A method for predicting critical speed and damping ratio from open-loop characteristics of a rotating shaft

In rotating machinery, resonance vibration occurs when an unbalanced force acts on the shaft rotating at its natural frequency, known as the “critical speed”. In most cases, mechanical designers typically set the rated speed of such machinery just below the critical speed to reduce the vibration response to unbalanced forces. Vibration at the rated speed is therefore highly sensitive to an unbalanced force. This abnormality in vibration is compensated by “field balancing” to achieve safe rotational operation under small vibrations. As for filed balancing, it is known that the critical speed is close to the rated speed (within a small margin), but its exact value has not been determined by test runs (even after shipping of the machinery in question). Traditional methods for evaluating the critical speed and damping ratio require the rotating shaft to be operated above its critical speed. If the rotor exceeds the critical speed, the critical speed and its corresponding damping ratio are evaluated by using the “half-power method”. By contrast, when the rotor does not exceed the critical speed, the half-power method cannot be used to evaluate the critical speed and damping ratio. In this paper, we propose a method for predicting the unknown critical speed and damping ratio by calculating the approximated open-loop characteristics of the rotating shaft from the unbalanced-vibration response measured during field balancing without exceeding through the critical speed. The open-loop characteristics around the critical speed are extrapolated as lines that can predict the critical speed and damping ratio. The proposed method was verified by a hardware-in-the-loop simulation of the unbalanced-vibration response of a rotor model, and the simulation results show that the critical speed and damping ratio can be predicted by the proposed method without exceeding the critical speed.