# A New Car-Body Structure Design for High-Speed EMUs Based on the Topology Optimization Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Topology Optimization Method of Car-Body Structure

#### 2.1. Homogenization Method

#### 2.2. Variable-Density Method

#### 2.3. Progressive Structural Optimization Method

#### 2.4. Topology Optimization Process of Car-Body Structure

## 3. Selection of Topology Optimization Design Domain and Model Establishment

#### 3.1. Selection of Topology Optimization Design Domain

#### 3.2. Establishment of Topology Optimization Design Domain Model

^{4}MPa, the density is 2.7 × 10

^{3}kg/m

^{3}, and Poisson’s ratio is 0.33. The working conditions and boundary conditions are shown in Table 2.

#### 3.3. Results of Static Analysis

#### 3.4. Results of Modal Analysis

## 4. Topology Optimization of Car-Body Structure

#### 4.1. Topology Optimization Design

#### 4.2. Topology Optimization Results

## 5. Reconstruction of Car-Body Bearing Structure

#### 5.1. Design Method of Truss Car-Body Structure Reconstruction

#### 5.2. Establishment of Car-Body Geometry Model and Finite Element Model

#### 5.3. Finite Element Analysis of the Reconstructed Model

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ding, S.S. Research on Key Technology of High-Speed Train Body Design. Ph.D. Thesis, Beijing Jiaotong University, Beijing, China, 2016. [Google Scholar]
- Zhang, Q.G.; Qiao, K.; Cao, Y. The development of foreign high-speed double decker EMU and its inspiration to China. China Railw.
**2018**, 7, 103–107. [Google Scholar] [CrossRef] - Liu, C.Q.; Wang, L. 400 km/h cross-country interconnection high-speed EMUs. Electr. Drive Locomot.
**2020**, 2, 1–6. [Google Scholar] [CrossRef] - Deng, H.; Zhang, G.Q.; Zhang, Y.; Wang, S.B.; Wang, C. Development Concept of Next Generation High-speed Intelligent EMU. Urban Mass Transit
**2022**, 25, 11–15. [Google Scholar] - Harte, A.M.; McNamara, J.F.; Roddy, I.D. A multilevel approach to the optimisation of a composite light rail vehicle bodyshell. Compos. Struct.
**2003**, 63, 447–453. [Google Scholar] [CrossRef] - Chiandussi, G.; Gaviglio, I.; Ibba, A. Topology optimisation of an automotive component without final volume constraint specification. Adv. Eng. Softw.
**2014**, 35, 609–617. [Google Scholar] [CrossRef] - Chen, B.Z.; Zhang, X.Q.; Qiu, G.Y. Topology Optimization of Underframe for 400km/h High-Speed Train. Mach. Des. Manuf.
**2021**, 7, 272–275. [Google Scholar] [CrossRef] - Zhang, Q.; Sun, Q.Z.; Liu, G.F. Finite Element Analysis and Topological Optimization of a Tracked Vehicle Body Based on Hypermesh. J. Jiamusi Univ. (Nat. Sci. Ed.)
**2020**, 38, 123–126. [Google Scholar] - Ji, B.K. Research on Topology Optimization Design of High-Speed Train Body Structure Based on CRH EMU. Master’s Thesis, Sichuan University of Science & Engneering, Zigong, China, 2019. [Google Scholar]
- Zhang, L.; Zhang, J.Y.; Li, T.; Zhang, Y.D. Multi-objective aerodynamic optimization design of high-speed train head shape. J. Zhejiang Univ.-Sci. A
**2017**, 18, 841–854. [Google Scholar] [CrossRef] - Zhang, L.; Dai, Z.Y.; Li, T.; Zhang, J.Y. Multi-objective aerodynamic shape optimization of a streamlined high-speed train using Kriging model. J. Zhejiang Univ.-Sci. A
**2022**, 23, 225–245. [Google Scholar] [CrossRef] - Deb, A.; Chou, C.; Dutta, U.; Gunti, S. Practical Versus RSM-Based MDO in Vehicle Body Design. SAE Int. J. Passeng. Cars-Mech. Syst.
**2012**, 5, 110–119. [Google Scholar] [CrossRef] - Chen, X.; Wang, Y.Q.; Sun, K.; Feng, Z.Y.; Zhao, W.H.; Lu, B.H. Multi-Objective Optimization for Section of Sandwich Plate Applied to High-Speed Train Compartments. J. Xi’an Jiaotong Univ. Nat. Sci. Ed.
**2013**, 47, 62–67. [Google Scholar] - Sahib, M.M.; Kovács, G. Elaboration of a Multi-Objective Optimization Method for High-Speed Train Floors Using Composite Sandwich Structures. Appl. Sci.
**2023**, 13, 3876. [Google Scholar] [CrossRef] - Miao, B.R.; Zhang, L.M.; Zhang, W.H.; Yin, H.T.; Jin, D.C. High-speed Train Carbody Structure Fatigue Simulation Based on Dynamic Characteristics of the Overall Vehilce. J. China Railw. Soc.
**2010**, 32, 101–108. [Google Scholar] [CrossRef] - Tang, Q.C.; Ma, L.; Zhao, D.; Lei, J.Y.; Wang, Y.H. A multi-objective cross-entropy optimization algorithm and its application in high-speed train lateral control. Appl. Soft Comput.
**2022**, 115, 108151. [Google Scholar] [CrossRef] - Wang, Q.S.; Zeng, J.; Shi, H.L.; Jiang, X.S. Parameter optimization of multi-suspended equipment to suppress carbody vibration of high-speed railway vehicles: A comparative study. Int. J. Rail Transp.
**2023**, 2023, 2291202. [Google Scholar] [CrossRef] - Wang, S.M.; Peng, Y.; Wang, T.T.; Che, Q.W.; Xu, P. Collision performance and multi-objective robust optimization of a combined multi-cell thin-walled structure for high speed train. Thin-Walled Struct.
**2019**, 135, 341–355. [Google Scholar] [CrossRef] - Peng, Y.; Hou, L.; Che, Q.W.; Xu, P.; Li, F. Multi-objective robust optimization design of a front-end underframe structure for a high-speed train. Eng. Optim.
**2019**, 51, 753–774. [Google Scholar] [CrossRef] - Lu, S.S.; Xu, P.; Yan, K.P.; Yao, S.G.; Li, B.H. A force/stiffness equivalence method for the scaled modelling of a highspeed train head car. Thin-Walled Struct.
**2019**, 137, 129–142. [Google Scholar] [CrossRef] - Wang, R.; Gao, S.M.; Wu, H.Y. Progress in Hexahedral Mesh Generation and Optimization. J. Comput.-Aided Des. Comput. Graph.
**2020**, 32, 693–708. [Google Scholar] - Papanicolau, G.; Bensoussan, A.; Lions, J.L. Asymptotic Analysis for Periodic Structures; Elsevier: New York, NY, USA, 1978; ISBN 978-0-444-85172-7. [Google Scholar]
- Wang, J. Application and Analysis of Asymptotic Homogenization Method in Masonry. Master’s Thesis, Xiangtan University, Xiangtan, China, 2013. [Google Scholar]
- Guedes, J.; Kikuchi, N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput. Method. Appl. M
**1990**, 83, 143–198. [Google Scholar] [CrossRef] - Zhang, G.F.; Xu, L.; Li, D.S.; Yu, F.C. Research on Sensitivity Filtering of Continuum Topology Optimization. Modul. Mach. Tool Autom. Manuf. Tech.
**2021**, 06, 29–32. [Google Scholar] [CrossRef] - Xie, Y.M.; Steven, G.P. Evolutionary Structural Optimization; Berlin Springer-Verlag: London, UK, 1997; ISBN 978-3-540-76153-2. [Google Scholar]

**Figure 2.**Geometric model of car-body structure: (

**a**) axonometric drawing of car body; (

**b**) cross-section of the car body; (

**c**) the view of the car-body frame.

**Figure 4.**Finite element analysis of stress nephogram in design domain: (

**a**) longitudinal load; (

**b**) vertical load; (

**c**) torsional load; (

**d**) crosswind load; (

**e**) three-point support load.

**Figure 5.**Mode shapes of each order in the state of the steel structure of the car body: (

**a**) first vertical bending deformation; (

**b**) first diamond deformation; (

**c**) first transverse bending deformation; (

**d**) breathing deformation.

**Figure 6.**The optimization results of 75 iterations with different thresholds were obtained: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 7.**The optimization results of 106 iterations with different thresholds were obtained: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 8.**The optimization results of 139 iterations with different thresholds were obtained: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 9.**The optimization results of 155 iterations with different thresholds were obtained: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 10.**The optimization results of 200 iterations with different thresholds were obtained: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 12.**Optimization results with different thresholds in 139 iterations: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 14.**The optimization results of 75 iterations with different thresholds were obtained: (

**a**) threshold 0.05; (

**b**) threshold 0.1; (

**c**) threshold 0.2; (

**d**) threshold 0.3; (

**e**) threshold 0.4; (

**f**) threshold 0.5.

**Figure 15.**Contrast modeling of underframe structure: (

**a**) results of topology optimization of underframe structure; (

**b**) geometric modeling of underframe structure.

**Figure 16.**Contrast modeling of end-wall structure: (

**a**) results of topology optimization of end-wall structure; (

**b**) geometric modeling of end-wall structure.

**Figure 17.**Contrast modeling of results of end structure: (

**a**) results of topology optimization of results of end structure; (

**b**) geometric modeling of results of end structure.

**Figure 18.**Contrast modeling of side beam structure (

**a**) results of topology optimization of side beam structure; (

**b**) geometric modeling of side beam structure.

**Figure 19.**Contrast modeling of roof structure: (

**a**) results of topology optimization of side wall structure; (

**b**) geometric modeling of roof structure.

**Figure 20.**Contrast modeling of side wall structure: (

**a**) results of topology optimization of side wall structure; (

**b**) geometric modeling of side wall structure.

**Figure 21.**Contrast modeling of supporting structure: (

**a**) results of topology optimization of supporting structure; (

**b**) geometric modeling of supporting structure.

**Figure 25.**The stress nephogram of car-body model is reconstructed by finite element method: (

**a**) stress cloud diagram (longitudinal load); (

**b**) stress cloud diagram (vertical load); (

**c**) stress cloud diagram (torsional load); (

**d**) stress cloud diagram (crosswind load); (

**e**) stress cloud diagram (three-point support load).

Structure Size | L/mm |
---|---|

Car-body length | 25,000 |

Fixed distance | 17,800 |

Car-body width | 3360 |

Car-body height | 4050 |

Height from coupler centerline to rail surface | 950 |

Working Condition | Load | Restraint | Condition Design Diagram |
---|---|---|---|

Longitudinal load | Compression force of 1500 kN for front-end coupler seat Compression forces of 300, 300, and 400 kN to the front-end wall near the roof, side wall, and chassis, respectively | Longitudinal constraint at the rear end wall | |

Vertical load | 1.3 times the weight of the car body | Vertical restraint at the secondary suspension | |

Torsional load | Unit torsional load 1 kN·m | Full restraint at the secondary suspension | |

Crosswind load | Unit wind pressure 450 Pa | Full restraint at the secondary suspension | |

Three-point support load | - | Apply vertical displacement to constrained support points |

Working Condition | Maximum Von Mises Stress/MPa |
---|---|

Longitudinal load | 86.8 |

Vertical load | 63.3 |

Torsional load | 67.9 |

Crosswind load | 45.0 |

Three-point support load | 36.0 |

Modal Order Number | Mode Shape of the Car-Body Mode | |
---|---|---|

Frequency/Hz | Vibration Mode | |

1 | 21.25 | First vertical bending deformation |

2 | 22.69 | First diamond deformation |

3 | 23.51 | First transverse bending deformation |

4 | 30.64 | Breathing deformation |

Parameter | Description | Value |
---|---|---|

MINDIM | Minimum member size | 150 |

MAXDIM | Maximum member size | 400 |

OBJTOL | Tolerance of target function | 0.005 |

CHECKER | Checkerboard parameter | 1 |

DISCRETE | Discrete parameter | 1 |

Sequence | Description | Number/t | |
---|---|---|---|

1 | Weight of vehicle maintenance equipment (excluding bogie and car-body structure) | 25.46 | |

2 | Weight of bogie | 8.0 | |

3 | Passengers (80 kg/per person) | Capacity: 85 | 6.8 |

Overcrowding: 120 | 9.6 | ||

4 | Servicing equipment | 0.4 | |

5 | Weight of vehicle with capacity passengers (excluding bogie and car-body structure) | 32.26 | |

6 | Weight of vehicle with overcrowding passengers (excluding bogie and car-body structure) | 35.06 |

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, C.; Ma, K.; Zhu, T.; Ding, H.; Sun, M.; Wu, P.
A New Car-Body Structure Design for High-Speed EMUs Based on the Topology Optimization Method. *Appl. Sci.* **2024**, *14*, 1074.
https://doi.org/10.3390/app14031074

**AMA Style**

Liu C, Ma K, Zhu T, Ding H, Sun M, Wu P.
A New Car-Body Structure Design for High-Speed EMUs Based on the Topology Optimization Method. *Applied Sciences*. 2024; 14(3):1074.
https://doi.org/10.3390/app14031074

**Chicago/Turabian Style**

Liu, Chunyan, Kai Ma, Tao Zhu, Haoxu Ding, Mou Sun, and Pingbo Wu.
2024. "A New Car-Body Structure Design for High-Speed EMUs Based on the Topology Optimization Method" *Applied Sciences* 14, no. 3: 1074.
https://doi.org/10.3390/app14031074