A Finite Element Model for Distributed Parameter Turborotor Systems

Abstract

A specific numerical calculation procedure is outlined for a general turborotor-bearing system in which distributed inertia and elasticity are consistently represented. Bearings are represented by up to sixteen linear cross coupled coefficients each for stiffness and for damping. Discrete (as well as distributed) masses are allowed. As an example, for stability analysis (free response) a non-dimensional parameter study is made for the special case of a simple rotor supported on two short (Ocvirk) fluid film bearings. A comparison of discrete and distributed parameter rotor representations shows that the discrete parameter model predicts onset of instability at a lower speed ratio and is, therefore, more conservative. For unbalanced response (forced response), comparison is made to Prohl’s method, which represents mass discretely. A considerable reduction in the number of degrees of freedom necessary for accurate system representation is observed with the finite element formulation.

Vibration Analysis of Hollow Tapered Shaft Rotor

“…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.…”

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“…However, as the transfer matrix method provides dynamic responses only at the endpoints of a 1D system, postprocessing is necessary to compute the dynamic responses at the interim positions of the system. [Ruhl and Booker 1972] and [Nelson 1980] used FEM to investigate the stability and dynamics of rotor systems. In general, a large number of degrees of freedom (DOFs) are required for an FEM model of a large flexible rotor system, which may result in an increase in the computational cost as well as a widely spread frequency spectrum which may include many insignificant vibration modes.…”

Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

“…Thus, rotor dynamacs began modeling the rotor systems using these beambased models via FEM for rotor analysis [28,29]. Although there are higher computational costs associated with FEM compared with TMM, FEA "accommodates coupled behaviors of flexible disks, flexible shafts, and flexible support structures into a single massive multidimensional model" [26].…”