Vibration Analysis of Hollow Tapered Shaft Rotor

Shafts or circular cross-section beams are important parts of rotating systems and their geometries play important role in rotor dynamics. Hollow tapered shaft rotors with uniform thickness and uniform bore are considered. Critical speeds or whirling frequency conditions are computed using transfer matrix method and then the results were compared using finite element method. For particular shaft lengths and rotating speeds, response of the hollow tapered shaft-rotor system is determined for the establishment of dynamic characteristics. Nonrotating conditions are also considered and results obtained are plotted. 1. Introduction Shaft is a major component of any rotating system, used to transmit torque and rotation. Hence the study shaft-rotor systems has been the concern of researchers for more than a century and will continue to persist as an active area of research and analysis in near future. Geometry of shaft is of the main concern during the study of any rotating system. Most papers related to shaft-rotor systems consider cylindrical shaft elements for study and analysis of rotating systems. The first idea of transfer matrix method (TMM) was compiled by Holzer for finding natural frequencies of torsional systems and later adapted by Myklestad [1, 2] for computing natural frequencies of airplane wings, coupled in bending and torsion. Gyroscopic moments were first introduced by Prohl [3] for rotor-bearing system analysis. Lund [4] used complex variables as the next significant advancement in the method. An improved method for calculating critical speeds and rotor stability of turbo machinery was investigated by Murphy and Vance [5]. Whalley and Abdul-Ameer [6] used frequency response analysis for particular profiled shafts to study dynamic response of distributed-lumped shaft rotor system. They studied the system behavior in terms of frequency response for the shafts with diameters which are functions of their lengths. They derived an analytical method which uses Euler-Bernoulli beam theory in combination with TMM. On the other hand, there are large numbers of numerical applications of finite element techniques for the calculation of whirling and the computation of maximum dynamic magnitude. In this regard, Ruhl and Booker [7] modeled the distributed parameter turbo rotor systems using finite element method (FEM). Nelson and McVaugh [8] reduced large number of eigenvalues and eigenvectors identified, following finite element analysis, and the erroneous modes of vibration predicted were eliminated. Nelson [9] again formulated the equations of motion