A Galerkin/hyper-reduction technique to reduce steady-state elastohydrodynamic line contact problems

Scurria, Leoluca; Fauconnier, Dieter; Jiránek, Pavel; Tamarozzi, Tommaso

doi:10.1016/j.cma.2021.114132

Cited by 6 publications

(4 citation statements)

References 21 publications

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“…[K]{U} = {F} (27) where [K] is the stiffness matrix of the structure, {U} is the vector of nodal displacements, and {F} is the vector of external nodal forces. The static condensation technique consists of separating needed dofs (named masters with subscript m) from unneeded ones (named slaves with subscript s).…”

Section: Static Condensationmentioning

confidence: 99%

“…Finally, it is important to note that the static condensation with splitting reduces the size of the problem from n do f = 2 × n e + n h + 1 + n t + n s to ndo f = 2 × n h + 1 + n t + n s for line contacts and from n do f = 3 × n e + n h + 1 + n t + 2 × n s to ndo f = 2 × n h + 1 + n t + 2 × n s for circular contacts. Even though the reduction is large, especially given that the elastic domain is one of the largest in the problem, it is not as significant as for other MOR techniques that are based on mode superposition principles [24][25][26][27]41]. On the other hand, the significance of this technique is that it is fast and efficient since the Jacobian matrix evaluation and its LU decomposition are not repeated at every splitting iteration i.…”

Section: Overall Numerical Proceduresmentioning

confidence: 99%

“…This technique was improved by Maier et al [25,26] who reduced the hydrodynamic domain to obtain even faster results. A novel reduction technique was also introduced by Scurria et al [27] based on Galerkin Projections for the structural part and a hyper-reduction for the Reynolds equation. Even though these MOR techniques are very efficient when it comes to computational speed, they face some significant downsides.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact Model Order Reduction for the Full-System Finite Element Solution of Thermal Elastohydrodynamic Lubrication Problems

Mounayer

Habchi

2023

Lubricants

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The derivation of fast, reliable, and accurate modeling procedures for the solution of thermal elastohydrodynamic lubrication problems is a topic of significant interest in the Tribology community. In this paper, a novel model order reduction technique is introduced for the analysis of thermal elastohydrodynamic lubrication problems. The method uses static condensation to reduce the size of the linear elasticity part within the overall matrix system, followed by a splitting algorithm to avoid the burden of solving a semi-dense matrix system. The results reveal the exactness of the proposed methodology, which does not introduce any additional model-reduction approximations to the overall solution. They also reveal the reduction in computational times, which is in the order of 10–20% for line contacts, while it is in excess of 50% for circular contacts. The robustness of the proposed method is displayed by using it to model some relatively highly loaded contacts whose numerical solution is known to be rather challenging.

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Section: Static Condensationmentioning

confidence: 99%

Section: Overall Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact Model Order Reduction for the Full-System Finite Element Solution of Thermal Elastohydrodynamic Lubrication Problems

Mounayer

Habchi

2023

Lubricants

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“…Over the years, various methods were implemented to reduce the computing time of simulations. One notable method is MOR, which reduces the size of the arising algebraic system of equations, either through projection into a reduced solution space [13,14] or through static condensation [15]. Despite the substantial decrease in computational effort and time, simulations still require considerable time to converge, particularly for high ellipticity and highly loaded cases.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning for Film Thickness Prediction in Elastohydrodynamic Lubricated Elliptical Contacts

Issa,

El Hajj,

Vergne

et al. 2023

Lubricants

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This study extends the use of Machine Learning (ML) approaches for lubricant film thickness predictions to the general case of elliptical elastohydrodynamic (EHD) contacts, by considering wide and narrow contacts over a wide range of ellipticity and operating conditions. Finite element (FEM) simulations are used to generate substantial training and testing datasets that are used within the proposed ML framework. The complete dataset entails 915 samples; split into an 823-sample training dataset and a 92-sample testing dataset, corresponding to 90% and 10% of the combined dataset samples, respectively. The proposed ML model consists of a pre-processing stage in which conventional EHD dimensionless groups are used to minimize the number of inputs into the model, reducing them to only three. The core of the model is based on Gaussian Process Regression (GPR), a powerful ML regression tool, well-suited for small-sized datasets, producing output central and minimum film thicknesses, also in dimensionless form. The last stage is a post-processing one, in which the output film thicknesses are retrieved in dimensional from. The results reveal the capabilities and potential of the proposed ML framework, producing quasi-instantaneous predictions that are far more accurate than conventional film thickness analytical formulae. In fact, the produced central and minimum film thickness predictions are on average within 0.3% and 1.0% of the FEM results, respectively.

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A fully coupled finite element solution for the mixed elastohydrodynamic lubrication of finite line contacts

Fang,

Peng,

Zhou

et al. 2024

Tribology International

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A Galerkin/hyper-reduction technique to reduce steady-state elastohydrodynamic line contact problems

Cited by 6 publications

References 21 publications

Exact Model Order Reduction for the Full-System Finite Element Solution of Thermal Elastohydrodynamic Lubrication Problems

Exact Model Order Reduction for the Full-System Finite Element Solution of Thermal Elastohydrodynamic Lubrication Problems

Machine Learning for Film Thickness Prediction in Elastohydrodynamic Lubricated Elliptical Contacts

A fully coupled finite element solution for the mixed elastohydrodynamic lubrication of finite line contacts

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