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  • 51.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Fabricius, John
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of a Reynolds equation describing compressible flow2012Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, nr 2, s. 456-471Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 52.
    Andersson, Joel
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Grahn, Mattias
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Minami, Ichiro
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Semi-deterministic chemo-mechanical model of boundary lubrication2012Ingår i: Faraday discussions (Online), ISSN 1359-6640, E-ISSN 1364-5498, Vol. 156, s. 343-360Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A model for tribofilm growth is developed. The model is used in combination with numerical contact mechanics tools to enable evaluation of the combined effects of chemistry and contact mechanics. The model is tuned with experimental data and is thereafter applied to rough surfaces. The growth of the tribofilm is evaluated for 3 different contact cases and short-term tribofilm growth behaviour is analyzed. The results show how tribofilms grow in patches. The model is expected to be used as a tool for analysis of the interaction between rough surfaces.

  • 53.
    Spencer, Andrew
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    A numerical model to investigate the effect of honing angle on the hydrodynamic lubrication between a combustion engine piston ring and cylinder liner2011Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 225, nr 7, s. 683-689Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A numerical model has been developed to investigate the effect of cylinder liner honing angle on hydrodynamic lubrication between piston ring and cylinder liner. The Reynolds equation was solved in 2D with periodic boundary conditions. An artificial surface texture was generated, based on a real surface measured with white light interferometry. Cavitation was modelled with the Vijayaraghavan and Keith algorithm. Honing angles between 25° and 75° were investigated to find the effect of honing angle on film thickness.

  • 54.
    Spencer, Andrew
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    A semi-deterministic model of the piston ring-cylinder liner contact incorporating an oil availability model2011Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In work presented last year at the 37th Leeds-Lyon Symposium on Tribology a semi-deterministic model of the piston ring-cylinder liner contact was developed. The honing grooves (texture) were considered on a global scale and the surface roughness was incorporated on a local scale using the homogenization mathematical averaging technique. However, as noted at the time, the contact throughout the full engine cycle was considered to be fully flooded. It was assumed that there was always enough lubricant present to fully flood the entrance to the contact. In reality this is unlikely to be the case, particularly during the midstroke of the cycle, as with high entraining speeds the predicted hydrodynamic films can be several microns thick and there is unlikely to be sufficient lubricant on the liner to form these thick films. Therefore, an oil availability model has been developed to track the quantity of oil available on along the length of the liner. The full ring pack, compression, scraper and oil control ring are modelled. It is assumed that the oil control ring always runs in the fully flooded condition and the scraper and compression ring have the oil available to them that they left behind on the previous stroke. In the previous work the honing grooves were modelled and the effect they have on film formation and cavitation investigated. However, their effect on the distribution and retention of oil on the liner could not be seen due to the fully flooded inlet condition. With the incorporated oil availability model the effect of different honing groove patterns can be further investigated.

  • 55.
    Spencer, Andrew
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    A semi-deterministic texture-roughness model of the piston ring-cylinder liner contact2011Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 225, nr 6, s. 325-333Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Many simulations already exist to model the piston ring-cylinder liner contact; however, very few models have been used to investigate the optimum surface texture. An axisymmetric, time-dependent two-dimensional semi-deterministic texture-roughness model of the piston ring to cylinder liner contact with periodic boundary conditions and mass preserving global cavitation has been developed. The cylinder liner texture, generated by honing, was considered deterministically on the global scale, after an investigation comparing deterministic and homogenized solutions. The surface texture of a real cylinder liner was measured with white light interferometry and an algorithm developed to generate an artificial periodic texture representative of the real surface. The effect of cylinder liner plateau roughness has been incorporated on the local scale by homogenization of the Reynolds equation and calculation of flow factors from real surface topography. Using the homogenization technique to incorporate the effect of surface roughness leads to a more efficient solution than mesh refinement of the deterministic problem as the roughness does not need to be resolved on the global solution domain, allowing for significantly less degrees of freedom in the global problem. The lubricant boundary pressures have been calculated using results from a numerical ring-pack model and the lubricant viscosity has been adjusted based on the cylinder liner wall temperature. It was found from the result of a comparison between deterministic and homogenized solutions that surface texture should be modelled on the global and not on the averaged roughness scale as is the case with many previous investigations.

  • 56.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Fabricius, John
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of a Reynolds equation describing compressible flow2011Rapport (Övrigt vetenskapligt)
  • 57.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Homogenization of the Reynolds equation governing hydrodynamic flow in a rotating device2011Ingår i: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 133, nr 2, s. 021705-1Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 58.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Campañá, C
    University of Ottawa, Department of Chemistry, Ottawa, Canada K1N6N5.
    Prodanov, N
    Sumy State University, 2 Rimskii-KorsakovStr., 40007 Sumy, Ukraine.
    Persson, B N J
    IFF, Jülich.
    Interfacial separation between elastic solids with randomly rough surfaces: Comparison between theory and numerical techniques2011Ingår i: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 59, nr 11, s. 2355-2369Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 59.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Essel, Emmanuel Kwame
    Department of Mathematics and Statistics, University of Cape Coast.
    Fabricius, John
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications2011Ingår i: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 9, nr 1, s. 17-40Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 60.
    Andersson, Joel
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Numerical simulation of a wear experiment2011Ingår i: Wear, ISSN 0043-1648, E-ISSN 1873-2577, Vol. 271, nr 11-12, s. 2947-2952Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A wear model including a deterministic FFT-accelerated contact mechanical tool to calculate pressure and elastic-plastic deformation, is employed to simulate the time dependent wear in a sphere on flat contact. The results of the wear simulations compared to experimental results from a reciprocating test in a ball on disk tribometer. The conditions of the simulations and the experiments are independently adjusted to match up. Similarities and differences shows upon the usefulness and limitation of wearmodelling of this type.

  • 61.
    Eliasson, Jens
    et al.
    Luleå tekniska universitet, Institutionen för system- och rymdteknik, EISLAB.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Projekt: Y-programmet2011Övrigt (Övrig (populärvetenskap, debatt, mm))
  • 62.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Fabricius, John
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Spencer, Andrew
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Similarities and differences between the flow factor method by Patir and Cheng and homogenization2011Ingår i: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 133, nr 3, s. 031702-1Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 63.
    Spencer, Andrew
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Dobryden, Illia
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Almqvist, Nils
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Surface characterization with functional parameters2011Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 64.
    Isaksson, Patrik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Nilsson, Daniel
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    The influence of surface roughness on friction in a flexible hybrid bearing2011Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 225, nr J10, s. 975-985Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The effect of surface roughness on friction in all lubrication regimes is studied for a flexible hybrid bearing of a radial piston hydraulic motor. The effect is studied by performing experiments in a specially designed test rig and numerical simulations of the real measured surface topographies of the bearings. The simulations are performed with a two-scale model where surface roughness is treated on a local asperity level by homogenized flow factors and a global scale where the bearing structure is included. Three bearings with different surface topographies are included in the study and both experimentally measured and simulated friction are analysed for each of them. Comparison of friction predicted by the model and experimentally measured friction is performed and it reveals that the model is a valuable tool for analysing the effect of surface roughness in this type of bearing

  • 65.
    Sahlin, Fredrik
    et al.
    Siemens Industrial Turbomachinery AB.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Lugt, Piet
    SKF Engineering & Research Center, Nieuwegein.
    Marklund, Pär
    A mixed lubrication model incorporating measured surface topography: Part 1: theory of flow factors2010Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 224, nr 4, s. 335-351Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A mixed lubrication model that permits real three-dimensional surface topography as input is developed. The theory of computing flow factors within the model is presented, and with a following paper (Part 2) the method of measuring and adapting the surface roughness, and model validation through flow measurements and application to a bearing is shown. A contact mechanics model is used to calculate the elastoplastic displacement of a periodic topography signal. A method based on homogenization is used to calculate flow factors for all lubrication regimes. The flow factors are compared with the Patir and Cheng method. Results indicate that the two methods compare well for longitudinal roughness lay, but differ significantly for a cross-patterned surface roughness due to the more complete flow description of the current model.

  • 66.
    Sahlin, Fredrik
    et al.
    Siemens Industrial Turbomachinery AB.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Marklund, Pär
    Almqvist, Andreas
    Lugt, Piet
    SKF Engineering & Research Center, Nieuwegein.
    A mixed lubrication model incorporating measured surface topography: Part 2: roughness treatment, model validation, and simulation2010Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 224, nr 4, s. 353-365Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A mixed lubrication flow factor model that permits real three-dimensional surface topography as input has been developed. Part 1 gives the theory of computing flow factors within the model. In this article, a method of adapting the measured surface topography signal to suit the numerical models is developed and presented in detail. The mixed lubrication model is validated through flow measurements for three different rough surface test specimens. Simulation of a hydrodynamic bearing was conducted and the results are presented in terms of pressure distributions and Stribeck curves covering all lubrication regimes. The results indicate that the model may be an efficient and accurate engineering design and research tool for tribological devices operating in all lubrication regimes.

  • 67.
    Spencer, Andrew
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Larsson, Roland
    A numerical model to investigate the effect of honing angle on the hydrodynamic lubrication between a combustion engine piston ring and cylinder liner2010Ingår i: 14th Nordic Symposium on Tribology: NORDTRIB 2010 : Storforsen, Sweden, June 8-11, 2010, Luleå: Luleå tekniska universitet, 2010Konferensbidrag (Refereegranskat)
    Abstract [en]

    A numerical model has been developed to investigate the effect of cylinder liner honing angle on hydrodynamic lubrication between piston ring and cylinder liner. The Reynolds equation was solved in 2D with periodic boundary conditions. An artificial surface texture was generated, based on a real surface measured with white light interferometry. Cavitation was modelled with the Vijayaraghavan and Keith algorithm. Honing angles between 25-75° were investigated to find the effect of honing angle on film thickness.

  • 68.
    Spencer, Andrew
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    A semi-deterministic texture-roughness model of the piston ring-cylinder liner contact2010Konferensbidrag (Refereegranskat)
  • 69.
    Marklund, Pär
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, AndreasKassfeldt, Elisabet
    Nordtrib 2010: 14th Nordic Symposium on Tribology, Storforsen, Sweden2010Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
  • 70.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Fabricius, John
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Reynolds equation flow factor estimates by means of homogenization2010Ingår i: ASIATRIB 2010: Frontiers in tribology - knowledge & friendship . proceedings of the fourth Asia International Conference on Tribology, 5-9 December 2010, Perth, Western Australia, 2010, s. 185-Konferensbidrag (Refereegranskat)
  • 71.
    Andersson, Joel
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Larsson, Roland
    Simulation of a wear experiment2010Ingår i: 14th Nordic Symposium on Tribology: NORDTRIB 2010 : Storforsen, Sweden, June 8-11, 2010, Luleå: Luleå tekniska universitet, 2010Konferensbidrag (Refereegranskat)
    Abstract [en]

    By using a deterministic FFT-accelerated contact mechanical tool to calculate pressure and elastic-plastic deformation, a wear model is utilized to simulate the time dependent wear from a sphere on at contact. The results of the simulated wear are compared to experimental results form a SRV ball on disk tribometer, from which worn surfaces are optically measured. The conditions of the simulation and the experiments are independently adjusted to match. Agreement and diversity shows upon the usefulness and limitation of wear modeling of this type.

  • 72.
    Larsson, Roland
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Isaksson, Patrik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Simulations of lubricated interfaces: a way to obtain efficient machines2010Konferensbidrag (Övrigt vetenskapligt)
  • 73. Kang, Shaojie
    et al.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Two-dimensional finite element analysis of elastic-plastic deformation in asperity-asperity collision2010Ingår i: 14th Nordic Symposium on Tribology: NORDTRIB 2010 : Storforsen, Sweden, June 8-11, 2010, Luleå: Luleå tekniska universitet, 2010Konferensbidrag (Refereegranskat)
    Abstract [en]

    The collision of cylindrical asperities is simulated by means of a commercial multiphysics software in this paper. The model combines a computational structure mechanics approach with a contact algorithm. Numerical results are first compared to classical Hertzian theory. Effects of the bulk material under the mating surfaces have been included in the simulation. Materials of top and bottom surfaces have been assigned different properties. Development of plastic deformation and friction are presented along the process of collision. Strain hardening is included in the elastic-plastic deformation. The effect of interference change and friction coefficient variation on deformation and friction has been studied. Deformed shape and subsurface residual stress in asperity are output parameters from this study.

  • 74. Almqvist, Andreas
    et al.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Sahlin, Fredrik
    Development of a lubrication simulation model2009Ingår i: Svenska mekanikdagarna: Södertälje 2009, Stockholm: Svenska nationalkommittén för mekanik , 2009, s. 74-Konferensbidrag (Övrigt vetenskapligt)
  • 75.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    On the effects of surface roughness in lubrication2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
  • 76. Rapetto, Marco
    et al.
    Almqvist, Andreas
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Lugt, Piet
    On the influence of surface roughness on real area of contact in normal, dry, friction free, rough contact by using a neural network2009Ingår i: Wear, ISSN 0043-1648, E-ISSN 1873-2577, Vol. 266, nr 5-6, s. 592-595Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A model previously developed at LTU was used in order to perform numerical simulations of normal, dry, friction free, linear elastic contact of rough surfaces. A variational approach was followed and the FFT-technique was used to speed up the numerical solution process. Five different steel surfaces were measured using a Wyko optical profilometer and several 2D profiles were taken. The real area of contact and the pressure distribution over the contact length were calculated for all the 2D profiles. A new slope parameter was defined. An artificial neural network was applied to determine the relationship between the roughness parameters and the real area of contact. The trained model was able to capture the dependence of the real area of contact on the roughness parameters. The ability of the neural network to generalize on unseen data was tested. The neural network was able to prove the correlation between the roughness parameters and the real area of contact.

  • 77. Almqvist, Andreas
    et al.
    Taylor, R.I.
    Shell Global Solutions, UK.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Simulation of piston ring: cylinder liner lubrication considering layered fluid films2009Ingår i: Tribologia : Finnish Journal of Tribology, ISSN 0780-2285, Vol. 28, nr 3-4, s. 44-58Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 78.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Essel, Emmanuel Kwame
    Fabricius, John
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Reiterated homogenization applied in hydrodynamic lubrication2008Ingår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 222, nr 7, s. 827-841Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 79.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Essel, Emmanuel Kwame
    Fabricius, John
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Reiterated homogenization of a nonlinear Reynolds-type equation2008Rapport (Övrigt vetenskapligt)
  • 80.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Taylor, Robert Ian
    Shell Global Solutions, UK.
    Larsson, Roland
    Simulation of piston ring: cylinder liner lubrication considering layered fluid films2008Ingår i: Proceedings of the 35th Leeds-Lyon Symposium on Tribology, 2008, 2008Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 81.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Essel, Emmanuel Kwame
    Department of Mathematics and Statistics, University of Cape Coast.
    Fabricius, John
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Variational bounds applied to unstationary hydrodynamic lubrication2008Ingår i: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 46, nr 9, s. 891-906Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper is devoted to the effects of surface roughness in hydrodynamic lubrication. The numerical analysis of such problems requires a very fine mesh to resolve the surface roughness, hence it is often necessary to do some type of averaging. Previously, homogenization (a rigorous form of averaging) has been successfully applied to Reynolds type differential equations. More recently, the idea of finding upper and lower bounds on the effective behavior, obtained by homogenization, was applied for the first time in tribology. In these pioneering works, it has been assumed that only one surface is rough. In this paper we develop these results to include the unstationary case where both surfaces may be rough. More precisely, we first use multiple-scale expansion to obtain a homogenization result for a class of variational problems including the variational formulation associated with the unstationary Reynolds equation. Thereafter, we derive lower and upper bounds corresponding to the homogenized (averaged) variational problem. The bounds reduce the numerical analysis, in that one only needs to solve two smooth problems, i.e. no local scale has to be considered. Finally, we present several examples, where it is shown that the bounds can be used to estimate the effects of surface roughness with very high accuracy.

  • 82. Sahlin, Fredrik
    et al.
    Almqvist, Andreas
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Glavatskih, Sergei
    A cavitation algorithm for arbitrary lubricant compressibility2007Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, nr 8, s. 1294-1300Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A general cavitation algorithm that accommodates for an arbitrary density-pressure relation is presented. It is now possible to model the compressibility of the lubricant in such a way that the density-pressure relation is realistic throughout the contact. The algorithm preserves mass continuity for cavitation caused by bearing geometry and surface topography. It is a commonly accepted physical assumption that the contribution of the pressure driven flow is negligible in the cavitated region. This phenomenon is adopted in the present algorithm, which is similar to that of Elrod, and is modeled by a switch function that terminates the pressure gradient at the cavitation regions. Results with this algorithm for different density-pressure relations are presented and discussed. The effects of inlet conditions, such as surface roughness and starvation, on the load carrying capacity of the contact are analyzed.

  • 83.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization applied in rough surface hydrodynamic lubrication2007Ingår i: Svenska Mekanikdagar 2007: Program och abstracts / [ed] Niklas Davidsson; Elianne Wassvik, Luleå: Luleå tekniska universitet, 2007, s. 31-Konferensbidrag (Övrigt vetenskapligt)
  • 84.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Essel, Emmanuel Kwame
    Persson, Lars-Erik
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of the unstationary incompressible Reynolds equation2007Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, nr 9, s. 1344-1350Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 85.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Lukkassen, Dag
    Meidell, Annette
    Narvik University College, 8505 Narvik, Norway.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    New concepts of homogenization applied in rough surface hydrodynamic lubrication2007Ingår i: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 45, nr 1, s. 139-154Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 86.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Sahlin, Fredrik
    Larsson, Roland
    Glavatskikh, Sergei
    On the dry elasto-plastic contact of nominally flat surfaces2007Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, nr 4, s. 574-579Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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 profiler used 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.

  • 87. Rapetto, Marco
    et al.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Lugt, Piet
    On the influence of surface roughness on real area of contact in normal, dry, friction free, rough contact by using a neural network2007Ingår i: Proceedings of the 11th International Conference on Metrology and Properties of Engineering Surfaces: Huddersfield, U.K., 17th - 20th July 2007 / [ed] Liam Blunt, Huddersfield: University of Huddersfield , 2007Konferensbidrag (Refereegranskat)
  • 88. Rapetto, Marco
    et al.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Almqvist, Andreas
    Lugt, Piet
    On the influence of surface roughness on real area of contact in normal, dry, friction free, rough contact by using a neural network2007Ingår i: Svenska Mekanikdagar 2007: Program och abstracts / [ed] Niklas Davidsson; Elianne Wassvik, Luleå: Luleå tekniska universitet, 2007, s. 32-Konferensbidrag (Övrigt vetenskapligt)
  • 89. Sahlin, Fredrik
    et al.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Glavatskih, Sergei
    Larsson, Roland
    Rough surface flow factors in full film lubrication based on a homogenization technique2007Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, nr 7, s. 1025-1034Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper describes a method to compute the flow factors that compensate for an arbitrary surface roughness in a compressible hydrodynamic lubrication based on a homogenization technique. The Reynolds equation is used as the governing equation and the two-scale expansion involved in the homogenization process enables the local roughness scale to be treated separately from the global geometry scale. With this method, it is possible to compute the flow factors for any deterministic roughness. Measured two-dimensional surface profiles are used as examples. Profiles having the same Abbot curve are also shown to have the same flow factors, providing an efficient classification of surfaces in hydrodynamic two-dimensional contacts. Flow factors are computed for the rough surface profiles, and solutions for global bearing geometry are obtained and compared with the corresponding solutions from a smooth geometry.

  • 90.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The homogenization process of the time dependent Reynolds equation describing compressible liquid flow2007Ingår i: Tribologia : Finnish Journal of Tribology, ISSN 0780-2285, Vol. 26, nr 4, s. 30-44Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    To increase the hydrodynamic performance in different machine elements during lubrication, e.g. journal bearings and thrust bearings, it is important to understand the influence of surface roughness. In this connection one encounters different approaches commonly based on some form of the Reynolds equation. They may generally be divided into deterministic- and averaging- techniques. The former regards all surface roughness information and provides a detailed understanding of the local effects that arise. The latter method is suitable when investigating how the surface roughness affects performance of the machine element as a whole. Homogenization is a rigorous mathematical concept that when applied to a certain problem may be thought of as an averaging technique also providing information about local effects. In this work the compressible time dependent Reynolds equation is homogenized. Related problems have recently been analyzed by homogenization techniques under various assumptions. In the present paper the compressibility is modeled assuming a constant lubricant bulk modulus. The formal method of multiple scale expansion is used to derive a so-called homogenized equation and a numerical solution method to solve both the deterministic problem and the homogenized problem is implemented. The numerical results clearly show that the solution of the homogenized equation is a suitable approximation to the solution of the deterministic problem. It is also demonstrated that for small values of the roughness wavelength, the homogenization technique is superior, since the solution of the deterministic problem requires an extremely fine discretization mesh. More over, the solution of the time dependent homogenized problem may in some cases be reduced to solve a stationary problem that facilitates the solution process and interpretation of results.

  • 91.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    On the effects of surface roughness in lubrication2006Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 92.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Dasht, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The homogenization process of the Reynolds equation describing compressible liquid flow2006Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 39, nr 9, s. 994-1002Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 93. Almqvist, Andreas
    et al.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The homogenization process of the time dependent Reynolds equation describing compressible liquid flow2006Rapport (Övrigt vetenskapligt)
  • 94. Sahlin, Fredrik
    et al.
    Almqvist, Andreas
    Glavatskih, Sergei
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    A cavitation algorithm for arbitrary lubricant compressibility2005Ingår i: Proceedings of the World Tribology Congress III - 2005: presented at ..., September 12 - 16, 2005, Washington, DC, New York: American Society of Mechanical Engineers , 2005, Vol. Paper no 63940, s. 541-542Konferensbidrag (Refereegranskat)
    Abstract [en]

    A general cavitation algorithm is presented that accommodates for an arbitrary density-pressure relation. Here it is possible to model the compressibility of the lubricant in such way the density-pressure relation is realistic from sub-cavity to high pressure regions respectively. The algorithm preserves mass continuity which is of importance when inter-asperity cavitation of rough surfaces is considered. Results with this algorithm for different density-pressure relations are presented and discussed.

  • 95.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Sahlin, Fredrik
    Larsson, Roland
    An Abbott curve based rough surface contact mechanics approach2005Ingår i: Proceedings of the World Tribology Congress III - 2005: presented at ..., September 12 - 16, 2005, Washington, DC, New York: American Society of Mechanical Engineers , 2005, Vol. Paper no 64038, s. 397-398Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 96.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Glavatskih, Sergei
    Larsson, Roland
    Marklund, Pär
    Sahlin, Fredrik
    Dasht, Johan
    Persson, Lars-Erik
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of Reynolds equation2005Rapport (Övrigt vetenskapligt)
  • 97.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Dasht, Johan
    Glavatskih, Sergei
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Marklund, Pär
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sahlin, Fredrik
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Homogenization of the Reynolds equation2005Rapport (Övrigt vetenskapligt)
  • 98. Almqvist, Torbjörn
    et al.
    Almqvist, Andreas
    Larsson, Roland
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    A comparison between computational fluid dynamic and Reynolds approaches for simulating transient EHL line contacts2004Ingår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 37, nr 1, s. 61-69Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 99.
    Almqvist, Andreas
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Sahlin, Fredrik
    Larsson, Roland
    Glavatskih, Sergei
    On the dry elasto-plastic contact of nominally flat surfaces2004Ingår i: Proceedings of the 11th Nordic symposium on tribology: NORDTRIB 2004 : Tromsø, Harstad, Hurtigruten, [Bodø], Norway, June [1 - 5], 2004, 2004, s. 753-762Konferensbidrag (Refereegranskat)
  • 100.
    Almqvist, Andreas
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
    Rough surface elastohydrodynamic lubrication and contact mechanics2004Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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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