Transverse Crack Modeling and Validation in Rotor Systems, Including Thermal Effects

N Bachschmid,S Audebert,E Tanzi,P Pennacchi

doi:10.1155/s1023621x03000101

N Bachschmid, S Audebert + Show 2 more

Open Access

https://doi.org/10.1155/s1023621x03000101

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Abstract

This article describes a model that allows the simulation of the static behavior of a transverse crack in a horizontal rotor under the action of weight and other possible static loads and the dynamic behavior of cracked rotating shaft. The crack breathes—that is, the mechanism of the crack's opening and closing is ruled by the stress on the cracked section exerted by the external loads. In a rotor, the stresses are time-dependent and have a period equal to the period of rotation; thus, the crack periodically breathes. An original, simplified model allows cracks of various shapes to be modeled and thermal stresses to be taken into account, as they may influence the opening and closing mechanism. The proposed method was validated by using two criteria. First the crack's breathing mechanism, simulated by the model, was compared with the results obtained by a nonlinear, threedimensional finite element model calculation, and a good agreement in the results was observed. Then the proposed model allowed the development of the equivalent cracked beam. The results of this model were compared with those obtained by the three-dimensional finite element model. Also in this case, there was a good agreement in the results.Therefore, the proposed models of the crack and the equivalent model of the beam can be inserted into the finite element model of the beam used for the rotor's dynamicbehavior simulation; the obtained equations have timedependent coefficients, but they can be integrated into the frequency domain by using the harmonic balance method.

Highlights

This article describes a model that allows the simulation of the static behavior of a transverse crack in a horizontal rotor under the action of weight and other possible static loads and the dynamic behavior of cracked rotating shaft
An original, simplified model allows cracks of various shapes to be modeled and thermal stresses to be taken into account, as they may influence the opening and closing mechanism
First the crack’s breathing mechanism, simulated by the model, was compared with the results obtained by a nonlinear, threedimensional finite element model calculation, and a good agreement in the results was observed

Summary

THE THERMAL BEHAVIOR AND BREATHING MECHANISM OF A CRACKED ROTOR

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. The behavior was as expected: during the negative transient, the positive tensile stresses on the skin and the negative compression stresses on the internal part vanish in correspondence with the crack; the crack is completely open This can be seen, which shows the relative axial displacements on the crack surface. The axial stress is roughly 0; in the inner part, a maximum compressive stresse of 11.8 MPa is reached; and on the outer part, close to the crack’s tip, a maximum tensile stress of 117 MPa is reached All these figures and some of the following were obtained using the nonlinear 3D model for the crack of 50% depth. The axial stress distribution over the cross-section of the beam, as obtained by the 1D model with the smoother thermal transient (±20◦C/min) after 15 min, is very similar to that obtained for ±100◦C/min gradient after 5 sec (see Fig. 3)

TRANSVERSE CRACK MODELING

VALIDATION OF THE BREATHING MECHANISM MODEL BY TEMPERATURE GRADIENTS

Findings

CONCLUSION