Finite Element Analysis of Coupled Lateral and Torsional Vibrations of a Rotor With Multiple Cracks

Abstract

The coupling between lateral and torsional vibrations has been investigated for a rotor dynamic system with breathing crack model. The stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node. Since the off-diagonal terms of the stiffness matrix represent the coupling of the respective modes, the special attention has been paid on accurate determination of their values. Based on the concepts of fracture mechanics, the variation of the stiffness matrix over the full shaft revolution is represented by the truncated cosine series where the fitting coefficient matrices are extracted from the stiffness matrices of the cracked shaft for a number of its different angular positions. The variation of the system eigenfrequencies and dynamic response of the rotor with two cracks have been studied for various shaft geometries, crack axial locations, and relative phase of cracks.

Condition Monitoring of Rotor Using Active Magnetic Actuator

“…The topic of cracked rotor vibrations has been analyzed in a great number of published works, for example [7][8][9][10][11][12][13][14]. They have been focused on the study of dynamic behavior of rotors with the so-called breathing type of crack during the passage through a critical speed at constant angular acceleration or deceleration.…”

“…They have been focused on the study of dynamic behavior of rotors with the so-called breathing type of crack during the passage through a critical speed at constant angular acceleration or deceleration. For example, Sawicki et al [7][8][9][10] studied the dynamics of accelerating cracked rotors, the crack-induced coupling between the torsional and lateral vibrations, and the application of nonlinear dynamics tools for crack diagnosis. Gasch [10] provided a comprehensive investigation of the stability behavior of a cracked Jeffcott rotor.…”

Discussion of the dynamic stability of a multi-degree-of-freedom rotor system affected by a transverse crack

“…The SERR approach cannot be extended to other intermediate situations that are typical of rotating shafts without the application of rather complex modifications to the SERR approach, as shown by Darpe et al [24] and Papadoupolos [25]. The same approach also has been used by Xu et al [26] for time-step calculations in which the breathing behaviour was also determined by the vibrations. Varé and Andrieux [27] developed a model in the time domain in which the true breathing mechanism, or the compliance of the cracked element, is directly evaluated by means of a 3D model as a function of the applied forces in each time step.…”

Controlled Deflection Approach for Rotor Crack Detection

“…Progressive development of the finite element method and its application to rotor dynamics [23,24] resulted in very sophisti cated crack models in which fracture mechanics methods are applied. Dimarogonas and Paipetis [25] introduced the full, 6 x 6 stiffness matrix for the finite element containing the continuously open crack (the so called "slotted crack").…”

“…This is due to the fact that they depend on the torsional angle. That is why, in case of nonrotating shafts, the models should be used where stresses (or deformations) at the crack location are calcu lated [17,24].…”