A train air brake force model: Locomotive automatic brake valve and brake pipe flow formulations

Abstract

The goal of this study is to integrate an air brake model with efficient algorithms for train longitudinal force calculation that are based on trajectory coordinate formulations. The air brake model, developed in this investigation and presented in this paper and a companion paper, consists of the locomotive automatic brake valve, air brake pipe and car control unit (CCU). The proposed air brake force model accounts for the effect of the air flow in long train pipes as well as the effect of leakage and branch pipe flows. This model can be used to study the dynamic behavior of the air flow in the train pipe and its effect on the longitudinal train forces during brake application and release. The governing equations of the air pressure flow are developed using the general fluid continuity and momentum equations, simplified using the assumptions of one-dimensional isothermal flow. Using these assumptions, one obtains two coupled air velocity/pressure partial differential equations that depend on time and the longitudinal coordinate of the brake pipes. The partial differential equations are converted to a set of first-order ordinary differential equations using the finite element method. The resulting air brake ordinary differential equations are solved simultaneously with the train’s second-order non-linear dynamic differential equations of motion that are based on the trajectory coordinates. The train car non-linear dynamics is defined using a body track coordinate system that follows the car motion. The body track coordinate system translation and orientation are defined in terms of one parameter that describes the distance traveled by the car. The configuration of the car with respect to its track coordinate system is described using two translation coordinates and three Euler angles. The operation modes of the brake system considered in this investigation are the brake release mode and the brake application mode that includes service and emergency brakes. A detailed model of the locomotive automatic brake valve is presented in this investigation and used to define the inputs to the air brake pipe during the simulation. A simplified model of this valve is also proposed in order to reduce the computational time of the simulation. In a companion paper, the detailed CCU formulation is presented. The coupling between the air brake, locomotive automatic brake valve, CCUs and train equations is established and used in the companion paper in the simulation of the non-linear dynamics of long trains. The air brake formulations presented in the two companion papers are implemented in a computer code called Analysis of Train/Track Interaction Forces (ATTIF) which is developed for the analysis of longitudinal train forces.

Keywords

Air brake locomotive valves longitudinal train dynamics railroad vehicles finite element

Get full access to this article

View all access options for this article.

References

American Association of Railroads. Manual of standards and recommended practices-Section M, RP-548, 2002.

American Association of Railroads. Manual of standards and recommended practices-Section M, RP-5132, 2002.

American Association of Railroads. Train make-up manual, report R-802, 1992.

Andrews

. Railway traction, Amsterdam: Elsevier, 1986.

Berzeri M, Sany JR and Shabana, AA. Curved track modeling using the absolute nodal coordinate formulation. Technical report MBS00-4-UIC, Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, 2000.

Garg

Dukkipati

. Dynamics of railway vehicle systems, New York: Academic Press, 1984.

Railway Technical Web Pages. Air brakes. http://www.railway-technical.com/air-brakes.shtml (site last updated on 16 July 2010, accessed 18 August 2010).

Sanborn G, Heineman J and Shabana AA. A low computational cost nonlinear formulation for multibody railroad vehicle systems. In: Proceedings of the 2007 ASME design engineering technical conference, Las Vegas, NV, 4–7 September 2007, paper no. DETC2007-34522.

Sanborn G, Heineman J and Shabana AA. Implementation of low computational cost nonlinear formulation for multibody railroad vehicle systems. In: Proceedings of the 2007 ASME design engineering technical conference, Las Vegas, NV, 4–7 September 2007, paper no. DETC2007-34525.

10.

Shabana

. Computational continuum mechanics, Cambridge, UK: Cambridge University Press, 2008.

11.

Abdol-Hamid KS. Analysis and simulation of the pneumatic braking system of freight trains. PhD Thesis, Department of Mechanical Engineering, University of New Hampshire, Durham, NH, 1986.

12.

Bansiter WN. A dynamic model of pneumatic control valve system. Master’s Thesis, University of New Hampshire, Durham, NH, USA 1979.

13.

Bharath

Nakra

Gupta

. Distributed mathematical model for pressure transient analysis in railway pneumatic brake system. Int J Mech Sci 1990; 32: 133–145.

14.

Funk

Robe

. Transients in pneumatic transmission lines subjected to large pressure changes. Int J Mech Sci 1970; 12: 245–257.

15.

Wetenkamp HR. Management of train operation and train handling. Air Brake Association, 1974.

16.

Limbert D. Undesired emergency brake study complete. Railway Age 1990.

17.

Shute BW, Wright BC, Taft CK and Banister WN. The effect of leakage distribution on brake pipe gradient and brake pipe flow rate. ASME paper 79-WA/RT-16, 1979.

18.

Gauthier RG. An analysis and simulation of a pneumatic control valve system. Master’s Thesis, University of New Hampshire, Durham, NH, 1977.

19.

Wright BW. A dynamic analysis of distributed pneumatic control system. Master Thesis, University of New Hampshire, Durham, NH, 1978.

20.

Wei

Lin

. Simulation of a freight train brake system with ‘120’ valves. Proc IMechE, Part F: J Rail Rapid Transit 2009; 223: 85–92.

21.

Nasr

Mohammadi

. The effects of train brake delay time on in-train forces. Proc IMechE, Part F: J Rail Rapid Transit 2010; 224: 523–534.

22.

Cantone

Crescentini

Verzicco

Vullo

. A numerical model for the analysis of unsteady train braking and releasing manoeuvres. Proc IMechE, Part F: J Rail Rapid Transit 2009; 223: 305–317.

23.

Shabana

Zaazaa

Sugiyama

. Railroad vehicle dynamics: A computational approach, Boca Raton, FL: Taylor & Francis, 2008.

24.

John

Keith

. Gas dynamics, third edn. New Jersey: Pearson, 2006.

25.

White

. Fluid mechanics, sixth edn. New York: McGraw Hill, 2008.

26.

Afshari

Specchia

Shabana

. A train air brake force model: Car control unit and numerical results. Proc IMechE, Part F: J Rail Rapid Transit 2012.

27.

Shabana

. Computational dynamics, third edn. New York: John Wiley, 2010.

28.

Shabana

Aboubakr

Ding

. Use of the non-inertial coordinates in the analysis of train longitudinal forces. J Comput Nonlinear Dyn 2012; 7: 1–10.