Dynamic response of vertical shaft Pelton turbine unit for forced vibration

Abstract

This research work was carried out to model the excitation force imparted by water jet in the form of Fourier series and determine the forced response of Pelton turbine unite of Khulelhani-I hydropower analytically by developing mathematical mode. Amplitude of forced vibration form analytical was compared with simulation result.

The mathematical model was developed by calculating the kinetic energy of disk and potential energy of both disk and shaft. Hamilton’s principle was used to determine equation of motion and then Galerkin method was used to determine response of the system. Fourier analysis was done to obtain the function in its exact form. The developed methodologies were followed to find the analytical solution of Kulekhani-I unit of 3100 kW rated at 600rpm. A rigid disk (runner and bucket assembly) was situated along end of flexible shaft with fixed support at the shaft.

First five Fourier components are to be considered in analysis for meaningful representation of forcing function. The amplitude of vibration of Pelton turbine unit with single nozzle in Y-direction (the direction of water jet) obtained by analytical method was closed with that obtained from the ANSYS simulation.