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Kinematic oscillations of railway wheelsets

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Abstract

We show that Klingel’s classical formula for the frequency of the small kinematic oscillations of railway wheelsets results in a significant error even in the simplest physically relevant cases. The exact 3D nonlinear equations are derived for single-contact-point models of conical wheels and cylindrical rails. We prove that the resulting nonlinear system exhibits periodic motions around steady rolling, which consequently is neutrally stable. The linearised equations provide the proper extension of Klingel’s formula. Our results serve as an essential basis for checking multibody dynamics models and codes used in railway dynamics.

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Acknowledgements

We thank Professor Istvan Zobory of the Budapest University of Technology and Economics for his advice on the engineering literature. This research was supported by the Hungarian Scientific Research Foundation OTKA under grant no. K101714.

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Authors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Mate Antali & Gabor Stepan

  2. Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, Bristol, BS8 1TR, UK

    S. John Hogan

  3. HAS-BME Research Group on Dynamics of Machines and Vehicles, Hungarian Academy of Sciences, Budapest, 1521, Hungary

    Gabor Stepan

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  1. Mate Antali
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  2. Gabor Stepan
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  3. S. John Hogan
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Correspondence to Gabor Stepan.

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Antali, M., Stepan, G. & Hogan, S.J. Kinematic oscillations of railway wheelsets. Multibody Syst Dyn 34, 259–274 (2015). https://doi.org/10.1007/s11044-014-9424-9

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  • DOI: https://doi.org/10.1007/s11044-014-9424-9

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