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TECHNICAL PAPERS

Robust Active Vibration Control of a Bandsaw Blade

[+] Author and Article Information
Christopher J. Damaren

Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

Lan Le-Ngoc

Industrial Research Ltd., 5 Sheffield Crescent, PO Box 20-028, Christchurch, New Zealand

J. Vib. Acoust 122(1), 69-76 (Feb 01, 1999) (8 pages) doi:10.1115/1.568437 History: Received August 01, 1998; Revised February 01, 1999
Copyright © 2000 by ASME
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References

Mote,  C. D., and Naguleswaran,  S., 1966, “Theoretical and Experimental Band Saw Vibrations,” ASME J. Eng. Ind.,88, pp. 151–156.
Naguleswaran,  S., and Williams,  C., 1968, “Lateral Vibration of Bandsaw Blades, Pulley Belts, and the Like,” Int. J. Mech. Sci., 10, pp. 239–250.
Alspaugh,  G., 1967, “Torsional Vibration of a Moving Band,” J. Franklin Inst., 283, pp. 328–338.
Soler,  J., 1968, “Vibrations and Stability of a Moving Band,” J. Franklin Inst., 286, pp. 295–307.
Ulsov,  A. G., and Mote,  C. D., 1982, “Vibration of Wide Bandsaw Blades,” ASME J. Eng. Ind.,104, pp. 71–78.
Lengoc,  L., and McCallion,  H., 1995, “Wide Bandsaw Blade Under Cutting Conditions, Part I: Vibration of a Plate Moving in its Plane While Subjected to Tangential Edge Loading,” J. Sound Vib., 186, No. 1, pp. 125–142; “Part II: Stability of a Plate Moving in its Plane while Subjected to Parametric Excitation,” 186, No. 1, pp. 143–162; “Part III: Stability of a Plate Moving in its Plane While Subjected to Non-conservative Cutting Forces,” 186, No. 1, pp. 163–179.
Lehmann,  B. F., and Hutton,  S. G., 1996, “The Mechanics of Bandsaw Cutting, Pt. I,” Holz als Roh-Werkstoff,54, pp. 423–428.
Lehmann,  B. F., and Hutton,  S. G., 1997, “The Mechanics of Bandsaw Cutting, Pt. II,” Holz als Roh-Werkstoff55, pp. 35–43.
Shamma,  J. S., 1994, “Robust Stability with Time-Varying Structured Uncertainty,” IEEE Trans. Autom. Control., 39, No. 4, pp. 714–724.
Poolla,  K., and Tikku,  A., 1995, “Robust Performance Against Time-Varying Structured Perturbations,” IEEE Trans. Autom. Control., 40, No. 9, pp. 1589–1602.
Doyle,  J. C., Glover,  K., Khargonekar,  P. P., and Francis,  B. A., 1989, “State-Space Solutions to Standard H2 and Hx Control Problems,” IEEE Trans. Autom. Control., 34, No. 8, pp. 831–847.
Bhat,  R. B., 1985, “Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method,” J. Sound Vib., 102, No. 4, pp. 493–499.
Packard,  A., and Doyle,  J., 1993, “The Complex Structured Singular Value,” Automatica, 29, No. 1, pp. 71–109.
Desoer, C. A., and Vidyasagar, M., 1975, Feedback Systems: Input-Output Properties, Academic Press, New York.
Safonov,  M. G., and Athans,  M., 1981, “A Multiloop Generalization of the Circle Criterion for Stability Margin Analysis,” IEEE Trans. Autom. Control., 26, No. 2, pp. 415–422.

Figures

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The first five modes under cutting conditions
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Maximum singular values of Tzpwp(jω) (5 mode plant model)
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Maximum singular values of TzΔwΔ(jω) (5 mode plant model)
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Maximum singular values of Tzpwp(jω) (10 mode plant model)
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Maximum singular values of TzΔwΔ(jω) (10 mode plant model)
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Bode plots for H(s), controller designs I-IV
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Instability regions for Ωc vs. Δ⁁c (q̄c=q⁁c=30 kN/m, open-loop system) (□□=unstable)
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Eigenloci for varying Kd(qc=qt=50 kN/m) (□ Kd=0,Kd=4 kN/m/s)
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Instability regions for Ωc vs. Δ⁁c (q̄c=q⁁c=7.5 kN/m, controller IV) (□□=unstable)
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Instability regions for Ωc vs. Δ⁁0 (q̄0=q⁁0=68 kN/m,qc=7.5 kN/m, controller IV) (□□=unstable)
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Simulation results for sinusoidal disturbances and parameter variation
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Eigenloci for varying qc=qt=q̄c (□ q̄c=0,q̄c=50 kN/m)

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