KooijmanSchwabMeijaard2008

KooijmanSchwabMeijaard2008 - Multibody Syst Dyn (2008) 19:...

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Multibody Syst Dyn (2008) 19: 115–132 DOI 10.1007/s11044-007-9050-x Experimental validation of a model of an uncontrolled bicycle J.D.G. Kooijman · A.L. Schwab · J.P. Meijaard Received: 22 September 2006 / Accepted: 26 February 2007 / Published online: 5 May 2007 © Springer Science+Business Media, Inc. 2007 Abstract In this paper, an experimental validation of some modelling aspects of an uncon- trolled bicycle is presented. In numerical models, many physical aspects of the real bicy- cle are considered negligible, such as the flexibility of the frame and wheels, play in the bearings, and precise tire characteristics. The admissibility of these assumptions has been checked by comparing experimental results with numerical simulation results. The numerical simulations were performed on a three-degree-of-freedom benchmarked bicycle model. For the validation we considered the linearized equations of motion for small perturbations of the upright steady forward motion. The most dubious assumption that was validated in this model was the replacement of the tires by knife-edge wheels rolling without slipping (non-holonomic constraints). The experimental system consisted of an instrumented bicycle without rider. Sensors were present for measuring the roll rate, yaw rate, steering angle, and rear wheel rotation. Measurements were recorded for the case in which the bicycle coasted freely on a level surface. From these measured data, eigenvalues were extracted by means of curve fitting. These eigenvalues were then compared with the results from the linearized equations of motion of the model. As a result, the model appeared to be fairly accurate for the low-speed low-frequency behaviour. Keywords Bicycle dynamics · Experiments · Instrumentation · Multibody dynamics · Non-holonomic constraints J.D.G. Kooijman · A.L. Schwab ( ± ) Laboratory for Engineering Mechanics, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands e-mail: a.l.schwab@tudelft.nl J.P. Meijaard School of MMME, The University of Nottingham, University Park, Nottingham NG7 2RD, UK e-mail: jaap.meijaard@nottingham.ac.uk
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116 J.D.G. Kooijman et al. Fig. 1 The bicycle model: four rigid bodies (rear wheel, rear frame, front handlebar assembly, front wheel) connected by three revolute joints (rear hub, steering axis, front hub), together with the coordinate system, the degrees of freedom, and the parameters 1 Introduction The governing dynamic equations for a general bicycle model have recently been bench- marked [ 17 ] and after more than a century of bicycle dynamics literature we are confident about the correctness. In this model, many physical aspects of the real bicycle are consid- ered negligible, such as the flexibility of the frame and wheels, play in the bearings, and precise tire characteristics. The admissibility of these assumptions is checked by comparing experimental results with numerical simulation results. Apart from flexibility and play, the most dubious assumption to be validated in this model is the replacement of the tires by knife-edge wheels rolling without slipping (non-holonomic constraints).
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KooijmanSchwabMeijaard2008 - Multibody Syst Dyn (2008) 19:...

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