Estudo analítico e numérico das tensões de Hertz em contato entre uma esfera/plano e um cilindro/plano
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Data
2019-12-02
Autores
Köhn, André Oliveira
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Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho é apresentado um estudo analítico e numérico a respeito das tensões superficiais entre dois elementos. Quando uma força externa é aplicada a dois corpos em contato, verifica-se a existência de uma pequena deformação entre os elementos, causando um achatamento no plano de contato e criando uma zona de altas tensões de formato elíptico. Com a repetição cíclica destes carregamentos, pode ocorrer a perda progressiva de material superficial dos elementos envolvidos. De forma a investigar este fenômeno, esta dissertação realizou a análise detalhada de dois casos específicos encontrados na mecânica: o contato existente entra a esfera e a pista interna de um rolamento (contato esfera/plano), e o contato entre uma roda e um trilho ferroviário (contato cilindro/plano). Este estudo é essencial para a compreensão de como a aplicação de um carregamento externo pode influenciarna superfície de dois elementos. A análise foi realizada através de duas abordagens: uma analítica, através das equações oriundas da Teoria de Hertz, e outra numérica, através de programas computacionais de elementos finitos. Com os resultados verificados, foi feito uma série de gráficos que ilustram o comportamento das tensões ao longo dos eixos, além da análise da área afetada pela ação das tensões superficiais. Por fim, verificou-se a existência de tensões normais compressivas máximas encontradas no plano de contato entre os elementos, sendo a maior tensão localizada na direção do eixo de aplicação do carregamento. À medida que se aumenta a profundidade, estas tensões tendem a se anular rapidamente. No plano de contato, as tensões só estão presentes dentro da elipse no contato causado pela deformação, sendo nula em suas bordas. Além das tensões normais, há a presença de tensões cisalhantes, sendo seu valor máximo encontrado a uma pequena profundidade. Foi verificado que as tensões de cisalhamento são os elementos mais significativos para possíveis desgastes superficiais futuros que podem levam o componente à falha e à fratura.
An analytical and numerical study regarding contact stresses between two elements is presented in this work. When an external force is applied to two bodies in contact, a small deformation between the elements appears, flattening the contact plane and creating high elliptical stresses. The cyclical repetition of these stresses can cause the progressive loss of surface material from the bodies. To verify this phenomenon, this work developed a detailed analysis of two specific cases found in many mechanical applications: the contact between a sphere and an inner ring of a bearing (sphere/plane contact) and the contact between a wheel and a rail track (cylinder/plane contact). This study is essential to the understanding of the influence in the surface of these two elements caused by an external load. The analysis was performed using two different approaches: one analytical, using Hertz equations, and one numerical, using computational simulations and finite element software. After the results were validated, a number of graphics were developed using the Hertz Equations for contact stresses to illustrate how the stresses behave along the axis, as well as the analysis of the area affected by the contact stresses. It was found that the maximum compressive stresses are located at the contact plane between the bodies, and the highest stress is found along the axis where the load was applied. When the depth is increased, all normal stresses tend to decrease until they became null. At the contact plane, all stresses are located inside an elliptical area, where the peak is found at its center and all borders are null. Along with the normal stresses, the external load causes the appearance of shear stresses, and its maximum value is found at a small depth from the contact surface. The shear stresses are the most significant elements are the most critical stresses regarding the presence of cracks and failures
An analytical and numerical study regarding contact stresses between two elements is presented in this work. When an external force is applied to two bodies in contact, a small deformation between the elements appears, flattening the contact plane and creating high elliptical stresses. The cyclical repetition of these stresses can cause the progressive loss of surface material from the bodies. To verify this phenomenon, this work developed a detailed analysis of two specific cases found in many mechanical applications: the contact between a sphere and an inner ring of a bearing (sphere/plane contact) and the contact between a wheel and a rail track (cylinder/plane contact). This study is essential to the understanding of the influence in the surface of these two elements caused by an external load. The analysis was performed using two different approaches: one analytical, using Hertz equations, and one numerical, using computational simulations and finite element software. After the results were validated, a number of graphics were developed using the Hertz Equations for contact stresses to illustrate how the stresses behave along the axis, as well as the analysis of the area affected by the contact stresses. It was found that the maximum compressive stresses are located at the contact plane between the bodies, and the highest stress is found along the axis where the load was applied. When the depth is increased, all normal stresses tend to decrease until they became null. At the contact plane, all stresses are located inside an elliptical area, where the peak is found at its center and all borders are null. Along with the normal stresses, the external load causes the appearance of shear stresses, and its maximum value is found at a small depth from the contact surface. The shear stresses are the most significant elements are the most critical stresses regarding the presence of cracks and failures
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Palavras-chave
Tensão superficial, Tensões de Hertz, Contato esfera/plano, Contato cilindro/plano, Contact stresses, Hertz stresses, Sphere/plane contact, Cylinder/plane contact