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TECHNICAL PAPERS

Motorcycle Steering Oscillations due to Road Profiling

[+] Author and Article Information
D. J. N. Limebeer, S. Evangelou

Department of Electrical and Electronic Engineering, Imperial College of Science Technology and Medicine, Exhibition Road, London SW7 2BT, UK

R. S. Sharp

School of Engineering, Cranfield University, Whittle Building, Bedford MD43 0AL, UK

J. Appl. Mech 69(6), 724-739 (Oct 31, 2002) (16 pages) doi:10.1115/1.1507768 History: Received October 21, 2001; Revised March 06, 2002; Online October 31, 2002
Copyright © 2002 by ASME
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References

Sharp,  R. S., 1971, “The Stability and Control of Motorcycles.” J. Mech. Eng. Sci., 13(5), pp. 316–329.
Sharp, R. S., 1994, Vibrational Modes of Motorcycles and Their Design Parameter Sensitivities, Vehicle NVH and Refinement, Proc Int Conf., Birmingham, May 3–5, Mech. Eng. Publications, London, pp. 107–121.
Limebeer,  D. J. N., Sharp,  R. S., and Evangelou,  S., 2001, “The Stability of Motorcycles Under Acceleration and Braking,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.), 215(C9), pp. 1095–1109.
Sharp,  R. S. and Limebeer,  D. J. N., 2001, “A Motorcycle Model for Stability and Control Analysis,” Multibody Syst. Dyn., 6(2), pp. 123–142.
Koenen, C., 1983, “The Dynamic Behavior of Motorcycles When Running Straight Ahead and When Cornering,” Ph.D. thesis, Delft University of Technology. Delft, The Netherlands.
Sharp, R. S., Limebeer, D. J. N., and Gani, M. R., 1999, “A Motorcycle Model for Stability and Control Analysis,” Euromech Colloquium 404, Advances in Computational Multibody Dynamics, J. A. C. Ambrosio and W. O. Schiehlen ed., pp. 287–312.
Sharp,  R. S., 1992, “Wobble and Weave of Motorcycles With Reference to Police Usage,” Automot. Eng., 17(6), pp. 25–27.
BMW statement to all (UK) chief constables, Dec. 14, 1993.
Cutts,  J., 1993, “The Boxer Rebellion,” Superbike, , pp. 4–10.
Evans,  J., 1993, BMW R1100RS, Motor Cycle Int., Mar., pp. 58–64.
Raymond,  K., 1993, “Could do Better,” Perform. Bikes, pp. 34–36.
“An Interview With Dr. Goeschel,” 1993, Motorcycle Sport, May,pp. 234–235.
“Boxer Comeback,” 1993, Which Motorcycle, Apr., pp. 26–32.
Duke,  O., 1997, “Planet Bike—Radical Thriller or Flawed Killer,” Bike, pp. 14–17.
“Safety Recall Notice, American Suzuki Motor Corporation,” 1997, Motorcycle, June 9.
Farr, K., 1997, “Suzuki TL1000 Recalled in UK,” Motorcycle News, June 18.
“Operating Stable,” 1997, Performance Bikes, July, pp. 44–51.
Farr, K., 1997, “Fats the Way To,” Motorcycle News, July 2.
Robinson,  J., 2001, “Wobble and Weave,” Performance Bikes, pp. 83–85.
Duke Marketing Ltd., 1999, “Motorcycle Magic.”
Farrar, S., 2002, “Orritt’s Story to Explain the Phenomena,” Times Higher Educational Supplement, Feb. 15.
Metropolitan Police, private communication, 2000.
Sharp,  R. S., 2001, “The Stability, Control and Steering Responses of Motorcycles,” Veh. Sys. Dyn., 35(4–5), pp. 291–318.
Breuer, T., and Pruckner, A., 1998, “Advanced Dynamic Motorbike Analysis and Driver Simulation,” Proc 13th European ADAMS Users’ Conference, Paris, Nov. 1998, 20pp.
Imaizumi,  H., and Fujioka,  T., 1996, “Motorcycle-Rider System Dynamics by Multibody Dynamics Analysis—Effects of the Rear Load and the Suspension Assembly on Wobble and Weave Motions,” JSAE Review, 19(1), pp. 54–57.
Mechanical Simulation Corporation, 1996, Autosim 2.5+ Reference Manual, http://www.trucksim.com.
The Mathworks, Inc., 2000, MATLAB 6 Reference Manual, http://www.mathworks.com.
Evangelou, S., and Limebeer, D. J. N., 2000, “Lisp Programming of the “Sharp 1971” Motorcycle Model,” http://www.ee.ic.ac.uk/control/motorcycles.
Evangelou, S., and Limebeer, D. J. N., 2000, “Lisp Programming of the “Sharp 1994” Motorcycle Model,” http://www.ee.ic.ac.uk/control/motorcycles.
Dunlop, “Wobble and Weave Videotape,” c1977.

Figures

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Motorcycle model in its nominal configuration
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Wheel and tire geometry, showing the migration of the ground contact point
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Straight running root-locus with speed the varied parameter. The speed is increased from 5 m/s (11 mph) (□) to 60 m/s (135 mph) (★).
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Root-locus for a fixed roll angle of 30 deg. The speed is increased from 6 m/s (□) to 60 m/s (★).
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Root-locus for a fixed speed of 13 m/s (29 mph). The roll angle in increased from 0, (□) to 30 deg (★).
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Root-locus for a fixed speed of 40 m/s (90 mph). The roll angle in increased from 0, (□) to 30 deg (★).
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Frequency response for gf(s) (solid), and e−sτgr(s) (dashed) (0 dB=1 deg/m). The steady-state conditions are a 30 deg roll angle and a forward speed of 13 m/s (29 mph).
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Frequency response for gf(s) (solid), and e−sτgr(s) (dashed) (0 dB=1 deg/m). The steady-state conditions are a 30 deg roll angle and a forward speed of 40 m/s (90 mph).
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 13 m/s (29 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 20% in the steering damper setting, while the dot-dash curve shows the effect of a 20% reduction in the steering damping.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 13 m/s (29 mph), 15 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 20% in the steering damping, while the dot-dash curve shows the effect of a 20% decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 13 m/s (29 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 40% in the rear damper setting, and the dot-dash curve shows the effect of a 40% decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 13 m/s (29 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 40% in the front damper setting and the dot-dash curve shows the effect of a 40% decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 40 m/s (90 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 20% in the steering damper setting and the dot-dash curve shows the effect of a 20% decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 40 m/s (90 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 40% in the rear damper setting and the dot-dash curve shows the effect of a 40% decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 40 m/s (90 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 40% in the front damper setting and the dot-dash curve shows the effect of a 40% decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 40 m/s (90 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an increase of 20 kg (4.1 lbs) in the mass of the upper body of the rider and the dot-dash curve shows the effect of a 20 kg (4.1 lbs) decrease.
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 40 m/s (90 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of a forward shift of 15 cm (5.91 ins) in the center of mass of the upper body of the rider and the dot-dash curve shows the effect of a rearward shift of 15 cm (5.91 ins).
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Bode magnitude plot of g(s) (0 dB=1 deg/m). Nominal state: 40 m/s (90 mph), 30 deg roll angle. The solid curve represents the nominal case, the dashed one shows the effect of an upward shift of 15 cm (5.91 ins) in the center of mass of the upper body of the rider and the dot-dash curve shows the effect of a downward shift of 15 cm (5.91 ins).
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Transient behavior of the roll and steering angles, and the yaw rate in response to sinusoidal road forcing that begins at t=1 s and has a peak amplitude of 0.5 cm. The forcing frequency is tuned to the front suspension pitch mode. The lean angle is 30 deg and the forward speed 13 m/s (29 mph).
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Transient behavior of the roll and steer angles and the yaw rate, in response to sinusoidal road forcing that begins at t=1 s and has a peak amplitude of 0.25 cm. The forcing frequency is tuned to the weave mode. The lean angle is 30 deg and the forward speed 40 m/s (90 mph).

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