Influence of Acceleration on the Critical Speed of a Jeffcott Rotor

The effects of angular acceleration on a Jeffcott rotor have been examined both theoretically and experimentally. The equations of motion were solved via numerical integration. The rotor’s response to unbalance was predicted for a number of cases of acceleration and damping. Both amplitude and phase responses were studied. In addition, techniques were developed for identifying system damping from data taken during accelerated runs. The results of the analysis indicate that for high acceleration rates the amplitude response at the critical speed may be reduced by a factor of four or more. The speed at which the peak response occurs can also be shifted by 20 percent or more. Experimentally, a small lightly damped rotor (ζ = 0.0088) was run for several acceleration rates. The peak responses typically agree within 6 percent of theoretical predictions. Also, a beat frequency was observed both theoretically and experimentally after the rotor had passed through the critical speed.