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240 and rollingstock gauges are clearly influenced by the British railway practice, as are braking systems. Wagon couplings on freight trains are predominately autocouplers with friction wedge type draft gear packages showing the North American influence. Privately owned railways on iron ore mines in the Australia’s North West show even moreNorth American influence with American style braking and larger structure and rollingstock gauges. Australia is also characterised bythree track gauges,alegacy of colonial and state governments before federation. The presence of narrow gauges of 1067 mm results in alarge fleet of rollingstock with adesign differing from standard gauge rollingstock in North America, Britain, and the southern states of Australia. This chapter is arranged to firstly give an overview of longitudinal train dynamics. The second section goes into considerable detail on approaches tomodelling longitudinal train dynamics. The mostspace is giventothe modellingofthe wagon connection model. Subsections are also devoted to modelling traction and dynamic braking systems, rolling resistance, air resistance, curving resistance, the effect of grades, and pneumatic braking. The subsection on pneumatic braking only provides an explanationofthe effect of pneumatic braking on train dynamics. Modelling pneumatic braking systems would require achapter in itself. Further more brief chapter sections are included on the interaction of longitudinal train dynamics with lateral/vertical wagon dynamics, crashworthiness, comfort and train management, and driving practices. A . A N O VERVIEW o F L ONGITUDINAL T RAIN D YNAMICS Handbook of Railway Vehicle Dynamics Longitudinal train dynamicsisdefined as the motions of rollingstock vehicles in the direction of the track. It therefore includes the motion ofthe train as awhole and any relative motions between vehicles allowed due to the loosenessofthe connections between vehicles. In the railway industry, the relative motion between vehicles is known as“slack action” due to the correct understanding that thesemotions are primarily allowed by the free slack in wagon connections, coupling freeslack beingdefined as the free movement allowed by the sum of the clearances in the wagon connection. These clearances consist of clearances in the autocoupler knuckles and draft gear assembly pins. Cases of slack action are further classified in the Australian industry vernacular as run-ins and runouts. The case of arun-in describes the situation where vehicles are progressively impacting each otherasthe train compresses. The case of arun-out describes the opposite situation where vehicles are reaching the extended extremeofconnection free slack as the train stretches.Longitudinal train dynamics therefore has implications for passenger comfort, vehicle stability, rollingstock design, and rollingstock metal fatigue. The study and understanding of longitudinal train dynamics was probably firstly motivated by the desire to reducelongitudinal oscillationsinpassenger trains and in so doing improve the general comfort of passengers. The practice of power braking, that being keeping power applied with minimum air braking, is still practiced widely in Australia on passenger trains. Power braking is also used on partly loaded mixed freight trains to keep the train stretched during braking and when operating on undulating track. In the Australian context,the studyoflongitudinal train dynamics is evidenced in technical papers coinciding with the development of heavy haul unit trains for the transport ofcoal and iron ore. Measurement and simulation of in-train forces on such trains in the Queensland coal haulage was reported by Duncan and Webb. 1 Moving to trains of double existing length was reported at the same time in New South Wales in apaper by Jolly and Sismey. 2 Interest was also evident in South Africa with the publication of apaper focused on train handling techniques on the Richards Bay Line. 3 The research was driven primarily by the occurrences of fatigue cracking and tensile failures in autocouplers. From these studies 1–3 an understanding of the force magnitudes and an awareness of the need to limit these forces with appropriate driving strategies was developed. During these developments, the first measurement of in-train forces in long trains utilising distributed locomotive placement were completed. An important outcome was that athird type of in-train force behaviour was identified. Prior to these studies in-forces were divided into two types, namely, steady forces and impact forces. Steady in-train forces are © 2006 by Taylor & Francis Group, LLC
Longitudinal Train Dynamics 241 associated with steady applications of power or braking from the locomotives or train air braking, combinedwith drag due to rolling resistance, air resistance, curve drag, and grades. Impact in-train forces are associated with run-in and run-out occurrences due to changes in locomotive power and braking settings, changes ingrade and undulations. In trains with distributed power, anew force phenomena known aslow frequency oscillations was identified. This new behaviour was further classified into two distinct modes, namely cyclic vibration and sustained longitudinal vibration. 1 Sustained longitudinal vibration occurred only when the entire train was in asingle stress state, either tensile or compression. The oscillation was underdamped and approximated to asmooth sinusoid. Of interest was that the magnitude of the in-train force associated with this low frequency oscillation could approach the magnitude of the steady in-train force, representing asubstantial increase inpossible fatigue damage and the risk of vehicle instability. Cyclic vibrations were characterised by oscillations approximating a square wave and occur due to run-in/run-out behaviour. Cyclic vibration differed from impacts in that the vibrations could be sustained for several seconds. The need to control, and where possible reduce, in-train forces resulted in the development of longitudinal train simulators for both engineering analysis and driver training. More recent research into longitudinal train dynamics was started in the early 1990s, motivated not this time by equipment failures and fatigue damage, but derailments. The direction of this research was concerned with the linkage of longitudinal train dynamics to increases in wheel unloading. It stands to reason that as trains get longer and heavier, in-train forces get larger. With larger in-train forces, lateral and vertical components ofthese forces resulting from coupler angles on horizontal and vertical curves are also larger. Atsome point these components will adversely affect wagon stability. The first known work publishedaddressing this issue was that of El-Siabie, 4 which looked atthe relationship between lateral coupler force components and wheel unloading. Further modesofinteraction were reported and simulated by McClanachan et al. 5 in 1999, detailing wagon body and bogie pitch. Concurrent with this emphasis onthe relationship between longitudinal dynamics and wagon stability is the emphasisontrain energymanagement. The operation of larger trains meant that the energy consequences for stopping atrain become more significant. Train simulators were also applied to the taskoftraining drivers to reduce energyconsumption. Measurements and simulations of energy consumed by trains normalised per kilometre–tonne hauled have showed that different driving techniques can cause large variances in the energy consumed. 6,7 II. MODELLING LONGITUDINAL TRAIN DYNAMICS A . T RAIN M ODELS The longitudinal behaviour of trains is afunction of train control inputs from the locomotive, train brake inputs, track topography, track curvature, rollingstock and bogie characteristics, and wagon connection characteristics. The longitudinal dynamic behaviour of atrain can be described by asystem of differential equations. For the purposes of setting up the equations, modelling, and simulation, it is usually assumed that there is no lateral or vertical movement of the wagons. This simplification of the system is employed byall known rail specific, commercial simulation packages and by texts such as Garg and Dukkipati. 8 The governing differential equations can be developed by considering the generalised three mass train in Figure 9.1. Itwill be noticed that the in-train vehicle, whether locomotive or wagon,can be classified as one of only three connection configurations, lead (shown as m 1 ), in-train, and tail. All vehicles are subject to retardation and grade forces. Traction and dynamic brake forces are added to powered vehicles. It will be noted onthe model inFigure 9.1 that the grade force can be in either direction. The sum of the retardation forces, F r is made up of rolling resistance, curving resistance or curve drag, air resistance and braking (excluding dynamic braking which is more © 2006 by Taylor & Francis Group, LLC
Page 1: 9 CONTENTS Longitudinal Train Dynam
Page 5 and 6: Longitudinal Train Dynamics 243 By
Page 7 and 8: Longitudinal Train Dynamics 245 Pol
Page 9 and 10: Longitudinal Train Dynamics 247 For
Page 11 and 12: Longitudinal Train Dynamics 249 If
Page 13 and 14: Longitudinal Train Dynamics 251 var
Page 15 and 16: Longitudinal Train Dynamics 253 For
Page 17 and 18: Longitudinal Train Dynamics 255 Com
Page 19 and 20: Longitudinal Train Dynamics 257 Tra
Page 21 and 22: Longitudinal Train Dynamics 259 Bra
Page 23 and 24: Longitudinal Train Dynamics 261 The
Page 25 and 26: Longitudinal Train Dynamics 263 G .
Page 27 and 28: Longitudinal Train Dynamics 265 Lon
Page 29 and 30: Longitudinal Train Dynamics 267 FIG
Page 31 and 32: Longitudinal Train Dynamics 269 tak
Page 33 and 34: Longitudinal Train Dynamics 271 “
Page 35 and 36: Longitudinal Train Dynamics 273 Res
Page 37 and 38: Longitudinal Train Dynamics 275 ope
Page 39: Longitudinal Train Dynamics 277 V f

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