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  • 1.
    Almqvist, Andreas
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Burtseva, Evgeniya
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    New insights on lubrication theory for compressible fluids2019In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, article id 103170Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Almqvist, Andreas
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Modelling Flows in Lubrication2020In: Modeling and Simulation of Tribological Problems in Technology / [ed] Marco Paggi & David Hills, Springer, 2020, 1, p. 229-278Chapter in book (Other academic)
  • 3.
    Almqvist, Andreas
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Scientific Computing with Applications in Tribology: A course compendium2019Other (Other academic)
    Abstract [en]

    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.

  • 4.
    Ernens, Dennis
    et al.
    Shell Global Solutions International. University of Twente.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Van Hoecke, Dennis
    Ocas N. V..
    Roijmans, Roel F. H.
    Shell Global Solutions International.
    van Rie, Egbert J.
    Shell Global Solutions International.
    Vande Voorde, John B. E.
    Ocas N.V..
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Bas de Rooij, Matthias
    University of Twente.
    Roggeband, Serge Mathieu
    Shell Global Solutions International.
    van Haaften, Willem Maarten
    Shell Global Solutions International.
    Vanderschueren, Marc
    Ocas N.V..
    Thibaux, Phillipe
    Ocas N.V..
    Pasaribu, Henry Rihard
    Shell Global Solutions International.
    On the Sealability of Metal-to-Metal Seals With Application to Premium Casing and Tubing Connections2019In: SPE Drilling & Completion, ISSN 1064-6671, E-ISSN 1930-0204, Vol. 34, no 4, article id 194146Article in journal (Refereed)
    Abstract [en]

    Metal-to-metal seals are used in connections of casing and tubing in oil and gas wells. This paper describes the mechanisms of sealing metal-to-metal seals as investigated using an experimental setup and a stochastic numerical sealing model. Experiments were conducted for a variety of thread compounds and applied pin/box surface coatings. The results were used to validate a stochastic numerical sealing model for sealability. The model couples a contact-mechanics model with a flow model and takes into account the influence of all the surface-topography features by introducing the concept of seal permeability. Once validated, the model was used together with the experimental results to better understand the sealing mechanisms of metal-to-metal seals.

    The sealing configuration is a face seal with an 80-mm roundoff radius on one face pressing against a flat on the other face. The face-seal specimens were manufactured from P110 tubing to ensure material properties that are representative for casing or tubing. The test setup used is designed for investigating only the metal-to-metal seal of the connection. The setup can perform rotary sliding under constant load to simulate surface changes during makeup and subsequently perform a leakage test. The sealing limit is determined by applying 700-bar fluid pressure and then gradually reducing the normal force until leakage is observed. The data are subsequently used to validate the previously published stochastic numerical sealing model.

    The results indicate a strong dependence on the type of thread compound used for the onset of leakage. The thread compound affects the amount of wear and thus changes the surface topography of the interacting surfaces. It is shown that the stochastic numerical sealing model is capable of predicting the onset of leakage within the experimental accuracy. The model shows further that certain surface topographical features improve the sealing performance. In particular, a surface manufactured by turning on a lathe that is in contact with, for instance, a smooth shot-blasted surface topography leads to highly localized contact areas, which in turn yield the best sealing performance.

  • 5.
    Ernens, Dennis
    et al.
    Shell Global Solutions International BV. University of Twente.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Van Hoecke, Dennis
    OCAS NV.
    Roijmans, Roel F. H.
    Shell Global Solutions International BV.
    van Riet, Egbert J.
    Shell Global Solutions International BV.
    Voorde, John Vande
    OCAS NV.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Bas de Rooij, Matthijn
    University of Twente.
    Roggeband, Serge Mathieu
    Shell Global Solutions International BV.
    Van Haaften, Willem Maarten
    Shell Global Solutions International BV.
    Vanderschueren, Marc
    OCAS NV.
    Thibaux, Phillipe
    OCAS NV.
    Pasaribu, Henry Rihard
    Shell Global Solutions International BV.
    On the Sealability of Metal-to-Metal Seals with Application to Premium Casing Connections2019Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Metal-to-metal seals are used in connections of casing in oil and gas wells. This paper describes the mechanisms of sealing of metal-to-metal seals as investigated using an experimental set-up and a sealability model. Experiments were conducted for a variety of thread compounds and applied pin/box surface coatings. The results were used to validate a numerical model for sealability. The stochastic model couples a contact mechanics model with a flow model and takes the influence of all the surface topography features into account. Once validated, the model was used together with the experimental results to explain the sealing mechanisms of metal-to-metal seals. The sealing configuration is a face seal with an R=80 mm round-off radius pressing against a flat. The face seal specimens were manufactured from P110 tubing. The used test set-up is designed for investigating only the metal-to-metal seal of the connection. The set-up can carry out rotary sliding under constant load to simulate surface evolution during make-up and subsequently perform a leakage test. The sealing limit is determined by applying 700 bar fluid pressure and then gradually reducing the normal force until leakage is observed. The data is subsequently used to validate a previously published model. The results indicate a strong dependence of the type of thread compound used on the onset of leakage. The thread compound affects the amount of wear and thus changes the surface topography of the interacting surfaces. It is shown that the sealability model is capable to predict the onset of leakage within the experimental accuracy. The model shows further that certain surface topographical features improve the sealing performance. Namely, a turned against a flat surface topography leads to highly localized contact areas, which in turn yields the best sealing performance. The combination of experimental data with the validated model leads to much deeper insights for the sealing mechanisms than what could be obtained using either on their own.

  • 6.
    Fabricius, John
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Tsandzana, Afonso Fernando
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pérez-Ràfols, Francesc
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A Comparison of the Roughness Regimes in Hydrodynamic Lubrication2017In: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 139, no 5, article id 051702Article in journal (Refereed)
    Abstract [en]

    This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength l, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/l, denoted as k, three different lubrication regimes exist: Reynolds roughness (k-0), Stokes roughness (0<γ<1), and high-frequency roughness (γ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on k. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter k. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

  • 7.
    Francesc, Pérez Ràfols
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Study of static seals by means of a stochastic two-scale model2016Conference paper (Other academic)
  • 8.
    Francesc, Pérez Ràfols
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Numerical study of the effect of coatings in static metal-to-metal seals2016In: STLE 2016 Annual Meeting and Exhibition, 2016, 2016Conference paper (Refereed)
  • 9.
    Perez Rafols, Francesc
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Two-scale stochastic modelling and analysis of leakage through metal-to-metal seals2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    A seal is a commonly used machine element whose function is to preventthe flow of a fluid from a high to a low pressure region. Metal-to-metalseals, in particular, are used whenever extreme conditions prevent theuse of less expensive rubber seals. Situations where such extreme condi-tions may be encountered are found, for example, in oil wells and nuclearpower plants. In such applications, the failure of a metal-to-metal sealcan become catastrophic, as it might mean the leakage of hazardousfluids to the environment. In order to minimize the risk, it is critical tounderstand the mechanisms controlling the seal’s performance and,if possible, be able to predict capability to prevent leakage on before-hand. Not surprisingly, the surface topography plays a crucial role hereand therefore requires careful consideration when conducting studies ofthis kind. Indeed, it has been shown that even very small details in thetopography (of size of the order of micrometres) can have a large effecton the performance of the whole seal (of size of the order of centimetresor larger). Another complicating factor is the topography’s stochas-tic nature, which makes even the identification of the relevant detailschallenging. Modelling is, in this context, a desirable approach, as itprovides the possibility to easily zoom in those fine details as well asisolate individual parameters. Moreover, it can provide for a predictionon the expected leakage.This work focuses primarily on the development of a model suitablefor studying the mechanisms controlling the performance of metal-to-metal seals and to enable prediction of leakage. To accomplish this, amodel that follows a two-scale approach is proposed. More precisely,the small details in the topography are considered in a local problemconnected to a highly resolved local-scale domain, while the componentlevel features are considered in a global problem allowing for a coarsegrid discretisation of the corresponding global-scale domain. During the present work it was also found that realistic results can only be obtainedif the model explicitly considers the surface topography’s stochastic na-ture. The model was first developed for liquids and was based on theassumption of incompressible and iso-viscous flow. Further work, withthe objective to enable studies of more complex type of flow situations,resulted in a versatile transformation translating results for incompress-ible and iso-viscous to compressible and piezo-viscous fluids and viceversa. This means that, the flow of gases and other more complex fluidscan be studied by combining the model for the simplistic incompressibleand iso-viscous flow with this newfound transformation.Using the model developed, the sealing performance of metal-to-metal seals during load cycling, i.e., by gradually increasing the load toa certain value and then releasing it again, is studied. The scope of thisstudy is to assess how the plastic deformation that the metal surfacesundergoes during the loading phase can affect the leakage during unload-ing. It is shown that this results in a change of the original topographythat may lead to a better sealing performance during unloading. Themain result obtained is, however, that given the right conditions, the ap-plied load can be released considerably (even down to half of the reachedbefore starting the unloading) with only a small increase in leakage asa result. This shows the seal’s capability to prevent leakage evenif an unexpected reduction of load occurs and is therefore is a valuabledescription of the robustness of the seal.

  • 10.
    Pérez Ràfols, Francesc
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements. 1990.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    On compressible and piezo-viscous flow in thin porous mediaManuscript (preprint) (Other academic)
  • 11.
    Pérez Ràfols, Francesc
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    On compressible and piezo-viscous flow in thin porous media2018In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 474, no 2209, article id 20170601Article in journal (Refereed)
    Abstract [en]

    n this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

  • 12.
    Pérez-Ràfols, Francesc
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    The benefits of plastic deformatin in the performance of metal-to-metal seals2017Conference paper (Other academic)
  • 13.
    Pérez-Ràfols, Francesc
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    van Riet, Egbert J.
    Shell Global Solutions International BV, Innovation, Research and Development.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    On the flow through plastically deformed surfaces under unloading: A spectral approach2018In: Proceedings of the Institution of mechanical engineers. Part C, journal of mechanical engineering science, ISSN 0954-4062, E-ISSN 2041-2983, Vol. 232, no 5, p. 908-918Article in journal (Refereed)
    Abstract [en]

    This study considers flow through the gap left between two surfaces during unloading, in other words, when an applied load is gradually reduced after loading to a state where plastic deformation occurs. In particular, the permeability of the gap is studied. It was found that a substantial reduction of the applied load is required before the permeability starts to increase significantly. The explanation for this phenomenon is given by the combination of components with different wavelengths present in the surface. Components with long wavelengths deform elastically and those with shorter wavelengths may also deform plastically. We found that plastic deformation acts to keep the permeability nearly constant at the beginning of the unloading and elastic spring-back is responsible for the rapid increase at lower loads. This principle constitutes a basis for the strategy that was developed in order to predict the load at which the rapid increase of permeability starts.

  • 14.
    Pérez-Ràfols, Francesc
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Van Riet, Egbert J.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    On the loading and unloading of metal-to-metal seals: A two scale stochastic approachManuscript (preprint) (Other academic)
  • 15.
    Rafols, Francesc Perez
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Modelling of leakage on metal-to-metal seals2016In: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 94, p. 421-427Article in journal (Refereed)
    Abstract [en]

    Surfaces in a typical seal exhibit both waviness and roughness. The influence of the interaction between these two scales on the leakage behaviour is expected to be relevant. Therefore, a model, which can study it, is developed here. The model is composed of state-of-the-art models for the contact mechanics between rough metal surfaces and for the liquid flow through the rough aperture in-between them. Correlation between percentage real contact area and actual contact topology and leak rate was confirmed through numerical analysis. Small changes in relative position between the contacting surfaces showed large deviation in leak rate. The validity of the model was justified by comparing results from numerical simulations using the model and experimental results found in literature qualitatively.

  • 16.
    Rafols, Francesc Perez
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Lundström, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    A stochastic two-scale model for pressure-driven flow between rough surfaces2016In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 472, no 2190, article id 20160069Article in journal (Refereed)
    Abstract [en]

    Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern.

  • 17.
    Ràfols, Francesc Pérez
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Modelling and numerical analysis of leakage through metal-to-metal seals2016Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Metal-to-metal seals are critical components as their failure can lead to leakage of hazardous fluids to the environment or to fatal failure of the systems they operate on. Most systems are subjected to increasingly more demanding conditions and deeper knowledge about how different parameters affect the leakage is necessary to design seals with the desired performance. Fundamental knowledge can be obtained by means of numerical simulations, since it can provide in-situ information which would be extremely difficult, if not impossible, to obtain by means of physical experiments only. Moreover, in the virtual experiments it is possible isolate the effect of variations in a single parameter. However, no model that can serve as a predictive tool and thus has been tested against experimental results has been found in literature. The reason for this is the complexity in accounting for both the multi-scale nature of surface roughness and its intrinsic randomness. This lack have defined the main objective of this work, i.e., to develop a model for the leakage through metal-to-metal seals, which can output quantitative results that can be used for comparison against experimental work. This has been accomplished by including the stochastic nature of the surface topography explicitly in a two-scale method. The model constructed following this approach fulfills the requirement of giving a quantitative prediction of metal-to-metal seals. Moreover, it also provides new insight on the expected variability in leakage introduced by the stochastic nature of the roughness.A secondary objective has been to investigate the seal behaviour during unloading, i.e., when the applied load is gradually released after having caused significant plastic deformation. The reason for assessing this topic is that metal-to-metal seals subjected to a certain load cycle exhibit, at any given load, a significantly larger leakage during the first loading than it does during the subsequent unloading for the same load. The numerical simulations of the seal behavior during unloading also confirmed the smaller leakage during unloading. Moreover, it was observed that a substantial load release was required before a significant leakage increase could be detected and that the leakage remained nearly constant up to that point. This is an important finding that can be used when designing seals in order to account for stress relaxation during service live.

  • 18.
    Ràfols, Francesc Pérez
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    An Enhanced Stochastic Two-Scale Model for Metal-to-Metal Seals2018In: Lubricants, ISSN 2075-4442, Vol. 6, no 4, article id 87Article in journal (Refereed)
    Abstract [en]

    Leakage in static metal-to-metal seals is predominantly determined by the topography of the contacting surfaces. The topography consists of features that span the entire range from its carefully engineered geometry down to micro-sized surface asperities. The mesh density necessary to fully resolve all the features, in this large span of length scales, generates too many degrees of freedom for a direct numerical approach to be applicable. Some kind of sophistication, either incorporated in the mathematical model or in the numerical solution procedure or even a combination of both is therefore required. For instance, in a two-scale model, the geometrical features can be addressed in the global-scale model, while the features belonging to length scales smaller than a given cut-off value are addressed in the local-scale model. However, the classical two-scale approaches do not explicitly address the stochastic nature of the surfaces, and this has turned out to be a requirement in order to obtain quantitative predictions of leakage in metal-to-metal seals. In this work, we present a continued development of an already existing two-scale model, which incorporates a stochastic element. The novelty lies in the way we characterise the permeability at the local scale and how this is used to build a more efficient and useful approach

  • 19.
    Ràfols, Francesc Pérez
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Generating randomly rough surfaces with given height probability distribution and power spectrum2019In: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 131, p. 591-604Article in journal (Refereed)
    Abstract [en]

    In this work we present a simple method to generate surface topography. The main advantage of the presented method as compared with those available in the literature is that the power spectrum and the height probability distribution can be specified independently. In this article we present the method and show its versatility by generating surface topographies with three different height probability distributions: the Weibull distribution, a bimodal distribution and a distribution containing a delta function that represents worn surfaces. The MATLAB-code we used to generate the numerical examples are also provided to the reader.

  • 20.
    Ràfols, Francesc Pérez
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Van Riet, Egbert J.
    Shell Global Solutions International BV, Innovation, Research and Development, Rijswijk, The Netherlands.
    Almqvist, Andreas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    On the loading and unloading of metal-to-metal seals: A two-scale stochastic approach2018In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 232, no 12, p. 1525-1537Article in journal (Refereed)
    Abstract [en]

    During operation, the mating surfaces of a metal-to-metal seal typically undergo significant plastic deformation, which in turn can have beneficial effect on its performance. In previous studies, it has, for instance, been shown that plastic deformation can provide for better sealing during unloading. Those studies did, however, only consider flow through unrealistically small domains. Therefore, it is possible that this might be a size effect, which would not be apparent in a real situation with a much larger domain. In this paper, we develop a model which can handle real-sized seal domains at the same time as fine details of the surface topography. More precisely, we construct a two-scale model, in which the global scale represents the seal domain and where the influence of the fine details at the local scale are represented by a stochastic element. By means of this stochastic two-scale model, we show that the beneficial effect associated with the plastic deformation persists also when real-sized seal domains are considered.

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