Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads

Houpert, L.; Hamrock, B. J.

doi:10.1115/1.3261220

Cited by 146 publications

(77 citation statements)

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“…An alternative solution technique is the fully-coupled approach, which consists of solving the discretized elasticity and lubrication equations simultaneously, see for example [25,33,34], with the goal of obtaining a faster convergence rate for the iterative solution. These examples are based on the half-space approach for the elastic deflection.…”

Section: Introductionmentioning

confidence: 99%

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

Ahmed

Goodyer

Jimack

2014

Computer Methods in Applied Mechanics and Engineering

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This paper presents an automatic locally adaptive finite element solver for the fullycoupled EHL point contact problems. The proposed algorithm uses a posteriori error estimation in the stress in order to control adaptivity in both the elasticity and the lubrication domains. The implementation is based on the fact that the solution of the linear elasticity equation exhibits large variations close to the the fluid domain on which the Reynolds equation is solved. Thus the local refinement in such region not only improves the accuracy of the elastic deformation solution significantly but also yield an improved accuracy in the pressure profile due to increase in the spatial resolution of fluid domain. Thus, the improved traction boundary conditions leads to even better approximation of the elastic deformation. Hence, a simple and an effective way to develop an adaptive procedure for the fully-coupled EHL problem is to apply the local refinement to the linear elasticity mesh. The proposed algorithm also seeks to improve the quality of refined meshes to ensure the best overall accuracy. It is shown that the adaptive procedure effectively refines the elements in the region(s) showing the largest local error in their solution, and reduces the overall error with optimal computational cost for a variety of EHL cases. Specifically, the computational cost of proposed adaptive algorithm is shown to be linear with respect to problem size as the number of refinement levels grows.

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Section: Introductionmentioning

confidence: 99%

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

Ahmed

Goodyer

Jimack

2014

Computer Methods in Applied Mechanics and Engineering

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“…Since tribologists, unlike coating specialists, are concerned with load carrying capacity rather than flow rate and film thickness prediction, Reynolds conditions prove sufficient and so it has not been necessary to consider different boundary conditions. Other references of interest are Houpert & Hamrock (1986), Jaffar (1990) and Xue, Gethin & Lim (1994.…”

Section: Compliant Layermentioning

confidence: 99%

A model for deformable roll coating with negative gaps and incompressible compliant layers

et al. 2003

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A soft elastohydrodynamic lubrication model is formulated for deformable roll coating involving two contra-rotating rolls, one rigid and the other covered with a compliant layer. Included is a finite-strip model (FSM) for the deformation of the layer and a lubrication model with suitable boundary conditions for the motion of the fluid. The scope of the analysis is restricted to Newtonian fluids, linear elasticity/viscoelasticity and equal roll speeds, with application to the industrially relevant highly loaded or ‘negative gap’ regime. Predictions are presented for coated film thickness, inter-roll thickness, meniscus location, pressure and layer deformation as the control parameters – load (gap), elasticity, layer thickness and capillary number, $\hbox{\it Ca}$ – are varied. There are four main results: Hookean spring models are shown to be unable to model effectively the deformation of a compliant layer when Poisson's ratio $\nu\rightarrow 0.5$. In particular, they fail to predict the swelling of the layer at the edge of the contact region which increases as $\nu\rightarrow 0.5$; they also fail to locate accurately the position of the meniscus, $X_M$, and to identify the presence, close to the meniscus, of a ‘nib’ (constriction in gap thickness) and associated magnification of the sub-ambient pressure loop.Scaling arguments suggest that layer thickness and elasticity may have similar effects on the field variables. It is shown that for positive gaps this is true, whereas for negative gaps they have similar effects on the pressure profile and flow rate yet quite different effects on layer swelling (deformation at the edge of the contact region) and different effects on $X_M$.For negative gaps and $\hbox{\it Ca}\,{\sim}\,O(1)$, the effect of varying either viscosity or speed and hence $\hbox{\it Ca}$ is to significantly alter both the coating thickness and $X_M$. This is contrary to the case of fixed-gap rigid roll coating.Comparison between theoretical predictions and experimental data shows quantitive agreement in the case of $X_M$ and qualitive agreement for flow rate. It is shown that this difference in the latter case may be due to viscoelastic effects in the compliant layer.

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“…The Newton-Raphson method has recently become very popular. Houpert and Hamrock [5] have successfully improved it. They developed an algorithm, which gives the convergent solutions even under extremely heavy loads (to 4.8 GPa) with short CPU times.…”

Section: Introductionmentioning

confidence: 99%

A Boundary Element Procedure for the Solution of the Elastohydrodynamic Lubrication Problem of Rolling Line Contacts by a Newtonian Fluid

Sadique¹

2005

eng

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ABSTRACT. The contact characteristics of stiff cylinders lubricated by Newtonian liquids are investigated using hard elastohydrodynamic lubrication (EHL) theory. Numerical modeling is formulated for the coupled set of generalized pressure and plane strain elasticity equations for a finite plane model and a circular representation of the junction under a pure hard rolling line contact using boundary element method. Also a numerical routine is developed to compute film thickness and pressure profiles, and the results are evaluated for a range of possible dimensionless parameters such as speed and load. The hydrodynamic equation is also transformed into a form of boundary integral equation, which is solved by Simpson's rule. The elasticity equation with boundary conditions was solved by constant and quadratic elements based on an iterative procedure by assuming an initial film thickness. The computed results are shown to be amenable to standard boundary element formulation of the EHL problem in the contact region, and show that speed and load have influential effects on the lubricating film shape.

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Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads

Cited by 146 publications

References 0 publications

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

A model for deformable roll coating with negative gaps and incompressible compliant layers

A Boundary Element Procedure for the Solution of the Elastohydrodynamic Lubrication Problem of Rolling Line Contacts by a Newtonian Fluid

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