Skip to main content
SpringerLink
Log in

Frenet force analysis in performance evaluation of railroad vehicle systems

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A data-driven science approach, based on integrating nonlinear multibody system (MBS) formulations and new geometric concepts, is used in this paper to compare the performance of two widely used railroad bogies: the three-piece bogie and the Y25 bogie. MBS algorithms are used to solve the bogie nonlinear differential/algebraic equations (DAEs) to determine the bogie motion trajectories. To have a better understanding of the bogie dynamic behavior, a distinction is made between the geometry of actual motion trajectories (AMT) and the track geometry. The AMT curves are described using the motion-dependent Frenet–Euler angles, referred to as Frenet bank, curvature, and vertical development angles, which differ from their counterparts used in the description of the track geometry. In particular, the Frenet bank angle defines the super-elevation of the AMT curve osculating plane, referred to as the motion plane, distinguishing this Frenet super-elevation from the fixed-in-time track super-elevation. The paper explains the difference between the lateral track plane force balance used in practice to determine the balance speed and the Frenet force balance which is based on recorded motion trajectories. Computer simulations of bogies travelling on a track, consisting of tangent, spiral, and curve sections are performed with particular attention given to the deviations of the AMT curves from the track centerline. The results obtained in this study demonstrate the dependence of the AMT curve geometry on the wheelset forward motion, highlighting the limitations of tests performed using roller test rigs which do not allow longitudinal wheelset motion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Andersson, C., Abrahamsson, T.: Simulation of Interaction between a train in general motion and a track. Veh. Syst. Dyn. 38(6), 433–455 (2002)

    Article  Google Scholar 

  2. Berghuvud, A.: Freight car curving performance in braked conditions. IMechE J. Rail Rapid Transit 216(1), 23–29 (2002)

    Article  Google Scholar 

  3. Bosso, N., Gugliotta, A., Somà, A.: Multibody simulation of a freight bogie with friction dampers. ASME/IEEE Joint Rail Conf. 35936, 47–56 (2002)

    Google Scholar 

  4. Cuenot, F., Gabriel, C.H.: Carbon Footprint of Railway Infrastructure. In: International Union of Railways (2016)

  5. De Pater, A.D.: The geometrical contact between track and wheelset. Veh. Syst. Dyn. 17(3), 127–140 (1988)

    Article  Google Scholar 

  6. Do Carmo, M.P.: Differential Geometry of Curves and Surfaces, 2nd edn. Dover Publications, New York (2016)

    MATH  Google Scholar 

  7. Dumitriu, M.: The stationary motion of a bogie along a circular curve. UPB Sci. Bull. Ser. D 74, 39–50 (2012)

    Google Scholar 

  8. Elkins, J.A., Gostling, R.J.: A general quasi-static curving theory for railway vehicles. Veh. Syst. Dyn. 6(2–3), 100–106 (1977)

    Article  Google Scholar 

  9. Endlicher, K.O., Lugner, P.: Computer simulation of the dynamical curving behavior of a railway bogie. Veh. Syst. Dyn. 19(2), 71–95 (1990)

    Article  Google Scholar 

  10. Farin, G.: Curves and Surfaces for CAGD, A Practical Guide, 5th edn. Morgan Kaufmann, Publishers, San Francisco (1999)

    Google Scholar 

  11. Gallier, J.: Geometric Methods and Applications: For Computer Science and Engineering. Springer, New York (2011)

    Book  Google Scholar 

  12. Ghazavi, M.R., Taki, M.: Dynamic simulations of the freight three-piece bogie motion in curve. Veh. Syst. Dyn. 46(10), 955–973 (2008)

    Article  Google Scholar 

  13. Ginsberg, J.: Engineering Dynamics. Cambridge University Press, New York (2008)

    MATH  Google Scholar 

  14. Goetz, A.: Introduction to Differential Geometry. Addison Wesley, London (1970)

    MATH  Google Scholar 

  15. Goldstein, H.: Classical Mechanics. Addison-Wesley, London (1950)

    MATH  Google Scholar 

  16. Grassie, S.L.: Dynamic modeling of the track and their uses. In: Kalker, J.J., Cannon, D.F., Orringer, O. (eds.) Rail Quality and Maintenance for Modern Railway Operation, pp. 165–184. Kluwer, Dordrecht (1993)

    Chapter  Google Scholar 

  17. Greenwood, D.T.: Principles of Dynamics, 2nd edn. Prentice Hall, Englewood Cliffs (1988)

    Google Scholar 

  18. Handoko, Y., Xia, F., Dhanasekar, M.: Effect of asymmetric brake shoe force application on wagon curving performance. Veh. Syst. Dyn. Dyn. 41, 113–122 (2004)

    Google Scholar 

  19. He, Y., Mcphee, J.: Optimization of curving performance of rail vehicles. Veh. Syst. Dyn. 43(12), 895–923 (2005)

    Article  Google Scholar 

  20. Huston, R.L.: Multibody Dynamics. Butterworth-Heinemann, Stoneham (1990)

    MATH  Google Scholar 

  21. Hecht, M.: European freight vehicle running gear: today’s position and future demands. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 215(1), 1–11 (2001)

    Article  Google Scholar 

  22. Iwnicki, S.D., Stichel, S., Orlova, A., Hecht, M.: Dynamics of railway freight vehicles. Veh. Syst. Dyn. 53(7), 995–1033 (2015)

    Article  Google Scholar 

  23. Jalili, M.M., Motavasselolhagh, M., Fatehi, R., Sefid, M.: Investigation of sloshing effects on lateral stability of tank vehicles during turning maneuver. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2020.1800490

    Article  Google Scholar 

  24. Jönsson, P.A.: Dynamic Vehicle-Track Interaction of European Standard Freight Wagons with Link Suspension. Doctoral dissertation, KTH (2007)

  25. Kataori, A., Iijima, H., Momosaki, S., Horioka, K.: Development of continuous measurement equipment for angle of attack and results of measurements. JR East Tech. Rev. 19, 46–49 (2011)

    Google Scholar 

  26. Kik, W.: Comparison of the behavior of different wheelset-track models. Veh. Syst. Dyn. 20(1), 325–339 (1992)

    Article  Google Scholar 

  27. Knothe, K.L., Grassie, S.L.: Modeling of railway track and vehicle/track interaction at high frequencies. Veh. Syst. Dyn. 22(3–4), 209–262 (1993)

    Article  Google Scholar 

  28. Knothe, K., Stichel, S.: Direct covariance analysis for the calculation of creepages and creep-forces for various bogie on straight track with random irregularities. Veh. Syst. Dyn. 23(1), 237–251 (1994)

    Article  Google Scholar 

  29. Kreyszig, E.: Differential Geometry. Dover Publications, London (1991)

    MATH  Google Scholar 

  30. Kovalev, R., Lysikov, N., Mikheev, G., Pogorelov, D., Simonov, V., Yazykov, V., Torskaya, E.: Freight car models and their computer-aided dynamic analysis. Multibody Sys. Dyn. 22(4), 399–423 (2009)

    Article  Google Scholar 

  31. Ling, H., Shabana, A.A.: Euler angles and numerical representation of the railroad track geometry. Acta Mech. (2021, in press)

  32. Pascal, J.P., Sany, J.R.: Dynamics of an isolated railway wheelset with conformal wheel-rail interactions. Veh. Syst. Dyn. 57(12), 1947–1969 (2019)

    Article  Google Scholar 

  33. Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, Berlin (1997)

    Book  Google Scholar 

  34. Rail Safety and Standards Board: Railway Wheelsets. Rail Safety and Standards Board Limited (2017)

  35. Railway Technical: Vehicle Suspension Systems. http://www.railway-technical.com/archive/vehicle-suspension-systems.pdf (2004). Accessed 02 April 2021

  36. Rogers, D.F.: An Introduction to NURBS with Historical Perspective. Academic Press, San Diego (2001)

    Google Scholar 

  37. Roberson, R.E., Schwertassek, R.: Dynamics of Multibody Systems. Springer, Berlin (1988)

    Book  Google Scholar 

  38. Sadeghi, M., Shadfar, M., Rezvan, M.: Dynamic modeling of three pieces bogies at curves and the parameters affecting its derailment index. In: International Heavy Haul Association Conference (2011)

  39. Shabana, A.A.: Dynamics of Multibody Systems, 5th edn. Cambridge University Press, New York (2020)

    Book  Google Scholar 

  40. Shabana, A.A.: Mathematical Foundation of Railroad Vehicle Systems: Geometry and Mechanics. Wiley, London (2021)

    Book  Google Scholar 

  41. Shabana, A.A.: Frenet Oscillations and Frenet-Euler Angles: Curvature Singularity and Motion-Trajectory Analysis. Nonlinear Dynamics (2021, in press)

  42. Shabana, A.A.: Geometric self-centering and force self-balancing of railroad vehicle hunting oscillations. Acta Mech. (2021, in press)

  43. Shabana, A.A., Ling, H.: Characterization and quantification of railroad spiral-joint discontinuities. Mech. Based Des. Struct. Mach. 6, 1–26 (2021)

    Google Scholar 

  44. SKF: Railway Technical Handbook Vol. 1: Axleboxes, wheelset bearings, sensors, condition monitoring, subsystems and services. In: SKF, Göteborg (2011)

  45. Sun, Y.Q., Cole, C.: Vertical dynamic behavior of three-piece bogie suspensions with two types of friction wedge. Multibody Syst. Dyn. 19(4), 365–382 (2008)

    Article  Google Scholar 

  46. Technical Specialist Rolling Stock Performance Standards: ESR 0331. Wheel and axles reference manual. RailCorp Engineering Standard (2013)

  47. The American Public Transportation Association: APTA PR-M-S-015-06 Standard for Wheel Flange Angle for Passenger Equipment. APTA PRESS Task Force (2007)

  48. The Contact Patch: https://the-contact-patch.com/book/rail. (2017). Accessed 03 Jan 2021

  49. True, H.: Does a critical speed for railroad vehicles exist? In: Proceedings of IEEE/ASME Joint Railroad Conference, pp. 125–131 (1994)

Download references

Acknowledgements

This research was supported by the National Science Foundation (Project # 1632302).

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL, 60607, USA

    Dario Bettamin & Ahmed A. Shabana

  2. Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italy

    Dario Bettamin, Nicola Bosso & Nicolò Zampieri

Authors
  1. Dario Bettamin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed A. Shabana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Bosso
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicolò Zampieri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmed A. Shabana.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bettamin, D., Shabana, A.A., Bosso, N. et al. Frenet force analysis in performance evaluation of railroad vehicle systems. Acta Mech 232, 4235–4259 (2021). https://doi.org/10.1007/s00707-021-03045-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-021-03045-x

Search

Navigation