Deformation prediction and topology optimization of end plates in vanadium flow battery stacks

doi:10.3785/j.issn.1006-754X.2026.05.183

Chinese Journal of Engineering Design

2026, Vol. 33

Issue (2): 242-253 DOI: 10.3785/j.issn.1006-754X.2026.05.183

Optimization Design

Deformation prediction and topology optimization of end plates in vanadium flow battery stacks

You WANG¹(

),Yongheng ZHAO¹,Xiaohu SHI²,Longhai YU²,Yanzhao SUN³

^1.School of Mechanical Engineering, Hubei University of Arts and Science, Xiangyang 441053, China
^2.Dali Energy Storage Technology Hubei Co. , Ltd. , Xiangyang 441000, China
^3.School of Automotive and Traffic Engineering, Hubei University of Arts and Science, Xiangyang 441053, China

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Abstract

To enhance the energy density of high-power vanadium flow battery stacks and address the issues of excessive structural mass coupled with the absence of efficient and precise design methods for end plates, a design method for the end plate of vanadium battery flow stacks is proposed, which integrates deformation prediction, lightweight design and manufacturing process constraints. Firstly, a theoretical method for calculating end plate pressure loads was proposed, and the numerical analysis models for springs and studs were constructed. Then, a numerical simulation method for predicting mechanical deformation of the end plate was established by integrating the complete assembly processes, including pressure loading, spring pre-tightening, stud locking and pressure unloading. Experimental results validated that this method had high prediction accuracy. Subsequently, by introducing manufacturing process and assembly displacement constraints, a topology optimization method enabling efficient iterative computation for lightweight end plate design was developed based on the variable density method. The optimized end plate yielded a 44.00% decrease in mass, maintained stress within the strength requirements, and exhibited a more uniform displacement distribution. Finally, the spatial distribution law of stud preload and the influence law of end plate configuration on stud preload and spring compression deformation were revealed. The results showed that the closer the distance to the end plate symmetry center, the greater the stud preload, with the maximum variation rate being 36.06%; the end plate configuration had a smaller influence on the spring compression deformation. The proposed method can achieve efficient lightweight design of vanadium flow battery stack end plates while meeting strength and stiffness requirements, which has significant engineering application value.

Key words： vanadium flow battery end plate deformation behavior numerical simulation topology optimization

Received: 02 September 2025 Published: 28 April 2026

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	You WANG
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	Yanzhao SUN

Cite this article:

You WANG,Yongheng ZHAO,Xiaohu SHI,Longhai YU,Yanzhao SUN. Deformation prediction and topology optimization of end plates in vanadium flow battery stacks. Chinese Journal of Engineering Design, 2026, 33(2): 242-253.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.183 OR https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/242

钒电池电堆端板的变形预测与拓扑优化

为提升大功率钒电池电堆的能量密度，以及解决其端板结构质量大、缺乏高效精确设计方法的问题，提出了一种集变形预测、轻量化设计及制造工艺约束于一体的钒电池电堆端板设计方法。首先，提出了端板压力载荷理论计算方法，构建了弹簧及螺柱的数值分析模型，建立了耦合压力加载、弹簧预紧、螺柱锁止和压力卸载等装配过程的端板受力变形数值模拟预测方法，并通过试验证实了该方法具有较高的预测精度。随后，通过引入制造工艺及装配位移约束，建立了基于变密度法的端板拓扑优化方法，实现了端板轻量化设计的高效迭代计算。优化后端板的质量减小了44.00%，应力满足强度要求，且位移分布更均匀。最后，揭示了螺柱预紧力的空间分布规律以及端板构型对螺柱预紧力与弹簧压缩变形的影响规律。结果显示：距离端板对称中心越近，螺柱预紧力越大，最大变化率为36.06%；端板构型对弹簧压缩变形的影响较小。所提出的方法可在满足强度与刚度要求的前提下，实现钒电池电堆端板的高效轻量化设计，具备重要的工程应用价值。

关键词： 钒电池, 端板, 变形行为, 数值模拟, 拓扑优化

Fig.1 Quarter geometric model of end plate in initial configuration

参数	数值	参数	数值
$ρ$ /( $k g / m 3$ )	2 700	n	0.79
$E$ /GPa	71.0	m	1.34
$v$	0.33	$θ m$ /K	877.6
$D$ /MPa	284.1	$θ t$ /K	293.0
B	247.83

Table 1 Material parameters of 6061-T6 aluminum alloy

Fig.2 Numerical analysis model for spring stiffness

Fig.3 Spring stiffness curve

Fig.4 Numerical simulation model for mechanical deformation of end plate in initial configuration

Fig.5 Stress distribution contour plots of end plate in initial configuration

Fig.6 Displacement distribution contour plots of end plate in initial configuration

Table 2 Numerical simulation results of end plate in initial configuration

Fig.7 Quarter geometric model of end plate in pre-optimized configuration

Table 3 Topology optimization results of end plate in pre-optimized configuration

Fig.8 Stress distribution contour plot of end plate in optimized configuration

Fig.9 Displacement distribution contour plots of end plate in optimized configuration

Fig.10 Overall structure of end plate in optimized configuration

Fig.11 Variation curves of stud preload of end plates with different configurations

Table 4 Stud preload after pressure unloading and its change rate

Fig.12 Variation curves of spring compression of end plates with different configurations

Fig.13 Variation curves of spring compression during pressure unloading

Table 5 Spring compression after pressure unloading and its change rate


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