| 1. |
- Abdikalikova, Zamira
(författare)
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Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions.Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we prove some new estimates for each function in a Tchebychev system. In order to be able to study compactness of the embeddings from Chapter 3 such estimates are crucial.In Chapter 3 we rewrite and present some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we rewrite and discuss some analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are not available in the Western literatures in this way and they are crucial for the proofs of the main results in Chapter 4. In Chapter 4 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of the spaces. However, with the help of our new embedding theorems we can extend theseresults to the case of strong degeneration.The main aim of Chapter 5 is to establish boundedness and compactness of the embedding considered in Chapter 4.In Chapter 4 basically only sufficient conditions for boundedness of this embedding were obtained. In Chapter 5 we obtain necessary and sufficient conditions for boundedness and compactness of this embedding and the main results are proved in a different way.
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| 2. |
- Aitomäki, Yvonne
(författare)
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Online fibre property measurements : foundations for a method based on ultrasound attenuation
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents the foundations of a method for estimating fibre properties of pulp suitable for online application in the pulp and paper industry. In the pulp and paper industry, increased efficiency and greater paper quality control are two of the industry's main objectives. It is proposed that online fibre property measurements are a means of achieving progress in both of these objectives. Optical based systems that provide valuable geometric data on the fibres and other pulp characteristics are commercially available. However, measurements of the elastic properties of the fibres are not currently implemented using these systems. To fill this gap an ultrasound based system for measuring the elastic properties of the wood fibres in pulp is proposed. Ultrasound propagation depends on the elastic properties of a solid. Hence attenuation measurements from suspensions of fibres depend on their elastic properties. The method is based on solving the inverse problem where the output is known and the objective is to establish the inputs. In this case, attenuation is measured and a model of attenuation based on ultrasound scattering is developed. A search algorithm is used for finding elastic properties that minimize the error between the model and measured attenuation. The results of the search are estimates of the elastic properties of the fibres in suspension. The results show resonance peaks in the attenuation, in the frequency region tested, for fibres with radii of the order of 10 microns. These peaks are found in both the measured and modelled attenuation spectra. Further investigation of these resonances suggests that they are due to modes of vibration in the fibre where the fibre modelled as an infinitely long cylinder. These resonances are shown to aid in the identification of the elastic properties. The attenuation is found to depend heavily on the geometry of the fibres. Hence fibre geometry, which can be obtained from online optical fibre measurement system, provides the key to extracting the elastic properties from the attenuation signal. Studies are also carried out on the effect of viscosity on attenuation as well as the differences in attenuation between hollow and solid synthetic fibres in suspensions. The measurement method is also applied to hardwood and softwood Kraft pulps. The results of these studies show that using the model derived in the thesis and attenuation measurements, estimates of the elastic properties can be obtained. The elastic property estimates for synthetic fibres agree well with values from other methods. The elastic property estimates for pulps require further validation due to the difficulty in comparing between different testing methods and different types of pulp. The conclusions, based on the work so far and under three realisable conditions, are that the shear modulus and the transverse Young's modulus of pulp fibres can be measured. Once these conditions are met a system based on this method can be implemented. By doing this the industry would benefit from the increase in paper quality control and energy saving such system could provide.
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| 3. |
- Alakangas, Lena
(författare)
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Sulphide oxidation, oxygen diffusion and metal mobility in sulphide-bearing mine tailings in Northern Sweden
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Large quantities of sulphide-bearing mining wastes produced from ore processing are deposited throughout the world. Sulphide oxidation in the wastes may release acidic water with high concentrations of metals to the environment. Remediation strategies are usually site specific, since the physical and chemical properties of the wastes vary. Therefore, sulphide oxidation, oxygen diffusion and metal mobility in unoxidised and oxidised, remediated and unremediated wastes have been studied in the present work. The efficiency of different cover systems on unoxidised tailings from Kristineberg, were studied in pilot-scale test cells (5*5*3 m3)under field conditions. Clayey till, sewage sludge, apatite and Trisoplast were used as sealing layers and unspecified till as a protective cover. In one cell tailings were left uncovered. Unoxidised tailings in the test-cells in the initial stage after deposition showed relatively low sulphur release (600- 800 mg/l)in leachate waters, which probably was an effect of high moisture content in the tailings prior to deposition. Near-neutral pH found in the leachates was an effect of neutralisation by carbonate minerals present and lime (Ca(OH)2) added prior to deposition. Similar sulphur concentrations were found also in the uncovered tailings. The sulphide oxidation rate increased with time in the uncovered tailings, and decreased in the covered. The lowest oxygen concentrations were observed below the cover system with sewage sludge, which was the most effective barriar against oxygen in a short-term perspective. The oxygen fluxes through the clayey till and apatite layers were within the same magnitude and varied between 0.5 and 4 mole/year,m2. The Trisoplast layer seemed to have failed as a barrier against oxygen. Tailings studied at field scale at Laver and Kristineberg had oxidised for more than 50 years. The tailings at Kristineberg have high pyrite content (c.25% and 50%) and those at Laver have low grade of pyrrhotite (2-3%). The Laver tailings are unremediated, while at Kristineberg the tailings were remediated in 1996. The transport of metals in the drainage water at Laver decreased during a study period of 8 years. The transport of dissolved sulphur indicated a declining trend of sulphide oxidation rate in the tailings, which was confirmed by oxygen measurements in the tailings and weathering rate estimations. The decline was considered to be natural as a result of the increased distance that oxygen has to travel to reach unoxidised sulphide grains. The major part of the amounts of metals released by sulphide oxidation were secondarily retained in the tailings, and to a small extent in layers cemented by jarosite and Fe-(oxy)hydroxides. Sequential extraction of these layers showed that metals such as Cu and Pb were mostly associated with crystalline Fe-(oxy)hydroxides. Most important retention mechanism was, however, sorption onto minerals surfaces below the oxidation front. The studied Impoundment 1 at Kristineberg was remediated by two different methods; on one part a dry cover consisting of a sealing layer and a protective cover were applied, and the groundwater table was raised and a single dry cover applied on the other part. When the groundwater table was raised in oxidised tailings, secondarily retained metals such as Fe, Mg, Mn, S and Zn were remobilised resulting in increased concentrations in the groundwater. The concentrations declined with time, due to dilution by inflowing uncontaminated water. Decreased concentrations of Fe, Mg, Mn, S and Zn were observed also in the groundwater below the dry cover as the amount of percolating water decreased. The concentrations of trace elements such as Cd, Co, Cr, Cu, Ni and Pb were almost depleted in the groundwater, since these metals were retained within the tailings by mechanisms such as co-precipitation, precipitation and sorption. Analysis of pyrite grains by LA-ICP-SMS showed that pyrite surfaces were important for retention of As and Cu, in particular, but also for Cd and Zn. This study shows that the physico-chemical conditions expressed by pH and redox potential have a large impact on element mobility’s. For example, As was mobilised as a result of remediation, while the concentrations of most metals decreased in the drainage waters.
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| 4. |
- Alander, Sara
(författare)
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Offentliga storkök i det gröna folkhemmet : diffrakterade berättelser om hållbar utveckling
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Det är nu 20 år sedan Brundtlandskommissionens rapport kom ut, och begreppet hållbar utveckling fick sin stora spridning och inter¬nationella uppmärksamhet. Nu, våren 2007, är begreppet inte omdiskuterat på samma sätt som det en gång var, idag är det i stället begrepp som ”klimathotet” som debatteras och får rubriker. Hållbar utveckling har blivit ett bärande begrepp i internationella överenskommelser och det finns också en allt mer akut medvetenhet om att hållbar utveckling fordrar omställningar och förändring av många av de förhållanden och förhållningssätt vi i västvärlden tar för givna. I de dokument som oftast pekas ut som ursprunget till aktualiseringen av hållbar utveckling, Brundtland¬rapporten och Agenda 21, framgår att hållbar utveckling vilar på tre ben; ekologiskt, ekonomiskt och socialt. I avhandlingen fokuseras offentliga sektorns storhushåll som i runda tal serverar 2 600 000 måltider varje dag, knappt 2 100 000 av dessa i grund-, gymnasie- och förskolor (Sundström 2000). Särskilt studeras den måltids¬produktion som sker i samband med skol- och förskoleverksamhet, en verksamhet som de flesta i Sverige i dag på något sätt berörs av. Hållbar måltidsproduktion förutsätter hållbara teknologier och hållbar teknologianvändning och -utveckling, med hänsyn till alla tre dimensionerna av hållbarhet. Hur hållbar utveckling kan relateras till teknologi¬användning inom offentliga sektorns måltidsproduktion har därför undersökts med hjälp av feministisk teknovetenskap. Forskningsfrågorna är: Vilka förutsättningar ger och kräver teknologianvändning i den offentliga sektorns storköks¬verksamhet? Hur rimmar dessa med socio¬kulturell, ekonomisk och ekologisk hållbarhet? För att kunna besvara dessa frågor har avhandlingen ytterligare ett syfte; att, med natur- och teknikvetenskapligt språkbruk experimentera med Donna Haraways figuration "diffraktion" som metodologi och därigenom uppmärksamma den mångfald av kunskaper och röster som är nödvändiga för att skapa hållbarhet som beaktar alla tre aspekterna av hållbar utveckling. I analyserna spelar också "situerade kunskaper" stor roll. Avhandlingens empiri består av deltagande observationer i kommunala storkök, intervjuer med kostchefer samt ledare av projekt för hållbar utveckling i offentliga sektorns måltidsproduktion och dokument. Med hjälp av feministisk teknovetenskap har jag kunnat visa på hur djupt involverad offentliga sektorns måltidsverksamhet är i teknologiska system som både fungerar småskaligt i varje enhet i verksamheten men också hur den är sammanlänkad i de storskaliga infrastrukturella systemen i vårt samhälle. Med feministisk forsknings¬metodologisk ansats har jag också visat på hur hållbar utveck¬ling kan förstås inom offentliga sektorns storköksverksamhet samt vad som kan krävas för att strävan efter hållbar utveckling ska bli lyckosam.I avhandlingsarbetet har jag rört mig mellan en fokusering på teknologiers funktioner och konsekvenser, särskilt med fokus på hållbar utveck¬ling, hanteringen av dem i förändringssammanhang och hur den teknologi¬intensiva måltids¬verk¬samheten i skolor och förskolor har betydelse för arbetet för hållbar utveckling men då inte endast som en följd av att verksamheten direkt blir föremål för resurseffektivisering. I den människotäta verksamhet som offentliga sektorns måltidsproduktion utgör är faktorer som omsorg, hälsa och välbefinnande starkt närvarande. Faktorer som är betydelsefulla för hållbar utveckling med hänsyn till alla dess dimensioner. I begreppet teknovetenskap ligger att kunskapsproduktionen och teknologi¬utvecklingen i dag äger rum i komplexa och utspridda sammanhang där universitet, företag och andra aktörer i samhället, till exempel offentliga sektorn, deltar och påverkar vägvalen, lokalt, nationellt och internationellt. Mot den bakgrunden är det väsentligt att överskrida de gränser som vi ofta drar upp mellan teknologi, vetenskap, politik och samhälle och i stället försöka visa på hur dessa länkas samman i användningen och utvecklingen av teknologi, något som är en nödvändighet för den förändringsaspekt som utmärker feministisk teknovetenskap och som feministiska vetenskapsstudier ofta syftar till. Min fokusering på hur materiella-diskursiva praktiker med en mångfald av apparaturer som teknologier, maskiner, människor, livsmedel, beräknade näringsrekommenda¬tioner etc är djupt involverade i det mer abstrakta som värderingar, skolarbete, inlärningsförmåga, sinnesintryck, förebilder… kan inspirera till ökat engagemang i de senare när förändringar och utveckling av teknologier är på gång. Avhandlingens experimenterade kan beskrivas som samtal mellan policies om hållbar utveckling, offentliga sektorns storkök som praktik, och feministisk teknovetenskap. Dessa samtal ger nya perspektiv som kan ge nya möjligheter i skapandet av hållbar utveckling.
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| 5. |
- Alberg, Henrik
(författare)
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Simulation of welding and heat treatment : modelling and validation
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Many aerospace components with complex geometry are fabricated from smaller parts using joining techniques such as welding. Welding and the heat treatment which usually follows, can result in unwanted deformation and stresses. Expensive materials, tight geometrical tolerances and the need to decrease product and manufacturing development time, cost and associated risks have motivated the development of models and methods for the simulation of manufacturing processes. The work presented concerns methodologies and modelling techniques for the simulation of welding and heat treatment of fabricated aircraft-engine components. The aim of the work was to develop modelling practices to enable the use of finite element analysis for the prediction of deformation, residual stresses and material properties such as microstructure during and after welding and heat treatment. Achieving this aim has required investigation of geometrical discretisation, modelling of boundary conditions and material behaviour for these processes. The case study components were made of a martensitic stainless steel, Greek Ascoloy. Phase evolutions models and models for rate-independent, rate-dependent, and creep were used as the material models in the welding and heat treatment simulations. The work also includes discussion of numerical considerations in material modelling. A toolbox for evaluation of constitutive models and to obtain material parameters for the plasticity models was developed. The heat transfer coefficient is an important parameter for describing energy transfer between the component and a gas. Due to the complexity of the gas flow in the heat treatment furnace during cooling, a method using computational fluid dynamics was developed to obtain an approximate distribution of the heat transfer coefficient. Due to the impact that modelling and simulation predictions can have, the creditability of the computational results are of great concern to engineering designers, managers and other affected by decisions based on these predictions. In this work, a validation methodology for welding and post weld heat treatment models was developed. The model used for welding simulations gives results with the accuracy required for predicting deformation and residual stresses at all stages of the product and manufacturing development process. The heat treatment model predicts deformations and residual stresses resulting from stress relief heat treatment of sufficient accuracy to be used in the concept and preliminary stages of product and manufacturing development. The models and methodology have been implemented, tested and are in use at Volvo Aero.
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| 6. |
- Albing, Malin
(författare)
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Contributions to process capability indices and plots
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents contributions within the field of process capability analysis. Process capability analysis deals with how to assess the capability of processes. Based on process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability indices. This thesis focuses on process capability indices and process capability plots. The thesis consists of six papers and a summary. The summary gives a background to the research area, a short overview of the six papers, and some suggestions for future research. The thesis summary also consists of some new results, not presented in any of the appended papers. In paper I, the frequency and use of process capability analysis, together with statistical process control and design of experiments, within Swedish companies hiring alumni students are investigated. We also investigate what motivates organisations to implement or not implement these statistical methods, and what is needed to increase the use. In papers II-III we generalize the ideas with process capability plots and propose two graphical methods, for deeming a process capable at a given significance level, when the studied quality characteristic is assumed to be normally distributed. In paper II we derive estimated process capability plots for the case when the specification interval is one-sided. In paper III we derive elliptical safety region plots for the process capability index Cpk and its one-sided correspondences. The proposed graphical methods are helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In papers IV-VI we propose a new class of process capability indices designed for the situation with an upper specification limit, a target value zero, and where the studied quality characteristic has a skewed, zero- bound distribution with a long tail towards large values. The proposed class of indices is simple and possesses properties desirable for process capability indices. The results in papers IV-VI are also valid for the situation with a target value, not equal to zero but equal to a natural lower limit of the quality characteristic. Three estimators of the proposed class of indices are studied and the asymptotic distributions of these estimators are derived. We also consider decision procedures, based on the estimated indices, suitable for deeming the process capability at a given significance level. The new results in the summary combines the ideas from paper II with the results in papers IV-VI and a graphical method for the class of indices proposed in IV-VI are derived.
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| 7. |
- Alkebro, Jesper
(författare)
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Multiphase oxide ceramics in the alumina-yttria system
- 2002
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- As a means of creating dispersed multiphase oxide structures, high-energy milling has been used for pre-treating alumina-yttria powder mixtures before pressing and sintering. Processing was performed in a planetary ball mill with steel or alumina milling tools and measured effects of the treatment have served as data for a modeling study. Subsequent phase development and sintering during heat treatment of the milled powders have been examined. Two compositions likely to result in a minority phase dispersed in another phase in equilibrium were selected and subjected to the milling treatment. The two constituent powders were homogenously mixed and defects were injected into the crystal structures which were gradually destroyed. Subsequently, depending on milling parameters, there was either amorphization of the sample or formation of yttrium aluminum perovskite, an intermediate phase of the alumina-yttria system. Alumina milling tools exhibited a higher milling efficiency, but they were prone to chipping which lead to massive contamination. Steel milling tools were worn in a more controlled manner and the total amount of contamination was much lower. In heat treatment milled powders easily attained phase equilibrium and there was no metastable behavior noted. Transformation temperatures fell as a function of milling time but for longer milling times the effects of prolonged processing decreased. Sintering properties were also improved resulting in higher final density and lower sintering temperatures. Iron contamination from steel milling tools was suspected to be detrimental for the final solidification and to cause large porosity, but when oxidized the effect is inversed leading to very good densification in argon atmosphere. Relative densities as high as 96% were measured after sintering 1 h in 1500°C, but the process was sensitive to the environment resulting in poor sintering for oxidizing (air) or reducing (argon in graphite furnace) atmospheres. A dispersion of a second phase in the dominant matrix phase was observed but further improvement of the process should be needed to make it finer. The grain size could be estimated to be around 5 µm from fracture surface images.
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| 8. |
- Allard, Christina
(författare)
-
Two sides of the coin - rights and duties : the interface between environmental law and Saami law based on a comparison with Aoteoaroa/New Zealand and Canada
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The needs of indigenous peoples are related to land, water and other natural resources for sustaining a more or less traditional livelihood. Such needs typically compete with other societal interests. There are, on the one hand, specific interests in exploiting natural resources within traditional indigenous areas, while, on the other hand, concerns regarding conservation and preservation measures of valuable nature areas. This thesis contains two perspectives: an environmental protection perspective and a customary rights perspective. The thesis also contains a comparison of certain aspects of the law in Aotearoa/New Zealand, Canada and Sweden. Although the examination has a comparative approach, Swedish law is in prime focus. The objective is twofold. On the one hand, it includes an analysis of the interface between Saami customary rights, foremost the reindeer herding right, and environmental protection and natural resources legislation. On the other, it analyses and discusses ways in which the legislation may contribute to a sustainable use of land and natural resources within the reindeer herding area in Sweden. In this way, the second part of the objective is a succession of the former. It includes, above all, discussions de lege ferenda with the focus on Swedish environmental law. Evidently, it is the reindeer herding area per se that is in prime focus. Inherent in the examination as a whole, there are, hence, sustainability aspects. A correct comprehension of Saami customary rights is also important to the promotion of a sustainable use of the reindeer herding area. The interrelation of the two legal areas, environmental/natural resources law and aspects of the indigenous law, is, however, more evident with respect to the New Zealand and Canadian laws. Nevertheless, the connection also exists in a Swedish legal context, even though not as emphasised. Hence, there may be a call for a greater interrelation of these two legal areas. While general environmental requirements on the reindeer husbandry are abundant, specific requirements relating to regional or local circumstances are scarce. Such specific provisions may be designed to promote sustainability objectives better and, at the same time, to take into account specific Saami interests. Given the many conflicting land uses in the reindeer herding area, a stricter order of preferences taken on a strategic level generally provides advantages. Now, decisions are commonly left to be solved on a case by case basis with little guidance. Despite many shortcomings in specific legislation, above all, a regional and comprehensive environmental planning would greatly support the goal of sustainable uses of the land and resources in the area.
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| 9. |
- Almqvist, Andreas
(författare)
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On the effects of surface roughness in lubrication
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Tribology is a multidisciplinary field defined as the science and technology of interacting surfaces in relative motion, and embraces the study of friction, wear and lubrication. A typical tribological application is the rolling element bearing. Tribological contacts may also be found in other types of bearings, cam-mechanisms, gearboxes and hydraulic systems. Examples of bearings inside the human body are the operation of the human hip joint and the contact between teeth during chewing. To fully understand the operation of this type of application one has to understand the couplings between the lubricant fluid dynamics, the structural dynamics of the bearing material, the thermodynamical aspects and the resulting chemical reactions. This makes modeling tribological applications an extremely delicate task. Because of the multidisciplinary nature, such theoretical models lead to mathematical descriptions generally in the form of non-linear integro-differential systems of equations. Some of these systems of equations are sufficiently well posed to allow numerical solutions to be carried out, resulting in accurate predictions on performance. In this work, the influence on performance of a surface microscopical nature, the surface roughness, in contact interfaces between different types of machine element components is the subject of study. An example is the non-conformal lubricated contact between one of the rollers and the inner ring in a rolling element bearing. The tribological contact controlling the operation of the human hip joint is also very similar to this. Another example of a non-conformal contact occurs when driving on rainy roads, where the hydrodynamic action of the water separates the tire. To enable investigations of these types of problems, different theoretical models were studied; for the selected model, a numerical solution technique was developed within this project. This model is based on the Reynolds equation coupled with the film thickness equation. The numerical solution technique involves a multilevel technique to facilitate the solution process. Results presented in this thesis, utilizing this approach, study elementary surface features such as ridges and indentations passing each other inside the lubricated conjunction. The Reynolds equation is derived under the assumptions of thin fluid film and creeping flow, and considers in its most general form shear thinning of the lubricant. This type of equation describes the hydrodynamic action of the lubricant flow and may be used when the interfaces consist of either conformal or non-conformal conjunctions. Examples of applications having conformal interfaces are thrust- and journal- bearings or the contact between the eye and a (optical) contact lens. In such types of applications the load carried by the interface is distributed over a fairly large area that under certain circumstances helps to prevent mechanical deformation of the contacting surfaces. Such applications are said to operate in the hydrodynamic lubrication (HL) regime. Lubricant compressibility and cavitation are important aspects and have received some attention. However, the main objective when modeling HL has been to investigate and develop methods that enable the influence of surface roughness to be to be studied efficiently. Homogenization is a rigorous mathematical concept that when applied to a certain problem may be regarded as an averaging technique as well as it provides information about the induced effects of local surface roughness. Homogenization inflicts no restrictions on the surface roughness representation other than the representative part of the chosen surface roughness being assumed periodically distributed and of course the assumptions of thin film flow made through the Reynolds equation. The homogenization process leads to a two sets of equations one for the local scale describing surface roughness, scale and one for the global scale describing application geometry. The unequivocally determined coefficients of the global problem, which may be regarded as flow factors, are obtained through the solution of local problems. This makes homogenization an eminent approach to be used investigating the influence of surface roughness on hydrodynamic performance. In the present work, homogenization has been used to derive computationally feasible forms of problems originating from incompressible and compressible Reynolds type equations that describe stationary and unstationary flows in both cartezian and cylindrical co-ordinates. This technique enables simulations of surface roughness induced effects when considering surface roughness descriptions originating from measurements. Moreover, the application of homogenization facilitates the interpretation of results. Numerical investigations following the homogenization process have been carried out to verify the applicability of homogenization in hydrodynamic lubrication. Homogenization has also been shown here to enable efficient analysis of rough hydrodynamically lubricated problems. Also of note, in connection to the scientific contribution within tribology, collaboration with a group in applied mathematics has lead to the development of novel techniques in that area. These ideas have also been successfully applied, with some results presented in this thesis. At start-ups, the contact in a rolling element bearing could be both starved and drained from lubricant. In this case the hydrodynamic action becomes negligible in terms of load carrying capacity. The load is carried exclusively by surface asperities, the tribo film, or both. This is hereby modeled as the unlubricated frictionless contact between rough surfaces, i.e. a contact mechanical approach. A variational principle was used in which the real area of contact and the contact pressure distribution minimize the total complementary potential energy. The material model is linear elastic-perfectly plastic and the energy dissipation due to plastic deformation is accounted for. The numerics of this contact mechanical approach involve the fast Fourier transformation (FFT) technique in order to facilitate the solution process. Investigation results of the contact mechanics of realistic surfaces are presented in this thesis. In this investigation the variation in the real area of contact, the plasticity index and some surface roughness parameters due to applied load were studied.
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| 10. |
- Almqvist, Torbjörn
(författare)
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Computational fluid dynamics in theoretical simulations of elastohydrodynamic lubrication
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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).
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