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Crashworthiness-based multi-objective integrated optimization of electric vehicle chassis frame

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Abstract

Chassis frame of electric vehicle contains several thin-walled tube structures that can provide an important component for installing the power unit and supporting the body in white of vehicle. Thus, design a chassis frame is a multi-objective optimization and multi-parameter problem. To address it, the contributions of design variables to the performance indicators of chassis frame are studied first, and obtained the optimal design variables. The effects of the design parameters on the objective responses are analyzed based on a polynomial response surface model. Moreover, to determine optimal solution between the conflicting performance indicators of the chassis frame, an integrated approach based on lightweight and crashworthiness is presented to analysis the performance and determine the Pareto fronts. In addition, the optimal solution is acquired from the Pareto fronts by the grey relational analysis and game theory. Experiments corresponding to the numerical analysis are performed to verify the feasibility of the optimized strategy and the performance of the optimized chassis frame structure. Results show that according to the optimal parameters of chassis frame, the lightweight performance can be improved significantly, while the linear performance and crashworthiness performance of chassis frame are ensured.

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Acknowledgements

This research work was supported by the national key research and development project of china (2016YFB0101601) and Graduate innovation fund of jilin university (101832020CX131).

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Authors and Affiliations

  1. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, China

    Shuang Wang & Dengfeng Wang

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  1. Shuang Wang
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Correspondence to Dengfeng Wang.

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Appendix

Appendix

The cubic polynomial function of M can be expressed as:

$$ \begin{aligned} M =& {3353}.{27} + {22}.0{5}x_{{1}} + {12}.{75}x_{{3}} \\&+\, {275}.{14}x_{{4}} - {418}.{63}x_{{6}} + \ldots\\& +\, { 2}.{69}x_{1}^{3} + \, 0.{92}x_{3}^{3} + {3}.{3}x_{4}^{3}\\& -\, {4}.{78}x_{6}^{3} - {6}.{28}x_{12}^{3} + {17}.{96}x{3 13}\\& -\, {1}.{9}x_{26}^{3} - {1}.0{4}x_{27}^{3} \end{aligned} $$
(17)

The cubic polynomial function of fb can be depicted as:

$$ \begin{aligned} f_{b} = &{1572}.{33} + {1}0x_{{1}} + {3}.0{8}x_{{3}}\\& +\, {266}.{13}x_{{4}} - {76}.{78}x_{{6}} + \ldots\\& +\, 0.{76}x_{1}^{3} + \, 0.{73}x_{3}^{3} + {2}.{65}x_{4}^{3} \\&-\, 0.{49}x_{6}^{3} - {5}.{35}x_{12}^{3} + {9}.{93}x_{13}^{3}\\& -\, 0.{43}x_{26}^{3} + {4}.{13}x_{27}^{3} \end{aligned} $$
(18)

The cubic polynomial function of ft can be given as:

$$ \begin{aligned} f_{t} = &{247}0.{99} + {9}.{43}x_{{1}} - {1}.{26}x_{{3}}\\& +\, {226}.{29}x_{{4}} - {3}0{6}.{97}x_{{6}} + \ldots\\& +\, {1}.{37}x_{1}^{3} - {5}.{23}x_{3}^{3} - 0.0{5}x_{4}^{3}\\& -\, {4}.{48}x_{6}^{3} - {2}.0{2}x_{12}^{3} + {23}.{44}x_{13}^{3} \\&-\, {2}.{64}x_{26}^{3} + {3}.{13}x_{27}^{3} \end{aligned} $$
(19)

The cubic polynomial function of St can be written as:

$$ \begin{aligned} S_{t} =& -\, {55584}.{34} + {5385}.{13}x_{{1}} + {1964}.{83}x_{{3}}\\& -\, {4626}.{93}x_{{4}} + {1523}0.{81}x_{{6}} + \ldots\\& +\, {445}.{98}x_{1}^{3} + {149}.{54}x_{3}^{3} + {986}.{54}x_{4}^{3}\\& -\, {184}.{33}x_{6}^{3} - {9}0{3}.{94}x_{12}^{3} + {159}0.{76}x_{13}^{3}\\& +\, {166}.{23}x_{26}^{3} + {246}.{98}x_{27}^{3} \end{aligned} $$
(20)

The cubic polynomial function of Sb can be depicted as:

$$ \begin{aligned} S_{b} =& -\, {46748}.{23} + {5448}.{98}x_{{1}} + {5673}.{71}x_{{3}} \\&+\, {23}00{4}.{44}x_{{4}} + {28437}.{33}x_{{6}} + \ldots \\&+\, {673}.{16}x_{1}^{3} + {598}.{22}x_{3}^{3} + {1385}.{24}x_{4}^{3}\\& +\, {87}0.{47}x_{6}^{3} - {1826}.{44}x_{12}^{3} - {796}.{43}x_{13}^{3}\\& -\, {17}0.{5}0x_{26}^{3} + {17}0{1}.0{8}x_{27}^{3} \end{aligned} $$
(21)

The cubic polynomial function of Bd can be expressed as:

$$ \begin{aligned} B_{d} = &- \,{2}00{6}.{27} - {634}.{96}x_{{1}} - {588}.{27}x_{{3}}\\& -\, {4722}.{71}x_{{4}} - {5575}.{32}x_{{6}} + \ldots \\&-\, {71}.{15}x_{1}^{3} - {69}.{76}x_{3}^{3} - {92}.{3}x_{4}^{3} \\&-\, {74}.{71}x_{6}^{3} + {39}.{36}x_{12}^{3} - {414}.{83}x_{13}^{3}\\& +\, {62}.{25}x_{26}^{3} - {2}.{54}x_{27}^{3} \end{aligned} $$
(22)

The cubic polynomial function of Al can be given as:

$$ \begin{aligned} A_{l} =& {82}0.0{7} - {17}.{56}x_{{1}} - {14}.{19}x_{{3}} \\&+\, {1}.{51}x_{{4}} + {254}.{94}x_{{6}} + \ldots \\&-\, {1}.{65}x_{1}^{3} - {1}.{25}x_{3}^{3} - {3}.{29}x_{4}^{3}\\& +\, {4}.{14}x_{6}^{3} + {3}.{59}x_{12}^{3} - {11}.{15}x_{13}^{3}\\& +\, 0.{62}x_{26}^{3} - {5}.{95}x_{27}^{3} \end{aligned} $$
(23)

The cubic polynomial function of Ar can be written as:

$$ \begin{aligned} A_{r} =& {398}.{59} - {3}.0{8}x_{{1}} - {6}.{84}x_{{3}} \\&+\, {4}.{41}x_{{4}} + {254}.{67}x_{{6}} + \ldots \\&- \,0.{35}x_{1}^{3} - 0.{51}x_{3}^{3} - 0.{26}x_{4}^{3}\\& +\, {3}.{13}x_{6}^{3} - 0.{82}x_{12}^{3} - {15}.{2}0x_{13}^{3} \\&+\, 0.{99}x_{26}^{3} - {1}.{41}x_{27}^{3} \end{aligned} $$
(24)

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Wang, S., Wang, D. Crashworthiness-based multi-objective integrated optimization of electric vehicle chassis frame. Archiv.Civ.Mech.Eng 21, 103 (2021). https://doi.org/10.1007/s43452-021-00242-2

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