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 哈尔滨工程大学学报  2018, Vol. 39 Issue (4): 703-708  DOI: 10.11990/jheu.201612081 0

### 引用本文

ZHAO Jianhui, LEONID Grekhov, WANG Zhangjun, et al. Influence factors study on the electromagnetic force of high speed solenoid valves used in common rail injectors[J]. Journal of Harbin Engineering University, 2018, 39(4), 703-708. DOI: 10.11990/jheu.201612081.

### 文章历史

1. 哈尔滨工程大学 动力与能源工程学院, 黑龙江 哈尔滨 150001;
2. 莫斯科国立鲍曼技术大学 机械制造学院, 俄罗斯 莫斯科 115569

Influence factors study on the electromagnetic force of high speed solenoid valves used in common rail injectors
ZHAO Jianhui1, LEONID Grekhov2, WANG Zhangjun1, SHI Yong1, FAN Liyun1, MA Xiuzhen1, SONG Enzhe1
1. College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China;
2. College of Power Engineering, Bauman Moscow State Technical University, Moscow 115569, Russia
Abstract: To study the effects of key parameters on the electromagnetic force of a high speed solenoid valve (HSV) used in a common rail injector, a mathematical model for the electromagnetic force of HSV was established based on the principle of electromagnetic coupling. In this model, electromagnetic saturation phenomenon was considered. The agreement of simulation results with the experimental data confirmed the accuracy of the proposed model. Subsequently, an analysis of the structural parameters of HSV was performed on basis of the model. The results show that the changes in the electromagnetic force caused by driving current rely on the total magnetic reluctance of HSV and the range of the driving current. When the current is less than 4 A, the driving current primarily controls the increase in the electromagnetic force; When the current is higher than 4 A, the total reluctance becomes the determining factor that restricts the increase in the electromagnetic force. When the current is 10 A, the electromagnetic force decreases with an increase in the air gap and the degree of decrease gradually increases. The air gap directly affects the change in air gap reluctance and magnetic reluctance of the soft HSV material. The electromagnetic force increases with an increase in the number of coil turns, but the increased breadth gradually decreases; this is because the total reluctance of HSV to electromagnetic force increases with an increase in the number of coil turns.
Key words: electromagnetic force    B-H magnetization curve    driving current    high speed solenoid valve    high pressure common rail system    injector    common rail injector

1 数学模型 1.1 高速电磁阀数学模型和计算步骤

 Download: 图 1 共轨喷油器高速电磁阀三维简图 Fig. 1 The 3D schematic of HSV for common rail injector

 $\mathit{\Phi } = \frac{{N \cdot i}}{{{R_{{\rm{total}}}}}}$ (1)

 ${R_{{\rm{total}}}} = {R_{{\rm{gap1}}}} + {R_{{\rm{gap2}}}} + {R_{{\rm{arm}}}} + {R_{{\rm{iron}}}}$ (2)

 ${R_{{\rm{gap1}}}} = \frac{{{l_c}}}{{{\mu _0}{S_{{\rm{in}}}}}}$ (3)
 ${R_{{\rm{gap2}}}} = \frac{{{l_c}}}{{{\mu _0}{S_{{\rm{out}}}}}}$ (4)
 ${R_{{\rm{arm}}}} = \frac{{{r_g}}}{{2\mu {S_{{\rm{in}}}}}} + \frac{{{r_g}}}{{2\mu {S_{{\rm{out}}}}}} + \frac{{{l_d}}}{{\mu S''}}$ (5)
 ${R_{{\rm{iron}}}} = \frac{{{l_b}}}{{\mu {S_{{\rm{in}}}}}} + \frac{{{l_b}}}{{\mu {S_{{\rm{out}}}}}} + \frac{{{l_a}}}{{\mu S'}}$ (6)

 ${l_b} = \frac{{{r_1} + {r_2}}}{2}$ (7)
 ${l_a} = \frac{{{r_5} + {r_6} - {r_3} - {r_4}}}{4}$ (8)
 ${l_d} = {l_b}$ (9)
 ${l_c} = h$ (10)
 $S' = {\rm{ \mathsf{ π} }}\left( {{r_1} - {r_2}} \right)\frac{{{r_5} + {r_6} + {r_3} + {r_4}}}{4}$ (11)
 $S'' = {\rm{ \mathsf{ π} }}{r_8}\frac{{{r_5} + {r_6} + {r_3} + {r_4}}}{4}$ (12)
 ${S_{{\rm{in}}}} = \frac{{\rm{ \mathsf{ π} }}}{4}\left( {r_4^2 - r_3^2} \right)$ (13)
 ${S_{{\rm{out}}}} = \frac{{\rm{ \mathsf{ π} }}}{4}\left( {r_6^2 - r_5^2} \right)$ (14)

 ${F_{{\rm{mag}}}} = \frac{1}{2}\frac{{{\phi ^2}}}{{{\mu _0}{S_{{\rm{in}}}}}} + \frac{1}{2}\frac{{{\phi ^2}}}{{{\mu _0}{S_{{\rm{in}}}}}}$ (15)
1.2 B-H基本磁化曲线拟合公式

 $\left\{ \begin{array}{l} B = {p_1}\sqrt {\ln \left( {{p_2}H + 1} \right)} \\ {p_1} = {B_1}/\sqrt {\ln \left( {{p_2}H + 1} \right)} \\ {p_2} = \frac{1}{{{H_2} - {H_1}}}{{\rm{e}}^{B_2^2/B_1^2}} \end{array} \right.$ (16)

 Download: 图 3 B-H磁化曲线示意图 Fig. 3 Schematic diagram of B-H magnetization curve

 Download: 图 4 式(16)计算值和试验数据的对比 Fig. 4 Comparison between simulated by Eq(16) and experimental results of B-H curve
1.3 高速电磁阀电磁力数学模型的验证

0.10 mm和0.12 mm的气隙是目前MAN公司和WARTSILA公司船用共轨喷油器高速电磁阀的气隙宽度，因此选用上述两种气隙下的电磁力试验数据进行上述电磁阀静态电磁力数学模型的验证。从图 5看到，在0.1 mm和0.12 mm工作气隙下，在驱动电流1~18 A范围内，本文建立的高速电磁阀电-磁数学模型计算结果和试验值吻合较好，计算值和试验值最大偏差在可接受的范围内，这说明上述建立的电磁阀电磁力数学模型在预测电磁力方面的准确性。

 Download: 图 5 电磁力计算值和试验结果对比 Fig. 5 Comparison between simulated and experimental results of electromagnetic force
2 电磁力影响因素分析和讨论

2.1 驱动电流的影响

 Download: 图 6 驱动电流对电磁力增加量的影响 Fig. 6 Effect of i on electromagnetic force increment

 Download: 图 7 驱动电流对总磁阻的影响 Fig. 7 Effect o1f i on total magnetic reluctance

2.2 工作气隙的影响

 Download: 图 8 工作气隙对电磁阀电磁力和总磁阻的影响 Fig. 8 Effect of working air gap on electromagnetic force and total magnetic reluctance

 Download: 图 9 工作气隙对软磁材料磁阻和气隙内磁阻的影响 Fig. 9 Effect of working air gap on magnetic reluctance in soft material and in air gap
2.3 线圈匝数的影响

 Download: 图 10 线圈匝数对电磁力和总磁阻的影响 Fig. 10 Effect of coil turn on electromagnetic force and total magnetic reluctance

3 结论

1) 建立了考虑非线性磁化过程和磁饱和现象的共轨喷油器高速电磁阀电-磁数学模型，通过与试验数据对比，证明所建数学模型的准确性。

2) 驱动电流对高速电磁阀电磁力影响显著，驱动电流对电磁力的贡献率在不同的电流范围内是不同的。当驱动电流小于4 A时，电磁阀总磁阻较小，软磁材料不易发生磁饱和现象，驱动电流成为电磁力变化的主要影响因素；当驱动电流大于4 A时，尽管总磁通的增加是电磁力增大的主要因素，但电磁阀总磁阻的增加使得电磁力减小的程度逐渐增大，这导致电磁阀电磁力增加量逐渐减小。

3) 工作气隙越小, 电磁力越大, 但过小的气隙阻碍高压燃油从控制室的泄放, 过大的工作气隙降低电磁阀的电磁力, 需合理选择电磁阀工作气隙。

4) 随线圈匝数的增加，电磁阀的电磁力不断增大，但其增大的程度逐渐减小。在线圈匝数变化的过程中，总磁通量的变化程度和总磁阻的变化程度共同决定电磁力随线圈匝数的变化规律。在满足电磁力要求的前提下，尽量选择较小的线圈匝数。

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