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Research Papers

Active Control of the Longitudinal-Lateral Vibration of a Shaft-Plate Coupled System

[+] Author and Article Information
Zhiyi Zhang

State Key Laboratory of Mechanical Systems and Vibration,
Shanghai Jiao Tong University,
Shanghai, 200240, P. R. C.
e-mail: chychang@sjtu.edu.cn

Emiliano Rustighi

Institute of Sound and Vibration Research,
University of Southampton,
Highfield, Southampton, SO17 1BJ, UK
e-mail: er@isvr.soton.ac.uk

Yong Chen

e-mail: chenyong@sjtu.edu.cn

Hongxing Hua

e-mail: hhx@sjtu.edu.cn
State Key Laboratory of Mechanical Systems and Vibration,
Shanghai Jiao Tong University,
Shanghai, 200240, P. R. C.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 5, 2011; final manuscript received March 1, 2012; published online September 10, 2012. Assoc. Editor: Ranjan Mukherjee.

J. Vib. Acoust 134(6), 061002 (Sep 10, 2012) (11 pages) doi:10.1115/1.4006647 History: Received May 15, 2011; Revised March 01, 2012

The coupled longitudinal-lateral vibration of a shaft-plate system and its suppression by means of a feedback control scheme are discussed. A simplified model of the system is established through synthesis of frequency response functions (FRFs) and verified with the finite element method (FEM). This analytical model describes the coupled longitudinal-lateral vibration of the system induced by longitudinal periodic excitation at the free end of the shaft. Based on this model, vibration control via longitudinal actuation on the shaft and active vibration cancellation are studied. The active control scheme is based on an adaptive feedback scenario and a novel mechanism of adaptation of the controller’s gain, which is proposed for time-varying dynamics induced by the variation of the axial spring stiffness. Simulation results have demonstrated that the control scheme is effective in attenuating vibration of the system. Furthermore, axial actuation on the shaft is able to cancel the effect of the longitudinal disturbance acting at the free end of the shaft and consequently reduces the internal forces as well as the vibration in the plate. However, deviation of the actuation force from the shaft axis will deteriorate control of the lateral vibration and sufficiently small deviation needs to be guaranteed.

Copyright © 2012 by ASME
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References

Figures

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Fig. 1

The shaft-plate coupled system

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Fig. 2

Forces and displacements of the coupled shaft-plate system

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Fig. 3

Force F2 induced by the unit force F for different kt

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Fig. 4

x2 induced by the unit force F for different kt

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Fig. 6

Force F2 induced by the unit forces F and Fa

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Fig. 7

Displacement x2 induced by the unit forces F and Fa

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Fig. 8

The proposed adaptive feedback control scheme

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Fig. 9

Phase-frequency diagram of x¯2/Fa

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Fig. 10

Acceleration responses at Point 5 to the control force Fa

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Fig. 11

Identified FRF of the control channel: (jω)2x¯2Fa-1 at kt=107 N/m

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Fig. 12

Signals in the controlled system. The longitudinal stiffness switches between kt=105 N/m and kt=107 N/m. (a) u(t): output of the controller; (b) car(t)/(|dr(t)dt|+cb); (c) sign(mu): the sign of μ; (d) 1r(t)dr(t)dt: slope of r(t); (e) r(t); (f) e(t): error signal.

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Fig. 13

Signals in the controlled system. The plant model is fixed but excitation frequencies vary piecewisely from 50 Hz to 200 Hz. (a) u(t): output of the controller; (b) car(t)/(|dr(t)dt|+cb); (c) sign(mu): the sign of μ; (d) 1r(t)dr(t)dt: slope of r(t); (e) r(t); (f) e(t): error signal.

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Fig. 14

Comparison of acceleration responses at Point 5 with/without control

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Fig. 15

Forces in the controlled system

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Fig. 16

Comparison of the influence of Fa and Ta when ea=0.01 m

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