A Solution to Remove Railway Track Discontinuities at Spiral Junctions

Jean-Pierre Pascal

doi:doi:10.11648/j.ijmea.20200804.11

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A Solution to Remove Railway Track Discontinuities at Spiral Junctions

Jean-Pierre Pascal

Published in International Journal of Mechanical Engineering and Applications (Volume 8, Issue 4)

Received: 2 September 2020 Accepted: 17 September 2020 Published: 24 September 2020

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Abstract

To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.

Published in	International Journal of Mechanical Engineering and Applications (Volume 8, Issue 4)
DOI	10.11648/j.ijmea.20200804.11
Page(s)	95-102
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Railway Tracks, Track Layout, Dynamical Perturbations, Spirals, Doucines, Multibody Codes

References

[1]	Kalker J. J., "Three-Dimensional Elastic Bodies in Rolling Contact", 1st Ed., Kluwer Academic Publishers, Dordrecht/Boston/London, 1990.
[2]	Courtin, J. and Pascal, J. P., "Comprehensive Vehicle Testing with the Help of Numerical Modelling". Institution of Mechanical Engineers-(London-March 23 1994).
[3]	Kufver Bj., « Mathematical description of railway alignments and some preliminary comparative studies”, Swedish National Road and Transportation Research Institute, VTI rapport 420A, 1997.
[4]	Klauder L., Chrismer S., Elkins J., “Improved Spiral Geometry for High-Speed Rail and Predicted Vehicle Response” Transportation Research Record Journal of the Transportation Research Board 1785 (1): 41-49. DOI: 10.3141/1785-06, 2002.
[5]	Zboiński K., Woźnica P., “Optimisation of polynomial railway transition curves of even degrees”, Archives of Transport 35 (3): 71-86, 2015. DOI: 10.5604/08669546.1185194.
[6]	Prud’home, A., “Forces and Behavior of Railroad Tracks at Very High Train Speeds; Standards Adopted by SNCF for its Future High Speed Lines (250 to 300 km/h)”, in Railroad Track Mechanics and Technology, edited by A. D. Kerr, Pergamon Press, Oxford, UK. 1978.
[7]	Ayasse J. B., «Dynamique ferroviaire en coordonnées curvilignes et tracé de voie»-2003, book, ISBN: 9782857825753.
[8]	Pascal J. P. l, "Analysis of the behavior of unstable railway wagons using multibody dynamical codes", 2nd European Nonlinear Oscillation Conference, Prague, September 9-13 1996.
[9]	Pascal J. P., Sauvage G., "New Method for reducing the Multicontact Wheel/rail Problem to one equivalent Rigid Contact Patch," Proceedings 12th IAVSD-Symposium, Lyon, August 26-30, 1991.
[10]	Pascal J. P., Marquis B., “Rotational equations usable for railway wheelsets”. 2014, Vehicle System Dynamics, Vol. 52, pp. 390-409.
[11]	Pascal, J. P., Sany, J. R, Dynamics of an Isolated Railway Wheelset with Conformal Wheel–Rail Interactions. Vehicle System Dynamics, Vol. 54, pp. 1947-1969. 2019.
[12]	Ling, H., and Shabana, A. A., 2020, "Numerical Representation of Railroad Track Geometry Using Euler Angles", Technical Report # MBS2020-3-UIC, Department of Mechanical Engineering, The University of Illinois at Chicago, 2020.
[13]	J.P. Pascal, F. Jourdan-(2007) “The rigid Multi-Hertzian Method as applied to conformal Contacts” Proceedings of ASME DETC 2007-34379-Las Vegas, Nevada, USA.
[14]	Jean Alias, La Voie Ferrée : techniques de construction et d’entretien, 2e éd., Paris : Eyrolles, 1984.
[15]	Szabolcs Fischer, “Comparison of railway track transition curves”, Pollack Periodica 4 (3): 99-110, December 2009.

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Jean-Pierre Pascal. (2020). A Solution to Remove Railway Track Discontinuities at Spiral Junctions. International Journal of Mechanical Engineering and Applications, 8(4), 95-102. https://doi.org/10.11648/j.ijmea.20200804.11

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ACS Style

Jean-Pierre Pascal. A Solution to Remove Railway Track Discontinuities at Spiral Junctions. Int. J. Mech. Eng. Appl. 2020, 8(4), 95-102. doi: 10.11648/j.ijmea.20200804.11

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Jean-Pierre Pascal. A Solution to Remove Railway Track Discontinuities at Spiral Junctions. Int J Mech Eng Appl. 2020;8(4):95-102. doi: 10.11648/j.ijmea.20200804.11

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@article{10.11648/j.ijmea.20200804.11,
  author = {Jean-Pierre Pascal},
  title = {A Solution to Remove Railway Track Discontinuities at Spiral Junctions},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {8},
  number = {4},
  pages = {95-102},
  doi = {10.11648/j.ijmea.20200804.11},
  url = {https://doi.org/10.11648/j.ijmea.20200804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20200804.11},
  abstract = {To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.},
 year = {2020}
}

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TY  - JOUR
T1  - A Solution to Remove Railway Track Discontinuities at Spiral Junctions
AU  - Jean-Pierre Pascal
Y1  - 2020/09/24
PY  - 2020
N1  - https://doi.org/10.11648/j.ijmea.20200804.11
DO  - 10.11648/j.ijmea.20200804.11
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 95
EP  - 102
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20200804.11
AB  - To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.
VL  - 8
IS  - 4
ER  -

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Author Information

Jean-Pierre Pascal

Laboratoire de Mécanique et Génie Civil, Université de Montpellier, Montpellier, France

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Jean-Pierre Pascal. (2020). A Solution to Remove Railway Track Discontinuities at Spiral Junctions. International Journal of Mechanical Engineering and Applications, 8(4), 95-102. https://doi.org/10.11648/j.ijmea.20200804.11

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ACS Style

Jean-Pierre Pascal. A Solution to Remove Railway Track Discontinuities at Spiral Junctions. Int. J. Mech. Eng. Appl. 2020, 8(4), 95-102. doi: 10.11648/j.ijmea.20200804.11

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AMA Style

Jean-Pierre Pascal. A Solution to Remove Railway Track Discontinuities at Spiral Junctions. Int J Mech Eng Appl. 2020;8(4):95-102. doi: 10.11648/j.ijmea.20200804.11

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@article{10.11648/j.ijmea.20200804.11,
  author = {Jean-Pierre Pascal},
  title = {A Solution to Remove Railway Track Discontinuities at Spiral Junctions},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {8},
  number = {4},
  pages = {95-102},
  doi = {10.11648/j.ijmea.20200804.11},
  url = {https://doi.org/10.11648/j.ijmea.20200804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20200804.11},
  abstract = {To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Solution to Remove Railway Track Discontinuities at Spiral Junctions
AU  - Jean-Pierre Pascal
Y1  - 2020/09/24
PY  - 2020
N1  - https://doi.org/10.11648/j.ijmea.20200804.11
DO  - 10.11648/j.ijmea.20200804.11
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 95
EP  - 102
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20200804.11
AB  - To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.
VL  - 8
IS  - 4
ER  -

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