Elechtromechanical Modeling and Vibration Analysis of a Coupled Hydroturbine-Generator Set at Different Speeds Considering the Gyroscopic Effect

Vibrations in rotating equipment are inevitable phenomena and its analysis is necessary and useful to study the condition of the equipment. In a coupled hydroturbine-generator set, the vibrations are caused by the dynamic forces of both machines. Due to the coupling of the turbine and the generator the vibration analysis of each machine separately can not reveal all the phenomena and dynamic behaviors. The change in speed and torque of the turbine and the generator affect each other, so the results of the coupling analysis are closer to reality. In this paper, dynamic modeling of the generator-turbine coupling set is performed and the governing equations of the system are solved using numerical methods in MATLAB software. For more accurate modeling and analysis of the system, the rotational speed of the shaft is considered as variable. The gyroscopic effect and arcuate whirl are also included in the modeling of the set. The frequencies in the vibrations of the set are extracted and the dynamic phenomena related to each are identified. The results show that new dynamic and vibrational phenomena in this system. Also, considering that imbalance mass is never zero, the resulting force is considered in the modeling and the effect of the amount of imbalance mass is also studied and analyzed. Due to the nonlinearity of the governing equations, the analysis of vibrations using phase plane diagrams shows that in some operating conditions, the vibration behavior is chaotic, which can be used in the processing of experimental signals.