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

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.

Graphical abstract

Keywords

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

References

[1] Olivera A C , García-Nieto J M , Alba E . Reducing vehicle emissions and fuel consumption in the city by using particle swarm optimization. Applied Intelligence, 2015, 42(3): 389–405

[2] Li L , Wang X Y , Song J . Fuel consumption optimization for smart hybrid electric vehicle during a car following process. Mechanical Systems and Signal Processing, 2017, 87(1): 17–29

[3] Fu C L , Bai Y C , Lin C , Wang W W . Design optimization of a newly developed aluminum steel multi-material electric bus body structure. Structural and Multidisciplinary Optimization, 2019, 60(5): 2177–2187

[4] Duan L B , Jiang H B , Li H H , Xiao N C . Crashworthiness optimization of VRB thin-walled structures under manufacturing constraints by the eHCA-VRB algorithm. Applied Mathematical Modelling, 2020, 80: 126–150

[5] Sobieszczanski-Sobieski J , Kodiyalam S , Yang R Y . Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. Structural and Multidisciplinary Optimization, 2001, 22(4): 295–306

[6] Ide T , Otomori M , Leiva J P , Watson B C . Structural optimization methods and techniques to design light and efficient automatic transmission of vehicles with low radiated noise. Structural and Multidisciplinary Optimization, 2014, 50(6): 1137–1150

[7] Wang H Y , Xie H . Multi-objective optimization of crashworthiness of vehicle front longitudinal beam. Structural and Multidisciplinary Optimization, 2020, 61(5): 2111–2123

[8] Xiong F , Zou X H , Zhang Z G , Shi X H . A systematic approach for multi-objective lightweight and stiffness optimization of a car body. Structural and Multidisciplinary Optimization, 2020, 62(6): 3229–3248

[9] Kiani M , Yildiz A R . A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization. Archives of Computational Methods in Engineering, 2016, 23(4): 723–734

[10] Aulig N , Nutwell E , Menzel S , Detwiler D . Preference-based topology optimization for vehicle concept design with concurrent static and crash load cases. Structural and Multidisciplinary Optimization, 2018, 57(1): 251–266

[11] Wang D F , Xie C , Liu Y C , Xu W C , Chen Q . Multi-objective collaborative optimization for the lightweight design of an electric bus body frame. Automotive Innovation, 2020, 3(3): 250–259

[12] Jung Y , Lim S , Kim J , Min S . Lightweight design of electric bus roof structure using multi-material topology optimization. Structural and Multidisciplinary Optimization, 2020, 61(3): 1273–1285

[13] Ou H G , Tang X D , Xiao J P , Wang Y B , Ma Z M . Lightweight body-in-white design driven by optimization technology. Automotive Innovation, 2018, 1(3): 255–262

[14] Li C , Kim I Y , Jeswiet J . Conceptual and detailed design of an automotive engine cradle by using topology, shape, and size optimization. Structural and Multidisciplinary Optimization, 2015, 51(2): 547–564

[15] Qin H , Liu Z J , Zhong H L , Liu Y , Lv C . Two-level multiple cross-sectional shape optimization of automotive body frame with exact static and dynamic stiffness constraints. Structural and Multidisciplinary Optimization, 2018, 58(5): 2309–2323

[16] Xie C , Wang D F . Multi-objective cross-sectional shape and size optimization of S-rail using hybrid multi-criteria decision-making method. Structural and Multidisciplinary Optimization, 2020, 62(6): 3477–3492

[17] Zuo W J . Bi-level optimization for the cross-sectional shape of a thin-walled car body frame with static stiffness and dynamic frequency stiffness constraints. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2015, 229(8): 1046–1059

[18] De S , Singh K , Seo J , Kapania R K , Ostergaard E , Angelini N , Aguero R . Lightweight chassis design of hybrid trucks considering multiple road conditions and constraints. World Electric Vehicle Journal, 2021, 12(1): 3

[19] Lu S B , Ma H G , Xin L , Zuo W J . Lightweight design of bus frames from multi-material topology optimization to cross-sectional size optimization. Engineering Optimization, 2019, 51(6): 961–977

[20] Bai J T , Li Y W , Zuo W J . Cross-sectional shape optimization for thin-walled beam crashworthiness with stamping constraints using genetic algorithm. International Journal of Vehicle Design, 2017, 73(1–3): 76–95

[21] Zhong W , Su R Y , Gui L J , Fan Z J . Multi-objective topology and sizing optimization of bus body frame. Structural and Multidisciplinary Optimization, 2016, 54(3): 701–714

[22] Chen J , Wu Y J , Zhang L M , He X L , Dong S J . Dynamic optimization design of the suspension parameters of car body-mounted equipment via analytical target cascading. Journal of Mechanical Science and Technology, 2020, 34(5): 1957–1969

[23] Guo Z G , Zhang Y F , Zhao X B , Song X Y . CPS-based self-adaptive collaborative control for smart production-logistics systems. IEEE Transactions on Cybernetics, 2021, 51(1): 188–198

[24] Guarneri P , Gobbi M , Papalambros P Y . Efficient multilevel design optimization using analytical target cascading and sequential quadratic programming. Structural and Multidisciplinary Optimization, 2011, 44(3): 351–362

[25] DorMohammadi S , Rais-Rohani M . Exponential penalty function formulation for multilevel optimization using the analytical target cascading framework. Structural and Multidisciplinary Optimization, 2013, 47(4): 599–612

[26] Kim H M , Chen W , Wiecek M M . Lagrangian coordination for enhancing the convergence of analytical target cascading. AIAA Journal, 2006, 44(10): 2197–2207

[27] Etman L F , Kokkolaras M , Hofkamp A T , Papalambros P Y , Rooda J E . Coordination specification in distributed optimal design of multilevel systems using the χ language. Structural and Multidisciplinary Optimization, 2005, 29(3): 198–212

[28] Qu T , Huang G Q , Cung V D , Mangione F . Optimal configuration of assembly supply chains using analytical target cascading. International Journal of Production Research, 2010, 48(23): 6883–6907

[29] Ramakrishnan K , Mastinu G , Gobbi M . Multidisciplinary design of electric vehicles based on hierarchical multi-objective optimization. Journal of Mechanical Design, 2019, 141(9): 091404

[30] Kim H M , Rideout D G , Papalambros P Y , Stein J L . Analytical target cascading in automotive vehicle design. Journal of Mechanical Design, 2003, 125(3): 481–489

[31] Cui T W , Zhao W Z , Wang C Y , Guo Y H , Zheng H Y . Design optimization of a steering and suspension integrated system based on dynamic constraint analytical target cascading method. Structural and Multidisciplinary Optimization, 2020, 62(1): 419–437

[32] Blouin V Y , Fadel G M , Haque I Q , Wagner J R , Samuels H B . Continuously variable transmission design for optimum vehicle performance by analytical target cascading. International Journal of Heavy Vehicle Systems, 2004, 11(3–4): 327–348

[33] Kang N , Kokkolaras M , Papalambros P Y , Yoo S , Na W , Park J , Featherman D . Optimal design of commercial vehicle systems using analytical target cascading. Structural and Multidisciplinary Optimization, 2014, 50(6): 1103–1114

[34] Kim H M , Michelena N F , Papalambros P Y , Jiang T . Target cascading in optimal system design. Journal of Mechanical Design, 2003, 125(3): 474–480

[35] Choudhary R , Malkawi A , Papalambros P Y . Analytical target cascading in simulation-based building design. Automation in Construction, 2005, 14(4): 551–568

[36] Li Z J , Kokkolaras M , Papalambros P Y , Hu S J . Product and process tolerance allocation in compliant multi-station assembly using analytical target cascading. Journal of Mechanical Design, 2008, 130(9): 091701

[37] Tosserams S , Etmanl L F P , Papalambros P Y , Rooda J E . An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers. Structural and Multidisciplinary Optimization, 2006, 31(3): 176–189

Nomenclature

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_{\mathrm{c}}^{\mathrm{L}},d_{\mathrm{c}}^{\mathrm{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_{\text{o}} (i = 1,2,3)	Scaled Young’s modulus of each sub-structure and the base Young’s modulus, respectively
f_{ij}	Local objective function in ATC
f_{\mathrm{r},\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}^{\mathrm{L}},f_{\mathrm{r},\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}^{\mathrm{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_{\mathrm{s},\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}^{\mathrm{L}},f_{\mathrm{s},\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}^{\mathrm{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_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}	First-order torsional frequency of the entire structure
F_{\mathrm{s}\mathrm{y}\mathrm{s}},F_{\mathrm{s}\mathrm{u}\mathrm{b},i}	Entire structural performance and sub-structural performance, respectively
g_{ij},g	Inequality constraint
h_{ij},h	Equality constraint
M,M_{\mathrm{s}\mathrm{u}\mathrm{b},i}	Mass of the entire structure and the sub-structure, respectively
M_{\mathrm{c}},M_{\mathrm{r}},M_{\mathrm{s}}	Mass of the chassis structure, roof structure, and side structure, respectively
P_{ij}	Subsystem-level problem in ATC
r_{ij}	Response fed back to the superior level in ATC
t_{ij}	Local objective assigned from the superior level in ATC
\mathit{v}	Lagrangian multiplier vector
\mathit{w}	Quadratic punishment weight vector
{\mathit{X}}_{\mathrm{c}},{\mathit{X}}_{\mathrm{r}},{\mathit{X}}_{\mathrm{s}}	Local design variable vector of the chassis structure, roof structure, and side structure, respectively
{\mathit{X}}_{ij}	Local design variable vector in ATC
{\mathit{X}}_{\mathrm{s}\mathrm{y}\mathrm{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
{\rho }_i,{\rho }_{\mathrm{o}} (i = 1,2,3)	Scaled density of each sub-structure and the base density, respectively
\varphi \left(\mathit{c}\right)	Penalty-based coordinated function

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 51805032).

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