A study on the dynamics of a cracked Jeffcott rotor

The dynamic behavior of a horizontal cracked Jeffcott rotor is investigated in the paper. With the influence of whirl speed taken into account, the flexural stiffness matrix of the cracked shaft is derived. The equations of motion of the cracked rotor are derived and its dynamical behaviors are analyzed. Numerical analysis demonstrates that the responses of the vibration contain 2x,3x···exponents, reaching its maximum value when Ω = 1/2,1/3···resp components of high frequency almost disappear when the rotor runs in the supercritical region, but their phases change violently. β and e over-bar influence mainly 1X component. The center of the motion orbit of the rotor changes because of the existence of crack. The crack keeps open or close when the rotor runs near the critical speed. Otherwise, it opens and closes by turns if e over-bar is less than 1.