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Symbolic multibody methods for real-time simulation of railway vehicles

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Abstract

In this work, recently developed state-of-the-art symbolic multibody methods are tested to accurately model a complex railway vehicle. The model is generated using a symbolic implementation of the principle of virtual power. Creep forces are modeled using a direct symbolic implementation of the standard linear Kalker model. No simplifications, such as base parameter reduction, partial-linearization or lookup tables for contact kinematics, are used. An Implicit–Explicit integration scheme is proposed to efficiently deal with the stiff creep dynamics. Real-time performance is achieved: the CPU time required for a very robust \(1~\text{ms}\) integration time step is 203 μs.

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Notes

  1. Closed loops are opened to parametrize and closed through constraint equations.

  2. In comparison, this method presents the overhead of having to deal with the common atom search. Even using hash tables to do the search, the symbolic processing phase seems to take longer.

  3. Distance from the rotation axis to the contact point along the normal at the contact point.

  4. Including a step of the Newton–Raphson iteration used to project the coordinates.

  5. Single step of the Newton–Raphson iteration.

  6. The tolerance used is \(10^{-6}\), leading to a negligible error of \(\approx 10^{-3}~\text{mm}\) for lengths.

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Acknowledgements

This work was partially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) [grant numbers IPT-2011-1149-370000 and TRA2014-57609-R]. This support is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Public University of Navarre, Campus de Arrosadia, 31006, Pamplona, Navarre, Spain

    Javier Ros, Aitor Plaza, Xabier Iriarte & Jesús María Pintor

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  1. Javier Ros
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  2. Aitor Plaza
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  3. Xabier Iriarte
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  4. Jesús María Pintor
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Correspondence to Javier Ros.

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Ros, J., Plaza, A., Iriarte, X. et al. Symbolic multibody methods for real-time simulation of railway vehicles. Multibody Syst Dyn 42, 469–493 (2018). https://doi.org/10.1007/s11044-017-9608-1

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