Simulated comparisons of wagon coupler systems in heavy haul trains

Transcription

1 247 Simulated comparisons of wagon coupler systems in heavy haul trains C Cole and Y Q Sun Centre for Railway Engineering, Central Queensland University, Australia The manuscript was received on 16 August 2005 and was accepted after revision for publication on 18 April DOI: / JRRT35 Abstract: Three types of wagon connection coupling systems are evaluated in a train simulation model consisting of 107 vehicles. The three wagon connection coupling systems are autocouplers with standard draft gears, auto-couplers with draft gears with wedge unlocking features, and the traditional drawhook buffer system. The train is made up of 103 wagons and 4 locomotives. The locomotives are placed in groups of two at the head and mid-train positions. Dynamic response and fatigue damage is compared for a control disturbance on a crest and on a flat track section. The effect of coupling-free travel (slack) is also investigated. Keywords: longitudinal train modelling, wagon connection modelling, in-train force, fatigue life 1 INTRODUCTION The operation of freight trains in different continents is still differentiated by different wagon connections systems. The predominant wagon connection in North America and Australia is the autocoupler system. The system of drawhooks and buffers is now rare. In Europe, drawhook and buffer systems are still in wide use. Of particular interest in this article is the comparison of the performance of these systems in the context of heavy haul trains. 2 LITERATURE RESEARCH 2.1 Review of wagon connection modelling Linear models utilizing only linear springs and dampers are no longer taken seriously as a method of modelling wagon connections. All known commercial simulation implementations, both for driver training and engineering analysis, employ a nonlinearity of some kind. The long train simulator was developed by Ahmed and Bayoumi [1], using linear spring and damper constants included a nonlinearity for coupler slack. Another example of an Corresponding author: Centre for Railway Engineering, Central Queensland University, Building 70, Rockhampton Campus, QLD 4702, Australia. c.cole@cqu.edu.au implementation of a linear model was that of Sun and Chen [2]. This model was developed primarily to allow use of limited computational capacity. The piece-wise-linear characteristic has also been applied for the wagon connection modelling. The force displacement relationship of the connections is represented by a series of linear segments, because a draft gear can display the different characteristics during the loading and unloading process in the situation of draft or buff. Garg and Dukkipati [3] presented several examples of longitudinal train dynamics analysis using such wagon connection modelling. The other applications included an analysis of train longitudinal impulse by Yu et al. [4] and the dynamic research in connected trains by Sun and Sun [5]. 2.2 Non-linear models The state of the art in wagon connection modelling is demonstrated by the models employed in commercial simulation packages. Improvement in computer capabilities in recent years has seen the disappearance of longitudinal models from the market place, where groups of wagons are lumped together as one mass. In such models, a dynamically equivalent wagon connection model was placed between blocks of wagons. Modern computation speeds have allowed each wagon to be modelled as an individual mass. Modelling is now focused on matching the JRRT35 # IMechE 2006 Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit

2 248 C Cole and Y Q Sun wagon connection model to the actual behaviour of the several components that make up the wagon connection. The wagon connections using autocoupler systems or drawhook and buffer systems have experimentally proven non-linear characteristics, as observed by Duncan and Webb [6], El-Sibaie [7], and Bentley [8]. In order to analyse the performance of a freight train on the curved track, Horn et al. [9] modelled a buffer-pair as non-linear longitudinal springs with dry friction accounting for the telescopic behaviour of the buffer. In the simulations of collision behaviour of crashworthy vehicles, Lu [10] applied the modelling of an autocoupler that comprised a hydraulic buffer and a set of ring springs with strong non-linear characteristics of force stroke relationship. 3 MODELLING 3.1 Longitudinal train modelling The train is modelled with each vehicle mass having a longitudinal degree of freedom. There are three vehicle configurations (Fig. 1), lead (m 1 ), in-train (m 2 ), and tail (m 3 ), where m, v, and x refer to mass, velocity, and displacement, respectively. Function F c describes the non-linear characteristics of the wagon connection. Forces F g, F r, and F t/db describe gravity, retardation, and traction and dynamic brake forces, respectively. 3.2 Modelling of the autocoupler system The energy-absorbing component of an auto coupler system is the draft gear package (Fig. 2). This provides stiffness and either hydraulic or friction damping. The friction type is most common in Australia. The draft gear package is fitted in a wagon cavity and is loaded via a component called a yoke which is designed so that it applies compressive forces to the draft gear package for both compressive and tensile in-train forces. The complete interwagon connection also includes coupling-free travel (slack) and stiffness for steel components. The model must, therefore, include several non-linear components, as shown in Fig. 3. The auto coupler connections for this article are modelled using the friction wedge model, as described by Cole [11]. The friction wedge model gives a model that is dependent on impact conditions (i.e. deflection and velocity) for the model of the loading curve. All other aspects, locked unloading, unloading release, and unloading, of the wagon connection model are modelled using linear or piece-wise-linear functions, as are typically implemented in commercially available train simulation packages [6]. The friction wedge model adds a velocitydependent friction model to the piece-wise-linear model of the polymer spring. The friction properties of the wedge are approximated to a function such as F f ¼ m s N for v iw ¼ 0 F f ¼ m(v iw )N for 0, v iw, V f F f ¼ m k N for v iw 5 V f (1) The force predicted by any piece-wise-linear forcedisplacement function is of the form F ¼ f (x) (2) where f(x) is a piece-wise-linear function. The normal force N in equation (1) is proportional to the coupler force F c by means of wedge geometry. The polymer spring can, therefore, be modelled. The effect of wedge friction can then be incorporated as follows F c ¼ f (x)g(f f ) (3) where g(f f ) is a geometry function which relates the wedge friction force to the polymer spring force. Fig. 1 Train model schematic Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT35 # IMechE 2006

3 Simulated comparisons of wagon coupler systems 249 or F c ¼ f (x i, x iþ1, v i, v iþ1 ) (5) and k iw (6) Fig. 2 Schematics of auto coupler and drawhook/ buffer style wagon connections The model is now non-linear and has two independent variables x and v. In more general terms F c ¼ f (x iw, v iw ) (4) As the polymer spring is in series with the combined stiffness of other wagon components, the stiffness function f (x iw, v iw ) can be made to incorporate these stiffness components. Using this model, coupler model responses are as shown in Fig. 4. The model predicts the response for both severe impact conditions, similar to those in drop hammer tests, and very slow loading conditions, such as those that occur during some normal train running conditions. The locking behaviour of draft gear friction wedges is also of interest. In typical train operations, draft gears wedges remain locked during load relaxation until the force drops to a level close to the lower curve of published drop hammer tests. The locking behaviour is dependent on friction conditions and geometry. For comparison, simulations are completed both with and without wedge locking. 3.3 Modelling of the drawhook and buffer system Drawhooks and buffers were modelled as a combination of a piece-wise-linear function and a viscous damper. Typical of Australian systems (Fig. 2), damping and spring components are only located in the buffers. The tensile connection was modelled as a stiff linear spring representing the drawhook. The buffer models were given polymer springs of a characteristic equivalent to a typical draft gear system. Some difficulty was experienced in obtaining data on buffer damping characteristics. The nonlinear damping function developed was tuned to give hysteresis matching that published by Lu [10]. Viscous damping in the buffer was modelled by the equation making damping dependent on polymer spring compression, friction, and velocity-related viscous effects. Tensile model (x iw 5 0.0) F c ¼ 0:0 for x iw. 0; x iw, x slack F c ¼ k(x iw x slack ) for x iw. x slack (7) Fig. 3 Auto coupler wagon connection components and modelling Compression model (x iw, 0.0) F c ¼ F s þ F d (8) where F s is defined as a Fixed-Piece-Wise-Linear function, which refers to a mathematical relationship JRRT35 # IMechE 2006 Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit

4 250 C Cole and Y Q Sun Fig. 4 Wagon connection model responses for 0.1, 1.0, 10.0 Hz inputs made up of several linear segments F s ¼ f s (x iw ) F d ¼ C(v iw ) (1=9) j f s (x iw )j 4 METHOD (9) Simulations were completed for three types of wagon connection coupling systems and are evaluated in a train simulation model consisting of 107 vehicles. The train is made up of 103 wagons and four locomotives. The locomotives are placed in groups of two at the head and mid train positions in the train. Simulations were completed for two track profiles, one being a crest (Fig. 5) and the other flat track. A control disturbance was added to set up longitudinal dynamics in the train, Fig. 4. The control disturbance is rapid reduction and reapplication in power. It is an extreme event that is observed when a situation arises that might require emergency braking. It was selected for this study as it will set up low-frequency cyclic loading in long trains if applied on a crest or in a dip, and a single-stress state (either all couplers in compression or all couplers in tension) exists in the train. For this article, a track crest is selected, and the control disturbance is added on the downhill position. In this condition, draft gears are known to stay locked and low-frequency vibrations can persist in the train for some time [6]. These simulations are compared with the same control disturbance applied on flat track. Train simulations were completed for three different wagon connections, configurations, and different amounts of free slack. Train dynamic response, maximum forces, maximum wagon accelerations, and fatigue damage are compared. Fatigue calculations were completed following the guidelines specified in reference [12]. Indications of fatigue life were obtained by generating REPOS data from simulation output for 11 in-train positions, Fig. 5 Power control and track topography crest Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT35 # IMechE 2006

5 Simulated comparisons of wagon coupler systems 251 namely the lead loco group drawbar, couplers at intervals of 10 per cent train length, and the last loaded coupler. These fatigue calculations are used to compare the two common cases of cyclic tensile loading. A hypothetical component of cross-sectional area 9006 mm 2 was used for calculations indicating fatigue costs. Steel properties for the Modified Goodman diagram for the component were taken as Fatigue life in cycles was then given by N T ¼ 1 P ai =N i (11) where a i is the fraction of the total cycles. Fatigue life in kilometres was then obtained by S y ¼ 345:0 MPa b ¼ 51:0 MPa m ¼ 1:0 q ¼ 0:35 Life ¼ N i b where b is cycles/k. 5 SIMULATION RESULTS (12) The stress concentration factor of 2.0 was used. Fatigue life in cycles was calculated as the summation of damaging cycles as per N i ¼ N e (S max =S e ) 1=k (10) where N e ¼ and S max was the max stress in the cycle. Damaging cycles are defined as S max.s e. Of particular interest in long train behaviour is the low-frequency vibration that can occur when a single-stress polarity exists in the train and a control disturbance occurs. A typical response is shown in Fig. 6(a). An interesting consequence of changed friction conditions could result in a condition as in Fig. 6(b). The effect of coupling slack is illustrated by results in Fig. 7. Note that 50 mm slack is at the upper extreme of operational limits, while zero slack (Fig. 7(b)) is impossible to achieve practically. The simulation (Fig. 8) shows the effect of replacing Fig. 6 In-train force and wagon accelerations control disturbance, crest track, auto couplers, 50 mm slack JRRT35 # IMechE 2006 Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit

6 252 C Cole and Y Q Sun Fig. 7 In-train force and wagon accelerations control disturbance, flat track, auto couplers the power controls (Fig. 4) with an equivalent steady power level. Examples of the effect of using drawhooks and buffers are shown in Fig. 9. More comprehensive comparisons, using fatigue life as an indicator of train dynamics, are given in Figs 9 and DISCUSSION A typical example of low-frequency vibration is simulated and presented in Fig. 6. This type of behaviour was documented as early as 1989 [6] and conformed again later from field data in 1998 [11]. What was surprising from these studies was the locking behaviour of the draft gear wedges. This had not been observed in normal drop hammer tests and was only observed during normal train operations. Note that there is minimal vehicle acceleration in the region from t 140 s to t 170 s, where in-train forces fluctuate from 100 to 600 kn. The absence of vehicle accelerations proves the wedge lock state. An interesting question is explored in Fig. 6(b) with simulation of a wedge system without locking phenomena. This is of interest as this is rarely observed in the situation of a track crest or dip in train test data, as observed by Cole and Duncan and Webb [6, 11]. Conversely, the behaviour simulated in Fig. 6(a) is common and repetitive, Fig. 8 In-train force and wagon accelerations steady power, crest track, auto couplers, 50 mm slack Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT35 # IMechE 2006

7 Simulated comparisons of wagon coupler systems 253 Fig. 9 In-train force and wagon accelerations control disturbance, drawhooks, and buffers observable several times per train trip. It should also be noted that the test data used by Cole and Duncan and Webb [6, 11] are separated by almost a decade. The simulations without the locking phenomena are included to explore the effect that small changes in wedge design or the addition of lubricant or contamination may have. The result is much larger intrain forces, up to 1500 kn, and vehicle accelerations. While it can be argued that without locking behaviour there is the potential to dissipate more energy, unfortunately, the vehicle dynamics are so much more severe that the resulting in-train forces are higher. It should also be noted that oscillation frequency in Fig. 6(b) in the region t 140 s to t 170 s is much lower than that in Fig. 6(a). In the case of Fig. 6(b), the draft gear packages are deflecting, and stiffness is governed by the polymer springs. In the case of Fig. 6(a), the draft gears are locked, and stiffness is governed by steel components in the wagon connections and wagon body, resulting in a stiffer higher-frequency response. Coupling slack has little effect on the wagon dynamics when the train has a single-stress state on a track crest, as shown in Fig. 6(a). Simulations of the same control disturbance give a very different result on flat track (Fig. 7). The simulation of 50 mm slack on flat track (Fig. 7(a)) shows higher in-train forces and much larger vehicle accelerations than the zero-slack example (Fig. 7(b)). Note that slack cannot be reduced much,25 mm in normal auto coupler equipment, and reduced slack designs have typically 12.5 mm. The significance of control actions in long trains is demonstrated by the reduced in-train forces achieved in Fig. 7. Note that in-train forces are reduced from 600 kn to 400 kn (compare with Fig. 6(a)), and there is an absence of low-frequency vibration on the track crest. Vehicle accelerations, however, remain similar. Some examples are also produced for the drawhook and buffer simulations (Fig. 9). In practice, free slack of 5 mm is probably possible, but dependent on the diligence of staff. It also depends on the presence of track curvature during marshalling. It should be noted that the modelling for the buffer hysteresis (Fig. 4(b)) is derived from published values. There was no supporting experimental data available. Note that the low-frequency oscillations occurred after a control disturbance on the crest (Fig. 9(a)) but vehicle accelerations were more severe than either of the autocoupler simulations presented in Fig. 6. The case of control disturbance on flat track (Fig. 9(b)), even with the unrealistic zero-free slack, gave higher in-train forces and more severe vehicle accelerations than the zeroslack autocoupler simulation (Fig. 7(b)). The fatigue life results for 11 train positions shown in Figs 10(a) and (b) gave some surprising results. In JRRT35 # IMechE 2006 Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit

8 254 C Cole and Y Q Sun all cases, the poorest performance was achieved by autocoupler systems where the wedges did not have the self-locking feature. This is an interesting result to consider in autocoupler maintenance. Altered friction conditions due to wear and contamination could, therefore, significantly change longtrain dynamic behaviour. The best life results were achieved by autocouplers where the draft gear was behaving normally. There was only one exception to these generalizations; the auto coupler with no lock, 50 mm slack at last position in Fig. 10(b). Another surprising result was that the drawhook buffer simulation gave better results than that of the no-lock version of the autocoupler model. This can probably be attributed to the differences in free slack and not anything inherently superior in drawhook buffer systems. As should be expected, coupling slack had minimal effect on the fatigue damage levels for the conditions simulated over the crest track section (Fig. 10(a)). Most of the in-train forces were due to steady loads and vibrations, rather than impacts at couplings. Fig. 10 Comparison of indicated fatigue life Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT35 # IMechE 2006

9 Simulated comparisons of wagon coupler systems 255 The poor performance of the no-lock version of the draft gears was primarily due to the larger in-train forces (Fig. 6(b)). The distribution of fatigue damage at different train positions is masked by the logarithmic scaling. The tendency is for more damage to occur mid-train. This is due to the impacts between the mid-train locomotives and the front wagon group, and the occasional occurrence of large forces behind the mid-train locomotives in crests and dips. It should be noted that distributed power locomotive systems have the effect of leveling force profiles overall. The better life at the lead area of the train is due to the gentler dynamics at the lead of a train, a characteristic achieved by distributing locomotives and applying smaller drawbar forces. Longer life is predicted due to this factor, even though steady forces in this area are high due to drawbar forces. Longer life is also predicted at the tail of the train due to lower steady forces with occasional severe force impacts. The effect of zero slack on the drawhook and buffer system (Fig. 10(b)) is particularly noted. 7 CONCLUSIONS Simulations of a long train with distributed power and 107 vehicles were compared for different coupling systems. Reduction of coupling slack was shown to be beneficial to all coupling systems both in reduction of intrain forces and reduction of fatigue damage. The friction conditions in autocoupler draft gear units was shown to be a significant factor in control of in-train forces and minimization of fatigue damage. ACKNOWLEDGEMENTS The support of the Centre for Railway Engineering (CRE), Central Queensland University, and Faculty of Engineering and Physical Systems, Central Queensland University, is gratefully acknowledged. Queensland Rail is also gratefully acknowledged for funding and technical support of research programs in longitudinal train dynamics. REFERENCES 1 Ahmed, M. E. and Bayoumi, M. M. Simulation and control of a long freight train. In Simulation in engineering sciences (Eds J. Burger and Y. Jarny) 1983 (Elsevier Science Publishers BV, North Holland, IMACS). 2 Sun, X. and Chen, Q. A fast algorithm of longitudinal train dynamics. The Fourth International Heavy Haul Railway Conference, Brisbane, Gary, V. K. and Dukkipati, R. V. Dynamics of railway vehicle systems, 1984 (Academic Press, Canada) ISBN Yu, M. Y., Sun, X., and Lin, J. B. Analyses to mechanism of train longitudinal impulse. The Fourth International Heavy Haul Railway Conference, Brisbane, 1989, pp Sun, Z. and Sun, X. The dynamic research in connected trains. Proceedings of IAVSD-Symposium, Czech Technical University in Prague, Czechoslovakia, 1987, pp Duncan, I. B. and Webb, P. A. The longitudinal behaviour of heavy haul trains using remote locomotives. The Fourth International Heavy Haul Railway Conference, Brisbane, 1989, pp El-Sibaie, M. Recent advancements in buff and draft testing techniques. Proceedings of IEEE/ASME Joint Rail Conference, USA, 1993, pp Bentley, P. H. Development and application of autocoupler systems for a steelworks Proc. Instn Mech. Engrs, 1993, 207, Horn, H., Jaschinski, A., and Sedlmair, S. Dynamic simulation of freight cars with nonlinear suspensionand-buffer-models during curving. Proceedings of IAVSD-Symposium, Czech Technical University in Prague, Czechoslovakia, 1987, pp Lu. G. Collision behaviour of crashworthy vehicles in rakes. Proc. Instn Mech. Engrs, 1997, 213, Cole, C. Improvements to wagon connection modelling for longitudinal train simulation. CORE1998, Rockhampton, AAR. Manual of standards and recommended practices, 1988, chapter 7 (Association of American Railroads, Washington, DC). APPENDIX Notation b fatigue limit (MPa) for stress ratio ¼ 0 (y intercept on Goodman diagram) C damping constant (Ns/m) F force (N) F c coupler force (N) F d damping force (N) F f friction force (N) F g longitudinal force due to grades (N) F r longitudinal force due to rolling, air, and braking resistance (N) F s spring force (N) F t/db longitudinal force due locomotive traction and dynamic braking rolling, air, and braking resistance (N) k spring stiffness (N/m) m mass (kg) m mgd slope on modified Goodman diagram N surface normal force (N) fatigue life at stress level i (cycles) N i JRRT35 # IMechE 2006 Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit

10 256 C Cole and Y Q Sun N T fatigue life (cycles) q absolute value of slope on the S N curve R stress ratio (S min /S max ) S e fatigue limit, b /(1.0-m R) (MPa) S y yield stress (MPa) S min minimum stress in a cycle (MPa) S max maximum stress in a cycle (MPa) v velocity (m/s) interwagon velocity (m/s) v iw V f x x iw a i b m m s m k minimum velocity at which minimum kinetic friction occurs (m/s) deflection or displacement (m) interwagon displacement (m) proportion of fatigue cycles at stress level i cycles/km friction coefficient static friction coefficient kinetic friction coefficient Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT35 # IMechE 2006