Analyse numérique par la méthode des éléments finis du comportement vibratoire d’un rotor

Abstract

Vibration problems are one of the main causes of rotating machines in today's industrial world and to give more performance and reduce this phenomenon even more with good functionality and better reliability, researchers rely much more on simulation and calculations to get better results. This work offers a numerical analysis on the vibration behavior of a simple rotor. We determine the characteristics of the basic elements of the rotor: disc, shaft, bearing and unbalance then we will develop the expressions of kinetic energies and deformation as well as the virtual work corresponding to these elements by the Lagrange equations in order to determine the equations of motion The method followed for the resolution of computations is the modeling by the method of the trigonometric hierarchical finite elements which allowed us to predict the phenomena of the vibratory behavior of the rotors. This method makes it possible to determine the natural frequencies as a function of the rotational speed of the rotor, to plot the Campbell diagram, and to determine the possible critical speeds. The comparison of the results obtained is based on a finite element modeling with these calculations by means of an elaborate program and used to calculate the natural frequencies of a tree line constituted by an indefinite number of rotor elements