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TECHNICAL PAPERS

Direct Hybrid Adaptive Control of Gear Pair Vibration

[+] Author and Article Information
Yuan H. Guan, W. Steve Shepard

University of Alabama, Department of Mechanical Engineering, 290 Hardaway Hall, Box 870276, Tuscaloosa, AL 35487

Teik C. Lim

University of Cincinnati, Mechanical, Industrial and Nuclear Engineering, 624 Rhodes Hall, P.O. Box 210072, Cincinnati, OH 45221

J. Dyn. Sys., Meas., Control 125(4), 585-594 (Jan 29, 2004) (10 pages) doi:10.1115/1.1636771 History: Received July 26, 2002; Revised April 21, 2003; Online January 29, 2004
Copyright © 2003 by ASME
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References

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Chen, M. H., 1999, “Combining the Active Control of Gear Vibration with Condition Monitoring,” Ph.D. dissertation, University of Southampton.
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Cricenti, F., Lang, C. H. and Paradiso, D., 2000, “Development of an Analytical Model for the Static and Dynamic Transmission Error Calculation: Validation on a Single Vehicle Gear Vibration Test Bench,” Proceedings of the ASME, 8th Inter. Power Transmission & Gearing Conference, Baltimore, Paper number DETC2000/PTG-14426.
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Figures

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A torsional dynamic model of the spur gear pair
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Closed-loop system with both state feedback gain d and feed-forward gain Ψ
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Maximum eigenvalue of matrix P divided by q
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Time trajectory of the closed-loop system with control activated at time t=0.01 s: (a) displacement, (b) velocity, and (c) control force
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Time trajectory of the estimated state feedback gain d and first element of Ψ with control activated at time t=0.01 sec. (a) ——— , displacement feedback gain d(1); – – –, first element of Ψ ; (b) velocity feedback gain d(2)
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Time trajectory of the second to last elements of the estimated feed-forward gain Ψ with control activated at time t=0.01 sec. (⋅⋅⋅⋅⋅⋅ , i=2;——— , i=3;── , i=4; ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅, i=5)
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Convergence rates of the closed-loop system with control activated at time t=0.01 s. (——— ), λ=2.31; -⋅-, λ=0.8;⋅⋅⋅⋅⋅⋅⋅⋅ , λ=4.0)
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Time history response of the closed-loop system containing 5% frequency estimation error with control activated at time t=0.01 s: (a) displacement, (b) velocity
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Time trajectory of the estimated feed-forward gain Ψ in the presence of 5% frequency estimation error with control activated at time t=0.01 s. (– – –, i=1;⋅⋅⋅⋅⋅⋅ , i=2;——— , i=3; —, i=4; ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅, i=5)
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Predicted gear vibration response spectra with no control (⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅), and with control using the proposed (———) and filtered-x LMS (– – –) algorithms
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Comparison of the uncontrolled (⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅) and controlled (–) gear vibration response spectra due to the first four harmonics of transmission error excitation

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