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Crushing stress and vibration fatigue-life optimization of a battery-pack system

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Abstract

The mechanical failure of battery-pack systems (BPSs) under crush and vibration conditions is a crucial research topic in automotive engineering. Most studies evaluate the mechanical properties of BPSs under a single operating condition. In this study, a dual-objective optimization method based on non-dominated sorting genetic algorithm II (NSGA-II) is proposed to evaluate the crushing stress of BPS modules and the vibration fatigue life of the BPS. This method can obtain better combinations of the thicknesses of the BPS components, which helps engineers achieve robust and efficient designs. First, a nonlinear finite element (FE) model of a BPS is developed and experimentally verified. The crush and vibration simulations are performed, and the FE analysis data are obtained. Second, two third-order response surface models are created to characterize the relationship between the input (thicknesses of the BPS components) and the output (crushing stress of the BPS modules and vibration fatigue life of the BPS). Finally, a linear weighting model and an NSGA-II model are used to conduct dual-objective optimization. The solution of the linear weighting method and the non-dominated Pareto solution set of the thicknesses of the BPS components are obtained and compared. Furthermore, a reasonable interval in the Pareto frontier is defined and considered the best solution to the dual-objective optimization problem. Therefore, the reliability of the BPS is improved to ensure the safety of electric vehicles in crushing and vibration environments. This method offers an effective solution to the problem of evaluating the mechanical responses of BPSs under various operating conditions. It can be used to generate a robust design for safe and durable BPSs.

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Funding

This work was supported by the National Natural Science Foundation of China (Project Nos. 12072050 and 12211530029).

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Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, China

    Xiaoxi Zhang, Yongjun Pan, Haifeng Du & Binghe Liu

  2. China Automotive Engineering Research Institute, Chongqing, 401122, China

    Yue Xiong

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  1. Xiaoxi Zhang
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Correspondence to Yongjun Pan.

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The datasets analysed during the current study can be downloaded from the figshare repository, and are available from the authors upon reasonable request, https://doi.org/10.6084/m9.figshare.20741848.v1

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Appendix

Appendix

$$\begin{aligned} f_{1}&=-147.192x_{1}^{3}+161.012 x_{2}^{3}+441.474 x_{3}^{3}\nonumber \\&\quad -134.654 x_{4}^{3} -120.249 x_{5}^{3}+43.761 x_{6}^{3} \nonumber \\&\quad +888.905 x_{1}^{2}-1215.125 x_{2}^{2}-1291.753 x_{3}^{2}\nonumber \\&\quad +613.358 x_{4}^{2} +660.552 x_{5}^{2}-212.637 x_{6}^{2} \nonumber \\&\quad -1784.155 x_{1}+3036.495 x_{2}+1187.812 x_{3}\nonumber \\&\quad -922.679 x_{4} -1160.948 x_{5}+292.376 x_{6} \nonumber \\&\quad +7.068 x_{1} x_{2}+5.822 x_{1} x_{3}-7.018 x_{1} x_{4}\nonumber \\&\quad -5.732 x_{1} x_{5}-1.139 x_{1} x_{6}-3.502 x_{2} x_{3} \nonumber \\&\quad -1.069 x_{2} x_{4}-9.197 x_{2} x_{5}+14.158 x_{2} x_{6}\nonumber \\&\quad +13.789 x_{3} x_{4}+3.353 x_{3} x_{5}+9.885 x_{3} x_{6}\nonumber \\&\quad -6.808 x_{4} x_{5}+8.808 x_{4} x_{6}-1.226 x_{5} x_{6}-690.357 \end{aligned}$$
(A.1)
$$\begin{aligned} f_{2}&=0.526x_{1}^{3}-0.215 x_{2}^{3}-0.429 x_{3}^{3}-0.094 x_{4}^{3}-0.759 x_{5}^{3}\nonumber \\&\quad -1.080 x_{6}^{3} -3.069 x_{1}^{2}+2.175 x_{2}^{2} \nonumber \\&\quad +2.219 x_{3}^{2}+0.555 x_{4}^{2}+4.287 x_{5}^{2}+5.785 x_{6}^{2} +5.861 x_{1}\nonumber \\&\quad -5.238 x_{2}-3.410 x_{3}-1.099 x_{4}\nonumber \\&\quad -8.562 x_{5}-10.676 x_{6} +0.343 x_{1} x_{2}-0.139 x_{1} x_{3}\nonumber \\&\quad -0.059 x_{1} x_{4}-0.056 x_{1} x_{5}-0.185 x_{1} x_{6} \nonumber \\&\quad -0.660 x_{2} x_{3}-0.115 x_{2} x_{4}-0.151 x_{2} x_{5}-0.365 x_{2} x_{6}\nonumber \\&\quad +0.116 x_{3} x_{4}+0.184 x_{3} x_{5}\nonumber \\&\quad +0.374 x_{3} x_{6}+0.011 x_{4} x_{5}+0.056 x_{4} x_{6}\nonumber \\&\quad +0.313 x_{5} x_{6}+17.838 \end{aligned}$$
(A.2)
$$\begin{aligned} f_{1}^{*}&=-0.878x_{1}^{3}+0.960 x_{2}^{3}+2.633 x_{3}^{3}-0.803 x_{4}^{3}\nonumber \\&\quad -0.717 x_{5}^{3}+0.261 x_{6}^{3} +1.231 x_{1}^{2}-1.328 x_{2}^{2} \nonumber \\&\quad -4.436 x_{3}^{2}+1.094 x_{4}^{2}+0.909 x_{5}^{2}-0.353 x_{6}^{2} \nonumber \\&\quad -0.357 x_{1}+0.476 x_{2}+1.717 x_{3}-0.158 x_{4} \nonumber \\&\quad -0.333 x_{5}+0.460 x_{6} -0.105 x_{1} x_{2}-0.087 x_{1} x_{3}\nonumber \\&\quad +0.105 x_{1} x_{4}+0.085 x_{1} x_{5}+0.017 x_{1} x_{6} \nonumber \\&\quad +0.052 x_{2} x_{3}+0.016 x_{2} x_{4}+0.137 x_{2} x_{5}-0.211 x_{2} x_{6}\nonumber \\&\quad -0.206 x_{3} x_{4}-0.050 x_{3} x_{5} \nonumber \\&\quad -0.147 x_{3} x_{6}+0.102 x_{4} x_{5}-0.131 x_{4} x_{6}\nonumber \\&\quad +0.018 x_{5} x_{6}+0.159 \end{aligned}$$
(A.3)
$$\begin{aligned} f_{2}^{*}&=0.030 x_{1}^{3}-0.012 x_{2}^{3}-0.025 x_{3}^{3}-0.005 x_{4}^{3}\nonumber \\&\quad -0.044 x_{5}^{3}-0.062 x_{6}^{3} -0.058 x_{1}^{2}-0.063 x_{2}^{2} \nonumber \\&\quad -0.097 x_{3}^{2}-0.011 x_{4}^{2}+0.039 x_{5}^{2}+0.007 x_{6}^{2}\nonumber \\&\quad +0.075 x_{1}+0.224 x_{2}-0.284 x_{3}-0.075 x_{4} \nonumber \\&\quad -0.093 x_{5}-0.206 x_{6} -0.050 x_{1} x_{2}+0.020 x_{1} x_{3}\nonumber \\&\quad +0.008 x_{1} x_{4}+0.008 x_{1} x_{5}+0.027 x_{1} x_{6} \nonumber \\&\quad +0.095 x_{2} x_{3}+0.017 x_{2} x_{4}+0.022 x_{2} x_{5}\nonumber \\&\quad +0.053 x_{2} x_{6}-0.017 x_{3} x_{4}-0.027 x_{3} x_{5} \nonumber \\&\quad -0.054 x_{3} x_{6}-0.002 x_{4} x_{5}-0.008 x_{4} x_{6}\nonumber \\&\quad -0.045 x_{5} x_{6}+0.843 \end{aligned}$$
(A.4)

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Zhang, X., Xiong, Y., Pan, Y. et al. Crushing stress and vibration fatigue-life optimization of a battery-pack system. Struct Multidisc Optim 66, 48 (2023). https://doi.org/10.1007/s00158-023-03510-2

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