Elastohydrodynamic lubrication (EHL) allows transfer of power and forces in gears and rolling bearings without surface-to-surface contact and is the basis for a continuously variable transmission studied in this report. Previous research constructed models and derived solution methods, but often lacked full explanations of the approach and was usually applied to limited and specific cases. This report precisely develops the numerical solution of EHL contact and includes the more general cases of elliptical contacts and side-slip. The model and numerical method are validated on known benchmark cases and test results. Side-slip is investigated and the results shown in this report. Finally, the model is used to determine the film thickness and pressure of a contact patch under identical conditions to that in a physical drive developed by Fallbrook Technologies in Austin, TX. A minimum film thickness of 0.8978 [mu]m is found, setting a benchmark for the maximum allowable surface roughness values to prevent surface-to-surface contact. Additionally, under normal drive conditions the film thickness to surface roughness ratio is in the range of ideal values for maximum life. / text

Internal combustion (IC) engines used in road transport applications employ pistons to convert gas pressure into mechanical work. Frictional losses abound within IC engines, where only 38- 51% of available fuel energy results in useful mechanical work. Piston-bore and ring-bore conjunctions are fairly equally responsible for circa 30% of all engine friction - equivalent to 1.6% of the input fuel each. Therefore, reduction in piston assembly friction would have a direct impact on specific performance and / or fuel consumption. In motorsport, power outputs and duty cycles greatly exceed road applications. Consequently, these engines have a shorter useful life and a high premium is placed on measures which would increase the output power without further reducing engine life. Reduction of friction offers such an opportunity, which may be achieved by improved tribological design in terms of reduced contact area or enhanced lubrication or both. However, the developments in the motorsport sector are typically reactive due to a lack of relative performance or an ad-hoc reliance, based upon a limited number of actual engine tests in order to determine if any improvement can be achieved as the result of some predetermined action. A representative scientific model generally does not exist and as such, investigated parameters are often driven by the supply chain with the promise of improvement. In cylinder investigations are usually limited to bore surface finish, bore and piston geometrical form, piston skirt coatings and the lubricant employed. Of these investigated areas newly emerging surface coatings are arguably seen as predominate. This thesis highlights a scientific approach which has been developed to optimise piston-bore performance. Pre-existing methods of screening and benchmarking alterations have been retained such as engine testing. However, this has been placed in the context of validation of scientifically driven development. A multi-physics numerical model is developed, which combines piston inertial dynamics, as well as thermo-structural strains within a thermoelastohydrodynamic tribological framework. Experimental tests were performed to validate the findings of numerical models. These tests include film thickness measurement and incylinder friction measurement, as well as the numerically-indicated beneficial surface modifications. Experimental testing was performed on an in-house motored engine at Capricorn Automotive, a dynamometer mounted single-cylinder 'fired' engine at Loughborough University, as well as on other engines belonging to third party clients of Capricorn. The diversity of tests was to ascertain the generic nature of any findings. The multi-physics multi-scale combined numerical-experimental investigation is the main contribution of this thesis to knowledge. One major finding of the thesis is the significant role that bulk thermo-structural deformation makes on the contact conformity of piston skirt to cylinder liner contact, thus advising piston skirt design. Another key finding is the beneficial role of textured surfaces in the retention of reservoirs of lubricant, thus reducing friction.

Automotive industry is faced with numerous power train Noise, Vibration and Harshness issues. Particularly, in the driveline area of vehicles a noise commonly referred as differential axle whine which is a tonal response and becomes apparent under cruising conditions. This is one of the key concerns in rear wheel drive commercial vehicles. Although not a failure state, it is regarded as a quality issue and a source of annoyance, which can lead to warranty concerns. The associated cost of palliation to Ford Motor Company was estimated to be $25,000,000 in 2003. There have been several ways of studying axle whine through experimentation and numerical analysis. In this thesis, a new approach for investigating axle whine is highlighted, which is more integrative and detailed. Multi-body dynamics model of a light truck s driveline is developed with all the appropriate components, using constrained Lagrangian dynamics. Component flexibility is included for driveshaft pieces, rear axle half-shafts and the suspension elements. The connectivity of the components is accurately modelled such as the floating effect of rear half-shafts, linear bushings between driveline components to chassis connections, as well as the non-linear effect of tapered roller bearings, supporting the wheel hubs and gears. Furthermore, integrated to the previously described large scale model a detailed hypoid gear pair model is devised. This incorporates micro-scale physics for tooth contact analysis to predict geometric properties and deflections for the gear pair. At the same time thermo-elastohydrodynamic lubrication theory with non-Newtonian friction is applied. All these phenomena at different physical scales, such as large displacement rigid body dynamics and analytical equations for the detailed model are solved simultaneously, all within the same modelling environment. This multi-physics, multi-scale approach has not hitherto been reported in the literature, and constitutes a significant contribution to knowledge. Comparative studies of the model predictions and detailed vehicle tests are carried out, the combination of which points to resonant conditions in system responses and flexible component behaviour, coincident with the adverse conditions in the hypoid gear meshing. It is shown that vehicle drive and coast conditions, promoting teeth pair separations lead to irregular (improper) meshing of the differential gears. Such conditions induce impulsive actions that promote the axle whine phenomenon. This is a major finding of the research and contributes to a better understanding of the axle whine problem.

In electromagnetic launcher (EML) systems, the behavior of the materials and forces at the armature-rail interface involves fluid mechanics, electromagnetics, thermal effects, contact mechanics and deformation mechanics. These factors must interact successfully in order for a launch to be successful. A lubricant film either deposited on the rails prior to launch or injected from the armature during launch has been suggested as a means of improving the electrical conductivity of the rail-armature interface and of avoiding the occurrence of arcing. The fluid pressure generated by such film, together with the magnetic force, the contact force and the uneven temperature field in the armature, deforms the armature and changes the interface gap shape. An analytical model to study the interfacial behavior under these influences is necessary in order to predict the performance of a potential EML design and to provide optimization information. Studies of this interfacial behavior have been done by a number of researchers. However, many critical factors were not included, such as surface roughness, cavitation, injection, magnetic lateral force, interface deformation and thermal effects. The three models presented in this study investigate the influence of those factors on the EML interface problem. The magneto-hydrodynamic (MHD) model establishes a description of the lubrication process under electromagnetic stress but neglects interface deformation. The magneto-elastohydrodynamic (MEHD) model extends the MHD model by considering the lateral magnetic force, interface contact force and elastic deformation. Finally, the magneto-elastothermohydrodynamic (METHD) model adds the thermal effects to the deformation analysis. A coupled analysis of the interface behavior with the METHD model is developed and the history of a typical launch is studied. Detailed injection, lubrication and launch processes are revealed and the performance is predicted. A failed launch is simulated and the cause of failure is identified to be debris left on the rails. Several operation and design parameters, such as rail surface profile, electric current pattern, reservoir load, lubrication length, pocket size and geometry, injection conduit diameter, are analyzed and a recommended injection design procedure is developed. A scaling study is performed by doubling the dimensions to predict the scaling effects. In the end, the base case configuration and scaled configuration are optimized using the technique developed in this study.

[pt] Neste trabalho, apresenta-se uma modelagem numérica de um problema de contato unilateral com acoplamento elasto-hidrodinâmico. Emprega-se estruturas elásticas de baixa rigidez e apresenta-se o escoamento pela equação da lubrificação de Reynolds. O método dos elementos finitos é usado para discretização da estrutura e do campo de pressão hidrodinâmica. Um procedimento numérico para solução do problema proposto também é apresentado, que se baseia na projeção viável da direção de busca. O objetivo principal do trabalho é desenvolver uma ferramenta numérica para estudar as forças que oferecem resistência ao movimento de um pig em seu movimento no interior do duto. / [en] This work is concerned with numerical modeling of the unilateral contact problem involving low stiffness structures and a rigid surface under conditions of hydrodynamic lubrication. Reynolds fluid film lubrication theory is employed. The Finite Element Method is applied in the discretization of both the structure and the hydrodynamic pressure field. A numerical procedure to solve the proposed problem, based on the feasible projection search direction approach, is presented. The main motivation for the work reported in this dissertation is to develop a numerical tool to model the resistance forces acting against the motion of cleaning and inspecting pigs in pipelines.

Diploma thesis deals with elastohydrodynamic lubrication of point contacts, which surfaces are influenced by topography and velocity vector of one rubbing surface is misaligned. Author summarizes knowledge of previously published research articles, which fundamentally enrich current state of knowledge. Diploma thesis contains experimental measurement results of the film thickness and the way of lubrication film formation in elliptical contact for different ellipticity parameters, kinds of rubbing surfaces and angles of the velocity vector. New findings have helped to better understand the behaviour of highly loaded lubricated contacts taking place in machine components and completed the current state of knowledge with results that can be used in next thorough study of this issue.

[pt] O processo de revestimento por Extrusão é amplamente usado nos processo de manufatura de diferentes produtos. Em geral a mínima espessura de filme que pode ser obtida é proporcional à distância entre a barra de revestimento e o substrato (usualmente apoiado por um cilindro rígido) e inversamente proporcional à viscosidade do líquido. Na prática, existe uma distância mínima de operação, tipicamente em torno de 100 m, abaixo da qual o processo torna-se perigoso com o risco de colisão do cilindro de apoio com a barra e de quebra do substrato. Conseqüentemente, existe um limite da menor espessura de filme que pode ser depositada, principalmente no caso de líquidos de alta viscosidade. Uma solução comum é usar um cilindro rígido de apoio coberto com uma camada de borracha, que se deforma durante a operação. O líquido na região de aplicação produz uma pressão suficiente para deformar a camada elástica, mudando a geometria do escoamento, caracterizando uma interação elastohidrodinâmica. Apesar de muito usado na indústria, o conhecimento fundamental deste processo é bastante limitado. O entendimento desta interação líquido/sólido é vital para a otimização deste processo de revestimento. Um modelo teórico para descrever este processo deve considerar o escoamento viscoso, a deformação do cilindro e os efeitos da superfície livre a fim de predizer o comportamento do escoamento e conseqüentemente os limites de operação do processo. Uma análise teórica é apresentada neste trabalho, que consiste em resolver a equação de Navier-Stokes para descrever escoamento com superfície livre acoplado a um arranjo de molas para modelar a deformação da camada elástica. O sistema de equações foi resolvido pelo método Galerkin/MEF. O sistema de equações algébrica não-linear resultante foi resolvido pelo método de Newton. Os resultados indicam como os parâmetros de operação, as propriedades do líquido e da cobertura do cilindro afetam os limites de operação do processo. / [en] Slot coating is largely used in the manufacturing process of many products. In general, the minimum thickness that can be coated is proportional to the gap between the coating die and the substrate (usually backed- up by a rigid roll) and inversely proportional to the liquid viscosity. Therefore, in order to obtain thin films with liquid of high viscosity, a very small gap would be necessary. In practice, the clearance between the die and the web has to be large enough to avoid the risk of clashing two hard surfaces. A common solution is the use a backup rolls covered with an elastomeric layer. The liquid in the coating bead develops high enough pressure to deform the resilient cover, which changes the geometry of the flow, characterizing an elastohydrodynamic action. The understanding of the flow is vital to the optimization of this widely used coating method. Theoretical model has to take into account the viscous flow, the roll deformation and the free surface effects in order to predict the flow behavior. A theoretical analysis is presented here, that consisted of solving the Navier-Stokes equation to describe the free surface flow coupled with an array of springs to model the elastic cover deformation. The equation system was solved by the Galerkin / Finite element method. The resulting set of non- linear algebraic equations was solved by Newton´s method. The results indicate how different operating parameters, liquid and roll cover properties affect the flow.

Automotive transmission rattle is the noise generated due to impacts between manual transmissions meshing gear teeth in the presence of backlash. It is considered to be a Noise, Vibration and Harshness (NVH) phenomenon and is originated due to combustion irregularities (engine order vibrations), especially in diesel vehicles. This thesis focuses in the case of creep rattle for the MMT6 Ford Getrag transmission (six speeds plus reverse) with a DW10b, 4-cylinder, 4-stroke, 2.0 litres diesel engine. This particular rattle condition is fundamentally similar to any other where an engaged gear is pertained (drive, over-run or float), with the 1st or 2nd gear engaged at a very low engine speed. The numerical models include an initial single degree of freedom (DoF) simulation. It comprises either of the engaged gear pair under Hertzian contact conditions or of a loose gear pair under hydrodynamic regime of lubrication. Once the validity of this model is established and correlated with the results obtained from a single gear pair test rig, simulations of increasing complexity can be envisaged. A 7 DoF numerical model is, therefore, developed. The Hertzian contact model still prevails for the engaged gear pair, whereas an analytical hydrodynamic solution is implemented for the remaining 6 loose gear wheels and Petrov s law is applied to the needle bearings retaining the gear wheels. With the aim of accommodating a fully lubricated model of all the tribological conjunctions, an analytical elastohydrodynamic (EHL) Grubin type algorithm is employed. Also, the energy equation is analytically solved for hydrodynamic and elastohydrodynamic conjunctions, based on the assumptions dictated by the Peclet number. Therefore, under hydrodynamic conditions, the energy equation is governed by viscous heating and convective cooling, whereas in the EHL conjunctions the governing terms are viscous and compressive heating, together with conductive cooling. The retaining needle bearings follow the same heat generation mechanism as journal bearings. The effective viscosity, as obtained from the Houpert s equation accounting for pressure and thermal effects, is fundamental for the study of the friction in the contact. The hydrodynamic contacts are only governed by viscous friction, whereas EHL conjunctions exhibit asperity iv interactions as well as viscous effects. The results obtained from this new 7 DoF model are then compared to the experimental measurements taken from the vehicle tests and various purpose-built drivetrain rigs. A metric named Impulsion Ratio is hereby introduced, aiming to shed some light into the predictions obtained by the various models presented. This metric is the ratio of driving over resistive forces acting on each individual gear wheel. Its use is tested to predict single or double-sided rattle scenarios and, therefore, ascertaining higher and lower rattle levels. The 13 DoF model from which these conclusions were obtained includes shafts planar translation and rocking moments. The rolling element bearings supporting the shafts are, therefore, modelled to capture the inherent frequencies arising from their motion. The final model introduces the effects of transient thermo-elastohydrodynamics. This 7 DoF dynamic model accounts for a numerical solution of Reynolds equation with Elrod s cavitation algorithm for simultaneous teeth in mesh. The results obtained validate the previously used Grubin assumption by comparing the predicted central film thickness along the full mesh of one tooth. Also, the effect of starved input conditions and thermal and isothermal solutions are studied.

A prevalent morphology in the microscopic world of artificial microswimmers, bacteria and viruses is that of a helix. The intriguingly different physics at play at the small scale level make it necessary for bacteria to employ swimming strategies different from our everyday experience, such as the rotation of a helical filament. Bio-inspired microswimmers that mimic bacterial locomotion achieve propulsion at the microscale level using magnetically actuated, rotating helical filaments. A promising application of these artificial microswimmers is in non-invasive medicine, for drug delivery to tumours or microsurgery. Two crucial features need to be addressed in the design of microswimmers. First, the ability to selectively control large ensembles and second, the adaptivity to move through complex conduit geometries, such as the constrictions and curves of the tortuous tumour microvasculature. In this dissertation, a mechanics-based selective control mechanism for magnetic microswimmers is proposed, and a model and simulation of an elastic helix passing through a constricted microchannel are developed. Thereafter, a theoretical framework is developed for the propulsion by stiff elastic filaments in viscous fluids. In order to address this fluid-structure problem, a pertubative, asymptotic, elastohydrodynamic approach is used to characterise the deformation that arises from and in turn affects the motion. This framework is applied to the helical filaments of bacteria and magnetically actuated microswimmers. The dissertation then turns to the sub-bacterial scale of bacteriophage viruses, 'phages' for short, that infect bacteria by ejecting their genetic material and replicating inside their host. The valuable insight that phages can offer in our fight against pathogenic bacteria and the possibility of phage therapy as an alternative to antibiotics, are of paramount importance to tackle antibiotics resistance. In contrast to typical phages, flagellotropic phages first attach to bacterial flagella, and have the striking ability to reach the cell body for infection, despite their lack of independent motion. The last part of the dissertation develops the first theoretical model for the nut-and-bolt mechanism (proposed by Berg and Anderson in 1973). A nut being rotated will move along a bolt. Similarly, a phage wraps itself around a flagellum possessing helical grooves, and exploits the rotation of the flagellum in order to passively travel along and towards the cell body, according to this mechanism. The predictions from the model agree with experimental observations with respect to directionality, speed and the requirements for succesful translocation.

Une lubrification suffisante est essentielle au bon fonctionnement des mécanismes et/ou composants comme par exemple les paliers à roulement. Par contre, les lubrifiants contiennent souvent des débris d’usure ou des polluants extérieurs. Ces particules micrométriques peuvent pénétrer des contacts d’épaisseur inférieure au micromètre induisant des empruntes ou indents pouvant conduire à des endommagements irréversibles pour les surfaces en contact. L’objet de ce travail est l’étude du piégeage de polluants solides à l’aide de particules sphériques d’acier, d’un point de vue théorique, numérique et expérimental. Dans un premier temps, une étude phénoménologique a été proposée à l’aide d’une nouvelle méthode expérimentale basée sur la technique PIV combinée à un tribomètre bille/disque. Les trajectoires des polluants à l’entrée du contact ont pu ainsi être identifiées. En parallèle, un modèle numérique d’écoulement du lubrifiant a été développé pour permettre l’évaluation des conditions menant au piégeage ou non de particules. Finalement, des expériences sur une machine bi-disques en conditions de lubrification polluée contrôlée ont permis de valider les tendances observées pour le piégeage. Une première série de résultats a montré que le piégeage de contaminants est fortement dépendant du profil de vitesse du lubrifiant. Un taux de piégeage très hétérogène a été observé sur des contacts avec une ellipticité transverse à l’écoulement variable. De manière surprenante, malgré une augmentation de la largeur de contact, une forte diminution du nombre de particules piégées a été observée dans des contacts elliptiques. Il a été démontré que cette diminution pouvait être imputée à la présence d’importants reflux de lubrifiant dans les contacts elliptiques larges. L’étude de contacts hybrides, nitrure de silicium–acier, a montré une bonne résistance à l’indentation du nitrure de silicium. Il est à noter que les contacts hybrides présentent des niveaux de piégeage similaire à un contact tout acier. / Contact lubrication is essential in a wide range of mechanical systems like rolling element bearings (REBs). A minimum quantity of clean lubricant all along the bearing life is necessary but difficult to ensure. In fact, lubricants contain inevitably wear debris or external particles, like dust. Carried by the lubricant in the vicinity of elastohydrodynamic (EHD) contacts, particles can be entrapped with disastrous consequences for contacting surfaces. Entrapment of micrometric particles in submicrometric contacting gaps means irreversible damages for the surfaces. Damages weaken the surfaces and reduce significantly the REBs lifetime. The goal of this work is to analyze the critical particle entrainments in the contact inlet. Entrapment of steel spherical particles was investigated from the numerical and experimental point of view. Firstly, the phenomenology of entrapment was explored with a new experimental method based on Particle Image Velocimetry (PIV) technique installed on a tribometer. It enabled the evaluation of velocity profiles in the contact inlet and the tracking of particles within EHD contacts. Secondly, a numerical modelling of the inlet flow for EHD contacts, including the particle tracking, was developed. Finally, tests on a twin-disc machine with a controlled level of well-defined contamination were conducted to validate previous conclusions. A first set of results showed that particle entrapment is highly dependent on the lubricant velocity profile. Depending on contact geometry, from point to wide elliptical contacts, different entrapment probability were revealed. Surprisingly, increasing contact width with wide elliptical contacts leads to a drop of entrapped particles. It was demonstrated that this phenomenon is due to backflows occurring upstream from these contacts. Introducing a hybrid pair of contacting materials (silicon nitride–steel), dents on the surfaces due to entrapped particles were explored. It has been confirmed that silicon nitride surface offers a real ability to resist to indentation. It was also noticed that the entrapment probability for silicon nitride–steel contacts is equivalent to a steel–steel one.