Transient response analysis of simply supported Pelton turbine during starting and shutdown

Variations in speed of shaft-disc systems is due to starting, shutdown and maneuver. Starting and shutdown of hydraulic turbine is the condition in which system is subjected to dynamic load causing transient excitation. Previously, study on transient response of shaft-disc system is done by experimental approach. So, mathematical model should be developed to define shaft-disc system for dynamic input. Development of a mathematical model for the study of vibration of a simply supported Pelton turbine under dynamic input is the main objective of this work. Mathematical model is developed based on rigid bearings, rigid disk and flexible shaft. As energy method is used in this work, total kinetic and potential energies of the shaft and disk are derived. By using assumed mode method, system’s energies are formulated. Formulated energies are used in Lagrange's equation of motion from which system's governing equation of motion is obtained. MATLAB program is developed to solve governing equation of motion which gives peak amplitude of 58.34µm and 115.87µm for starting and shutdown respectively. Solution from mathematical model is compared with simulated solution from ANSYS which gives variations of 2.35 % and 0.58 %.