A computational homogenization framework for soft elastohydrodynamic lubrication

Budt, M.; Temizer, İ.; Wriggers, Peter

doi:10.1007/s00466-012-0709-7

Cited by 9 publications

(10 citation statements)

References 63 publications

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“…de Kraker, et al [22] developed a model based on flow factors to investigate more complex descriptions of lubricant flow than the conventional Reynolds equation such as the Navier-Stokes equations, FSI was only considered for the contacting region and was not examined at the scale of the topographical features. There are a number of recently published papers investigating other homogenisation techniques for EHL which span a range of applications including examining the constitutive equations of lubricant flow [23], cavitation [24], non-conformal contact [25], and soft contact [26].…”

Section: Introductionmentioning

confidence: 99%

“…[22] developed a model based on flow factors to investigate more complex descriptions of lubricant flow than the conventional Reynolds equation such as the Navier-Stokes equations, FSI was only considered for the contacting region and was not examined at the scale of the topographical features. There are a number of recently published papers investigating other homogenisation techniques for EHL which span a range of applications including examining the constitutive equations of lubricant flow [23], cavitation [24], non-conformal contact [25], and soft contact [26].The Heterogeneous Multiscale Methods (HMM) [27] are a set of general techniques which allows a problem to be described over multiple scales, the approach is applicable when the difference in scales is greater than an order of magnitude and periodicity applies to the geometric and flow features of the smaller scale. Gao and Hewson [28] first developed a framework for EHL and micro-EHL based on the HMM, a pressure gradientmass flux relationship was derived based on the homogenisation of periodic micro-EHL simulations which was subsequently used to solve the larger scale EHL problem.…”

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confidence: 99%

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Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts

Boer

Gao

Hewson

et al. 2017

Tribology International

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A multiscale method for the Elastohydrodynamic Lubrication (EHL) of line contacts is derived based on the Heterogeneous Multiscale Methods. Periodicity applies to the topographical features and lubricant flow, data is homogenised over a range of variables at a micro-scale and coupled into a macro-scale model. This is achieved using flow factors as calculated from metamodels, which themselves evolve with the solution procedure. Results are given for an idealised topography and illustrate significant deviations from smooth surface assumptions as quantified by the flow factors. Improvements in the accuracy and efficiency with previous work and large fluctuations due to micro-EHL are also presented. Validation of the multiscale method with a deterministic topography is provided demonstrating good accuracy and efficiency.Keywords: EHL; micro-EHL; Surface Topography; Metamodelling. INTRODUCTIONThe Elastohydrodynamic Lubrication (EHL) of line contacts generates high pressures which result in the bounding surfaces being separated by a thin lubricant film [1]. Surface topography can be of a similar scale to the film thickness and therefore has an effect on the performance of the tribological system [2]. For example Etsion et al. [3] showed that surface features can reduce the contacting friction of an EHL contact and Greenwood and Johnson [4] demonstrated that transverse waviness caused ripples in EHL pressure distributions. Reconciling the disparity in scales between surface topography and the contact region is a challenging computational problem for which many authors have sought solutions. Waviness in EHL has been modelled for example by Hooke [5] and Venner and Lubrecht [6] who investigated the amplitude reduction effect, but no such general method for describing the influence of surface topography in EHL as yet exists. The level of discretisation necessary to successfully solve fully deterministic problems, where both the contact region and surface topography are modelled simultaneously, has led to the development of homogenisation based models [7]. In such models information pertaining to the EHL of a topographical feature is characterised over a range of variables and subsequently coupled into a model for the EHL of the contact region. Periodicity in the lubricant flow and topographical features ensure that homogenisation of the solutions obtained at the smaller scale produces data which represents the behaviour of the larger scale [8,9]. Solutions to the EHL problem which are deterministic by nature also remain the subject of a significant amount of recent research [10][11][12][13][14][15][16][17].Patir and Cheng [18] first developed a two-scale model to include the effects of surface topography in hydrodynamic lubrication known as the flow factors method. In this approach the terms of the Reynolds equation, which describes the lubricant flow in the contact under smooth surface assumptions [19], were multiplied by flow factors which include the homogenised effects of surface topography. Sahlin, et al. [2...

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts

Boer

Gao

Hewson

et al. 2017

Tribology International

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“…This modification reflects the macroscopic observation that as ϵ → 0, the temperature within the material in the vicinity of the contact interface remains approximately equal to

{\overset{θ}{falsemml-overline}}_{c}

. This explicit enforcement of

{\overset{θ}{falsemml-overline}}_{c}

, similar to the ideas in , decouples the micromechanical analysis into two phases: Mechanical phase : The macroscopic contact pressure is applied to the two samples within a purely mechanical contact problem to solve for the deformed configuration and thereby resolve the real contact area. Within this setup, all temperature‐dependent material properties are evaluated at

{\overset{θ}{falsemml-overline}}_{c}

. Thermal phase : On the frozen mechanical configuration with a resolved contact interface, a purely thermal problem is solved where the macroscopic normal heat flux

\overset{h}{falsemml-overline}

is enforced and the temperature jump

{\overset{ϑ}{falsemml-overline}}_{c}^{(I)}

is measured via .…”

Section: A Two‐phase Self‐consistent Frameworkmentioning

confidence: 52%

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

Temizer

2013

Int. J. Numer. Meth. Engng

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SUMMARYA computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two-phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two-phase framework is cast within a self-consistent iterative scheme that acts as a first-order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar-based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non-uniform rational B-spline basis functions. Overall, the two-phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures.

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“…All terms starting from line 4 enforce the coupling conditions in the tangential direction. The fourth line includes the standard consistency boundary integrals in the tangential direction, which arise in the derivation of the weak form Equations (5) and (11). Using the dynamic equilibrium (18) and choosing the fluid stress to represent also the tangential interface traction lead to the presented contributions.…”

Section: Nitsche-based Methods On the Interface Between Fluid Domain Amentioning

confidence: 99%

“…In the works of Jai and Bou-Saïd 8 and Kane and Bou-Saïd, 9 it is shown that significantly fewer degrees of freedom are required for solving the homogenized equations compared to the direct equations in order to obtain the pressure field between rough surfaces. A framework to consider the effects of deformation of structural bodies interacting via a thin fluid film was presented in the works of Yang and Laursen 10 and Budt et al 11 A comparison of numerical solutions for the full spatially discretized fluid momentum and continuity equations and the Reynolds approach, tested for a problem setup with valid thin-film approximation presented in the work of Almqvist et al, 12 shows that there is no significant deviation of the results between both approaches. Nevertheless, with increasing film size, this result does not hold any longer, as the underlying geometrical assumptions of the Reynolds equation become invalid.…”

Section: Introductionmentioning

confidence: 99%

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

Ager

Schott

Vuong

et al. 2019

Numerical Meth Engineering

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Summary Simulation approaches for fluid‐structure‐contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are 2‐fold—one is to have a correct physical model for this scenario, and the other is to have a numerical method that is capable of working and being consistent down to a zero gap. Moreover, when analyzing such challenging setups of fluid‐structure interaction, which include contact of submersed solid components, it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model that is able to include the effects of the surface microstructure in a fluid‐structure‐contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid are included in the construction of the model. Although the physical model is not restricted to finite element–based methods, a numerical approach with its core based on the cut finite element method, enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a cut finite element method–based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective toward the potential capabilities of the presented physical model and numerical approach.

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A computational homogenization framework for soft elastohydrodynamic lubrication

Cited by 9 publications

References 63 publications

Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts

Heterogeneous Multiscale Methods for modelling surface topography in Elastohydrodynamic Lubrication line contacts

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

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