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

Abstract

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.

Development and Performance Measurements of Gas Foil Polymer Bearings with a Dual-Rotor Test Rig Driven by Permanent Magnet Electric Motor

“…Here, 𝑍 is the vibration with runout removed, Z is the vibration signal measured at each rotational speed, and 𝑍 is the runout of the rotor. The runout of the rotor is equivalent to the vibration signal of the measured displacement sensor, rotating the rotor at a low speed with no dynamic rotor vibration effect [23].…”

Quantification of Faults in Rotating Machines

“…Since then many studies on the shaft bow response have been carried out. Some of these studies are those by Flack et al (1982), Parkinson et al (1984), Meacham et al (1988), and Rao and Sharma (2000). These studies suggest that the bend or bow in the rotor can be very well predicated during machine run-down experiments, however it is also essential to know the bend profile along the rotor length so that the remedial action can be taken in time which is difficult, if not impossible, from the experiments alone.…”

Combined rotor fault diagnosis in rotating machinery using empirical mode decomposition

“…Parkinson et al [12] described the differences in whirl experienced by a rotating shaft subject to shaft bow and mass unbalance. Shaft bow behavior has also been investigated by many authors [13][14][15]. Lee [16] has discussed the analytical aspects of rotor dynamics ranging from simple Jeffcott rotor to multi-degree-offreedom systems.…”