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Optimum design of axisymmetric structures subjected to thermal loading (friction brakes)Elbella, Abdalla Mohamed Ali. January 1984 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographies.
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Development of novel eco-friendly friction materials for disc brake systemsLeonardi, Mara 03 April 2020 (has links)
Due to new environmental regulations, the demand for brake systems producing low polluting emissions and keeping high performance, is increasing. Therefore, a reduction in the toxic substances contained in brake friction materials is required that still meets all applicable safety standards and retaining properties such as low wear, high temperatures resistance, friction coefficient stability and consistency.
Among the various ingredients used in formulations, copper has recently become the subject of different regulations on brake pad materials and will be reduced, or even prohibited, in the coming years. Recent studies have found that brake pads are major contributors to the deposit of copper in rivers and lakes, and this has a toxic impact on the environment. This metal is currently added in brake material formulations because of its good physical properties and its contribution to the formation of a uniform and stable friction layer. Its characteristics make it a constituent that is not easy to replace and an adequate substitute covering all the roles of copper has not been found as yet.
The present research aims at developing, producing and testing new formulations for brake pads without copper. A relatively wide range of friction materials was investigated, in order to understand the role that selected constituents have in friction and wear behaviour.
In the first place, an investigation on the role of copper in friction materials was performed. The study was followed by the selection of a suitable replacement for this constituent in the formulation. To do so, different friction components were studied. Additionally, other aspects relating to friction materials, such as the deterioration of the binder, were subject of investigation.
The novel formulations, produced starting from commercially available compositions, were ranked in terms of wear and friction behaviour by means of a pin-on-disc tribometer. Cylindrical specimens were produced directly from powders, so that constituents could be easily modified based on the test outcome. This is a very effective method to study the role of individual constituents in the mixture, considering the relatively small amount of each specific composition to be prepared and the ease of processing it. In order to identify the principal wear mechanisms and their dependence on material properties and test conditions, the worn materials were analysed via scanning electron microscopy (SEM) techniques and Energy Dispersive X-Ray Spectroscopy (EDXS).
Part of the acquired knowledge from the first part of the work was used in the initial stages of the ECOPADS project (the project started during the doctoral period) to develop and manufacture real brake pads that were tested on brake dynamometers and evaluated in terms of both performance and emissions.
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Avaliação do desempenho de pastilhas automobilisticas nacionais / Evaluation of the Brazilian brake pads performanceSantos, Aliandro Henrique Costa 28 February 2005 (has links)
Orientador: Auteliano Antunes dos Santos Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia mecanica / Made available in DSpace on 2018-08-04T10:30:47Z (GMT). No. of bitstreams: 1
Santos_AliandroHenriqueCosta_M.pdf: 10616712 bytes, checksum: 57733fcc9ba5b442556901d87af2a403 (MD5)
Previous issue date: 2005 / Resumo: Os freios utilizados para veículos são normalmente por atrito. A tendência internacional é no sentido de utilizar somente freios por atrito à disco, eliminando os atuais tambores empregados em rodas traseiras para automóveis de passageiros. O aumento do desempenho de veículos automotivos e a conseqüente alteração em suas características dinâmicas tem levado a criação de sistemas de freio mais eficientes. A expansão do mercado para pastilhas e a necessidade de redução de custos tem levado ao surgimento de materiais sem a qualidade necessária para o desempenho da frenagem. Os procedimentos de ensaio existentes hoje e que permitem avaliar a qualidade do material de atrito são complexos e normalmente fazem uso de dinamômetros com inércia, de custo muito elevado e não disponíveis nos centros e instituições de pesquisa brasileiras. Este trabalho teve como objetivo caracterizar o desempenho de materiais de atrito para pastilhas de freio através da criação de um procedimento de ensaio que englobe as principais variáveis que influenciam o processo de frenagem. Foi utilizado o Dispositivo de Ensaio de Amostras, dinamômetro de baixo custo disponível no Departamento de Projeto Mecânico da FEM-Unicamp. Um planejamento experimental ortogonal L9 permitiu o estudo da influência de variáveis envolvidas no processo de utilização de pastilhas, que são a marca, o fornecedor, a pressão específica, a velocidade e a temperatura, em dois níveis de desgaste. Os resultados mostram que o procedimento proposto pode ser utilizado na avaliação da qualidade do material de atrito de pastilhas, de forma rápida, eficiente e com baixo custo / Abstract: Automotive brake systems are mainly friction based. The world tendency is toward using disc brakes instead of drum brakes, which are usually installed in the rear wheels. The increase in the performance of automotive vehicles and the changes in the dynamic characteristics have conducted to more efficient brake systems. The expansion of the brake pads market has impacted the quality of the products. Low quality products have been found, specially were no control exists. The actual test procedures to evaluate the quality of rnction materials are compIex and most of them require a fuII scale inertial dynamometer. Those machines are very expensive and most of the Brazilian research and quality centers do not have them. This work aimed to deveIop a procedure to characterize the performance of brake pads and analyzing the main factors of influence. A Iow cost non-inertial dynamometer, called D.E.A. - Fixture to text sampIes of friction material, was used. It is instalIed in the Department of Mechanical Design - FEM of the State University of Campinas, in Brazil. An experimental orthogonal design L9 was used to take the factor of influences in account. They are identified and the main factors are: contact pressure, disc speed, temperature and pad manufacturer. The influences were evaluated in two leveI of pad wearing. The results show that the procedure can be used to evaluate the quality of the rnction material for brake pads, in a fast and not expensive way / Mestrado / Projeto Mecanico / Mestre em Engenharia Mecânica
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Particulate Matter Emission Issues in Brake SystemsGomes Nogueira, Ana Paula 01 July 2022 (has links)
Automotive brake systems are source of particulate matter (PM) emissions, particularly in the urban areas. Several human ill-health are related with this kind of pollution. Along tire wear, road wear and dust from resuspension, the brake wear comprises the most relevant non-exhaust source of road traffic related emissions.
Aiming at studying the PM brake emissions, this thesis is composed of an introductory part containing the main concepts and the state of art of the main subjects; and the experimental part, which comprehends three investigations.
Chapters 2, 3, 4 and 5 are dedicated to the introduction part. Chapter 2 provides a brief description of the friction and wear, as well as the fundamental principles of braking by contact. Chapter 3 discuss the disc braking system, with particular attention to the pad friction materials. Chapter 4 is dedicated to friction layer: the layer usually developing at the disc/pad interface, affecting the performances of the tribological system. Finally, Chapter 5 provides an extensive discussion of the issues related to the particulate matter originated from disc brake systems.
The experimental part is presented in the Chapters 6, 7, 8 and 9. Chapter 6 describes the methodology applied in all the investigations. Chapter 7 investigates the PM emissions behavior and its interaction with the friction and wear, aiming to identify the mechanism of generation the PM emissions. A copper-containing and a copper-free commercial friction materials were used, with particular emphasis on the effect of the scorching treatment. The Chapter 8 is dedicated at investigating the tribological behavior and the corresponding PM emissions in two Cu-free commercial friction materials, aiming to a better understanding the effect of abrasive ingredients on the emissions generation. Finally, the Chapter 9 investigated the addition of natural ingredient rice husk in a new eco-friendly Cu-free brake friction material composition, focusing the attention on the tribological and emissions behavior. All tests were carried out using a pin-on-disc tribometer equipped with an enclosure, especially designed for investigating the tribological properties, as well as the airborne particles generated by contact. Low-metallic friction materials, both commercial and laboratory-produced, were tested against cast iron discs. The tests parameters used correspond to mild sliding conditions resembling those faced in real braking. Such conditions are characteristic of driving in urban areas, where the expose to traffic PM is concentrated. A specific methodology of analysis was developed, based on SEM/EDXS techniques. Using this methodology, comparative investigations between the elemental composition of the virgin friction materials, the worn surfaces of the friction materials and the airborne particles collected during the tribological tests were carried out. The results point out the triboxidative wear as the main mechanism of the PM brake emissions generation. Moreover, particles produced by abrasive wear can be also directly emitted to the environment.
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Projeto e construção de um tribômetro para estudos relacionados a materiais de fricção veicularesNeis, Patric Daniel January 2008 (has links)
Este trabalho apresenta o desenvolvimento de um tribômetro para a realização de ensaios com materiais de fricção utilizados em freios veiculares, capaz de servir como uma ferramenta adicional para pesquisa e desenvolvimento de novos produtos. São apresentadas todas as etapas de desenvolvimento da máquina, desde suas premissas básicas, projeto mecânico e de automação e procedimento de calibração até os testes finais para comprovação das suas potencialidades. Construiu-se um equipamento de pequeno porte (dimensões reduzidas), a fim de permitir ensaios rápidos e de baixo custo. O sistema atuador e de rotação foi dimensionado a partir de faixas de velocidade e pressão de contato que ocorrem em sistemas de freio comerciais. O tribômetro permite a troca rápida dos corpos de prova além do ajuste do raio de deslizamento do par de atrito. Além disso, um mecanismo de atuação próprio permite a realização de ensaios sem a influência do tipo de sistema de freio empregado. O sistema de automação, composto por hardware para aquisição de dados e programa para gerar interface gráfica, gerencia todos os processos envolvidos na máquina, além de tornar a sua operacionalidade simples e racional. Um conjunto composto por resistência aquecedora, soprador de ar, relé e termopares é responsável por controlar a temperatura do disco, separando esta variável dos demais parâmetros de operação (pressão e velocidade de escorregamento) durante os ensaios. O procedimento de calibração adotado mostra que o equipamento projetado fornece medições confiáveis da força normal, do torque de frenagem e, conseqüentemente, do coeficiente de atrito. Testes de avaliação do sistema atuador apontam que a força medida sofre a influência da rugosidade do disco, da baixa capacidade do reservatório de ar do sistema pneumático, de efeitos de histerese mecânica e da dilatação térmica e de ruídos eletromagnéticos. Os resultados dos ensaios de frenagem empregados comprovam que a máquina projetada é capaz de separar a variável temperatura do disco dos demais parâmetros de operação e, desta forma, pode servir de ferramenta adicional na compreensão do comportamento do atrito (e do desgaste em um momento posterior) frente às diferentes condições de operação contribuindo, de certa forma, para o aumento do conhecimento dos fenômenos tribológicos. / This work presents the development of a tribometer for friction tests with materials used in vehicular brakes, able to serving as an additional tool for research and development of new products. Every stage of the project are presented since its basic premises, mechanical and automation design, the calibration procedure until the final tests to prove its potential. It was constructed an equipment with small dimensions to enable rapid and low cost testing. The actuator and rotation system has been designed to operate in the range of velocity and contact pressures that occur in commercial brake systems. The tribometer allows the rapid exchange of specimen beyond the adjustment of the wear track radius. Furthermore, a special mechanism of action was designed to allow testing without the influence of the type of brake system employed. The automation system, composed of a data acquisition hardware and software to generate graphical interface, manages all processes involved in the machine, and makes its operation simple and rational. A set composed of heating resistance, air blower, relay and thermocouples is responsible for controlling the temperature of the disk, separating it from other variable operating conditions (pressure and slip velocity) during tests. The calibration procedure performed show that the equipment designed provides reliable measurements of normal force, braking torque and friction coefficient. The tests for evaluating the system actuator suggest that the force measurement has influence of the disk surface roughness, of low air capacity in the tank, of thermal dilation and mechanic hysteresis effects and of electromagnetic noise. The results of braking tests performed show that the designed machine is capable of separating the variable disk temperature of the other operation parameters and thus can serve as an additional tool in understanding the friction behavior (and wear a moment later) under a set of operating conditions. It can contribute, in some way, to enlarge the knowledge with respect to tribologics phenomenons.
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Projeto e construção de um tribômetro para estudos relacionados a materiais de fricção veicularesNeis, Patric Daniel January 2008 (has links)
Este trabalho apresenta o desenvolvimento de um tribômetro para a realização de ensaios com materiais de fricção utilizados em freios veiculares, capaz de servir como uma ferramenta adicional para pesquisa e desenvolvimento de novos produtos. São apresentadas todas as etapas de desenvolvimento da máquina, desde suas premissas básicas, projeto mecânico e de automação e procedimento de calibração até os testes finais para comprovação das suas potencialidades. Construiu-se um equipamento de pequeno porte (dimensões reduzidas), a fim de permitir ensaios rápidos e de baixo custo. O sistema atuador e de rotação foi dimensionado a partir de faixas de velocidade e pressão de contato que ocorrem em sistemas de freio comerciais. O tribômetro permite a troca rápida dos corpos de prova além do ajuste do raio de deslizamento do par de atrito. Além disso, um mecanismo de atuação próprio permite a realização de ensaios sem a influência do tipo de sistema de freio empregado. O sistema de automação, composto por hardware para aquisição de dados e programa para gerar interface gráfica, gerencia todos os processos envolvidos na máquina, além de tornar a sua operacionalidade simples e racional. Um conjunto composto por resistência aquecedora, soprador de ar, relé e termopares é responsável por controlar a temperatura do disco, separando esta variável dos demais parâmetros de operação (pressão e velocidade de escorregamento) durante os ensaios. O procedimento de calibração adotado mostra que o equipamento projetado fornece medições confiáveis da força normal, do torque de frenagem e, conseqüentemente, do coeficiente de atrito. Testes de avaliação do sistema atuador apontam que a força medida sofre a influência da rugosidade do disco, da baixa capacidade do reservatório de ar do sistema pneumático, de efeitos de histerese mecânica e da dilatação térmica e de ruídos eletromagnéticos. Os resultados dos ensaios de frenagem empregados comprovam que a máquina projetada é capaz de separar a variável temperatura do disco dos demais parâmetros de operação e, desta forma, pode servir de ferramenta adicional na compreensão do comportamento do atrito (e do desgaste em um momento posterior) frente às diferentes condições de operação contribuindo, de certa forma, para o aumento do conhecimento dos fenômenos tribológicos. / This work presents the development of a tribometer for friction tests with materials used in vehicular brakes, able to serving as an additional tool for research and development of new products. Every stage of the project are presented since its basic premises, mechanical and automation design, the calibration procedure until the final tests to prove its potential. It was constructed an equipment with small dimensions to enable rapid and low cost testing. The actuator and rotation system has been designed to operate in the range of velocity and contact pressures that occur in commercial brake systems. The tribometer allows the rapid exchange of specimen beyond the adjustment of the wear track radius. Furthermore, a special mechanism of action was designed to allow testing without the influence of the type of brake system employed. The automation system, composed of a data acquisition hardware and software to generate graphical interface, manages all processes involved in the machine, and makes its operation simple and rational. A set composed of heating resistance, air blower, relay and thermocouples is responsible for controlling the temperature of the disk, separating it from other variable operating conditions (pressure and slip velocity) during tests. The calibration procedure performed show that the equipment designed provides reliable measurements of normal force, braking torque and friction coefficient. The tests for evaluating the system actuator suggest that the force measurement has influence of the disk surface roughness, of low air capacity in the tank, of thermal dilation and mechanic hysteresis effects and of electromagnetic noise. The results of braking tests performed show that the designed machine is capable of separating the variable disk temperature of the other operation parameters and thus can serve as an additional tool in understanding the friction behavior (and wear a moment later) under a set of operating conditions. It can contribute, in some way, to enlarge the knowledge with respect to tribologics phenomenons.
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Projeto e construção de um tribômetro para estudos relacionados a materiais de fricção veicularesNeis, Patric Daniel January 2008 (has links)
Este trabalho apresenta o desenvolvimento de um tribômetro para a realização de ensaios com materiais de fricção utilizados em freios veiculares, capaz de servir como uma ferramenta adicional para pesquisa e desenvolvimento de novos produtos. São apresentadas todas as etapas de desenvolvimento da máquina, desde suas premissas básicas, projeto mecânico e de automação e procedimento de calibração até os testes finais para comprovação das suas potencialidades. Construiu-se um equipamento de pequeno porte (dimensões reduzidas), a fim de permitir ensaios rápidos e de baixo custo. O sistema atuador e de rotação foi dimensionado a partir de faixas de velocidade e pressão de contato que ocorrem em sistemas de freio comerciais. O tribômetro permite a troca rápida dos corpos de prova além do ajuste do raio de deslizamento do par de atrito. Além disso, um mecanismo de atuação próprio permite a realização de ensaios sem a influência do tipo de sistema de freio empregado. O sistema de automação, composto por hardware para aquisição de dados e programa para gerar interface gráfica, gerencia todos os processos envolvidos na máquina, além de tornar a sua operacionalidade simples e racional. Um conjunto composto por resistência aquecedora, soprador de ar, relé e termopares é responsável por controlar a temperatura do disco, separando esta variável dos demais parâmetros de operação (pressão e velocidade de escorregamento) durante os ensaios. O procedimento de calibração adotado mostra que o equipamento projetado fornece medições confiáveis da força normal, do torque de frenagem e, conseqüentemente, do coeficiente de atrito. Testes de avaliação do sistema atuador apontam que a força medida sofre a influência da rugosidade do disco, da baixa capacidade do reservatório de ar do sistema pneumático, de efeitos de histerese mecânica e da dilatação térmica e de ruídos eletromagnéticos. Os resultados dos ensaios de frenagem empregados comprovam que a máquina projetada é capaz de separar a variável temperatura do disco dos demais parâmetros de operação e, desta forma, pode servir de ferramenta adicional na compreensão do comportamento do atrito (e do desgaste em um momento posterior) frente às diferentes condições de operação contribuindo, de certa forma, para o aumento do conhecimento dos fenômenos tribológicos. / This work presents the development of a tribometer for friction tests with materials used in vehicular brakes, able to serving as an additional tool for research and development of new products. Every stage of the project are presented since its basic premises, mechanical and automation design, the calibration procedure until the final tests to prove its potential. It was constructed an equipment with small dimensions to enable rapid and low cost testing. The actuator and rotation system has been designed to operate in the range of velocity and contact pressures that occur in commercial brake systems. The tribometer allows the rapid exchange of specimen beyond the adjustment of the wear track radius. Furthermore, a special mechanism of action was designed to allow testing without the influence of the type of brake system employed. The automation system, composed of a data acquisition hardware and software to generate graphical interface, manages all processes involved in the machine, and makes its operation simple and rational. A set composed of heating resistance, air blower, relay and thermocouples is responsible for controlling the temperature of the disk, separating it from other variable operating conditions (pressure and slip velocity) during tests. The calibration procedure performed show that the equipment designed provides reliable measurements of normal force, braking torque and friction coefficient. The tests for evaluating the system actuator suggest that the force measurement has influence of the disk surface roughness, of low air capacity in the tank, of thermal dilation and mechanic hysteresis effects and of electromagnetic noise. The results of braking tests performed show that the designed machine is capable of separating the variable disk temperature of the other operation parameters and thus can serve as an additional tool in understanding the friction behavior (and wear a moment later) under a set of operating conditions. It can contribute, in some way, to enlarge the knowledge with respect to tribologics phenomenons.
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Low friction hybrid nanocomposite material for brake pad applicationGbadeyan, Oluwatoyin Joseph January 2017 (has links)
Submitted in fulfillment of the requirements for the degree of Master in Engineering: Mechanical Engineering, Durban University of Technology, Durban, South Africa, 2017. / Despite the huge improvements made in the development of vehicle brake pad materials, problems such long stopping distances, noise pollution, and heat dissipation still continue to persist. In this regard, a novel polymer-based hybrid nanocomposite brake pad (HC) has been developed. Here, a combination of carbon-based materials, including those at a nanoscale, was used to produce the brake pad. The coefficient of friction, wear rate, noise level, and interfacial temperature was investigated and compared with that of a commercial brake pad material (CR). It was found that the brake pad performance varied with the formulation of each pad. Hybrid nanocomposite brake pads material exhibited superior performance in most tests when compared to the commercial brake pad. They exhibited a 65% lower wear rate, 55% lower noise level, 90% shorter stopping distance, and 71 % lower interfacial temperature than the commercial brake pad (CR).
Furthermore, mechanical properties such as hardness, compressive strength, shear strength, and impact resistance were also evaluated. The material exhibited a 376% higher shear strength, 100% improved compressive strength, 77% greater modulus and 100% higher impact strength than the commercial brake pad. The hardness of both brake pads material was statistically comparable. Additionally, the thermal stability, degradation, water and oil absorption behaviour were measured. It was found that HC brake pad material exhibited a 100% lower water absorption and 80% oil absorption rate. The brake pads also exhibited a thermal stability within the brake pad standard maximum working temperature of 300 -400 0C.
The superior performance of hybrid nanocomposite brake pad material observed was due to synergism between the carbon-carbon additives and uniform dispersion of carbon fiber as shown in Figure 4.16. Scanning electron microscopy study was subsequently performed on fracture and worn surfaces of the brake pads. The micrographs show changes in the structural formation after the incorporation of carbon based fillers. It also shows the smooth structure and uniform dispersion of the carbon fiber. The smooth surface of the worn brake pad is an indicative of a harder structure. No ploughing or score marks were evident. Hence, it was deduced that the reinforced had superior mechanical and tribological properties. These improved properties are suggestive of materials that may be successfully used for brake pad application. / M
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Wear of Truck Brake Lining Materials Using Three Different Test MethodsBlau, Peter J., Jolly, Brian C. 01 August 2005 (has links)
Frictional stability and wear resistance are key performance requirements for heavy truck brake linings. Lining-counterface friction affects the rate of vehicle deceleration, but wear also affects stopping characteristics because uneven or high wear can alter the contact geometry of the lining, change the pattern of frictional heat generation, and degrade the response of the braking system. Inertia dynamometer wear tests are commonly conducted in the linings industry, but are expensive and time consuming. It is therefore of interest to seek more convenient, lower-cost test methods that still enable wear rates of various linings to be effectively differentiated. The purposes of the current study were to determine whether the wear of brake lining materials can be measured in shorter-term laboratory tests, and if so, to determine to what extent the relative ranking of several lining materials' wear resistance depends on the method of testing. To investigate these issues, three commercial truck brake lining materials were worn against gray cast iron using three different laboratory-scale wear testing machines. Assessments of wear by gravimetric methods and dimensional changes using the same test apparatus were compared. The three linings ranked in similar order in all three kinds of wear tests, but the relative differences between the wear of one lining and another differed among the test methods. Results are discussed in terms of what test conditions are required to simulate brake lining wear in trucks, and how in situ lining material aging and transfer film formation can affect the wear of brake lining materials. Differences in the entrapment of third-bodies entering the contact had an important influence on the wear results and an additional set of block-on-ring experiments was conducted to demonstrate that effect. Removing wear debris with a wiper pad altered the relative wear ranking of the three materials.
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Influência da porosidade no módulo de elasticidade de um material compósito com foco na indústria de materiais de fricçãoMichelena, Isis January 2013 (has links)
O presente trabalho propõe uma modelagem matemática simplificada que tem como foco o cálculo do módulo de elasticidade em matérias de fricção levando em consideração a porosidade. A modelagem proposta foi desenvolvida tendo como base a Lei das Misturas Modificada e os equacionamentos propostos por Spriggs e Kingery. Para simplificação do modelo, foi analisado um compósito com um aglomerante e um elemento de reforço. A escolha das matérias-primas levou em consideração os elementos mais utilizados em um material de fricção, desta forma o aglomerante utilizado foi uma resina fenólica e os agentes de reforço foram fibras de vidro e aramida. O equacionamento foi verificado utilizando dados empíricos. Para tanto, foram utilizados dois grupos de compósitos, um com resina fenólica e fibra de vidro e o outro com resina fenólica e fibra aramida. A verificação da influência das fibras no compósito foi feita variando o percentual de fibra, de 5% a 30% em peso, com um aumento de 5% entre as amostras. Os materiais foram confeccionados segundo o método de cura a quente sob pressão, seguido de tratamento térmico. Para a verificação das propriedades mecânicas foi realizado o teste de flexão a 3-pontos, segundo a norma ASTM D790,07. Em uma primeira análise, foi verificado o teor mínimo para que a fibra comece a atuar como reforço estrutural, e este para os dois grupos investigados foi de aproximadamente 2%, ou seja em todas as amostras as fibras estão atuando como elemento de reforço. O ensaio de porosidade seguiu a norma Volkswagen PV 3005 Por esse, foi possível verificar que para o compósito com fibra de vidro, quanto maior o teor de fibra, menor a porosidade apresentada pelo compósito. Para o compósito com aramida, a porosidade só diminui até 15%, após mantém-se constante. Este resultado pôde ser explicado pelo fato da aramida se apresentar na forma de polpa, dificultando a molhabilidade da resina. Como não há correlação linear entre porosidade e módulo de elasticidade para o compósito com fibra aramida, é proposto um modelo que seja apto à avaliação dos dois compósitos em questão. A utilização deste modelo visou a redução expressiva no tempo despendido e esforços de desenvolvimento de produtos, colaborando para a redução dos custos de projeto e aumento da competitividade destes produtos. A modelagem matemática simplificada proposta permitiu obter uma correlação entre o módulo de elasticidade e a porosidade. Os dados calculados através do modelo proposto concordam de forma satisfatória com os resultados experimentais. / The present work shows a simplified mathematical modeling focused on the modulus of elasticity in a friction material considering the inherent porosity of this material. The suggested model was developed based on the modified Law of Mixtures and equations proposed by Spriggs and Kingery. To obtain a simplified model a composite constituted of a binder and a reinforcement element was analyzed. Raw materials used in these tests were chosen based on raw materials most used in a friction industry, the binder used is a phenolic resin and reinforcing components are glass fiber and aramid fiber. The proposed model was verified based on the empirical data, analyzing two groups of composite material, one with a phenolic resin and fiber glass and another one with phenolic resin and aramid fiber. To understand the influence of the reinforcing components in the composite, the percentage of fibers was varied from 5% to 30%, the difference between samples is 5%. The materials were manufactured using the process typically used for friction materials, heat curing under pressure followed by heat treatment. The samples were tested under 3-points bending test procedure, according to ASTM D790-07 standard. In a preliminary analysis the minimum fraction of fiber that works as a reinforcing component is 2%, according to critical volume equation. Then in all the samples analyzed the fibers are acting as reinforcement elements. The porosity test was made according to VW PV 3005 standard Using this method, it was possible to verify that increasing the percentage of glass fiber the percentage of porosity decrease. For the aramid composite the percentage of porosity decreases up to 15% of fiber, from this point the value is kept constant. This result can be explained if we consider the fact that the aramid fiber is used in the pulp form, hindering the wettability of the resin. Since there is no linear correlation between porosity and elastic modulus for the composite with aramid fiber, it is proposed a model that is able to appraisal the two composites in question. The use of this model aims a significant reduction in time spent and resources on development, helping to reduce the project cost and increasing the product competitiveness. The simplified mathematical model proposed supported a correlation between modulus of elasticity and porosity. Data calculated by the proposed model agrees satisfactorily with the experimental results.
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