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J. Cent. South Univ. (2017) 24: 18981908 DOI: /10.1007/s11771-017-3597-3 Dynamic performance of heavy-haul combined train applying emergency braking on straight line LIU Peng-fei(刘鹏飞)1, 2, WANG Kai-yun(王开云)2 1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China; 2. State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China Central South University Press and Springer-Verlag GmbH Germany 2017 Abstract: A heavy-haul train-track coupled model is developed. Taking the emergency braking of the 2104 t combined train as example, the train longitudinal impulse, the coupler dynamic behaviors and wheel-rail interactions of vehicles distributing in the different positions are analyzed. The results indicate that under the coupler compressing forces, the couplers of middle locomotives may tilt to the free swing limits, which induces the unidirectional tilt of their connected wagon couplers. Consequently, the coupler longitudinal forces produce the lateral components, and then affect the wheelrail dynamic interaction. The performance of the middle locomotive and their neighboring freight wagons deteriorate significantly, becoming the most dangerous parts in the combined train. The wagons disconnecting with the locomotives can basically keep their couplers to stabilize in the centering positions, even though the maximum coupler longitudinal force acts on it. And its corresponding running safety also has little changes. Key words: heavy-haul train; longitudinal impulse; vehicletrack coupled dynamics; emergency braking 1 Introduction The heavy-haul railway has been playing an important role in the freight transportation, and has achieved a rapid development in the world wide. However, the operation of the longer and heavier train brings a serious challenge to its running safety and the maintenance work of the train-track system. The longitudinal impulse induced by the train control further worsens the situation. For example, a heavy-haul locomotive has ever derailed due to the electric braking operation 1, and the increase of the derailment coefficient in a freight wagon was found in a braking test 2. Previously, CN and CPR surveyed the proportional distributions of the failure equipments in the derailment accidents from 1999 to 2006 3. It was found that the axles/wheels make the maximum proportion, followed by the body/coupler components. For the track, the geometry status took the largest percentage, followed by the rail failure. Statistically, the equipment fault type was regarded as the inducement of the derailments. However, the on-site investigation was still limited for exactly exploring the correlations between the specific accident and the influence factors. Therefore, the assessment of the train running safety needed to be executed systematically, considering the train maximum forces in curves, the wheelrail forces, the wheel load reduction and so on 4. For a long term, the researches about the heavy-haul train dynamcs are carried out mainly from the aspect of the longitudinal impulse. With the developments of computer technique, COLE 5, 6 pointed out that each wagon as well as the coupler and draft gear system should be simulated in detail, and the action mechanism of the friction wedge should be considered. In his following work, the calculation of quasi-static coupler lateral force was integrated into the train longitudinal model, which was then used to study the influence of the coupler force on the wheel-rail forces. CHOU et al 7 established the longitudinal dynamic model of the train equipped with the electrically controlled pneumatic (ECP) brake system. NASR and MOHAMMADI 8 studied the influence of braking delay on the freight train longitudinal impulse. QI et al 9 introduced the expression formula of the impact force into the calculation of the coupler force for studying the train positioning operations. AFSHARI et al 10 established the air braking force model, which considered the comprehensive influence of factors such as the air flow, Foundation item: Projects(51605315, 51478399) supported by the National Natural Science Foundation of China; Project(2013BAG20B00) supported by the National Key Technology R Project(TPL1707) supported by the Open Project Program of the State Key Laboratory of Traction Power, China Received date: 20151130; Accepted date: 20170116 Corresponding author: WANG Kai-yun, PhD; Tel: +862887600773; E-mail: J. Cent. South Univ. (2017) 24: 18981908 1899 gas leakage, brake pipe and so on. So far, the research methods of the train longitudinal dynamics have tended to be mature. Considering the severe longitudinal impulse and wheelrail dynamic interaction coexisted in the heavy-haul train, numerous scholars focused on the research of the influences of the coupler and braking forces on the train running safety. CHEN 11 found that if the lateral tilt angle of a coupler existed, the coupler longitudinal force would affect its lateral component force, and the track irregularity might also induce the transfer of the coupler force. To prevent the running risks induced by the coupler forces, the coupler tilt angle should be limited, and the track structure needed to be strengthened. For studying the braking safety of train passing through the switch sections, PUGI et al 12 established a mixed train model composed by a 1-DOF vehicle and some multi-DOF vehicles. ZHANG DHANASEKAR 13 pointed out that the combined actions of the track irregularity and the braking torque might affect the wheel load reduction obviously. To assess the curving performance when the braking occurred, YANG et al 14 established the mixed train model composed by the vehicles with different degrees of freedom in SIMPACK, and considered the nonlinear factors of the buffer hysteresis property and the pneumatic brake forces. ALLOTA et al 15 developed a hardware in the loop (HIL) architecture on test rig to reproduce the degraded adhesion phenomena in the braking condition, which could also be used to research the braking behaviors of railway vehicle. WEI et al 16 analyzed the anti- jackknifing mechanism of couplers under the compressive in-train forces based on the theoretical train model and the laboratory propelling test. In summary, the researches about the heavy-haul running safety have achieved the significant progress. However, some problems still need further study, such as the synthetic modeling method of the long train and elastic track, the relations between the train longitudinal impulse and the wheel-rail interaction, and so on. In this paper, a three-dimensional train-track coupled dynamics model is developed by considering the dynamic behaviors of the coupler and draft gear systems. Taking the emergency braking condition of a 2104 t combined train as example, the wheelrail dynamic interactions of vehicles distributing in the different positions are analyzed, and the dangerous part of the train is extracted. In the following content, the train-track coupled model is introduced firstly. 2 Train-track coupled dynamics model A heavy-haul train-track coupled dynamic model (see Fig. 1) is established based on the vehicle-track coupled dynamics theory 17 which has been widely used in the heavy-haul railway dynamics 1820. The model involves the subsystems of the locomotive, freight wagon, wheel-rail interaction, inter-vehicle interaction and so on. Among them, the detailed mathematic descriptions of the submodels in front can be found in the literature 17, 19. Specially, the modeling method of the inter-vehicle interaction will be illustrated below. It should be emphasized that, in the train dynamics analysis the focused vehicles are usually the locomotives subjected to a large coupler force or the wagons in the positions where the maximum longitudinal impulse occurs. Therefore, for calculating conveniently and effectively, the focused vehicles can be simulated by the three dimensional vehicle-track coupled dynamic model while others are simplified as the single-mass model. 3 Submodel of inter-vehicle interaction The inter-vehicle interaction is mainly used to represent the dynamic coupler forces between the adjacent vehicles. From three aspects, the detailed methods are given below. 3.1 Coupler longitudinal force Figure 2 shows the dynamic model of the coupler and draft gear system, in which the system is simplified as a nonlinear force function with the hysteresis characteristics. In this figure, F0 and F1 are the quasi-static coupler force and the initial pressure of the draft gear respectively. fc and fe represent the coupler free slack and the maximum elastic compression amount Fig. 1 Heavy-haul traintrack coupled dynamic model J. Cent. South Univ. (2017) 24: 18981908 1900 Fig. 2 Dynamic model of coupler and draft gear system of the draft gear. Fd is the damping force, which is defined as the half of the difference value between the loading force and unloading force 21. When the buffer deformation varies, the dynamic coupler force will change within the region bounded by the loading and unloading curves. If the longitudinal relative displacement x between the adjacent vehicles is less than the coupler slack, the coupler longitudinal force Fc is Fc=0 (1) If the relative displacement varies between the coupler free slack and the maximum compression amount of the draft gear, then the coupler force depends on both the inter-vehicle relative displacement x and speed v. x0 and x0 when the locomotive pulls wagons. In this case, if v0, the coupler force will increase, changing along the dashed line. If v0, the coupler force will decrease, varying along the solid line as the arrow points. If v=0, the force changes according to the trend of the quasi-static force (F0). As for x0 of the compressive zone, it has the similar working principle. To reduce the numerical oscillation induced by the abrupt change of v between the positive and negative, the switching speed vf is introduced, which can be viewed as an intermediate interval between v0 and v0. Then the coupler force can be uniformly expressed as f f d01 fd01 c if ),(sign | )(sign if ),(sign)(sign vv x v v vFFF vvxvFFF F(2) If the relative displacement is larger than the maximum deformation, then )(sign)| ( buffefcs1c xFxKFF (3) where v denotes the inter-vehicle relative velocity, Fbuf is the reacting force of draft gear in its maximum stroke, Ks represents the structural stiffness of vehicle chassis. 3.2 Coupler lateral force The coupler lateral force is closely related to the coupler lateral swing angle. It is assumed that the couplers between two adjacent vehicles are connected together as a rigid-straight bar without relative rotation. The coupler swing angle relative to the car body is defined as positive when it rotates around the draft key clockwise in the top view, otherwise it is negative. In the straight line, the coupler swing angle is mainly affected by the relative displacements of the adjacent two vehicles, as shown in Fig. 3. If the vehicles run along the track center line straightly, the included angle between the car body center line and the line connecting the coupler yoke keys is zero. Once the car body has the spatial motions in other directions, the lateral displacements of draft keys in the front and rear vehicles can be calculated as cgici i cgicicii lhy) 1( (4) where yci, ci and ci represent the lateral displacement, rolling angle and yaw angle of the ith car body, respectively; hcgi and lcgi denote the vertical distance between the coupler and the mass center of ith car body, respectively; for the front and rear vehicles, i=1, 2 in sequence. Fig. 3 Coupler swing angle in straight line The included angle for the coupler relative to its centering position is 21 21 0 LL (5) where L1 and L2 represent the lengths of front and rear couplers, respectively. The coupler swing angles 1 and 2 can be expressed as iic0 21 cg2c2cg2c2c2cg1c1cg1c1c1 )( LL lhylhy ic (6) J. Cent. South Univ. (2017) 24: 18981908 1901 In practice, the amplitude of coupler swing angle is limited by the structures of the coupler and draft gear system. Once the coupler sways beyond the free swing limit, a restoring torque (M) will generate against its swing motion. Taking a pair of couplers as the analysis object, the coupler lateral force acting on the draft keys 1 and 2 in Fig. 3 can be calculated as )cos()( sin)( )cos()( sin)( 221 21221c 2 121 21121c 1 LL MMLLF F LL MMLLF F y y (7) where M1 and M2 are the restoring torques acting on the front and rear couplers. 3.3 Coupler vertical force For the non-rigid couplers, the connected coupler heads permit their vertical relative motions. Therefore, the maximum force transferred is the maximum static friction force. The mechanical model of coupler vertical force is given in Fig. 4, where the coupler body is regarded as a rigid bar fixed on its corresponding car body. The relative research indicates that the coupler inertia has little influence on coupler force 22, so the vibrations of coupler itself are neglected. The vehicle system motions are the main factors affecting the coupler vertical force. Fig. 4 Mechanical model of coupler vertical force If the coupler longitudinal relative displacement is less than the coupler free slack, then Fcz=0. Otherwise, the calculation is discussed in two conditions. 1) If | c0c FFz, then zkF czcz (8) 2) If |,| c0c FFz then r0cc r0cc | ),(sign| | ),(sign | | vzzFF vzz v z FF xz r xz (9) where z is the vertical relative displacement between the connected coupler heads, kcz is the vertical equivalent stiffness of coupler, vr is the switching speed, and 0 is the friction coefficients. 4 Submodel of railway vertical section The vertical section can be simplified as the function of gradient i varying with the line length l. At the grade change point of the actual line, a vertical curve is usually inserted to connect the adjacent ramps, which may decrease the gradient varying rate. The geometric relations between the ramps and vertical curves are shown in Figure 5. According to Ref. 23, the length of the vertical curve is Lvc2Lta, and its tangent length is LtaRvci/2000, where i is the the thousandth of the gradient difference between the adjacent ramps. Then, the vertical distance can be calculated as vcta vc 2 vc ta vc 2 , 2 )( , 2 LxL R xL h Lx R x h (10) So, the gradient in the vertical curve can be expressed as , , vcta21 ta vc 11 LxL R xL ihii Lx R x ihii vc vc x x (11) For the convex and concave curves, the upper and under signs of are selected, respectively. 5 Dynamic behaviours of coupler and draft gear systems for combined train 5.1 Train formation and calculation conditions In the coal dedicated lines of China, the heavy-haul Fig. 5 Relations between ramps and vertical curves J. Cent. South Univ. (2017) 24: 18981908 1902 unit train and combined train are the two main marshalling types usually applied at present. Their hauling weights are within the range from 1104 t to 2104 t. In this section, the 2104 t train is regarded as the research objective with the marshalling mode of HXD+105C80+HXD+105C80+train tail device. The coupler DFC-E100 of locomotive HXD has a free swing angle of 3. And the freight wagon C80 is assembled with the No. 16 coupler and MT-2 draft gear. And the emergency braking with the braking initial speed of 80 km/h is chosen as the research operating condition. The maximum gradients of the upline and downline of Daqin and Shuohuang railways are 4 and 12 respectively, and the maximum gradient difference reaches 8. Based on the actual line data, six line conditions are set, including the straight line, the convex and concave vertical curves with the 8 gradients difference, and three ramps with 4, 4 and 12 gradients respectively. At the initial time, the grade change points of vertical curves are in the middle of train 5.2 Train longitudinal impulse in emergency braking condition Based on the numerical model developed in section 2, the longitudinal dynamics for train emergency braking operation is analyzed firstly. In the calculations of pneumatic braking forces, the tested brake cylinder pressures of 2104 t combined train in the emergency braking condition are used 24, as shown in Fig. 6. The brake cylinder pressures in different vehicles have different trends and the pressures in other vehicles are obtained by the interpolating calculation within the given Fig. 6 Tested brake cylinder pressures of 2104 t train in emergency braking condition curves. Then, the braking forces can be calculated easily. Figure 7 compares the coupler force distributions along the train length in different line conditions. It can be found that, in most lines, the maximum coupler tensile forces occur in the positions of 98110th couplers, which distribute within the range of 9041014 kN. For the coupler compression force, the peak values in the conditions of the straight line and single gradient ramps are 1523 kN, while that in the convex curve reduces to 924 kN. The largest compression force occurs in the concave curve, exceeding 2100 kN. It is also indicated that the simulated results for lines without vertical curve has little difference between each other, which means the gradient different has a more significant influence than the gradient. Besides, it needs to be explained that the similar emergency braking test has ever been carried out in a single ramp of Daqin railway line in July 2007. The tested compressive coupler force of the combined train