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.
DownLoad: