Mathematical Modelling of an Unbalanced Rotor Subjected to Transverse Vibrations

Abstract

The static and dynamic balancing of a rotor plays a very important role in deciding the life-span of any turbo-machinery which is running at a very high speed. The major problems which face during the running of turbo machineries are unbalancing of the rotor. Rotor unbalance may be due to wrong selection of the manufacturing process, method of manufacturing, wear and tear of rotating component, thermal deformations, deposition of material on the rotor surface, etc. There are various static and dynamic balancing methods depending upon the type of rotor used in industries, power-plant, heavy machineries, automobiles, etc. This paper examines the transverse vibrations which is the main cause of the unbalance in a machine rotor. A rotor is balanced at a constant speed but in actual practice, the rotor is operated at various speeds. So, this paper also determines the range of angular velocity for which the machine under consideration exhibits a stable behaviour. Mathematical models of an unbalanced rotor are developed for free un-damped, free damped and force damped conditions that are developed and analyzed.