Vibrations of a Cracked Rotor : 3/2-Order Super-Subharmonic and 1/2-Order Subharmonic Oscillations

Most of the studies on the vibrations of cracked shafts investigated the major critical speed and the secondary critical speed. However, it is known that other kinds of vibrations appear in cracked shafts. In this paper, resonance phenomena of the 3/2-order super-subharonic and 1/2-order subharmonic oscillations are investigated. They occur when the natural frequency is equal to 3/2 or 1/2 times the rotating speed. In the theoretical analysis, a two-degree-of-freedom model whose spring characteristic is represented approximately by a power series is adopted. The following are clarified. (a) These two kinds of oscillations have similar characteristics. (b) They occur only in horizontal shafts. (c) Only the steady-state oscillations appear. (d) The amplitude of the steady-state oscillation decreases as the unbalance increases. (e) These theoretical results are verified by experiments.