Abstract
In this article, a model is described that allows one to simulate the static behavior of a transversal crack in a horizontal rotor, under the action of the weight and other possible static loads and the dynamical behavior of the rotating cracked shaft. The crack “breaths,” i.e., the mechanism of opening and closing of the crack, is ruled by the stress acting on the cracked section due to the external loads; in a rotor the stress is time‐depending with a period equal to the period of rotation, thus the crack “periodically breaths.” An original simplified model is described that allows cracks of different shape to be modeled and thermal stresses to be taken into account, since they may influence the opening and closing mechanism. The proposed method has been validated using two criteria. Firstly, the crack “breathing” mechanism, simulated with the model, has been compared with the results obtained by a nonlinear 3‐D FEM calculation and a good agreement in the results has been observed. Secondly, the proposed model allows the development of the equivalent cracked beam. The results of this model are compared with those obtained by the above‐mentioned 3‐D FEM. There is a good agreement in the results, of this case as well.Therefore, the proposed crack model and equivalent beam model can be inserted in the finite beam element model used for the rotor dynamical behavior simulation—the obtained equations have time‐depending coefficients, but they can be integrated in the frequency domain by using the harmonic balance method. The model is suitable for finite beam elements with six degrees of freedom per node, in order to account also for torsion vibrations and coupling between torsion and flexural vibrations.
Highlights
A model is described that allows one to simulate the static behavior of a transversal crack in a horizontal rotor, under the action of the weight and other possible static loads and the dynamical behavior of the rotating cracked shaft
The crack “breaths,” i.e., the mechanism of opening and closing of the crack, is ruled by the stress acting on the cracked section due to the external loads; in a rotor the stress is time-depending with a period equal to the period of rotation, the crack “periodically breaths.”
An original simplified model is described that allows cracks of different shape to be modeled and thermal stresses to be taken into account, since they may influence the opening and closing mechanism
Summary
To determine the temperature distribution, the equation of the thermal exchange is used in the case of axial-symmetry and of an infinite cylinder: ρcp ∂T k ∂t. In each position, following iterative calculations are performed on the discretized section shown, in order to define the open and closed sections of the cracked area, the position of the center of gravity G of the closed surface, the position of the main axis of inertia (angle θ) with origin in G, and the second area moments with respect to the main axis and the moments MBx , MBy due to the thermal stress distribution. The bow which has been calculated with the equivalent length lc beam generates a relative angular deflection of the end nodes: the same relative angular deflection can be applied directly to the crack faces, in the local crack model
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