Film thickness prediction in Zero Entrainment Velocity line contacts: The squeeze film effect

Bilel Meziane^1)*, Nicolas Fillot¹⁾ , Guillermo E. Morales-Espejel^2,1)

Université de Lyon, INSA Lyon, CNRS, LaMCoS UMR5259,Villeurbanne Cedex, 69621, France

2) SKF Research and Technology Development, Nieuwegein, The Netherlands

^*Corresponding author: bilel.meziane@insa-lyon.fr

INTRODUCTION:

In 1962, Christensen[1] described the contact between two approaching bodies. This work showcased the differences in the solution when taking viscosity variation with pressure or solid deformations into account. It also showed the existence of a bump in the solids where fluid is present. In 1967, Dowson and Jones[2] conducted experiments using interferometry techniques to measure film thicknesses between two approaching bodies. They introduced the term of entrapment to corroborate the results obtained by Christensen. A similar experiment, showcasing measuring techniques was done the same year by Westlake and Cameron[3].

The transient problem was studied numerically and experimentally in various papers, but it wasn’t until 1984 that the deformation rate was taken into account by Oh[4] in a full Elastohydrodynamic model.

Various mechanical components can be represented using EHL models. In some specific kinematic conditions, both solids move at the same velocity but in opposite directions. This is called Zero Entrainment Velocity. In stationary ZEV contacts, the load bearing capacity can be explained by the Viscosity Wedge, first described by Cameron[5]. In that case, the high shearing heats the fluid in such a way that viscosity gradients appear. That is sufficient enough to generate a load carrying capacity through a fluid film.

The first objective of this study is to verify whether or not there are differences between ZEV isothermal contacts and pure squeeze contact (where sliding is zero). Depending on the existence of differences, a careful study on the prediction of film thickness will be done for the isothermal transient ZEV contact. The second objective is to compare the influence of thermal and transient effects when they exist together, using results obtained for stationary thermal ZEV and transient isothermal ZEV as a baseline for comparison.

METHODS:

When looking at squeeze film problems, one could control the applied linear load or the solid separation. The model presented here considers the latter. As such, finding a solution to the load balance equation can be avoided during the computation process.

The transient isothermal case is composed of two defining equations. First, the Reynolds equation that links the pressure to the film thickness. Second, the elastic body deformation equation that links the applied pressure to the deformation, using the equivalent body theory to reduce mesh size.

The film thickness can be explicitly calculated as the sum of the solid separation, the rigid body curvature and the elastic body deformation.

If the analysis extends to consider thermal effects, this can be implemented by changing the Reynolds equation in order to take viscosity and density dependency with temperature into account. The resulting equations is the Generalized Reynolds equation. A thermal model is also needed to represent the temperature profiles in the fluid and solids. The classical energy equations will be written along with the corresponding boundary conditions.

STUDY:

To complete the first objective, a battery of computations with sliding speed will be compared to results obtained for pure squeeze. If there are differences, then the prediction of film thickness will be studied regarding the variation of various input parameters.

The introduction of thermal effects will require the introduction of new characteristic times similarly to the work done by Raisin[6].

In both cases, a criterion must be defined. In this study, an important value that will be calculated is the minimum film thickness between the two contacting bodies. The model will also be able to compute central film thickness, pressure values, temperature extremums, which can also show interesting behaviors.

REFERENCES:

[1]         H. Christensen, “The Oil Film in a Closing Gap,” Proc. R. Soc. A Math. Phys. Eng. Sci., vol. 266, no. 1326, pp. 312–328, Mar. 1962.

[2]         D. Dowson and D. A. Jones, “Lubricant Entrapment between Approaching Elastic Solids,” Nature, vol. 214, pp. 947–948, 1967.

[3]         F. J. Westlake and A. Cameron, “A Study of Ultra-Thin Lubricant Films Using an Optical Technique - 1967,” Proc. Inst. Mech. Eng., vol. 182, no. 7, pp. 75–78, 1967.

[4]         K. P. Oh, “The Numerical Solution of Dynamically Loaded Elastohydrodynamic Contact as a Nonlinear Complementarity Problem,” J. Tribol., vol. 106, no. 1, pp. 88–95, Jan. 1984.

[5]         A. Cameron, “The Viscosity Wedge,” A S L E Trans., vol. 1, no. 2, pp. 248–253, Jan. 1958.

[6]         J. Raisin, N. Fillot, D. Dureisseix, P. Vergne, and V. Lacour, “Characteristic times in transient thermal elastohydrodynamic line contacts,” Tribol. Int., 2015.