Дисертації з теми "Theory of lubrication"

In this licentiate thesis we study some mathematical problems in hydrodynamic lubrication theory. It is composed of two papers (A and B) and a complementary appendix. Lubrication theory is devoted to fluid flow in thin domains. The main purpose of lubrication is to reduce friction and wear between two solid surfaces in relative motion. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation which describes the motion of viscous fluids. In thin domains several approximations are possible which leads to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict different important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field.In many practical situations the surface roughness amplitude and the film thickness are of the same order. Therefore, any realistic model should account for the effect of surface roughness. This implies that the mathematical modelling leads to partial differential equations with coefficients that will oscillate rapidly in space and time due to the relative motion of the surfaces. A direct numerical analysis is very difficult since an extremely fine mesh is required to describe the different scales. One method which has proved successful to handle such problems is to do some averaging (asymptotic analysis). The branch in mathematics which has been developed for this purpose is called homogenization.In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness ε and wavelength μ of the roughness tend to zero is analyzed and described. The results are obtained using the formal method of multiple scale expansion. The limit equation depends on how fast the two small parameters ε and μ go to zero relative to each other. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime).In paper B we present a mathematical model in hydrodynamic lubrication that takes into account cavitation (formation of air bubbles), surface roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness. A one-dimensional problem describing a step bearing is also solved explicitly and by numerical methods.

Godkänd; 2014; 20140415 (afotsa); Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Afonso Fernando Tsandzana Ämne: Matematik/Mathematics Uppsats: Homogenization with Applications in Lubrication Theory Examinator: Professor Peter Wall, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Professor Anders Holmbom, Mittuniversitetet, Östersund Tid: Onsdag den 11 juni 2014 kl 10.00 Plats: E231, Luleå tekniska universitet

Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without effective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional effects, unsteadiness, turbulence, variable material properties, non-newtonian fluids, multi-phase flows, wall slip, and thermal effects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working fluids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse effects due to fouling, and compatibility with power system working fluids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-fitting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses five problems involving our new Reynolds equation. In the first, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the "effective bulk modulus". The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplified formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically three-dimensional flows. A finite difference scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed flows. This Reynolds equation is then solved using perturbation methods for high-speed flows. It is found that the flow structure is comprised of five boundary layer regions in addition to the main ``core'' region. The flow in two of these boundary layer regions is governed by a nonlinear heat equation and the flow in three of these boundary layers is governed by nonlinear relaxation equations. Finite difference schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the flow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical flows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the first detailed discussions of the physics of lubrication in dense and supercritical flows, and the discovery of boundary layer structures in flows associated with thrust bearings.
Doctor of Philosophy
Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without eective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional eects, unsteadiness, turbulence, variable material properties, non-newtonian uids, multi-phase ows, wall slip, and thermal eects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working uids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse eects due to fouling, and compatibility with power system working uids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-tting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses ve problems involving our new Reynolds equation. In the rst, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the eective bulk modulus. The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplied formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically threedimensional ows. A nite dierence scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed ows. This Reynolds equation is then solved using perturbation methods for high-speed ows. It is found that the ow structure is comprised of ve boundary layer regions in addition to the main core region. The ow in two of these boundary layer regions is governed by a nonlinear heat equation and the ow in three of these boundary layers is governed by nonlinear relaxation equations. Finite dierence schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the ow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical ows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the rst detailed discussions of the physics of lubrication in dense and supercritical ows, and the discovery of boundary layer structures in ows associated with thrust bearings.

Thesis (M.S.) University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 20, 2007) Vita. Includes bibliographical references.

We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation, which describes the motion of viscous fluids. In thin domains several approximations are possible which lead to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict vorous important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field. In hydrodynamic lubrication the effect of surface roughness is not negligible, because in practical situations the amplitude of the surface roughness are of the same order as the film thickness. Moreover, a perfectly smooth surface does not exist in reality due to imperfections in the manufacturing process. Therefore, any realistic lubrication model should account for the effects of surface roughness. This implies that the mathematical modeling leads to partial differential equations with coefficients that will oscillate rapidly in space and time. A direct numerical computation is therefore very difficult, since an extremely dense mesh is needed to resolve the oscillations due to the surface roughness. A natural approach is to do some type of averaging. In this PhD thesis we use and develop modern homogenization theory to be able to handle the questions above. Especially, we use, develop and apply the method based on the multiple scale expansions and two-scale convergence. The thesis is based on five papers (A-E), with an appendix to paper A, and an extensive introduction, which puts these publications in a larger context. In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness  and wavelength  of the roughness tend to zero is analyzed and described. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime). In paper C we extend the work done in Paper A where we compare the roughness regimes by numeric computations for the stationary case. In paper B we present a mathematical model that takes into account cavitation, surfaces roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness.In the paper D we derive a mathematical model of thin film flow between two close rough surfaces, which takes into account cavitation, surface roughness and pressure dependent density. Moreover, we use two-scale convergence to homogenize the model. Finally, in paper E we prove the existence of solutions to a frequently used mathematical model of thin film flow, which takes cavitation into account.

We investigate the behavior of moving droplets and rivulets, driven by a combination of gravity and surface shear (wind). The problem is motivated by a desire to model the behavior of raindrops on aircraft wings. We begin with the Stokes equations and use the approximations of lubrication theory to derive the specific thin film equation relevant to our situation. This fourth-order partial differential equation describing the height of the fluid is then solved numerically from varying initial conditions, using a fully implicit discretization for time stepping, and a precursor film to avoid singularities at the drop contact line. Results describing general features of droplet deformation, limited parameter studies, and the applicability of our implementation to the long-term goal of modeling wings in rain are discussed.

This thesis is devoted to the study of some homogenization problems with applications in lubrication theory. It consists of an introduction, five research papers (I–V) and a complementary appendix.Homogenization is a mathematical theory for studying differential equations with rapidly oscillating coefficients. Many important problems in physics with one or several microscopic scales give rise to this kind of equations, whence the need for methods that enable an efficient treatment of such problems. To this end several mathematical techniques have been devised. The main homogenization method used in this thesis is called multiscale convergence. It is a notion of weak convergence in  Lp spaces which is designed to take oscillations into account. In paper II we extend some previously obtained results in multiscale convergence that enable us to homogenize a nonlinear problem with a finite number of microscopic scales. The main idea in the proof is closely related to a decomposition of vector fields due to Hermann Weyl. The Weyl decomposition is further explored in paper III.Lubrication theory is devoted to the study of fluid flows in thin domains. More generally, tribology is the science of bodies in relative motion interacting through a mechanical contact. An important aspect of tribology is to explain the principles of friction, lubrication and wear. The mathematical foundations of lubrication theory are given by the Navier–Stokes equation which describes the motion of a viscous fluid. In thin domains several simplifications are possible, as shown in the introduction of this thesis. The resulting equation is named after Osborne Reynolds and is much simpler to analyze than the Navier--Stokes equation.The Reynolds equation is widely used by engineers today. For extremely thin films, it is well-known that the surface micro-topography is an important factor in hydrodynamic performance. Hence it is important to understand the influence of surface roughness with small characteristic wavelengths upon the solution of the Reynolds equation. Since the 1980s such problems have been increasingly studied by homogenization theory. The idea is to replace the original equation with a homogenized equation where the roughness effects are “averaged out”. One problem consists of finding an algorithm for computing the solution of the homogenized equation. Another problem consists of showing, on introducing the appropriate mathematical definitions, that the homogenized equation is the correct method of averaging. Papers I, II, IV and V investigate the effects of surface roughness by homogenization techniques in various situations of hydrodynamic lubrication. To compare the homogenized solution with the solution of the deterministic Reynolds equation, some numerical examples are also included.
Godkänd; 2011; 20110408 (johfab); DISPUTATION Ämnesområde: Matematik/Mathematics Opponent: Professor Guy Bayada, Institut National des Sciences Appliquées de Lyon (INSA-LYON), Lyon, France, Ordförande: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Tid: Tisdag den 7 juni 2011, kl 10.00 Plats: D2214/15, Luleå tekniska universitet

Materials can flow down a slope in a wide range of geophysical and industrial contexts, including lava flows on volcanoes and thin films on coated surfaces. The aim of my research is to provide quantitative insight into these forms of motion and their dependence on effects of the topography, the volume and the rheology of the flowing structure. Numerous different problems are investigated through mathematical models, which are developed analytically and confirmed by laboratory experiments. The initial advance of long lava flows is studied by considering the flow of viscous fluid released on sloping channels. A scaling analysis, in agreement with analog experiments and field data, offers a practical tool for predicting the advance of lava flows and conducting hazard analysis. A simple and powerful theory predicts the structure of flows resulting from any time-dependent release of fluid down a slope. Results obtained by the method of characteristics reveal how the speed of the advancing front depends importantly on the rate of fluid supplied at an earlier time. Viscous flows on surfaces with different shapes are described by similarity solutions to address problems motivated by engineering as well as geophysical applications. Pouring viscous fluid out of a container can be a frustratingly slow process depending on the shape and the degree of tipping of the container. The discharge rate of the fluid is analysed in simple cases, shedding light on how containers can be emptied most quickly in cosmetic and food industries. In a separate study motivated by coating industries, thin films are shown to evolve with uniform thickness as they drain near the top of a horizontal cylinder or sphere. The leading edge eventually splits into rivulets as predicted theoretically and confirmed by experiments. Debris flows can develop levees and trigger avalanches which are studied by considering dense granular flows down a rough inclined plane. Granular materials released down a slope can produce a flowing structure confined by levees or trigger avalanches at regular intervals, depending on the steady rate of supply. The experimental results are discussed using theoretical ideas of shallow granular flows. Finally, materials flowing in long and slender ducts are investigated theoretically to better understand the digestive and urinary systems in biology. The materials are pumped in an elastic tube by translating waves of muscular contraction and relaxation. The deformation of the tube is predicted by solving a free-boundary problem, a similar mathematical exercise to predicting the moving boundaries of materials spreading on slopes.

Three topics are considered in this thesis. The first is evaluation of the effective elastic moduli of porous materials and considers materials such as porous glass, sandstone, sintered bronze and iron materials, porous ceramics. Models with spherical pores were first considered showing good agreement for some materials but not for materials prepared by powder sintering. A number of modifications of increasing complexity were introduced accounting for non-spherical pores and their interaction. The models then compare well with experimental data for sintered materials. The other topics of the thesis can be used to model mixed lubrication in plain bearings where part of the load is carried by contacting asperities and part by the lubricant film. The roughness features affect the ability of the lubricant to flow in the gap between the surfaces and surface deflection is caused by asperity contact pressures only. A method is presented to solve dry contact problems for nominally plane surfaces using a simple elastic-plastic model at asperity contacts and a differential formulation for the elastic deflection. Periodic roughness defined over a representative area is incorporated using Fourier transforms to calculate the convolutions. The method is validated by comparison with the results of an elastic-plastic rough surface contact analysis obtained using a finite element method. A method is then developed to model the mixed lubrication problem based on the homogenised Reynolds equation where the effect of the roughness features is isolated from that of the global geometry of the bearing. Local rough problems are solved and the average effect of the roughness on lubricant flow expressed in terms of flow factors, which are functions of global film thickness. When direct asperity contact occurs the deflected shape is obtained from dry contact analysis of the representative roughness area. The global problem is then solved using the Reynolds equation modified with appropriate flow factors taking the mean contact pressure obtained from the local problem into account in load determination. The homogenised method is validated against the series of deterministic solutions and cases of surfaces with measured roughness are presented.

We try to explain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin film equation and existing mathematical theory in the literature are also introduced. To explain the thin film evolution we derive a new family of degenerate parabolic equations. We prove results on existence, uniqueness, long time behavior, regularity and support properties of solutions for this equation. At the end of the thesis we consider the classical thin film Cauchy problem on the whole real line for which we use asymptotic equipartition to show H^1(R) convergence of solutions to the unique self-similar solution.

Thin liquid films driven by surface tension gradients are studied in diverse applications, including the spreading of a droplet and fluid flow in the lung. The nonlinear partial differential equations that govern thin films are difficult to solve analytically, and must be approached through numerical simulations. We describe the development of a numerical solver designed to solve a variety of thin film problems in two dimensions. Validation of the solver includes grid refinement studies and comparison to previous results for thin film problems. In addition, we apply the solver to a model of surfactant spreading and make comparisons with theoretical and experimental results.

High-Frame-Rate Oil Film Interferometry Jonathan Charles White This thesis presents the design and implementation of a high-frame-rate oil film interferometry technique (HOFI) used to directly measure skin friction in time dependent flows. Experiments were performed to determine the ability of a high-speed camera to capture oil film interferometry images. HOFI was found to be able to capture these interferometry images at frequencies up to 105 Hz. Steady laminar and turbulent flows were tested. Transient flows tested consisted of a wind tunnel ramping up in velocity and a laminar boundary layer which was intermittently tripped to turbulence by puffing air out of a pressure tap. Flow speeds ranged from 0 to 108 ft/sec and 10 and 50 cSt Dow Corning 200 dimethylpolysiloxane silicone oil was used. The skin friction was determined from the rate of change of the height of the oil film using lubrication theory. The height of the oil film was determined from the high speed camera interferogram images using a MATLAB script which determined fringe spacing by fitting a four-parameter sine wave to the intensity levels in each image. The MATLAB script was able to determine the height of the oil film for thousands of interferogram images in only a few minutes with sub-pixel error in fringe spacing. The skin friction was calculated using the oil film height history allowing for the direct measurement of skin friction in time dependent flows.

Le frottement à l’interface des surfaces influence les performances des éléments mécaniques. Le frottement a été étudié expérimentalement dans la plupart des études. Dans ce travail, le frottement est prédit à l'aide d'une simulation numérique dans des conditions de contact rugueux avec une lubrification élastohydrodynamique (EHL). La technique classique Multigrille fonctionne bien pour limiter le temps de calcul et les besoins en mémoire. Cependant, le choix de la grille grossière a une influence importante sur la robustesse du code et son efficacité pour résoudre le problème brut. Dans la première partie de ce travail, une méthode de construction de grille grossière proposée par Alcouffe et al. est implémenté dans le code EHL Multigrille indépendamment du temps. Ensuite ce solveur modifié est étendu aux cas transitoires pour résoudre le problème de contact avec rugosité. La courbe de frottement est généralement représentée en fonction du « ratio », le rapport entre l'épaisseur du film d'huile et la valeur moyenne quadratique de la rugosité de la surface. Cependant, ce paramètre est moins approprié pour tracer les variations de frottement dans des conditions de haute pression (régime élasto piézo-visqueux). Dans la deuxième partie de ce travail, le coefficient de frottement est calculé à l'aide du code EHL modifié pour de nombreuses conditions de fonctionnement ainsi que pour les paramètres d'ondulation de surface. Les résultats de la simulation montrent qu'il n'y a pas de courbe de frottement unique lorsque l'ancien paramètre « ratio »est utilisé. En se basant sur la théorie de la réduction d'amplitude, un nouveau paramètre de dimensionnement qui dépend des conditions de fonctionnement et des paramètres d'ondulation est trouvé, ce qui peut donner une courbe de frottement unique pour les situations de haute pression. Pour les surfaces rugueuses plus complexes, une méthode basée sur la densité spectrale de puissance (PSD) est proposée pour prédire les variations de frottement dans la troisième partie de ce travail. La rugosité artificielle de la surface est utilisée pour tester d’abord la méthode de prédiction rapide. Un bon accord est trouvé entre la simulation numérique complète et cette prédiction rapide. La méthode de prédiction rapide est ensuite appliquée pour analyser la variation de frottement de la rugosité de surface mesurée. Le nouveau paramètre d’échelle et l’augmentation du frottement prédite par la méthode PSD montrent une bonne précision technique pour une utilisation pratique
The friction of interfacial surfaces greatly influences the performance of mechanical elements. Friction has been investigated experimentally inmost studies. In this work, the friction is predicted by means of numerical simulation under an elastohydrodynamic lubrication (EHL) rough contact condition. The classical Multigrid technique performs well in limiting computing time and memory requirements. However, the coarse grid choice has an important influence on code robustness and code efficiency to solve the rough problem. In the first part of this work, a coarse grid construction method proposed by Alcouffe et al. is implemented in the current time-independent EHL Multi-Grid code. Then this modified solver is extended to transient cases to solve the rough contact problem. The friction curve is usually depicted as a function of “lambda ratio”, the ratio of oil film thickness to root-mean-square of the surface roughness. However this parameter is less suitable to plot friction variations under high pressure conditions (piezoviscous elastic regime). In the second part of this work, the friction coefficient is computed using themodified EHL code for many operating conditions as well as surface waviness parameters. Simulation results show that there is no single friction curve when the old parameter "lambda ratio" used. Based on the Amplitude Reduction Theory, a new scaling parameter depends on operating condition and waviness parameters is found, which can give a unified friction curve for high pressure situation. For more complex rough surfaces, a power spectral density (PSD) based method is proposed to predict friction variations in the third part of this work. The artificial surface roughness is employed to test the rapid prediction method firstly. Good agreement is found between the full numerical simulation and this rapid prediction. Then the rapid prediction method is applied to analyze the friction variation of measured surface roughness. Both the new scaling parameter and the friction increase predicted by the PSD method show good engineering accuracy for practical use

Il est bien connu que les particules inertielles dans un écoulement périodique ont tendance à se focaliser sur des trajectoires privilégiées. Le but de ce travail de thèse est d'étudier l'influence de cette focalisation sur le transport et la sédimentation de particules dans une fracture plane à rugosité périodique. Tout d'abord, un écoulement monophasique dans une fracture est analysé asymptotiquement dans le cas de faible rugosité. Les résultats classiques de la théorie de la lubrification inertielle sont généralisés au cas de fractures avec des parois asymétriques. Les corrections non linéaires à la loi de Darcy sont calculées explicitement en fonction des facteurs géométriques de la fracture. Le transport de particules dans une fracture horizontal est étudié asymptotiquement dans le cas de particules de faible inertie. Les particules se focalisent sur une trajectoire attractrice, si le débit d'écoulement est assez fort par rapport à la gravité. Un diagramme complet de focalisation a été obtenu, qui prédit l'existence de l'attracteur en fonction du nombre de Froude et des facteurs géométriques de la fracture. Les paramètres quantitatifs du transport ont été calculés également. L'influence de la force de portance sur la migration de particules a été étudiée également. Dans un canal vertical, la portance (provoquée par la gravité) modifie le nombre d'attracteurs et leurs positions. En absence de gravité, la portance peut provoquer une dynamique chaotique des particules. En outre, le captage des particules par une paire de tourbillons a été étudié. Le diagramme d'accumulation obtenu démontre que toute paire de tourbillons peut être un piège à particules
It is well-known that inertial particles tend to focus on preferential trajectories in periodic flows. The goal of this thesis was to study the joint effect of particle focusing and sedimentation on their transport through a model 2D fracture with a periodic corrugation. First, single-phase flow though the fracture has been considered: the classical results of the inertial lubrication theory are revisited in order to include asymmetric fracture geometries. Cubic corrections to Darcy's law have been found analytically and expressed in terms of two geometric factors, describing channel geometry. For weakly-inertial particles in a horizontal channel it has been shown that, when inertia is strong enough to balance out the gravity forces, particles focus to some attracting trajectory inside the channel. The full trapping diagram is obtained, that predicts the existence of such attracting trajectory regime depending on the Froude number and on geometric factors. Numerical simulations confirm the asymptotic results for particles with small response times. The influence of the lift force on particle migration has also been studied. In a vertical channel the lift is induced by gravity and leads to complex trapping diagrams. In the absence of gravity the lift is caused by inertial lead/lag of particles and can lead to chaotic particle dynamics. Finally, for dust particles in a vortex pair it has been shown that particles can be trapped into one or two equilibrium points in a reference frame rotating with the vortices. A full trapping diagram has been obtained, showing that any pair of vortices can trap particles, independently of their strength ratio and the direction of rotation

Mobile Miner 40V is a machine used for rock excavation and developed by Epiroc. This machine is equipped with a large cutter wheel to perform the excavation. After a test run, some surfaces associated with bearings within the cutter wheel were found to be damaged due to scuffing - severe sliding wear. There is a static load applied to the surfaces due to gravity. However, the reason for this damaged issue was believed that there is a large dynamic load applied to the surfaces during the excavation. This dynamic load was not found in a previous FE model used to verify safety issues. Therefore, a new FE model that is more in line with reality, and a failure analysis were required. Additionally, a feasibility study for a cutter wheel with a larger dimension was also needed since a larger cutter wheel is desirable. Firstly, wear mechanisms were reviewed, and some theories were chosen to analyze the damaged issue. Since it was unknown whether the surfaces were well-lubricated or not, both cases were investigated. The Archard wear equation was used to analyze the poor-lubricated situation, while the lubrication number and the Reynolds equation were used to analyze the well-lubricated case. Secondly, contact mechanisms between the surfaces were also investigated. The investigation of the contact mechanisms involved several theories, such as the Hertzian contact theory and the impact load factor. Besides these theoretical analyses, a numerical analysis was performed. Lastly, a new FE model was established in Ansys. Both the cutter wheel which was subjected to scuffing(existing cutter wheel), and the cutter wheel with a larger dimension(larger cutter wheel) were analyzed by the use of the new FE model. The maximum and minimum wear rates obtained by the Archard wear equation are approximately 1.9・10-2mm3/m and 4.8・10-3mm3/m, which are considered as a completely unacceptable level in engineering applications. The maximum and minimum critical loads obtained by the Reynold equation are approximately 1.8kN and 24.8kN, which both are larger than the static load applied to the surfaces. The maximum and minimum critical mean contact pressures obtained by the lubrication number are approximately 65MPa and 240MPa, which both are larger than the mean contact pressure generated by the static load. No evidence shows that there is a large dynamic load applied to the surfaces during the excavation. The largest possible contact pressure on the bearings in the existing cutter wheel is very close to the limit of severely damaged. The largest possible contact pressure on the bearings in the larger cutter wheel is believed to exceed the limit of severely damaged. The previous assumption that the surfaces were damaged due to a large dynamic load was wrong. The obtained results support that the surfaces were only subjected to a static load and were damaged due to inadequate lubrication. The existing cutter wheel is operated safely with the current load cases. However, the forward thrust force is suggested to decrease when the cutting angle is large. There is a high risk if the larger cutter wheel is operated with the current load cases.

L’intérêt pour le recyclage du béton est né d’une volonté d’inscrire le secteur du BTP dans une logique de développement durable. Les granulats de bétons recyclés (GBR) sont constitués de granulats naturels et de pâte de ciment adhérente durcie. La porosité élevée des GBR est à l’origine d’une modification de l’eau efficace du béton au détriment de ses performances aux états frais et durci. Un protocole expérimental basé sur des mesures d’étalement de mortier est proposé pour suivre quantitativement le transfert d’eau entre des sables de GBR et une pâte de ciment fraîche. Ce protocole est testé sur des sables de pâte de ciment (SPC) de rapport eau/ciment (E/C) égal à 0,3, 0,5 et 0,7. Les résultats montrent que le degré de saturation des SPC atteint un maximum avant 6 minutes d’immersion dans une pâte de filler puis reste quasi-constant. Le degré de saturation augmente avec le rapport E/C des SPC mais reste inférieur à 1. De plus, les cinétiques de transfert d’eau vers la porosité des SPC initialement secs immergés dans une pâte de filler ou de ciment sont similaires. Le protocole établi repose sur l’hypothèse d’une corrélation entre le rayon d’étalement et la quantité d’eau efficace du mortier. Afin d’étudier cette corrélation, d’une part, sous l’approximation de lubrification, les seuils d’écoulement des mortiers sont calculés à partir du rayon d’étalement. D’autre part, ces seuils sont calculés avec une approche bi-phasique des mortiers assimilés à des suspensions non colloïdales dans des fluides à seuil. La cohérence entre les deux approches est examinée
The increased interest in concrete recycling results from a willingness to reconcile the construction industry with sustainability. Recycled concrete aggregates (RCA) consist of a mix of natural aggregates and attached cement. The high porosity of RCA modifies the effective water content of a recycled concrete at the expense of its fresh and hardened performances. A testing method based on spread measurements is suggested to follow quantitatively water transfers between RCA sand and a fresh cement paste. This protocol is tested on cement paste sands (CPS) having 0.3, 0.5 and 0.7 water/cement ratios (W/C). Results show that the saturation degree of CPS embedded in a filler paste reaches a maximum no later than 6 minutes then remains quasiconstant. The saturation degree increases with the W/C of CPS ratios but remains less than 1. Moreover, similar water transfer kinetics are found whether initially dry CPS are immersed in a filler or a cement paste. The established protocol assumes a correlation between spread and effective water content of a mortar. In order to study this correlation, on the one hand, under the lubrication approximation, the yield stress of mortars is calculated from their spread radius. On the other hand, yield stress of mortars is calculated using a biphasic modelling of mortars viewed as non-colloidal suspensions in a yield stress fluid. Consistency between the two approaches is examined

Дисертаційна робота присвячена дослідженню впливу гідродинаміки в'язких і аномально в'язких мастильних матеріалів у конічних зазорах зі змінною величиною конусності. Подібні завдання є актуальними при дослідженні конічних опорних підшипників, які знайшли широке застосування в гідротурбінобудуванні та інших сферах гідромашинобудування. Одним з важливих питань у даному напрямку є визначення крутного моменту сил в'язкого тертя в щілинних конічних зазорах. В роботі, проведено критичний аналіз досліджень, присвячених даній темі, зроблено висновок про недостатність досліджень і поставлена задача, розв’язання якої пропонується в даній роботі. На підставі досліджень інших авторів виведені основні критерії подібності, які можуть охарактеризувати цей процес поведінки рідини в зазорі, де одна з поверхонь (внутрішня) може обертатися навколо своєї осі. Проведено фізичне і математичне моделювання поведінки рідини в конічних підшипниках. На підставі експериментальних досліджень були отримані функціональні залежності визначення крутного моменту як функції частоти обертання внутрішнього конуса, в'язкості змащує рідини, ширини щілинного зазору між конічними поверхнями. Отримані результати були зіставлені з аналогічними даними для циліндричних щілинних зазорів (циліндричних підшипників ковзання). Представлені рекомендації по розрахунку основних характеристик потоку. Проведення математичне моделювання дало можливість оцінити ступінь відмінності між результатами експерименту і теорії, пояснити розбіжності в результатах. Одним з найважливіших моментів дослідження є результат, пов'язаний з поведінкою аномально-в'язких рідин (деякі з мастильних матеріалів за своєю поведінкою близькі до рідин, поведінка яких можна описати рівнянням Освальда де Віля). Проведене моделювання процесів, що розглядаються в конічних щілинних зазорах, дало можливість забезпечити раціональний вибір змащувальних матеріалів для зниження моменту тертя (сил тертя) в конічних зазорах.

Diploma thesis deals with a topic of lubrication and cooling of the ball screw rotary nuts. The first part is focused on a research behind the theory of ball screws and ball screw rotary-nuts. The three types of construction were developed in the second half of the thesis. Each construction is designed as an external attachable cooling and lubrication unit, which can be installed on an existing, slightly modified ball screw rotary-nut. For cooling and lubrication, only one type of medium is used and that is a cooled oil. External unit provides medium flow to ball screws working space. On top of diploma thesis tasks a design concept of ball screw rotary-nut with an integrated cooling and lubrication is introduced itself. Both described designs could become interesting for an industrial market.

博士
國立成功大學
材料科學及工程學系
105
In this study, a lubrication theory that includes the coupled effects of anisotropic slip on both the solid-liquid interface, rheology and surface roughness on the lubrication (journal bearing) performance is proposed. A modified average Reynolds equation (modified ARE) as well as Poiseuille and Couette flow rate correctors and the related factors (pressure and shear flow factors, and shear stress factors) are then derived by applying the rheology model, Navier slip boundary conditions and flow factor with orthogonal principal slip lengths ( b ix , b iy ). The results show that the existence of boundary slip can dilute the effects of surface roughness. And contours of constant load ratios are plotted and then the parameters in flow rheology and boundary slip can be located while designing functional surfaces in journal bearings. Finally,a bearing with desired performance can be designed by the processing method of the surface texture.

碩士
國立成功大學
材料科學及工程學系
107
Debye Huckel and nonlinear Poisson-Boltzmann solution is classical solution derived by semi-infinite space boundary conditiom. In this research, Our electric double layer model want to deviate from the topic of classic assumption, and developed a numerical solution for electrical double layer with asymmetric boundary condition instead of symmetric boundary condition. 　　In past study, the electric conductivity in classic Reynold is constant, In our new modified Reynold equation, the electric conductivity varies with temperatue and ionic coconcentration, at the same time, our new modified Reynold equation is derived with asymmetric boundary condition and ionic conservation rule.

A lubrication-flow model for a free film in a corner is presented. The model, written in the hyperbolic coordinate system ξ = x² – y², η = 2xy, applies to films that are thin in the η direction. The lubrication approximation yields two coupled evolution equations for the film thickness and the velocity field which, to lowest order, describes plug flow in the hyperbolic coordinates. A free film in a corner evolving under surface tension and gravity is investigated. The rate of thinning of a free film is compared to that of a film evolving over a solid substrate. Viscous shear and normal stresses are both captured in the model and are computed for the entire flow domain. It is shown that normal stress dominates over shear stress in the far field, while shear stress dominates close to the corner.