单轴静压条件下高压多层陶瓷电容的容值变化

doi:10.12382/bgxb.2022.0103

摘要/Abstract

摘要：

针对高压陶瓷电容在外力作用下的容值漂移,提出外力作用下陶瓷电容容值变化的主要原因为材料介电性能的变化,而不是电容间距的变化。针对高压电容的应用场景,通过唯象热力学理论模型分析介质材料在相应场强下受外力时的介电性能变化,张应力将引起材料介电常数增大,压应力将引起材料介电常数减小。进一步的单轴试验结果与有限元仿真结果表明,平行于内电极方向的压力将使介质材料产生张应力,引起材料介电常数增大,导致电容容值升高;垂直于内电极方向的压力将使介质材料产生压应力,引起材料介电常数减小,导致电容容值降低。研究结果证明了通过材料唯象热力学理论模型来分析外力作用下陶瓷电容容值漂移的正确性,为高压陶瓷电容在更加复杂环境条件下的适应性分析与设计提供指导。

关键词: 高压电容, 容值, 唯象热力学模型, 静压

Abstract:

In view of the capacitance drift of the high-voltage ceramic capacitor under external force, it is proposed that the main reason for the capacitance change of the ceramic capacitor under external force is the change of dielectric properties of the material, rather than the change of capacitance spacing. For the application scenarios of the high-voltage capacitor, the change of the dielectric properties of dielectric materials under external force under certain field strengths is analyzed by the theoretical model of phenomenological thermodynamics. Tensile stress increases the dielectric constant of materials, and compressive stress decreases the dielectric constant of materials. The results of further uniaxial tests and finite element simulations show that: the pressure parallel to the inner electrode produce tensile stress, leading to the increase of the dielectric constant and rising capacitance of the dielectric material; the pressure perpendicular to the inner electrode causes the dielectric material to produce compressive stress, thus reducing the dielectric constant of the material as well as the capacitance. The research results prove that the theoretical model of phenomenological thermodynamics can be used to analyze the capacitance drift of the ceramic capacitor under external force, which may provide important guidance for the adaptability analysis and design of high-voltage ceramic capacitors under more complex environmental conditions.

Key words: high voltage capacitor, capacitance, phenomenological thermodynamic model, static pressure

刘波, 杨荷, 赵慧, 吴学星, 李华梅, 程祥利. 单轴静压条件下高压多层陶瓷电容的容值变化[J]. 兵工学报, 2023, 44(6): 1858-1866.

LIU Bo, YANG He, ZHAO Hui, WU Xuexing, LI Huamei, CHENG Xiangli. Capacitance Variation of High-Voltage Multilayer Ceramic Capacitors Under Uniaxial Static Pressure[J]. Acta Armamentarii, 2023, 44(6): 1858-1866.

图/表 21

图1 高压陶瓷电容外观结构示意图[12-13]

Fig.1 Structure diagram of high-voltage ceramic capacitor[12-13]

表1 内电极与介质材料的材料参数[14-15]

Table 1 Material parameters of the electrode and dielectric material[14-15]

材料	密度ρ/ (kg·m^-3)	弹性模量 E/GPa	泊松比 ν	屈服强度 σ_s/MPa	热膨胀系数/ (10^-6K^-1)
Ni	8900	207	0.31	690	13.5
BaTiO₃	6000	91	0.33		7.6

表2 吉布斯自由能的相关系数[18]

Table 2 Coefficients of Gibbs free energy[18]

相关系数	α₁/ (J·m·C^-2)	α₁₁/ (J·m⁵·C^-4)	α₁₂/ (J·m⁵·C^-4)	α₁₁₁/ (J·m⁹·C^-6)	α₁₁₂/ (J·m⁹·C^-6)	α₁₂₃/ (J·m¹³·C^-8)	α₁₁₁₁/ (J·m¹³·C^-8)	α₁₁₁₂/ (J·m¹³·C^-8)
数值	4.124×10⁵(T-115)	-2.097×10⁸	-7.974×10⁸	1.294×10⁹	-1.95×10⁹	-2.500×10⁹	3.863×10¹⁰	2.529×10¹⁰
相关系数	α₁₁₂₂/ (J·m¹³·C^-8)	α₁₁₂₃/ (J·m¹³·C^-8)	Q₁₁/ (m⁴·C^-2)	Q₁₂/ (m⁴·C^-2)	Q₄₄/ (m⁴·C^-2)	S₁₁/ (m²·N^-1)	S₁₂/ (m²·N^-1)	S₄₄/ (m²·N^-1)
数值	1.637×10¹⁰	1.367×10¹⁰	0.11	-0.043	0.059	8.3×10^-12	-2.5×10^-12	9.24×10^-12

图2 高压陶瓷电容施加外力示意图

Fig.2 Force diagram of high-voltage ceramic capacitor

图3 介质材料的相对介电常数随张应力的变化

Fig.3 Variation of relative dielectric constant of the dielectric material with tensile stress

图4 介质材料的相对介电常数随压应力的变化

Fig.4 Variation of relative dielectric constant of the dielectric material with compressive stress

图5 高压电容试验件示意图

Fig.5 Schematic diagram of capacitor test piece

图6 高压电容断面局部图

Fig.6 Partial section of high-voltage capacitor

图7 高压电容试验样品

Fig.7 Test pieces of the high-voltage capacitor

图8 压缩试验示意图

Fig.8 Schematic diagram of compression test

表3 不同方向施加的压力历程

Table 3 Histories of stress applied to capacitor from different directions

时间/min	平行于内电极方向的压力/kN	垂直于内电极方向的压力/kN	对应电容表面压力/MPa
0	0	0.45	0
5	2.55	0.90	10
10	5.10	1.80	20
15	10.20	2.70	40
20	15.30	3.60	60
25	20.40	0.45	80
30	2.55	5.40	100
35	30.60	0.45	120

图9 电容承受应力与电容容值随时间变化

Fig.9 Variations of stress and capacitance with pressure

图10 压力平行于内电极方向时电容容值随压力变化

Fig.10 Variation of capacitance with pressure parallel to the direction of inner electrode

图11 电容承受压力与容值随时间变化

Fig.11 Variations of stress and capacitance with pressure

图12 压力垂直于内电极方向时容值随压力变化

Fig.12 Variation of capacitance with pressure perpendicular to the direction of inner electrode

图13 简化高压电容局部几何模型

Fig.13 Simplified geometric model of the high-voltage capacitor

图14 电容在平行于内电极方向压力作用下的应力分布

Fig.14 Stress distribution of capacitor under pressure parallel to the inner electrode

图15 电容在垂直于内电极方向压力作用下的应力分布

Fig.15 Stress distribution of capacitor under pressure perpendicular to the inner electrode

表4 不同幅值的压力作用下介质材料的应力状态

Table 4 Stress state of the dielectric material under pressure of different amplitudes MPa

方向	压力/MPa
方向	10	20	40	60	80	100	120
平行于内电极	0.2	0.5	0.9	1.4	1.8	2.3	2.8
垂直于内电极	-8.2	-16.0	-32.0	-48.8	-65.1	-81.4	-97.3

图16 平行于内电极方向的压力作用下材料介电常数变化率计算结果与高压陶瓷电容容值变化率测试结果对比

Fig.16 Comparison of simulation results and test results of the change rate of dielectric constant of the material under pressure parallel to the inner electrode

图17 垂直于内电极方向的压力作用下材料介电常数变化率计算结果与高压陶瓷电容容值变化率测试结果对比

Fig.17 Comparison of simulation results and test results of the change rate of dielectric constant of the material under pressure perpendicular to the inner electrode

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