The nonlinear dynamics of a very flexible body with time-variant length encompasses several industrial applications such as high-speed automatic coiling machines and copy machines. Among others, the significant increase in the vibration that occurs when the material length is shortened with time is known as the spaghetti problem. In this paper, the modeling method and the experimental procedure for the analysis of the spaghetti problem are presented. The change in the state of the forces and displacements at the boundary with a clearance is taken into consideration by modeling the mechanical interactions resulting from the clearance. A flexible beam is modeled using the finite segment method to account for the geometric nonlinearities due to the large rotation. The contact forces at the boundary are modeled using a set of springs and dampers. The numerical results obtained using the proposed modeling method agree well with the results obtained using the experiment. The effect of the transport velocity and the clearance are demonstrated, and the cause of the significant increase in the flexible body vibration is discussed from an energy balance viewpoint.
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February 2005
Article
Modeling and Experimental Methods for Dynamic Analysis of the Spaghetti Problem
Hiroyuki Sugiyama,
Hiroyuki Sugiyama
Department of Mechanical Engineering, University of Illinois at Chicago, 842 W Taylor Street, Chicago, Illinois 60607
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Nobuyuki Kobayashi,
Nobuyuki Kobayashi
Department of Mechanical Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Sagamihara, Kanagawa, 2298558, Japan
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Yoshimasa Komaki
Yoshimasa Komaki
Mechanical Systems Center, Mitsubishi Electric Engineering Co. Ltd., 730 Kamimachiya, Kamakura, Kanagawa 2470065, Japan
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Hiroyuki Sugiyama
Department of Mechanical Engineering, University of Illinois at Chicago, 842 W Taylor Street, Chicago, Illinois 60607
Nobuyuki Kobayashi
Department of Mechanical Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Sagamihara, Kanagawa, 2298558, Japan
Yoshimasa Komaki
Mechanical Systems Center, Mitsubishi Electric Engineering Co. Ltd., 730 Kamimachiya, Kamakura, Kanagawa 2470065, Japan
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 24, 2003; final revision, January 13, 2004. Review conducted by D. Quinn.
J. Vib. Acoust. Feb 2005, 127(1): 44-51 (8 pages)
Published Online: March 21, 2005
Article history
Received:
February 24, 2003
Revised:
January 13, 2004
Online:
March 21, 2005
Citation
Sugiyama, H., Kobayashi, N., and Komaki, Y. (March 21, 2005). "Modeling and Experimental Methods for Dynamic Analysis of the Spaghetti Problem ." ASME. J. Vib. Acoust. February 2005; 127(1): 44–51. https://doi.org/10.1115/1.1857919
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