Fast and reduced full-system finite element solution of elastohydrodynamic lubrication problems: Line contacts

Habchi, Wassim; Issa, Jimmy

doi:10.1016/j.advengsoft.2012.11.009

Cited by 26 publications

(28 citation statements)

References 22 publications

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“…The latter is written as a function of H 0 and the nodal values of P and U. Since Reynolds equation is nonlinear in P, this would lead to an overall linearized matrix system (to be solved using a damped-Newton [25] procedure) of the following form: (16) The above system of equations describes the "full model" of an EHL contact. The matrix on the left-hand side is the overall Jacobian matrix of the nonlinear EHL problem.…”

Section: Overall Matrix Formulation Once the Field Variables P Andmentioning

confidence: 99%

“…These remain unchanged for subsequent iterations. The system of equations (16) has the same form for both line and circular contacts. Only, in the former case, U is made out of two-dimensional elastic deflection components U and W, while in the latter case it is made out of three-dimensional elastic deflection components U, V, and W. Let n h be the number of nodes in the discretized contact domain X c , and let n e be the total number of nodes in the discretized computational domain X.…”

Section: Overall Matrix Formulation Once the Field Variables P Andmentioning

confidence: 99%

“…This is not the case with other MOR techniques used so far in the numerical treatment of the EHL problem (e.g., Refs. [16][17][18][19]). It is also important to mention that, if needed, the deformations and stresses within the original solid domain may be recovered using Eq.…”

Section: Static Condensation Static Condensation Is a Techniquementioning

confidence: 99%

“…This gave rise in recent years to a surge for model order reduction (MOR) techniques that allowed a significant reduction in the size of the arising matrix system to be solved as well as a significant speed-up in computational time. First, Habchi and Issa [16,17] introduced the "EHL-basis technique" which allowed reducing the size of the elastic problem to less than 30DOFs/unknowns. Maier et al [18,19] used similar MOR approaches, but extended the model reduction to the hydrodynamic problem too, reducing its size and giving rise to an even faster resolution procedure.…”

Section: Introductionmentioning

confidence: 99%

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An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

Habchi

Issa

2017

Journal of Tribology

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This work presents an exact and general model order reduction (MOR) technique for a fast finite element resolution of elastohydrodynamic lubrication (EHL) problems. The reduction technique is based on the static condensation principle. As such, it is exact and it preserves the generality of the solution scheme while reducing the size of its corresponding model and, consequently, the associated computational overhead. The technique is complemented with a splitting algorithm to alleviate the hurdle of solving an arising semidense matrix system. The proposed reduced model offers computational time speed-ups compared to the full model ranging between a factor of at least three and at best 15 depending on operating conditions. The results also reveal the robustness of the proposed methodology which allows the resolution of very highly loaded contacts with Hertzian pressures reaching several GPa. Such cases are known to be a numerical challenge in the EHL literature.

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Section: Overall Matrix Formulation Once the Field Variables P Andmentioning

confidence: 99%

Section: Overall Matrix Formulation Once the Field Variables P Andmentioning

confidence: 99%

Section: Static Condensation Static Condensation Is a Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

Habchi

Issa

2017

Journal of Tribology

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“…The test results for the modal reduction and Ritz-vectorlike methods will not be shown in this paper. The interested reader is referred to [20] for further details.…”

Section: Reduced Modelmentioning

confidence: 99%

Fast and Reduced Full-System Finite Element Solution of Line Contact Elastohydrodynamic Lubrication Problems

Habchi¹,

Issa²

Proceedings of the Eighth International Conference on Engineering Computational Technology

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This paper presents a reduced full-system finite element solution of elastohydrodynamic lubrication (EHL) problems. It aims to demonstrate the feasibility of this approach by applying it to the simple isothermal Newtonian line contact case. However the proposed model can be easily extended to more complex situations. This model is based on a full-system finite element resolution of the EHL equations: Reynolds, linear elasticity and load balance. A reduced model is proposed for the linear elasticity problem. For this, a novel "EHL-basis" model order reduction technique is introduced. The latter requires only a few degrees of freedom to compose the elastic deformation of the solid components. In addition, a comparison with the full model shows an order of magnitude cpu time gain with errors of the order of only 1‰ for the central and minimum lubricant film thicknesses.

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Elastohydrodynamic Lubrication (EHL)

2018

Finite Element Modelling of Elastohydrodynamic Lubrication Problems

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Fast and reduced full-system finite element solution of elastohydrodynamic lubrication problems: Line contacts

Cited by 26 publications

References 22 publications

An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

Fast and Reduced Full-System Finite Element Solution of Line Contact Elastohydrodynamic Lubrication Problems

Elastohydrodynamic Lubrication (EHL)

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