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  • 1. Almqvist, Torbjörn
    Computational fluid dynamics in theoretical simulations of elastohydrodynamic lubrication2004Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The work presented in this thesis concerns computer simulations of lubrication processes, and the main part deals with simulations in the elastohydrodynamic lubrication (EHL) regime. The thesis summarises the work performed in the five papers referred to as Paper A, B, C, D and E. The aim is to give the reader a more explanatory description of the investigations performed in the papers and of the physical processes present in EHL. Lubrication is a sub-area of tribology, which is the science of interacting bodies in relative motion, two other sub-areas being wear and friction. Lubrication is commonly referred to as a way of reducing friction and protecting the surfaces from wear. Typical devices where EHL is present are machine components. Examples of these are bearings, cams and gears. The lubricant can in such an application have many different tasks. The ultimate goal is that the surfaces in motion should be separated by a fluid film, thus reducing the friction and wear. That leads to low frictional losses and long operating life for the machine components. This goal is, however, not always fulfilled, and to protect the surfaces from wear when the lubricating film collapses, there are additives added to the lubricant. Commonly, lubricants contain of a number of additives, but these are not in focus in this thesis. Common to many EHL-applications, especially machine components, are thin lubricating films and high fluid pressures. The high pressures result in elastic deformation of the contacting bodies. The lubricating films in such applications are very thin, often in the range 0.1-1 10^-6m with pressures ranging from 0.5-3 GPa. The contact diameter is approximately 1 mm and the time a fluid element needs to pass through the contact is approximately 0.1 ms. The altering geometrical scales and rapid changes in the physical variables, such as pressure, viscosity and temperature etc., make numerical simulations to a challenging task. The variables of primary interest in the numerical simulations are: film thickness, pressure, temperature and friction. The film thickness is an important variable that gives information as to whether the surfaces are separated by the lubricating film. It is the lifting force generated by the hydrodynamic pressure that governs the separation of the surfaces in motion. However, even if a lubricating film is present, EHL machine components deteriorate when they have been in service for a long time. It is then that the cycling in pressure and temperature leads to fatigue of the surfaces, so that the level of these variables is also of importance. The friction that has developed in the EHL-contacts leads to a loss of energy, which increases the temperature in the conjunctions. Friction is therefore important not only for the efficiency, but also when thermal aspects have to be considered. The physical processes present in EHL are inter-disciplinary, closely related to other fields of science such as fluid mechanics, solid mechanics, and rheology. In almost all numerical simulations of lubrication performed today, the hydrodynamics are modelled by an equation referred to as the Reynolds equation. This equation is derived from a simplified form of the momentum equations, which are combined with the continuity equation; and the result is a Poisson equation for the fluid pressure. The assumptions made when deriving this equation limit the size of the computational or spatial domain, and the equation cannot predict pressure variations across the lubricating fluid film. In the work presented in this thesis, an extended approach, where the technique is based on CFD (computational fluid dynamics), is used to simulate the lubricant flow. The extended approach is here based on more complete forms of the equations of momentum, continuity and energy and the above degeneracy will be removed. That implies, if such an approach works, that it should now be possible to simulate the lubricant flow under conditions where the Reynolds equation is not valid. So far, only few attempts have been made to use the CFD-technique. From the preceding discussion of rapid changes in accordance with elastic deformation of the contacting surfaces, a great deal of work has been carried out to modify the numerical algorithm in the CFD-software to fit EHL-problems. The CFD- software used throughout the work in this thesis is CFX4 (2003).

  • 2. Almqvist, Torbjörn
    Numerical simulation of elastohydrodynamic and hydrodynamic lubrication using the Navier-Stokes and Reynolds equations2001Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The work presented in this thesis concerns computer simulations of the lubrication process. The main subject of interest is elastohydrodynamic lubrication (EHL) and, to some extent, hydrodynamic lubrication (HD). The thesis comprises an introductory section and three papers; referred to as A, B and C. Simulation of EHL is an inter-disciplinary task, incorporating the fields of fluid mechanics, solid mechanics, thermodynamics and rheology. In almost all numerical simulations of lubrication performed today, the hydrodynamics are modelled using the Reynolds equation. This equation is derived from the equations of momentum and continuity and using the thin film approximation. However, the assumptions made when deriving this equation limits the size of the computational/spatial domain and the equation cannot predict pressure variations across the lubricating oil film. The subject of papers A and B are numerical simulations using the full equations of momentum and continuity, (Paper B), and the equation of energy (Paper A). The main aim of the work was to investigate the possibilities of carrying out numerical simulations based on the above equations. The rheology was assumed to be Newtonian; the equations are then commonly referred to as the Navier-Stokes equations (N-S). The second aim of the work was to investigate the possibilities of using a commercial software, CFX 4.3 [1], to carry out the numerical simulations. The results in Paper A show that it is possible to simulate thermal EHL line contacts up to pressures of approximately 1 GPa. The limitations of the approach are due to a singularity that can occur in the equation of momentum when a critical shear stress is reached. With a more complete rheological model (non-Newtonian rheology) it should be possible to perform simulations at even higher contact pressures. Paper B presents the results of isothermal simulations comparing the N-S and Reynolds equation approaches. The result show that there may be some discrepancies between the two approaches; although only small discrepancies have been observed in the smooth line contact simulations made. The characteristics of the EHL-contact with a wide range of scales and large gradients in pressure, viscosity and temperature make developing accurate numerical simulations to a difficult task. The computational cost is high due to the small under-relaxations factors that must be used in order to obtain converged numerical solutions. The work to date has shown that is possible to use the extended approach in conjunction with a commercial software, CFX 4.3 [1]. This approach makes it possible to extend the computational domain in future in EHL-simulations, where the Reynolds approach is not valid. Paper C presents the results of simulations of a lubricated pivoted thrust bearing. The objective of this study was to verify a thermo-hydrodynamic (THD) model for this type of bearing. The model developed handles three-dimensional temperature distribution in the oil film and pad, as well as two-dimensional temperature variation in the runner. The viscosity and density are treated as functions of both temperature and pressure. Experiments have been performed in a test rig consisting of two identical equalising pivoted pad thrust bearings. Experimentally measured power loss, runner temperature and pressure profiles as a function of load and rotational speed were compared with the theoretical investigations. The results showed fairly good agreement when the oil inlet temperature and heat transfer coefficients were modified in order to obtain the same runner temperature in both theory and experiment.

  • 3. Almqvist, Torbjörn
    et al.
    Almqvist, Andreas
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    A comparison between computational fluid dynamic and Reynolds approaches for simulating transient EHL line contacts2004In: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 37, no 1, p. 61-69Article in journal (Refereed)
    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

  • 4. Almqvist, Torbjörn
    et al.
    Glavatskikh, Sergei
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Larsson, Roland
    THD analysis of tilting pad thrust bearings: comparison between theory and experiments2000In: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 122, no 2, p. 412-417Article in journal (Refereed)
    Abstract [en]

    The objective of the present research is to verify a THD model of hydrodynamic thrust bearings. The developed model of a pivoted pad bearing, which can tilt both radially and circumferentially, allows for three-dimensional temperature distribution in the oil film and in the pad, as well as two-dimensional temperature variation in the runner. Viscosity and density are treated as functions of both temperature and pressure. Experiments have been performed on a test rig, containing two identical equalizing pivoted pad thrust bearings. Power loss, runner temperature, and pressure profiles as a function of load and rotational speed are compared for both theoretical and experimental investigations. Fairly good agreement has been found when the oil inlet temperature and heat transfer coefficients have been estimated in order to get the same runner temperature in both theory and experiment.

  • 5. Almqvist, Torbjörn
    et al.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Comparison of Reynolds and Navier-Stokes approach for solving isothermal EHL line contacts2001In: Tribology 2001: scientific achievements, industrial applications, future challenges ; plenary and session key papers from the 2nd World Tribology Congress, Vienna, Austria, 3 - 7 September / organized by the Austrian Tribology Society (Österreichische Tribologische Gesellschaft, ÖTG) / [ed] Friedrich Franek, Wien: ÖTG , 2001Conference paper (Refereed)
  • 6. Almqvist, Torbjörn
    et al.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Some remarks on the validity of Reynolds equation in the modeling of lubricant film flows on the surface roughness scale2004In: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 126, no 4, p. 703-710Article in journal (Refereed)
    Abstract [en]

    The objective of this paper is to investigate the flow in a lubricant film on the surface roughness scale and to compare the numerical solutions obtained by two different solution approaches. This is accomplished firstly by the CFD-approach (computational fluid dynamic approach) where the momentum and continuity equations are solved separately, and secondly the Reynolds equation approach, which is a combination and a simplification of the above equations. The rheology is assumed to be both Newtonian and non-Newtonian. An Eyring model is used in the non-Newtonian case. The result shows that discrepancies between the two approaches may occur, primarily due to a singularity which appears in the momentum equations when the stresses in the lubricant attain magnitudes that are common in EHL. This singularity is not represented by the Reynolds equation. If, however, the rheology is shifted to a non-Newtonian Eyring model the deviations between the two solution approaches is removed or reduced. The second source of discrepancies between the two approaches is the film thickness to wavelength scale ω. It will be shown that the Reynolds equation is valid until this ratio is approximately O(10-2).

  • 7. Almqvist, Torbjörn
    et al.
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    The Navier-Stokes approach for thermal EHL line contact solutions2002In: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 35, no 3, p. 163-170Article in journal (Refereed)
    Abstract [en]

    The complicated nature of the EHL-problem has so far forced researchers to develop their own computer codes. These codes are ultimately based on the Reynolds equation, and if thermal EHL-simulations are required, a simultaneous solution of the equation of energy also has to be performed. To date only a few attempts to solve the full equations of momentum and continuity as well as equations of energy have been performed. However, such an approach will give extended possibilities of simulating EHL-contacts; i.e. the computational domain can be expanded and it will be possible to simulate the flow, not only in the contact but also around the contact. Another possibility is to investigate how the altering length scales of the surface roughness influence the behaviour of the flow in the contact. However, the aim of the work presented in this paper is to investigate the possibilities of using a commercial CFD-code (computational fluid dynamics code) based on the above-mentioned equations for simulating thermal EHL. The rheology is assumed to be Newtonian and the equations of momentum and continuity are then commonly referred to as the Navier-Stokes equations (N-S equations). The geometry chosen for the simulations is a smooth line contact geometry, for which the results from the simulations show that it is possible to use the N-S equations for thermal EHL for contact pressures up to approximately 0.7 GPa. The code used in this work is the commercial CFD software (CFX 4.3 user guide). There is a limitation in the N-S approach due to a singularity that can occur in the equation of momentum when the principal shear stresses in the film become too high. However, a thermal approach makes it possible to simulate EHL-contacts at higher loads compared with an isothermal approach, due to the reduction of the viscosity in the former approach. The singularity is not present in the Reynolds approach.

  • 8. Sahlin, Fredrik
    et al.
    Glavatskih, Sergei
    Almqvist, Torbjörn
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    2D CFD-analysis of micro-patterned surfaces in hydrodynamic lubrication2004In: Proceedings of the ASME/STLE international joint tribology conference 2004: October 24 - 27, 2004, Long Beach, California, USA, New York, 2004, Vol. Paper no 64009, p. 1637-1645Conference paper (Refereed)
    Abstract [en]

    Results of a numerical study of the influence of micro-patterned surfaces in hydrodynamic lubrication of two parallel walls are reported. Two types of parameterized grooves with the same order of depth as the film thickness are used on one stationary wall. The other wall is smooth and is sliding with a specified tangential velocity. Isothermal incompressible two dimensional full film fluid flow mechanics is solved using a Computational Fluid Dynamics method. It is shown that, by introducing a micro-pattern on one of two parallel walls, a net pressure rise in the fluid domain is achieved. This produces a load carrying capacity on the walls which is mainly contributed by fluid inertia. The load carrying capacity increases with Reynolds number. The load carrying capacity is reported to increase with groove width and depth. However, at a certain depth a vortex appears in the groove and near this value the maximum load carrying capacity is achieved. It is shown that the friction force decreases with deeper and wider grooves. Among all geometries studied, optimum geometry shapes in terms of hydrodynamic performance are reported.

  • 9. Sahlin, Fredrik
    et al.
    Glavatskikh, Sergei
    Almqvist, Torbjörn
    Larsson, Roland
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
    Two-dimensional CFD-analysis of micro-patterned surfaces in hydrodynamic lubrication2005In: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 127, no 1, p. 96-102Article in journal (Refereed)
    Abstract [en]

    Results of a numerical study of the influence of micro-patterned surfaces in hydrodynamic lubrication of two parallel walls are reported. Two types of parameterized grooves with the same order of depth as the film thickness are used on one stationary wall. The other wall is smooth and is sliding with a specified tangential velocity. Isothermal incompressible two dimensional full film fluid flow mechanics is solved using a Computational Fluid Dynamics method. It is shown that, by introducing a micro-pattern on one of two parallel walls, a net pressure rise in the fluid domain is achieved. This produces a load carrying capacity on the walls which is mainly contributed by fluid inertia. The load carrying capacity increases with Reynolds number. The load carrying capacity is reported to increase with groove width and depth. However, at a certain depth a vortex appears in the groove and near this value the maximum load carrying capacity is achieved. It is shown that the friction force decreases with deeper and wider grooves. Among all geometries studied, optimum geometry shapes in terms of hydrodynamic performance are reported

  • 10. Tuomas, Roger
    et al.
    Almqvist, Torbjörn
    Åhrström, Bert-Olof
    Berg, Sven
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Influence of molecular structure on the lubrication properties of four different esters2000In: Tribologia, ISSN 0780-2285, Vol. 19, no 4, p. 3-8Article in journal (Refereed)
    Abstract [en]

    The lack of published data on the chemical structures of lubricants makes it almost impossible to investigate the influence of structure on lubrication properties. In this investigation, the lubricating properties of three esters with known chemical structure have been investigated and compared with a commercial ester. The lubrication properties that were expected to be dependent on chemical structure such as film thickness and traction, viscosity and friction coefficients were compared by experiment. To measure the film thickness a Ball and Disc Apparatus was used, the traction coefficient was measured in a Jumping Ball Apparatus, the viscosity in a rotational cylindrical viscometer and the friction coefficient in a reciprocating friction and wear test apparatus. The results showed that molecular length has a significant influence on lubrication properties, with longer molecules giving the highest viscosity and greatest film thickness. The length of the molecule did not influence the coefficients of friction, but the traction coefficient, Υ, decreased with increasing molecular length.

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