# Finite Element Modeling and Optimal Design of an Electromagnetic Pneumatic Flow Servo Valve

Authors: Zedan Wang; Zixuan Guo; Guangyu Zhu; Xin Wang; Xiao Li
Journal: Mathematical Problems in Engineering
 (2023)

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## Abstract

The electromagnet pneumatic proportional servo valve is widely used in industrial automation, medical equipment, scientific composition detectors, and other fields that require precise adjustment of high-pressure air flow due to its simple working structure, large output power, large working frequency response, and good control performance. However, the output pressure of the valve is small, making it vulnerable to the impact of the external environment. Based on the practical electromagnet-type pneumatic proportional servo valve, this paper establishes a finite element dynamic mathematical model, conducts finite element analysis on the electromagnet magnetic field in the valve, then improves the structural parameters of the original proportional valve through the analysis of the valve performance parameters and structural optimization, and finally, the physical experiment proves that the optimized electric proportional valve can effectively reduce the hysteresis within the working pressure range and has good response characteristics to step signals. This paper can provide support for performance analysis and structural parameter improvement of the electric proportional valve.


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## Body

## 1. Introduction

In the field of industrial automation, pneumatic control technology has been used more and more widely due to its many significant advantages, such as its simple structure, high reliability, fast working speed, and strong adaptability to overload, and has become an indispensable and important means for industrial automation [1, 2]. The automation system design has continuously improved the work requirements of the pneumatic control system, from the initial simple switch control to the continuous adjustable high-precision control requirements of the position, speed, and force of the actuator, especially for the pneumatic proportional servo technology [3]. As one of the frontier research fields of pneumatic technology, pneumatic proportional servo control technology is gaining importance [4]. The pneumatic flow servo valve is the core component of the pneumatic proportional control system. It has the advantages of low cost, antipollution, good dynamic characteristics, and high control accuracy. It is widely used in feedback control systems such as pneumatic pressure, speed, output force, and servo positioning [5]. The static, dynamic, and flow characteristics of the pneumatic flow servo valve directly affect or even determine the performance of the control system [6]. Therefore, studying the pneumatic proportional control valve deeply, analyzing its working principle and process, and clarifying the effect of changes in various physical parameters of the valve is very important and necessary to the performance impact [7].The electromagnetic pneumatic flow servo valve has the advantages of a simple structure, high output control accuracy, and a small working volume. It is widely used in industrial pneumatic servo control systems that require precise adjustment of high-pressure air sources [8, 9]. However, because this type of pneumatic valve uses a high-speed solenoid valve as an electro-mechanical actuator, it has the disadvantages of poor control performance and an output characteristic susceptible to interference from the working environment in actual work, so it needs to be targeted for this solenoid valve, studying the basic theory and in-depth optimization design of the servo valve [10–12].In order to improve the performance of pneumatic flow valves, the current domestic research direction is mainly to solve the problem between high-frequency response and large flow while optimizing the working performance of the valve [13–15]. For example, in the “Design and Simulation of High-Pressure Pneumatic Large Flow Solenoid Valve” proposed by Ding and Pan [1], the high-pressure pneumatic large flow solenoid on-off valve is designed to meet the requirements of limited volume decompression on the control components, and the genetic algorithm is used to optimize the structural parameters and control parameters, achieving a good optimization effect [6]. Ru and Xiang proposed the “Optimum Design of High-Flow Pneumatic High-Speed On-Off Valve” [3], aiming at the long switching time problem of large-flow and high-speed on-off valves, and design a high-flow and high-speed on-off valve with reduced response time. The research results show that the optimized on-off valve has a flow rate of 720 L/min when the inlet pressure is 7 bar, and the switching time is only 9.5 ms.It can be seen that the current research on flow valves can be divided into multiple directions, such as low power consumption, high-frequency response, long life, microflow and large flow, modularization, and integration. Summarizing its research content, there are mainly two aspects [16–18]. On the one hand, it is the research of the electro-mechanical converter and its drive circuit; on the other hand, it is the optimization design of the valve core and valve body structure [19]. Therefore, through the optimization analysis and optimization of the key parameters and working conditions of the solenoid structure of the solenoid valve type flow valve, the dynamic characteristics of the valve are studied, and the performance optimization of the valve is finally realized [20–22]. For dynamic analysis of an electromagnetic pneumatic flow servo valve, Rashid et al. evaluated different flow features for a modified cross-model fluid flow, which aims to analyze the parameters and choose accurate solutions. A wide range of parameters and coefficients of drag and lift had been performed [23, 24]. Shi et al. proposed a transfer feature learning method that applied a new method to achieve the acquired parameters and dynamic characteristics of the valve [25, 26]. Sun et al. analyzed the characteristics of a solenoid valve in a pneumatic spring testing system [27].Based on the research and applications at home and abroad, this paper takes an electromagnet-type pneumatic proportional flow valve as the research object. First, the finite element analysis of the solenoid magnetic field in the valve is carried out, and then the finite element dynamic mathematical model is established to study its dynamic characteristics. Second, through physical experiments, the performance of the valve by optimizing is verified, and the research results provide a theoretical basis for the design and development of large flow and high-speed electromagnetic flow valves. The main focus of this article is on the structural design of the electromagnetic flow valve and its electromagnet performance optimization design, so as to solve the contradiction between the valve’s flow and response characteristics and finally realize the optimization and improvement of the low-power, large-flow flow valve.


## 2. Configuration Model of the Solenoid Valve Type Pneumatic Flow Servo Valve

The electromagnet pneumatic flow servo valve has the advantages of a simple working structure, large output power, and a large working frequency response. It is widely used in industrial pneumatic servo control systems that require precise adjustment of high-pressure air sources [28]. This type of pneumatic flow servo valve is widely used in large-scale pneumatic servo control systems. The valve structure studied in this paper is shown in Figure 1. Its working principle is that in the initial power-off state of the valve, the valve core closes the air gap under the action of the annular spring. When the valve is energized, the valve core acts to open the closed air gap, and high-pressure gas flows to the working container through the valve port. Applying the PWM control signal, if the electromagnetic force generated by the electromagnet structure is greater than the force of the annular spring leaf, the valve core moves downward, so that the air gap of the working chamber opens and the gas flow at the exhaust port gradually increases [29]. The electromagnetic force generated by the structure is less than the force of the annular spring plate, and the valve core moves upward to make the air gap in the working chamber gradually decrease. At this time, the gas flow at the exhaust port gradually decreases until the valve core is completely reset and the air gap is closed. When the gas flow is zero, the valve stops working. By adjusting the PWM control signal to the valve, the effective area of the air gap in the working chamber is changed so that the gas flow at the exhaust port is the target value.Figure 1
Configuration model of the solenoid valve type of pneumatic flow servo valve: (1) air inlet; (2) sealing rubber ring; (3) air outlet; (4) ring spring plate; (5) valve core; (6) coil winding; (7) working cavity; (8) lower part of the fixed part.


## 3. Modeling of the Solenoid Valve Type Pneumatic Flow Servo Valve

According to the working principle and the actual working condition of the regulator, for easy calculation and simulation, the following assumptions can be made:(1)
The ideal gas is used in the working section, the movement of the gas at the throttle is an isentropic process, and the gas temperature is kept at room temperature(2)
The gas flow process in the long pipeline is ignored(3)
Rubber sealing parts are equivalent to spring-damper systems, ignoring the gas leakage that occurs during the operation of the regulatorBased on the assumptions and analysis, the following mathematical models can be established.


### 3.1. Mathematical Model of the Valve’s Main Mechanical Structure

The mathematical model of the main mechanical structure of the valve can be established according to the working principle of the valve, which mainly describes the gas state and flow change of the upper working chamber and the movement state of the valve core.(1)
The pressure equation of the working chamber can be described as follows:(1)dpcdt=mRVcdTcdt+RTcVcGc−pcScVcX˙,wherepc is the working chamber pressure, R is the gas constant, Tc is the temperature, Sc is the effective area of the diaphragm, Vc is the working chamber volume, and X is the valve core displacement [29].(2)
The flow equation of the working cavity can be described as follows:(2)Gc=SepsϕTs.among themwhenp2/p1≤0.5283, φ=kR2/k+1k+1/k−1; when p2/p1>0.5283, φ=2k/k−11/Rp2/p12/k−p2/p1k+1/k; where p2 is the gas pressure for the diaphragm cavity, Se is the effective area of the upper diaphragm cavity, Ts is the gas source temperature, p1 is the gas source pressure, R is the gas constant factor, and k is the specific heat of air [30].(3)
The spool motion equation can be described as follows:(3)mX¨=pc−poSo−KX−Ff−mg,wherep0 is the pressure below the diaphragm, that is the outlet pressure; So is the effective area of the spool; K is the spring coefficient of the spool; Ff=rX˙ is the friction of the regulator core [31].(4)
Approximate engineering method for effective cross-sectional area(4)Se1=11/A12+1/A22+1/A32+1/A42,whereA1=d1X is the rectangle area, A2=πd2X is the side area of the cylinder, A3=πd22/4−πd32/4 is the area of an annular passage formed by the regulator core and regulator body, and A1=C is the fixed value [32].


### 3.2. Mathematical Model of Electromagnet Structure

In order to solve the difficulty of establishing the mathematical model of the electromagnet structure and dynamic simulation, the finite element simulation of the electromagnet part of the valve is carried out, and the electromagnet structure is simulated by the Ansoft Maxwell electromagnetic simulation software. The relevant structural parameters of the electromagnet are changed. The effect of the performance is analyzed and studied, as shown in Figure2, which is a two-dimensional finite element model of the electromagnet structure in the valve.Figure 2
Finite element model of electromagnet structure.


### 3.3. Finite Element-Parameter Dynamic Mathematical Model of Valve

Through the finite element modeling of the solenoid parts of the valve, the finite element data group under its dynamic working state is constructed, the finite element data group is mathematically processed and analyzed, and the parameterized model based on current changes is designed to be available. The finite element analysis data set is applied to the mechanical structure model of the valve. The finite element-lumped parameter model of the valve is established in MATLAB. The mathematical model structure is shown in Figure3.Figure 3
The finite element-parameter dynamic mathematical model structure of the valve.


## 3.1. Mathematical Model of the Valve’s Main Mechanical Structure

The mathematical model of the main mechanical structure of the valve can be established according to the working principle of the valve, which mainly describes the gas state and flow change of the upper working chamber and the movement state of the valve core.(1)
The pressure equation of the working chamber can be described as follows:(1)dpcdt=mRVcdTcdt+RTcVcGc−pcScVcX˙,wherepc is the working chamber pressure, R is the gas constant, Tc is the temperature, Sc is the effective area of the diaphragm, Vc is the working chamber volume, and X is the valve core displacement [29].(2)
The flow equation of the working cavity can be described as follows:(2)Gc=SepsϕTs.among themwhenp2/p1≤0.5283, φ=kR2/k+1k+1/k−1; when p2/p1>0.5283, φ=2k/k−11/Rp2/p12/k−p2/p1k+1/k; where p2 is the gas pressure for the diaphragm cavity, Se is the effective area of the upper diaphragm cavity, Ts is the gas source temperature, p1 is the gas source pressure, R is the gas constant factor, and k is the specific heat of air [30].(3)
The spool motion equation can be described as follows:(3)mX¨=pc−poSo−KX−Ff−mg,wherep0 is the pressure below the diaphragm, that is the outlet pressure; So is the effective area of the spool; K is the spring coefficient of the spool; Ff=rX˙ is the friction of the regulator core [31].(4)
Approximate engineering method for effective cross-sectional area(4)Se1=11/A12+1/A22+1/A32+1/A42,whereA1=d1X is the rectangle area, A2=πd2X is the side area of the cylinder, A3=πd22/4−πd32/4 is the area of an annular passage formed by the regulator core and regulator body, and A1=C is the fixed value [32].


## 3.2. Mathematical Model of Electromagnet Structure

In order to solve the difficulty of establishing the mathematical model of the electromagnet structure and dynamic simulation, the finite element simulation of the electromagnet part of the valve is carried out, and the electromagnet structure is simulated by the Ansoft Maxwell electromagnetic simulation software. The relevant structural parameters of the electromagnet are changed. The effect of the performance is analyzed and studied, as shown in Figure2, which is a two-dimensional finite element model of the electromagnet structure in the valve.Figure 2
Finite element model of electromagnet structure.


## 3.3. Finite Element-Parameter Dynamic Mathematical Model of Valve

Through the finite element modeling of the solenoid parts of the valve, the finite element data group under its dynamic working state is constructed, the finite element data group is mathematically processed and analyzed, and the parameterized model based on current changes is designed to be available. The finite element analysis data set is applied to the mechanical structure model of the valve. The finite element-lumped parameter model of the valve is established in MATLAB. The mathematical model structure is shown in Figure3.Figure 3
The finite element-parameter dynamic mathematical model structure of the valve.


## 4. Valve Performance Parameter Analysis and Structural Optimization

By establishing the finite element-parameter dynamic mathematical model of the valve, the performance-influencing parameters of the valve can be analyzed, and the effect of parameter changes on the performance of the valve can be studied. Additionally, the structural optimization parameters of the valve can be obtained. The main research content is the influence of the valve’s electromagnet structure parameter changes on the valve’s operating characteristics. Now the valve core diameter and the number of ampere-turns (Nr) are used as structural variables, and the overshoot, adjustment time, and error are the operating characteristics indicators. Through the use of different structural parameter variables in the finite element-lumped parameter dynamic mathematical model, a comparative analysis of its working characteristics is possible.As shown in Figure4, when the spool diameter is between 4.7 cm and 5.2 cm and the number of coil ampere-turns increases, the valve overshoot will reach a smaller value and then gradually increases. This is because, for the coil, with the increase of the number of ampere-turns and the radius of the valve core, the electromagnetic force provided by the electromagnet structure in the valve increases under the same working state, but after the electromagnetic force increases to a certain extent, the magnetic flux of the spool is close to the saturation value, and the change of electromagnetic force on the spool gradually slows down, but when the spool diameter is 5.2 cm, the overshoot is generally larger due to the larger mass of the spool.Figure 4
The influence of solenoid valve structure characteristics on overshoot.As shown in Figure5, when the number of coil ampere-turns increases, the overall change trend of the valve adjustment time is to decrease. At the same time, when the valve core diameter is 4.7 cm, the adjustment time is smaller. However, if the valve core diameter is too small, the average effective magnetic field of the valve core will be smaller, the magnetic resistance of the inner magnetic column will increase, the electromagnetic force will decrease, and the adjustment time will be longer. On the contrary, if the spool diameter is too large, due to the larger mass of the spool, the adjustment time will be longer under the same electromagnetic force.Figure 5
The influence of the structural characteristics of the solenoid valve on the adjustment time.As shown in Figure6, when the number of coil ampere-turns increases, the error of the valve decreases according to the overall trend, but the change is small and the optimization effect is limited. If the diameter of the spool is changed, the error value can be effectively reduced. When the spool diameter is 4.7 cm, the error value is the smallest. This is because the spool diameter is too small and its electromagnetic force is small, which makes it difficult to adjust the spool position in time, but the spool diameter is too large and the spool quality is too high. The electromagnetic force has a small effect on the force of the valve core, and the error value is also large.Figure 6
The influence of the structural characteristics of the solenoid valve on the error value.Through the data analysis of the finite element-parameter dynamic mathematical model, in the comparison experiment of the working characteristics with the spool diameter and the number of ampere-turns as the structural variables, the work with the parameter combination of “coil 450 turns, spool diameter 4.7 cm” showed better characteristics, and the power of the valve is small under the condition of ensuring that the electromagnetic force meets the opening conditions. The use of “coil is 450 turns, spool diameter is 4.7 cm” can make the overshoot 13.05%, the adjustment time 0.23 s, and the error value 2.25%. The valve has better working characteristics.


## 5. Physical Experiment Analysis of a Valve

As shown in Figures7 and 8, an open-loop experimental loop of the solenoid valve type pneumatic flow servo valve has been established, and the structural optimization of the flow valve has been verified to improve its working characteristics. In this experimental circuit, the high-pressure air source and the pneumatic pressure-reducing valve can provide a pressure-controllable and stable high-pressure airflow within a certain range; the electrical switch valve is used as the switch structure of the pneumatic circuit to control the on and off of the main circuit to achieve air pressure signal switching control; a solenoid valve type pneumatic flow servo valve is used as the experimental test component; a gas flow sensor is used to measure the gas flow value at the input and output of the flow valve; an adjustable throttle valve and a gas box are used as the adjustable system load.Figure 7
Open loop experimental circuit of a solenoid valve-type pneumatic flow servo valve: (1) high-pressure gas source; (2) pneumatic pressure relief regulator; (3) flow sensors; (4) controller; (5) no lid box; (6) throttle regulator; (7) solenoid valve type pneumatic flow servo valve; (8) electrical switch regulator.Figure 8
Experimental station of the pneumatic flow servo valve.As shown in Figure9, the inlet air pressure of the valve is set to 0.3 MPa, the rest of the working conditions remain unchanged, and the forward and reverse stroke flow output values of the original valve and the modified valve are tested, respectively. From the numerical analysis of the stroke flow, it can be seen that the starting current of the modified valve is larger than that of the original valve. This is because the number of coil turns in the modified valve is less, and a higher starting current is required to make the spool start moving. At the same time, the modified valve was compared with the original valve. The hysteresis value is reduced to about 72% of the original hysteresis value, which is less than 9% of the maximum flow rate, and its repeatability is also improved to less than 5% of the maximum flow rate.Figure 9
Flow output value of the positive and negative strokes of the valve under an air pressure of 0.3 MPa.As shown in Figure10, the inlet air pressure of the valve is set to 0.5 MPa, the rest of the working conditions remain unchanged, and the forward and reverse stroke flow output values of the original valve and the modified valve are tested, respectively. From the numerical analysis of the stroke flow, it can be seen that the starting current of the modified valve is similar to that of the original valve. This is because when the air pressure value is kept high, the air pressure generated by the pressure difference in the working chamber is larger, and the valve core needs a higher starting current. The spool can start to move, so the starting current of the modified valve and the original valve is larger than the low pressure of 0.3 MPa. At the same time, the hysteresis value of the modified valve is reduced compared to the original valve, which is 68% of the original hysteresis value. Around 9% of the maximum flow rate and its repeatability have also been improved to 3% or less of the maximum flow rate. But at the same time, the maximum output flow that the modified valve can provide is small. This is also due to the small solenoid force on the valve core after the valve coil turns and the valve core diameter is optimized, which makes the air gap in the working chamber smaller and the output flow smaller.Figure 10
Flow output value of the positive and negative strokes of the valve under an air pressure of 0.5 MPa.As shown in Figure11, the inlet air pressure of the valve is set to 0.5 MPa constantly, and the control signal adopts a 0–90 mA step signal. Through the numerical analysis of the flow, in the process of increasing the gas flow, the time to reach 20% of the target flow value of 60 L/min is the start time of the valve; that is, the time it takes for the spool movement to open the working chamber air gap, then the valve is in the pneumatic time under this working condition is about 0.11 s, and the starting time is relatively small. When the gas flow reaches a stable process, the flow remains relatively stable, and the error value is about 5.1%. This is because the gas source pressure is limited by the experimental conditions and cannot be kept constant at 0.5 MPa, which will be affected by the working state of the experimental loop. Therefore, a flow error occurs.Figure 11
Flow output value of the valve with a 0 mA–90 mA step signal as the control signal.As shown in Figure12, the inlet pressure of the valve is set to 0.5 MPa constantly, and the control signal adopts a 120-90 mA step signal. Through the flow numerical analysis, it can be seen that the flow output state of the valve is poor when the 120 mA signal is controlled, and its flow output error reaches about 7%. This is because the valve core is subjected to a large electromagnetic force at this time and is easily affected by signal noise. The valve core produces irregular movement, the effective working area of the air gap in the working cavity cannot be kept constant, and the valve output flow value error is large. In the transition process from 120 mA to 90 mA, it can be seen that the conversion speed is relatively fast, about 0.19 s, which indicates that the step signal response speed of the modified valve is faster. Compared with the original valve, its step response characteristic is optimized. Its flow-control effect is also better.Figure 12
Flow output value of the valve with a 120 mA-90 mA step signal as the control signal.As shown in Figure13, the inlet air pressure of the valve is set to 0.3 MPa constantly, and the control signal adopts a 0 mA–80 mA step signal. Through the numerical analysis of the flow, it can be seen that during the increase of the gas flow, the start time of the valve under the lower air pressure working condition can be obtained. The start time of the valve under this working condition is about 0.16 s, the start speed is faster, and the flow rate increases. There are certain fluctuations in this large process. This is because under this working condition, as the coil is energized, the valve core starts to act, the opening of the valve port increases, and the flow increases rapidly. In this process, the force on the rebound spring is obvious, and the ring spring plate shakes when approaching the maximum displacement; after the gas flow reaches a steady state, the flow value remains relatively stable, and the error value is about 6.3%, which is due to the fact that at the gas source, the pressure cannot be kept constant at 0.3 MPa, and its output pressure is affected by the load, so a flow error occurs.Figure 13
Flow output value of the valve with a 0 mA–80 mA step signal as the control signal.As shown in Figure14, the inlet pressure of the valve is set to 0.3 MPa constantly, and the control signal adopts an 80 mA-0 mA step signal. Through the numerical analysis of the flow, it can be seen that in the process of reducing the gas flow, the closing time of the valve under lower atmospheric pressure can be obtained. The closing time of the valve under this working condition is about 0.08 s; the closing time is shorter, and the flow rate is reduced. There are certain fluctuations in this small process. This is because, under this working condition, it is also affected by the action of the return spring. When the valve element resets, the air gap in the working chamber is completely closed under the action of the sealing ring, and the output flow of the valve is 0 L/min. No flow leakage indicates that the valve has good air tightness.Figure 14
Flow output value of valve with 80 mA-0 mA step signal as the control signal.As shown in Figure15, the inlet pressure of the valve is set to 0.3 MPa constantly, and the control signal adopts a 100 mA-80 mA step signal. Through the flow numerical analysis, it can be seen that in the 100 mA signal control stage, the output flow fluctuation is small, and the maximum output error is about 4.7%. The larger control signal generates a greater electromagnetic force. When it is balanced with aerodynamic force, the force generated by the return spring and ring spring is large, resulting in obvious flow jitter, and the flow value has an error; In the transition process from 100 mA to 80 mA, the conversion time is about 0.12 s, indicating that the valve’s step signal response speed is faster; in the 80 mA signal control stage, the output flow fluctuation is small, and the maximum output error is about 3.9%.Figure 15
Flow output value of the valve with a 100 mA-80 mA step signal as the control signal.Based on the above experimental data and analysis, the following conclusions can be drawn: (1) the experimental system designed in this paper is reasonable; (2) after the structure optimization of the valve coil turns and the valve core diameter, the operating characteristics of the flow valve are improved; (3) through structural optimization, the hysteresis value of the valve within the working pressure range can be effectively reduced, and the total flow can be maintained below 70% of the maximum flow rate, and its repeatability can be improved. The total flow rate can be maintained below 5% of the maximum flow rate; (4) through structural optimization, the step signal response characteristics of the valve can be effectively improved. Under the working conditions of a higher working pressure, the output flow conversion time of the valve can be made to be about 0.19 s, while the flow rate remains relatively stable and its error value is nearly 5.1%. Under working conditions of lower working pressure, the output flow conversion time of the valve can be made at about 0.12 s, while the flow remains relatively stable, and the error value is about 3.9%.


## 6. Conclusion

This paper uses an electromagnet-pneumatic proportional flow valve as the research object. The finite element dynamic mathematical model of the valve is established, the dynamic characteristics of the valve are studied through the finite element analysis of the solenoid magnetic field in the valve, and the key structural parameters of the valve are optimized. Afterward, relevant verification and analysis were carried out through physical experiments, and three main conclusions were obtained as follows:(1)
By establishing the finite element dynamics mathematical model of the electromagnet pneumatic proportional flow valve, using the simulation experiment, optimizing the electromagnet structure parameters of the valve, studying the change of its dynamic characteristics, and optimizing the key structure affecting the valve performance within a certain range of parameters, the valve has better working characteristics when the coil is 450 turns and the valve core is 4.7 cm, which provides a research basis for the research in this paper.(2)
The open-loop experimental system of the pneumatic flow servo valve is designed to verify the performance effect of the optimized valve structure parameters. By comparison, the initial voltage of the valve increases slightly under low-pressure conditions, and the output flow of the valve under high-pressure conditions is slightly smaller, but it can effectively reduce the hysteresis of the valve within the working pressure range and enhance the repeatability of the valve. The hysteresis value is reduced to about 70% of the nonoptimized valves, and the valve repeatability remained below 5% of the maximum flow, demonstrating the effectiveness of the optimization.(3)
The response characteristics of the valve under the step signal are verified. Under the condition of relatively high working pressure (0.5 MPa), the switching time of the output flow of the valve can reach about 0.19 s, while the flow remains relatively stable with an error value of about 5.1%. Under the working condition of low working pressure (0.3 MPa), the switching time of the valve output flow can reach about 0.12 s, while the flow remains relatively stable, with an error value of about 3.9%. Compared with the published data, the maximum output error of the valve is significantly reduced.This paper does not consider other key structures of the valve in terms of structural parameter optimization, and the scope of optimization is not large, but the research method in this paper has contributed to the optimization and verification of valve performance, which can provide a basis for the design and development of high-flow and high-speed electromagnetic flow valves. The theoretical basis provides a direction for the optimization and improvement of low power consumption and large flow valves.



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