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Exploring the Relationship Between Vertical and Lateral Forces, Speed and Superelevation in Railway Curves

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Exploring the Relationship Between Vertical and Lateral Forces, Speed and Superelevation in Railway Curves Exploring the relationship TECHNICAL PAPER JOURNAL OF THE SOUTH AFRICAN between vertical and INSTITUTION OF CIVIL ENGINEERING ISSN 1021-2019 lateral forces, speed Vol 59 No 3, September 2017, Pages 25–35, Paper 1736 and superelevation ALEX POWELL is an Associate Member of the South African Institution of Civil Engineering and a Candidate Engineer with the Engineering in railway curves Council of South Africa. He obtained the following degrees: BEng Civil Engineering, BEng Hons Geotechnical Engineering, BEng Hons A F Powell, P J Gräbe Environmental Engineering, and MEng Transportation Engineering. He has been employed by Bombela Maintenance (Pty) Ltd since 2012 as the track engineer responsible for technical inputs regarding track maintenance on the Gautrain The research described in this paper is based on an experiment which involved running a Rapid Rail Link. He started his career in railway engineering in 2006 at test train through a curve at various speeds, changing the cant of the curve by tamping and Transnet Freight Rail in their Track Testing Centre in Jeppestown, repeating the train runs. The cant was changed due to high wheel wear rates. The curve already Johannesburg, and was with Transnet Freight Rail until his move to Bombela had a cant deficiency, and this cant deficiency was subsequently increased by reducing the Maintenance (Pty) Ltd. curve’s cant. Assessing the before and after tamping test data validated the existence of the Contact details: expected relationships between the vertical and lateral rail forces, the speed and the cant. Bombela Maintenance (Pty) Ltd Gautrain Depot The change in cant had a minimal effect on the magnitude of the vertical forces, although Waterval K60 Road a transfer of loading between the high and low legs did occur. The theory indicates that the Midrand 14% reduction in cant in this curve, given all of the other curve characteristics, should have South Africa resulted in an increase in the lateral forces. There was, however, a roughly 50% reduction in the T: +27 11 253 0136 maximum lateral forces, after the cant had been reduced, which can be explained from a train E: [email protected] dynamics point of view. In addition, there was an increase in safety, due to a reduced derailment ratio at this curve’s normal operating speed of 85 km/h. It is not unreasonable to presume that a PROF HANNES GRÄBE Pr Eng, FSAICE, is a civil engineer with experience in the fields of track 50% reduction in the maximum lateral forces could lead to a halving of the wear rate of the rail technology, geotechnology, advanced and wheels in this curve, with similar results to be expected in other curves on the rail network. laboratory testing, field investigations, maintenance models and numerical analysis of track structures. He is currently employed by the University of Pretoria as Associate Professor: INTRODUCTION between Johannesburg and the OR Tambo Transnet Freight Rail Chair in Railway Track geometry is a critical facet of any International Airport. Travelling at speeds Engineering, where he lectures under- and post-graduate courses in railway railway system, directly affecting the per- of up to 160 km/h, the Gautrain system is engineering. He is also responsible for railway research, as well as for formance of the railway track itself and the the first of its kind in South Africa, and in continuing professional development in the form of short courses presented behaviour of the railway vehicles using the fact in Africa. The Gautrain airport service to industry. system. Superelevation (also known as cant) has been operational since June 2010 and Contact details: is the term used to denote the raising of the the commuter service has been operational Transnet Freight Rail Chair in Railway Engineering outer rail on curved track to allow higher since August 2011. The relative newness and Department of Civil Engineering University of Pretoria speeds than if the two rails were level. In uniqueness of this state-of-the-art railway Pretoria 0001 curves, cant is one of the most important engineering project in the South African South Africa track geometry parameters, which can context therefore provided an excellent T: +27 12 420 4723 change the wheel/rail contact relationship opportunity for carrying out this research. E: [email protected] and then influence the dynamic interaction After the opening of the Gautrain system (Wang et al 2013), including the vertical and the initial wear rates of the Gautrain wheels lateral forces experienced by both the track were higher than expected. Specifically and the railway vehicles. the wheel flange wear resulted in more This paper presents an investigation into frequent wheel re-profiling needing to be the relationship between vertical and lateral done than originally planned as part of the forces, speed and cant in railway curves maintenance schedules. Assuming that the that was undertaken on the Gautrain Rapid track gauge of a railway system is within an Rail Link. acceptable tolerance range (which is the case for the Gautran system), then it is known that wheel flange wear predominantly takes BACKGROUND place in curves. The Gautrain Rapid Rail Link is a rail An experimental curve was selected and transit system that links the two cities this curve was found to be experiencing high of Johannesburg and Pretoria in the leg contact to the gauge side of the rail, while province of Gauteng, South Africa. The the low leg contact was to the field side of the system also provides an airport service rail. In order to move the high leg contact Keywords: vertical forces, lateral forces, superelevation (or cant), speed Powell AF, Gräbe PJ. Exploring the relationship between vertical and lateral forces, speed and superelevation in railway curves. J. S. Afr. Inst. Civ. Eng. 2017:59(3), Art. #1736, 11 pages. http://dx.doi.org/10.17159/2309-8775/2017/v59n3a4 25 lateral accelerations, and, given a situation with sufficient cant deficiency, the train may derail due to rail roll over, the car rolling over or sim- Transverse vertical plane ply derailing to the outside of the curve. The balance speed is the speed at which the Cant or compensation due to cant balances the accel- Longitudinal vertical plane superelevation eration due to curving. Relative to the track plane, the perceived lateral acceleration is then zero. The cant which gives lateral accelerations equal to zero at a given radius (R) and given Twist vehicle speed (v) is called the equilibrium cant (heq) and is calculated by Equation 1. Twist base Horisontal plane 2a ∙ v2 heq = (1) g ∙ R where 2a = effective gauge (for the Gautrain standard rail gauge of 1.435 m, 2a ≈ 1.500 m). Figure 1 Cant and twist in the transverse vertical plane (University of Pretoria 2010) The equilibrium speed, or balance speed (veq), is the vehicle speed at which lateral accelerations are equal to zero for a given radius (R) and a given cant (h), and is given by Equation 2. R ∙ g ∙ h veq = (2) 2a At speeds under the balance speed, cant Experimental curve excess exists, meaning the track has exces- sive cant for the present speed. With cant excess, perceived accelerations are to the inside of the curve. At speeds over the bal- ance speed, cant deficiency exists, meaning the track has insufficient cant for the present speed. With cant deficiency, perceived accel- erations are to the outside of the curve. Figure 2 Geographical location of the experimental curve (Google Earth 2015) Cant excess and cant deficiency can be mathematically represented by means of band away from the gauge side of the rail, Cant compensates for the centrifugal Equations 3 and 4. the cant needs to be reduced (as was done in force arising from a train traversing a curve. this research) or alternatively the operational If a track was canted to the level required for v2 h Cant excess (he): < g ∙ (3) speed of the train needs to be increased. The the maximum speed of the fastest train, the R 2a curve already had a cant deficiency, and this level of tilt would be too high for a slower cant deficiency was subsequently increased train. A compromise degree of cant is there- v2 h Cant deficiency (hd): > g ∙ (4) by reducing the curve’s cant. fore used, known as ‘cant deficiency’. R 2a From a curving point of view, a stationary train in a curve with cant, will be experienc- CANT ing overbalance in the form of an excess EXPERIMENTAL WORK Descriptions, figures and the derivations of of cant, at which point the train will be The basis of the investigation was to deter- the various formulae used in this discussion experiencing negative lateral accelerations, mine how to minimise wheel and rail wear of cant are taken from Lindahl (2001) and and given a situation with sufficient cant by optimising the interaction between the Esveld (2001), unless stated otherwise. excess, the stationary train may roll over to wheel and rail, with the focus of the investi- Cant is the difference in elevation the inside of the curve. gation being the relationship between cant between a point on one rail and elevation of As the train’s speed increases from station- and speed. The experimental work involved a point on the other rail measured along a ary, this overbalance situation (cant excess) running a test train through a curve at vari- line perpendicular to the track centre line as will reduce up until the speed where a balance ous speeds, changing the cant of the curve indicated in Figure 1. Also shown in Figure 1 is achieved, at which point the train will be by tamping and repeating the train runs.
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