The focus of this literature survey and review is model reduction methods and their application to rotor dynamic systems. Rotor
dynamic systems require careful consideration in their dynamic models as they include unsymmetric stiffness, localized nonproportional
damping, and frequency-dependent gyroscopic effects. The literature reviewed originates from both controls and
mechanical systems analysis and has been previously applied to rotor systems. This survey discusses the previous literature
reviews on model reduction, reduction methods applied to rotor systems, the current state of these reduction methods in rotor
dynamics, and the ability of the literature to reduce the complexities of large order rotor dynamic systems but allow accurate
solutions.

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

In some industrial applications, influence coefficient balancing methods fail to find the optimum vibration reduction due to the limitations of the least-squares optimization methods. Previous min-max balancing methods have not included practical constraints often encountered in industrial balancing. In this paper, the influence coefficient balancing equations, with suitable constraints on the level of the residual vibrations and the magnitude of correction weights, are cast in linear matrix inequality (LMf) forms and solved with the numerical algorithms developed in convex optimization theory. The effectiveness and flexibility of the proposed method have been illustrated by solving two numerical balancing examples with complicated requirements. It is believed that the new methods developed in this work will help in reducing the time and cost of the original equipment manufacturer or field balancing procedures by finding an optimum solution of difficult balancing problems. The resulting method is called the optimum min-max LMI balancing method.

Balancing of Flexible Rotors Using Convex Optimization Techniques : Optimum Min-Max LMI Influence Coefficient Balancing

A method of balancing an assembly of rotary parts of a gas turbine engine (10) comprising measuring at least one of the concentricity and parallelism of each component and considering globally all possible component stacking positions to generate an optimized stacking position for each component of the assembly to minimize assembly unbalance.

Method of balancing a gas turbine engine rotor

The aim of this work is to propose a methodology for the experimental determination of the matrix relating unbalance forces to measured displacements for a rotating machine. The goal is to obtain an alternative solution to special situations found in the industrial context, especially for highly flexible rotors that may lead to a nonlinear behavior of the system. The trial-weights-based techniques, such as the influence coefficients method or the modal method, cannot be applied in such configurations. The proposed balancing method is based on the use of an identified model for the system. A pseudo-random optimization technique using genetic algorithms was applied for the identification process. The basic idea is to obtain the flexible rotor unbalance response, which is then mimicked by using a finite element method model in which the unbalance masses and their corresponding angular positions are the design variables from the optimization viewpoint. This way, an inverse problem is solved and the corrective...

On the balancing of flexible rotating machines by using an inverse problem approach

Methods of assembling a rotor assembly of a gas turbine engine having a plurality of components. The method comprises, in one aspect, determining a static unbalance force of each component using the mass and the center of mass location, and determining an optimum assembly arrangement minimizing static unbalance forces. Optimal component stacking positions, among other things, may then be established.

Gas turbine rotor assembly method

The traditional balancing methods using trial or calibration weights are quite effective, yet too many trials may result in a lengthy balancing process. It had been suggested in the literature that it is possible to balance flexible rotors without the use of trial weights, if a rotor model is available. A procedure is developed in this paper to balance flexible rotors using complex modes and complex vibration measurements. It is shown that a complex rotor model is essential for the success of the technique. Moreover, careful calibration of the rotor model is the major cornerstone of the procedure. Experimental results illustrate the success of the procedure.

Rotor Balancing Without Trial Weights

In this paper, a method for calibrating rotordynamic models of speed-dependent systems with anisotropic support is presented. The method is based on the comparison between the calculated eigenvalues and those extracted from the measured synchronous frequency response functions. An eigensensitivity analysis is conducted to calculate the sensitivity of the computed eigenvalues to the selected elements to be updated. This method is suitable for field application since it requires simple coastdown tests. The method is illustrated on a test rig with fluid film bearings and is shown to be effective in the calibration of rotordynamic models at the speeds of the modes excited within the operating speed range.

Model Calibration of Anisotropic Rotordynamic Systems With Speed-Dependent Parameters

The traditional balancing methods using trial or calibration weights are quite effective, yet too many trials may result in a lengthy balancing process. It had been suggested in the literature that it is possible to balance flexible rotors without the use of trial weights, if a rotor model is available. A procedure is developed in this paper to balance flexible rotors using complex modes and complex vibration measurements. It is shown that a complex rotor model is essential for the success of the technique. Moreover, careful calibration of the rotor model is the major cornerstone of the procedure. Experimental results illustrate the success of the procedure.Copyright © 2002 by ASME

A. A. Younan

Papers

Rotor Balancing Without Trial Weights

Model Calibration of Anisotropic Rotordynamic Systems With Speed-Dependent Parameters

Rotor Balancing Without Trial Weights