Advanced Multilevel Solution of the EHL Line Contact Problem

Venner, Cornelis H.; Napel, W.E. ten; Bosma, R.H.

doi:10.1115/1.2920277

Cited by 182 publications

(302 citation statements)

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“…Results indicated the effect of squeeze in the response in which there was some deviation from exact periodicity in the cavitation location, contact separation and minimum film thickness under the dynamic loading imposed. Minimum film thickness calculations demonstrated that the ALE formulation accurately describes the EHL response established in the literature [9,10,[50][51][52] to within 5% of the predicted values. It was also presented under hydrodynamic conditions that the ALE formulation has better numerical converge and computes in less time than comparative problems solved using the Elrod (Heaviside) approach.…”

Section: Discussionmentioning

confidence: 98%

“…Later Lubrecht et al [52] derived a solution based on the multilevel methods and Moe's non-dimensional parameters. This was further developed by Venner [10] who derived an expression that is considered the best approximation for calculating the minimum film thickness in a line contact to date. It is of note that, despite the differences in model assumptions, the solutions obtained by Dowson and Higginson [9] are widely used because of the accuracy of the solution when comparing to the modern alternatives [53].…”

Section: Investigation Of the Minimum Film Thicknessmentioning

confidence: 99%

“…It should be noted that the ALE formulation is limited by the load parameter M, for high values of which the problem becomes mathematically stiff and the series of equations is much harder to solve computationally. The multilevel method [10][11][12] was developed to study this effect and is the preferred approach for highly-loaded EHL problems. However, the ALE formulation can readily be used within a reasonable range of the non-dimensional parameters to solve EHL problems with a high level of accuracy.…”

Section: Analysis Of the Minimum Film Thicknessmentioning

confidence: 99%

“…It was for this reason that multilevel methods for EHL were developed, the works of Venner [10] and Venner and Lubrecht [11] on the subject outline in detail this numerical procedure. Using these techniques and the same treatment for cavitation as implemented by the forward iterative method the authors were able to solve EHL contact problems over a wide range of operating conditions and material properties.…”

Section: Introductionmentioning

confidence: 99%

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An Arbitrary Lagrangian–Eulerian Formulation for Modelling Cavitation in the Elastohydrodynamic Lubrication of Line Contacts

Boer

Dowson

2018

Lubricants

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Abstract:In this article an arbitrary Lagrangian-Eulerian (ALE) formulation for modelling cavitation in elastohydrodynamic lubrication (EHL) is derived and applied to line contact geometry. The method is developed in order to locate the position of cavitation onset along the length of the contacting region which gives the transition from liquid to vapour in the fluid. The ALE is implemented by introducing a spatial frame of reference in which the solution is required and a material frame of reference in which the governing equations are solved. The spatial frame is moved from the material frame according to the error in the Neumann pressure gradient constraint required at the cavitation location when Dirichlet constraints are imposed for pressure in the liquid phase. Results are calculated under both steady-state and transient operating conditions using a multigrid solver. The solutions obtained are compared to established literature and conventional approaches to modelling cavitation which show that the ALE formulation is an alternative, straightforward and accurate means of implementing such conditions in EHL. This is achieved without the penalties associated with the numerical modelling of Heaviside functions or free boundaries.

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Section: Discussionmentioning

confidence: 98%

Section: Investigation Of the Minimum Film Thicknessmentioning

confidence: 99%

Section: Analysis Of the Minimum Film Thicknessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Arbitrary Lagrangian–Eulerian Formulation for Modelling Cavitation in the Elastohydrodynamic Lubrication of Line Contacts

Boer

Dowson

2018

Lubricants

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“…The Reynolds equation was solved by a multi-grid (MG) method, while the elastic deformation was calculated using a multi-level multi-integration (MLMI) technique (Gao et al, 2007;Venner, 1991). Three levels of grid were used in the multilevel solver.…”

Section: Elastohydrodynamic Lubricationmentioning

confidence: 99%

Contact mechanics and elastohydrodynamic lubrication in a novel metal-on-metal hip implant with an aspherical bearing surface

Meng

Gao

Liu

et al. 2010

Journal of Biomechanics

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Diameter and diametral clearance of the bearing surfaces of metal-on-metal hip implants and structural supports have been recognized as key factors to reduce the dry contact and hydrodynamic pressure and improve lubrication performance. On the other hand, application of aspherical bearing surfaces can also significantly affect the contact mechanics and lubrication performance by changing the radius of the curvature of a bearing surface and consequently improving the conformity between the head and the cup. In this study, a novel metal-on-metal hip implant employing a specific aspherical bearing surface, Alpharabola, as the acetabular surface was investigated for both contact mechanics and elastohydrodynamic lubrication under steady state conditions. When compared with conventional spherical bearing surfaces, a more uniform pressure distribution and a thicker lubricant film thickness within the loaded conjunction were predicted for this novel Alpharabola hip implant. The effects of the geometric parameters of this novel acetabular surface on the pressure distribution and lubricant thickness were investigated. A significant increase in the predicted lubricant film thickness and a significant decrease in the dry contact and hydrodynamic pressures were found with appropriate combinations of these geometric parameters, compared with the spherical bearing surface.

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A control volume-based discretization of the Reynolds equation for the numerical solution of elastohydrodynamic lubrication problems

Čermák¹

1998

Int. J. Numer. Meth. Fluids

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This paper deals with the discretization of the one‐dimensional Reynolds equation coupled with the film shape equation, that is used for the numerical solution of elastohydrodynamically lubricated contacts. The derivation of the developed discretization formula is based on the control volume approach. To reduce the discretization error caused by the upwind expression of the Couette (velocity) term, non‐symmetric control volumes are used for discretization of the Reynolds equation, while for the elasticity equation the standard approach is used. A numerical method for the solution of the pressure and the film thickness profiles of elastohydrodynamically lubricated isothermal line contacts is presented. Results are presented for chosen typical parameters of a highly loaded contact. To show the formula efficiency, the convergence speed of both the presented discretization formula and a chosen comparative discretization formula (A.A. Lubrecht, Ph.D. Thesis, University of Twente, The Netherlands, 1987 and C.H. Venner, Ph.D. Thesis, University of Twente, The Netherlands, 1991) are checked. The results show that the presented formula gives better approximations of film thickness values for a given number of equidistant grid nodes. Moreover, the presented approach is probably suitable for more sophisticated cases, such as transient situations and elliptical contacts. © 1998 John Wiley & Sons, Ltd.

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Advanced Multilevel Solution of the EHL Line Contact Problem

Cited by 182 publications

References 10 publications

An Arbitrary Lagrangian–Eulerian Formulation for Modelling Cavitation in the Elastohydrodynamic Lubrication of Line Contacts

An Arbitrary Lagrangian–Eulerian Formulation for Modelling Cavitation in the Elastohydrodynamic Lubrication of Line Contacts

Contact mechanics and elastohydrodynamic lubrication in a novel metal-on-metal hip implant with an aspherical bearing surface

A control volume-based discretization of the Reynolds equation for the numerical solution of elastohydrodynamic lubrication problems

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