Theoretical and experimental study of a motor-flexible coupling-rotor system subject to misalignment and unbalance

Shaft misalignment and rotor imbalance are major concerns in rotating machinery. The vibrations caused by misalignment and unbalance may destroy critical parts of the machine, such as bearings, seals, gears, and couplings. It is important to understand the dynamic characteristics of misalignment and unbalance in order to identify these machinery faults and to prevent machine failures. With this in mind, a theoretical model of a complete motor-flexible coupling-rotor system capable of describing the mechanical vibrations resulting from misalignment and unbalance was developed. The universal joint effect was included in the model to take the misalignment into account. Generalized equations of motion for a general system under unbalance and misalignment conditions were derived using the component mode synthesis technique. The derived equations indicate that the forcing frequencies due to shaft misalignment are even multiple frequencies of the motor rotational speed. The system response depends heavily on the relation between the system natural frequencies and the motor rotational speed. If any of the even multiples of the motor rotational speed is at or close to one of the system natural frequencies, the resonant condition occurs. As a result of this, the vibrations induced by misalignment are amplified into major vibration sources.;In order to verify the theoretical model, an experimental study was performed on a rotordynamic test apparatus. A self-designed, double-cross, flexible coupling and a commercial helical coupling were used in the experiments. The rotor shaft displacements were measured under the different misalignment and unbalance conditions. Numerical results were also obtained in both time and frequency domains. The numerical predictions are in good agreement with the experimental results. Both the tested and predicted results show that unbalance and misalignment can be characterized by 1x and 2x shaft running speed, respectively. However, misalignment effects sometimes may not be apparent because the forcing frequency (2x shaft running speed) is not close to one of the system natural frequencies to excite the system appreciably. Therefore, in some cases the misalignment is hidden and can not be identified in the vibration spectrum. On the other hand, if the 2x shaft running speed is at or close to one of the system natural frequencies, the misalignment effect can be magnified and a high frequency density level at 2x shaft running speed is pronounced in the frequency spectrum. In this case, either shaft alignment is needed or the shaft running speed needs to be changed in order to avoid excessive vibrations.