Open AccessArticle

Research on Response Postures of Subway Train in Straight Line Collision

Shuhao Liu

¹,

Yiqun Yu

^2,3,

Yi Li

^2,3,

Rongqiang Liu

¹ and

Rong Zhang

^2,3,*

State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150001, China

Key Laboratory of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China

Key Laboratory of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information, Harbin Institute of Technology, Harbin 150090, China

Author to whom correspondence should be addressed.

Appl. Sci. 2025, 15(1), 252; https://doi.org/10.3390/app15010252

Submission received: 7 December 2024 / Revised: 24 December 2024 / Accepted: 27 December 2024 / Published: 30 December 2024

Download

Browse Figures

Figure 1
Carriage model. "> Figure 2
Bogie simplified model. "> Figure 3
Hollow aluminum alloy simplified model. "> Figure 4
Train head and coupler model. (a) Weak points on leading car. (b) Moment–rotation curve of joint between the front chassis and cab frame. (c) Swing angle in the horizontal plane, and rotating angle in the vertical plane of coupler. (d) Force–displacement curve of coupler buffer device. "> Figure 5
Total internal energy time history curve. "> Figure 6
Simplified diagram of train collision. "> Figure 7
Simplified force–displacement curve of coupler buffer devices. "> Figure 8
Force situation of a single carriage. "> Figure 9
Velocity history curves in head-on collision. "> Figure 10
Energy absorption history curves of major coupler buffer devices in head-on collision conditions. "> Figure 11
Carriages and couplers number. "> Figure 12
Energy absorption of subway train under different velocity. The blue rectangular prism represents the moving train, the red cylinder represents the stationary train, the blue circle represents the derailment of a carriage of the moving train, and the red triangle represents the derailment of a carriage of the stationary train. The aluminum alloy front frame is numbered as 0. "> Figure 13
Energy absorption history curves of coupler buffer device in 25 km/h head-on collision condition. "> Figure 14
Maximum vertical displacement of wheelsets. "> Figure 15
Ordered energy absorption characteristic before second impact. The dash lines correspond to the time points t1 to t3 mentioned in the described ordered energy absorption. "> Figure 16
Energy absorption history curves of carriage in 45 km/h collision with obstacle. "> Figure 17
Vertical displacement history curves of wheelset in 45 km/h collision with obstacles. "> Figure 18
Energy absorption in front oblique collision. "> Figure 19
Front-side collision conditions. "> Figure 20
Wheelset displacement under different front-side collisions. "> Figure 21
Overriding phenomenon and vertical arch. "> Figure 22
Derailment and large lateral movement of the train front in oblique collision. "> Figure 23
Lateral and vertical impact force on wheelset. "> Figure 24
Lateral displacement history curves of leading car. "> Figure 25
Vertical displacement history curves of leading car. "> Figure 26
Lateral impact force on the first wheelset. "> Figure 27
Vertical displacement history curves of leading car at different impact velocity. (a) Vertical displacement history curves of leading car under C1 condition. (b) Vertical displacement history curves of leading car under C3 condition. "> Figure 28
Lateral buckling under front side collision. "> Figure 29
Lateral displacement history curves of wheelset under C1 condition. ">

Versions Notes

Abstract

A six-car subway train finite element model was developed to investigate possible response postures under impact accidents. Considering the plastic deformation of carriages and weak points of the train front, the simulation included two conditions: train–train collision and collision with an obstacle. Comprehensive response postures were obtained. A one-dimensional dynamic theory model was established to verify the rationality of the FEM model. The influence of impact speed, impact angle, and impact position on the energy consumption and response postures were discussed. The results show that one accident condition is accompanied by a variety of response postures. The main factors of climbing are asynchronism of yaw and pitch motions of adjacent carriages and plastic deformation of carriage ends, which leads to vertical arch. In oblique and front-side collision, the lateral force and the deviation of train front cause rapid derailment, and large lateral movement of the front and lateral buckling happen subsequently.

Keywords:

subway train collision; elastoplastic model; one-dimensional dynamic model; train–obstacle; energy absorption; response postures

1. Introduction

At present, urban rail transit systems in countries around the world have made significant progress, providing people with more convenient transportation options. With the increasing dependence on rail transit, the complexity of rail track alignment and train operation control also rises, leading to safety issues that cannot be ignored. Over the years, serious train collision accidents have occurred occasionally [1,2,3,4,5]. In response to these issues, scholars have conducted extensive research on train crashworthiness design and evaluation, collision response postures, and derailment mechanisms.

In the area of train crashworthiness design and evaluation, researchers primarily focus on the study of energy-absorbing devices. More efficient energy absorption devices and layout schemes were proposed, and the longitudinal stiffness of the train was optimized to maximize the safety of personnel [6]. The study of collision response postures and derailment mechanisms can provide guidance for crashworthiness design to further enhance passive safety in train collisions.

Due to the nonlinear behavior of materials, large deflections and rotations, multiple units, and varying collision conditions, the response postures of the train in collision are highly complex. Theoretical modeling and prototype test studies are extremely difficult, and the size effect of scaled tests can not be avoided. Numerical simulation is the most widely used and effective method for studying the collision response of urban rail trains.

In numerical simulation studies of train collisions, most research simplifies the train’s front and carriage to rigid bodies, or only treats the train front and vehicle ends as elastic-plastic bodies or nonlinear springs. For example, regarding the study of train front ends, Syaifudin et al. [7] investigated the impact of the shape (circular, square, and hexagonal) and configuration of the crash modules on energy absorption for medium-speed trains. They constructed a finite element model of the medium-speed train to simulate a collision, treating the train front shell as a deformable body and the train structure as a rigid body. Dias et al. [8] simplified both the train front and carriages as rigid bodies and used multibody kinematics to analyze the dynamic response of the train during a collision. Wang et al. [9] simplified the middle part of carriages as a mass point and performed collision simulation of the local structure at the front and carriage ends, obtaining the force-deformation characteristics of the main energy-absorbing parts of the train. They then simplified the energy-absorbing parts into nonlinear springs in a train set collision simulation. Zhao et al. [10] also simplified the carriage as a rigid body and analyzed the crashworthiness of coupled trains based on machine learning methods. To further analyze the failure mechanisms of coupled trains, they set the train front as an elastoplastic body [11], while the carriage remained a rigid body, and analyzed the destruction process of the train front frame during a high-speed train collision with a rigid wall. These simplification approaches are beneficial for improving computational efficiency, but the neglect of full or partial deformation of the carriages hinders the accurate capture of the true energy-absorbing characteristics and response postures of urban rail trains under various and complex collision conditions.

Some studies have also conducted numerical simulation analyses of collisions using elastoplastic urban rail train models. When conducting a rigorous assessment of a train’s crashworthiness based on existing standards, it is necessary to use an elastoplastic finite element model for train collision simulation [12,13]. Liang et al. [14] modeled both the train front and carriages as elastoplastic bodies and analyzed the failure process of coupled train collisions based on a subway collision accident in Beijing. They found weak points in the train front frame that need to be considered in collision analysis. LIU et al. [15] compared the standards for subway train body structure requirements in Europe and the United States. The crash pillar is explicitly required only in the U.S. standards. Through finite element analysis, they conducted a comprehensive assessment of the role of the crash pillar in passenger survival space and vehicle design and verified the elastic and plastic performance of the crash pillar through specific collision tests. Xie et al. [16] modeled the entire train as an elastoplastic body, using the same steel material for all parts. The results of the collision simulation at 36 km/h showed that only elastic deformation occurred in the passenger area of the carriages. Zhou et al. [17] also modeled the entire train as an elastoplastic body, using 6005A aluminum alloy for the train materials. In a simulation of a collision between two trains at a relative speed of 36 km/h, the results showed varying degrees of plastic deformation in the train body. Zhao et al^. [18] constructed a three-dimensional train collision model, in which the car body exhibited elastoplastic behavior, and the collision speed was set at 36 km/h. They optimized the design of the collision area at the front of the train by selecting the linear impact force slope of the energy-absorbing device as the design variable. Wang et al. [19] established a finite element model for the collision of a three-car train set, considering typical collision dynamics nonlinear features. They simulated the dynamic response of the train body structure and the derailment behavior caused by a frontal oblique collision with a rigid wall. Xu et al. [20] used a four-car train’s elastoplastic finite element model to validate the accuracy of the three-dimensional dynamic collision model under low-speed impact conditions and identified five parameters that are highly sensitive to wheelset lift. Wang et al. [21] conducted an elasticity analysis of the train body, integrating the flexible train body with other rigid parts of the vehicle system to form a complete rigid–flexible coupling model. It was found that compared to traditional multibody models, the rigid–flexible coupling model can more accurately capture the vibration and deformation behaviors of the train body during a collision. Zhu et al. [22] studied the response of subway vehicles made from three typical materials—carbon steel, stainless steel, and aluminum alloy—during a single-vehicle collision. By extracting the dynamic stiffness characteristics of the vehicle structure, they simplified the complex collision process into a system composed of mass and springs. They found that underframe was the primary path for collision force transmission. Zhang et al. [23] established a model of an eight-car train impacting a rigid wall at a speed of 25 km/h. Based on longitudinal crushing characteristics, they developed a four-stage rigid-flexible coupling finite element model for the coupler, considering the coupler’s deformation and energy absorption characteristics at different stages. They analyzed the impact of different coupler buckling loads on the train’s longitudinal, vertical, and horizontal buckling behaviors and proposed recommendations for the design of the intermediate couplers. However, there is less research on elastoplastic urban rail train models for higher collision speeds (greater than 36 km/h), oblique impacts, and front-side impacts. Additionally, there is insufficient research on energy absorption characteristics of the carriages and the response postures of elastoplastic train models under different conditions, with the influence of weak points in the train front frame often being overlooked.

In the study of train collision response postures, scholars generally adopt train–rigid wall or train-to-train frontal collision scenarios [24]. HOU et al. [25] studied a collision scenario where a moving train collided head-on with a stationary train. They obtained the different dynamic response and analyzed the derailment mechanisms during the collision process, including the behaviors of pitching, yawing, and overturning of the vehicles. Zhou et al. [17] used a combined simulation method of nonlinear finite element analysis and multi-rigid body dynamics to analyze the climbing behavior of a three-car train collision. They found that factors such as train mass, center of gravity height, and pitching frequency significantly affect the climbing behavior in a collision. Han et al. [26] established a multi-body dynamics 3D computational model of a twenty-car train to study its collision behavior. They discovered that when the train collides with rigid obstacles either head-on or at an angle, the train exhibits climbing, arching, and lateral buckling behaviors. In recent years, some researchers have begun to focus on the response postures of trains under asymmetric collision scenarios. Liang et al. [27] analyzed train collisions at railway–road intersections and pointed out that derailments are more likely to occur on curves with smaller radii. Yao et al. [28] used a 3D model of a four-car train to analyze the collision process of coupled trains with an inclined rigid wall, proposing that different collision angles affect the damage modes of coupled trains. Lyu et al. [29] took a metropolitan subway train as the subject and analyzed the influence of the initial state at the single-car level on the collision response under four typical geometric attitudes using a three-dimensional head-on collision model of a four-car train. However, the aforementioned studies simplified the entire or most of the train cars as rigid bodies or mass points, which improves computational efficiency but neglects the energy dissipation of the carriages during asymmetric collisions at higher speeds.

Based on the extensive research results of projects such as SAFETRAIN and SAFETRAM, the EN15227 standard “Requirements for the Collision Resistance of Railway Vehicle Bodies” [30] has been developed. This standard is primarily referenced and applied in Europe and Asia. It specifies the general methods for testing railway vehicles, defines the characteristics of the reference obstacle models used in collision scenarios, and outlines verification methods to confirm whether the vehicle’s passive safety performance meets the standards. The British standard [31] requires that the collision-resistant structural design of all railway vehicles must comply with EN15227. The three-collision scenarios defined in the International Union of Railways (UIC) standard system under UIC660 [32] also overlap with the content of EN15227. In contrast, the Japanese JIS E-series standards do not provide clear provisions on collision scenarios. The U.S. standards for evaluating the collision resistance of subway trains are similar to EN15227 [33], but with speed requirements of 24 km/h and 40 km/h. For locomotive vehicles, the impact conditions involve collisions with different types of obstacles, head-on and at an angle [34]. The Russian standards for passenger locomotive collision scenarios differ from EN15227, as they specify impacts with rigid walls and do not differentiate between vehicle types [35]. The collision scenarios for subway vehicles in the aforementioned standards all involve head-on symmetrical impacts. However, with the frequent occurrence of accidents involving side impacts and collisions with obstacles (such as civil defense doors, construction cranes, etc.) during subway operations, such asymmetric collision scenarios, which are more likely to cause derailments, should also receive attention.

Based on the above studies, this paper establishes a numerical model of a six-car metro train using ABAQUS/CAE 2021, considering the elastic-plastic deformation of the carriage and the weak nodes of the train front. A one-dimensional dynamic theory model was established to verify the rationality of the numerical model. The dynamic response of the metro train during a straight-line collision (train-to-train collision and train-to-obstacle collision) is studied. The collision response postures under both symmetric collision scenarios (train-to-train collisions, train vertical collisions with rigid walls) and asymmetric collision scenarios (train-to-train angled collisions, front-side collisions with rigid walls, angled collisions with rigid walls) are summarized, and causes are analyzed.

2. The Subway Train Numerical Model

2.1. Carriage and Bogie

The numerical model in this paper is based on China’s urban rail transit metro Type B vehicle. The model’s geometric dimensions are set in accordance with the relevant provisions of Code for design of metros [36]. The model features an aluminum alloy integral load-bearing structure, with the main material of the carriages being aluminum alloy profiles. The carriage model is shown in Figure 1. The bogie is based on the SDB-80 type bogie used in Chengdu Metro Line 1’s Type B trains, which includes the frame, wheelset, primary suspension, secondary suspension, and other components. To improve computational efficiency, the model is simplified as shown in Figure 2: the axle and frame are simplified to beam elements, the wheels are modeled as solid elements coupled with the axle ends, and the axle box, central traction device, and driving device are simplified as mass points applied to the corresponding locations on the frame. The material properties of the train body and main parameters of the train model are shown in Table 1. The model takes into account the dynamic constitutive effects of materials and uses the Johnson–Cook constitutive model, which considers the strain rate effect as shown in Equation (1), for simulation. To handle the complex contact issues between components during the collision process, the wheel–rail and crashing contacting surfaces contact adopt the penalty coefficient contact model defined by general contact in ABAQUS. The friction coefficient was set to 0.2.

σ = [A + B ε^{n}] (1 + C \ln ε^{' *})

(1)

The train carriage floor, side walls, roof, and end walls are all made of hollow aluminum alloy profiles. The middle section of this profile has a trapezoidal shape. To reduce computation time, in the simulation analysis, this hollow aluminum alloy profile can be simplified into an equivalent model where the middle corrugated sheet and the two side plates work together. The simplification process is shown in Figure 3. The middle corrugated sheet can be further simplified as an orthotropic flat plate, and the calculation formulas for its equivalent mechanical parameters are referenced in [37]. Finally, the hollow aluminum alloy profile is simulated using the composite shell material properties of shell element in ABAQUS. The calculation formulas for the equivalent mechanical parameters of the hollow aluminum alloy profile are shown in Equations (2)–(6).

E_{x} = \frac{E_{f x} 2 t_{f} + E_{c x} 2 h}{h + 2 t_{f}}

(2)

E_{y} = \frac{E_{f y} 2 t_{f} + E_{c y} 2 h}{h + 2 t_{f}}

(3)

\frac{1}{G_{x z}} = \frac{1}{G_{f x z}} \frac{2 t_{f}}{H} + \frac{1}{G_{c x z}} \frac{h}{H}

(4)

G_{x y} = \frac{1}{G_{f x z}} \frac{2 t_{f}}{H} + G_{c x y} \frac{h}{H}

(5)

ρ = \frac{2 ρ_{f} t_{f} + ρ_{c} h}{2 t_{f} + h}

(6)

where E_x and E_y are the equivalent elastic modulus in the x and y directions of the hollow aluminum alloy profiles, E_f is the elastic modulus of the two side plates, E_fx = E_fy = E (E is the elastic modulus of the aluminum alloy), and E_cx and E_cy are the equivalent elastic modulus of the middle corrugated sheet. H is the total thickness of the hollow aluminum alloy plate (the thickness of the surrounding components of the vehicle body is uniformly taken as 70 mm). l is the length of the inclined edge of the trapezoidal core material (taken as 35 mm). θ is the angle between the inclined edges of the trapezoidal corrugated sheet core material and the side plate (taken as 60°). 2a and b are the projection lengths of the straight edge and the inclined edge of the trapezoidal core material. t_f is the thickness of the side plates (taken as 3.5 mm), t is the thickness of the trapezoidal corrugated sheet core material (taken as 3 mm), ρ_f is the density of the aluminum alloy material, and ρ_c is the equivalent density of the middle corrugated sheet.

In addition to the thin-shell-type structures mentioned above, parts of the train body floor (edge beams, buffer beams, cross beams, and bolster beams), the roof (edge beams, the longitudinal stiffeners of the large arc, the rectangular cross beams), the side walls (the columns, door and window frames), the end walls (the door posts, upper door cross beams, corner posts) are simulated using beam elements, with the material being aluminum alloy.

Since the train mass [17] affects the climbing behavior, the model takes into account the ballast condition based on the passenger load status. The passenger load is calculated assuming full occupancy at six people per square meter, with an average weight of 60 kg per person. The total passenger weight is then evenly distributed as the density of the car floor.

2.2. Train Front and Coupler Buffer Device

The train front frame has weak points [14,15] that need to be considered in the collision analysis. As shown in Figure 4a, the simulation model of the train front takes into account the weak connection points between the upper end of the anti-collision column and the upper frame beam, and between the lower end of the anti-collision column and the anti-collision beam. These weak connections are modeled using semi-rigid node connections. ABAQUS is used to simulate the bolt connection at these nodes to obtain the bending moment–rotation curves in three directions, as shown in Figure 4b. The coupler buffer device is simplified as a nonlinear spring, the load–displacement curve shown in Figure 4d [38]. The limit values for the yaw angle β and pitch angle α are set to ±20° and ±6°, respectively, as shown in Figure 4c. The stroke of the buffer device is set to 0.5 m.

2.3. Mesh Analysis

In this section, a train collision with a rigid wall at 25 km/h is selected as an example to investigate the effect of mesh size, with a focus on the carriage. The mesh sizes are divided into three groups: fine mesh, medium mesh, and coarse mesh. In the fine mesh, the approximate global size of shell and beam elements is 20 cm, and the size of solid elements is 3 cm. In the medium mesh, the approximate global size of shell and beam elements is 30 cm, and the size of solid elements is 4.5 cm. In the coarse mesh, considering that the passenger area in the middle of the carriage does not directly bear the impact and its deformation is relatively small, the mesh for the passenger area in all carriages is enlarged to 3–5 times that of the medium mesh.

As a result, compared to the fine mesh, the number of beam elements is reduced by 57%, the number of solid elements is reduced by 61.5%, and the number of shell elements is reduced by 70.2%. The total internal energy time history curve for all carriages is shown in the Figure 5. The collision with the rigid wall ends at 0.7 s. Compared to the fine mesh, the maximum error in internal energy is 13.9%, and the calculation time is reduced by approximately 50%. Therefore, the coarse mesh is selected for the subsequent simulation analysis.

2.4. Model Validation

2.4.1. One-Dimensional Collision Dynamics Model for Trains

To verify the accuracy of numerical simulation results, this section constructs a one-dimensional mathematical model to simulate the longitudinal collision process of trains. To achieve a balance between accuracy and precision, the following basic assumptions are made when constructing and simplifying the model:

(1): The car bodies are treated as rigid bodies, and their masses are assumed to be concentrated at their respective geometric centers.
(2): Each carriage is divided into three rigid bodies, which are connected by springs. The deformation of the carriages is equivalent to the deformation of these springs.
(3): For the couplers and springs inside the carriages, only their equivalent stiffness characteristics are considered.

Based on the above assumptions, the longitudinal collision model of the train can be simplified as a multi-rigid-body mass-spring system, where each carriage is simplified into three rigid body segments and the energy absorption devices are simplified into a nonlinear spring system. The longitudinal collision condition is set as head-on collision. The carriage numbering and condition diagram are shown in Figure 6.

The elastic loading phase of the coupler buffer device is simplified to a line segment with a constant slope, and the plastic loading phase is simplified to a horizontal line segment, representing its steady-state force, as shown in Figure 7.

The axial force of the coupler can be expressed as:

F = p (k_{l}, f_{s}, k_{u}, x_{u}) = \{\begin{cases} k_{l} Δ x & Δ \dot{x} > 0, Δ x \leq x_{l} \\ f_{s} & Δ \dot{x} > 0, x_{l} < Δ x \leq x_{u} \\ k_{u} Δ x & Δ \dot{x} < 0, x_{u} - \frac{f_{s}}{k_{u}} < Δ x < x_{u} \\ 0 & Δ \dot{x} < 0, 0 < Δ x \leq x_{u} - \frac{f_{s}}{k_{u}} \end{cases}

(7)

where p represents the loading and unloading function of the coupler; k_l represents the compression stiffness; f_s steady-state force; k_u represents the unloading stiffness; x_u represents the compression stroke.

Take a certain carriage as a separate body and analyze its stress situation, as shown in Figure 8.

Based on the force analysis of a single carriage, the longitudinal collision motion of the train can be described using a system of nonlinear differential equations:

\{\begin{cases} m_{11} {\ddot{x}}_{11} = - F_{11} \\ m_{11} {\ddot{x}}_{12} = F_{11} - F_{12} \\ ⋮ \\ m_{i 2} {\ddot{x}}_{i 2} = F_{i 1} - F_{i 2} \\ ⋮ \\ m_{n 2} {\ddot{x}}_{n 2} = F_{n 1} - F_{n 2} \\ m_{n 3} {\ddot{x}}_{n 3} = F_{n 2} \end{cases}

(8)

where m is the mass of the rigid bodies of the carriages. F_i are the collision force between the two carriages, which is function of the relative displacement between the two carriages. Carriage ① is subjected to a longitudinal load on only one end, so F₀ = 0.

The collision force between carriages is expressed as:

F_{i} = k_{i} (x_{i 3} - x_{i + 1, 1}) + b_{i}

(9)

The internal collision force within the carriage is expressed as:

F_{i 1} = k_{i 1} (x_{i 1} - x_{i, 2}) + b_{i 1}, F_{i 2} = k_{i 2} (x_{i 2} - x_{i, 3}) + b_{i 2}

(10)

Substitute the above equations into Equation (8):

\{\begin{cases} m_{11} {\ddot{x}}_{11} = - k_{11} (x_{11} - x_{12}) - b_{11} \\ m_{12} {\ddot{x}}_{12} = k_{11} (x_{11} - x_{12}) + b_{11} - k_{12} (x_{12} - x_{13}) - b_{12} \\ ⋮ \\ m_{i 2} {\ddot{x}}_{i 2} = k_{i 1} (x_{i 1} - x_{i 2}) + b_{i 1} - k_{i 2} (x_{i 2} - x_{i 3}) - b_{i 2} \\ ⋮ \\ m_{n 2} {\ddot{x}}_{n 2} = k_{n 1} (x_{n 1} - x_{n 2}) + b_{n 1} - k_{n 2} (x_{n 2} - x_{n 3}) - b_{n 2} \\ m_{n 3} {\ddot{x}}_{n 3} = k_{n 2} (x_{n 2} - x_{n 3}) + b_{n 2} \end{cases}

(11)

Rearrange the above equation into matrix form:

M \ddot{X} + K X = B

(12)

where M is the mass matrix of the system, K is the stiffness matrix, and B is the steady-state force matrix. By solving the system of Equation (11) using numerical integration methods, we can obtain the displacement, velocity, and acceleration curves of each carriage rigid body during the longitudinal collision process, as well as the energy absorption of the structures between each rigid body.

2.4.2. Comparison Between Theoretical and Simulation Results

Head-on collision simulation was conducted using both one-dimensional theoretical model and finite element model at two speeds (15 km/h and 25 km/h). In the one-dimensional theoretical model, each carriage is represented by three mass points, and the average velocity of the three mass points is taken as the velocity of the carriage. The force–displacement curve of the coupler is set with reference to Figure 4d. In the finite element model, the stiffness of the carriage is much greater than that of the coupler, and the impact of carriage stiffness on velocity decay is minimal, so the stiffness is set to 10 times that of the coupler. In the collision scenarios at 15 km/h and 25 km/h, the energy absorption values of the first four couplers are all greater than 97% of the total energy absorption, and the carriages are all in the elastic stage. Therefore, the velocity–time curves of the first four carriages and the corresponding energy absorption–time curves of the first four couplers are extracted, as shown in Figure 9 and Figure 10.

The velocity decay curves of the first two carriages overlap well in the one-dimensional theoretical model, while the velocity decay of the third and fourth carriages slows down initially and then accelerates. This difference is related to the simplified coupler stiffness. In the finite element model, the input force–displacement curve of the coupler (as shown in Figure 4d) has a stiffness greater in the 0 to 28 mm compression range than in the 28 to 120 mm range, before the platform pressure is reached. In the one-dimensional model, this section is simplified to a single stiffness, resulting in the difference in velocity decay and the fluctuation in energy absorption values before the platform force is reached, as shown in Figure 9.

The maximum error in the energy absorption values of the couplers is 40% and 25%, respectively, and both occur between the second and third carriages at Coupler-2. The error for Coupler-3 is the second largest. The reason is that the simplification of the coupler force rise segment in the theoretical model causes certain stiffness differences, resulting in significant fluctuations in the internal energy of the couplers before the platform force is reached. However, this has a small effect on the accumulation of plastic deformation energy and the final total energy absorption value. The error in the energy absorption values of the remaining couplers is less than 10%. The errors in the total energy absorption values for the 15 km/h and 25 km/h collision conditions are −6.53% and 2.76%, respectively, which verifies the rationality of the finite element model.

3. Straight-Line Collision Condition Setting

In this paper, the straight-line collision of six-car subway trains includes two types of collision conditions: the collision between two identical trains and the collision of a train with an obstacle. The parameter analysis variables include impact speed, impact angle, impact position, etc. The specific conditions and train response postures are shown in Table 2, and the meaning of the name and the numbering method of each part of the train are shown in Figure 11.

The calculation time for the train-to-train collision is 2 s, while the calculation time for the train collision with obstacles is 1 s. The response postures shown in Table 2 represent the state of the first three carriages at the moment when the calculation time ends. The derailment criterion for the carriages is that at least one set of wheels has lost track constraint (i.e., the wheels have fallen off the track, or the uplift is greater than the distance from the top of the wheel flange to the track surface, and due to the lateral movement or rotation of the axle, the wheels cannot return to the track surface). The criterion for carriage overturning is that the carriage floor and axle form an angle with the ground, and the carriage undergoes a certain angle of rotation around the longitudinal axis parallel to the track; the side of the carriage even touches the ground (carriage has rotated 90° around the longitudinal axis). Other response postures such as the large lateral movement of the train front (LLMF) and lateral buckling are detailed in Section 5.

For straight-line collision between two identical trains, the standard EN 15227: In 2020 Railway Applications-Crashworthiness requirements for railway vehicles (hereinafter referred to as EN 15227) [30], the collision condition set for C-II railway vehicles is as follows: A subway train with an initial speed of 25 km/h collides with another stationary subway train of the same type. The physical quantities used to evaluate crashworthiness include: impact force and wheel–rail relative vertical displacement. The energy absorption value of each part is extracted to evaluate the deformation or damage of the train. Therefore, this paper carried out the parameter analysis under seven working conditions of no angle impact at different speeds and oblique impact with angle at 25 km/h.

For straight-line collision between train and obstacle, 30 working conditions were conducted with variables such as impact speed, impact angle and impact position to obtain a variety of response postures. The causes for the response postures were analyzed according to the data such as pitching and yawing, plastic deformation of the carriage, relative displacement of the wheel and rail, and the force between the wheel and rail.

4. Train–Train Collision

4.1. Frontal Collision

As shown in Figure 12, under the collision conditions specified by EN 15227 for C-II class railway vehicles (i.e., subway trains), the primary energy-absorbing components are the coupler buffer devices on the moving train set and the stationary train set. Figure 13 illustrates the energy absorption process of the coupler buffer device between carriages of the moving train set under above condition. It can be seen that energy absorption by the coupler buffer device ends at 0.8 s, and the energy absorption starts sequentially, with the energy absorption values decreasing from the front to the rear. The energy absorbed by the carriages is primarily recoverable elastic strain energy, accounting for only 4.9% to 7% of the total energy absorption of the coupler buffer devices. The energy absorption of the front aluminum alloy frame accounts for only 1.47% of the energy absorbed by the front coupler buffer device, and similarly, there is essentially no plastic deformation. It can be concluded that under the collision condition specified by EN 15227, the aluminum alloy frame at the front of the train and all carriages essentially do not undergo plastic deformation. The impact energy is entirely absorbed by the coupler buffer devices, and there is no damage to the train.

By extracting the vertical (Y-direction) displacement of the wheelsets of the moving and stationary train sets, it is found that the maximum vertical relative displacement between the wheel and rail for the moving train set is 2.5 mm, while for the stationary train set it is 12 mm. According to EN 15227, the requirement for the climbing control of railway vehicles is that the lift of the wheelset relative to the track surface should not exceed 75% of the flange height [21]. The maximum vertical displacement for both train sets is below this value, indicating that the subway model meets the standard requirements

When the relative collision speed increases, energy absorption values of each part at 36 km/h and 45 km/h are shown in Figure 12. The energy dissipation is basically completed by the coupler buffer device at relative collision speed of 25 km/h and 36 km/h, and there is basically no plastic deformation or little plastic deformation of the carriage. As the impact velocity increases to 45 km/h, the energy absorption value of the aluminum alloy front frame increases significantly, the degree of plastic deformation increases.

The distance from the top of the wheel flange to the track surface for this train model is 22 mm. That is, when the vertical relative displacement between the wheel and rail exceeds 22 mm, the wheel loses its constraint from the track at that moment. The maximum vertical displacement of each wheelset at different collision speeds is shown in Figure 14. During the relative collision speeds between 25 km/h and 45 km/h, only a few wheelsets of the moving and stationary trains experienced a brief derailment phenomenon (i.e., the wheels briefly lifted off the track, with the vertical relative displacement between the wheel and rail exceeding 22 mm, but eventually returning to the track surface. The briefly derailed carriage is shown in Figure 7. No derailment or climbing phenomena occurred.

It can be seen that in the above collision speed range of the six-car subway train model, the impact energy absorption is mainly completed by the train body and buffer device in front of the fourth carriage, without derailment and other accident risks. When the collision speed reaches 45 km/h, the energy absorption involved in the deformation of the carriage cannot be ignored. Therefore, for the simulation analysis of higher collision speed and collision with obstacles, it is necessary to consider the influence of carriage deformation on train response postures.

4.2. Angled Collision

In addition to collisions or rear-end accidents occurring on the same track, two trains may also collide at an angle at a switch, as in the 2009 collision incident on Shanghai Metro Line 1. No national standards specify the specific operating conditions for angled head-on collisions of subway trains. In this paper, this type of condition involves a moving subway train with an initial speed v colliding at an angle with another identical stationary subway train. In this section, v is set to 25 km/h, and simulations are conducted for four impact angles: 5°, 10°, 15°, and 30° to carry out preliminary research.

In the angled collision scenarios, the energy absorbed by the train cars is all below 3 kJ, while the plastic deformation of the train front frame is significant, with the plastic deformation energy exceeding 60 kJ. Compared to the case of a straight vertical collision, where the kinetic energy of the moving train is relatively evenly converted into the deformation energy of both the moving and stationary trains, in an angled collision, the kinetic energy of the moving train is not fully converted into deformation energy. As the collision angle increases, the proportion of energy dissipated by the moving train out of the total dissipated energy increases, but the total energy dissipation decreases. The anti-climbing device fails to effectively restrain the relative displacement between the two train fronts, causing the trains to derail quickly. The stationary train slides out of the impact range of the moving train, resulting in an early end to the collision. However, the moving train continues to derail at a high speed, which poses a significant safety risk to passengers onboard.

Regarding the collision of two trains at a switch, further research is needed to address more dangerous and complex scenarios, such as collisions between the train’s front and the side of the carriage.

5. Collision with a Rigid Wall

5.1. Vertical Collision

Multiple collisions occur in a six-car subway train collision with a rigid wall during the speed range from 25 km/h to 45 km/h. The first impact is the train front colliding with the rigid wall, and the second impact is the collision between the first carriage (hereinafter referred to as C-1) after deceleration and the second carriage C-2 at the rear, and so on. At different speeds, there are varying degrees of collision between the carriages. The plastic deformation energy is extracted as shown in Figure 15, before the second impact of the subway train at each speed, the energy-absorbing devices and the train body are orderly deformed during the collision:

(1): From 0 to t₁, the buffer device at the front deforms and absorbs energy;
(2): From t₁ to t₂, after the crushing failure of the front buffer device, the aluminum alloy frame deforms and absorbs energy;
(3): From t₂ to t₃, the train front and C-1 are rapidly decelerated in the first impact, while C-2 maintains its initial speed and continues to move. Prior to the second impact, the Coupler-1 between C-1 and C-2 deforms and absorbs energy until the second impact at t₃;
(4): At t₃, Coupler-1 stops absorbing energy, and C-1 directly absorbs the impact from C-2, resulting in significant plastic deformation.

The coupler buffer devices sequentially absorb energy, starting from the side near the collision end, reducing the relative impact speed before the direct collision between adjacent carriages. As the rear carriage continues to impact, the degree of plastic deformation in the aluminum alloy front frame and each carriage increases with each collision, leading to the accumulation of damage to the train body.

The plastic deformation of the train body and the relative vertical displacement between the wheel and rail increase with speed. At an impact speed of 25 km/h, the energy dissipated by the plastic deformation of the train body accounts for only 22.2% of the total energy dissipation, with the energy-absorbing device absorbing most of the energy. In this scenario, the end of the carriage sustains minor damage, while the passenger area generally maintains its structural integrity. However, at an impact speed of 45 km/h, the energy absorption capacity of the buffer device is largely exhausted, and the energy dissipated through plastic deformation of the train body accounts for 68.2% of the total energy dissipation. The energy dissipation time history curve for each carriage is shown in Figure 16. Meanwhile, the maximum relative vertical displacement between the wheel and rail increases from 175 mm at 25 km/h to 1209 mm at 45 km/h, with large lifting amplitudes observed in multiple wheelsets, as shown in Figure 17. Under these conditions, multiple collisions between carriages and wheel lifting (vertical arching) pose significant safety risks to passengers. The specific response process and cause analysis are presented in Section 6.2.1.

5.2. Angled Collision

In this section, the speed range of the working conditions is from 25 km/h to 45 km/h. Collision simulations are conducted at seven impact angles: 0°, 5°, 10°, 15°, 20°, 30°, and 45° with a total of 21 different conditions. The total energy absorption of the train body and buffer device is shown in Figure 18. The energy absorption values for various parts of the train at each speed decrease as the impact angle increases.

Compared to a frontal vertical impact, when the obstacle surface is hit at an angle, the lateral impact force causes Wheelset-1 to derail first. The front then slides along the inclined direction of the obstacle once it is no longer constrained by the track. As the relative angle between the coupler buffer device at the front and the obstacle surface decreases, the frontal impact force gradually diminishes and the coupler buffer device can no longer be further compressed, causing energy absorption to cease. The aluminum alloy front frame becomes the primary component absorbing the impact. When the impact angle exceeds 15°, the lateral impact force on the wheelset causes the derailment of C-1 before the coupler buffer device can perform energy absorption. The rapid offset of the front prevents the coupler buffer device from being compressed and absorbing energy, and the aluminum alloy front frame becomes the first part to undergo plastic deformation and absorb energy.

In Yao et al.’s [39] simulation of a subway oblique collision with an obstacle (impact speed of 25 km/h), when the collision occurs at an angle, the large lateral movement of the train front is observed. As the impact angle increases, the longitudinal force on the front decreases, while the lateral force increases. Due to the significant transverse movement traveled by the train front after derailment, the energy absorption efficiency of buffer devices both on the front and between the carriages is very low during the sliding motion along the inclined obstacle. The entire train continues to move in the oblique direction at residual speed, and the kinetic energy of the train is not completely dissipated. Consequently, the total energy dissipation decreases significantly as the impact angle increases. During this process, not only is derailment severe, but there is also an increased likelihood of other adverse events, such as the overturning of the carriages.

5.3. Front–Side Collision

The speed range of the working conditions in this section is 25 km/h to 45 km/h, and the vehicle impact simulation is carried out under 12 working conditions in four front–side impact positions. The frontal impact condition is numbered as C0, and three special positions of the train front are selected. According to the different lateral movement degree of the obstacles, three working conditions as shown in Figure 19 are set, numbered as C1, C2 and C3, respectively.

Under front-side impact conditions, the energy dissipation of the entire train remains relatively stable as the deviation of the obstacle changes. However, compared to the frontal impact, the relative displacement between the wheel and rail increases significantly. Additionally, the plastic deformation at the end of the carriage becomes more pronounced, while the energy absorption values due to plastic deformation in the middle section of the carriage decreases. As shown in Figure 20, when the impact speed increases to 36 km/h, both the horizontal and vertical displacements of the wheelset after detachment from the track increase. Notably, the horizontal displacement grows more significantly than the vertical displacement. At this point, the train exhibits a substantial lateral buckling, with climbing and overturning occurring between the carriages. The carriage can be divided into three sections: the front impact end, the middle passenger area, and the rear impact end. For instance, in carriage C-2, the energy absorption per unit length of each section is shown in Table 3. It can be observed that due to the deviation of the obstacle, the degree of plastic deformation at the front and rear ends of the carriage increases significantly, surpassing that in the middle passenger area.

When the impact speed increases to 45 km/h, the relative lateral displacement of the wheel-rail decreases, but the relative vertical displacement increases greatly, which is similar to the response attitude of Section 5.1. At this time, the climbing phenomenon between the carriages is aggravated. The wheelset still moves laterally after leaving the track, but the vertical arch of the train is the dominant response attitude, and the end of the carriage is seriously deformed.

6. Response Postures Analysis

6.1. Response Postures Summary

As shown in Table 4, when the collision speed is less than 45 km/h, there is almost no derailment phenomenon in the collision between two trains. The trains maintain a frontal collision on the track, and there are multiple collisions between the carriages, mainly axial deformation. When the speed of hitting the obstacle reaches 45 km/h, the weak joints on the front frame generally fail. Under the condition of colliding with a rigid wall, the failure process of the train is accompanied by a variety of response postures (climbing, vertical arching, lateral buckling, carriage overturning, etc.). The lateral buckling is the most obvious in front-side collision with a rigid wall. In oblique collision with a rigid wall, large lateral movement of the train front is most noticeable.

6.2. Analysis of the Response Processes and Causes of Different Response Postures

6.2.1. Climbing Between Carriages and Vertical Arch

Within the range of impact velocities studied in this paper, the failure process between the carriages can be summarized as follows:

(1): End Deformation: After the first impact, due to the deceleration of C-1 and the collapse of coupler buffer device between the carriages, a direct impact occurs between the end of C-1 (which has slowed down) and the higher-speed C-2. The collision ends undergo large plastic deformation.
(2): Climbing: After decelerating, C-2 collides with C-3, leading to a second impact between C-1 and C-2. The plastic deformation at the collision end of C-2 increases, and its ability to continue absorbing the impact diminishes. Due to the inconsistent pitching and yawing motions of the carriage, the relative distance between the ends of the carriages increases both vertically and horizontally. The rear end of the bottom plate of C-1 rides over the front end of the bottom plate of C-2 (as shown in Figure 21), and Wheelset-2 at the rear of car C-1 begins to lift off the rail surface.
(3): Vertical Arching: As the impact from the rear carriages continues, the overlap between C-1 and C-2 increases, and the end structure is severely damaged (as shown in Figure 21). Eventually, the two ends begin to arch vertically while remaining embedded in each other, leading to a significant increase in the relative vertical displacement between the wheel and the rail. If the impact energy is high enough, this damage process will occur similarly between the rear carriages.
(4): Overturning/Lateral Buckling: After the train speed drops to zero, the cars that were vertically arched fall back, while those that have shifted laterally or are angled relative to the track are unable to return to the track surface. This results in lateral buckling of the train and eventual overturning of the carriages.

When the train impacts a rigid wall at the front or front-side, the maximum relative vertical displacement (i.e., the vertical arch amplitude) between the wheel and rail increases with speed. When the speed exceeds 36 km/h, the height of the wheelset lifting off the ground due to this response exceeds 1 m. This results in significant impact and overturning as the carriages fall back.

In the simulation, the addition of an anti-climbing device between C-1 and C-2 significantly reduced end damage and the climbing phenomenon, with the vertical arch amplitude dropping to 0.1 m. Therefore, the primary causes of the climbing phenomenon and the subsequent severe vertical arching are the serious plastic deformation at the carriages’ end and the asynchronous pitching and yawing behavior between adjacent carriages. Zhou et al. [17] used a combined multi-body dynamics and finite element analysis to study car-climbing behavior during train collision, also noting the impact of asynchronous pitching and height differences at the carriages’ ends on the climbing behavior.

6.2.2. Large Lateral Movement of the Train Front

When the impact direction is not perpendicular to the rigid wall, the train may deviate from the track due to the significant lateral movement of the front of the train. This results in the train slipping out of the impact zone and continuing to move with residual velocity, almost without any track constraint. The process and causes of the front movement can be analyzed as follows:

(1): Under these conditions, the buffer device at the front of the train cannot function normally, so the aluminum alloy frame at the front, which bears the impact and dissipates energy, becomes the primary component in this process. The impact point is subjected to both longitudinal force (F_x) and lateral force (F_z). The force exerted on the car body is transmitted to the axle through the bogie suspension system, leading to an increase in the wheel–rail contact force.
(2): Oblique Impact and Nodding Movement: During an oblique impact, the front of the car, subjected to greater lateral forces, shifts along the inclined direction of the obstacle, accompanied by pitching. The axle of Wheelset-1 rotates slightly along the longitudinal axis at the point where the right wheel contacts the track, as shown in Figure 22. At 0.11 s, the left wheel is lifted more than 22 mm ahead of the right wheel, causing the carriage to overturn, although the right wheel remains on the track. At this point, the wheelset loses the track’s constraint on the left side. Figure 22 illustrates the derailing process for an impact angle of 15° and an impact speed of 36 km/h. The time history curve of the impact force on the lower edge of Wheelset-1 prior to derailing is shown in Figure 23, with the force direction indicated in Figure 22. After 0.13 s of lateral impact, Wheelset-1 completely jumps off the rail, initiating a rail-jumping event [40].
(3): Post-Derailment Behavior: Once Wheelset-1 is derailed, the front of the wheelset, no longer constrained by the track, slides forward along the inclined direction of the obstacle. As the lateral movement increases, C-1, tilted relative to the ground, becomes more prone to overturning.

In the process of the train front sliding along the inclined direction of the obstacle, the rear carriage also moves sideways and flips at different angles because of the connection of the coupler buffer devices. If carriage C-1 is not completely overturned, the train will continue to move at a certain speed, accompanied by the continuous derails of the rear carriage wheelset, which is also easy to cause overturning. If C-1 is completely overturned, there will be multiple collisions between carriages.

6.2.3. Lateral Buckling

The lateral buckling is most obvious in the front-side collision with a rigid wall. Taking the impact speed of 36 km/h as an example, the displacement time history curve (vertical and lateral) of the front middle position of the first carriage and the lateral contact force time history curve between Wheelset-1 (i.e., the first Wheelset) and the track are extracted under each working condition, as shown in Figure 24, Figure 25 and Figure 26.

Based on the simulation results, under the front-side impact conditions of C1, C2, and C3, the front wheelset of the first carriage left the track at approximately 0.1 s. The displacement history curve illustrates the amplitude of the pitching and yawing motions of the first carriage across the four conditions. In the frontal impact condition C0, prior to 0.1 s, there is almost no noticeable head shaking. However, under the other conditions, the first car experiences varying degrees of lateral and vertical displacement. Under the combined effects of nodding and shaking motions, the front end of the carriage exhibits a downward-slanting movement trend. The impact force is transmitted from the car body to the axle through the suspension system, as shown in Figure 26, where the wheel experiences a lateral force from the track. As a result, Wheelset-1 at the front of the first carriage jumps off the track. When the lateral movement of the obstacles is consistent, but the collision speed differs, as depicted in Figure 27, it can be observed that before the wheelset derails, an increase in speed leads to a rise in both the amplitude and frequency of the nodding motion. Consequently, the risk of train derailment increases with higher speeds.

Once the wheelset derails, it loses track constraint. As shown in Figure 28, the front of the carriage becomes prone to rotating around the Y-axis, which is perpendicular to the rail surface at the impact point. Consequently, C-1 and the rigid wall cannot remain perpendicular. As the rear carriage continues to impact, the front end of C-1 rotates around the Y-axis at an increasing angle, while the rear end of C-1 moves laterally, and the front end of C-2 also shifts laterally as the derailment progresses. As illustrated in Figure 29, the lateral displacement time curve for each wheelset shows the largest movement occurs during the collision between the first and second carriages, followed by the collision position between the second and third carriages. The displacement of Wheelset-1 exhibits the greatest transverse displacement in the opposite direction.

When the train impact speed is less than or equal to 36 km/h, the greater the impact speed, the larger the lateral displacement at the bending point. Zhao [41] investigated the main causes of train lateral buckling behavior through dynamic modeling analysis and found that the initial yawing motion of the vehicle connection structure has a direct impact on the lateral motion of the vehicle during the collision process. When train wheelsets run along the track, their lateral degree of freedom generates a periodic lateral oscillation known as “snake motion”. As the operating speed increases, the lateral stability decreases [42], leading to an increase in the amplitude of lateral oscillation, which in turn increases the yawing motion of the vehicle. This results in a greater difference in lateral displacement at the ends of the vehicle during the collision.

When the train impact speed reaches 45 km/h with a rigid wall, the maximum wheel–rail relative lateral displacement (i.e., lateral buckling amplitude) caused by the front-side impact decreases, but the vertical arch amplitude increases significantly. The reason is that when the impact speed between carriages is large, the plastic deformation of the carriages ends and the overlap/riding caused by climbing are more serious, resulting aggravation of vertical arch response attitude. This can be improved or avoided by adding or optimizing the anti-climbing device between the carriages.

7. Conclusions

This paper explores the response postures of subway trains under various collision scenarios. By establishing a finite element model of a six-car elastic-plastic subway train and a one-dimensional multi-body dynamics theoretical model, the energy absorption characteristics and collision response postures of the subway train were studied. Multiple accident modes were observed in the finite element simulations, among which:

(1): A one-dimensional theoretical model is proposed, in which the train car is regarded as a deformable body divided into three mass points, representing the front collision end, the middle passenger area, and the rear collision end, respectively. These mass points are connected by two springs to simulate the deformation of the train car. When the longitudinal collision speed is less than or equal to 25 km/h, the total energy absorption error of the theoretical model compared with the simulation results is less than 6.53%, and the velocity curve matches well. The coupler is simplified as a nonlinear spring, and the definition of stiffness in the force rise phase is particularly important for the accuracy of the velocity attenuation curve.
(2): Except for oblique collisions, when the train collision speed exceeds 25 km/h, direct collisions between the ends of the carriages are unavoidable. At this point, the out-of-sync pitch and yaw motions, along with the plastic deformation at the ends, aggravate the vertical arch phenomenon of the train, which is extremely detrimental to the safety of passengers inside the train. A front-side impact can easily lead to lateral buckling, and as the collision speed increases, the degree of lateral buckling becomes more severe. However, when the collision speed reaches 45 km/h, the degree of lateral buckling decreases by a certain percentage, and the vertical arch increases, becoming the dominant response posture. In the simulation, the addition of anti-climbing devices between the carriages significantly reduced the maximum vertical displacement of the wheels.
(3): In the case of an oblique collision, the lateral impact force causes the train’s front to laterally shift and slide, which is the fundamental cause of rapid derailment of the front wheels. When the collision angle exceeds 10°, the energy absorption efficiency of the coupler device can be reduced by up to 83.9%, and the train’s front frame experiences direct impact, leading to rapid derailment. The post-impact behavior is extremely dangerous. For such scenarios, it is necessary to consider adding anti-derailment devices or installing lateral energy absorption devices on the wheels.
(4): For train collisions at a switch, in the case of an angled head-on collision (25 km/h), the train fronts misalign and quickly derail. The energy-absorbing structures fail to operate as intended, and the moving train continues to derail and slide with a relatively high residual speed. More complex collision scenarios at switches require further study.

For the various dangerous postures after a train derailment, such as vertical arch, lateral buckling, and overturning, it is necessary not only to take measures to prevent derailment from occurring, but also to implement protective measures to reduce the threat posed by the train’s continued movement to the passengers inside—for example, optimizing the carriage stiffness to ensure survival and escape space for passengers.

The failure of the weak bolt points in the train’s front frame (which commonly occurs under conditions where the train impacts a rigid wall at 45 km/h) has minimal impact on the overall energy absorption of the train and its different parts, but it does pose a certain threat to the driver’s survival space. This issue is not clearly addressed in the standards of various countries, and reinforcement measures need further in-depth research.

Regarding subway train collision accidents, in most real-life cases, emergency braking is applied before a collision occurs. At this point, some longitudinal force transmission between the carriages has already taken place. Including this factor in the simulation can make it more representative of real-world collision conditions and facilitate a detailed analysis of actual cases. The application of the corresponding model [43] requires further research.

Author Contributions

Conceptualization, R.L. and R.Z.; Methodology, R.L. and R.Z.; Software, Y.Y. and Y.L.; Validation, R.Z.; Formal analysis, Y.Y. and Y.L.; Resources, S.L.; Writing—original draft, Y.Y.; Writing—review & editing, R.Z.; Supervision, S.L., R.L. and R.Z.; Project administration, S.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Key Research and Development Program of China (grant number 2023YFC3805605) and Heilongjiang Natural Science Foundation (grant number LH2022E069).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Dataset available on request from the authors.

Acknowledgments

During the preparation of this manuscript/study, the author(s) used GPT-4.0 for the purposes of grammar optimization. The authors have reviewed and edited the output and take full responsibility for the content of this publication.

Conflicts of Interest

The authors declare no conflict of interest.

References

Sutton, A. The development of rail vehicle crashworthiness. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 2002, 216, 97–108. [Google Scholar] [CrossRef]
Evans, A.W. Fatal train accidents on Europe’s railways: 1980–2009. Accid. Anal. Prev. 2011, 43, 391–401. [Google Scholar] [CrossRef]
Beijing Municipal Government Accident Investigation Team. Investigation Report on “12·14” Train Rear-End Collision on Changping Line of Beijing Metro. Available online: https://yjglj.beijing.gov.cn/art/2024/2/5/art_7466_656.html (accessed on 5 February 2024).
CCTV. Accident on Test Line 10 Under Construction in Xi’an Metro. Available online: https://news.cctv.com/2024/04/21/ARTI6QaRqwDHMFvVPPzCKU30240421.shtml (accessed on 21 April 2024).
CCTV. One Person was Killed and Three Injured in a Train Accident on Chongqing’s Circular Line. Available online: https://news.cctv.com/2019/01/09/VIDEwNHZVNMUJ66i0w2AsQrj190109.shtml (accessed on 9 January 2019).
Scholes, A.; Lewis, J.H. Development of crashworthiness for railway vehicle structures. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 1993, 207, 1–16. [Google Scholar] [CrossRef]
Syaifudin, A.; Windharto, A.; Setiawan, A.; Farid, A.R. Energy Absorption Analysis on Crash-Module Shape and Configuration of Medium-Speed Train; Recent Advances in Renewable Energy Systems: Select Proceedings of ICOME 2021; Springer Nature: Singapore, 2022; pp. 171–179. [Google Scholar]
Dias, J.P.; Pereira, M.S. Optimization methods for crashworthiness design using multibody models. Comput. Struct. 2004, 82, 1371–1380. [Google Scholar] [CrossRef]
Wang, W.; Kang, K.; Zhao, H. Joint simulation of crashworthy train set based on finite element and multi-body dynamic. J. Tongji Univ. Nat. Sci. 2011, 39, 1552–1556. [Google Scholar]
Tang, Z.; Zhu, Y.; Nie, Y. Data-driven train set crash dynamics simulation. Int. J. Veh. Mech. Mobil. 2016, 55, 1–18. [Google Scholar] [CrossRef]
Tang, Z.; Liu, F.J. Evaluation of coupled finite element meshfree method for a robust full-scale crashworthiness simulation of railway vehicles. Adv. Mech. Eng. 2016, 8, 1–13. [Google Scholar] [CrossRef]
Xie, S.; Du, X.; Zhou, H.; Wang, D.; Feng, Z. Analysis of the crashworthiness design and collision dynamics of a subway train. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 2020, 234, 1117–1128. [Google Scholar]
Zhao, G. Research on Front Collision and Rollover Collision of Metro Vehicle; Dalian Jiaotong University: Dalian, China, 2019. [Google Scholar]
Wei, L.; Zhang, L.; Xin, T.; Cui, K. Crashworthiness study of a subway vehicle collision accident based on finite-element methods. Int. J. Crashworthiness 2019, 26, 159–170. [Google Scholar] [CrossRef]
Liu, H.; Wang, J.; Liu, X.; Wang, K.; Luo, Q.; Liu, Y.; Fang, Z.; Hong, H. Design and analysis of elastic-plastic collision post for railway vehicles. ASME/IEEE Jt. Rail Conf. Am. Soc. Mech. Eng. 2020, 83587, V001T12A002. [Google Scholar]
Zhou, H.; Xu, S.; Zhan, J.; Zhang, J. The design of crashworthy subway vehicle and crash research of whole car-body. J. Railw. Sci. Eng. 2008, 5, 65–70. [Google Scholar]
Hechao, Z.; Shizhou, X.; Jun, Z.; Zhang, J. Research on the overriding phenomenon during train collision based on FEM and MBS joint simulation. J. Mech. Eng. 2017, 53, 166–171. [Google Scholar]
Zhao, H.; Xu, P.; Jiang, S.; Li, B.; Yao, S.; Xing, J.; Huang, Q.; Xu, K. A novel design method of the impact zone of a high-speed train. Int. J. Crashworthiness 2022, 27, 476–485. [Google Scholar] [CrossRef]
Wang, C.; Zhou, X.; Liu, L.; Liu, K.; Jing, L. Derailment behavior and mechanism of a train under frontal oblique collisions. J. Railw. Sci. Eng. 2023, 20, 1821–1832. [Google Scholar]
Xu, J.; Wu, Q.; Wang, H.; Xiao, S.; Wang, S. Effects of Crash Dynamic Parameters of Urban Rail Transit Train on Climbing Behavior. Urban Mass Transit 2024, 27, 74–80. [Google Scholar]
Wang, R. Study on Rigid-Flexible Coupling Dynamic Modeling and Longitudinal Dynamic Behavior of Railway Flat Car in Collision Process; Shijiazhuang Tiedao University: Shijiazhuang, China, 2023. [Google Scholar]
Zhu, T.; Xiao, S.; Hu, G.; Yang, G.-W.; Yang, C. Crashworthiness analysis of the structure of metro vehicles constructed from typical materials and the lumped parameter model of frontal impact. Transport 2019, 34, 75–88. [Google Scholar] [CrossRef]
Zhang, J.; Zhu, T.; Yang, B.; Wang, X.; Xiao, S.N.; Guangwu, Y.; Liu, Y.; Che, Q. A rigid–flexible coupling finite element model of coupler for analyzing train instability behavior during collision. Railw. Eng. Sci. 2023, 31, 325–339. [Google Scholar] [CrossRef]
Jing, L.; Liu, K.; Wang, C. Recentadvances in the collision passive safety of trains andimpact biological damage of drivers and passengers. Explos. Shock. Waves 2021, 41, 121405-1–121405-33. [Google Scholar]
Hou, L.; Yong, P.; Dong, S. Dynamic analysis of railway vehicle derailment mechanism in train-to-train collision accidents. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 2021, 235, 1022–1034. [Google Scholar] [CrossRef]
Han, H.-S.; Koo, J.-S. Simulation of Train Crashes in Three Dimensions. Veh. Syst. Dyn. Int. J. Veh. Mech. Mobil. 2003, 40, 435–450. [Google Scholar] [CrossRef]
Ling, L.; Dhanasekar, M. Assessment of road-rail crossing collision derailments on curved tracks. Aust. J. Struct. Eng. 2017, 18, 125–134. [Google Scholar] [CrossRef]
Yao, S.; Yan, K.; Lu, S.; Xu, P. Energy-absorption optimisation of locomotives and scaled equivalent model validation. Int. J. Crashworthiness 2017, 22, 441–452. [Google Scholar] [CrossRef]
Lyu, R.; Lei, C.; Zhu, T.; Xiao, S.N.; Yang, G.W.; Yang, B. Simulation Analysis of Single-vehicle-level Initial Operating States on Metro Train Collision Responses. Urban Mass Transit 2022, 25, 113–119. [Google Scholar]
BS EN 15227-2020; Railway Applications: Crashworthiness Requirements for Railway Vehicles. Technical Committee CEN/TC 256 Railway Applications, British Standard Institution: London, UK, 2020.
GM/RT2100; Structural Requirements for Railway Vehicles. Rail Safety and Standards Board: London, UK, 2010.
UIC (Union Internationale des Chemins de fer). UIC 660: Measures to Ensure the Technical Compatibility of High-Speed Trains; UIC: Paris, France, 2002. [Google Scholar]
ASME RT-2-2014; Safety Standard for Structural Reauirements for Heavy Rail. Transit Vehicles; The American Society of Mechanical Engineers: New York, NY, USA, 2014.
Federal Railroad Administration. 49 CFR Parts 229 Railroad Locomotive Safety Standards. Fed. Regist. 2006, 71, 229.1–229.319. [Google Scholar]
GOST 32410-2013; Emergency Crash-Systems Railway Rolling Stock for Passenger Transportations. Technical Requirements and Methods of Control. Rosstandart: Moscow, Russian, 2014; p. 11. Available online: https://runorm.com/catalog/125/877213/ (accessed on 15 June 2016).
GB_50157-2013; Code for Design of Metro. National standard of the People ’s Republic of China, China Construction Industry Press: Beijing, China, 2013.
Briassoulis, D. Equivalent orthotropic Properties of Corrugated Sheets. Comput. Struct. 1986, 23, 129–139. [Google Scholar] [CrossRef]
Lu, R. Impact Characteristics of Metro Train Couplers and Draft Gears and Its Effects on Derailment Behavio; Southwest Jiaotong University: Chengdu, China, 2021. [Google Scholar]
Yao, S.; Zhu, H.; Yan, K. The derailment behaviour and mechanism of a subway train under frontal oblique collisions. Int. J. Crashworthiness 2021, 26, 133–146. [Google Scholar] [CrossRef]
Shi, H.; Luo, R.; Zeng, J. Review on domestic and foreign dynamics evaluation criteria of high-speed train. J. Traffic Transp. Eng. 2021, 21, 36–58. [Google Scholar]
Zhao, H. A Plastic Hinge Dynamics Modeling and Collision Behavior Response Research of High-Speed Train; Central South University: Changsha, China, 2023. [Google Scholar]
Sun, L.; Yao, J. Hunting derailment safety evaluation method of high speed railway vehicle. China Railw. Sci. 2013, 3, 82–91. [Google Scholar]
Pugi, L.; Rindi, A.; Ercole, A.G.; Palazzolo, A.; Auciello, J.; Fioravanti, D.; Ignesti, M. Preliminary studies concerning the application of different braking arrangements on Italian freight trains. Veh. Syst. Dyn. 2011, 49, 1339–1365. [Google Scholar] [CrossRef]

Figure 1. Carriage model.

Figure 2. Bogie simplified model.

Figure 3. Hollow aluminum alloy simplified model.

Figure 4. Train head and coupler model. (a) Weak points on leading car. (b) Moment–rotation curve of joint between the front chassis and cab frame. (c) Swing angle in the horizontal plane, and rotating angle in the vertical plane of coupler. (d) Force–displacement curve of coupler buffer device.

Figure 5. Total internal energy time history curve.

Figure 6. Simplified diagram of train collision.

Figure 7. Simplified force–displacement curve of coupler buffer devices.

Figure 8. Force situation of a single carriage.

Figure 9. Velocity history curves in head-on collision.

Figure 10. Energy absorption history curves of major coupler buffer devices in head-on collision conditions.

Figure 11. Carriages and couplers number.

Figure 12. Energy absorption of subway train under different velocity. The blue rectangular prism represents the moving train, the red cylinder represents the stationary train, the blue circle represents the derailment of a carriage of the moving train, and the red triangle represents the derailment of a carriage of the stationary train. The aluminum alloy front frame is numbered as 0.

Figure 13. Energy absorption history curves of coupler buffer device in 25 km/h head-on collision condition.

Figure 14. Maximum vertical displacement of wheelsets.

Figure 15. Ordered energy absorption characteristic before second impact. The dash lines correspond to the time points t₁ to t₃ mentioned in the described ordered energy absorption.

Figure 16. Energy absorption history curves of carriage in 45 km/h collision with obstacle.

Figure 17. Vertical displacement history curves of wheelset in 45 km/h collision with obstacles.

Figure 18. Energy absorption in front oblique collision.

Figure 19. Front-side collision conditions.

Figure 20. Wheelset displacement under different front-side collisions.

Figure 21. Overriding phenomenon and vertical arch.

Figure 22. Derailment and large lateral movement of the train front in oblique collision.

Figure 23. Lateral and vertical impact force on wheelset.

Figure 24. Lateral displacement history curves of leading car.

Figure 25. Vertical displacement history curves of leading car.

Figure 26. Lateral impact force on the first wheelset.

Figure 27. Vertical displacement history curves of leading car at different impact velocity. (a) Vertical displacement history curves of leading car under C1 condition. (b) Vertical displacement history curves of leading car under C3 condition.

Figure 28. Lateral buckling under front side collision.

Figure 29. Lateral displacement history curves of wheelset under C1 condition.

Table 1. The main parameters of the subway vehicle.

	Parameter	Value
AL6005A-T6 Johnson–Cook model	Yield strength/(MPa)	260
	Elasticity modulus/(MPa)	70,000
	Density/(kg/m³)	2700
	Poisson ratio	0.3
	A	251.38
	B	175.32
	n	0.56
	C	0.00371
Vehicle model	Train mass/t	166
	Bogie mass/t	6.68
	Coupler height/mm	980
	Center of gravity height/mm	1500
Suspension system	Primary vertical spring coefficient/(N/mm)	2000
	Primary lateral spring coefficient/(N/mm)	4000
	Primary longitudinal spring coefficient/(N/mm)	30,000
	Secondary vertical spring coefficient/(N/mm)	660
	Secondary lateral spring coefficient/(N/mm)	360
	Secondary longitudinal spring coefficient/(N/mm)	360

Table 2. Parameter analysis conditions and collision response postures.

	Working Condition	Impact Velocity/(km/h)	Impact Angle/(°)	Impact Position	Response Postures
	Working Condition	Impact Velocity/(km/h)	Impact Angle/(°)	Impact Position	Carriage-1	Carriage-2	Carriage-3
Collision with a rigid wall	TR-V25-A0-Z	25	0	Frontal collision	Rear wheel derailment	Derailment	Derailment
	TR-V25-A0-C1			Front–side collision C1	Lateral buckling
	TR-V25-A0-C2			Front–side collision C2	Lateral buckling
	TR-V25-A0-C3			Front-side collision C3	Lateral buckling
	TR-V25-A5		5	/	Lateral buckling
	TR-V25-A10		10	/	LLMF	Lateral buckling
	TR-V25-A15		15	/	LLMF, Carriage overturn	Lateral buckling
	TR-V25-A20		20		LLMF, Carriage overturn	Carriage overturn	Derailment
	TR-V25-A30		30	/	LLMF, Carriage overturn	Lateral buckling
	TR-V25-A45		45	/	LLMF, Carriage overturn	Carriage overturn	Derailment
	TR-V25-A45		45	/	LLMF, Carriage overturn	Lateral buckling
	TR-V36-A0-Z	36	0	Frontal collision	Rear wheel derailment	Derailment	Derailment
	TR-V36-A0-C1			Front-side collision C1	Derailment	Carriage overturn	Derailment
	TR-V36-A0-C1			Front-side collision C1	Lateral buckling
	TR-V36-A0-C2			Front-side collision C2	Derailment	Carriage overturn	Carriage overturn
	TR-V36-A0-C2			Front-side collision C2	Lateral buckling
	TR-V36-A0-C3			Front-side collision C3	Carriage overturn	Carriage overturn	Derailment
	TR-V36-A0-C3			Front-side collision C3	Lateral buckling
	TR-V36-A5		5	/	LLMF	Carriage overturn	Derailment
	TR-V36-A10		10	/	LLMF, Carriage overturn	Derailment	Derailment
	TR-V36-A15		15	/	LLMF	Carriage overturn	Carriage overturn
	TR-V36-A20		20		LLMF, Carriage overturn	Carriage overturn	Carriage overturn
	TR-V36-A30		30	/	LLMF, Carriage overturn	Derailment	Carriage overturn
	TR-V36-A30		30	/	LLMF, Carriage overturn	Lateral buckling
	TR-V36-A45		45	/	LLMF, Carriage overturn	Carriage overturn	Carriage overturn
	TR-V36-A45		45	/	LLMF, Carriage overturn	Lateral buckling
	TR-V45-A0-Z	45	0	Frontal collision	Carriage overturn	Carriage overturn	Carriage overturn
	TR-V45-A0-C1			Front-side collision C1	Lateral buckling
	TR-V45-A0-C2			Front-side collision C2	Derailment	Carriage overturn	Derailment
	TR-V45-A0-C2			Front-side collision C2	Lateral buckling
	TR-V45-A0-C3			Front-side collision C3	Derailment	Carriage overturn	Derailment
	TR-V45-A0-C3			Front-side collision C3	Lateral buckling
	TR-V45-A5		5	/	LLMF	Lateral buckling, Carriage overturn
	TR-V45-A10		10	/	LLMF	Lateral buckling, Carriage overturn
	TR-V45-A15		15	/	LLMF, Carriage overturn	Lateral buckling, Carriage overturn
	TR-V45-A20		20		LLMF, Carriage overturn	Lateral buckling, Carriage overturn
	TR-V45-A30		30	/	LLMF, Carriage overturn	Lateral buckling, Carriage overturn
	TR-V45-A45		45	/	LLMF, Carriage overturn	Lateral buckling, Carriage overturn
Train-train collision	TT-V25-A0-Z	25	0	Frontal collision	/	/	/
	TT-V25-A5		5	/	/	/	/
	TT-V25-A10		10	/	/	/	/
	TT-V25-A15		15	/	/	D Temporary derailment	/
	TT-V25-A30		30	/	/	D Derailment	D Temporary derailment
	TT-V36-A0-Z	36	0	Frontal collision		S Temporary derailment	S Temporary derailment
	TT-V45-A0-Z	45	0	Frontal collision	S, D Temporary derailment	/	/

Table 3. Energy absorption per unit length of Carriage-2 in different parts at 36 km/h (kJ/m).

	Front End	Middle Passenger Area	Rear End
C0	89.88	13.29	62.94
C1	97.53	8.05	112.38
C2	113.88	8.55	71.59
C3	154.82	10.99	100.71

Table 4. Response postures and corresponding conditions.

Response Attitude	Conditions
Frontal impact	Train-train collision (Speed ≤ 45 km/h) Frontal collision with a rigid wall (Speed ≤ 25 km/h) Accompanied by temporary derailment
Climbing	Collision with a rigid wall (Speed > 25 km/h) Accompanied by severe derailment
Vertical arch	Collision with a rigid wall (Speed > 25 km/h) Accompanied by severe derailment
large lateral movement of the train fron	Angled collision with a rigid wall (Angle > 5°) Accompanied by severe derailment
Lateral buckling	Angled collision and front-side collision with a rigid wall
Carriage overturn	Oblique and front-side collision with rigid wall Frontal collision with a rigid wall at 45 km/h Accompanied by severe derailment

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Liu, S.; Yu, Y.; Li, Y.; Liu, R.; Zhang, R. Research on Response Postures of Subway Train in Straight Line Collision. Appl. Sci. 2025, 15, 252. https://doi.org/10.3390/app15010252

AMA Style

Liu S, Yu Y, Li Y, Liu R, Zhang R. Research on Response Postures of Subway Train in Straight Line Collision. Applied Sciences. 2025; 15(1):252. https://doi.org/10.3390/app15010252

Chicago/Turabian Style

Liu, Shuhao, Yiqun Yu, Yi Li, Rongqiang Liu, and Rong Zhang. 2025. "Research on Response Postures of Subway Train in Straight Line Collision" Applied Sciences 15, no. 1: 252. https://doi.org/10.3390/app15010252

APA Style

Liu, S., Yu, Y., Li, Y., Liu, R., & Zhang, R. (2025). Research on Response Postures of Subway Train in Straight Line Collision. Applied Sciences, 15(1), 252. https://doi.org/10.3390/app15010252

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu