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Applied Sciences
Volume 15
Issue 21
10.3390/app152111769
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Comparative Study of Continuous versus Discontinuous Numerical Models for Railway Vehicles Suspensions with Dry Friction

by
Razvan Andrei Oprea
,
Cristina Mihaela Tudorache
*,
Marius Adrian Spiroiu
,
Sorin Arsene
and
Camil Ion Craciun
Rolling Stock Department, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(21), 11769; https://doi.org/10.3390/app152111769 (registering DOI)
Submission received: 24 September 2025 / Revised: 29 October 2025 / Accepted: 3 November 2025 / Published: 4 November 2025
(This article belongs to the Special Issue Nonlinear Dynamics in Mechanical Engineering and Thermal Engineering)
Versions Notes

Abstract

Dry friction dampers are widely used in railway vehicle suspensions due to their simplicity, robustness, and cost-effectiveness compared to hydraulic alternatives. However, accurately modelling their behaviour remains challenging because of the discontinuous nature of friction forces. This paper presents a comparative study between two modelling approaches: continuous (regularized) models, which smooth out discontinuities, and discontinuous (switch-based) models, which explicitly capture stick–slip transitions. Using a two-degree-of-freedom suspension system, both models are implemented and analyzed under steady-state and transient conditions. Results show that while continuous models are easier to implement and integrate numerically, they fail to capture key physical phenomena such as zero relative velocity intervals and force discontinuities. In contrast, discontinuous models offer superior physical fidelity and significantly better computational efficiency, especially during static friction phases. This study highlights the trade-offs between modelling simplicity and accuracy, providing valuable insights for the simulation and design of railway suspension systems. The findings support the use of discontinuous models in safety-critical simulations and suggest avenues for hybrid modelling strategies.
Keywords: railway vehicles; vertical vibrations; dry friction; suspension; damping railway vehicles; vertical vibrations; dry friction; suspension; damping

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MDPI and ACS Style

Oprea, R.A.; Tudorache, C.M.; Spiroiu, M.A.; Arsene, S.; Craciun, C.I. Comparative Study of Continuous versus Discontinuous Numerical Models for Railway Vehicles Suspensions with Dry Friction. Appl. Sci. 2025, 15, 11769. https://doi.org/10.3390/app152111769

AMA Style

Oprea RA, Tudorache CM, Spiroiu MA, Arsene S, Craciun CI. Comparative Study of Continuous versus Discontinuous Numerical Models for Railway Vehicles Suspensions with Dry Friction. Applied Sciences. 2025; 15(21):11769. https://doi.org/10.3390/app152111769

Chicago/Turabian Style

Oprea, Razvan Andrei, Cristina Mihaela Tudorache, Marius Adrian Spiroiu, Sorin Arsene, and Camil Ion Craciun. 2025. "Comparative Study of Continuous versus Discontinuous Numerical Models for Railway Vehicles Suspensions with Dry Friction" Applied Sciences 15, no. 21: 11769. https://doi.org/10.3390/app152111769

APA Style

Oprea, R. A., Tudorache, C. M., Spiroiu, M. A., Arsene, S., & Craciun, C. I. (2025). Comparative Study of Continuous versus Discontinuous Numerical Models for Railway Vehicles Suspensions with Dry Friction. Applied Sciences, 15(21), 11769. https://doi.org/10.3390/app152111769

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