Rotor Model Updating and Validation for an Active Magnetic Bearing Based High-Speed Machining Spindle

Abstract

This paper presents an experimentally driven model updating approach to address the dynamic inaccuracy of the nominal finite element (FE) rotor model of a machining spin dle supported on active magnetic bearings. Modeling error is minimized through the application of a numerical optimization algorithm to adjust appropriately selected FE model parameters. Minimizing the error of both resonance and antiresonance frequencies simultaneously accounts for rotor natural frequencies as well as for their mode shapes. Antiresonance frequencies, which are shown to heavily influence the model's dynamic properties, are commonly disregarded in structural modeling. Evaluation of the updated rotor model is performed through comparison of transfer functions measured at the cut ting tool plane, which are independent of the experimental transfer function data used in model updating procedures. Final model validation is carried out with successful imple mentation of robust controller, which substantiates the effectiveness of the model updat ing methodology for model correction.

Resonance Vibration Control for AMB Flexible Rotor System Based onµ-Synthesis Controller

“…Subject to gyroscopic effect and rotor internal damping, rotor dynamic is inherently speed dependent, which complicates the controller design [10]. Meanwhile, due to the nonlinear material properties in laminations, shrink fits, assembling and manufacture error, the rotor modal perturbation should be considered during controller design [11]. Therefore, the resonance vibration control of flexible rotor has been the focus of much research over the past decades.…”

Active Magnetic Bearing Rotor Model Updating Using Resonance and MAC Error

“…The AMB system is open loop unstable and feedback control is needed for levitation. This function is commonly achieved by single input and single output (SISO) controller design such as proportional-integral-derivative (PID) controller [3]. However, decentralized PID controllers do not always provide the desired performance and robustness especially when the operating speed is above the system's critical speed and the gyroscopic effect is involved.…”

“…For rotor AMB system, the rotor dynamic characteristics such as resonance and mode shape calculated by the rotor model are not always equivalent to the experimental results since the rotor adopted in AMB system is assembled by several components with interference fits. When assembled, the resulting AMB rotor exhibits inhomogeneous material properties which are assumed as a source of modelling error [7]. For example, a typical rotor AMB system includes rotor shaft, front/rear AMB lamination stacks, thrust AMB lamination stacks, sensor rings, and motor ( Figure 2), which are assembled with interference fits and shrink effects, contributing to the bending stiffness of the rotor shaft [8].…”

“…Dynamic modelling is an important consideration for structure design and almost always results in errors to some degree when compared to experimental result [9]. The difference between experimental data and finite element models is generated for various reasons which primarily originate from unknown structure features and simplifications [7,10]. Finite element model updating techniques are used to adjust selected parameters of models to minimize the discrepancy and establish a model which is more compatible with experimental data and more closely represents the dynamic characteristic of the object [11].…”

“…Iterations are terminated when satisfactory accuracy is reached. This approach commonly employs optimization routines which minimize an error function [7].…”