Critical speeds and unbalance response of cantilever-sleeve rotors using finite elements with efficient higher order basis functions

Design of industrial rotor-bearing systems requires an understanding of their dynamic behavior, which involves the determination of their critical speeds and unbalance response. Dynamic behavior of simple rotor systems can be studied using analytical techniques. However, for complex rotor systems it is necessary to use approximate techniques. The finite element method is one such approximate technique and has been in use as a computational method for solving these problems. In most cases finite element method requires a fine discretization of the rotor model and this leads to setting up and solving a large number of simultaneous and coupled linear differential equations for the unknown displacements. With such large systems the calculation becomes very time consuming, which may not be economically feasible. The prime objective of the present investigation is to develop an efficient and economical technique for the determination of the critical speeds and the unbalance response of complex rotorbearing systems such as cantilever-sleeve rotor. The technique is based on higher order finite elements. By using this technique the size of system equations can be significantly reduced without affecting the dynamic characteristics of the system. The technique also incorporates all the natural and essential boundary conditions right in the basis functions at element formulation. Thus, this element adequately represents all the physical situations involved in any combination of displacement, rotation, bending moment and shearing force boundary conditions. The dynamic behavior of a cantilever-sleeve rotor with a disk at the end is studied using such higher order finite elements. More accurate results are obtained using a coarse mesh that has increased number of degrees of freedom. Further no errors are introduced-during post processing for stresses, strains, etc.