| 1. |
- Almqvist, Torbjörn, et al.
(författare)
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A comparison between computational fluid dynamic and Reynolds approaches for simulating transient EHL line contacts
- 2004
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Ingår i: Tribology International. - 0301-679X .- 1879-2464. ; 37:1, s. 61-69
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Tidskriftsartikel (refereegranskat)abstract
- When simulating elastohydrodynamic lubrication (EHL), the Reynolds equation is the predominating partial differential equation for prediction of the fluid flow. Also very few attempts have been carried out using the full momentum and continuity equations separately. The aim of this investigation is to compare two different approaches for simulation of EHL line contacts where a single ridge travels through an EHL conjunction. One of the approaches is based on the Reynolds equation, addressing the coupling between the pressure and the film thickness. The solver uses the advantages of multilevel techniques to speed up the convergence rate. The other approach is based on commercial CFD software. The software uses the momentum and continuity equations in their basic form, enabling numerical simulations outside the contact regions, as well as in the thin film region to be carried out. The numerical experiments show that, under the running conditions chosen, only small deviations between the two approaches can be observed. The results are encouraging from several viewpoints: validation of the codes, the possibilities of further developments of the CFD approach and the justification of using a Reynolds approach under the running conditions chosen
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| 2. |
- Furustig, Joel, et al.
(författare)
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The measurement of wear using AFM and wear interpretation using a contact mechanics coupled wear model
- 2016
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Ingår i: Wear. - : Elsevier BV. - 0043-1648 .- 1873-2577. ; 350-351, s. 74-81
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Tidskriftsartikel (refereegranskat)abstract
- Detailed understanding of wear processes is required to improve the wear resistance and lifetime of machine components. Atomic force microscopy (AFM) is used to measure surface height profiles with high precision, before and after a wear experiment. The distribution and depth of wear on steel surfaces is then calculated using a relocation method. A numerical investigation of wear based on Archard's equation is conducted on the same measured surfaces. A good correlation was found between the model and experiment for wear larger than a hundred nm. The wear mechanisms considered in the numerical simulation was thus found to be the cause of the majority of the wear. On the scale of tens of nm the correlation was limited, but the measured wear was still analysed in detail.
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| 3. |
- Marian, Max, et al.
(författare)
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Numerical micro-texture optimization for lubricated contacts—A critical discussion
- 2022
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Ingår i: Friction. - : Springer. - 2223-7690 .- 2223-7704. ; 10:11, s. 1772-1809
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Forskningsöversikt (refereegranskat)abstract
- Despite numerous experimental and theoretical studies reported in the literature, surface micro-texturing to control friction and wear in lubricated tribo-contacts is still in the trial-and-error phase. The tribological behaviour and advantageous micro-texture geometries and arrangements largely depend on the contact type and the operating conditions. Industrial scale implementation is hampered by the complexity of numerical approaches. This substantiates the urgent need to numerically design and optimize micro-textures for specific conditions. Since these aspects have not been covered by other review articles yet, we aim at summarizing the existing state-of-the art regarding optimization strategies for micro-textures applied in hydrodynamically and elastohydrodynamically lubricated contacts. Our analysis demonstrates the great potential of optimization strategies to further tailor micro-textures with the overall aim to reduce friction and wear, thus contributing toward an improved energy efficiency and sustainability.
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| 4. |
- Schaumberg, Katherine, et al.
(författare)
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Patterns of diagnostic transition in eating disorders : a longitudinal population study in Sweden
- 2019
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Ingår i: Psychological Medicine. - : Cambridge University Press. - 0033-2917 .- 1469-8978. ; 49:5, s. 819-827
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: Transition across eating disorder diagnoses is common, reflecting instability of specific eating disorder presentations. Previous studies have examined temporal stability of diagnoses in adult treatment-seeking samples but have not uniformly captured initial presentation for treatment. The current study examines transitions across eating disorder diagnostic categories in a large, treatment-seeking sample of individuals born in Sweden and compares these transitions across two birth cohorts and from initial diagnosis.METHODS: Data from Swedish eating disorders quality registers were extracted in 2013, including 9622 individuals who were seen at least twice from 1999 to 2013. Patterns of remission were examined in the entire sample and subsequently compared across initial diagnoses. An older (born prior to 1990) and younger birth cohort were also identified, and analyses compared these cohorts on patterns of diagnostic transition.RESULTS: Although diagnostic instability was common, transition between threshold eating disorder diagnoses was infrequent. For all diagnoses, transition to remission was likely to occur following a diagnosis state that matched initial diagnosis, or through a subthreshold diagnostic state. Individuals in the younger cohort were more likely to transition to a state of remission than those in the older cohort.CONCLUSIONS: Results indicate more temporal continuity in eating disorder presentations than suggested by previous research and highlight the importance of early detection and intervention in achieving remission.
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| 5. |
- Spencer, Andrew, et al.
(författare)
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Surface characterization with functional parameters
- 2011
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Typically engineering surfaces are characterized with traditional roughness parameters that perform some type of height averaging over the surface. Although these parameters describe the topography of the surface none of them necessarily describe the ability of the surface to carry out its function in a tribological contact. In this study an ICE cylinder liner has been investigated.The traditional Rk parameters (based on the Abbott curve) have been calculated as well as functional ‘flow factors’which modify the Reynolds equation to incorporate the effects of surface topography.To calculate flow factors the homogenization technique has been implemented and a full 3D contact mechanics model has been incorporated so that surface functionality in mixed lubrication can be studied. Furthermore, the cylinder liner surface has been measured with both white light interferometery and an AFM so that the effect of measuring technique on roughness and functional parameters can be investigated.
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| 6. |
- Spencer, Andrew, et al.
(författare)
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The influence of AFM and VSI techniques on the accurate calculation of tribological surface roughness parameters
- 2013
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Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 57, s. 242-250
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Tidskriftsartikel (refereegranskat)abstract
- Vertical Scanning Interferometry (VSI) may induce optical artefacts in surface topography measurements. The influence of these optical artefacts on the calculation of Rk surface roughness parameters, contact stiffness and flow factors were studied. Two surface measurement techniques were used: Atomic Force Microscopy (AFM) and VSI. Calibration grids were used to make it easier to isolate the causes of these artefacts, while a real engineering surface was used to compare these two techniques in an industrially applied case. It was found that the optical artefacts have a large influence on all the roughness parameters, contact stiffness and flow factors calculated on the calibration grids. However, for the engineering surface the differences between AFM and VSI measurements were much smaller.
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| 7. |
- Aberg, V., et al.
(författare)
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Synthesis and absolute configuration of methyl(-)-(3R)-8-(4-bromophenyl)-7-(naphthalen-1-yl-methyl)-5-oxo-2,3-dihydro-5H-thiazolo 3,2-a pyridine-3-carboxylate
- 2002
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Ingår i: Acta Crystallographica Section E. - : International Union of Crystallography (IUCr). - 1600-5368. ; 58, s. o812-o814
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Tidskriftsartikel (refereegranskat)abstract
- The title molecule, C26H20BrNO3S, contains a ring-fused 2-pyridinone framework substituted with a 4-bromo-phenyl-, a naphthalen-1-ylmethyl and a methoxycarbonyl substituent. The main goal of this work was to confirm the stereochemistry for the methoxycarbonyl substituent, which proved to be 3R. Moreover, the 4-bromophenyl substituent was shown to be rotated out of the plane of the 2-pyridinone ring, with a torsion angle of 61.2 (5)degrees. To allow the best packing arrangement, the naphthalen-1-ylmethyl substituent is positioned to mediate an intermolecular pi-pi interaction.
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| 8. |
- Almqvist, Andreas, et al.
(författare)
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A new approach for studying cavitation in lubrication
- 2014
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Ingår i: Journal of tribology. - : ASME International. - 0742-4787 .- 1528-8897. ; 136:1
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Tidskriftsartikel (refereegranskat)abstract
- The underlying theory, in this paper, is based on clear physical arguments related to conservation of mass flow and considers both incompressible and compressible fluids. The result of the mathematical modeling is a system of equations with two unknowns, which are related to the hydrodynamic pressure and the degree of saturation of the fluid. Discretization of the system leads to a linear complementarity problem (LCP), which easily can be solved numerically with readily available standard methods and an implementation of a model problem in matlab code is made available for the reader of the paper. The model and the associated numerical solution method have significant advantages over today's most frequently used cavitation algorithms, which are based on Elrod-Adams pioneering work
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| 9. |
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| 10. |
- Almqvist, Andreas, et al.
(författare)
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A Scientific Perspective on Reducing Ski-Snow Friction to Improve Performance in Olympic Cross-Country Skiing, the Biathlon and Nordic Combined
- 2022
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Ingår i: Frontiers in Sports and Active Living. - : Frontiers Media S.A.. - 2624-9367. ; 4
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Tidskriftsartikel (refereegranskat)abstract
- Of the medals awarded at the 2022 Winter Olympics in Beijing, 24% were for events involving cross-country skiing, the biathlon and Nordic combined. Although much research has focused on physiological and biomechanical characteristics that determine success in these sports, considerably less is yet known about the resistive forces. Here, we specifically describe what is presently known about ski-snow friction, one of the major resistive forces. Today, elite ski races take place on natural and/or machine-made snow. Prior to each race, several pairs of skis with different grinding and waxing of the base are tested against one another with respect to key parameters, such as how rapidly and for how long the ski glides, which is dependent on ski-snow friction. This friction arises from a combination of factors, including compaction, plowing, adhesion, viscous drag, and water bridging, as well as contaminants and dirt on the surface of and within the snow. In this context the stiffness of the ski, shape of its camber, and material composition and topography of the base exert a major influence. An understanding of the interactions between these factors, in combination with information concerning the temperature and humidity of both the air and snow, as well as the nature of the snow, provides a basis for designing specific strategies to minimize ski-snow friction. In conclusion, although performance on “narrow skis” has improved considerably in recent decades, future insights into how best to reduce ski-snow friction offer great promise for even further advances.
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| 11. |
- Almqvist, Andreas, et al.
(författare)
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An Abbott curve based rough surface contact mechanics approach
- 2005
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Ingår i: Proceedings of the World Tribology Congress III - 2005. - New York : American Society of Mechanical Engineers. ; , s. 397-398
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Konferensbidrag (refereegranskat)abstract
- In this way all the height information of the surface profile is preserved and not only a few parameters, like Ra, Rq, Rz, Rsk, etc. The aim of this work is to investigate how classes of surfaces based on a single Abbott curve perform in terms of contact mechanical parameters like the real area of contact. The result shows that surfaces taken from a class of random surfaces generated from a specific Abbott curve behaves similar in a contact mechanics simulation. That is, the distribution of for example the real area of contact within such a class is compact, having a small deviation from its mean.This implies that it is possible to simulate classes of surfaces based on Abbott curves and to use the results to predict contact mechanical properties of real surface topographies.
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| 12. |
- Almqvist, Andreas, et al.
(författare)
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Development of a lubrication simulation model
- 2009
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Ingår i: Svenska mekanikdagarna. - Stockholm : Svenska nationalkommittén för mekanik. ; , s. 74-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 13. |
- Almqvist, Andreas, et al.
(författare)
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Different Together : Design for Radical Placemaking
- 2023
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Ingår i: Proceedings of the 2023 CHI Conference on Human Factors in Computing Systems. - : Association for Computing Machinery (ACM). ; , s. 1-16
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Konferensbidrag (refereegranskat)abstract
- This work responds to isolating urban places, and contributes new ways for thinking about placemaking. Progressing through autoethnography and prototyping, we critique design proposals with Lefebvre’s theory of utopia. There inhabitants can enjoy and shape their place together without risking depletion of their abilities and motivations to do so. The critique produces political sensibilities that help us make sense of common tensions among inhabitants, landowners, and visitors, and generate possible responses. The critique process itself illustrates how designing through critique with theory can help us think in new ways. This paper contributes a display of how design with critical theory can happen, ultimately to support our abilities and motivations to envision and make places of social flourishing that can respond to our socio-environmental crises.
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| 14. |
- Almqvist, Andreas, et al.
(författare)
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Flow in thin domains with a microstructure : Lubrication and thin porous media
- 2017
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Ingår i: AIP Conference Proceedings. - : AIP Publishing. - 0094-243X .- 1551-7616. ; 1798
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to homogenization of different models of flow in thin domains with a microstructure. The focus is on applications connected to the effect of surface roughness in full film lubrication, but a parallel to flow in thin porous media is also discussed. Mathematical models of such flows naturally include two small parameters. One is connected to the fluid film thickness and the other to the microstructure. The corresponding asymptotic analysis is a delicate problem, since the result depends on how fast the two small parameters tend to zero relative to each other. We give a review of the current status in this area and point out some future challenges.
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| 15. |
- Almqvist, Andreas
(författare)
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Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem
- 2021
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Ingår i: Lubricants. - : MDPI. - 2075-4442. ; 9:8
-
Tidskriftsartikel (refereegranskat)abstract
- This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial and boundary value problems described by linear ordinary differential equations. The objective with this technical note is not to develop a numerical solution procedure which is more accurate and efficient than standard finite element- or finite difference-based methods, but to give a fully explicit mathematical description of a PINN and to present an application example in the context of hydrodynamic lubrication. It is, however, worth noticing that the PINN developed herein, contrary to FEM and FDM, is a meshless method and that training does not require big data which is typical in machine learning.
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| 16. |
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| 17. |
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| 18. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of a Reynolds equation describing compressible flow
- 2012
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 390:2, s. 456-471
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Tidskriftsartikel (refereegranskat)abstract
- We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressiblity factor in the pressure-density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term we also obtain strong convergence in the Sobolev norm.
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| 19. |
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| 20. |
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| 21. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of the Reynolds equation
- 2013
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Ingår i: Encyclopedia of Tribology. - Berlin : Springer-Verlag New York Inc.. - 9780387928968 - 9780387928975 ; , s. 1685-1690
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Bokkapitel (refereegranskat)
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| 22. |
- Almqvist, Andreas
(författare)
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Homogenization of the Reynolds equation governing hydrodynamic flow in a rotating device
- 2011
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Ingår i: Journal of tribology. - : ASME International. - 0742-4787 .- 1528-8897. ; 133:2, s. 021705-1
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a method facilitating the analysis of the effects of surface roughness on the lubrication of a rotating device is presented. The analysis utilizes homogenization—a suitable technique for averaging the effects of roughness as modeled by the Reynolds equation. The originality of this work lies in a novel way of deriving the so called local problems, also known as microbearing problems. It is clearly shown how this increases the computational efficiency by eliminating the dependence of the global coordinates on the formulation of these local problems. This does not only speed up the computation, it also means that the derived flow factors or flow tensors require less storage space. To provide for good usability, alongside the flow factors for the averaged Reynolds equation, the correction factors for the averaged friction torque (and force) and the expression for averaged load carrying capacity are presented here.
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| 23. |
- Almqvist, Andreas, et al.
(författare)
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Homogenization of the unstationary incompressible Reynolds equation
- 2007
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Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 40:9, s. 1344-1350
-
Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.
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| 24. |
- Almqvist, Andreas, et al.
(författare)
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Interfacial separation between elastic solids with randomly rough surfaces : Comparison between theory and numerical techniques
- 2011
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Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 59:11, s. 2355-2369
-
Tidskriftsartikel (refereegranskat)abstract
- We study the distribution of interfacial separations at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for the distribution of interfacial separations using Persson's theory of contact mechanics, and is compared to numerical solutions obtained using (a) a half-space method based on the Boussinesq equation, (b) a Green's function molecular dynamics technique and (c) smart-block classical molecular dynamics. Overall, we find good agreement between all the different approaches.
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| 25. |
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| 26. |
- Almqvist, Andreas, et al.
(författare)
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Modelling cavitation in (elasto)hydrodynamic lubrication
- 2016
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Ingår i: Advances in tribology. - Croatia : INTECH. - 9789535127420 - 9789535127437 ; , s. 198-213
-
Bokkapitel (refereegranskat)abstract
- In this chapter we will present a derivation of a mathematical model describing how cavitation influences the pressure distribution in a thin lubricant film between two moving surfaces. The main idea in the derivation is to first describe the influence of cavitation on the mass flow and thereafter using a conservation law for the mass. This leads to a nonlinear system with two complementary variables: one is the pressure distribution and the other is related to the density, i.e. a nonlinear complementarity problem (NLCP). The proposed approach is used to derive a mass conserving cavitation model considering that density, viscosity and film thickness of the lubricant depend on the pressure. To demonstrate the applicability and evaluate the proposed model and the suggested numerical implementation, a few model problems are analysed and presented.
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| 27. |
- Almqvist, Andreas, et al.
(författare)
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Modelling Flows in Lubrication
- 2020. - 1
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Ingår i: Modeling and Simulation of Tribological Problems in Technology. - Cham : Springer. ; , s. 229-278
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter introduces the reader to lubrication theory and describes the governing equations, models and methods that can be used to simulate various types of lubricated systems. It starts with an introduction to the tribological contact and to the different lubrication regimes. The basis for the classical lubrication theory is then given and thereafter follows a presentation of how to obtain the Reynolds equation by means of scaling and asymptotic analysis of the Navier–Stokes equations. After having obtained the Reynolds equation, a quite elaborate presentation of cavitation algorithms is given. It includes discretisation and presents the analytical solution for a pocket bearing as a benchmark model problem. Then, the concept of homogenisation of surface roughness is introduced. This starts from the simplest iso-viscous and incompressible case, expands to include compressibility with a constant bulk modulus constitutive relation and then also addresses the case of ideal gases. Thereafter, the relation between homogenised coefficients and the Patir and Cheng flow factors is described and finally it is shown how to incorporate the effect of mixed lubrication into the model.
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| 28. |
- Almqvist, Andreas, et al.
(författare)
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Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications
- 2011
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 9:1, s. 17-40
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Tidskriftsartikel (refereegranskat)abstract
- We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as epsilon -> 0 of the solutions u(epsilon) of the nonlinear equation div a(epsilon)(x, del u(epsilon)) = div b(epsilon), where both a(epsilon) and b(epsilon) oscillate rapidly on several microscopic scales and a(epsilon) satisfies certain continuity, monotonicity and boundedness conditions. This kind of problem has applications in hydrodynamic thin film lubrication where the bounding surfaces have roughness on several length scales. The homogenization result is obtained by extending the multiscale convergence method to the setting of Sobolev spaces W-0(1,p)(Omega), where 1 < p < infinity. In particular we give new proofs of some fundamental theorems concerning this convergence that were first obtained by Allaire and Briane for the case p = 2.
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| 29. |
- Almqvist, Andreas, et al.
(författare)
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New concepts of homogenization applied in rough surface hydrodynamic lubrication
- 2007
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Ingår i: International Journal of Engineering Science. - : Elsevier BV. - 0020-7225 .- 1879-2197. ; 45:1, s. 139-154
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Tidskriftsartikel (refereegranskat)abstract
- This work introduces a new concept of homogenization that enables efficient analysis of the effects of surface roughness representations obtained by measurements in applications modeled by the Reynolds equation. Examples of such applications are trust- and journal-bearings. The numerical analysis of these types of applications requires an extremely dense computational mesh in order to resolve the surface roughness, suggesting some type of averaging. One such method is homogenization, which has been applied to Reynolds type equations with success recently. This approach is similar to the technique proposed by Patir and Cheng, who introduced flow factors determining the hydrodynamic action due to surface roughness. The difference is, however, that the present technique has a rigorous mathematical support. Moreover, the recipe to compute the averaged coefficients is simple without any ambiguities. Using either the technique proposed by Patir and Cheng or homogenization, the coefficients determining the averaged Reynolds equation are obtained by solving differential equations on a local scale. Unfortunately, this is detrimental when investigating the effects induced by real, measured, surface roughness, even though these local problems may be solved in parallel. The present work presents a solution by applying the technique based on bounds. This technique transforms the stationary Reynolds equation into two computationally feasible forms, one for the upper bound and one for the lower bound, where the flow factors are obtained by straightforward integration. Together with the preciseness of these bounds, the bounds approach becomes an eminent tool suitable for investigating the effect of real, measured, surface roughness on hydrodynamic performance.
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| 30. |
- Almqvist, Andreas, et al.
(författare)
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New insights on lubrication theory for compressible fluids
- 2019
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Ingår i: International Journal of Engineering Science. - : Elsevier. - 0020-7225 .- 1879-2197. ; 145
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Tidskriftsartikel (refereegranskat)abstract
- The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.
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| 31. |
- Almqvist, Andreas, et al.
(författare)
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On flow of power-law fluids between adjacent surfaces : Why is it possible to derive a Reynolds-type equation for pressure-driven flow, but not for shear-driven flow?
- 2023
-
Ingår i: Applications in Engineering Science. - : Elsevier. - 2666-4968. ; 15
-
Tidskriftsartikel (refereegranskat)abstract
- Flows of incompressible Navier–Stokes (Newtonian) fluids between adjacent surfaces are encountered in numerous practical applications, such as seal leakage and bearing lubrication. In seals, the flow is primarily pressure-driven, whereas, in bearings, the dominating driving force is due to shear. The governing Navier–Stokes system of equations can be significantly simplified due to the small distance between the surfaces compared to their size. From the simplified system, it is possible to derive a single lower-dimensional equation, known as the Reynolds equation, which describes the pressure field. Once the pressure field is computed, it can be used to determine the velocity field. This computational algorithm is much simpler to implement than a direct numerical solution of the Navier–Stokes equations and is therefore widely employed by engineers. The primary objective of this article is to investigate the possibility of deriving a type of Reynolds equation also for non-Newtonian fluids, using the balance of linear momentum. By considering power-law fluids we demonstrate that it is not possible for shear-driven flows, whereas it is feasible for pressure-driven flows. Additionally, we demonstrate that in the full 3D model, a normal stress boundary condition at the inlet/outlet implies a Dirichlet condition for the pressure in the Reynolds equation associated with pressure-driven flow. Furthermore, we establish that a Dirichlet condition for the velocity at the inlet/outlet in the 3D model results in a Neumann condition for the pressure in the Reynolds equation.
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| 32. |
- Almqvist, Andreas, et al.
(författare)
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On lower-dimensional models in lubrication, Part A : Common misinterpretations and incorrect usage of the Reynolds equation
- 2021
-
Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - : Sage Publications. - 1350-6501 .- 2041-305X. ; 235:8, s. 1692-1702
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Tidskriftsartikel (refereegranskat)abstract
- Most of the problems in lubrication are studied within the context of Reynolds’ equation, which can be derived by writing the incompressible Navier-Stokes equation in a dimensionless form and neglecting terms which are small under the assumption that the lubricant film is very thin. Unfortunately, the Reynolds equation is often used even though the basic assumptions under which it is derived are not satisfied. One example is in the mathematical modelling of elastohydrodynamic lubrication (EHL). In the EHL regime, the pressure is so high that the viscosity changes by several orders of magnitude. This is taken into account by just replacing the constant viscosity in either the incompressible Navier-Stokes equation or the Reynolds equation by a viscosity-pressure relation. However, there are no available rigorous arguments which justify such an assumption. The main purpose of this two-part work is to investigate if such arguments exist or not. In Part A, we formulate a generalised form of the Navier-Stokes equation for piezo-viscous incompressible fluids. By dimensional analysis of this equation we, thereafter, show that it is not possible to obtain the Reynolds equation, where the constant viscosity is replaced with a viscosity-pressure relation, by just neglecting terms which are small under the assumption that the lubricant film is very thin. The reason is that the lone assumption that the fluid film is very thin is not enough to neglect the terms, in the generalised Navier-Stokes equation, which are related to the body forces and the inertia. However, we analysed the coefficients in front of these (remaining) terms and provided arguments for when they may be neglected. In Part B, we present an alternative method to derive a lower-dimensional model, which is based on asymptotic analysis of the generalised Navier-Stokes equation as the film thickness goes to zero.
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| 33. |
- Almqvist, Andreas, et al.
(författare)
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On lower-dimensional models in lubrication, Part B : Derivation of a Reynolds type of equation for incompressible piezo-viscous fluids
- 2021
-
Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - : Sage Publications. - 1350-6501 .- 2041-305X. ; 235:8, s. 1703-1718
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Tidskriftsartikel (refereegranskat)abstract
- The Reynolds equation is a lower-dimensional model for the pressure in a fluid confined between two adjacent surfaces that move relative to each other. It was originally derived under the assumption that the fluid is incompressible and has constant viscosity. In the existing literature, the lower-dimensional Reynolds equation is often employed as a model for the thin films, which lubricates interfaces in various machine components. For example, in the modelling of elastohydrodynamic lubrication (EHL) in gears and bearings, the pressure dependence of the viscosity is often considered by just replacing the constant viscosity in the Reynolds equation with a given viscosity-pressure relation. The arguments to justify this are heuristic, and in many cases, it is taken for granted that you can do so. This motivated us to make an attempt to formulate and present a rigorous derivation of a lower-dimensional model for the pressure when the fluid has pressure-dependent viscosity. The results of our study are presented in two parts. In Part A, we showed that for incompressible and piezo-viscous fluids it is not possible to obtain a lower-dimensional model for the pressure by just assuming that the film thickness is thin, as it is for incompressible fluids with constant viscosity. Here, in Part B, we present a method for deriving lower-dimensional models of thin-film flow, where the fluid has a pressure-dependent viscosity. The main idea is to rescale the generalised Navier-Stokes equation, which we obtained in Part A based on theory for implicit constitutive relations, so that we can pass to the limit as the film thickness goes to zero. If the scaling is correct, then the limit problem can be used as the dimensionally reduced model for the flow and it is possible to derive a type of Reynolds equation for the pressure.
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| 34. |
- Almqvist, Andreas, et al.
(författare)
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On lower-dimensional models of thin film flow, Part C: Derivation of a Reynolds type of equation for fluids with temperature and pressure dependent viscosity
- 2023
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Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - : Sage. - 1350-6501 .- 2041-305X. ; 237:3, s. 514-526
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Tidskriftsartikel (refereegranskat)abstract
- This paper constitutes the third part of a series of works on lower-dimensional models in lubrication. In Part A, it was shown that implicit constitutive theory must be used in the modelling of incompressible fluids with pressure-dependent viscosity and that it is not possible to obtain a lower-dimensional model for the pressure just by letting the film thickness go to zero, as in the proof of the classical Reynolds equation. In Part B, a new method for deriving lower-dimensional models of thin-film flow of fluids with pressure-dependent viscosity was presented. Here, in Part C, we also incorporate the energy equation so as to include fluids with both temperature and pressure dependent viscosity. By asymptotic analysis of this system, as the film thickness goes to zero, we derive a simplified model of the flow. We also carry out an asymptotic analysis of the boundary condition, in the case where the normal stress is specified on one part of the boundary and the velocity on the remaining part.
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| 35. |
- Almqvist, Andreas, et al.
(författare)
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On the dry elasto-plastic contact of nominally flat surfaces
- 2007
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Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 40:4, s. 574-579
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Tidskriftsartikel (refereegranskat)abstract
- A model to be used for numerical simulation of the contact of linear elastic perfectly plastic rough surfaces was developed. Energy dissipation due to plastic deformation is taken into account. Spectral theory and an FFT-techique are used to facilitate the numerical solution process. Results of simulations using four two-dimensional profiles with different topographies in contact with a rigid plane for a number loads are reported. From the results it is clear that the real area of contact (Ar) changes almost linearly with load and is only slightly affected by the difference in topography. A plasticity index is defined as the ratio of plastically deformed area (Ap) and Ar. Plastic deformation occurs even at low loads and there is a significant difference in plasticity index between the surface profiles considered. An investigation on how the spectral content of the surface profile influences the results presented is also performed. This is to ensure that the metrological limitations of the optical profilerused to measure the surfaces do not have a significant influence. It is concluded that the highest frequencies of the measured profile have a negligible influence on the real area of contact.
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| 36. |
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| 37. |
- Almqvist, Andreas
(författare)
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On the effects of surface roughness in lubrication
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Tribology is a multidisciplinary field defined as the science and technology of interacting surfaces in relative motion, and embraces the study of friction, wear and lubrication. A typical tribological application is the rolling element bearing. Tribological contacts may also be found in other types of bearings, cam-mechanisms, gearboxes and hydraulic systems. Examples of bearings inside the human body are the operation of the human hip joint and the contact between teeth during chewing. To fully understand the operation of this type of application one has to understand the couplings between the lubricant fluid dynamics, the structural dynamics of the bearing material, the thermodynamical aspects and the resulting chemical reactions. This makes modeling tribological applications an extremely delicate task. Because of the multidisciplinary nature, such theoretical models lead to mathematical descriptions generally in the form of non-linear integro-differential systems of equations. Some of these systems of equations are sufficiently well posed to allow numerical solutions to be carried out, resulting in accurate predictions on performance. In this work, the influence on performance of a surface microscopical nature, the surface roughness, in contact interfaces between different types of machine element components is the subject of study. An example is the non-conformal lubricated contact between one of the rollers and the inner ring in a rolling element bearing. The tribological contact controlling the operation of the human hip joint is also very similar to this. Another example of a non-conformal contact occurs when driving on rainy roads, where the hydrodynamic action of the water separates the tire. To enable investigations of these types of problems, different theoretical models were studied; for the selected model, a numerical solution technique was developed within this project. This model is based on the Reynolds equation coupled with the film thickness equation. The numerical solution technique involves a multilevel technique to facilitate the solution process. Results presented in this thesis, utilizing this approach, study elementary surface features such as ridges and indentations passing each other inside the lubricated conjunction. The Reynolds equation is derived under the assumptions of thin fluid film and creeping flow, and considers in its most general form shear thinning of the lubricant. This type of equation describes the hydrodynamic action of the lubricant flow and may be used when the interfaces consist of either conformal or non-conformal conjunctions. Examples of applications having conformal interfaces are thrust- and journal- bearings or the contact between the eye and a (optical) contact lens. In such types of applications the load carried by the interface is distributed over a fairly large area that under certain circumstances helps to prevent mechanical deformation of the contacting surfaces. Such applications are said to operate in the hydrodynamic lubrication (HL) regime. Lubricant compressibility and cavitation are important aspects and have received some attention. However, the main objective when modeling HL has been to investigate and develop methods that enable the influence of surface roughness to be to be studied efficiently. Homogenization is a rigorous mathematical concept that when applied to a certain problem may be regarded as an averaging technique as well as it provides information about the induced effects of local surface roughness. Homogenization inflicts no restrictions on the surface roughness representation other than the representative part of the chosen surface roughness being assumed periodically distributed and of course the assumptions of thin film flow made through the Reynolds equation. The homogenization process leads to a two sets of equations one for the local scale describing surface roughness, scale and one for the global scale describing application geometry. The unequivocally determined coefficients of the global problem, which may be regarded as flow factors, are obtained through the solution of local problems. This makes homogenization an eminent approach to be used investigating the influence of surface roughness on hydrodynamic performance. In the present work, homogenization has been used to derive computationally feasible forms of problems originating from incompressible and compressible Reynolds type equations that describe stationary and unstationary flows in both cartezian and cylindrical co-ordinates. This technique enables simulations of surface roughness induced effects when considering surface roughness descriptions originating from measurements. Moreover, the application of homogenization facilitates the interpretation of results. Numerical investigations following the homogenization process have been carried out to verify the applicability of homogenization in hydrodynamic lubrication. Homogenization has also been shown here to enable efficient analysis of rough hydrodynamically lubricated problems. Also of note, in connection to the scientific contribution within tribology, collaboration with a group in applied mathematics has lead to the development of novel techniques in that area. These ideas have also been successfully applied, with some results presented in this thesis. At start-ups, the contact in a rolling element bearing could be both starved and drained from lubricant. In this case the hydrodynamic action becomes negligible in terms of load carrying capacity. The load is carried exclusively by surface asperities, the tribo film, or both. This is hereby modeled as the unlubricated frictionless contact between rough surfaces, i.e. a contact mechanical approach. A variational principle was used in which the real area of contact and the contact pressure distribution minimize the total complementary potential energy. The material model is linear elastic-perfectly plastic and the energy dissipation due to plastic deformation is accounted for. The numerics of this contact mechanical approach involve the fast Fourier transformation (FFT) technique in order to facilitate the solution process. Investigation results of the contact mechanics of realistic surfaces are presented in this thesis. In this investigation the variation in the real area of contact, the plasticity index and some surface roughness parameters due to applied load were studied.
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| 38. |
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| 39. |
- Almqvist, Andreas
(författare)
-
Preface
- 2021
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Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - : Sage Publications. - 1350-6501 .- 2041-305X. ; 235:12, s. 2504-2505
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 40. |
- Almqvist, Andreas, et al.
(författare)
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Reiterated homogenization applied in hydrodynamic lubrication
- 2008
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Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology. - 1350-6501 .- 2041-305X. ; 222:7, s. 827-841
-
Tidskriftsartikel (refereegranskat)abstract
- This work is devoted to studying the combined effect that arises due to surface texture and surface roughness in hydrodynamic lubrication. An effective approach in tackling this problem is by using the theory of reiterated homogenization with three scales. In the numerical analysis of such problems, a very fine mesh is needed, suggesting some type of averaging. To this end, a general class of problems is studied that, e.g. includes the incompressible Reynolds problem in both artesian and cylindrical coordinate forms. To demonstrate the effectiveness of the method several numerical results are presented that clearly show the convergence of the deterministic solutions towards the homogenized solution.Moreover, the convergence of the friction force and the load carrying capacity of the lubricant film is also addressed in this paper. In conclusion, reiterated homogenization is a feasible mathematical tool that facilitates the analysis of this type of problem.
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| 41. |
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| 42. |
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| 43. |
- Almqvist, Andreas
(författare)
-
Rough surface elastohydrodynamic lubrication and contact mechanics
- 2004
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the field of tribology, there are numerous theoretical models that may be described mathematically in the form of integro-differential systems of equations. Some of these systems of equations are sufficiently well posed to allow for numerical solutions to be carried out resulting in accurate predictions. This work has focused on the contact between rough surfaces with or without a separating lubricant film. The objective was to investigate how surface topography influences contact conditions. For this purpose two different numerical methods were developed and used. For the lubricated contact between rough surfaces the Reynolds equation were used as a basis. This equation is derived under the assumptions of thin fluid film and creeping flow. In highly loaded, lubricated, non- conformal contacts of surfaces after running-in, the load concentration no longer results in plastic deformations, however large elastic deformations will be apparent. It is the interaction between the hydrodynamic action of the lubricant and the elastic deformations of the surfaces that, in certain applications, enable the lubricant film to fully separate the surfaces. This is commonly referred to as full film elastohydrodynamic (EHD) lubrication. Typical machine elements that operates in the full film EHD lubrication (FL) regime include rolling element bearings, cams and gears. Unfortunately, a cost effective way of machining engineering surfaces seldom results in a surface topography that influence contact conditions in the same way as a surface after running-in. Such topographies may prevent the lubricant from fully separating the surfaces because of deteriorated hydrodynamic action. In this case the applied load is carried in part by the lubricant and in part by surface asperities and/or surface active lubricant additives. This could also be the case in lubricant starved contacts, which is a common situation in not only grease lubricated contacts but also in many liquid lubricated contacts, such as high speed operating rolling element bearings. The load sharing between the highly compressed lubricant and the surface and/or surface active lubricant additives is the reason why this lubrication regime is most commonly referred to as mixed EHD lubrication (ML). Machine elements that while running operate in the FL regime may experience a transition into the ML regime at stops or due to altered operating conditions. It is not possible to simulate direct contact between the surfaces using a numerical method based on Reynolds equation. A parameter study, of elementary surface features passing each other inside the EHD lubricated conjunction, was performed. The results obtained, even though no direct contact could be simulated, does indicate that a transition from the FL to the ML regime would occur for certain combinations of the varied parameters. At start-ups, the contact in a rolling element bearing could be both starved and drained from lubricant. In this case the hydrodynamic action becomes negligible in terms of load carrying capacity. The load is carried exclusively by surface asperities and/or surface active lubricant additives. This regime is referred to as boundary lubrication (BL). Operation conditions could also make both FL and ML impossible to achieve, for example, in the case in a low rpm operating rolling element bearing. The BL regime is in this work modeled as the unlubricated frictionless contact between rough surfaces, i.e., a dry contact approach. A variational principle was used in which the real area of contact and contact pressure distribution are those which minimize the total complementary energy. A linear elastic-perfectly plastic deformation model in which energy dissipation due to plastic deformation is accounted for was used. The dry contact method was applied to the contact between four different profiles and a plane. The variation in the real area of contact, the plasticity index and some surface roughness parameters due to applied load were investigated. The surface roughness parameters of the profiles differed significantly.
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| 44. |
- Almqvist, Andreas, et al.
(författare)
-
Scientific Computing with Applications in Tribology : A course compendium
- 2022
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This compendium comprises models and numerical solution procedure for tribological interfaces. It describes the tribological contact and the classical lubrication regimes. A thorough derivation of the Reynolds equation, governing the fluid pressure, from the Navier-Stokes momentum equations and the continuity equation for conservation of mass, is presented along with its analytical solution for the infinitely wide linear slider bearing.The compilation of the compendium was conducted by the first author during his tenure as Professor at the Division of Machine Elements, Department of Engineering Sciences and Mathematics, Luleå University of Technology and by the second author during his tenure as a postdoctoral researcher at the same division.Although the compilation of this text is the work solely of the authors, the models and solution procedure presented herein is joint development of many good colleagues and co-authors. Our sincere gratitude is extended towards them all.
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| 45. |
- Almqvist, Andreas, et al.
(författare)
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Selected papers from those presented at the 3rd International Tribology Symposium of IFToMM
- 2014
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Ingår i: Lubrication Science. - : Wiley. - 0954-0075 .- 1557-6833. ; 26:5, s. 273-275
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Selected papers presented at the 3rd International Tribology Symposium of the International Federation for the Promotion of Mechanism and Machine Science (IFToMM) are discussed. The 3rd International Tribology Symposium of IFToMM was organized by the Division of Machine Elements of Luleå University of Technology in Sweden from March 19 21, 2013. The symposium was held in the university campus, providing a perfect forum for the tribologists for presenting their latest research and exchange of ideas. The participants were also given the opportunity to experience the snowy landscape during a memorable outdoor dinner. The symposium attracted 146 participants from 26 countries along with 92 papers spread over 32 sessions. These papers covered the fundamental and applied aspects of wide ranging topics such as friction, wear, lubrication, lubricants, tribology in hostile environment, tribomaterials, solid lubricants, surface engineering, and tribotesting.
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| 46. |
- Almqvist, Andreas, et al.
(författare)
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Similarities and differences between the flow factor method by Patir and Cheng and homogenization
- 2011
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Ingår i: Journal of tribology. - : ASME International. - 0742-4787 .- 1528-8897. ; 133:3, s. 031702-1
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Tidskriftsartikel (refereegranskat)abstract
- Different averaging techniques have proved to be useful for analyzing the effects of surface roughness in hydrodynamic lubrication. This paper compares two of these averaging techniques, namely the flow factor method by Patir and Cheng (P&C) and homogenization. It has been rigorously proved by many authors that the homogenization method provides a correct solution for arbitrary roughness. In this work it is shown that the two methods coincide if and only if the roughness exhibits certain symmetries. Hence, homogenization is always the preferred method.
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| 47. |
- Almqvist, Andreas, et al.
(författare)
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Simulation of piston ring : cylinder liner lubrication considering layered fluid films
- 2009
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Ingår i: Tribologia : Finnish Journal of Tribology. - 0780-2285. ; 28:3-4, s. 44-58
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Tidskriftsartikel (refereegranskat)abstract
- During the operation of hydrodynamically lubricated devices a fully formulated lubricant has the ability to form layers at the surfaces. A friction modifier's task is to adjust the interaction between lubricant and the surface so that friction is lowered. An antiwear additive creates a protective layer on the surface and this definitely influence the performance of the lubricated device. To gain fundamental understanding, models that address the modified liquid - solid interaction due to the formation of layers, but also models that may be used to study the effects of layers already formed on the contacting surfaces are required. In this paper, two non-Newtonian lubricant rheology models that may be used to simulate reacted layers resembling those created by lubricant additives are adopted for the simulation of the piston ring - cylinder liner lubrication problem. The possibility of layer to layer interaction, which is likely to occur in the convex conjunction between the ring and the liner, is considered and this extends the models found in the literature. The effects induced by this type of layering are studied by using a modified Reynolds' equation where the coefficients have been corrected with factors that accounts for the layer properties. This enables, effectively, studies of layers resembling those created by lubricant additives during the operation of the lubricated conjunction between a piston ring and a cylinder liner.
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| 48. |
- Almqvist, Andreas, et al.
(författare)
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Simulation of piston ring : cylinder liner lubrication considering layered fluid films
- 2008
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Ingår i: Proceedings of the 35th Leeds-Lyon Symposium on Tribology, 2008.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- During the operation of hydrodynamically lubricated devices a fully formulated lubricant has the ability to form layers at the surfaces. Such layers alter the interaction between the lubricant and the surface that definitely will influence the performance of the lubricated device.To gain fundamental understanding, models that address the formation of layers and the altered liquid – solid interaction, but also models that may be used to study the effects of existing layers are required. In this paper, non-Newtonian lubricant rheology models that may be used to resemble layers of variable shear strength – wall-slip specifically – are considered for the simulation of the piston ring - cylinder liner lubrication problem.The effects induced by this type of layering are studied by using a modified Reynold’s equation where the coefficients have been corrected with factors that accounts for layer properties. This enables, effectively, studies of immobile layers as well as wall-slip in the lubricated conjunction between a piston ring and a cylinder liner.
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| 49. |
- Almqvist, Andreas, et al.
(författare)
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The effect of two-sided roughness in rolling/sliding EHL line contacts
- 2004
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Ingår i: Transient processes in tribology. - Amstersam : Elsevier. - 0444517065
-
Konferensbidrag (refereegranskat)abstract
- In most theoretical studies carried out to date on the effect of surface roughness in elastohydrodynamic lubrication (EHL) one surface is considered smooth and one as being rough. In real tribological contacts however, both surfaces normally have similar roughness heights. When modelling a rolling contact it is possible to simply sum the roughness of the two contact surfaces but in a sliding EHL contact, a continuously changing effective surface roughness occurs. The aim of this work was to investigate the influence of elementary surface features such as dents and ridges on the film thickness and pressure. This was done numerically using transient non-Newtonian simulations of an EHL line contact using a coupled smoother combined with a multilevel technique. Four different "overtaking" phenomena were investigated; ridge-ridge, dent-ridge, ridge-dent, and dent-dent. It was shown that the minimum film-thickness produced by a ridge is further reduced in a dent-ridge overtaking event. The squeeze effect seen in the ridge-ridge case resulted in large deformations and film-thickness heights comparable to the corresponding smooth case just before the overtaking event occurred. These local effects arising from simulating two-sided roughness were compared to simulations using a traditional "one-sided rough surface contacting a perfectly smooth surface.".
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| 50. |
- Almqvist, Andreas, et al.
(författare)
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The homogenization process of the Reynolds equation describing compressible liquid flow
- 2006
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Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 39:9, s. 994-1002
-
Tidskriftsartikel (refereegranskat)abstract
- This paper summarizes the homogenization process of rough, hydrodynamic lubrication problems governed by the Reynolds equation used to describe compressible liquid flow. Here, the homogenized equation describes the limiting result when the wavelength of a modeled surface roughness goes to zero. The lubricant film thickness is modeled by one part describing the geometry/shape of the bearing and a periodic part describing the surface topography/roughness. By varying the periodic part as well as its wavelength, we can try to systematically investigate the applicability of homogenization on this type of problem. The load carrying capacity is the target parameter; deterministic solutions are compared to homogenized by this measure. We show that the load carrying capacity rapidly converges to the homogenized results as the wavelength decreases, proving that the homogenized solution gives a very accurate representation of the problem when real surface topographies are considered
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