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Research Papers

A Solution for the Stabilization of Electrodynamic Bearings: Modeling and Experimental Validation

[+] Author and Article Information
Andrea Tonoli

 Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italyandrea.tonoli@polito.it

Nicola Amati

 Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italynicola.amati@polito.it

Fabrizio Impinna

 Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italyfabrizio.impinna@polito.it

Joaquim Girardello Detoni

 Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italyjoaquim.detoni@polito.it

J. Vib. Acoust 133(2), 021004 (Mar 01, 2011) (10 pages) doi:10.1115/1.4002959 History: Received August 01, 2009; Revised August 03, 2010; Published March 01, 2011; Online March 01, 2011

Electrodynamic bearings are a kind of passive magnetic bearings based on eddy currents that develop between a rotating conductor and a static magnetic field. Relative to active magnetic bearings, their passive nature implies several advantages such as the reduced complexity, improved reliability, and smaller size and cost. Electrodynamic bearings have also drawbacks such as the difficulty in ensuring a stable levitation in a wide speed range. The most common solution to improve the stability is to add a nonrotating damping between the rotor and the stator. Although effective, this solution implies the installation of a dedicated magnet on the rotor. This increases the rotor weight and complexity and rises some concerns about the mechanical resistance. The aim of the present work is to experimentally validate the model of an electrodynamic bearing proposed by the same Authors in a previous paper and to investigate a new solution for the stabilization of electrodynamic bearings based on the introduction of compliant and dissipative elements between the statoric part of the bearing and the ground. The performances of the proposed solution are studied in the case of a simple Jeffcott rotor by means of root loci to investigate the stability of the system. The results show an improved stability relative to the test cases reported in the literature.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 8

Impact test result. Time response acquisitions at different rotating speeds. (a) Ω=0 rad/s, (b) Ω=31.4 rad/s, (c) Ω=62.8 rad/s, and (d) Ω=94.2 rad/s. Experimental (—) and analytic (- - -) results.

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Figure 9

Behavior of the main poles of the test bench. s1 and s2 are the poles that describe the dynamic of the statoric mass ms. Analytic (˟) and experimental (○) results.

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Figure 10

(a) Scheme of an electrodynamic bearing stabilized by introducing the damping between the rotating part of the bearing and the casing and (b) schematization of the equivalent Jeffcott rotor model

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Figure 7

Comparison between the impact measured FRF (—) and the model transfer function (- - -). The lowest peak represents the behavior of the system at Ω=0 rad/s; the middle one is reached at Ω=31.4 rad/s; and the highest one is obtained considering Ω=69.1 rad/s.

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Figure 11

(a) Scheme of an electrodynamic bearing stabilized by introducing the damping between the nonrotating part of the bearing and the casing and (b) representation of the equivalent Jeffcott rotor model

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Figure 12

Sensitivity analysis of the damper parameters. (a) 2D map of Ωs as a function of cs and ks with ms=1 kg and (b) Ωs as a function of cs for three representative values of ks. The analysis is related to stabilization method 2. The line with square marks refers to Ωs as a function of cn in the case of stabilization method 1.

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Figure 13

Optimal stabilizing rotation speeds that can be achieved for different values of the stator mass ms

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Figure 14

(a) Root locus of the system characterized by ms=1 kg, ks=15000 N/m, and cs=663 N s/m and (b) detailed behavior of poles s2, s3, and s4

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Figure 1

(a) Short circuited coil moving relative to a constant magnetic field, (b) mechanical equivalent model, and (c) mechanical impedance as a function of the frequency

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Figure 2

(a) Scheme of an electrodynamic bearing and (b) schematic representation of the related dynamic model

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Figure 3

Test rig for quasi-static and dynamic tests: (a) picture, (b) cross-sectional view, and (c) EDB cross-sectional view

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Figure 4

(a) Scheme of the test rig. The rotating shaft is rigidly connected to the ground, and the magnetic circuit is supported by compliant beams. (b) Representation of the rotor on electrodynamic bearing in the configuration of the test rig.

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Figure 5

Steady state behavior of an electrodynamic bearing, analytic parallel (⋯) and perpendicular (—) components of the force. Measured parallel (˟) and perpendicular (○) components: (a) zco=0.5 mm, (b) zco=1 mm, and (c) zco=1.5 mm.

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Figure 6

Evolution of the electromagnetic force Fz generated by the EDB for increasing rotation speeds. Constant eccentricity (⋯) and constant speed (- - -), analytic curves. Constant eccentricity (○) and constant speed (˟), experimental results.

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