Mathematical modeling of vibration failure caused by balancing effect in hydraulic turbines

This article discusses the causes of vibrations depending on unbalanced hydraulic forces in rotating and non-rotating equipment in hydraulic plants within the scope of vibration measurement standards. The radial and axial positions of the turbine shaft, normal operating conditions, the absolute vibration of the signal output velocity during startup and shutdown during unbalance condition of the turbine, the proximity probes have been measured by TMO 793 accelerometer sensor and TMO 793 velocity sensor. The results obtained from the monitoring are analyzed and the first discussion is over the comparison of the current operating levels and vibration standards. Secondly, the comparison is analyzed in order to examine the improvement in vibration level of the elimination of hydraulic imbalance more comprehensively, considering the stability of the hydro turbine-generator unit, a proportional row damping force, proportional-order oil-film force and a hydraulic force and by creating a new non-linear proportional-order mathematical model. Changes in vibration levels and spectral bands for failure types are stated as well. The solution of this integrated and accurate mathematical model shows that it is useful and concise in the diagnosis and prediction of faults in hydropower plants.