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锂离子电池过充时, 负极超过最大嵌锂浓度会发生表面析锂, 而正极则处于贫锂状态导致颗粒内部应力升高, 从而引发严重的寿命和安全问题. 本文基于单层电芯颗粒尺度, 建立了镍钴锰正极和石墨负极颗粒尺度下的三维电化学-力-热耦合过充模型, 能够准确地反映充电过程中析锂和应力-应变规律. 基于此, 分析了充电倍率和负极颗粒半径设计参数对负极表面析锂的影响. 结果表明: 高倍率下析锂的触发电压较低, 而低倍率下由于极化和温度较低的影响, 过充至4.8 V时析锂浓度较高; 相较于大粒径颗粒, 小颗粒表面呈现最大锂离子浓度高、析锂过电位低、平均冯·米塞斯应力大, 更容易发生析锂. 在应力方面, 探究了正极颗粒空间分布和热效应的影响, 定义了接触深度因子${J_{\text{r}}}$, 发现颗粒的接触深度与接触界面区域的应力成反比关系; 而且, 随着充电倍率增大, 温度相关电化学参数显著变化, 在计算颗粒层面应力时不能忽略. 相关结果可为优化电池设计和充电管理策略提供理论依据和指导.During overcharging of lithium-ion batteries, lithium plating can occur on the anode surface when the maximum lithium intercalation concentration is exceeded, while the cathode is in a lithium-poor state, which can result in shortened battery lifespan and safety. In this work, the geometric structure of the positive electrode particles is designed based on the tomography data, while the negative electrode particles are represented by spheres with different sizes. The homogenization method is used, with the carbon filler, binder and electrolyte regarded as a single porous conductive adhesive domain. Based on the main mechanism of lithium-ion battery overcharge, a coupled three-dimensional electrochemical-mechanical-thermal overcharge model on a particle scale is developed for NCM cathode and graphite anode. The coupled mathematical model consists of four parts, namely the electrochemical model, the lithium plating model, the thermal model and the stress-strain model. In terms of lithium precipitation, the particle radius parameter and charging rates are investigated. The results show that the lithium plating concentration of the particles near the separator is higher, following the “principle of proximity” , namely the sequence of lithium deintercalation is related to the migration path. The surface of anode particles with small particle size is more prone to lithium precipitation due to the high maximum lithium ion concentration on the surface of the particles, the low surface lithium precipitation overpotential, and the high average Von Mises stress. At high charging rate, fast charge transfer rate and ion diffusion rate result in a low voltage at the anode, triggering off lithium precipitation. At a low rate, polarization and low temperature can lead to the precipitation of more lithium on the surface of the anode particles. In terms of stress, the spatial distribution between particles and thermal effects are investigated. The ratio of the distance from the contact surface to the center of the particle to the particle radius is calculated and defined as the contact depth ($Jr$), in order to better describe the law of particle contact stress. It is shown that the contact depth between particles is inversely proportional to the stress on the contact area. When the heat generation effect is considered, the temperature of the battery rises faster with the increase of the charging rate. The electrochemical parameters related to temperature and the lithium concentration diffusion gradient increase significantly, and the influence of temperature on the particle stress is also more significant. The relevant results can provide theoretical basis and guidance for designing battery and optimizing charge strategies.
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图 1 模型几何图和耦合关系图 (a) 几何模型; (b) 网格; (c) 数学模型之间的耦合关系
Fig. 1. Geometric shape and coupling relationship diagram of the model: (a) Geometric shape; (b) mesh; (c) coupling relationship between mathematical models.
图 4 电压的仿真数据与实验数据的对比 (a) 充电至4.2 V时, 充电倍率为0.2C, 0.5C, 1C和1.5C的电压变化图; (b) 充电至4.8 V时, 充电倍率为0.2C, 0.5C的电压变化图
Fig. 4. Comparison between simulated and experimental data of voltage: (a) Voltage variation graphs charging to 4.2 V at charging rates of 0.2C, 0.5C, 1C and 1.5C; (b) voltage variation graphs charging to 4.8 V at charging rates of 0.2C and 0.5C.
图 5 (a) 负极颗粒表面析出锂金属浓度分布; (b) 负极颗粒表面析锂过电位绝对值分布; (c) 不同粒径颗粒位置示意(蓝色标记)
Fig. 5. (a) Lithium metal concentration on the particle surface; (b) the absolute value of overpotential of lithium plating on the particle surface; (c) position of particles with different sizes (the blue area).
图 6 在负极两个颗粒表面的过充过程 (a) 析出锂金属浓度; (b) 最大锂离子浓度; (c) 平均析锂过电位; (d) 平均冯·米塞斯应力
Fig. 6. Overcharging process on the surfaces of two negative particles: (a) Concentration of lithium metal precipitated; (b) maximum lithium ion concentration; (c) average lithium precipitation overpotential; (d) average von Mises stress.
图 7 不同倍率下的负极整个表面析出的锂金属浓度(a)和负极颗粒的温度(b)
Fig. 7. (a) Lithium metal concentration precipitated on the whole surface of the negative electrode and (b) the temperature of the negative electrode particles at different charging rates.
图 8 (a) 0.5C充电至4.8 V的正极应力-应变; (b) 0.5C充电至4.8 V的正极与负极应力
Fig. 8. (a) Stress-strain of the cathode charged to 4.8 V at 0.5C; (b) stress of the cathode and anode charged to 4.8 V at 0.5C.
图 9 0.5C充电至3.9 V, 4.2 V, 4.5 V, 4.8 V的正极颗粒应力-应变分布图
Fig. 9. Stress-strain distribution diagrams of cathode particles charged to 3.9 V, 4.2 V, 4.5 V and 4.8 V at 0.5C.
图 10 A, B, C和D四组颗粒的接触应力-应变(a)和位置(b)
Fig. 10. (a) Contact stress and strain of particles and (b) corresponding position in groups A, B, C and D.
图 11 0.2C (a), (c) 和0.5C (b), (d)倍率下, 正极颗粒平均冯·米塞斯应力, 以及温度相关系数随充电过程变化
Fig. 11. Average von Mises stress of positive electrode particles and temperature-dependent coefficient at 0.2C (a), (c) 和0.5C (b), (d).
表 1 电化学过充模型中的几何参数和结构
Table 1. Geometric parameters and structure of the electrochemical overcharge model.
参数 负极 隔膜 正极 长度L/μm 80 30 95 颗粒平均半径Rs_avg/μm 4.15 — 6.19 颗粒最大/最小半径Rsmax/min/μm 14.61/1.03 — 14.25/1.62 颗粒面积Ap/μm2 24997 — 20553 颗粒体积Vp/μm3 37892 — 36193 电池截面长度Lcross/μm 37 电池截面宽度Across/μm2 34.4 比表面积av/m–1 2.52×105 — 1.69×105 固相体积分数ψs 0.3833 — 0.2984 液相体积分数ψe 0.6167 — 0.7015 
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参数 负极 隔膜 正极 密度ρ/kg·m3 2300 1000 4530 杨氏模量E/ GPa 1047 78 泊松比nu 0.3 0.25 热膨胀系数αT/K–1 4.06×10–6 1.2×10–5 电池比热容Cp/(J·kg–1·K–1) 881 1260 1009.21 对流系数h/(W·m–2·K–1) 10
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参数 负极 隔膜 正极 固相电子电导率σs/(S·m–1) 100 — 3.8 固相有效电子电导率σs, eff/(S·m–1) ψs1.5σs ψs1.5σs 液相离子电导率σe/(S·m–1) ce(5.38-3.49×10–4ce+2.3×10–7ce2)2×10–4 液相有效离子电导率σe, eff/(S·m–1) ψe1.5σe 液相电子电导率σca/(S·m–1) 10 σe的活性能Ea, σe/(kJ·mol–1) 30 初始电解质浓度ce, 0/(mol·m–3) 1200 最大固相锂浓度cs, max/(mol·m–3) 24407 — 30017 化学计量系数x在1/0 SOC 0.115/0.98 — 0.92/0.222 容量比N/P 1.09 固相扩散系数Ds/(m2·S–1) 1.45×10–13 — 2×10–13 液相扩散系数De/(m2·S–1) $ {10^{[ - 8.43 - 54/(59.15 - 0.05{c_{\text{e}}}}}^{) - 2.2 \times {{10}^{ - 4 c_{\text{e}}^2}}]} $ 液相有效扩散系数De, eff/(m2·S–1) ψe1.5De De的活化能Ea, De/(kJ·mol–1) 72
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参数 负极 隔膜 正极 反应的传递系数αa, 1, αc, 1 0.5, 0.5 0.5, 0.5 反应速率常数k1, ref/(m·s–1) 2×10–11 2×10–11 k1的活化能Ea, k1/(kJ·mol–1) 71 45 析锂反应传递系数αa, 2, αc, 2 0.3, 0.7 析锂反应速率常数k2, ref/(m·s–1) 2.5×10–7 k2的活化能Ea, k2/(kJ·mol–1) 50 锂的摩尔质量Mpl/(kg·mol–1) 6.94×10–5 锂的密度ρpl/(kg·m–3) 534 电导率σfilm/(S·m–1) 6×10–5 析锂的平衡电位Eeq, Li/V 0
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