A shaft finite element for analysis of viscoelastic tapered Timoshenko rotors

Abstract

Finite element modeling of thick rotor (deep rotor) requires the use of the Timoshenko element, which takes care of shear deformation. Modeling a rotor whose cross section varies can be done using uniform stepped cylindrical elements, but the number of elements required for the converged results is enormous. Further modeling of doubly tapered rotors and rotors with sharp changes in taper angle using such methods become difficult and does not appear feasible that is why the formulation of conical rotor elements is necessary. The complexity in formulations arises due to the presence of the shear parameter in the denominator. Till now, in the literature of the Timoshenko rotor, geometric properties are taken to be linearly varying; the shear parameter is the approximation of average values of two end nodes. On the other hand, the modeling of damping in rotors becomes essential as it controls the stability limit. The present paper develops three different viscoelastic tapered rotor elements using the Maxwell-Wiechert model. While the first element (VTRE 1) uses the average shear parameter, the second element (VTRE 2) uses a higher degree polynomial to approximate the shear parameter. While the first two-rotor elements are solid, the third element (VTRE 3) is hollow. Results show that viscoelastic tapered elements provide better results with the lesser number of elements. For the rotor with a large taper angle, VTRE 2 performs better than VTRE 1. Further modeling of the hollow tapered rotor with a linear variation of taper angle and discontinuities at definite points is not possible by the use of uniform elements. Modeling such a rotor using VTRE 3 is rendered simple. Practical usage of such rotors further enhances the importance of the present work.