 85–94. [CrossRef]
Thompson, J. F., Soni, B. K., and Weatherill, N. P., 2010, Handbook of Grid Generation, CRC Press, Boca Raton.
Plewa, T., Linde, T., and Weirs, V. G., 2005, Adaptive Mesh Refinement: Theory and Applications, Springer, New York.
Huang, W., and Russell, R. D., 2010, Adaptive Moving Mesh Methods, Springer, London.
Bazilevs, Y., Takizawa, K., and Tezduyar, T. E., 2012, Computational Fluid–Structure Interaction: Methods and Applications, Wiley, West Sussex, UK.
Belytschko, T., Liu, W. K., Moran, B., and Elkhodary, K., 2013, Nonlinear Finite Elements for Continua and Structures, Wiley, West Sussex, UK.
Sussman, T., and Bathe, K. J., 1987, “A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis,” Comput. Struct., 26(1), pp. 357–409. [CrossRef]
Shinkarenko, A., Kligerman, Y., and Etsion, I., 2009, “The Validity of Linear Elasticity in Analyzing Surface Texturing Effect for Elastohydrodynamic Lubrication,” ASME J. Tribol., 131(2), p. 021503. [CrossRef]
Eterovic, A., and Bathe, K., 1991, “On the Treatment of Inequality Constraints Arising From Contact Conditions in Finite Element Analysis,” Comput. Struct., 40(2), pp. 203–209. [CrossRef]
Bathe, K.-J., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
Pantuso, D., Bathe, K. J., and Bouzinov, P. A., 2000, “A Finite Element Procedure for the Analysis of Thermo-Mechanical Solids in Contact,” Comput. Struct., 75(6), pp. 551–573. [CrossRef]
Zhang, H., and Bathe, K. J., 2001, “Direct and Iterative Computing of Fluid Flows Fully Coupled With Structures,” Computational Fluid and Solid Mechanics, Proceedings First M.I.T. Conference on Computational Fluid and Solid Mechanics, Amsterdam, pp. 1440–1443.
Adina R&D, Inc., 2011, “Theory and Modeling Guid Volum III: Adina CFD&FSI,” Report No. ARD 11-10.
Bathe, K. J., and Zhang, H., 2002, “A Flow-Condition-Based Interpolation Finite Element Procedure for Incompressible Fluid Flows,” Comput. Struct., 80(14), pp. 1267–1277. [CrossRef]
Bathe, K. J., and Pontaza, J. P., 2002, “A Flow-Condition-Based Interpolation Mixed Finite Element Procedure for Higher Reynolds Number Fluid Flows,” Math. Models Methods Appl. Sci., 12(4), pp. 525–539. [CrossRef]
Bathe, K. J., Zhang, H., and Zhang, X., 1997, “Some Advances in the Analysis of Fluid Flows,” Comput. Struct., 64(5–6), pp. 909–930. [CrossRef]
Rugonyi, S., and Bathe, K., 2001, “On Finite Element Analysis of Fluid Flows Fully Coupled With Structural Interactions,” Comput. Model. Eng. Sci., 2(2), pp. 195–212. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=
Yang, B., and Salant, R., 2011, “Elastohydrodynamic Lubrication Simulation of O-Ring and U-Cup Hydraulic Seals,” Proc. Inst. Mech. Eng., Part J, 225(7), pp. 603–610. [CrossRef]
Salant, R. F., Maser, N., and Yang, B., 2007, “Numerical Model of a Reciprocating Hydraulic Rod Seal,” ASME J. Tribol., 129(1), pp. 91–97. [CrossRef]


Grahic Jump Location
Fig. 1

A typical rod seal system and its deformed shape: (a) initial state before installed and (b) pressured state

Grahic Jump Location
Fig. 2

Interpolation method of the fluid node displacement by using the solid node displacements

Grahic Jump Location
Fig. 3

Displacement relation between the leader point (L) and the follower point (F), (λf = 1)

Grahic Jump Location
Fig. 4

Mesh shape comparison between the conventional moving mesh strategy (mesh 1) and the proposed strategy (mesh 2) after the solid part (seal) is large deformed

Grahic Jump Location
Fig. 5

Meshes distribution, deformation, and movement of the U-cup rod seal system

Grahic Jump Location
Fig. 6

The pressure distribution under the fluid pressure of 7 MPa when the rod is static: (a) pressure distribution contour and (b) pressure distribution of the solid along the seal zone

Grahic Jump Location
Fig. 7

Rod speeds change with time at different target rod speeds

Grahic Jump Location
Fig. 8

The pressure distributions (a)–(c) and mesh shape (d) at the rod speed of 400 mm/s, instroke

Grahic Jump Location
Fig. 9

The pressure distributions (a)–(c) and mesh shape (d) at the rod speed of 400 mm/s, outstroke

Grahic Jump Location
Fig. 10

Development processes of the fluid pressure and film thickness in the seal zone at the rod speed of 200 mm/s, instroke

Grahic Jump Location
Fig. 11

Development processes of the fluid pressure and film thickness in the seal zone at the rod speed of 400 mm/s, instroke

Grahic Jump Location
Fig. 12

Pressure and film thickness development processes of the seal zone at the rod speed of 200 mm/s, outstroke

Grahic Jump Location
Fig. 13

Pressure and film thickness development processes of the seal zone at the rod speed of 400 mm/s, outstroke

Grahic Jump Location
Fig. 14

Pressure and film thickness distributions along the seal zone, steady-states, and instroke

Grahic Jump Location
Fig. 15

Pressure and film thickness distributions, steady-states, and outstroke

Grahic Jump Location
Fig. 16

Y-axis fluid velocity composite distributions along: (a) the minimum film thickness lines and (b) the maximum pressure lines in the lubricating zone, during instroke (rod speeds > 0) and outstroke (rod speeds < 0)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In