Comparison of the Unbalance Responses of Jeffcott Rotors With Shaft Bow and Shaft Runout

The unbalance response of a Jeffcott rotor with shaft bow and/or runout was theoretically and experimentally studied. Bow refers to a rotor which is warped; bow is a function of running speed. Runout refers to electrical or mechanical asymmetrics of the shaft and is not dynamical. Included in the theoretical model is the capability of low-speed response compensation, such that the response at low speed can be vectorially subtracted from the total response at any rotational speed. Responses of rotors with equal amounts of bow or runout are shown to be significantly different in both Bode and Nyquist forms. Using low speed compensation is shown to “correct” the unbalance response of a rotor with runout to an ideal (unbowed - no runout) case. The amplitude response plot of a bowed rotor is not corrected to the ideal response plot by the use of such compensation; however, the shape of the phase response plot closely resembles the ideal case for most cases. A small scale lightly damped Jeffcott rotor rig was also tested. The magnitude and angular position of the shaft bow were parametrically varied. The vibration data from the rotor tests were plotted using a synchronous tracking filter by two methods: both not using and using low speed compensation. Experimental data agree excellently with predictions for a bowed rotor for all cases and differences less than 8 percent were usually found.