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Research Papers

Multiharmonic Adaptive Vibration Control of Misaligned Driveline via Active Magnetic Bearings

[+] Author and Article Information
Hans A. DeSmidt

MABE Department, The University of Tennessee, 606 Doughterty Hall, Knoxville, TN 37996-2210

K. W. Wang

 The Pennsylvania State University, 157 Hammond Building, University Park, PA 16802kwwang@psu.edu

Edward C. Smith

 The Pennsylvania State University, 157 Hammond Building, University Park, PA 16802

J. Dyn. Sys., Meas., Control 130(4), 041006 (Jun 06, 2008) (13 pages) doi:10.1115/1.2907382 History: Received January 17, 2006; Revised August 19, 2007; Published June 06, 2008

Active magnetic bearings (AMBs) have been proposed by many researchers and engineers as an alternative to replace traditional contact bearings in rotor and driveshaft systems. Such active, noncontact bearings do not have frictional wear and can be used to suppress vibration in sub- and supercritical rotor-dynamic applications. One important issue that has not yet been addressed by previous AMB-driveline control studies is the effect of driveline misalignment. Previous research has shown that misalignment causes periodic parametric and forcing actions, which greatly impact both driveline stability and vibration levels. Therefore, in order to ensure closed-loop stability and acceptable performance of any AMB controlled driveline subjected to misalignment, these effects must be accounted for in the control system design. In this paper, a hybrid proportional derivative (PD) feedback/multiharmonic adaptive vibration control (MHAVC) feedforward law is developed for an AMB/U-joint-driveline system, which is subjected to parallel-offset misalignments, imbalance, and load-torque operating conditions. Conceptually, the PD feedback ensures closed-loop stability while the MHAVC feedforward suppresses steady-state vibration. It is found that there is a range of P and D feedback gains that ensures both MHAVC convergence and closed-loop stability robustness with respect to shaft internal damping induced whirl and misalignment effects. Finally, it is analytically and experimentally demonstrated that the hybrid PD-MHAVC law effectively adapts to and suppresses multiharmonic vibration induced by imbalance, misalignment, and load-torque effects at multiple operating speeds without explicit knowledge of the disturbance conditions.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Misaligned AMB-driveline system with universal joint couplings

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Figure 2

Eight pole radial magnetic bearing

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Figure 3

AMB inductive load/power amplifier system: (a) actual system and (b) modeled system

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Figure 4

AMB-driveline with hybrid PD/MHAVC

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Figure 5

Whirl speed versus PD control gain parameters with δ=0deg and TL=Top.

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Figure 6

δ-Ω0 instability regions of PD controlled driveline with kp=kp* and kd=kd* for load-torque bounds: (a) [0⩽TL⩽Top], (b) [0⩽TL⩽2Top], and (c) [0⩽TL⩽3Top]

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Figure 7

δ-Ω0 instability regions of PD controlled driveline with kp=kp* and kd=kd* for load-torque bounds: (a) [0⩽TL⩽Top], (b) [0⩽TL⩽2Top], and (c) [0⩽TL⩽3Top]

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Figure 8

kp-Ω0 instability regions of PD controlled driveline with kd=kd* for operating condition bounds: [0⩽TL⩽2Top] and (a) [0⩽δ⩽3deg], (b) [0⩽δ⩽4deg], and (c) [0⩽δ⩽6deg]

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Figure 9

kp-Ω0 instability regions of PD-MHAVC controlled driveline with kd=kd* for operating condition bounds: [0⩽TL⩽2Top] and (a) [0⩽δ⩽3deg], (b) [0⩽δ⩽4deg], and (c) [0⩽δ⩽6deg]

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Figure 11

HFC calculator block

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Figure 12

MHAVC synthesis block

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Figure 13

AMB-driveline response at Ω0=4815rpm with kp=kp* and kd=kd*, and ecc=20μm; (a) load torque, (b) misalignment, ((c) and (e)) PD control, and ((d) and (f)) PD-MHAVC control

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Figure 14

AMB-driveline response under PD-MHAVC control at Ω0=4815rpm with kp=kp* and kd=kd* for δ=4deg and TL=3Top

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Figure 16

Photo of AMB-driveline testrig facility

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Figure 17

Photo of magnetic bearing, shaft, and U-joint coupling.

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Figure 18

Schematic of AMB-driveline testrig with adjustable misalignments: top view

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Figure 19

Implemented digital PD feedback control system

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Figure 20

AMB coil/power amplifier transfer function: (a) magnitude and (b) phase

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Figure 21

AMB coil current/shaft displacement transfer function of levitated driveline under PD feedback control: (a) AMB1, (b) AMB2, and (c) AMB3

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Figure 22

Experimental results: shaft vibration with δ=3.0deg and TL=5.2Nm at speed; (a) Ω0=966rpm, (b) Ω0=1350rpm, and (c) Ω0=1806rpm

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Figure 23

Experimental results: AMB control current with δ=3.0deg and TL=5.2Nm at speed; (a) Ω0=966rpm, (b) Ω0=1350rpm, and (c) Ω0=1806rpm

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Figure 24

Experimental results: shaft vibration spectra with δ=3.0deg and TL=5.2Nm at speed; (a) Ω0=966rpm, (b) Ω0=1350rpm, and (c) Ω0=1806rpm

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Figure 15

AMB-driveline response at Ω0=4815rpm with kp=kp* and kd=kd*, and ecc=20μm; (a) load torque, (b) misalignment, ((c) and (e)) PD control, and ((d) and (f)) PD-MHAVC control

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