A Novel Simplified FE Rail Vehicle Model in Longitudinal and Lateral Collisions

Abstract

It is a challenge to efficiently and accurately predict train dynamic responses during complex collisions. In this paper, a novel numerical simplification method for high-speed rail vehicles during complex impact configurations is proposed. The central section of high-speed rail vehicles is a sandwich corrugated hollow double-shell structure. Starting with a baseline detailed finite element (FE) model of a high-speed train, the central section was first simplified as a solid single-shell structure. A parametric study with various simplification thickness ratios of the simplified FE rail vehicle model in different longitudinal rigid-wall collisions and lateral rigid-cylinder impacts was then performed using LS-DYNA. Furthermore, a correlation and analysis (CORA) objective rating method was used to evaluate the related responses between the simplified and detailed baseline FE rail vehicle models. The results demonstrate that the simplified FE model could effectively predict the rail vehicle impact responses. The displacement and impact force time histories of the simplified vehicle model with a thickness ratio of 0.38 matched closely with the results of the baseline detailed FE model under both longitudinal and lateral impacts (total combined CORA rating score: 93%). The rail vehicle impact deformations of the simplified vehicle model were similar to those of the baseline detailed model. The application of the simplified vehicle FE model substantially reduced the computational time (approximately 55% reduction). This work provides a solid basis for efficiently exploring train impact responses in complex collisions, and will be especially useful for train occupant injury assessment.

1. Introduction

Safety is a fundamental and essential topic in railway transportation, especially for high-speed trains. Train safety performance has been improved by integrating active and passive safety technologies. However, train collisions and derailments continue to occur, resulting in passenger casualties. To protect passengers in complex train collisions, rail vehicle crashworthiness performance [1,2,3] and occupant impact injury responses have been studied [4,5,6].

Rail vehicle impact experiments are a valuable approach to improving train crashworthiness [7,8,9,10]. However, the cost of these experiments is too high to carry out parametric studies, and numerical simulation is therefore an important tool to study train collision dynamics [11,12]. However, as trains consist of multiple vehicles, the model complexity and computational time need to be considered. Multi-body (MB) and finite element (FE) methods with some simplifications are usually employed. Han et al. [13] explored train impact responses with longitudinal and oblique rigid walls by establishing a twenty-vehicle coupled train MB dynamic model, consisting of a three-dimensional MB model for the first five vehicles and a lumped mass model for the remainder. Cole et al. [14] investigated the effect of wagon number, force–displacement characteristics of the energy-absorbing devices and crash speeds on locomotive collision dynamics using a MB train model.

A detailed FE train model is too computationally expensive, even on a high-performance computer (e.g., it takes >100 h to simulate a 1000 ms collision of two four-vehicle marshalling trains on a typical high-performance workstation). Hence, simplification methods for FE simulations of train collisions have been extensively reported [15,16,17], and a simplified train FE modelling method for train longitudinal crash simulations was proposed in the rail vehicle crashworthiness standard EN 15227 [15]. This standard stipulates that only the first one/two rail vehicles be modelled in detail, with the remaining vehicles represented as lumped mass/spring systems. Yao et al. [16] established a four-vehicle coupled subway train FE model, consisting of the detailed head car FE model and rigid models of the remaining three vehicles to investigate subway derailment in longitudinal oblique collisions. Afazov et al. [17] established a one-dimensional beam element FE model to study train collisions at the concept design stage. Lu et al. [18,19] developed a 1/8th-scale FE model for high-speed trains based on a force/stiffness equivalence and performed multi-objective optimization of the energy absorption components in a longitudinal crash for a moving eight-vehicle coupled 1/8th-scale train. The deformation of the rail vehicle was analyzed. The impact forces and the compressions between the original FE model and the scaled FE model were compared. To study the longitudinal crash responses of multiple-train collisions, Xie et al. [20] established a simplified FE rail vehicle model using mass and beam elements to represent the middle sections of the train. The validity of the simplified FE model was verified by comparing the impact forces between the simplified model and the detailed model.

The above-mentioned studies provide essential insights into train longitudinal impact dynamics using simplified MB and FE simulations. However, due to the coupling effect of multiple-vehicle crashes and the great impact energy involved, train collisions and train post-derailment collisions (i.e., derailment-induced collisions) usually include both a longitudinal collision and a lateral collision (e.g., a vehicle striking the side of another vehicle, vehicles striking the ground and surrounding structures/infrastructure), as shown in Figure 1. Lateral impacts have high potential for serious injury/death, especially because passengers are not restrained. However, the aforementioned studies have not addressed rail vehicle lateral collisions and the previous simplification methods are not directly applicable to lateral impacts.

This work presents the development and objective assessment of an effective numerical simplification method for rail vehicles that can be applied to both longitudinal and lateral impacts. A detailed FE model of a single vehicle of a high-speed train was used as a baseline model in this study. Simplifications of the central section of the rail vehicle were implemented and a parametric study was carried out using LS-DYNA. The impact responses of the simplified and detailed FE rail vehicle models were compared for both lateral and longitudinal collisions using an objective rating method. This research provides a basis for modelling complex train collisions that include both longitudinal and lateral impacts (e.g., the train colliding with surrounding buildings after derailment).

2. Materials and Methods

2.1. FE Baseline Detailed Model of Rail Vehicle

High-speed trains generally have a sandwich corrugated hollow double-shell structure; see Figure 2. The detailed vehicle model used as a baseline in this paper is a Chinese high-speed train, for which the head car was modelled using the same method and verified for impact force and displacement against impact experiments [21].

The body was modelled using 2D shell elements because the length of the plate girder structures (e.g., the roof, the sidewall, and the floor) is much larger than the thickness. The shell model was generally from the middle layer of the vehicle plate structure (Figure 2), and the actual thickness of different plates and shells was defined. Before discretizing the vehicle model, a geometry edit was carried out and the components (e.g., air conditioners, pantographs) with minimal structural influence were replaced with lumped mass/1D rigid components. In the baseline FE model, to capture the structural characteristics of the rail vehicle body, the large deformation areas at both ends of the car body were discretized into a maximum mesh size of 40 mm, while the corresponding regions of the middle part were discretized into a maximum mesh size of 70 mm. Symmetric meshing was employed to ensure structural symmetry. Local areas required finer manual meshing after initial automatic meshing. The maximum element length was 25 mm for the end wall and rounded corners [22]. The aspect ratio and Jacobian for the 2D shell elements were always less than 5 and greater than 0.7, respectively. Mesh convergence analysis of 10 m/s rail vehicle rigid-wall impacts for the detailed model shows that the mesh size of 40 mm can basically guarantee the calculation accuracy (Figure 3). The number of elements and nodes in this baseline detailed FE vehicle model were 508,465 and 415,228, respectively.

Different aluminum alloy materials were used for different structures according to their specific conditions. For example, the material 6082-T6 [23] was mainly used in the vehicle’s load-bearing members, while the 6005A aluminum alloy [24] was used in the profile structures of the floor, sidewall and roof.

Table 1. Material mechanical parameters for the high-speed rail vehicle.

Aluminum Alloy	Density (kg/m3)	Poisson’s Ratio	Young’s Modulus (GPa)	Yield Stress (MPa)	Ultimate Strength (MPa)	Tangent Modulus (MPa)
6082-T6	2700	0.3	71	260	310	250
6005A	2700	0.3	71	215	255	200

shows the aluminum alloy material mechanical properties. The strain rate effect of the aluminum alloy materials was not obvious and the influence of the strengthening of strain rate on the bearing capacity of the rail vehicle body was not obvious [23,25]. Thus, the strain rate effect of the rail vehicle body was not considered in this paper.

For high-speed rail vehicle bogies, the primary suspension consists of the vertical damper and the steel spring, while the secondary suspension is comprised of the air spring and the lateral/vertical damper. The bogies also include lateral stoppers, anti-rolling bars, anti-hunting dampers, z-shape traction rods and axle box joint positioning. A general nonlinear 6DOF discrete beam material model (*MAT_119) was mainly used to express the vehicle suspension parameters and to simulate the three-dimensional linear and torsional stiffness [22]. All vehicle parameters were supplied by the manufacturer of high-speed trains, CRRC. The connection between the bogie and the vehicle body was modelled using the “*CONSTRAINED_EXTRA_NODES” connection algorithm. The wheelsets, axle boxes and frame were modelled as rigid bodies using the material model of *MAT_RIGID [16].

2.2. FE Simplified Model of Rail Vehicle

According to the structural characteristics of high-speed rail vehicles, only the middle section of the original rail vehicle with the thicker corrugated hollow double-shell was simplified to the thinner solid single-shell structures (but still modelled as 2D shell elements), as shown in Figure 2 and Figure 4. Both ends of the vehicle body (i.e., equipment zones) were still the original corrugated hollow double-shell structures. To ensure the normal propagation of impact force, at the interface between the original detailed structure and the simplified structure, the free-ends of the original detailed structures and the simplified structures were connected by 1D rigid elements (Figure 4). The constitutive model and parameters used in the simplified structures were the same as the baseline FE model. The bogies were also unchanged. However, the thickness of the simplified structure was less than that of the original detailed structure. Because the car body was a corrugated hollow double-shell structure, even if the thickness of different parts (e.g., the sidewall, the roof, and the floor) was different, a thickness ratio (α) was defined, which was the ratio of the simplified structure’s thickness to the thickness of the detailed structure (Figure 2). A parametric study was then performed to investigate the effect of thickness ratio on impact responses. The total mass, center of gravity position and mass moment of inertia of the simplified model were made consistent with the baseline model using distributed 0D mass elements. Overall, the number of elements and nodes in the simplified FE vehicle model were 312,807 and 282,426, respectively, corresponding to 62% and 68% of those in the baseline detailed model, respectively.

2.3. Longitudinal and Lateral Collision Simulations

To compare high-speed rail vehicle dynamic responses between the baseline and the simplified FE model, three longitudinal and lateral collision simulations were implemented (Figure 5). For the longitudinal crashes, according to rail vehicle crashworthiness standard EN 15227 [15] and TB/T 3500-2018 [26], a collision speed of 10 m/s into a rigid barrier was selected. In addition, considering the collision between two vehicles in higher speed derailment and collision accidents, the impact velocity of 22.2 m/s into a rigid barrier was selected to represent a higher-speed crash. For the lateral collision, the crash speed of 10 m/s from rail vehicle longitudinal crashworthiness standard EN 15227 was applied in the absence of a standard for rail vehicle lateral impacts. For the lateral impact barrier, there are almost no railway level crossings in China now, especially for high-speed railways, which results in lateral train impacts often being collisions between trains and surrounding fixed buildings rather than collisions between trains and road vehicles at level crossings (Figure 1b,c). Hence, the lateral impact was with a rigid cylinder (radius 3.34 m and length 10 m).

2.4. Objective Evaluation Method

To objectively evaluate the crash response of the simplified FE rail vehicle model compared to the detailed baseline rail FE vehicle model, the CORA rating tool was used; see Figure 6. The CORA rating accounts for both the corridor and the cross-correlation methods [27,28]. The corridor method calculates the deviation between curves, while the cross-correlation method analyzes different curve characteristics such as phase shift and the signal shape. Both methods were applied as their limitations compensated each other. The phase shift, size and shape differences were implemented in the cross-correlation method. The total rating score was calculated by integrating the sub-metrics with different weighting factors, and it ranged from “0” (no correlation) to “100%” (perfect match). In this study, the weighting factors (w_i) for each sub-metric were based on ISO/TS 18571 [29]; see Figure 6. The CORA objective rating method has been widely used in vehicle passive safety [30,31].

The CORA rating score (C) was calculated using the following equations [27,28,29]:

$$C=w_1·C_1+w_2·C_2$$

(1)

$$C_2=w_{2a}·C_{2a}+w_{2b}·C_{2b}+w_{2c}·C_{2c}$$

(2)

$${{\displaystyle \sum }}^{}{w}_i=1$$

(3)

where C₁ is the corridor score; C₂ is the cross-correlation score; w₁ is the weighting factor of the corridor method; w₂ is the weighting factor of the cross-correlation method; C_2a is the phase score; C_2b is the size score; C_2c is the shape score; w_2a is the weighting factor of the phase sub-metric method; w_2b is the weighting factor of the size sub-metric method; and w_2c is the weighting factor of the shape sub-metric method.

The corridor metric assessed the compliance of a curve with corridors. The two sets of corridors, the inner and the outer corridors, were defined along the mean curve (Figure 5). If the comparison curve was within the inner corridor, the score was “100%” (perfect match). If the comparison curve was outside the outer corridor, the result was “0” (poor correlation). Otherwise, an interpolation of the rating score was performed. The total corridor score C₁ was the average of all time step scores ci, which was calculated at every time step within the evaluation interval [t_min, t_max]:

$$c_i=\{\begin{array}{c}1\\ {\left(\frac{{\delta }_0\left(t\right)-\left|y\left(t_i\right)-x\left(t_i\right)\right|}{{\delta }_0\left(t\right)-{\delta }_i\left(t\right)}\right)}^k\\ 0\end{array}\begin{array}{c},\mathrm{i}\mathrm{f} \left|y\left(t_i\right)-x\left(t_i\right)\right|<{\delta }_i\left(t\right)\\ \\ \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} k\in N>0\\ \\ ,\mathrm{i}\mathrm{f} \left|y\left(t_i\right)-x\left(t_i\right)\right|>{\delta }_i\left(t\right)\end{array}$$

(4)

$$C_1=\frac{{{\displaystyle \sum }}_{i=1}^n{C}_i}{n}, 0\le C_1\le 1$$

(5)

where ${\delta }_0\left(t\right)$ is the lower/upper bounds of the outer corridor at time t; ${\delta }_i\left(t\right)$ is the lower/upper bounds of the inner corridor at time t; $y\left(t_i\right)$ is the reference signal (i.e., the responses of the detailed FE model); $x\left(t_i\right)$ is the evaluation signal (i.e., the responses of the simplified FE model); $c_i$ is the rating score at different time; k is the exponent factor for calculating the corridor score between the inner and outer corridors; and N is all natural numbers without zero.

The cross-correlation rating was performed by moving the reference curve by multiples of the time step within the evaluation interval. For each of these time-shifts, the cross-correlation rating score was calculated. Phase shift, size and shape were calculated at the time-shift of the maximum cross-correlation. Total cross-correlation rating value was calculated by weighting these three values together. The cross-correlation was calculated according to the following equation:

$$K_{xy}\left(m\right)=\frac{{{\displaystyle \sum }}_{i=0}^{n-1}x\left(t_{min}+\left(m+i\right)·\Delta t\right)·y\left(t_{min}+i·\Delta t\right)}{\sqrt{{{\displaystyle \sum }}_{i=0}^{n-1}{x}^2\left(t_{min}+\left(m+i\right)·\Delta t\right)·{{\displaystyle \sum }}_{i=0}^{n-1}{y}^2\left(t_{min}+i·\Delta t\right)}}\hspace{1em}\hspace{1em}\hspace{1em}-1\le K_{xy}\le 1$$

(6)

where $K_{xy}\left(m\right)$ is cross-correlation; tmin is the minimum value of the evaluation interval; x is the evaluation signal; y is the reference curve; and n is the total number of time steps in the evaluation interval. The reference curve was shifted by an alterable time shift of $m·\Delta t$ with m = 0, 1, −1, 2….

The phase shift rating score (C_2a) was constrained by the parameters $D_{min}$ and $D_{max}$ and was calculated at the maximum cross-correlation K and the corresponding time shift δ as follows:

$${\delta }_{min}=D_{min}·\left(t_{max}-t_{min}\right) 0\le D_{min}\le 1$$

(7)

$${\delta }_{max}=D_{max}·\left(t_{max}-t_{min}\right) 0\le D_{max}\le 1$$

(8)

$$C_{2\mathrm{a}}=\{\begin{array}{c} 1 , \mathrm{i}\mathrm{f} \left|\delta \right|<{\delta }_{min} \\ {\left(\frac{\left|{\delta }_{max}-\left|\delta \right|\right|}{{\delta }_{max}-{\delta }_{min}}\right)}^{k_p} \\ 0 , \mathrm{i}\mathrm{f}\left|\delta \right|>{\delta }_{max}\end{array}{k}_p\in N>0$$

(9)

where $D_{max}$ is the maximum allowable percentage of time shift; $D_{min}$ is the minimum allowable percentage of time shift; ${\delta }_{max}$ is maximum value of time shift; ${\delta }_{min}$ is minimum value of time shift; $\left|\delta \right|$ is the value of time shift; and $k_p$ is the exponent factor for calculating the phase score.

The size rating score (C_2b) was calculated by comparing the square of the areas between the two curves and the time axis. Since both curves have equidistant supporting points, the following ratio can be calculated:

$$\frac{F_x}{F_y}=\frac{{{\displaystyle \sum }}_{i=1}^n{x}^2\left(t_{min}+\delta +i·\Delta t\right)}{{{\displaystyle \sum }}_{i=1}^n{y}^2\left(t_{min}+i·\Delta t\right)}$$

(10)

$$C_{2b}=\{\begin{array}{c}{\left(\frac{F_x}{F_y}\right)}^{k_G}, \mathrm{if} F_y>F_x\\ {\left(\frac{F_y}{F_x}\right)}^{k_G}, \mathrm{if} F_y<F_x\end{array}\mathrm{with} k_G\in \mathrm{N}>0$$

(11)

where $F_x$ and $F_y$ are the mean square value of the evaluation curve and the reference curve, respectively; and $k_G$ is the exponent factor for size rating.

The shape rating score (C_2c) was derived from the maximum cross-correlation K:

$$C_{2c}={\left(\frac{1}{2}\left(K+1\right)\right)}^{k_v}\mathrm{with}{k}_v\in \mathrm{N}>0\mathrm{and}0\le C_{2c}\le 1$$

(12)

where $k_v$ is the exponent factor for calculating the shape score.

3. Results

The detailed results of the CORA rating scores for all crash simulations are presented in

Table 2. Detailed CORA rating scores for effectiveness assessment.

Case	Thickness Ratio	Signal	Corridor Score (%)	Cross-correlation Metric (%)			Cross Correlation Score (%)	Total CORA (%)
				Shape Score	Phase Score	Size Score
10 m/s longitudinal crash	0.20	Displacement	49.43	82.03	100	41.62	74.55	64.50
		Force	48.90	43.29	100	52.95	65.41	58.81
	0.30	Displacement	97.26	99.18	100	97.94	99.04	98.33
		Force	83.92	87.34	100	92.93	93.42	89.62
	0.34	Displacement	100	99.97	100	94.08	98.02	98.81
		Force	98.13	97.85	100	95.99	97.95	98.02
	0.36	Displacement	100	99.98	100	95.00	98.33	99.00
		Force	97.13	97.36	100	95.21	97.52	97.37
	0.38	Displacement	100	99.99	100	96.69	98.89	99.34
		Force	96.58	97.13	100	95.44	97.52	97.15
	0.42	Displacement	100	99.98	100	99.29	99.76	99.86
		Force	96.78	97.30	100	96.51	97.93	97.47
	0.47	Displacement	100	99.97	100	97.93	99.30	99.58
		Force	96.41	97.22	100	96.59	97.93	97.33
	0.51	Displacement	100	99.97	100	96.05	98.68	99.21
		Force	96.38	97.06	100	97.59	98.22	97.48
	0.60	Displacement	100	99.98	100	92.55	97.51	98.51
		Force	95.87	96.65	100	99.17	98.60	97.51
22.2 m/s longitudinal crash	0.20	Displacement	40.97	88.14	100	41.69	76.61	62.35
		Force	67.87	48.94	100	71.50	73.48	71.24
	0.30	Displacement	71.18	97.95	100	75.66	91.20	83.20
		Force	79.27	67.60	100	87.95	85.18	82.82
	0.34	Displacement	93.46	99.53	100	89.94	96.49	95.28
		Force	81.00	70.05	100	98.48	89.51	86.11
	0.36	Displacement	98.18	99.67	100	93.95	97.87	97.99
		Force	88.89	83.55	100	94.78	92.78	91.22
	0.38	Displacement	100	99.94	100	95.49	98.48	99.09
		Force	95.65	92.70	100	98.16	96.95	96.43
	0.42	Displacement	97.67	99.94	100	89.17	96.37	96.89
		Force	95.42	93.30	100	95.96	96.42	96.02
	0.47	Displacement	92.38	99.86	100	85.90	95.25	94.10
		Force	93.70	91.30	100	94.70	95.34	94.68
	0.51	Displacement	85.31	99.63	100	81.62	93.75	90.38
		Force	88.38	85.09	100	88.66	91.25	90.10
	0.60	Displacement	79.72	99.29	100	78.24	92.51	87.39
		Force	81.25	75.45	100	81.63	85.69	83.92
10 m/s lateral crash	0.20	Displacement	40.30	89.30	100	48.50	79.27	63.68
		Force	69.43	34.50	100	48.56	61.02	64.38
	0.30	Displacement	84.17	97.98	100	85.44	94.47	90.35
		Force	85.06	64.14	100	97.14	87.09	86.28
	0.34	Displacement	98.67	99.78	100	92.94	97.57	98.01
		Force	89.66	67.02	100	84.42	83.81	86.15
	0.36	Displacement	86.32	98.84	100	82.26	93.70	90.75
		Force	89.25	69.73	100	77.02	82.25	85.05
	0.38	Displacement	69.39	96.28	100	71.65	89.31	81.34
		Force	87.28	69.41	100	69.25	79.55	82.64
	0.42	Displacement	48.71	88.85	100	55.72	81.52	68.40
		Force	84.22	69.18	100	59.49	76.22	79.42
	0.47	Displacement	34.45	78.11	100	39.86	72.66	57.37
		Force	79.45	59.28	100	49.30	69.53	73.50
	0.51	Displacement	29.74	65.71	100	30.30	65.34	51.10
		Force	73.66	51.86	100	42.89	64.92	68.42
	0.60	Displacement	25.20	10.12	100	18.47	42.86	35.80
		Force	69.00	42.68	100	32.59	58.42	62.65

and are color-coded (cutoff threshold is 58% [28]) based on the score. Green indicates a higher and better score, which is established in the Excel sheet with three values (min = 10%, max = 100%, cutoff = 58%). The displacement and force time histories were used to establish the rating for each impact simulation. The phase scores of the two signals demonstrated an excellent matching (100% rating score) between the simplified FE rail vehicle model and the baseline FE rail vehicle model for all simplification thickness ratios and all three collision configurations, indicating no phase change between the detailed and the simplified models, similar to previous research [31]. For the 10 m/s longitudinal rigid-wall impacts, the total CORA rating scores of the displacement and force signals were greater than 90% when the thickness ratio was greater than 0.30 (α > 0.30). The assessment scores for the simplified vehicle FE model with a thickness ratio of less than 0.30 were poor, especially for the corridor response. For the 22.2 m/s longitudinal rigid-wall impacts, the total CORA rating scores of the displacement and force signals were greater than 90% when the thickness ratio was between 0.36 and 0.51. The rating scores for the simplified FE rail vehicle models with large and small thickness ratios were poor, especially for the simplified model with a small thickness ratio (e.g., α = 0.20). For the 10 m/s lateral rigid-cylinder collisions, compared with longitudinal impacts, the total CORA scores exceeded 80% only when the thickness ratio was between 0.30 and 0.38, and the scores were low in other cases.

The combined average CORA scores for the displacement and force signals for each simplified FE rail vehicle model for all impacts are shown in Figure 7a. The combined average CORA scores increased first and then decreased with the increase in thickness ratio for the 22.2 m/s longitudinal impact and 10 m/s lateral impact, while the combined average CORA scores increased first and then remained almost unchanged with the increase in thickness ratio for the 10 m/s longitudinal impact. The average CORA score for all three collision configurations is clearly best when the thickness ratio is between 0.35 and 0.40.

In addition, the total combined CORA score for the three collision configurations using the simplified FE rail vehicle model is shown in Figure 7b. Here, two sets of weighting factors were used to calculate the total combined CORA scores. Firstly, a simple average score of each simplified FE model in three collision simulations (score-average) was applied. Secondly, the number of overturned carriages of a train in train collision and post-derailment collisions (Figure 1c,d,f) was statistically counted. The ratio of the number of overturned carriages to the total number of carriages in a train was the weight factor of the lateral impact’s rating score, while the weights of different longitudinal impact scores were the same (Figure 7b). The results show that the total combined CORA rating score increased first and then decreased with the increase in thickness ratio. The combined CORA scores of the simplified FE rail vehicle models with thickness ratios of 0.36 and 0.38 were 93%, and these were the optimal simplification thickness ratios.

Table 3. Comparison of the computation time.

Impact Simulations	Impact Duration (ms)	Calculate Time (h)		Time Reduction (%)
		Original Detailed Model	Simplified Model
10 m/s longitudinal crash	100	4	1.8	55
22.2 m/s longitudinal crash	250	9.5	4.2	56
10 m/s lateral crash	300	11.2	5	55

shows the computation time for the detailed and simplified FE models. All simulations were performed using a PC with an 8-core AMD Ryzen 9 5900HX CPU. In the vehicle impact simulations, the mass scaling percentage of all FE models was limited to 0.1% and hourglass control algorithms were employed to keep the hourglass energy contribution below 5%. The results demonstrate that the simplified FE rail vehicle model achieves substantial computational efficiency, with a time reduction of 55%.

4. Discussion

4.1. 10 m/s Longitudinal Rigid-Wall Collisions

Compared with the baseline detailed FE rail vehicle model, except for the simplified rail vehicle models with thickness ratios less than 0.30, the displacement and impact force responses of the simplified models agreed well with the baseline detailed FE model in the 10 m/s longitudinal rigid-wall crash; see Figure 8. In this work, because only the middle section of the rail vehicle was simplified to a single-shell structure and the two ends of the vehicle were still the original sandwich corrugated hollow double-shell structures, the impact responses (including the displacement and impact force time histories and vehicle final deformations) of the simplified models matched well with the detailed model when only the front-end structures deformed in the low-speed (10 m/s) longitudinal collision (Figure 8 and Figure 9). However, for thickness ratios less than 0.30, the middle section of the rail vehicle experienced plastic deformation (Figure 9), causing greater vehicle compression and lower impact forces (Figure 8), reducing the CORA rating scores.

4.2. 22.2 m/s Longitudinal Rigid-Wall Collisions

For the simplified FE rail vehicle model, plastic compression decreased and impact force increased with increase in the thickness ratio for 22.2 m/s longitudinal rigid-wall collisions (Figure 10 and Figure 11). In higher speed (22.2 m/s) longitudinal rigid-wall impacts, large plastic deformation occurred not only in the front-end area (i.e., equipment zone) but also in the middle section of the car body (Figure 11). The simplified rail vehicle becomes stiffer with increase in thickness ratio, resulting in decreased compression and increased impact force, again changing the subsequent CORA rating scores. Additionally, for simplification thickness ratios below 0.38 (α < 0.38), the middle section of the rail vehicle deforms excessively and the wheels also hit the rigid-wall, resulting in the obvious peak of the impact force after 120 ms. Increasing the thickness ratio increases the stiffness of the car body, which inhibits this artifact. When the simplification thickness ratio reaches 0.60 (α = 0.60), the simplified middle section of the car body shows almost no deformation (Figure 11).

4.3. 10 m/s Lateral Rigid-Cylinder Collisions

For the simplified FE rail vehicle model, plastic compression substantially decreased and the impact force increased with increase in the thickness ratio for the 10 m/s lateral rigid-cylinder impacts; see Figure 12 and Figure 13. Since the deformations are complex in lateral rigid-cylinder crashes, the displacement time histories were recorded by using the displacement of the node at the accelerometer location in the middle of the rail vehicle (Figure 5). Therefore, the negative displacement value at around 300 ms (Figure 12a) means that the car body rebounded beyond its original location (e.g., the simulation case of the simplified vehicle with a thickness ratio of 0.60). In lateral rigid-cylinder impacts, plastic deformation occurs in the middle of the car body (Figure 13). For increased thickness ratios, the rail vehicle models become stiffer, increasing the impact force and decreasing the compression, altering the CORA rating scores. Even when the thickness ratio reached 0.60 (α = 0.60), the vehicle rebounded beyond its initial location (Figure 12a and Figure 13).

4.4. Effectiveness of the Simplification Method

Considering the CORA rating values and final vehicle deformations, the best simplified FE rail vehicle model for longitudinal and lateral collisions was the simplification thickness ratio of 0.38 (α = 0.38). Firstly, the total combined CORA rating scores of α = 0.36 and α = 0.38 were the greatest values (CORA ratings: 93%) in all simplification cases. Although the CORA rating score of α = 0.36 was slightly higher than α = 0.38, the two scores were close (Figure 7b). Secondly, compared with the simplified model of α = 0.36, the final vehicle deformation modes of the simplified model with a thickness ratio of 0.38 were closer to that of the baseline detailed model, especially for higher-speed (22.2 m/s) longitudinal impacts (Figure 11). Overall, the simplified model of α = 0.38 matched best with the baseline detailed model.

To ensure the reliability of the simplification method, the front-end with the pantograph was selected to impact the rigid wall in the longitudinal impact simulations. The top installation location of the pantograph was hollow (Figure 5). Compared with the rear of the vehicle, the stiffness of the front end with the pantograph was therefore lower, leading to greater deformations in longitudinal collisions. Hence, selecting this end could more reasonably evaluate the effectiveness of the simplified model.

This rail vehicle numerical model simplification method was independent of the vehicle geometry. The impact simulations for the subway vehicle under 10/22.2 m/s rigid-wall longitudinal and 10 m/s lateral rigid-cylinder crashes were performed by using this simplification method with a thickness ratio of 0.38. The geometry of the subway vehicle is different from that of the high-speed rail vehicle (Figure 14). The vehicle displacements and impact forces of the simplified subway vehicle FE model matched closely with the results of the detailed vehicle model under the three collisions, as shown in Figure 15. For the subway vehicle impact deformations, the simplified subway vehicle model also performed similarly to the detailed vehicle model (Figure 16). Thus, the simplification method for rail vehicle crash models presented high applicability.

4.5. Limitations

The single middle vehicle was not validated against rail vehicle impact tests due to the lack of crash tests, while the head car of the high-speed train using this same FE modelling approach has been verified against impact experiments in our previous study [21]. Further full-scale crash test data for the middle vehicle will help confirm the accuracy of the baseline detailed finite element rail vehicle model under consideration in this work.

In a preliminary approach, the sandwich theory and anisotropic constitutive models were employed for the model simplification, but this did not work well. Hence, the method of changing the thickness without changing the material mechanical parameters was directly used to simplify the rail vehicle model. The macroscopic impact dynamic responses (e.g., the compression, impact force, and vehicle final deformation mode) of the simplified FE rail vehicle model are close to the baseline detailed model. However, some of the local responses of the simplified rail vehicle model, such as the stress profiles, are likely different from the detailed model. Nonetheless, this simplified modelling approach will be a useful tool for subsequent complex train collision and occupant injury analysis.

5. Conclusions

To address computational time challenges with detailed FE rail vehicle models, a simplification method for assessing rail vehicles under longitudinal and lateral crashes is proposed in this paper. Based on the structural characteristics of the rail vehicle body, the vehicle’s middle section with the sandwich corrugated hollow double-shell structure was simplified using solid single-shell structures. A comparative analysis and correlation evaluation via the CORA objective rating method shows that the simplified FE vehicle model can reasonably predict the rail vehicle impact dynamic responses. The displacement and impact force time-histories closely agree with the results of the original detailed FE model under both longitudinal and lateral impacts (total combined average CORA rating scores for α = 0.38:10 m/s longitudinal collision = 98%, 22.2 m/s longitudinal collision = 98%, 10 m/s lateral collision = 82%). The simplified rail vehicle model also performed similarly to the baseline detailed rail vehicle model in rail vehicle impact deformations. Compared to the detailed FE model of the rail vehicle, the simplified model shows a substantial reduction in the computational time (approx. 55%) for simulations of complex train collisions. This study lays a solid approach foundation for efficiently and effectively investigating train dynamic responses in complex collisions. Moreover, unlike previous rail vehicle model simplification methods, which only replaced the central part of the vehicle model with one-dimensional beam elements, this method retains the structure of the vehicle’s central part and therefore the crash pulses at different locations of the vehicle can be recorded, which can be used for train occupant injury assessment.