A Simple Viscoelastic Model of Rotor-Shaft Systems

Abstract

Damping exists in every material in varying degrees; so materials in general are viscoelastic in nature. Energy storage as well as dissipation in varying degrees, accompany every time varying deformation, with the effect that stress and strain in a material get out of phase. This work presents the development of preliminary equations of motion of a simple viscoelastic rotor-shaft-system by using differential operator algebra. Sample results of stability limit of spin speed and stability limit of uniform angular acceleration at a stable spin speed are also presented. Use of operators enables one to consider linear multi-element (e.g., 3, 4 or higher elements) material model for better representation of the viscoelastic rotor continuum rather than a two-element Voigt model used generally. The primary inspiration for a multi-element model arises from the need to capture broad band spectral behaviour of materials, primarily polymers and polymer composites. Additionally such a model is generic, as with suitable choice of model parameters, the formulation may also be used to obtain the equations of motion, if a two-element (Voigt model) or a single element (purely elastic) model is used to represent the rotor material behaviour. The equations developed may be easily used to find the time response of the rotor-disc subjected to any dynamic forcing function.