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TECHNICAL PAPERS

Equilibrium and Belt-Pulley Vibration Coupling in Serpentine Belt Drives

[+] Author and Article Information
L. Kong, R. G. Parker

Department of Mechanical Engineering, The Ohio State University, 206 W 18th Avenue, Columbus, OH 43210

J. Appl. Mech 70(5), 739-750 (Oct 10, 2003) (12 pages) doi:10.1115/1.1598477 History: Received March 17, 2002; Revised September 27, 2002; Online October 10, 2003
Copyright © 2003 by ASME
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References

Hawker, L. E., 1991, “A Vibration Analysis of Automotive Serpentine Accessory Drives Systems,” Ph.D. dissertation, University of Windsor, Ontario, Canada.
Barker, C. R., Oliver, L. R., and Breig, W. F., 1991, “Dynamic Analysis of Belt Drive Tension Forces During Rapid Engine Acceleration,” SAE Paper No. 910687.
Hwang,  S. J., Perkins,  N. C., Ulsoy,  A. G., and Meckstroth,  R., 1994, “Rotational Response and Slip Prediction of Serpentine Belt Drives Systems,” ASME J. Vibr. Acoust., 116, pp. 71–78.
Leamy,  M. J., and Perkins,  N. C., 1998, “Nonlinear Periodic Response of Engine Accessory Drives With Dry Friction Tensioners,” ASME J. Vibr. Acoust., 120, pp. 909–916.
Beikmann, R. S., 1992, “Static and Dynamic Behavior of Serpentine Belt Drive Systems: Theory and Experiments,” Ph.D. dissertation, The University of Michigan, Ann Arbor, MI.
Beikmann,  R. S., Perkins,  N. C., and Ulsoy,  A. G., 1996, “Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance,” ASME J. Mech. Des., 119, pp. 162–168.
Beikmann,  R. S., Perkins,  N. C., and Ulsoy,  A. G., 1996, “Free Vibration of Serpentine Belt Drive Systems,” ASME J. Vibr. Acoust., 118, pp. 406–413.
Parker, R. G., 2003, “Efficient Eigensolution, Dynamic Response, and Eigensentivity of Serpentine Belt Drives,” J. Sound Vib., in press.
Ascher,  U., and Russell,  R., 1981, “Reformulation of Boundary Value Problems into ‘Standard’ Form,” SIAM (Soc. Ind. Appl. Math.) Rev., 23, pp. 238–254.
Kong, L., and Parker, R. G., 2003, “Coupled Belt-Pulley Vibration in Serpentine Drives With Belt Bending Stiffness,” ASME J. Appl. Mech., in press.
Wang,  K. W., and Mote,  C. D., 1986, “Vibration Coupling Analysis of Band/Wheel Mechanical Systems,” J. Sound Vib., 109, pp. 237–258.
Mote,  C. D., and Wu,  W. Z., 1985, “Vibration Coupling in Continuous Belt and Band Systems,” J. Sound Vib., 102, pp. 1–9.
Zhang,  L., and Zu,  J. W., 1999, “Modal Analysis of Serpentine Belt Drive Systems,” J. Sound Vib., 222(2), pp. 259–279.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley and Sons, New York, pp. 447–455.
Shampine, L. F., Kierzenka, J., and Reichelt, M. W., 2000, “Solving Boundary Value Problems for Ordinary Differential Equations in Matlab With Bvp4c,” available at ftp://ftp.mathworks.com/pub/doc/papers/bvp/
Mote,  C. D., 1965, “A Study of Band Saw Vibrations,” J. Franklin Inst., 279, pp. 430–444.

Figures

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A prototypical three-pulley serpentine belt drive system
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Detail of tensioner region and pulley 2, defining alignment angles
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Equilibrium deflections of spans 1 and 3 for varying belt bending stiffness: s=0,ks=4, γ=400, P1=P2=P3=1
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Equilibrium deflections of spans 1 and 3 for varying span tensions: ε=0.05, s=0,ks=4, γ=400
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Equilibrium deflections of spans 1 and 3 for varying speed: ε=0.05, ks=4, γ=400, P1=P2=P3=1
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Equilibrium deflections of spans 1 and 3 for varying tensioner spring stiffness: ε=0.05, s=0, γ=400, P1=P2=P3=1
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Equilibrium deflections of spans 1 and 3 for varying longitudinal belt stiffness: ε=0.05, s=0,ks=4,P1=P2=P3=1
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System coupling indicator Γ for varying belt bending stiffness: s=0,ks=4, γ=400, P1=P2=P3=1
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System coupling indicator Γ for varying span tensions: ε=0.015, s=0,ks=4, γ=400
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System coupling indicator Γ for varying speed: ε=0.015, ks=4, γ=400, P1=P2=P3=1.η=0.78 corresponds to tensioner orientation β1=135.79 deg, β2=178.74 deg in Table 1; while η=0 corresponds to tensioner orientation β1=68.53 deg, β2=111.47 deg.
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Tension variation with different tensioner orientation: ks=4, γ=400, P1=P2=P3=1. (a) β1=135.79 deg, β2=178.74 deg, η=0.78. (b) β1=68.53 deg, β2=111.47 deg, η=0.
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Equilibrium deflections of the first and third spans: ε=0.01, s=0.6,ks=4, γ=400, P1=P2=P3=1
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Equilibrium deflections of the first and third spans: ε=0.01, s=0.9,ks=4, γ=400, P1=P2=0.9395,P3=1.5395

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