Multiscale and Modern Solutions in the Simulation of Lubricated Contacts

A special issue of Lubricants (ISSN 2075-4442).

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 20129

Special Issue Editors


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Guest Editor
Institut Pprime CNRS, Université de Poitiers, ENSMA Dept GMSC 11 Boulevard Marie et Pierre Curie, 86360 Chasseneuil du Poitou, France
Interests: lubrication; tribology; numerical modeling; surface analysis; heat transfer; friction; numerical analysis; fluid sealing

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Guest Editor
Institut Pprime CNRS, Université de Poitiers, ENSMA UPR 3346 Dept GMSC IUT Angouleme 4 Warsaw Avenue, CEDEX, 16021 Angouleme, France
Interests: machine learning; rough surface lubrication

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Guest Editor
School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK
Interests: computational tribology; multiscale modelling; fluid–structure interactions

Special Issue Information

Dear Colleagues,

The usual solutions used for reducing energy consumption in mechanical systems are to reduce the size of components (downsizing) and to use lower-viscosity lubricants while maintaining the loading level and operating speed. The consequence for lubricated contacts is a change in the functioning regime from full film to mixed lubrication, in which surface roughness plays a significant role. Surface texturing is now currently used to avoid the detrimental consequences of these new approaches, such as asperity contact and wear, by improving hydrodynamic lubrication. It is, thus, crucial to be able to simulate such problems, including surface texture and/or roughness, with accurate and efficient methods in order to increase our knowledge on these problems and, eventually, to provide design tools for engineers. The main difficulty is considering the different scales (from surface roughness and texture all the way up to contact size) that range over several orders of magnitude.

Several modelling or solution methods have now been developed to reduce the computational burden of this multiscale problem. One popular method in engineering is the multiscale approach. This consists of modelling the different scales by using relevant approaches that are coupled together. New computer architectures offer multithread or GPU calculation possibilities that can be used to share the calculation process and reduce the computation time. Moreover, machine learning has been attracting interest for several years in many fields; however, when it comes to lubrication, it remains little used.

Authors are encouraged to explore the benefits of multiscale methods, multithreading computation and machine learning techniques, or any other modern methods for lubricated contacts, and submit their results along with the structure of the algorithm to this Special Issue.

Dr. Noël Brunetière
Dr. Arthur Francisco
Dr. Greg de Boer
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • multiscale methods
  • multithreading computation
  • GPU calculation
  • machine learning
  • hydrodynamic lubrication
  • roughness
  • surface texture

Published Papers (9 papers)

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Research

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16 pages, 4691 KiB  
Article
Characterisation of the Contact between Cross-Country Skis and Snow: On the Multi-Scale Interaction between Ski Geometry and Ski-Base Texture
by Kalle Kalliorinne, Gustav Hindér, Joakim Sandberg, Roland Larsson, Hans-Christer Holmberg and Andreas Almqvist
Lubricants 2023, 11(10), 427; https://doi.org/10.3390/lubricants11100427 - 03 Oct 2023
Cited by 1 | Viewed by 2062
Abstract
In elite endurance sports, marginal differences in finishing times drive ongoing equipment improvement to enhance athlete performance. In cross-country skiing, researchers, since the 1930s, have faced the challenge of minimising the resistance caused by friction in the contact between skis and snow. This [...] Read more.
In elite endurance sports, marginal differences in finishing times drive ongoing equipment improvement to enhance athlete performance. In cross-country skiing, researchers, since the 1930s, have faced the challenge of minimising the resistance caused by friction in the contact between skis and snow. This study was designed to evaluate the multi-scale interaction between the macro-scale ski-camber profile and the micro-scale ski-base texture. Considerations included real contact area, average interfacial separation, and total reciprocal interfacial separation between the ski and snow, which are properties that are intimately coupled to ski–snow friction. We found that both the profile of the ski camber and the texture of the ski base play decisive roles in determining viscous friction. At the same time, the texture of the ski base exerts a greater impact on the average real contact pressure, real contact area, and minimal average interfacial separation between the ski and snow than the ski-camber profile. Full article
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25 pages, 719 KiB  
Article
On the Numerical Modeling of Friction Hysteresis of Conformal Rough Contacts
by Kristof Driesen, Sylvie Castagne, Bert Lauwers and Dieter Fauconnier
Lubricants 2023, 11(8), 326; https://doi.org/10.3390/lubricants11080326 - 01 Aug 2023
Viewed by 802
Abstract
In this work, a numerical model simulating friction hysteresis for lubricated rough and textured surfaces in contact is presented. Friction hysteresis occurs in sliding contacts that are subjected to a non-constant (e.g., sinusoidal) motion. It refers to the phenomenon where the observed friction [...] Read more.
In this work, a numerical model simulating friction hysteresis for lubricated rough and textured surfaces in contact is presented. Friction hysteresis occurs in sliding contacts that are subjected to a non-constant (e.g., sinusoidal) motion. It refers to the phenomenon where the observed friction force during acceleration differs from that during deceleration. Besides the dynamics of the sliding system, a classic mixed friction model is adopted, in which the transient Reynolds equation for the description of the thin lubricant film is combined with a statistical Greenwood–Williamson model for the description of rough surface asperity contacts. The model enables the prediction of the friction hysteresis for predefined contact descriptions (i.e., surface profile and roughness, lubricant, etc.) and allows the study of the physics and parametric influences of dynamically sliding contacts. In this paper, it is shown that (i) friction hysteresis is captured by classic transient models for mixed lubrication; (ii) system parameters, such as roughness, applied load, viscosity and velocity, including the offset, amplitude and motion reversal, influence the shape and area of friction hysteresis; and (iii) the selection of the aforementioned parameters may minimize friction hysteresis. Full article
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22 pages, 9196 KiB  
Article
A New Thermal Elasto-Hydrodynamic Lubrication Solver Implementation in OpenFOAM
by James Layton, Benjamin C. Rothwell, Stephen Ambrose, Carol Eastwick, Humberto Medina and Neville Rebelo
Lubricants 2023, 11(7), 308; https://doi.org/10.3390/lubricants11070308 - 22 Jul 2023
Viewed by 1010
Abstract
Designing effective thermal management systems within transmission systems requires simulations to consider the contributions from phenomena such as hydrodynamic lubrication regions. Computational fluid dynamics (CFD) remains computationally expensive for practical cases of hydrodynamic lubrication while the thermo elasto-hydrodynamic lubrication (TEHL) theory has demonstrated [...] Read more.
Designing effective thermal management systems within transmission systems requires simulations to consider the contributions from phenomena such as hydrodynamic lubrication regions. Computational fluid dynamics (CFD) remains computationally expensive for practical cases of hydrodynamic lubrication while the thermo elasto-hydrodynamic lubrication (TEHL) theory has demonstrated good accuracy at a lower computational cost. To account for the effects of hydrodynamic lubrication in high-power transmission systems requires integrating TEHL into a CFD framework such that these methodologies can be interfaced. This study takes an initial step by developing a TEHL solver within OpenFOAM such that the program is prepared to be interfaced with a CFD module in future versions. The OpenFOAM solver includes the Elrod–Adams cavitation model, thermal effects, and elastic deformation of the surfaces, and considers mixing between the recirculating flow and oil feed by applying energy and mass continuity. A sensitivity study of the film mesh is presented to show the solution variation with refinement along the circumferential, axial and radial directions. A validation case is presented of an experimental single axial groove journal bearing which shows good agreement in the pressure and temperature results. The peak pressure in the film is predicted within 12% and the peak temperature in the bush is predicted within 5% when comparing the centerline profiles. Full article
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19 pages, 10175 KiB  
Article
Characterisation of the Contact between Cross-Country Skis and Snow: A Micro-Scale Study Considering the Ski-Base Texture
by Kalle Kalliorinne, Bo N. J. Persson, Joakim Sandberg, Gustav Hindér, Roland Larsson, Hans-Christer Holmberg and Andreas Almqvist
Lubricants 2023, 11(5), 225; https://doi.org/10.3390/lubricants11050225 - 16 May 2023
Cited by 3 | Viewed by 1791
Abstract
In winter sports, the equipment often comes into contact with snow or ice, and this contact generates a force that resists motion. In some sports, such as cross-country skiing, this resistive force can significantly affect the outcome of a race, as a small [...] Read more.
In winter sports, the equipment often comes into contact with snow or ice, and this contact generates a force that resists motion. In some sports, such as cross-country skiing, this resistive force can significantly affect the outcome of a race, as a small reduction in this force can give an athlete an advantage. Researchers have examined the contact between skis and snow in detail, and to fully understand this friction, the entire ski must be studied at various scales. At the macro scale, the entire geometry of the ski is considered and the apparent contact between the ski and the snow is considered and at the micro-scale the contact between the snow and the ski-base textures. In the present work, a method for characterising the contact between the ski-base texture and virtual snow will be presented. Six different ski-base textures will be considered. Five of them are stone-ground ski bases, and three of them have longitudinal linear textures with a varying number of lines and peak-to-valley heights, and the other two are factory-ground “universal” ski bases. The sixth ski base has been fabricated by a steel-scraping procedure. In general, the results show that a ski base texture with a higher Spk value has less real contact area, and that the mutual differences can be large for surfaces with similar Sa values. The average interfacial separation is, in general, correlated with the Sa value, where a “rougher” surface exhibits a larger average interfacial separation. The results for the reciprocal average interfacial separation, which is related to the Couette type of viscous friction, were in line with the general consensus that a “rougher” texture performs better at high speed than a “smoother” one, and it was found that a texture with high Sa and Spk values resulted in a low reciprocal average interfacial separation and consequently low viscous friction. The reciprocal average interfacial separation was found to increase with increasing real contact area, indicating a correlation between the real area of contact and the Couette part of the viscous friction. Full article
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20 pages, 12842 KiB  
Article
Investigation of Microflow Effects in Textures on Hydrodynamic Performance of Journal Bearings Using CFD Simulations
by Yujun Wang, Georg Jacobs, Florian König, Shuo Zhang and Stephan von Goeldel
Lubricants 2023, 11(1), 20; https://doi.org/10.3390/lubricants11010020 - 05 Jan 2023
Cited by 9 | Viewed by 2112
Abstract
Adequately designed and positioned surface textures are recognized as a promising way to increase load-carrying capacity and reduce frictional losses of journal bearings. The aim of this work is to analyze the local lubrication mechanisms of textures in journal bearings from microflow perspective, [...] Read more.
Adequately designed and positioned surface textures are recognized as a promising way to increase load-carrying capacity and reduce frictional losses of journal bearings. The aim of this work is to analyze the local lubrication mechanisms of textures in journal bearings from microflow perspective, while considering the interactions between textures and the film formation in the whole bearing. For this purpose, hydrodynamic lubrication models of textured journal bearings are built. The results show that placing textures downstream of the high-pressure region leads to a reduced friction force, with a less severe loss of load-carrying capacity. The effects of textures on the load-carrying capacity include the positive micro-hydrodynamic pressure effect and the negative effect caused by the discontinuity of the high-pressure region. The micro-hydrodynamic pressure of textures can be generated on one hand by limiting pressure drop (cavitation) in the divergent gap and on the other hand by the inertia effect. For the friction, the vortex inside textures affects the friction force by influencing the maximum shear stress at the minimum oil film. In turn the vortex is influenced by the bearing lubrication film. The research provides the fundamental reference and theoretical basis for the design and optimization of textured journal bearings. Full article
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22 pages, 5702 KiB  
Article
Full and Hybrid Multiscale Lubrication Modeling
by Arthur Francisco and Noël Brunetière
Lubricants 2022, 10(12), 329; https://doi.org/10.3390/lubricants10120329 - 23 Nov 2022
Viewed by 1078
Abstract
The numerical solution for the lubrication of parallel rough surfaces cannot be obtained using the well-known flow factors of Patir and Cheng. Nor can it be determined using homogenization techniques. Is there an alternative, besides a purely long-term deterministic way of solving the [...] Read more.
The numerical solution for the lubrication of parallel rough surfaces cannot be obtained using the well-known flow factors of Patir and Cheng. Nor can it be determined using homogenization techniques. Is there an alternative, besides a purely long-term deterministic way of solving the problem? The present paper aims at proposing a multiscale approach in order to reduce the computing time, specific to deterministic resolutions, while maintaining good accuracy. The configuration is a parallel rough surface slider, with imposed hydrodynamic operating conditions. The domain consists of independent macro-elements, on which the Reynolds equation is solved. Then, the macro-element boundaries are adjusted to ensure global mass conservation. In its hybrid version, the algorithm replaces some well-chosen macro-elements by simple linear finite elements. The results clearly show the potential of our method. Because the lubrication of each macro-element can be processed independently, the multicore architecture of the processor is exploited. Even if the performance depends on the ratio roughness/height, the computing time is half than for the classical deterministic method, with a few percent errors. The work concludes with some recommendations on the configurations for which the multiscale method is best suited, such as surfaces with short correlation lengths. Full article
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17 pages, 17806 KiB  
Article
Mixed EHL Problems: An Efficient Solution to the Fluid–Solid Coupling Problem with Consideration of Elastic Deformation and Cavitation
by Chunxing Gu, Di Zhang, Xiaohui Jiang, Xianghui Meng, Shuwen Wang, Pengfei Ju and Jingzhou Liu
Lubricants 2022, 10(11), 311; https://doi.org/10.3390/lubricants10110311 - 16 Nov 2022
Cited by 4 | Viewed by 1870
Abstract
For transient mixed Elastohydrodynamic lubrication (EHL) problems, a novel solution is required to predict friction loss and wear in sliding or rolling parts. However, existing solutions have numerous limitations. In general, the lower the oil film thickness is, the more serious the non-linear [...] Read more.
For transient mixed Elastohydrodynamic lubrication (EHL) problems, a novel solution is required to predict friction loss and wear in sliding or rolling parts. However, existing solutions have numerous limitations. In general, the lower the oil film thickness is, the more serious the non-linear problem is. This paper presents an efficient solution to tackle the non-linearity of the mixed EHL problem. The elastic deformation in the fluid–solid iteration coupling problem is divided into two parts: One is induced by the hydrodynamic pressure. This part of the deformation is obtained by the unsteady EHL-FBNS (Fischer–Burmeister–Newton–Schur) solver by considering both mass-conserving cavitation and elastic deformation. The other part of the deformation is introduced by the asperity contact pressure. It can be obtained by the Newton–Raphson method. After some limited iterations, the mixed EHL problems can be solved by evaluating the residual total pressure (including hydrodynamic pressure and asperity contact pressure). The proposed methodology was validated against the results from the published literature and applied to characterize the tribological performance of point contact with moving texturing. It appears that the developed method can be effectively used for tracking the tribological behavior of friction pairs. Full article
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15 pages, 6435 KiB  
Article
Characterisation of the Contact between Cross-Country Skis and Snow: A Macro-Scale Investigation of the Apparent Contact
by Kalle Kalliorinne, Joakim Sandberg, Gustav Hindér, Roland Larsson, Hans-Christer Holmberg and Andreas Almqvist
Lubricants 2022, 10(11), 279; https://doi.org/10.3390/lubricants10110279 - 26 Oct 2022
Cited by 6 | Viewed by 4193
Abstract
In a cross-country skiing competition, the time difference between the winner and the skier coming in at second place is typically very small. Since the skier spends much of the energy on overcoming resistive forces, a relatively small reduction in these forces can [...] Read more.
In a cross-country skiing competition, the time difference between the winner and the skier coming in at second place is typically very small. Since the skier spends much of the energy on overcoming resistive forces, a relatively small reduction in these forces can have a significant impact on the results. The resistive forces come partly from the friction, at the tribological interface between the ski and the snow, and as with many tribological processes, the characterisation of its origin plays an important role in determining the frictional properties. Furthermore, in cross-country ski friction, there are several scales impacting the frictional performance, with the major contributors being the ski-camber profile and ski-base structure. Macro-scale measurements of the ski-camber profile under loading are often used to determine how adequate the ski is for use under specific conditions. The characteristic properties usually assessed are the force required to collapse the ski in order to obtain a certain camber height, the topography of the kick-wax zone, and the length (determined by simple means) of the frictional interfaces associated with the rear- and front glide zones, i.e., the apparent contact length. These measurements are, however, commonly performed by loading the ski against a much stiffer counter surface than snow and this affects the quantification of the characteristic properties. To date, some mathematical models have been proposed, but there is no reliable approach for determining the macro-scale properties of the contact between a cross-country ski and a counter surface using simulations. In the present paper, an Artificial Neural Network (ANN) has been trained to predict the ski-camber profile for various loads applied at different positions. A well-established deterministic approach has been employed to simulate the contact between the ANN-predicted ski-camber profile and a linearly elastic body with a flat upper surface, representing the snow. Our findings indicate that this method is feasible for the determination of relevant macro-scale contact characteristics of different skis with snow. Moreover, we show that the apparent contact area does not linearly depend on the load and that the material properties of the counter surface also exert a large impact when quantifying the apparent contact area and the average apparent contact pressure. Full article
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Review

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28 pages, 2359 KiB  
Review
A Review on Modelling of Viscoelastic Contact Problems
by Dongze Wang, Gregory de Boer, Anne Neville and Ali Ghanbarzadeh
Lubricants 2022, 10(12), 358; https://doi.org/10.3390/lubricants10120358 - 12 Dec 2022
Cited by 8 | Viewed by 4096
Abstract
Approaches to solving viscoelastic problems have received extensive attention in recent decades as viscoelastic materials have been widely applied in various fields. An overview of relevant modelling approaches is provided in the paper. The review starts with a brief introduction of some basic [...] Read more.
Approaches to solving viscoelastic problems have received extensive attention in recent decades as viscoelastic materials have been widely applied in various fields. An overview of relevant modelling approaches is provided in the paper. The review starts with a brief introduction of some basic terminologies and theories that are commonly used to describe the contact behaviour of viscoelastic materials. By building up the complexity of contact problems, including dry contact, lubricated contact, thermoviscoelastic contact and non-linear viscoelastic contact, tentative analytical solutions are first introduced as essential milestones. Afterwards, a series of numerical models for the various types of contact problems with and without surface roughness are presented and discussed. Examples, in which computational tools were employed to assist the analysis of viscoelastic components in different fields, are given as case studies to demonstrate that a comprehensive numerical framework is currently being developed to address complex viscoelastic contact problems that are prevalent in real life. Full article
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