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Accurate estimation of the coefficient of friction (CoF) is essential to accurately modeling railroad dynamics, reducing maintenance costs, and increasing safety factors in rail operations. The assumption of a constant CoF is popularly used in simulation studies for ease of implementation, however many evidences demonstrated that CoF depends on various dynamic parameters and instantaneous conditions. In the real world, accurately estimating the CoF is difficult due to effects of various uncertain parameters, such as wheel and rail materials, rail roughness, contact patch, and so on. In this study, the newly developed 3-D nonlinear CoF model for the dry rail condition is introduced and the CoF variation is tested using this model with dynamic parameters estimated from the wheel-rail simulation model. In order to account for uncertain parameters, a stochastic analysis using the polynomial chaos (poly-chaos) theory is performed using the CoF and wheel-rail dynamics models. The wheel-rail system at a right traction wheel is modeled as a mass-spring-damper system to simulate the basic wheel-rail dynamics and the CoF variation. The wheel-rail model accounts for wheel-rail contact, creepage effect, and creep force, among others. Simulations are performed at train speed of 20 m/s for 4 sec using rail roughness as a unique excitation source. The dynamic simulation has been performed for the deterministic model and for the stochastic model. The dynamics results of the deterministic model provide the starting point for the uncertainty analysis. Six uncertain parameters have been studied with an assumption of 50% uncertainty, intentionally imposed for testing extreme conditions. These parameters are: the maximum amplitude of rail roughness (MARR), the wheel lateral displacement, the track stiffness and damping coefficient, the sleeper distance, and semi-elliptical contact lengths. A symmetric beta distribution is assumed for these six uncertain parameters. The PDF of the CoF has been obtained for each uncertain parameter study, for combinations of two different uncertain parameters, and also for combinations of three different uncertain parameters. The results from the deterministic model show acceptable vibration results for the body, the wheel, and the rail. The introduced CoF model demonstrates the nonlinear variation of the total CoF, the stick component, and the slip component. In addition, it captures the maximum CoF value (initial peak) successfully. The stochastic analysis results show that the total CoF PDF before 1 sec is dominantly affected by the stick phenomenon, while the slip dominantly influences the total CoF PDF after 1 sec. Although a symmetric distribution has been used for the uncertain parameters considered, the uncertainty in the response obtained displayed a skewed distribution for some of the situations investigated. The CoF PDFs obtained from simulations with combinations of two and three uncertain parameters have wider PDF ranges than those obtained for only one uncertain parameter. FFT analysis using the rail displacement has been performed for the qualitative validation of the stochastic simulation result due to the absence of the experimental data. The FFT analysis of the deterministic rail displacement and of the stochastic rail displacement with uncertainties demonstrates consistent trends commensurate with loss of tractive efficiency, such as the bandwidth broadening, peak frequency shifts, and side band occurrence. Thus, the FFT analysis validates qualitatively that the stochastic modeling with various uncertainties is well executed and is reflecting observable, real-world results. In conclusions, the development of an effective model which helps to understand the nonlinear nature of wheel-rail friction is critical to the progress of railroad component technology and rail safety. In the real world, accurate estimation of the CoF at the wheel-rail interface is very difficult since it is influenced by several uncertain parameters as illustrated in this study. Using the deterministic CoF value can cause underestimation or overestimation of CoF values leading to inaccurate decisions in the design of the wheel-rail system. Thus, the possible PDF ranges of the CoF according to key uncertain parameters must be considered in the design of the wheel-rail system. / Ph. D.

A eficiência dos sistemas mecânicos é influenciada diretamente pelo coeficiente de atrito local, sendo este relacionado com os regimes de lubrificação. O coeficiente de atrito pode ser estudado usando o método de elementos finitos (MEF) com a finalidade de substituir ensaios experimentais e reduzir tempo de análise. Esta dissertação teve como objetivo desenvolver uma metodologia para avaliar o coeficiente de atrito em um par tribológico e seu efeito na eficiência por simulação numérica. Para esta modelagem foi definido um sistema composto por um par de engrenagens helicoidais. Em uma primeira análise, foi empregado o programa AVL Excite Power Unit, que utiliza a ferramenta MBD (Multi-Body Dynamic - Dinâmica de Multi-Corpos), possibilitando a simulação da transmissão com seus principais elementos em um modelo 1D, que leva em consideração a teoria da lubrificação elastohidrodinâmica (EHL). Também foi utilizado o programa Abaqus®, da Dassault Systèmes, para a criação de um modelo 3D, que considera o par engrenado e sendo necessário o desenvolvimento de uma subrotina para a aplicação do modelo de lubrificação da literatura. Em todas as simulações foram considerados condições de operação de um banco de provas e três diferentes acabamentos superficiais dos dentes das engrenagens em função do processo de fabricação: fresamento, retificação e polimento. Além da rugosidade, avaliou-se o efeito da velocidade angular nas perdas do sistema. O modelo 3D foi comparado com o modelo 1D e com resultados de eficiência de ensaios de banco de prova. O modelo 3D permitiu avaliar o coeficiente de atrito local na linha de contato do dente engrenado. Maiores velocidades angulares aumentaram a espessura de específica de filme, diminuindo assim o coeficiente de atrito e promovendo uma melhoria na eficiência do sistema. Os menores valores de coeficiente de atrito estão na região do diâmetro primitivo, onde o SRR é nulo. A velocidade angular influenciou mais do que a rugosidade. As análises dos modelos 1D e 3D indicaram que o modelo 1D superestima a eficiência da transmissão, enquanto que o modelo 3D apresentou resultados compatíveis com o banco de provas. / The efficiency of mechanical systems is influenced directly by the local friction coefficient, which is related to the lubrication regimes. The coefficient of friction can be studied using the finite element method (FEM) to replace experimental tests and reduce analysis time. This dissertation had the objective to develop a methodology to evaluate the coefficient of friction in a tribological pair and the effect on the efficiency by numerical simulation. In this model, a system composed of a pair of helical gears was defined. In a first analysis, the AVL Excite Power Unit software was used, which uses the tool MBD (Multi-Body Dynamic), enabling the simulation of the transmission with the main elements in a 1D model, which takes into account the theory of elastohydrodynamic lubrication (EHL). The Abaqus® software was used to create a 3D model, which considers the pair of helical gear and a developed subroutine for application of the literature lubrication model. In all simulations, the conditions of operation of a rig tests and three different surface finishes of the gear teeth were considered, depending on the manufacturing process: milling, grinding and polishing. Besides the roughness, the effect of angular velocity on the losses of the system was evaluated. The 3D model was compared with the 1D model and with the results of rig tests efficiency. The 3D model allowed to evaluate the coefficient of local friction in the contact line of the tooth. Higher angular velocities increased the film specific thickness, thus reducing the coefficient of friction and promoting an improvement in the efficiency of the system. The lowest values of coefficient of friction are in the region of the primitive diameter, there the SRR is zero. The angular velocity influenced more than the roughness. The analyzes of the 1D and 3D models indicated that the 1D model overestimates the transmission efficiency, while the 3D model presented results compatible with the rig tests.

Uma parte significativa das perdas por atrito num motor automotivo resulta da ação de partículas abrasivas. Dentre as fontes possíveis, podem ser citados o próprio meio ambiente - partículas que passam pelo filtro de ar - o desgaste de partes metálicas do motor ou mesmo resíduos de combustão. Essas partículas podem ficar encrustadas em anéis do pistão, ou ficar na interface entre pistão e bloco ou camisa, e são responsáveis por sulcos axiais, na direção do movimento do pistão, observáveis em motores usados. O objetivo deste trabalho foi obter um melhor entendimento dos mecanismos de desgaste relacionados com o sulcamento de camisa/bloco e identificar conjuntos de testes laboratoriais capazes de reproduzi-los sob condições controladas. Amostras de ferro fundido cinzento (FoFo) e de aço AISI 1070 com dureza de matriz próxima daquela encontrada em FoFo (?200HV30) foram submetidas a ensaios de riscamento em tribômetros. Verificou-se que riscos executados com um endentador cônico submetido a cargas na faixa de 20 a 50 mN eram similares aos sulcos observados em camisas ou blocos. Ensaios com outros materiais, como alumínio e latão e mesmo aço de diferentes durezas contribuíram para melhorar o entendimento dos resultados. Não foi observada transição brusca entre mecanismos de abrasão. O cálculo do fator de remoção de material, fab, a partir de perfilometria óptica resultou em valores com dispersão elevada; não foi possível associa-los aos diferentes mecanismos de abrasão observados. Valores obtidos para o coeficiente de atrito no riscamento permitiram fazer uma estimativa inicial de energia gasta nos processos abrasivos do motor. / A significant part of the friction losses in an automotive engine results from the abrasive action of particles. Among possible sources of such particles one can mention the environment - particles that were not retained by the filters - metallic residues from worn parts or even combustion residues. They may be picked up by piston rings and become part of their surfaces or stay loose in the piston/liner interface. Those particles are responsible for axial grooves that are observed in the liners of used engines. The objective of this work was to get a better understanding of the wear mechanisms related to liner/bore grooving and to identify a laboratory testing setup that might reproduce them under controlled conditions. Specimens of Gray Cast Iron (GCI) and of AISI 1070 steel with matrix hardness close to that found in GCI (?200HV30) were submitted to scratch tests in a tribometer. It was found that scratches performed under 20-50 mN indenter load (conical tip) were similar to grooves observed in cylinder liners. Tests with other materials such as aluminum, brass and even steel with different hardness values contributed to a better understanding of the results. No sharp transition between abrasion mechanisms was observed. Calculation of material removal factor fab from optical profilometry resulted in values with a large dispersion; they could not be associated with different abrasion mechanisms. Friction coefficient values obtained from the tests were used to make preliminary estimates of energy consumption due to abrasive processes in the engine.

Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bord. / My PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up.

Uma parte significativa das perdas por atrito num motor automotivo resulta da ação de partículas abrasivas. Dentre as fontes possíveis, podem ser citados o próprio meio ambiente - partículas que passam pelo filtro de ar - o desgaste de partes metálicas do motor ou mesmo resíduos de combustão. Essas partículas podem ficar encrustadas em anéis do pistão, ou ficar na interface entre pistão e bloco ou camisa, e são responsáveis por sulcos axiais, na direção do movimento do pistão, observáveis em motores usados. O objetivo deste trabalho foi obter um melhor entendimento dos mecanismos de desgaste relacionados com o sulcamento de camisa/bloco e identificar conjuntos de testes laboratoriais capazes de reproduzi-los sob condições controladas. Amostras de ferro fundido cinzento (FoFo) e de aço AISI 1070 com dureza de matriz próxima daquela encontrada em FoFo (?200HV30) foram submetidas a ensaios de riscamento em tribômetros. Verificou-se que riscos executados com um endentador cônico submetido a cargas na faixa de 20 a 50 mN eram similares aos sulcos observados em camisas ou blocos. Ensaios com outros materiais, como alumínio e latão e mesmo aço de diferentes durezas contribuíram para melhorar o entendimento dos resultados. Não foi observada transição brusca entre mecanismos de abrasão. O cálculo do fator de remoção de material, fab, a partir de perfilometria óptica resultou em valores com dispersão elevada; não foi possível associa-los aos diferentes mecanismos de abrasão observados. Valores obtidos para o coeficiente de atrito no riscamento permitiram fazer uma estimativa inicial de energia gasta nos processos abrasivos do motor. / A significant part of the friction losses in an automotive engine results from the abrasive action of particles. Among possible sources of such particles one can mention the environment - particles that were not retained by the filters - metallic residues from worn parts or even combustion residues. They may be picked up by piston rings and become part of their surfaces or stay loose in the piston/liner interface. Those particles are responsible for axial grooves that are observed in the liners of used engines. The objective of this work was to get a better understanding of the wear mechanisms related to liner/bore grooving and to identify a laboratory testing setup that might reproduce them under controlled conditions. Specimens of Gray Cast Iron (GCI) and of AISI 1070 steel with matrix hardness close to that found in GCI (?200HV30) were submitted to scratch tests in a tribometer. It was found that scratches performed under 20-50 mN indenter load (conical tip) were similar to grooves observed in cylinder liners. Tests with other materials such as aluminum, brass and even steel with different hardness values contributed to a better understanding of the results. No sharp transition between abrasion mechanisms was observed. Calculation of material removal factor fab from optical profilometry resulted in values with a large dispersion; they could not be associated with different abrasion mechanisms. Friction coefficient values obtained from the tests were used to make preliminary estimates of energy consumption due to abrasive processes in the engine.

Solid lubricant coatings with controlled microstructures are good candidates in providing lubricity in moving mechanical assembly applications, such as orthopedics and bearing steels. Nanocrystalline ZnO coatings with a layered wurtzite crystal structure have the potential to function as a lubricious material by its defective structure which is controlled by sputter deposition. The interrelationships between sputtered ZnO, its nanocrystalline structure and its lubricity will be discussed in this thesis. The nanocrystalline ZnO coatings were deposited on silicon substrates and Ti alloys by RF magnetron sputtering with different substrate adhesion layers, direct current biases, and temperatures. X-ray diffraction identified that the ZnO (0002) preferred orientation was necessary to achieve low sliding friction and wear along with substrate biasing. In addition, other analyses such as scanning electron microscopy (SEM), transmission electron microscopy (TEM), and selected area electron diffraction (SAED) were utilized to study the solid lubrication mechanisms responsible for low friction and wear.

This master´s thesis deals with the experimental analysis of the coefficient of friction and lubrication film in total knee replacement. The experiments are performed on a knee joint simulator, with an implemented module for measuring friction. To observe film formation, fluorescent microscopy is used. The experiments are mainly focused on a detailed description of the influence of parameters occurring during the gait cycle. This approach should significantly help in describing the tribological processes that occur in the total knee replacement. The results confirm previous investigations in terms of axial load, where the coefficient of friction decreases with the increasing load. In the case of lubrication film, no significant changes are observed. On the contrary, while investigating the influence of SRR, noticeable changes in film formation are observed while the coefficient of friction being unaffected. While describing the whole gait cycle, precise results are obtained only in the first half of the cycle as the second half is accompanied by the occurrence of large deviations from a rapid decrease of load. This work provides a better understanding of the field of lubrication film in total knee replacements. Moreover, thanks to the simultaneous measurement of the coefficient of friction and the observation of the contact area, it is possible to draw better conclusions than if the experiments had been carried out separately.

The main objective of this work is to give contribution in both additive manufacturing (AM) and tribometry derived from the application and study of materials available with the use of biomimetic designs. Additional contributions are determining what effects treatments for flooring surfaces may have on the dynamic coefficient of friction and the effects of these products on common surfaces. The validity of the proposed methodology for a proof of concept was demonstrated by comparing measured dynamic coefficient of friction for designs using standardized equipment and comparing these values to plantar skin tested using an accepted and standardized testing method that has been extensively researched and validated. Initial biomimetic designs and characteristics unique to each design were researched and compared. Eleven designs were selected to be fabricated, tested, and compared to select the most desirable applications for further investigation. Research into potential treatments commercially available for use was done to determine the efficacy of these products. Prototype sensor designs were selected and fabricated using direct light processing (DLP) technology. Examination of the measured values was done through an analysis of the variances in the response variable and comparisons using Fisher and Tukey pairwise comparison method. Future work recommendations are provided for further development and improvement of the topics presented in this thesis.

This thesis presents the design and development of a versatile test rig specifically tailored for measuring frictional properties of diverse materials across a wide range of velocities and pressures. The ability to accurately quantify frictional behaviour under varying conditions is essential for understanding material performance in numerous applications, such as automotive, aerospace, and manufacturing industries. The primary objective of this research is to design a test rig capable of simulating real-world operating conditions, facilitating the evaluation of frictional forces experienced by different materials. The experimental setup incorporates a carefully designed sliding mechanism, pressure control system, and instrumentation to measure frictional forces with high precision. The test rig's sliding mechanism is built to accommodate various material samples, allowing for controlled movement along different planes with adjustable velocities. By subjecting these samples to controlled loads, the influence of pressure on frictional behaviour can be systematically investigated. Moreover, the test rig features to replicate conditions encountered in practical scenarios. To ensure accurate measurements, the frictional forces are captured using high-resolution load cells and strain gauges integrated into the test rig. This thesis contributes to the field of material science and engineering by providing a comprehensive framework for evaluating frictional behaviour under controlled conditions. The developed test rig serves as a reliable and versatile platform for studying material performance, guiding the design and development of more efficient and reliable systems in numerous industrial applications. / Denna avhandling presenterar designen och utvecklingen av en mångsidig testrigg speciellt anpassad för att mäta friktionsegenskaperna hos olika material vid olika hastigheter och tryck. Förmågan att exakt kvantifiera friktionsbeteendet under varierande förhållanden är avgörande för att förstå prestandan hos material inom många applikationsområden, såsom fordons-, flyg- och tillverkningsindustrin. Det primära målet med denna forskning är att designa en testrigg som kan simulera verkliga driftsförhållanden och underlätta utvärderingen av friktionskrafter som upplevs av olika material. Den experimentella uppställningen inkluderar en noggrant utformad glidmekanism, ett tryckkontrollsystem och mätutrustning för att mäta friktionskrafter med hög precision. Testriggens glidmekanism är utformad för att kunna hantera olika materialprover och möjliggör kontrollerad rörelse längs olika plan med justerbara hastigheter. Genom att utsätta dessa prover för kontrollerade belastningar kan tryckets inverkan på friktionsbeteendet systematiskt undersökas. Testriggen har dessutom funktioner för att återskapa förhållanden som uppstår i praktiska scenarier. För att säkerställa korrekta mätningar fångas friktionskrafterna med hjälp av högupplösta lastceller och töjningsgivare som är integrerade i testriggen. Denna avhandling bidrar till materialvetenskap och ingenjörskonst genom att tillhandahålla ett omfattande ramverk för att utvärdera friktionsbeteende under kontrollerade förhållanden. Den utvecklade testriggen fungerar som en pålitlig och mångsidig plattform för studier av materialprestanda och vägleder design och utveckling av effektivare och pålitligare system i många industriella applikationer.