# Optimization Design of Magnetic Isolation Ring Position in AC Solenoid Valves for Dynamic Response Performances

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## Abstract

**:**

## 1. Introduction

## 2. Modeling of the AC Solenoid Valve

_{0}is the offset voltage in volts, V

_{a}is the peak amplitude in volts, IFreq is the signal frequency, T

_{d}is the delay time in seconds, $Phase$ is the signal phase delay, and Df is the damping factor in 1/seconds.

_{b}is the known voltage source between the two conductors,

**j**is the total current density to be solved for, σ is the conductivity, l is the thickness of the model, and

_{t}**A**is the magnetic vector potential.

^{−5}. The specific value is obtained by experimental measurement.

**F**has a ϕ-component only, these operators are defined as

**F**is a vector quantity.

**A**. The time-dependent magnetic equation is expressed as

_{c}is the coercivity of the permanent magnet, $v$ is the velocity of the moving parts,

**A**is the magnetic vector potential,

**V**is the electric potential, σ is the reluctance, and

**J**is the current source density.

_{s}**T**is the stress tensor,

**E**is the electric field,

**B**is the magnetic field, ε

_{0}is the electric constant, μ

_{0}is the magnetic constant, and δ

_{ij}is the Kronecker function.

**T**and ∇. The equation is expressed as

**F**is the electromagnetic force on the moving iron core.

## 3. Design and Development of Measurement Platform

## 4. Results and Discussion

#### 4.1. Simulation Results

_{0}(x

_{z}= 0 mm), and the position of the MIR is adjusted along the direction of the Z-axis. The effects of different MIR positions on the solenoid valve’s response time t and the electromagnetic force are investigated by simulation.

_{z}, the time from turning on the power supply to the moving iron core reaching the working position is defined as the response time t, and the electromagnetic force received by the moving iron core after the suction is defined as f. The relationship between the position of the MIR, the response time, and the electromagnetic force are shown in Table 2. With the positive change in the position of the MIR, the response time of the solenoid valves, the electromagnetic force, and the displacement of the MIR do not have a linear relationship. However, there is an optimal position interval that takes both into account. With the positive increase of x

_{z}, the electromagnetic force increases and then decreases, and the maximum value is 1.416 N. The response time gradually increases. The response time decreases first and then increases, and the minimum value is 13.0 ms.

#### 4.2. Experimental Verification

#### 4.3. Effect of MIR Position on Electromagnetic Force and Response Time

_{z}< 0 mm, a large electromagnetic force response is obtained in the initial stage, but the average electromagnetic force is low. At x

_{z}= −3 mm, the subsequent electromagnetic force is even significantly lower than the initial response electromagnetic force. Conversely, the initial response electromagnetic force becomes weaker and weaker as x

_{z}increases positively. Especially at x

_{z}= 3 mm, the electromagnetic force basically has no obvious response in the first 25 ms. It is obvious that x

_{z}has better performance in the (−1 mm, 1 mm) interval, the electromagnetic force response is faster, and the value of the force is also larger.

_{z}< 0 mm, the moving iron core displacement curve has little change, and the response performance is better. The response dynamic process and time are basically unchanged, and the experimental results can also be confirmed from the data in Table 2. Subsequently, with the increase of x

_{z}, the time required for displacement becomes larger and larger, and the moving speed of the moving iron core becomes more slowly. Even at x

_{z}= −3 mm, the time required for displacement reaches 32 s, and the displacement time is higher than two times the shortest. The electromagnetic force mainly limits the displacement time on the moving iron core.

#### 4.4. Effect of MIR on Magnetic Field Intensity and Distribution of Magnetic Force Lines

_{0}is the air permeability, B

_{0}is the magnetic field intensity in the air gap, and S

_{0}is the gap area. It is evident that under the structure of the solenoid valve is unchanged, the size of the magnetic force is proportional to the square of the magnetic induction strength in the air gap. The role of the MIR is mainly manifested in the change of the magnetic path.

#### 4.5. Optimized Design for Dynamic Response Performances

_{z}is 1.5 mm. However, the optimal response time value occurs when x

_{z}is −1.5 mm. When x

_{z}is greater than this position, the response time gradually increases, and the rate increases continuously. Finally, the two gradually tend to be linear. Through analysis, a reasonable selection interval is obtained. This position interval is (−1.5 mm, 1.5 mm). Within this interval, the two performance parameters have the same trend with the increase of MIR position. The ability of the solenoid valve to respond quickly to overcome the electromagnetic force is worse when the electromagnetic force increases.

_{z}is −1.5 mm. The response time can reach 13 ms. In contrast, the maximum electromagnetic force can be obtained at the MIR position of 1.5 mm; i.e., the electromagnetic force can be greater than 1.4 N. This method can provide certain theoretical guiding significance for the optimization of the solenoid valves.

## 5. Conclusions

- (1)
- Through the experimental verification of the developed detection platform, the error rate of the proposed AC solenoid valve simulation model is generally stable at about 10%, which meets the accuracy requirements of the solenoid valve structure optimization.
- (2)
- The electromagnetic force affected after armature absorption increases first and then decreases with the increase of x
_{z}position and reaches the maximum value at x_{z}= 1.5 mm and F_{max}= 1.416 N. Response time decreased first and then increased and reached a minimum at x_{z}= −1.5 mm, with t_{min}= 13.0 ms. - (3)
- The position of the magnetic partition ring changes the distribution of the magnetic path in the solenoid valve and then changes the magnetic flux in the air gap, thus affecting the dynamic response characteristics.
- (4)
- The solenoid valve used in this study is an example, the optimal interval of the magnetic ring position is (−1.5 mm, +1.5 mm), in which the solenoid valve has a relatively balanced dynamic response characteristic.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Structural diagram and (

**b**) optical image of the solenoid valve; the initial working air gap of the model is 12.16 mm, and the working stroke of the movable iron core is 5 mm.

**Figure 2.**(

**a**) Solution settings and (

**b**) the meshing length of the magnetic conductive material is set to 0.5 mm, and the rest are set to 1.5 mm.

**Figure 3.**Experimental schematic diagram of measurement platform. (

**a**) Electromagnetic force measurement with a measurement accuracy of 0.01 N, (

**b**) response time measurement with a resolution of not less than 0.025 μm, and (

**c**) magnetic field strength measurement with a measurement accuracy of 0.01 mT.

**Figure 7.**The distribution of the magnetic induction intensity at (

**a**) without MIR and MIR’s position at (

**b**) −3 mm, (

**c**) −2 mm, (

**d**) −1 mm, (

**e**) 0 mm, (

**f**) 1 mm, (

**g**) 2 mm, (

**h**) 3 mm.

Item | Setting |
---|---|

Moving iron core | Steel-1008 |

Magnetic isolation tube | Polyester |

Coil | Copper |

Magnetic isolation ring | Copper |

Concentrating flux sleeve | Iron |

Concentrating flux plate | Steel-1008 |

Solution region | Vacuum |

Motion domain | Vacuum |

x_{z}/mm | t/ms | f/N |
---|---|---|

−3.0 | 14.0 | 0.503 |

−2.5 | 13.6 | 0.614 |

−2.0 | 13.2 | 0.747 |

−1.5 | 13.0 | 0.925 |

−1.0 | 13.6 | 1.023 |

−0.5 | 14.4 | 1.077 |

0 | 15.2 | 1.115 |

0.5 | 16.6 | 1.293 |

1.0 | 18.2 | 1.368 |

1.5 | 21.4 | 1.416 |

2.0 | 24.4 | 1.294 |

2.5 | 28.2 | 1.292 |

3.0 | 32.0 | 1.203 |

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**MDPI and ACS Style**

Guo, J.; Li, L.; Qin, P.; Wang, J.; Ni, C.; Zhu, X.; Lu, D.; Tang, J.
Optimization Design of Magnetic Isolation Ring Position in AC Solenoid Valves for Dynamic Response Performances. *Micromachines* **2022**, *13*, 1065.
https://doi.org/10.3390/mi13071065

**AMA Style**

Guo J, Li L, Qin P, Wang J, Ni C, Zhu X, Lu D, Tang J.
Optimization Design of Magnetic Isolation Ring Position in AC Solenoid Valves for Dynamic Response Performances. *Micromachines*. 2022; 13(7):1065.
https://doi.org/10.3390/mi13071065

**Chicago/Turabian Style**

Guo, Jiang, Linguang Li, Pu Qin, Jinghao Wang, Chao Ni, Xu Zhu, Dingyao Lu, and Jiwu Tang.
2022. "Optimization Design of Magnetic Isolation Ring Position in AC Solenoid Valves for Dynamic Response Performances" *Micromachines* 13, no. 7: 1065.
https://doi.org/10.3390/mi13071065