In order to diagnose the existence of a crack in rotating machinery

the transient vibration of a cracked rotor through parametric resonance range is investigated.By means of primary harmonic transformation

the normal motion equation of the cracked rotor is transformed into a new differential one.From direct solution of this equation

the amplitude of primary harmonic vibration can be obtained under nonstationary or stationary excitation.In respective consideration of ideal and nonideal sources of energy

it is found that:(1)Whether the source of energy is ideal or not

the largest amplitude of transient vibration near 2ω c/3 and 2ω c (Parametric resonance range) of the rotor with crack is bigger than that without crack (where ω c is the critical speed of the rotor without crack).And the deeper the crack

the larger the amplitude in the case of the ratio of crack depth to shaft diameter less than 0 4.(2)When the source of energy is ideal

the larger the acceleration

the less the largest amplitude of transient vibration through parametric resonance ranges of the cracked rotor.Because parametric resonance is the exclusive characteristic of cracked rotor according to the authors′ previous work

the authors believe that the transient vibration behaviors near 2ω c/3 and 2ω c may be a basis of diagnosing cracks on a shaft of rotating machinery.