Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

By considering time-dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analyzed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady-state harmonic component, the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit, and the amplitude and phase of the response signals are analyzed, taking into account the effect of crack size, crack location, rotor speed, and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depend on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the subcritical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full-speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis, and the phase angle difference between vertical and horizontal vibration signals.