Análise computacional do comportamento dinâmico de um sistema vibro-impacto
Carregando...
Data
2017-01-24
Autores
Lourenço, Rodrigo Francisco Borges [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
São diversos os equipamentos de engenharia que apresentam vibrações mecânicas, e estas podem ser observadas em forma de acelerações, deslocamentos e velocidade. Os primeiros estudos envolvendo vibrações foram direcionados aos fenômenos naturais e modelagem matemática de sistemas vibrantes, então, começou a aplicação desses estudos em equipamentos de engenharia. Vibrações mecânicas, na maioria dos sistemas dinâmicos, são consideradas como algo indesejado e podem ser danosos. Porém, existem situações que são utilizadas para melhorar o funcionamento e desempenho de máquinas. São diversas as causas de vibrações em sistemas de engenharia, neste trabalho, destaca-se as vibrações causadas por impacto. Quando componentes destes sistemas impactam entre si, causando ruídos de curta duração, são caracterizados como sistemas tipo vibro - impacto. Podem ser citados diversos equipamentos com essas características, como rolos compactadores de solo, martelos de impacto, perfuratrizes de solo, etc. Neste trabalho, demonstra-se o comportamento dinâmico de um sistema vibro – impactante. Para análise deste sistema, foram desenvolvidos códigos computacionais, através do software Octave. No diagrama de estabilidade de Lyapunov, verificou-se que, pontualmente o sistema se apresenta de forma estável. A partir da variação da frequência de excitação, foi observado através dos históricos no tempo, espectros de frequência, mapas de Poincaré e planos de fase, um comportamento periódico e estável, com situações diversas de respostas. Ao analisar a evolução temporal dos expoentes de Lyapunov, para todas as condições de velocidade e deslocamento impostas, o sistema se apresentou de forma caótica. Implementou-se um controlador linear ótimo ao sistema, afim de atenuar as vibrações nas regiões de operação nas quais o sistema é instável. Comprovou-se que a estratégia de controle linear ótimo (LQR, do inglês Linear Quadratic Regulator) demonstra eficiência para este tipo de situação e pode ser utilizada na redução de danos, evitando prejuízos econômicos, perdas biológicas e materiais.
There are several engineering equipment’s that present mechanical vibrations, and these can be observed in the form of displacement, acceleration, and speed. The first studies involving were directed to the natural phenomena and mathematical modeling of vibrations systems, then the application of these studies began in engineering equipment. In most dynamic systems Mechanical vibrations are considered to be unwanted and can be harmful. However, there are situations that are used to improve the operation and performance of machines. There are several causes of vibrations in engineering systems. In this work, the vibrations caused by impact are highlighted. For components of these systems impacting each other, causing short - term noise, they are characterized as vibro-impact systems. Various equipment with these characteristics can be mentioned, such as soil compacting rollers, impact hammers, soil drills, etc. In this work the dynamic behavior of a vibro-impacting system is demonstrated. For the computational analysis of this system, were implemented codes using the software Octave. In the Lyapunov stability diagram, is was verified that, the system presents is stable. From the variation of the excitation frequency, a periodic and stable behavior was observed through time histories, frequency spectrump, poincaré maps and phase planes, with different situations of responses. When analyzing the time evolution of the Lyapunov is exponents, for all imposed conditions of velocity and displacement, the system appeared chaotic. An optimum linear controller was implemented in the system in order to attenuate the vibrations in the operating regions in which the system is unstable. It was verified that the Linear Quadratic Regulator (LQR) demonstrates efficiency for this type of situation and it can be used to reduce damages, avoiding economic, biological, and material losses.
There are several engineering equipment’s that present mechanical vibrations, and these can be observed in the form of displacement, acceleration, and speed. The first studies involving were directed to the natural phenomena and mathematical modeling of vibrations systems, then the application of these studies began in engineering equipment. In most dynamic systems Mechanical vibrations are considered to be unwanted and can be harmful. However, there are situations that are used to improve the operation and performance of machines. There are several causes of vibrations in engineering systems. In this work, the vibrations caused by impact are highlighted. For components of these systems impacting each other, causing short - term noise, they are characterized as vibro-impact systems. Various equipment with these characteristics can be mentioned, such as soil compacting rollers, impact hammers, soil drills, etc. In this work the dynamic behavior of a vibro-impacting system is demonstrated. For the computational analysis of this system, were implemented codes using the software Octave. In the Lyapunov stability diagram, is was verified that, the system presents is stable. From the variation of the excitation frequency, a periodic and stable behavior was observed through time histories, frequency spectrump, poincaré maps and phase planes, with different situations of responses. When analyzing the time evolution of the Lyapunov is exponents, for all imposed conditions of velocity and displacement, the system appeared chaotic. An optimum linear controller was implemented in the system in order to attenuate the vibrations in the operating regions in which the system is unstable. It was verified that the Linear Quadratic Regulator (LQR) demonstrates efficiency for this type of situation and it can be used to reduce damages, avoiding economic, biological, and material losses.
Descrição
Palavras-chave
Análise de estabilidade, Caos, Controle linear ótimo, Simulação numérica, Vibrações mecânicas, Stability analysis, Chaos, Optimal linear control, Numerical simulation, Mechanical vibrations