This paper presents a methodology for analytical calculation and computational simulation using the finite element method for piezoresistive graphite sensor element on flexible polymer substrate, A4 paper. The computer simulation aims to find the region of greatest mechanical tension and deflection of the circular diaphragm set in the circumference edges. The steps for simulation are geometry definition, mesh generation, inclusion of material physical properties and simulation execution. The mathematical modeling of maximum mechanical stress and deflection is described analytically and computationally. The analytical calculations were compared with the computer simulation and presented a relative percentage error of 3.38% for the maximum deflection. The results show that the piezoresistor should be positioned at the edges of the circular diaphragm to take advantage of maximum mechanical stress by defining the best location for graphite film deposition for sensor device designs and fabrications.

This work proposes a new procedure to extract characteristic parameters of MEMS structures, using systems identification. The target structures are the nuclei of micro-rotors and the characteristic parameters are the mass, the damping coefficient, and the spring constant. The structures are described in 3D solid model and the behavioral data necessary to the extraction of characteristic parameters, used in macro-models, are obtained through numerical simulations based on finite elements. To parameter extraction were adopted the ARX model and the RLS estimator. Experimental data obtained from three topologies of micro-nuclei, with one degree of freedom, demonstrates satisfactory estimate results when applied to analytical models that the extracted parameters, when applied to analytical models, which motivates the application of other techniques available in the systems identification domain.

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Abstract    The growing demand for MEMS requires each device to be tested, ensuring the quality of all devices that go to market. However the tests are expensive, increasing the final price. Mathematical modeling is an alternative to verify the quality of MEMS quickly and efficiently. The objective is to find a satisfactory model in with the order selected under the Partial Autocorrelation Function (PACF) criteria. The technique consists of five steps of system identification. The first step is to collect the data obtained from an experimental platform. Then the model order is selected based on the PACF. Then the model parameters are estimated by the least squares method. Then, the model is validated by calculating the percentage error. Quantitatively, the model has an error below 2%. The behavioral performance provides satisfactory results, proving that it is possible to define the order of an appropriate model under the presented criteria.Keywords    Dynamic System, Gray box modeling, MEMS Sensors, System identification, Time seriesResumo    A crescente demanda de MEMS exige que cada dispositivo seja testado, garantindo a qualidade de todos os dipositivos que vão para o mercado. Porém os testes são caros, aumentando o seu preço final. A modelagem matemática surge como uma alternativa para verificar a qualidade dos MEMS de forma rápida e eficiente. O objetivo do estudo é encontrar um modelo satisfatório com ordem selecionada sob o critério da Função de Autocorrelação Parcial (PACF). A técnica consiste das cinco etapas da identificação de sistemas. A primeira etapa é coletar os dados obtidos de uma plataforma experimental. Então a ordem do modelo é selecionada baseada na PACF. Em seguida os parâmetros do modelo são estimados pelo método dos mínimos quadrados. Depois o modelo é validado calculando o erro percentual e o erro percentual médio absoluto. Quantitativamente, o modelo apresenta erro inferior a 2%. O desempenho comportamental apresenta resultados satisfatórios, comprovando que é possível definir a ordem de um modelo adequado sob os critérios apresentados.Palavras-chave    Identificação de sistemas, Modelagem caixa cinza, Sensores MEMS,Séries temporais, Sistema Dinâmico