Calculation of friction in steady-state and transient EHL simulations

Commun. Numer. Meth. Engng.

et al. 2005

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SUMMARYIn this paper a high order Discontinuous Galerkin method is used to solve steady-state isothermal line contact elastohydrodynamic lubrication problems. This method is found to be stable across a wide range of loads and is shown to permit accurate solutions using just a small number of degrees of freedom provided suitable grids are used. A comparison is made between results obtained using this proposed method and those from a very large finite difference calculation in order to demonstrate excellent accuracy for a typical highly loaded test problem.

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

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High-order discontinuous Galerkin method for elastohydrodynamic lubrication line contact problems

Commun. Numer. Meth. Engng.

et al. 2005

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“…This work only resolved the spike using up to 1000 points, however it did still highlight the importance of this area of the solution. More recent results in [11,12] used over a million mesh points and illustrated both the smoothness of the pressure spike and the need for appropriate levels of mesh refinement. Consequently, calculating the friction accurately depends on achieving the necessary resolution of the pressure profile.…”

Section: Introductionmentioning

confidence: 99%

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Hart

Numerical Methods in Fluids

et al. 2010

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SUMMARYThe use of an adjoint technique for goal-based error estimation described by Hart et al. (Int. J. Numer. Meth. Fluids 2005; 47:1069-1074) is extended to the numerical solution of free boundary problems that arise in elastohydrodynamic lubrication (EHL). EHL systems are highly nonlinear and consist of a thinfilm approximation of the flow of a non-Newtonian lubricant which separates two bodies that are forced together by an applied load, coupled with a linear elastic model for the deformation of the bodies. A finite difference discretization of the line contact flow problem is presented, along with the numerical evaluation of an exact solution for the elastic deformation, and a moving grid representation of the free boundary that models cavitation at the outflow in this one-dimensional case. The application of a goal-based error estimate for this problem is then described. This estimate relies on the solution of an adjoint problem; its effectiveness is demonstrated for the physically important goal of the total friction through the contact. Finally, the application of this error estimate to drive local mesh refinement is demonstrated.

“…In the case of EHL an additional complicating factor is the presence of cavitation which leads to a free boundary in the mathematical model. An initial investigation into the application of adjoints to this type of problem has been made by Hart et al 1 , where the free boundary problem was considered in the context of uniform mesh refinement only. In this work we extend the approach to demonstrate that the adjoint solution can also yield local information that may be used to drive non-uniform refinement in an effective manner.…”

mentioning

confidence: 99%

Adjoint Error Estimation and Spatial Adaptivity for EHL-Like Models

Hart

IUTAM Symposium on Elastohydrodynamics and Micro-Elastohydrodynamics

et al.

Abstract:The use of adjoint error estimation techniques is described for a model problem that is a simplified version of an EHL line contact. Quantities of interest, such as friction, may be dependent upon the accuracy of the solution in some parts of the domain more than in others. The use of an inexpensive extra solve to calculate an adjoint solution is described for estimating the intergrid error in the value of friction calculated, and as a basis for local refinement. It is demonstrated that this enables an accurate estimate for the quantity of interest to be obtained from a less accurate solution of the model problem.