Análise por elementos finitos da influência de descontinuidades geométricas sobre o comportamento dinâmico de rotores flexíveis.

Abstract

This work deals with a finite element analysis of the dynamic behavior of cracked flexible rotors supported by hydrodynamic journal bearing. Geometric discontinuities such as cracks, holes, undercuts, etc. can strongly affect the vibrational response of rotating systems due to the rotor local flexibility changes. The rotor model is based on theTimoshenko beam theory, in which the translational inertia, rotary inertia, gyroscopic effects and shear effects are accounted for. The hydrodynamic bearings are modeled by using a linearized perturbation procedure applied on the classical Reynolds equation, which permits to render the bearing dynamic force coefficients. The rotor crack is represented onthe rotor model by the localized modification of the shaft element stiffness matrix. The fundamentals of the Fracture Mechanics are employed to obtain a relationship between the geometric discontinuity and the modified rotor stiffness matrix. The global equation of motion of the rotor-bearing system describes the bending vibration problem of rotatingshafts supported by fluid-film bearings. A formulation of state variables is employed to generate an eigenvalue problem associated with damping gyroscopic systems. The cracked rotor eigenvalues are estimated for various transverse crack sizes. The critical speed maps are computed for continuous and cracked rotors, depicting the influence of transversecracks on the dynamic behavior of rotating systems.