Dynamic response of a shaft of a Pelton turbine due to impact of water jet

The performance and reliability of any rotating machine can be studied by proper dynamic analysis of the machine. This paper presents a method to study the dynamic response of a Pelton turbine shaft due to the impact of a water jet. Equations of motion for the bending vibration of the Pelton turbine assembly, in two transverse directions, are developed using the Lagrange equation of motion with the help of assumed mode’s method. The Pelton wheel is assumed as a rigid disk attached to an Euler-Bernoulli shaft. The impact provided by the water jet is represented in the form of a Fourier series. Critical speeds of the system are determined by performing free vibration analysis and presented in the form of the Campbell diagram. The response plots due to the impact of water are generated by performing forced response analysis. Both free and forced analyses are carried out by considering the first three modes of vibration.