The use of computational methods in tribology can be a valuable approach to deal with engineering problems, ultimately saving time and resources. In this work, amodel problem and methodology is developed to deal with a common situation found in experiments in tribology, namely a linearly reciprocating block-on-flat drysliding contact. The modelling and simulation of such case would allow a better understanding of the contact pressure distribution, wear and geometry evolutionof the block as it wears out during a test. Initially, the introduction and motivation for this work is presented, followed by a presentation of relevant scientific topics related to this work. Wear modelling of published studies are reviewed next, along with studies available in the literature and the goals for this thesis.The fourth section refers to the methodology used and the built-up of the model problem. In this work the Finite Element Method and Archard’s wear model through COMSOL Multiphysics® and MATLAB® are used to study the proposed contact problem. The construction of the model problem is detailed and the procedure for wear, geometry update and long term predictions, is presented inspired by the literature reviewed. Finally, the results are presented and discussed; wear increment and new geometries evolution are presented in the figures, followed by pressure profile evolution at selected times. The final geometry is also compared for different time steps. At last, conclusions and recommendations for future work are stated.

Friction and wear have been observed m mechanical systems when there is a relative motion between two solid bodies Friction mainly results in loss of energy and wear results in matenal loss The proper understanding of friction and wear mechanisms provides practical solutions to tribological related problems Various models are available m tribology literature to calculate function coefficient and wear rate of matenals However, expenments suggest that these models are incomplete and fortuitous as the tnbological response is system dependent The objective of present investigation is to understand the tribological lesponse of commercially puie titanium and OFHC copper pins sliding on polyciystallme alumina discs Di\ shdm% tests were conducted in air, and vacuum (1 5 x 10~2Pa) at room tempeiatuie under different experimental conditions The normal load was vaned from 15 3 N to 76 0 N, sliding speed was vaned from 0 01 ms"1 to 1 4 ms"1, and tempeiatuie was varied from 293 K to 793 K It is found that the haidness of metals do not have any effect on their tribological response The experimental obseivations indicate that tribological response of metals mainly depends up on miciostructural evolution, oxygen activity and relative shear strength of metals and ceramics Chapter 1 starts with the background and concepts of tribology A brief literature survey is given with published work in relation with the present work In Chapter 2, the experimental proceduies of the dry sliding test and compression test are given Chapter 3 explains the tribological response of titanium during shdmg against alumina Different wear mechanisms such as oxidation, deformation and adhesion were identified Deformation wear mechanism is explained using strain rate response approach Chapter 4 explains the tribological response of copper during sliding against alumina The influence of environment and microstructural evolution on its tribological behavior are studied Chaptei 5 explains the dependence of tribological response of metals on micro structural evolution, oxygen activity and relative shear strength of metals and ceramics This thesis ends with the conclusions of the present investigation

O objetivo principal do estudo é comparar o teste em 3 pontos com braquetes com o teste de resistência ao deslizamento utilizando um novo dispositivo que realiza a mensuração simultânea do coeficiente de atrito, das forças e dos momentos nos braquetes de ancoragem e da força de desativação no braquete desalinhado, exercidos por fios ortodônticos. Os objetivos secundários foram desenvolver o dispositivo e comparar, no teste em 3 pontos: (i) a influência, nas grandezas e no coeficiente de atrito cinético, da variação da simetria nas distâncias inter-braquetes, do tipo de braquete de ancoragem (canino ou 2º pré-molar), do deslocamento (3 ou 5mm) do braquete central, do sentido do desalinhamento (vestibular ou lingual) do braquete central e da marca de fio-braquete; (ii) as 3 formas de cálculo do coeficiente de atrito cinético; (iii) os 10 ciclos, para vestibular ou lingual, para verificar se eles são semelhantes ou não entre si. Foram utilizados braquetes autoligáveis (dentes 13, 14 e 15) e fios 0.014\'\' NiTi e CuNiTi das marcas Aditek e Ormco. O teste de resistência ao deslizamento foi realizado no desalinhamento lingual, nos dois deslocamentos e na configuração simétrica. O teste em 3 pontos com braquetes foi realizado no desalinhamento lingual e vestibular, nos dois deslocamentos e na configuração simétrica e assimétrica. Por meio da ANOVA, foram comparados, entre os dois tipos de teste: (A) as grandezas e o coeficiente de atrito e (B) o coeficiente de atrito gerado apenas no braquete de 2º pré-molar. Utilizando-se do mesmo teste estatístico foram comparados, no teste em 3 pontos com braquetes: (A) na configuração simétrica, algumas grandezas e o coeficiente de atrito advindos da variação da marca de fio-braquete, do deslocamento, do desalinhamento e do tipo de braquete; (B) algumas grandezas e o coeficiente de atrito gerados na configuração simétrica e assimétrica; (C) os valores das 3 formas de cálculo do coeficiente de atrito na configuração simétrica; e (D) algumas grandezas e o coeficiente de atrito encontrados nos 10 ciclos. Resultados: (A) a maioria dos valores das grandezas e do coeficiente de atrito gerados pelos dois tipos de teste foram diferentes estatisticamente; (B) o braquete de 2º pré-molar apresentou valores de coeficiente de atrito diferentes entre os dois tipos de teste; (C) na configuração simétrica, as variáveis foram estatisticamente significantes na maioria dos casos para as grandezas analisadas e para o coeficiente de atrito; (D) houve diferença entre a configuração simétrica e assimétrica; (E) o coeficiente de atrito baseado nas duas normais e na força de atrito se aproximou mais da realidade clínica e foi sensível à variação da geometria da relação fio-braquete; e (F) os 10 ciclos para lingual foram semelhantes entre si em 70% dos casos e os 10 ciclos para vestibular foram diferentes em 57% dos casos. Conclusões: o teste em 3 pontos com braquetes é diferente do teste de resistência ao deslizamento; a variação das configurações geométricas e da marca de fio-braquete pode influenciar nos valores das grandezas e do coeficiente de atrito cinético; os 10 ciclos para lingual foram mais semelhantes entre si que os 10 ciclos para vestibular. / The main objective of the study is to compare the three-bracket bending test with the resistance to sliding test using a new device that performs simultaneous measurement of coefficient of friction, the forces and moments on the anchor brackets and deactivation force in misaligned bracket, exercised by orthodontic wires. Secondary objectives were to develop the device and compare, in the three-bracket bending test: (i) the influence, on the physical quantities and on the kinetic friction coefficient, of the variation of the symmetry in the inter-bracket distance, of the type of anchor bracket (canine or 2nd premolar), of displacement (3 or 5mm) and misalignment (buccal or lingual) of the central bracket, and of the wire and bracket brand; (ii) the three ways to calculate the coefficient of kinetic friction; (iii) the 10 cycles, for buccal or lingual, to see if they are similar or not. Self-ligating brackets were used (teeth 13, 14 and 15) and wires 0.014 \'\' NiTi and CuNiTi of Aditek and Ormco brands. The resistance to sliding test was conducted on the lingual misalignment, on both displacements and on symmetrical configuration. The three-bracket bending test was held at the lingual and vestibular misalignment, at both displacements and at the symmetrical and asymmetrical configuration. Through ANOVA, were compared, between the two types of tests: (A) the quantities and the coefficient of friction and (B) the coefficient of friction generated only in the second premolar bracket. Using the same statistical test were compared, in three-bracket bending test: (A) in symmetrical configuration, the quantities and the coefficient of friction arising from the variation in the wire and bracket brands, displacement, misalignment and the type of bracket; (B) the quantities and the coefficient of friction generated by the symmetric and asymmetric configuration; (C) the values of the three ways of calculating friction coefficient; and (D) the quantities and the coefficient of friction encountered in 10 cycles. Results: (A) most of the values of the quantities and the coefficient of friction generated by the two types of test were statistically different; (B) the 2nd premolar bracket showed different friction coefficient values between the two types of test; (C) in the symmetrical configuration, the variables were statistically significant in the most of cases for quantities and the friction coefficient; (D) was found difference between symmetric and asymmetric configuration; (E) the friction coefficient based on both normal forces and frictional force was closer to the clinical reality and was sensitive to variations in the geometry of the wire-bracket relationship; and (F) the 10 cycles for lingual were similar in 70% of cases and the 10 cycles for buccal desalignment were different in 57% of cases. Conclusions: The three-bracket bending test is different from the resistance to sliding test; the variation of geometric configurations and wire and bracket brands may influence the values of the quantities and the coefficient of kinetic friction; the 10 cycles for lingual were more similar to each other than the 10 cycles for buccal.

O objetivo principal do estudo é comparar o teste em 3 pontos com braquetes com o teste de resistência ao deslizamento utilizando um novo dispositivo que realiza a mensuração simultânea do coeficiente de atrito, das forças e dos momentos nos braquetes de ancoragem e da força de desativação no braquete desalinhado, exercidos por fios ortodônticos. Os objetivos secundários foram desenvolver o dispositivo e comparar, no teste em 3 pontos: (i) a influência, nas grandezas e no coeficiente de atrito cinético, da variação da simetria nas distâncias inter-braquetes, do tipo de braquete de ancoragem (canino ou 2º pré-molar), do deslocamento (3 ou 5mm) do braquete central, do sentido do desalinhamento (vestibular ou lingual) do braquete central e da marca de fio-braquete; (ii) as 3 formas de cálculo do coeficiente de atrito cinético; (iii) os 10 ciclos, para vestibular ou lingual, para verificar se eles são semelhantes ou não entre si. Foram utilizados braquetes autoligáveis (dentes 13, 14 e 15) e fios 0.014\'\' NiTi e CuNiTi das marcas Aditek e Ormco. O teste de resistência ao deslizamento foi realizado no desalinhamento lingual, nos dois deslocamentos e na configuração simétrica. O teste em 3 pontos com braquetes foi realizado no desalinhamento lingual e vestibular, nos dois deslocamentos e na configuração simétrica e assimétrica. Por meio da ANOVA, foram comparados, entre os dois tipos de teste: (A) as grandezas e o coeficiente de atrito e (B) o coeficiente de atrito gerado apenas no braquete de 2º pré-molar. Utilizando-se do mesmo teste estatístico foram comparados, no teste em 3 pontos com braquetes: (A) na configuração simétrica, algumas grandezas e o coeficiente de atrito advindos da variação da marca de fio-braquete, do deslocamento, do desalinhamento e do tipo de braquete; (B) algumas grandezas e o coeficiente de atrito gerados na configuração simétrica e assimétrica; (C) os valores das 3 formas de cálculo do coeficiente de atrito na configuração simétrica; e (D) algumas grandezas e o coeficiente de atrito encontrados nos 10 ciclos. Resultados: (A) a maioria dos valores das grandezas e do coeficiente de atrito gerados pelos dois tipos de teste foram diferentes estatisticamente; (B) o braquete de 2º pré-molar apresentou valores de coeficiente de atrito diferentes entre os dois tipos de teste; (C) na configuração simétrica, as variáveis foram estatisticamente significantes na maioria dos casos para as grandezas analisadas e para o coeficiente de atrito; (D) houve diferença entre a configuração simétrica e assimétrica; (E) o coeficiente de atrito baseado nas duas normais e na força de atrito se aproximou mais da realidade clínica e foi sensível à variação da geometria da relação fio-braquete; e (F) os 10 ciclos para lingual foram semelhantes entre si em 70% dos casos e os 10 ciclos para vestibular foram diferentes em 57% dos casos. Conclusões: o teste em 3 pontos com braquetes é diferente do teste de resistência ao deslizamento; a variação das configurações geométricas e da marca de fio-braquete pode influenciar nos valores das grandezas e do coeficiente de atrito cinético; os 10 ciclos para lingual foram mais semelhantes entre si que os 10 ciclos para vestibular. / The main objective of the study is to compare the three-bracket bending test with the resistance to sliding test using a new device that performs simultaneous measurement of coefficient of friction, the forces and moments on the anchor brackets and deactivation force in misaligned bracket, exercised by orthodontic wires. Secondary objectives were to develop the device and compare, in the three-bracket bending test: (i) the influence, on the physical quantities and on the kinetic friction coefficient, of the variation of the symmetry in the inter-bracket distance, of the type of anchor bracket (canine or 2nd premolar), of displacement (3 or 5mm) and misalignment (buccal or lingual) of the central bracket, and of the wire and bracket brand; (ii) the three ways to calculate the coefficient of kinetic friction; (iii) the 10 cycles, for buccal or lingual, to see if they are similar or not. Self-ligating brackets were used (teeth 13, 14 and 15) and wires 0.014 \'\' NiTi and CuNiTi of Aditek and Ormco brands. The resistance to sliding test was conducted on the lingual misalignment, on both displacements and on symmetrical configuration. The three-bracket bending test was held at the lingual and vestibular misalignment, at both displacements and at the symmetrical and asymmetrical configuration. Through ANOVA, were compared, between the two types of tests: (A) the quantities and the coefficient of friction and (B) the coefficient of friction generated only in the second premolar bracket. Using the same statistical test were compared, in three-bracket bending test: (A) in symmetrical configuration, the quantities and the coefficient of friction arising from the variation in the wire and bracket brands, displacement, misalignment and the type of bracket; (B) the quantities and the coefficient of friction generated by the symmetric and asymmetric configuration; (C) the values of the three ways of calculating friction coefficient; and (D) the quantities and the coefficient of friction encountered in 10 cycles. Results: (A) most of the values of the quantities and the coefficient of friction generated by the two types of test were statistically different; (B) the 2nd premolar bracket showed different friction coefficient values between the two types of test; (C) in the symmetrical configuration, the variables were statistically significant in the most of cases for quantities and the friction coefficient; (D) was found difference between symmetric and asymmetric configuration; (E) the friction coefficient based on both normal forces and frictional force was closer to the clinical reality and was sensitive to variations in the geometry of the wire-bracket relationship; and (F) the 10 cycles for lingual were similar in 70% of cases and the 10 cycles for buccal desalignment were different in 57% of cases. Conclusions: The three-bracket bending test is different from the resistance to sliding test; the variation of geometric configurations and wire and bracket brands may influence the values of the quantities and the coefficient of kinetic friction; the 10 cycles for lingual were more similar to each other than the 10 cycles for buccal.