Simulation Modeling of Single-pulse Electrical Discharge Bubble Behaviors

doi:10.3969/j.issn.1004-132X.2026.05.007

Abstract

Abstract:

Based on the underwater explosion theory and the ideal gas equation of state， considering the energy loss caused by the wall resistance when the fluid flows in the machining gaps， and combining the maximum expansion volume and the steady-state volume of the bubbles observed in the experiments， a calculation method was determined for the initial temperature， pressure and volume of the bubbles generated by a single-pulse EDM within the inter-electrode gaps. A simulation model for single-pulse discharge bubble behaviors was further developed by using the volume of fluid（VOF） method. The results of the single-pulse discharge bubble observation experiments show that the simulation results are in good agreement with the experimental ones.Using this model， the influences of peak current and pulse duration on bubble evolution behaviors were analyzed. Finally， based on the experimental data obtained from high-speed camera observations， the calculation formulas for the maximum expansion volume， expansion time and steady-state volume of the bubbles were derived under different peak currents and pulse durations. Moreover， the simulation calculation of the single-pulse discharge bubble behaviors may be carried out without observing the experiments.

Key words: electrical discharge machining（EDM）, single-pulse, bubble, flow field

摘要：

基于水下爆炸理论和理想气体状态方程，考虑了流体在加工间隙内流动时因壁面阻力导致的能量损失，结合实验观测的气泡最大膨胀体积和稳态体积，确定了极间间隙内单脉冲电火花放电产生气泡的初始温度、压力和体积的计算方法。进一步采用流体体积（VOF）法构建了单脉冲放电产生气泡行为的仿真模型，单脉冲放电气泡观测实验结果表明仿真与实验结果吻合良好。利用该模型分析了峰值电流和脉冲宽度对气泡演变行为的影响。最后基于高速摄像机观测实验数据拟合得出了不同峰值电流和脉冲宽度下气泡最大膨胀体积、膨胀时间及稳态体积的计算公式，且无需观测实验即可对单脉冲放电气泡行为进行仿真计算。

关键词: 电火花加工, 单脉冲, 气泡, 流场

CLC Number:

TG661

WANG Jin, QIAO Chunkai, JIA Zhixin, HE Hu. Simulation Modeling of Single-pulse Electrical Discharge Bubble Behaviors[J]. China Mechanical Engineering, 2026, 37(5): 1072-1081.

王津, 乔春凯, 贾志新, 何虎. 单脉冲电火花放电气泡行为仿真建模[J]. 中国机械工程, 2026, 37(5): 1072-1081.

Figures/Tables 22

Fig.1 Schematic diagram of the experimental setup

Tab.1 Parameters of ITO conductive glass

型号	IT0导电玻璃
尺寸/（mm×mm×mm）	20×20×1.1
方阻/Ω	10
膜层厚度/nm	185
透光率/%	≥84

Fig.2 Experimental diagram of bubble steady-state observation（pulse duration of 60 μs， peak current of 10 A， inter-electrode gap of 40 μm）

Fig.3 Geometric model of the inter-electrode gap in parallel plate electrical discharge machining

Tab.2 Solver algorithm settings

算法	设定值
求解器	压力基、隐式、瞬态
多相流	相数：2；VOF策略：显式、激活体积力；层流
控制方程	开启能量方程
求解控制参数	PISO； Discretization； PRESTO！； QUICK； Geometric
收敛判据	残差：10 $- 6$
迭代计算参数	库朗数：2；各时间步最大迭代次数：40

Tab.2 Solver algorithm settings

算法	设定值
求解器	压力基、隐式、瞬态
多相流	相数：2；VOF策略：显式、激活体积力；层流
控制方程	开启能量方程
求解控制参数	PISO； Discretization； PRESTO！； QUICK； Geometric
收敛判据	残差：10 $- 6$
迭代计算参数	库朗数：2；各时间步最大迭代次数：40

Fig.4 Comparison chart of the simulation and experimental results of the electric spark bubble between parallel plates

Fig.5 Curve of bubble volume varying with time

Fig.6 Curve of bubble volume varying with time when the peak current is as 5 A

Fig.7 Curve of bubble volume varying with time when the peak current is as 10 A

Fig.8 Curve of bubble volume varying with time when the peak current is as 15 A

Fig.9 Curve graph of bubble expansion time varying with peak current（pulse duration of 90 μs）

Fig.10 Curve of bubble volume varying with time when the pulse duration is as 60 μs

Fig.11 Curve of bubble volume varying with time when the pulse duration is as 120 μs

Fig.12 Curve of bubble volume varying with time when the pulse duration is as 180 μs

Fig.13 Curve graph of bubble expansion time varying with pulse duration（peak current of 10 A）

Fig.14 Relationship curve among different peak currents and the volume of electric spark bubbles in the inter-electrode gap（pulse duration of 90 μs）

Fig.15 Relationship curve among different pulse durations and the volume of electric spark bubbles in the inter-electrode gap（peak current of 10 A）

Fig.16 Fitting results of bubble volume and electrical parameters

Fig.17 Fitting results of bubble expansion time and electrical parameters

Tab.3 Experimental results and errors of bubble expansion time verification

实验组号	实验条件（峰值电流，脉冲宽度）	实验测量结果/μs	公式计算结果/μs	误差/%
1	I=1 A， $t o n$ =5 μs	208	199.936	$-$ 4.84
2	I=2 A， $t o n$ =15 μs	230	219.578	$-$ 4.56
3	I=5 A， $t o n$ =60 μs	369	376	2.17
4	I=10 A， $t o n$ =110 μs	378	396	4.76
5	I=12 A， $t o n$ =170 μs	409	401	$-$ 2.20
6	I=15 A， $t o n$ =180 μs	414	403	$-$ 2.66

Tab.3 Experimental results and errors of bubble expansion time verification

实验组号	实验条件（峰值电流，脉冲宽度）	实验测量结果/μs	公式计算结果/μs	误差/%
1	I=1 A， $t o n$ =5 μs	208	199.936	$-$ 4.84
2	I=2 A， $t o n$ =15 μs	230	219.578	$-$ 4.56
3	I=5 A， $t o n$ =60 μs	369	376	2.17
4	I=10 A， $t o n$ =110 μs	378	396	4.76
5	I=12 A， $t o n$ =170 μs	409	401	$-$ 2.20
6	I=15 A， $t o n$ =180 μs	414	403	$-$ 2.66

Table.4 Experimental results and errors of the verification for the maximum expansion volume of bubbles

实验组号	实验条件（峰值电流，脉冲宽度）	实验测量结果/mm³	公式计算结果/mm³	误差/%
1	I=1 A， $t o n$ =5 μs	0.051 56	0.046 68	$-$ 9.46
2	I=2 A， $t o n$ =15 μs	0.096 68	0.091 95	$-$ 4.89
3	I=5 A， $t o n$ =60 μs	0.668 92	0.637 11	$-$ 4.76
4	I=10 A， $t o n$ =110 μs	1.863 86	2.016 76	8.20
5	I=12 A， $t o n$ =170 μs	2.623 85	2.754 27	4.97
6	I=15 A， $t o n$ =180 μs	4.216 26	3.915 90	$-$ 7.12

Table.4 Experimental results and errors of the verification for the maximum expansion volume of bubbles

实验组号	实验条件（峰值电流，脉冲宽度）	实验测量结果/mm³	公式计算结果/mm³	误差/%
1	I=1 A， $t o n$ =5 μs	0.051 56	0.046 68	$-$ 9.46
2	I=2 A， $t o n$ =15 μs	0.096 68	0.091 95	$-$ 4.89
3	I=5 A， $t o n$ =60 μs	0.668 92	0.637 11	$-$ 4.76
4	I=10 A， $t o n$ =110 μs	1.863 86	2.016 76	8.20
5	I=12 A， $t o n$ =170 μs	2.623 85	2.754 27	4.97
6	I=15 A， $t o n$ =180 μs	4.216 26	3.915 90	$-$ 7.12

Table.5 Experimental results and errors of bubble steady-state volume verification

实验组号	实验条件（峰值电流，脉冲宽度）	实验测量结果/mm³	公式计算结果/mm³	误差/%
1	I=1 A， $t o n$ =5 μs	0.013 95	0.012 71	$-$ 8.89
2	I=2 A， $t o n$ =15 μs	0.039 56	0.037 06	$-$ 6.31
3	I=5 A， $t o n$ =60 μs	0.566 48	0.542 89	$-$ 4.16
4	I=10 A， $t o n$ =110 μs	1.483 70	1.575 41	6.18
5	I=12 A， $t o n$ =170 μs	1.836 26	1.938 09	5.55
6	I=15 A， $t o n$ =180 μs	2.369 64	2.297 42	$-$ 3.05

Table.5 Experimental results and errors of bubble steady-state volume verification

实验组号	实验条件（峰值电流，脉冲宽度）	实验测量结果/mm³	公式计算结果/mm³	误差/%
1	I=1 A， $t o n$ =5 μs	0.013 95	0.012 71	$-$ 8.89
2	I=2 A， $t o n$ =15 μs	0.039 56	0.037 06	$-$ 6.31
3	I=5 A， $t o n$ =60 μs	0.566 48	0.542 89	$-$ 4.16
4	I=10 A， $t o n$ =110 μs	1.483 70	1.575 41	6.18
5	I=12 A， $t o n$ =170 μs	1.836 26	1.938 09	5.55
6	I=15 A， $t o n$ =180 μs	2.369 64	2.297 42	$-$ 3.05

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