Dynamic behavior of a rotating shaft containing a breathing crack

Abstract

As the modern rotating machinery has the tendency of increasing the operating speed and decreasing the weight and volume for higher efficiency and performance, the vibration responses due to the presence of unexpected abnormalities may become excessive in many occasions. In rotating machinery, the growth of cracks in the rotating components, if undetected, can cause severe accidents: the earlier the time of crack detection, the smaller the effort and expenses for repair. Since 1970``s many works on cracked rotor have been reported. In order to analyze the effects of crack in the shaft the equation of motion should be formulated considering the stiffness modification, while the effect of abnormalities such as unbalance and initial shaft bow in the rotor system are in general treated as the external forcing terms in governing equation. In this work, a breathing crack model is developed from the fracture mechanics concept, and the behavior and propagation phenomena of the transverse crack in a simple rotor are studied and crack identification schemes are proposed. The change of shaft stiffness due to crack breathing is expressed by using the direct and cross-coupled stiffnesses, which are functions of responses. The responses and the stiffnesses are solved by simultaneous numerical integration of the coupled governing and stiffness equations. The variations in stress intensity factor at crack front are calculated based on the gravitational responses of the cracked rotor, as the crack depth and the rotational speed are varied. The crack propagation phenomenon is clarified based on the stress intensity factors calculated. The crack propagation velocity in a cracked rotor increases as the crack depth increases, and the crack propagation pattern is dependent upon the rotational speed and direction. An approximate approach is carried out to simplify the behavior of cracked rotor, by using the switching crack model having two different direct stiffnesses, depending upon...