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Abstract
Fatigue cracks may appear in horizontal rotating machinery due to periodic stresses imposed to its shaft. The investigation of stability behavior of cracked rotors can lead to proper diagnosis of machinery and to prevent possible accidents caused by the rotor failure. In this study, the dynamic stability of a rotor with a transverse crack is investigated. Models of both open and breathing cracks are developed and then used in the model of a cracked Jeffcot (de Laval) rotor. The stability of rotor motion equations represented by differential equations with periodic coefficients is investigated using Floquet theory. While both crack models show instability regions around the first un-damped frequency, sub-harmonic regions are predicted by the breathing crack models. Compared to perturbation methods frequently used to determine the stability regions, the transition matrix approach used in this study can be applied to complex models of rotors and consequently may help in the identification of cracks in rotating machinery.
Highlights
Rotordynamic systems, such as gas turbine and compressors, are extensively used in industry for many decades
The investigation of stability behavior of cracked rotors can lead to proper diagnosis of machinery and to prevent possible accidents caused by the rotor failure
The transition matrix approach was successfully applied in calculation of stability regions of a cracked rotor
Summary
Rotordynamic systems, such as gas turbine and compressors, are extensively used in industry for many decades. The fatigue cracks in the shaft of rotors are usually transverse, so the model of a rotordynamic system becomes asymmetric (open crack model). The crack may open and close as shaft rotates due to the rotor weight or unbalance, which leads to periodically time-varying equations of motion for the system (breathing crack model). A traditional approach to investigate the stability of rotor systems with cracks is to apply perturbation methods [4] to determine approximations of stability borderlines. This approach provides intuitive values of sub/ super-harmonic resonances of un-damped cracked rotors, but its application to complex rotor models is limited. Even though the current approach is more computational expensive than the perturbation method, the advantage is that it can be applied to any rotor or structure which has one or multiple cracks
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