The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system.
This paper aims at constructing a stochastic model for the hysteretic behaviour of the nonlinear bit-rock interaction of a drill string under torsional vibrations using field data. The proposed model takes into account the fluctuations of the stick-slip oscillations and the hysteretic effect due to the nonlinear bit-rock interaction observed during the drilling process. These fluctuations are modelled by introducing a stochastic process associated with the variations of the bit-rock interaction during the drilling. The parameters of the stochastic model are calibrated with field data. Finally, independent trajectories of the proposed stochastic model are generated and used to simulate the stochastic response of the drill string torsional dynamics in presence of random bit-rock interaction. The stochastic model is then used to estimate statistics on the stability of the drill string.
In this paper a new strategy for modeling uncertainties in the substructures and interfaces of a dynamical system is presented. This strategy is based on (1) the reduction of the dynamical model of each substructure using the Craig-Bampton method and (2) the use of the nonparametric probabilistic approach for the global modeling of uncertainties in each substructure. As an improvement with respect to existing nonparametric methods, the methodology proposed here constructs separated models of uncertainties for the inner and interface degrees of freedom, which allows to control separately the levels of fluctuation induced by these two sources of uncertainties. This methodology is applied for the analysis of the random vibration of a drill-string. Three strategies are compared: (1) a full nonparametric probabilistic approach on all the system, (2) the existing nonparametric probabilistic approach together with the Craig-Bampton substructuring method, and (3) the new nonparametric probabilistic approach proposed here with the separation of the inner and interface degrees of freedom uncertainties. It turns out that, for the same level of uncertainty, the three approaches give similar results but the new approach gives more flexibility for the control of the probabilistic model.
RESUMOHoje existem propostas e políticas em várias regiões do planeta com metas de adoção de fontes renováveis. Neste contexto, a energia eólica apresenta-se como uma importante fonte em ascensão na geração de energia elétrica, tornando-a cada vez mais competitiva se comparada às fontes convencionais.Um dos problemas atuais no monitoramento da operação de aerogeradores (turbinas eólicas) é a determinação de parâmetros relacionados à sua estrutura, que se alteram ao longo do tempo. Este trabalho aplica o método do Filtro de Kalman Estendido [2, 5] em um modelo matemático não-linear para multicorpos rígidos [1, 4] para a identificação dos coeficientes de elasticidade e de amortecimento na análise estrutural de um aerogerador de três pás, a partir de dados de campo tratados.As equações da dinâmica do sistema de multicorpos rígidos são derivadas das seguintes equações [3]: A partir das equações (1) e (2) chega-se a um sistema de equações não-lineares acopladas, onde são desconhecidos os ângulos de deslocamento de cada pá em relação ao sistema fixo de referência e os deslocamentos relativos a dois eixos perpendiculares entre si em relação ao topo da torre.Foi aplicado o método do Filtro de Kalman Estendido (EKF) para a identificação do coeficiente de elasticidade no sistema de cinco equações não-lineares acopladas a partir de dados experimentais tratados utilizando o software MATLAB. Alguns resultados são mostrados na Figura 1, de (a) até (d).
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