The influence of crack breathing and imbalance orientation angle on the characteristics of the critical speed of a cracked rotor

• Published in: Journal of sound and vibration Vol. 330; no. 9; pp. 2031 - 2048
• Main Authors: Cheng, Li, Li, Ning, Chen, Xue-Feng, He, Zheng-Jia
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 25.04.2011; Elsevier
• Subjects: Applied sciences; Breathing; Cracks; Dominance; Drives; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Mathematical analysis; Mechanical engineering. Machine design; Nonlinearity; Orientation; Physics; Rotors; Shafts, couplings, clutches, brakes; Solid mechanics; Structural and continuum mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Jeffcott shaft; Vibration; Equation of motion; Surface crack; Turbojet; Unbalanced conditions; Critical speed; Modeling; Weight; Natural frequency; Transverse crack; Center of mass; Shaft; Vibration control; Propfan; Non linear effect; Dynamic load; Cracked beam
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2010.11.012

By analyzing the limitations of weight dominance and by taking the complicated whirl of the rotor into account, general equations of motion have been developed in case of a Jeffcott rotor with a transverse crack. The angle between the crack direction and the shaft deformation direction is used to determine the closing and opening of the crack, allowing one to study the dynamic response without assuming weight dominance. Using the new equations, the dynamic response of a cracked rotor near its critical speed has been computed via a numerical method to investigate the influence of nonlinear breathing of the crack and that of the imbalance orientation angle β on the stability, critical speed and peak response of the rotor. The results show that nonlinear breathing can improve the stability of a rotor in contrast to a rotor with an open crack, and, with a reversed imbalance (70°<β<270°), that it can reduce the vibration response in contrast to an uncracked rotor. The basic characteristics of a cracked rotor near its critical speed are similar to those of an uncracked rotor. The critical speed can be determined by measuring the rotation of the center of gravity. The critical speed of a cracked rotor is located between the natural frequencies of the fully open crack and those of the fully closed crack and depends on the imbalance orientation angle. Its value is lowest at β≈90° and highest at β≈270°. The peak in the response at the critical speed is mainly determined by the imbalance orientation angle. At β≈0° and 180°, the peak corresponds to the maximum and minimum response, respectively.