Heavy haul train impulse and reduction in train force method.
The heavy haul trains, with their worldwide recognition of high efficiency, have become more popular for freight train in the world. Even though heavy haul trains are high efficiency and low transportation cost, there is an increasingly prominent issue, namely longitudinal impulse which causes more and more failures including coupler breakage, fatigue and car components damages, and may cause the risk of railway safety.
As heavy haul trains operate under complex conditions with many non-linear factors, study on train longitudinal impulse by physical tests has been more commonly used. However, physical tests will cost heavily, take long time and require complicated arrangement, though it may be able to obtain the real operational performance of trains. Therefore, physical tests are not feasible to test all plans and that is also the reason why most countries use combinational way of test and simulation to study the longitudinal dynamics of heavy haul trains. With mature computer simulation technology, it is possible to use simulations method to study train longitudinal dynamics. Compared with tests, simulations can offer benefits including low cost, repeatability and zero risk.
For many countries including China, air brake systems are used for heavy haul trains. However, as air brake systems usually have asynchronous braking performance, it has been regarded as the main source for heavy haul train longitudinal impulse. The characteristics of air brake systems are usually obtained in train tests and interpolated by numerical methods to get the brake characteristics of each vehicle. Those characteristics are then used in all train configurations for different longitudinal simulations. However, as multi-locomotives in connected trains discharge compressed air at different time, and especially in China the end-of-train exhaust devices are fitted, whose discharging characteristics is not as same as the locomotives, it is very difficult to obtain brake characteristics of all vehicles in all train configurations by interpolation from the test data. Therefore, many researchers turn to air flow models of train brake systems for the purpose. This model method can establish automatically brake system models based on actual train configurations and then calculate brake characteristics of trains based on air flow theories. The advantages of this method include reducing the necessity of humanly adjusting the brake characteristics in interpolation of test data, and hence can obtain the brake characteristics of train in any marshalling in a more realistic way, and provide a basis for accurate simulation longitudinal dynamics of heavy haul trains.
United States started train air brake system simulations in earlier days and established the simulation model for ABDW valve (Abdol-Hamid et al. 1990; Johnson, Booth, and Mattoon 1986). This model can predict air brake system characteristics of train with single locomotive. Japan established the model of train main pipe and branch pipe to study the effect of pipe end orifice on train pipe pressure reduction characteristics. But the model did not include vehicle distribution valve and therefore could not obtain brake system characteristics (Hiroshi and Izumi 1986). India established vacuum brake system model in detail (Bharath, Nakra, and Gupta 1990; Murtaza 1993). China established the brake system simulation model integrating brake main pipe and branch pipe in 1992, and solved air unsteady flow equations by characteristics method (Wei, Zhang, and Liu 1992). And completed the model of train brake system including GK distributing valve in 1994 (Wei and Kai-wen 1994). However all the above studies focused on establishment brake system models only from the perspective of brake system performance, but did not apply for the research of train longitudinal dynamics. Researchers in Poland however considered heat conduction in their model to study brake systems and introduced results in their study of simple train longitudinal impulse (Tadeusz 2009, 2010). University of Florence and Rome University (Tor Vergata) in Italy started simulation on UIC brake system (Cantone et al. 2009; Pugi, Palazzolo, and Fioravanti 2008). The former used matlab to develop the brake system linear simulation model and commercial software AMEsim to develop the nonlinear models. And ADAMS code was used to calculate train longitudinal dynamics by introducing the brake system simulation results. The reference (Wei et al. 2012) developed an integral simulation system combining a train air brake system model with a longitudinal dynamics model. This integral simulation system can directly modify brake system structure to get different brake characteristics and meanwhile to obtain the train longitudinal impulse, and this simulation system is examined by standard examples issued by reference (Qing et al. 2017). Hence it provides a better method of analysis the train longitudinal impulse by optimising brake system structures.
2. Train brake system and longitudinal dynamics model
2.1. The vehicle brake system model
120 distribution valve is widely used in China heavy haul trains, According to the composition of vehicle braking systems used in China heavy haul trains, a vehicle brake system with 120 distribution valve is modelled with six pipes, six chambers and one control unit (distribution valve). The model is shown in Figure 1. The detailed model can be found in reference (Wei et al. 2017)
In this model, instantaneous pressure of pipes and chambers are calculated based on air flow theory and the force acting on each piston are calculated according to the 120 distribution valves working mechanisms. The [[phi].sub.1] ~ [[phi].sub.9] orifice dimensions are decided by the piston's positions, and new flow boundary equations were solved with the new orifice dimensions. This will be repeated for each step until the end the whole brake and release processing.
The pipe model is used to calculate the air-flow in brake pipe, branch pipe and connection pipe between valves and chambers. The pipe is a long and thin pipe, it is reasonable that the airflow in the pipe to be assumed as one dimension with friction, heat transfer, non-homentropic flow. Based on the momentum conservation, energy conservation and mass conservation, the following equations are obtained.
[mathematical expression not reproducible] (1)
where, u is the particle velocity, [rho] is the particle density, p is fluid pressure, F is cross section area of pipe, a is the speed of sound, f is friction factor of pipe wall, q is the heat transfer energy per unit mass per unit time, k is specific heat ratio, D is diameter, t is time, x is distance. The characteristics method is used to solve the equations (Wei, Zhang, and Liu 1992).
For the brake system model, except the air flow equations in the pipe, some boundary equations should be added, and all air flow states can be decided. These boundary equations include the pipe joint with resistance, partially open end, closed end, pipe and chamber connection etc., detail equations for the boundaries can be seen in reference (Wei et al. 2017).
2.2. The train longitudinal dynamics model
A train consisting of locomotives and vehicles connected by coupler and draft gear is shown in Figure 2.
In this model, each vehicle (include locomotive) is taken as a lumped mass. Each concentrated mass is connected by spring-damping device of stiffness and damping feature. Presume coupler height is same as vehicle mass centre height, forces applied to each vehicle are shown in Figure 3.
Each vehicle has the following force equilibrium equation:
[m.sub.i][[??].sub.i](t) = [F.sub.Gi](t) - [F.sub.Gi+1](t) - [F.sub.Ai](t) - [F.sub.Bi](t) + [F.sub.Li](t) - [F.sub.Ci](t) - [F.sub.Wi](t) (2)
For i = 1, [F.sub.G1](t) = 0; i = n, [F.sub.Gn+1](t) = 0
where [m.sub.i][[??].sub.i](t) inertial force for ith vehicle, [F.sub.Gi](t) coupler force, [F.sub.Ai](t) running resistance, [F.sub.Bi](t) air brake force, [F.sub.Li](t) traction force or dynamic brake force, traction force is positive and dynamic brake force is negative, [F.sub.Wi](t) grade resistance, [F.sub.Ci](t) curve resistance, n total number of locomotive and vehicles in the train.
The C80 vehicle's running resistance is:
[r.sub.0] = 0.92 + 0.0048v + 0.000125[v.sup.2](N/kN) (3)
HXD1 locomotive's running resistance is:
[r.sub.0] = 1.40 + 0.0038v + 0.00013[v.sup.2] (N/kN) (4)
The accuracy of simulation results depend many factors, among them the major ones are draft gear features and brake system performance. In this paper, the draft gear features are obtained from actual single car impacting single car test. The relation between deflection and force is showed in Figure 4.
3. Mechanism for longitudinal impulse of heavy haul train
To analyse coupler force characteristics in heavy haul trains during braking, simulations were made on coupler forces in 10,000-tonne trains with normal configuration in China. The configuration is 1HXD1 loco + 105 C80 cars (100-tonne total). The train was fitted with the 120 type Chinese distributing valve air brake system, and MT-2 draft gear.
Figure 5 gives the coupler force-time curves at two typical positions when the train applies a service application. Two typical positions are at middle and rear of train. 46th car is at the middle and 105th car is at the rear of train. The coupler force curve for 46th car shows that it is a straight level line before 11 s as at that time the impact wave has not reached the 46th car. But after 11 s, the curve obviously drops, namely a sudden compressive coupler force increasing at a rapid speed and the curve basically turns into a vertical line. Then the coupler force reduces to about half of original peak immediately and continues to drop but with a slower speed till to a larger peak of around 750kN at around 20 s. Then it continues to reduce and then increase and after a few of cycles gradually returns to zero. It can be seen from the change of coupler force that the rapid change of coupler force only happens once. Other changes all have slower changing rate. The coupler force curve for 105th cars shows that there is a sudden increase in coupler force at around 17 s and then an instant reduce. This change is similar to that of 46th car at about 11 s. The first force peak changes rapidly, and other increase and decrease gradually. It has been found that such instant change of coupler force is resulted from impact when coupler slack between two adjacent cars is removed. The feature of such force is happened when the coupler force just appeared, and changes instantly. As they change rapidly, in this paper they are referred to as impacting forces. After an impacting force appears, the coupler force changes gradually. For example there are 4 larger coupler force peaks for 46th car and there is basically no larger coupler force for 105th car. To differentiate impacting coupler forces, coupler force peak gradually formed is termed in this paper as squeezing force.
Reference (Wei, Zhang, and Zhang 2011) showed that when the train was in braking, the maximum coupler force in a train could be either the squeezing force or impacting force termed as above. To analyse the pattern for the maximum coupler forces, distribution of coupler forces was calculated for the train of 50 cars in service application at an initial speed of 80 km/h. Figure 6 is the distribution of the maximum coupler force along the length of train with different coupler slacks.
The curves in the Figure 6 are formed by the maximum coupler forces of all cars in the train in the service braking. In the curve with slack of 0 mm, it can be seen that the distribution of the maximum coupler forces show a fish belly shape where the maximum coupler force occurred at the front to centre of train. When the coupler slack is zero, the maximum coupler forces of all cars are squeezing forces, not impacting forces. In the curve with slack of 5 mm, before the 38th car, the maximum coupler force curve is still like a fish belly shape, however after the 38th car, the maximum coupler force increases gradually with the increase in car number, and returns to zero at the end car of the train. It can be seen that before the 38th car when the curve is bell shape, the maximum coupler forces are resulted from squeezing force, while after the 38th car, the maximum coupler forces are resulted from impacting force. In the curve with slack of 50 mm, there is no fish belly shape as all coupler forces change in the same pattern as they do in the curve with slack of 5 mm after the 38th car, namely all coupler forces are impacting forces.
In above curves, the peaks are the maximum coupler forces of the train. For example, in the coupler force curve with slack of 0 mm, the maximum coupler force of the train occurred at the 20th car, front to centre of the train. In the coupler curve with slack of 50 mm, the maximum coupler force of the train occurred at the 48th car, almost end of the train. The above results demonstrate the effect of coupler slack on the maximum coupler force. If the maximum coupler force of the train is impacting force, it must happen at the end of the train, and if the maximum coupler force is squeezing force, it must not happen at the end of the train, but near the centre of the train.
The calculation results of the same marshalling train but with different coupler slacks show when the coupler slack is small, it is highly possible that the maximum coupler force of the train is squeezing force, while when the coupler force slack is large, it is highly possible that the maximum coupler force of the train is impacting force.
As the length of trains may influence the kind of the maximum coupler force, i.e. the maximum forces are squeezing forces or the impacting forces, more simulations are done to different vehicle numbers of train. Figure 7 shows the boundary between squeezing force and impacting force with respect to the maximum coupler force for train with different vehicle numbers and different coupler slacks, when the train is at service application with brake pipe pressure reduction of 170 kPa from an initial train speed of 80 km/h. The boundary is represented by the curve in the figure. The lower right corner area is impacting area in which the train is relatively shorter but the slack is larger. In this area, the maximum coupler force of train is impacting force, namely the force happened when the coupler slack is eliminated and coupler force just appeared, and the force changes rapidly. While in the upper left corner of the Figure 7, the maximum coupler force of train is squeezing force. In that area the train is longer but the slack is smaller. It can be concluded from the above boundary curve that for trains with shorter length but larger slack, in service applications, the maximum coupler force is most likely to be impacting force. However, for trains with longer length but smaller slack, the maximum coupler force is most likely to be squeezing force. As the heavy haul train is normally longer, it is most likely that the maximum coupler force is squeezing force. The simulation results proved that number of cars in the train, the brake reduction amount, initial train speed at braking will all affect the boundary line of impacting area and squeezing area.
4. The ways to reduce the maximum impacting coupler force
From the above results, it is known that for trains with shorter length and larger slack, in service applications, the maximum coupler force is impacting force. As the impacting force is related with coupler slack, reduction of coupler slack may decrease coupler forces. To this aim, it is necessary to analyse the effect of coupler slack on coupler forces. Figure 8 shows the distribution of the maximum coupler force of every car along the length of train which consists of 40 cars and of three different coupler slacks. It can be seen from those three curves that the coupler forces of front half of cars are small and form a half of fish belly shape. Those coupler forces are squeezing forces. But the coupler forces of the rear half of obviously increase with the car number, basically in linear relationship. Those maximum coupler forces are impacting forces. The calculation results of three coupler slacks show that reduction of coupler slack can obviously decrease the maximum coupler force of train. In this calculation, when the coupler slack was increased from 10 to 15 and 20 mm respectively, the maximum coupler force of train was increased from 130 to 162 and 192kN, by increased 24.6% and 47.7%, respectively. The calculation results prove the conclusion when the maximum coupler force of train is impacting force, reduction of coupler slacks can obviously reduce coupler forces.
To analyse the effect of slacks on coupler forces for a longer train, simulations and calculations are also conducted on distribution of coupler forces for trains with 10,000-tonne train and with different coupler slacks. The maximum coupler forces of all cars in the train in braking are recorded and plotted in Figure 9, there are three curves of maximum coupler forces corresponding to three coupler slacks in Figure 9. Comparison with Figure 8 for shorter train, it shows that both figures are of fish belly shape at the front part, and form a straight line at the rear part. The differences between two figures are that for the longer train, the numbers of cars in the fish belly part of curve are more than that in the straight line of curve. The other difference, more prominently, is that for the longer train the maximum coupler force of train happens in the fish belly area, which is near to the centre of train. While for the shorter train, as shown
in Figure 8, the maximum coupler force of train happens in the straight line area, which is near the end of train. Coupler force in fish belly area is squeezing force and in straight line area is impacting force. It can be seen from Figure 9 that coupler slack has a larger effect on coupler forces forming a near straight line at the end of train, rather not coupler forces forming fish belly shape at the front of train. As for longer train, the maximum coupler force of train happens in the fish belly area and it was squeezing force, it is not feasible to decrease the maximum coupler force of train by reducing coupler slacks.
For shorter trains, as the maximum coupler force of train is impacting force, reduction of coupler slack can effectively decrease the maximum coupler force of train. But for longer trains, as the maximum coupler force of train is squeezing force, reduction of coupler slack does not obviously decrease the maximum coupler force of train, therefore it is necessary to study mechanism of occurrence of squeezing force to find way to reduce the maximum coupler force of longer heavy haul train.
5. The ways to reduce the maximum squeezing coupler force
When a train is in service applications, cars at the front of train firstly start brake application to slow down the speed. At same time, cars at the rear of train have not braked yet. That is why there are speed differences between cars at the front and at the rear of train. Because of such speed differences and coupler slacks, cars at the rear bump into the cars at the front, resulting in coupler impacting force. After the impacting force is absorbed in some ways, coupler slack does not continue to affect. However, at that time, there are still velocity differences, rear cars continue to move forward, the whole train is squeezing and coupler force continues to increase till velocity differences reduce to zero for adjacent vehicles. At this time, the whole train squeezing reaches to the maximum, and the maximum coupler force appears. When the maximum coupler force happens the coupler slack has no effect, therefore the maximum coupler force is mainly resulted from rear cars moving forward and front cars blocking off. Rear cars moving forward are due to their brake forces are smaller than front cars. Thus, it can be concluded that poor brake forces of rear cars are the main reason for the maximum coupler force.
Figure 10 shows charging curves in brake cylinders at typical positions. It can be seen from the curve that, in addition to different of initial charging time, pressure increase rates are also different. The nearer cars to the end of train are, the slower the cylinder pressure increasing rates are. But it should be noted that pressure increasing rates do not decreases gradually as the car's position.
Brake cylinder pressure increase rate is controlled by the train pipe pressure reduction rate. The quicker the train pipe pressure decreases, the quicker the brake cylinder pressure increases. Figure 11 shows the pressure--time curve of train pipe for the front and the rear of train. It can be seen that there is a great difference in pressure reduction rate between cars at the front and at the rear of train.
The main reason why brake cylinder charging speed is affected by train pipe pressure reduction speed is that the slide valve(which is located in distribution valve) displacement changes with the train pipe pressure reduction rate, as forces acting on main piston of distributing valve are directly related with train pipe pressure reduction rate. The higher pipe pressure reduction rate can cause larger forces acting on main piston, and consequently main piston moves longer distance, brake cylinder charging orifice has wider opening and brake cylinder charging speed is faster. The relationship between main piston displacement and brake cylinder charging orifice opening area for Chinese 120 (120-1 type) distributing valve is basically linear, as shown in Figure 12. Different charging rate for cars at different positions just explain the difference in main piston travels for cars at different positions in train. This also provides a basis for adjusting orifice area in accordance with piston travel distance.
Accelerating train pipe pressure reduction rate for cars at the rear of train can accelerate the brake cylinder charging rate. The simulation results in the reference (Wang and Wei 2013) show that acceleration of train pipe pressure reduction rate can be achieved by adding service application acceleration valve in long and heavy haul train. Chinese 120-1 type valve is the example with addition of acceleration valve on basis of 120 valve to achieve accelerating train pipe pressure reduction speed. In addition, the distribution valve structure can be modified in order to slow down cylinder charging rate for cars at the front and speed up cylinder charging rate for cars at the train rear, which can be achieved by modifying the relationship between sliding valve(main piston) displacement and brake cylinder charging orifice while train pipe pressure reduction speed keeps unchanged. The final purpose is to minimise difference in brake capacity for cars between the front and the rear of train.
Brake pipe pressure reduction rate controls sliding valve displacement, and sliding valve displacement controls the brake cylinder charging orifice. When the brake pipe pressure reduction rate unchanged we can modified the relation between sliding valve displacement and the orifice. Figure 13 shows the new relationship between sliding valve displacement and charging orifice area obtained through extensive simulations and calculations. Comparison between this modified relationship with old relationship shows that when the sliding valve displacement is shorter, the orifice area is larger, but when the distance is longer, the orifice area is smaller. Such relationship realises the charging rate for cars at the front is slowed down, and charging rate for cars at the rear is accelerated, but with the same train braking capacity, namely the train stop distance is unchanged. The comparison in maximum coupler force for every car of train along the length of train between original orifice and optimised orifice is shown in Figure 14. The maximum coupler force is reduced from 586kN for the original structure to 365kN for the optimised structure. In this design, squeezing coupler force has almost same numerical value as impacting coupler force. Further force reduction shall require optimisation of coupler slack at the same time.
The coupler slack and the relation between main piston displacement and orifice area in distribution valve can change the in-train force when braking, and the other case, such as traction or dynamic brake, the distribution valve structure change will not effects the in-train force. But the coupler slack may have some effect for traction, for extreme condition as coupler slack is 0 mm, the starting of train will becomes difficult because of the greater starting resistance, it need a great power locomotive. But in the real train condition, 0 mm slack is exist short time even the initial coupler design for zero slack because the wearing. For the coupler slack larger than 0 mm, the traction or other case, there is no change compared to the ordinary train used today. Drawbar in train used now is a kind example of reducing coupler slack.
(1) In train braking, the maximum coupler force of train is resulted from impacting force or squeezing force.
(2) For shorter trains but with larger coupler slacks, the train's maximum coupler force in service applications normally is impacting force, while for longer trains with smaller coupler slacks, the train's maximum coupler force is normally squeezing force.
(3) Impacting force is caused by elimination coupler slacks between cars, while squeezing force is caused by different braking capacity between cars at the front and at the rear of train.
(4) For the cases where maximum coupler forces are impacting forces, the maximum forces can be decreased by reducing coupler slack, while for the cases where the maximum coupler forces are squeezing forces, the way to reduce coupler slack does little effect for reducing maximum coupler.
(5) For long heavy haul trains, as the maximum coupler force is squeezing force, it can be reduced by slowing down brake cylinder charging rate for cars at the front and speed up charging rate for cars at the rear without changing train brake capacity.
(6) The relationship between sliding valve displacement and brake cylinder charging orifice can be modified to realise slowing down brake cylinder charging rate for cars at the front and speed up charging rate for cars at the rear, and keeping the train's braking ability unchanged.
No potential conflict of interest was reported by the authors.
This work was supported by China Railway Corporation [grant number 2015J007-O].
Notes on contributors
Wei Wei is a professor of Railway Vehicle Engineering at Dalian Jiaotong University. Professor Wei's research activities are mainly in the field of train air brake system and train longitudinal dynamics. He developed a Train Air Brake and Longitudinal Dynamics Simulation System (TABLDSS), and established Chinese train air brake system model based on air flow dynamics.
Jun Zhang is an associate professor of Vehicle Engineering at Dalian Jiaotong University. His mainly research are in the field of train longitudinal dynamics and engineering mechanics, focusing on mechanical modeling and mechanics characteristic optimal design of draft gear.
Xubao Zhao is a PhD candidate majoring in Mechanical Engineering at Dalian Jiaotong University, China. His research mainly focuses on Vehicle Dynamics.
Yuan Zhang works in Dalian Jiaotong University and is also a PhD candidate at Dalian Jiaotong University. Research interest mainly focuses on longitudinal dynamics of rail vehicles.
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Wei Wei, Jun Zhang, Xubao Zhao and Yuan Zhang
School of Traffic and Transportation Engineering, Dalian Jiaotong University, Dalian, China
Received 10 October 2017
Accepted 7 December 2017
CONTACT Wei Wei [??] firstname.lastname@example.org
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|Author:||Wei, Wei; Zhang, Jun; Zhao, Xubao; Zhang, Yuan|
|Publication:||Australian Journal of Mechanical Engineering|
|Date:||Jun 1, 2018|
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