Abstract
This work illustrates the modelling aspects of an advanced motorcycle multibody model which captures the most important features of the vehicle, including five different suspensions schemes (telescopic fork, telelever, duolever, swingarm and paralever) all provided with their own flexibilities. Several lumped stiffness are used to model the structural compliance of the frame as well as the flexibility of the transmission system. A passive rider model which simulates the interaction of the rider with the handlebar and the chassis and a 3D road-tire model which takes into account both the carcass geometry and compliance are also included.
The presented mathematical model performs non-linear time domain simulations, non-linear steady state analysis, linear stability and frequency domain analyses. Some simulation examples are presented: a steady state cornering manoeuvre where the decomposition of steering torque in its main components is carried out, a stability analysis where the effects of rider’s impedance and structural flexibilities on weave and wobble vibration modes is highlighted, a stability analysis of a braking motorcycle which experiences a chatter instability and a lane change manoeuvre where the main handling indexes are computed.
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References
Sharp RS (2001) Stability, control and steering responses of motorcycles. Veh Syst Dyn 35(4–5):291–318
Spierings PTJ (1981) The effect of lateral front fork flexibility on the vibration modes of straight-running single-track vehicles. Veh Syst Dyn 10:21–35
Koenen C, Pacejka HB (1982) Influence of frame elasticity, simple rider body dynamics and tyre moments on free vibrations of motorcycles in curves. In: Proc of the IAVSD symposium
Hikichi T, Takaci K (1990) Dynamic characteristics of a motorcycle with a single-side supported swing arm. In: SAE 905214, pp 721–731
Cossalter V, Lot R, Massaro M (2007) The influence of frame compliance and rider mobility on the scooter stability. Veh Syst Dyn 45:315–326
Katayama T, Aoki A, Nishimi T, Okayama T (1987) Measurement of structural properties of riders. In: Proc of the 4th international pacific conference on automotive engineering. Melbourne, Australia
Nishimi T, Aoki A, Katayama T (1985) Analysis of straight running stability of motorcycles. In: Proc of the 10th international technical conference on experimental safety vehicles. Oxford, England
Marumo Y, Katayama T (2005) Effect of motorcycle tandem riding on weave mode stability. Thesis collection of the J Autom Technol Assoc 36(6)
Limebeer DJN, Sharp RS (2004) Nonlinear steering oscillations of motorcycles. In: Proc of the 43rd IEEE conference on decision and control. Atlantis, Paradise Island, Bahamas, December 14–17, 2004
Sharp RS, Limebeer DJN (2004) On steering wobble oscillations of motorcycles. Proc IMechE, Part C, J Mech Eng Sci 18:1449–1456
Pick AJ, Cole DJ (2004) Neuromuscular dynamics and the vehicle steering task. Veh Syst Dyn Suppl 41:l82–l91
Pick AJ, Cole DJ (2007) Dynamic properties of a driver’s arms holding a steering wheel. Proc IMechE, Part D, J Automob Eng 221
Cossalter V, Doria A, Lot R, Massaro M (2010) The effect of rider’s passive steering impedance on motorcycle stability: identification and analysis. Meccanica. doi:10.1007/s11012-010-9304-1
Cossalter V, Doria A, Lot R, Maso M (2006) A motorcycle riding simulator for assessing the riding ability and for testing rider assistance systems. In: DSC 2006 Europe. Paris, October 4–6, 2006
Cossalter V, Lot R, Maso M, Massaro M, Sartori R (2008) A motorcycle riding simulator for the improvement of the rider safety. In: Proc of the FISITA world automotive congress. Munich, Germany, 14–19 September 2008
Sharp RS, Evangelou S, Limebeer DJN (2004) Advances in motorcycle dynamics. Multibody Syst Dyn 12:251–283
Evangelou S, Limebeer DJN, Tomas-Rodriguez M (2008) Influence of road camber on motorcycle stability. J Appl Mech, Trans ASME 75
Pacejka HB (2005) Tire and vehicle dynamics. SAE International. ISBN: 978-0-7680-1702-1
Cossalter V, Lot R (2002) A motorcycle multi-body model for real time simulations based on the natural coordinates approach. Veh Syst Dyn 37:423–447
Lot R (2004) A motorcycle tire model for dynamic simulations. Meccanica 39:207–220
Massaro M (2008) Modellazione multi-body analitica e sviluppo di strategie di controllo. PhD dissertation, University of Padova (In Italian)
Lot R, Da Lio M (2004) A symbolic approach for automatic generation of the equations of motion of multibody systems. Multibody Syst Dyn 12:147–172
Genta G (1997) Motor vehicle dynamics. World Scientific, Singapore. ISBN: 9789810229115
Torok JS (2000) Analytical mechanics. Wiley, New York. ISBN: 9780471332077
Lot R, Massaro M (2006) A combined model of tire and road surface for the dynamics analysis of motorcycle handling. In: Proc of the FISITA world automotive congress. Yokohama, Japan, 22–27 October 2006
Cossalter V, Lot R, Massaro M (2008) The chatter of racing motorcycle. Veh Syst Dyn 46:339–353
Massaro M, Sartori R, Lot R (2010) Numerical investigation of engine-to-slip dynamics for motorcycle traction control applications. Veh Syst Dyn. doi:10.1080/00423110903530992
NASA (1978) Anthropometric source book. Vol I: Anthropometry for designers. NASA Reference Publication 1024
Hairer E, Wanner G (1996) Solving ordinary differential equations II: Stiff and differential-algebraic problems, 2nd edn. Springer, Berlin
Garcia de Jalón J, Bayo E (1994) Kinematic and dynamic simulation of multibody systems. The real-time challenge. Springer, New York. ISBN 0-387-94096-0, 440 pp
Cheli F, Pennestrì E (2006) Cinematica e dinamica dei sistemi multibody. CEA. ISBN: 8840813454
Cossalter V, Lot R, Peretto M (2007) Steady turning of motorcycles. Proc IMechE, Part D, J Automob Eng 221(11):1343–1356
Cossalter V (2006) Motorcycle dynamics. www.Lulu.com. ISBN: 978-1-4303-0861-4
Cossalter V, Sadauckas J (2006) Elaboration and quantitative assessment of manoeuvrability for motorcycle lane change. Veh Syst Dyn 44(12):903–920. ISSN 0042-3114
Massaro M, Lot R (2007) Application of Laplace transform techniques to non-linear control optimization. In: Proc of the multibody dynamics 2007. Milano, Italy, June 25–28, 2007
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Cossalter, V., Lot, R. & Massaro, M. An advanced multibody code for handling and stability analysis of motorcycles. Meccanica 46, 943–958 (2011). https://doi.org/10.1007/s11012-010-9351-7
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DOI: https://doi.org/10.1007/s11012-010-9351-7