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2024 | OriginalPaper | Chapter

Analysis of the Influence of Tyre Cross-Sectional Parameters on the Stability of a Nonlinear Bicycle Model with Elliptic Toroidal Wheels

Authors : A. G. Agúndez, D. García-Vallejo, E. Freire

Published in: Perspectives in Dynamical Systems I — Applications

Publisher: Springer International Publishing

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Abstract

In this work, the stability of a bicycle with elliptic toroidal wheels is analysed in detail. The influence of the tyre cross-sectional parameters on the self-stability velocity range of the steady forward motion is studied. The bicycle multibody model is based on a well-acknowledged bicycle benchmark, which has been extensively used in several works. The nonlinear equations of motion, constituting a Differential-Algebraic Equations (DAE) system, are derived and linearized along the steady forward motion. The robustness of the linearization approach allows obtaining the resulting Jacobian matrix as a function of the tyre cross-sectional parameters. Therefore, a sensitivity analysis of the eigenvalues with the wheels’ geometric parameters is performed. Different scenarios are considered, and the influence of the tori aspect ratios and the elliptic cross-sections are illustrated with various stability regions.

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Francis JohnWelsh Whipple. The stability of the motion of a bicycle. Quarterly Journal of Pure and Applied Mathematics, 30(120):312–321, 1899.

Karl J Astrom, Richard E Klein, and Anders Lennartsson. Bicycle dynamics and control: adapted bicycles for education and research. IEEE Control Systems Magazine, 25(4):26–47, 2005.

David JN Limebeer and Robin S Sharp. Bicycles, motorcycles, and models. IEEE Control Systems Magazine, 26(5):34–61, 2006.

Jaap P Meijaard, Jim M Papadopoulos, Andy Ruina, and Arend L Schwab. Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review. Proceedings of the Royal society A: mathematical, physical and engineering sciences, 463(2084):1955–1982, 2007.

Pradipta Basu-Mandal, Anindya Chatterjee, and Jim M Papadopoulos. Hands-free circular motions of a benchmark bicycle. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463(2084):1983–2003, 2007.

José L Escalona and Antonio M Recuero. A bicycle model for education in multibody dynamics and real-time interactive simulation. Multibody System Dynamics, 27(3):383–402, 2012.

Jiaming Xiong, Nannan Wang, and Caishan Liu. Stability analysis for the whipple bicycle dynamics. Multibody System Dynamics, 48(3):311–335, 2020.MathSciNetCrossRef

JDG Kooijman, AL Schwab, and Jacob Philippus Meijaard. Experimental validation of a model of an uncontrolled bicycle. Multibody System Dynamics, 19(1–2):115–132, 2008.

Jiaming Xiong, Nannan Wang, and Caishan Liu. Bicycle dynamics and its circular solution on a revolution surface. Acta Mechanica Sinica, 36(1):220–233, 2020.MathSciNetCrossRef

10.

JP Meijaard and AL Schwab. Linearized equations for an extended bicycle model. In III European Conference on Computational Mechanics, pages 772–772. Springer, 2006.

11.

AL Schwab, JP Meijaard, and JDG Kooijman. Some recent developments in bicycle dynamics. In Proceedings of the 12th World Congress in Mechanism and Machine Science, pages 1–6. Citeseer, 2007.

12.

Robin S Sharp. On the stability and control of the bicycle. Applied mechanics reviews, 61(6), 2008.

13.

Jason Keith Moore. Human control of a bicycle. University of California, Davis Davis, CA, 2012.

14.

Vera E Bulsink, Alberto Doria, Dorien van de Belt, and Bart Koopman. The effect of tyre and rider properties on the stability of a bicycle. Advances in mechanical engineering, 7(12):1687814015622596, 2015.

15.

A García-Agúndez, D García-Vallejo, and E Freire. Linearization approaches for general multibody systems validated through stability analysis of a benchmark bicycle model. Nonlinear Dynamics, Article in press (2020).

16.

José L Escalona and Rosario Chamorro. Stability analysis of vehicles on circular motions using multibody dynamics. Nonlinear Dynamics, 53(3):237–250, 2008.

17.

Francisco González, Pierangelo Masarati, Javier Cuadrado, and Miguel A Naya. Assessment of linearization approaches for multibody dynamics formulations. Journal of Computational and Nonlinear Dynamics, 12(4), 2017.

18.

Carmine M Pappalardo, Antonio Lettieri, and Domenico Guida. Stability analysis of rigid multibody mechanical systems with holonomic and nonholonomic constraints. Archive of Applied Mechanics, 2020.

19.

Dale L Peterson, Gilbert Gede, and Mont Hubbard. Symbolic linearization of equations of motion of constrained multibody systems. Multibody System Dynamics, 33(2):143–161, 2015.

20.

21.

Jaap P. Meijaard, Jim M. Papadopoulos, Andy Ruina, and Arend L. Schwab. Linearized dynamics equations for the balance and steer of a bicycle: A benchmark and review. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463(2084):1955–1982, 2007.MathSciNetCrossRef

22.

Ahmed A Shabana and Jalil R Sany. An augmented formulation for mechanical systems with non-generalized coordinates: application to rigid body contact problems. Nonlinear dynamics, 24(2):183–204, 2001.

23.

W. Schiehlen. Multibody system dynamics: Roots and perspectives. Multibody System Dynamics, 1(2):149–188, 1997.MathSciNetCrossRef

Title: Analysis of the Influence of Tyre Cross-Sectional Parameters on the Stability of a Nonlinear Bicycle Model with Elliptic Toroidal Wheels
Authors: A. G. Agúndez
D. García-Vallejo
E. Freire
Publisher: Springer International Publishing
Book: Perspectives in Dynamical Systems I — Applications
Print ISBN: 978-3-031-56491-8

Electronic ISBN: 978-3-031-56492-5

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-56492-5_3

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