Lightweight design of an electric bus body structure with analytical target cascading

doi:10.1007/s11465-022-0718-y

Front. Mech. Eng.

2023, Vol. 18

Issue (1) : 2 https://doi.org/10.1007/s11465-022-0718-y

RESEARCH ARTICLE

Lightweight design of an electric bus body structure with analytical target cascading

Puyi WANG^1,², Yingchun BAI¹, Chuanliang FU¹, Cheng LIN¹

¹. National Engineering Research Center for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China
². Northwest Institute of Mechanical and Electrical Engineering, Xianyang 712099, China

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Abstract

Lightweight designs of new-energy vehicles can reduce energy consumption, thereby improving driving mileage. In this study, a lightweight design of a newly developed multi-material electric bus body structure is examined in combination with analytical target cascading (ATC). By proposing an ATC-based two-level optimization strategy, the original lightweight design problem is decomposed into the system level and three subsystem levels. The system-level optimization model is related to mass minimization with all the structural modal frequency constraints, while each subsystem-level optimization model is related to the sub-structural performance objective with sub-structure mass constraints. To enhance the interaction between two-level systems, each subsystem-level objective is reformulated as a penalty-based function coordinated with the system-level objective. To guarantee the accuracy of the model-based analysis, a finite element model is validated through experimental modal test. A sequential quadratic programming algorithm is used to address the defined optimization problem for effective convergence. Compared with the initial design, the total mass is reduced by 49 kg, and the torsional stiffness is increased by 17.5%. In addition, the obtained design is also validated through strength analysis.

Keywords electric vehicle body in white (BIW) lightweight analytical target cascading (ATC)

Corresponding Author(s): Yingchun BAI

About author: Changjian Wang and Zhiying Yang contributed equally to this work.

Just Accepted Date: 30 June 2022 Issue Date: 02 March 2023

Cite this article:

Puyi WANG,Yingchun BAI,Chuanliang FU, et al. Lightweight design of an electric bus body structure with analytical target cascading[J]. Front. Mech. Eng., 2023, 18(1): 2.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0718-y
https://academic.hep.com.cn/fme/EN/Y2023/V18/I1/2

Fig.1 Principle of analytical target cascading method.

Fig.2 Information interactions in the

i t h

subsystem with penalty-based analytical target cascading method.

Fig.3 Composition and connections of electric bus body structure.

Fig.4 Constraints and load conditions under (a) bending case and (b) torsional case.

Fig.5 Experimental modal test set up: (a) free support, (b) accelerometer, and (c) data acquired system.

Fig.6 Comparisons between experimental and simulated modal shapes: (a) experimental first-order bending modal shape, (b) simulated first-order bending modal shape, (c) experimental first-order torsional modal shape, and (d) simulated first-order torsional modal shape.

Fig.7 Analytical target cascading-based two-level lightweight optimization formulation of electric bus body structure.

Fig.8 Specific section bars of the side structure.

Fig.9 Specific section bars of the roof structure.

Fig.10 Specific section bars of the chassis structure.

Tab.1 Comparisons of optimization results with the initial design and Ref. [3]

Fig.11 Iteration curves of optimization history: (a) system-level optimization and (b) subsystem-level optimization.

Tab.2 Results of local variables in subsystem levels

Fig.12 Loads on the present electric bus body structure.

Fig.13 Bending stress distributions of (a) the aluminum alloy structure and (b) the high strength steel structure.

Fig.14 Torsional stress distributions of (a) the aluminum alloy structure and (b) the high strength steel structure.

Tab.3 Comparisons of validated stresses and yield stresses

$a 1, a 2, a 3$	Scaled material properties of the side structure, roof structure, and chassis structure, respectively
A	Scaled material properties vector
c	Consistency index
$d c L, d c U$	Maximum displacements of the chassis structure, where “L” and “U” indicate that the performance is evaluated in the subsystem level and the system level, respectively
$E i, E o$ (i = 1,2,3)	Scaled Young’s modulus of each sub-structure and the base Young’s modulus, respectively
$f i j$	Local objective function in ATC
$f r, t o r s i o n L, f r, t o r s i o n U$	First-order torsional frequencies of the roof structure, where “L” and “U” indicate that the performance is evaluated in the subsystem level and the system level, respectively
$f s, b e n d L, f s, b e n d U$	First-order bending frequencies of the side structure, where “L” and “U” indicate that the performance is evaluated in the subsystem level and the system level, respectively
$f t o r s i o n$	First-order torsional frequency of the entire structure
$F s y s, F s u b, i$	Entire structural performance and sub-structural performance, respectively
$g i j, g$	Inequality constraint
$h i j, h$	Equality constraint
$M, M s u b, i$	Mass of the entire structure and the sub-structure, respectively
$M c, M r, M s$	Mass of the chassis structure, roof structure, and side structure, respectively
$P i j$	Subsystem-level problem in ATC
$r i j$	Response fed back to the superior level in ATC
$t i j$	Local objective assigned from the superior level in ATC
$v$	Lagrangian multiplier vector
$w$	Quadratic punishment weight vector
$X c, X r, X s$	Local design variable vector of the chassis structure, roof structure, and side structure, respectively
$X i j$	Local design variable vector in ATC
$X s y s$	Global design variable vector of the entire electric bus body structure
X₁?X₉	Thicknesses of specific section bars in the side structure
X₁₀?X₂₀	Thicknesses of specific section bars in the roof structure
X₂₁?X₃₃	Thicknesses of specific section bars in the chassis structure
β	Relaxation factor
ε	Convergence threshold
$ρ i, ρ o$ (i = 1,2,3)	Scaled density of each sub-structure and the base density, respectively
$? (c)$	Penalty-based coordinated function

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