Dynamic Modelling and Response of a Pelton Bucket

Abstract

The study of rotating cantilever beam has a wide range of practical engineering applications, including turbine blades, aircraft wings, etc. From the literature review, it was perceived that the research works lack the use of a rotating cantilever beam model for the vibrational study of a bucket of the Pelton turbine. This research work focuses the study of vibrational characteristics of a single bucket in the Pelton turbine under the action of jet force considering it as a rotating cantilever beam. The potential and kinetic energy are determined to obtain the mathematical model. Hamilton's principle is used to construct the governing equations for Cartesian deformation variables which include axial, and transverse deformations. Coriolis and Centrifugal Effects are indulged automatically, rather than the aid of ad hoc provisions. The dynamic force imparted by water jet is modeled in harmonic series by using Fourier Expansion. Equations were discretized using Galerkin’s Method to obtain the dynamic response of the system. Performing the analysis in the bucket of length 75𝑚𝑚 and attached with rotor rotating at speed of 1500 rpm, the first lower natural frequency is found to be 5281.4 𝐻𝑧 in the direction of jet for the first mode of vibration and the effect of Coriolis terms in natural frequency is found to be insignificant due to shorter length of the bucket. The bending stiffness was found to be increased with the increase in the rotational speed. Forced vibration analysis is carried out to determine the steady-state amplitudes of bending vibration. In the direction of jet, the maximum deformation is found to be 1.921 𝜇𝑚. The findings can be used as a guide for the dynamic analysis as well as a basis for design or advancement.