Modelagem matemática e simulação numérica de um sistema rotativo eixo-disco-palhetas

Abstract

Rotating systems composed of a shaft-disc-blades assembly (SDB) have several industrial applications, specially on turbo machinery such as turbines, compressors, and aircraft engines. In this context, the rotating blades are critical components due to their considerable flexibility and high rotation operation, being subject to failure due to fatigue. Therefore, it is important to establish dynamical models to these systems, allowing the understanding of its behavior in the design phase. In this context, the present work formulates a mathematical model devoted to represente tha dynamic behavior a SDB system that considers the flexibility both of shaft and blades, modeled as beams. Their displacements are discretized by the Assumed Modes Method, and the Lagrange's Equation are used to obtain the equations of movement of the coupled system. The model is validated by comparing finite elements simulation woth experimental results achieved by other authors, showing good accuracy. The influence of rotation speed, number of blades and disc position on the natural frequencies is assessed. Finally, the unbalance response is analyzed for the damped and undamped system, identifying the presence of parametric frequencies on the corresponding vibration responses. The results show that the model is capable of describing the system's dynamic behavior.