Heavy-haul railway transportation has been one of the main directions of railway development and has received more and more attentions due to its advantages of low cost, high efficiency, and energy conservation. In China, Datong-Qinhuangdao Railway is the first double-tracked heavy-haul electric coal-dedicated line undertaking Chinese coal resources transportation, and has successfully been operating the 20,000-ton combined train since 2006. As the vehicles continue to use air braking systems and the length of a 20,000-ton combined train is about 2700 m, the asynchronization of each vehicle air braking arises and causes the problem of longitudinal impulse during the train braking. Aiming to reduce the longitudinal impulse during the 20,000-ton combined train braking, the controllable train-tail device was officially utilized in 2007 to exhaust the compressed air at the brake pipe end to improve braking synchronization. For the difference between the controllable train-tail device and the locomotives, the exhaust performance of the controllable train-tail device will affect the vehicle air braking transmission and the longitudinal impulse of the train. Therefore, it is necessary to study the influence of controllable train-tail characteristics on the longitudinal impulse of the 20,000-ton combination train.
Researchers usually adopt experimental and numerical simulation methods to study longitudinal train dynamics. However, the numerical simulation method is widely used because of its high efficiency, low risk, low cost, and ability to conduct multi-parameter influence analysis. Cole et al. [
1,
2] introduced the important development of longitudinal train simulation and explained the longitudinal train modeling methods, which cover the numerical solver, vehicle draft gear model, traction and dynamic brake model, pneumatic brake model, propulsion resistance, curving resistance, gravitational components, and presented applications of longitudinal train simulation. Wu et al. [
3] focused on dynamics models that can be used for freight train air brake simulations, sorted out the 24 braking models, and analyzed the modeling principles of the empirical model, fluid dynamic model, and fluid empirical dynamic model, finally discussed the challenges and research gaps in air braking modeling. Because the longitudinal impulse of heavy haul trains is closely related to the characteristics of their vehicle braking systems, it is necessary to conduct a joint analysis of the train braking system and the train longitudinal dynamics system. Specchia et al. [
4,
5] established the locomotive automatic brake valve, air brake pipe and vehicle control unit model (CCU), then predicted the train braking performance, and simulated the train dynamics by combining the train longitudinal dynamic model. Aboubakr et al. [
6] built up the electronically controlled pneumatic (ECP) brake model including the train line, locomotive automatic brake valve, air brake pipe, and manifold, predicted the longitudinal dynamic characteristics of 50 vehicles, and compared the simulation results with the safety and operation of the American Railway Association and the test results in other references. Pugi et al. [
7,
8] set up a simplified model of longitudinal train dynamics based on the three-dimensional freight car with the braking model and buffer model, then simulated various working conditions and studied the relationship between train braking characteristics, buffer characteristics, and train formation with longitudinal train impulse. Mohammadi et al. [
9,
10] established the longitudinal dynamic model of the train by using MATLAB software to discuss the influence of braking system characteristics on the train longitudinal impulse. Many scholars have conducted longitudinal dynamics research in China based on the Chinese braking system and heavy haul trains operation. Chang et al. [
11] established the longitudinal dynamics and air braking system model based on the nonlinear equations that obtained the brake pipe pressure distribution by measured data in the brake test, and the longitudinal coupler-force was verified by the 20,000-ton heavy-haul train with a configuration of the locomotive (SS4) + 51 vehicles (C80) + locomotive (SS4) + 51 vehicles (C80) + locomotive (SS4) + 51 vehicles (C80) + locomotive (SS4) + 51 vehicles (C80). Sun et al. [
12] built up a longitudinal train dynamic model with a buffer model based on the vehicle impact test data and the train brake model using an air brake characteristic multi-parameter mathematical method and analyzed the longitudinal dynamics under different line conditions and braking action. Yang et al. [
13] set up a dynamic model of the 20,000-ton heavy-haul train in Matlab/Simulink and obtained air braking force according to the brake cylinder’s pressure change curve. The longitudinal impulse of the locomotive (SS4) + 102 vehicles (C80) + 2 locomotives (SS4) + 102 vehicles (C80) + locomotive (SS4) combination train was analyzed by considering the influence of factors such as lag time of the slave locomotive, vehicle type, draft gear device, and operating conditions under emergency braking. Wei et al. [
14‐
18] developed the simulation system TABLDSS by combining the air brake simulation system with the longitudinal dynamics simulation system in FORTRAN to conduct the synchronous simulation of air braking and longitudinal dynamics. In the TABLDSS, the air brake simulation system is based on the air-flow theory, which can reflect the pressure distribution and air brake force under the operation of braking and releasing. It gets rid of the limitation of empirical formulas and numerical interpolation on test results to obtain the air braking force and provides an analysis tool for the influence of the air braking system characteristic on the longitudinal impulse of the train. In the international evaluation of the train longitudinal dynamics simulation system, the TABLDSS simulation system was the one with the fastest calculation speed, better simulation accuracy, and high simulation accuracy among nine simulation systems from six countries [
19].
The controllable train-tail device has been used in the 20,000-ton combined train of Datong–Qinhuangdao Railway for many years, relevant studies are few except that Wei et al. [
20] studied the effect of train-tail characteristics on the 20,000-ton combined train longitudinal impulse by TABLDSS under full-service braking. According to the driving instruction manual of Datong–Qinhuangdao Railway, the initial braking by 50 kPa reduction operates most frequently, and the fixed pressure reduction in the controllable train-tail device is 50 kPa. Therefore, this work establishes the controllable train-tail device model in the train air braking simulation system that reflects the characteristics of Datong–Qinhuangdao Railway, conducts joint simulation with the train longitudinal dynamics, mainly studies the influence of the exhaust characteristics of the controllable train-tail device on the longitudinal impact of the 20,000-ton combined train under the initial braking of 50 kPa pressure reduction, and provides theoretical reference and analysis tools for the design and improvement of the controllable train-tail device.