A COHESIVE ZONE MODEL FOR THE INVESTIGATION OF THE BREATHING MECHANISM OF TRANSVERSAL CRACKS IN ROTORS

Abstract

The presence of a crack reduces the mean stiffness of the rotor system and intro- duces a stiffness variation during the revolution of the shaft. How the variable part of the rotor stiffness varies between a minimum (for a closed crack) and a maximum (for an open crack), depends on the so-called breathing mechanism. The breathing mechanism is known when the open and closed parts of the cracked area are known for all angular positions of the rotor. Here, finite element (FE) and multi-body simulation (MBS) is introduced. It is based on a representation of the fracture process zone by a cohesive zone model (CZM). First, the cracked elastic shaft with various relative crack depths is modelled by FE. As a second step, the FE model of the shaft is transferred into an MBS model in order to analyze the dynamic loads, due to the crack, and the inertia force acting during rotation at different rotating speeds. Finally, the vibration responses in the centroid of the shaft obtained from the MBS have been exported into the FE model in order to observe the breathing mechanism. This proposed tech- nique provides a useful tool for the analysis of rotor systems containing cracks, reveals the shape of the open crack part during rotation and helps investigating the dynamic behaviour of cracked shafts. Fatigue cracking of rotor shafts has long been identified as a limiting factor for safe and reliable operation of turbomachines. It can lead to catastrophic failure and great economic loss if not detected early. A crack in the rotor causes local changes in stiffness. These changes, in turn, affect the dynamics of the system: frequency of the natural vibrations and the ampli- tudes of forced vibrations are changed. If a cracked shaft rotates under external loading, the crack opens and closes regularly during the revolution of the shaft, it breathes. The breathing mechanism is produced by the stress distribution around the crack mainly due to the action of bending moment, while the effect of torsion is negligible. Usually, shaft cracks breathe when crack sizes are small, running speeds are low and radial forces are large (1). Breathing of the