# Modeling and Dynamic Analysis on the Direct Operating Solenoid Valve for Improving the Performance of the Shifting Control System

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## Abstract

**:**

## 1. Introduction

## 2. Valve Structure and Principle

## 3. Modeling

#### 3.1. Electro-Magnetic Subsystem

_{Ei}consists of the voltage drop and the induced voltage.

_{Ei}is the electric resistance.

_{a}is the area of air gap.

_{m}can be stated as

_{c}is

#### 3.2. Hydraulic Subsystem

_{clu}should be 0. Thus, the differential pressure in Equation (16) should be |P

_{con}-P

_{clu}|, simplified as P

_{con}.

#### 3.3. Dynamics Motion

#### 3.4. The Simulation Model

#### 3.5. Validation of Model

## 4. Results and Discussion

#### 4.1. Analysis of Pressure Response

#### 4.2. Analysis of Forces

#### 4.3. Analysis of Leakage Flow

## 5. Conclusions

- (1)
- The simulation results of this study agreed with the experimental results. Thus, the mathematical model developed in this study was effective and accurate.
- (2)
- Both the magnetic force and the viscous force had significantly influence on the pressure response. The pressure response time would be shortened if the magnetic force responded faster or the viscous force was reduced.
- (3)
- To improve the response time of the solenoid valve, the clearance height should be reduced. The resultant force on the spool in 10 µm would reach the equilibrium point 0.1 s earlier than that in 30 µm.
- (4)
- The clearance height was proved to have great influence on the leakage of the solenoid valve. The leakage increases with the growing clearance height, which showed the leakage in 30 µm was triple the amount of that in 20 µm.
- (5)
- The leakage of the shifting control system employing the direct acting solenoid valve can be reduced by 60% compared to the conventional two-stage pilot valve in our previous product.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 7.**Comparison of experimental and numerical control pressure in the direct operating solenoid valve.

**Figure 8.**Control pressure and displacement of the valve. (

**a**) Input signal (

**b**) Control pressure (

**c**) Spool displacement.

**Figure 12.**The static characteristics of the magnetic force as a function displacement for different electric current.

**Figure 17.**(

**a**) Forces on the valve and the spool displacement in 10 µm (

**b**) Forces on the valve and the spool displacement in 20 µm (

**c**) Forces on the valve and the spool displacement in 30 µm.

**Figure 20.**Leakage flow characteristics in the direct operating solenoid valve for different clearance.

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**MDPI and ACS Style**

Xu, X.; Han, X.; Liu, Y.; Liu, Y.; Liu, Y.
Modeling and Dynamic Analysis on the Direct Operating Solenoid Valve for Improving the Performance of the Shifting Control System. *Appl. Sci.* **2017**, *7*, 1266.
https://doi.org/10.3390/app7121266

**AMA Style**

Xu X, Han X, Liu Y, Liu Y, Liu Y.
Modeling and Dynamic Analysis on the Direct Operating Solenoid Valve for Improving the Performance of the Shifting Control System. *Applied Sciences*. 2017; 7(12):1266.
https://doi.org/10.3390/app7121266

**Chicago/Turabian Style**

Xu, Xiangyang, Xiao Han, Yanfang Liu, Yanjing Liu, and Yang Liu.
2017. "Modeling and Dynamic Analysis on the Direct Operating Solenoid Valve for Improving the Performance of the Shifting Control System" *Applied Sciences* 7, no. 12: 1266.
https://doi.org/10.3390/app7121266