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TECHNICAL PAPERS

Analysis of Piecewise Linear Systems With Boundaries in Displacement and Time

[+] Author and Article Information
Mikio Nakai

Department of Precision Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501 Japan

Shinji Murata

Japan Electric Power Information Center, Inc., 4-15-33 Shibaura Minato-ku, Tokyo, 108-0023 Japan

Seiji Hagio

Kawasaki Heavy Industry Ltd., 1-1, Kawasaki-cho, Akashi-shi, Hyogo, 673-8666 Japan

J. Vib. Acoust 124(4), 527-536 (Sep 20, 2002) (10 pages) doi:10.1115/1.1502668 History: Received November 01, 2000; Revised February 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

Figures

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Approximated stiffness k(τ) of a pair of gears as a rectangular wave
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Meshing behavior of a pair of gears in two time and three displacement regions
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Defining nomenclatures used in this methodology
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The necessary condition for periodic solution
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Restoring forces in two time regions
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Nomenclatures for this methodology
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Phase portraits and time histories for a stable period-one orbit at the point B (ω=0.7) in Fig. 6(a)
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Phase portraits and time histories for a stable period-two orbit at the point B (ω=1.5) in Fig. 6(a)
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Phase portraits and time histories of x calculated with our present method (2×2 matrix) and numerical results at the point B (ω=1.5) in Fig. 6(a)
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Solution curves (solid line: stable solution, thick solid line: stable solution in bifurcation diagrams of Figs. 6(a) and (b), thick dotted: directly unstable solution, dotted line: inversely unstable solution, all at τ [mod(2π/ω)]=0)
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Phase portraits and time histories of x calculated with our present method (2×2 matrix) and numerical results for a stable period-three orbit at point C (ω=0.598) in Fig. 6(b)

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