Mechanical Characteristics and Miniaturization Design of the Electromagnetic Valve Used in Drilling Robots

Abstract

The maximum radial size of the conventional three-bit four-way electromagnetic cartridge valve is greater than the largest containable size of the fluid control valve used for downhole robots. This paper proposes two kinds of solutions to reduce the radial dimension of the three-bit four-way electromagnetic insertion valve: one is to reduce the radial arrangement of the coil and increase the axial arrangement of the coil, and the other is to reduce the diameter of the moving iron core to reduce the winding radius of the coil. Using the theoretical model established in the following text, a simulation experiment was conducted. The results show that the movement of the valve spool is basically completed within 30 ms. Then, a matching experiment on the electromagnetic insertion valve was designed and conducted. The experimental results show that the opening time of the solenoid valve on the left coil is about 52 ms, and the opening time of the solenoid valve on the right coil is about 44 ms. The reaction time of the valve spool is suitable for the practical application of the solenoid valve. The significance of this paper is the reduced radial size of the three-bit four-way electromagnetic insertion valve. These improvements have reduced the size of downhole drilling robots, which facilitates the application of downhole drilling robots in narrower environments.

1. Introduction

Over time, the main areas of oil and gas exploration and development [1] have changed. Specifically, the exploration and development of shale gas, coalbed methane, and other oil and gas resources have gradually become the mainstream [2]. With the increasing requirements for the exploration and development of oil and gas resources, conventional drilling technology has become insufficient for the exploitation of these resources. Compared with conventional drilling technology [3], coiled tubing technology is more intelligent and automated and can reduce the cuttings and gravel produced by drilling. Coiled tubing technology can also significantly reduce mining costs and reduce the drilling time.

With the increasing depth of horizontal wells and the increasing length of horizontal sections, the delivery of drilling tools becomes increasingly difficult. Compared with methods such as coil conveying, drilling conveying, and pump conveying, a downhole robot can deliver instruments more quickly and accurately. Using a downhole robot [4] to deliver instruments significantly saves time and reduces the transportation cost.

To address the difficulty of extending coiled tubing in horizontal wells [5], in 1987, Hallundbæk first proposed using downhole robots for downhole operations. In 1994, a downhole robot first completed an onsite application. Since the introduction of downhole robots in 1996, the number of downhole operations using downhole robots has increased. In 2008, more than 75% of Statoil’s downhole operations used downhole robots. According to the principle of motion, downhole robots can be divided into three types, namely, wheeled, crawler, and stretch. The telescopic robot has the advantages of good obstacle-crossing performance [6], high motion stability [7,8,9], and great traction force [10]. The telescopic downhole robot is used to pull the coiled tubing to solve the problem of coiled tubing transportation. To a great extent, using downhole robots significantly saves time and reduces the cost of pipeline transportation [11].

The size of a telescopic downhole robot determines the size of coiled tubing that can be delivered in a horizontal well. To tow smaller coiled tubing, the size of the downhole robot must be reduced. Considering that the hydraulic system is placed in the axial position of the telescopic downhole robot, we chose to modify the size of the hydraulic system. The size optimization design of the solenoid valve in the hydraulic system will become the key to the size reduction in downhole robots.

At present, the three-bit four-way solenoid valve used in the hydraulic system of underground robots is the standard model. To further expand the space use range of the underground robot, the dimensional design of the three-bit four-way solenoid valve is carried out. The modeling of the solenoid valves is mainly based on methods including magnetoresistive networks and finite element analysis (FEA) [12]. The above methods are also needed to optimize the design of the size of the solenoid valve. In the magnetostatic network approach [13], the flux path of the device is approximate and characterized by the properties and geometry of the material. The result is a magnetic path in which each different device region forms an element. Mechanical forces can be derived by solving the circuit, allowing the calculation of the flux density in any particular region. The drawback of this design is the difficulty of including flux edges, leakage, and material saturation. Methods based on finite element analysis usually fail to simultaneously predict electrical, magnetic, and mechanical responses [14,15]. It is also impractical to obtain the computational time required to obtain the system response through a magnetic field simulation with software. In the actual optimization scheme, magnetoresistance network design and finite element analysis (FEA) need to be carried out to obtain the theoretical value after the magnetic field simulation analysis. In addition, a response experiment on the solenoid valve should be designed to verify the correctness of the experiment and the reliability of the equipment.

This paper explores an optimization design to reduce the radial dimensions for the installation size of the three-bit four-way electromagnetic valve in the hydraulic system of a downhole robot. The mechanical model was established, the mechanical analysis and finite element analysis were conducted, an electromagnetic valve experimental device was developed, and the experimental research was conducted.

2. Optimization Method

The maximum radial size of the conventional three-bit four-way electromagnetic cartridge valve is greater than the maximum radial size that can be accommodated by the fluid control valve designed in this paper [16,17], which is 24 mm. Thus, the conventional three-bit four-way electromagnetic cartridge valve does not meet the design requirements of this paper. Therefore, this section proposes the optimization of the size of the design of the same type of cartridge valve. Because the maximum size of the valve body appears at the coil, the radial size of the coil should be limited. In order to ensure that the magnetic force provided by the coil [18] is not reduced, and the valve spool action can still be controlled, the following two optimization methods [19] are proposed:

• In the case where the number of turns of the coil and the specifications of the copper wire are unchanged, the radial arrangement of the coil is reduced, and the axial arrangement is increased. That is, the number of turns of the single-layer coil is increased and the number of the winding layers is reduced, which can reduce the radial size under the same number of turns.
• The diameter of the moving iron core is reduced, thereby reducing the winding radius of the coil.

The increase in the axial size of the coil can lead to the increase in the magnetic leakage, which will affect the excitation effect of the iron core, thus affecting the magnetic force. The reduction in the radius of the moving iron core can reduce the air gap area of the moving and fixed iron core, which can also affect the magnetic force.

Since these two optimization methods have an impact on the magnetic force, in order to ensure that after optimizing the size, the coil can still generate enough magnetic force to ensure the rapid movement of the valve spool, the magnetic field finite element analysis and the magnetic force solution should be carried out on the solenoid valve to determine the most favorable design method. The flow of the two methods is shown in Figure 1.

3. Modeling and Simulation

In this chapter, based on the two optimization methods in the previous chapter, the structure model of the three-bit four-way solenoid valve was established, and the mechanical model was established. The mechanical analysis of the structure model verified the rationality of the structural model after the optimization design. Through the simulation and analysis of the three-bit four-way solenoid valve, the maximum outer diameter of the solenoid valve is reduced to 17 mm, which is smaller than the radial installation size of the fluid control valve, which is 24 mm.

3.1. Structure Model of Three-Bit Four-Way Electromagnetic Cartridge Valve

As shown in Figure 2, according to the limit of the maximum size of the fluid control valve, the structural size of the valve body and spool were redesigned. As shown in Figure 3, the electromagnetic cartridge valve has three operating states, namely, powering on upper position, powering off median, and powering on lower position. As shown in Figure 3b, when the distance between the moving iron core and the upper and lower valve seats is 2.5 mm, the electromagnetic cartridge valve is in the powering outage median state, and the air gap size of the solenoid valve is the initial air gap size.

3.2. Mechanical Analysis of Three-Bit Four-Way Electromagnetic Cartridge Valve

The working process of the electromagnetic cartridge valve is the process of the valve spool opened, and the power-off center moves to the power-off upper or lower position. This movement process is a mirroring movement process. Therefore, taking the electromagnetic cartridge valve from the power-off center to the power-off upper position as an example, the force model was established, which is shown in Figure 4.

$$F_e+F_r=F_{si}+F_s+F_m+F_v+F_l$$

(1)

In the formula, $F_e$—electromagnetic force, N; $F_r$—right end fluid pressure, N; $F_l$—left end fluid pressure, N; $F_{si}$—spool inertia force, N; $F_0$—friction resistance, N; $F_m$—hydrodynamic force; $F_v$—viscous damping force; $F_s$—spring force.

The right end fluid pressure and left end fluid pressure are the liquid pressures (N) at both ends of the spool. Because the right and left ends of the hydraulic chamber of the electromagnetic cartridge valve are connected, the right end fluid pressure is equal to the left end fluid pressure, and they can cancel each other out.

For the inertia force generated by the movement of the spool, the calculation formula is as follows:

$$F_{si}=m\ddot{x}$$

(2)

where $m$—spool mass, kg; $\ddot{x}$—spool displacement, m.

$F_0$ is the friction resistance of the valve spool [20] (constant 6 N).

$F_m$ is the hydrodynamic force, which is an additional force to the valve spool caused by the flow of the hydraulic oil in the solenoid cartridge valve. No matter how the hydraulic oil flows, the axial hydrodynamic force always tries to close the valve port, which is the resistance to drive the valve spool movement. The direction and size of the hydraulic force are related to the direction and position of the valve spool. The hydraulic force calculation formula is as follows:

$$F_m=K_{s}x\Delta p$$

(3)

where $K_s$—hydrodynamic coefficient, $K_s=2C_d{C}_v\omega \cos \theta$; $\Delta p$—Pressure difference before and after the valve port, MPa; $C_d$—discharge coefficient; $C_v$—velocity coefficient, $\omega$—valve port gradient; for round port, $\omega =\pi d_0$, $d_0$—valve port diameter, mm; $\theta$—valve port jet angle, °.

$F_v$ is the viscous damping force at the movement of the valve spool. The specific calculation formula is as follows:

$$F_v=B\dot{x}$$

(4)

where $B$—viscous damping coefficient, N/m.

$F_{si}$ is the spool spring force, which can increase with the increase in the stroke of the valve spool. When the action position is reached, that is, the end of the stroke, the spring force reaches the maximum. Because the valve is a three-bit four-way solenoid valve, which is in the neutral position when normally closed, the spring is in the natural original state, the spring is compressed when the valve spool moves upward, and the spring is pulled when the valve spool moves downward; whether the valve spool moves up or down, the movement stroke and the spring force are both in slope, which is a positive correlation of the spring stiffness. That is,

$$F_{si}=kx$$

(5)

where $k$—spring stiffness, N/mm.

In summary, the force model of the valve spool can be written as

$$F_e=m\ddot{x}+F_0+K_{s}x\Delta p+B\dot{x}+kx$$

(6)

The static equation of the electromagnetic attraction is

$$F_e={\displaystyle \frac{B^{2}S}{2{\mu }_0}}={\displaystyle \frac{{\Phi }^2}{2{\mu }_{0}S}}$$

(7)

where $B$—magnetic field strength, T; $S$—air gap area, m²; ${\mu }_0$—vacuum permeability; $\Phi$—magnetic flux, Wb:

$$\Phi ={\displaystyle \frac{B}{S}}=IN{G}_{\delta }=IN{\mu }_0{\displaystyle \frac{S}{x_0}}=IL\left(x_0\right)$$

(8)

where $I$—current, A; $N$—coil turns; $x_0$—air gap spacing, m; $L$—inductance, H.

Hence,

$$F_e={\displaystyle \frac{I^2}{2}}{\displaystyle \frac{dL\left(x_0\right)}{{dx}_0}}$$

(9)

The relationship between the inductance and the air gap spacing cannot be completely expressed by Formula (9). Formula (9) can only be used to judge the macro change trend of the electromagnetic force and cannot be used as an accurate expression of the electromagnetic force. From Formula (9), it can be concluded that when the number of the coil turns is determined, the electromagnetic force is a function of the air gap spacing. With the increase in the valve spool stroke, the air gap spacing decreases, and the electromagnetic force increases accordingly. The change trend of the electromagnetic force is the same as the change trend of the action resistance.

3.3. Finite Element Analysis of Three-Bit Four-Way Electromagnetic Cartridge Valve in Electromagnetic Field

The valve body structure is symmetrical. In order to reduce the calculation workload, only half of the actual structure is considered here for analysis, and the air gap spacing of the upward and downward action and the corresponding resistance are the same. In order to consider the maximum resistance to overcome, the upper part of the coil that needs to overcome the gravity of the valve spool and the moving iron core are selected for analysis. The specific structure is shown in Figure 5.

Among them, the fixed iron core and moving iron core are defined as iron. The magnetic conductive block is made of silicon steel D21_50. The magnetic insulation material 1 is stainless steel. The magnetic insulation material 2 is copper.

In order to achieve the electromagnetic force that drives the valve spool and maintains the action position, under the premise of meeting the limit of the design size, the feasibility of two dimensional optimization schemes was verified, respectively. The influence of the schemes on the electromagnetic force was determined, and the structural scheme with the least influence on the electromagnetic force was finally determined.

According to the structure of the standard solenoid valve coil, the coil turns are set to $N$ = 800 turns, the copper wire diameter is set to $d$ = 0.3 mm, and the coil current is set to $I$ = 1 A. The corresponding window area of the copper wire is

$$S_0=N{\displaystyle \frac{d^2}{4}}\pi =56.52 {\mathrm{mm}}^2$$

(10)

According to the design size, when the initial coil winding radius is 5.4 mm, and the maximum outer diameters of the corresponding coil are 8 mm, 8.5 mm, 9 mm, 9.5 mm, and 10 mm, the electromagnetic field analysis was carried out. The corresponding coil heights are 21.7 mm, 18.2 mm, 15.7 mm, 13.8 mm, and 12.3 mm. Accordingly, in order to ensure the maximum magnetic density at the air gap, the size of the moving iron core is adjusted accordingly so that the air gap is located in the middle of the coil length.

Keeping the length and width of the coil section unchanged, the radial size of the iron core is reduced, which can reduce the winding radius of the coil, so as to limit the maximum diameter. According to the design size, when the radius of the moving iron core is 3 mm, 3.5 mm, and 4 mm, the electromagnetic field analysis is carried out. Part of the magnetic circuit distribution is shown in Figure 6.

The magnetic circuit distribution is affected by permeability, current density, magnetoresistance, air gap, and other factors. Where the material is determined, the permeability is also determined. According to the design of the valve body structure and the setting current density, the residual reluctance and the air gap are also determined, and the magnetic circuit distribution is then determined. According to the magnetic circuit distribution, the structure of the valve body conforms to the principle of the minimum magnetic resistance [21], which can generate upward magnetic force on the moving iron core. As shown in Figure 7, after post-processing, the trend of the electromagnetic force changes with the moving iron core.

As can be seen from Figure 7, the smaller the radius of the moving iron core, the larger the axial electromagnetic force generated. The main reason is that reducing the radius of the moving iron core can reduce the area of the magnetic field. Thus, under the same magnetic field strength, a larger magnetic flux density is beneficial to enhance the magnetic force. Meanwhile, due to the reduction in the radius of the moving iron core, the winding radius of the coil is also reduced accordingly, and the generated magnetic field can be better constrained in the designed magnetic circuit. The corresponding excitation effect will be better, and the magnetic density will be higher. However, when the moving magnetic core is too small, the magnetic flux will be saturated, resulting in the damage to the magnetic core. Therefore, in this design, the radius of the moving iron core is 3 mm. The moving iron core with the radius of 3 mm is used for the magnetic field analysis with the coil outer diameters of 8 mm, 8.5 mm, 9 mm, 9.5 mm, and 10 mm. The model is shown in Figure 8.

As shown in Figure 9, after post-processing, the electromagnetic force changes with the maximum outside diameter of the coil.

As can be seen from Figure 9, the electromagnetic force increases with the displacement, and the axial magnetic force gradually increases. When the cross-sectional area and the number of turns of the coil is constant, the larger the maximum outer diameter of the coil, the greater the magnetic force generated.

To ensure that the valve spool can move, the electromagnetic force must be greater than the sum of the valve spool resistance. As can be seen from Formula (6), except for the friction resistance $F_0$, other valve spool resistance is a function of the spool displacement $x$. Therefore, the movement process of the valve spool needs to be analyzed. When the radius of the moving iron core used is 3 mm, and the coil outer radius used is 8.5 mm, the magnetic field simulation is conducted. Parameter values are shown in

Table 1. Main parameter values of the electromagnetic cartridge valve.

Parameter	Numerical Value	Parameter	Numerical Value	Parameter	Numerical Value
$m$ (kg)	0.0015	$B$ (N·s/m)	0.8	$C_d$	0.61
$C_v$	0.98	$d_0$ (mm)	10	$\theta$ (°)	69
$\Delta p$ (MPa)	0.3	$k$ (N/m)	3	$F_0$ (N)	6

.

Considering the inertia force of the spool, viscous force, hydraulic force, and other resistance, the motion curve of the valve spool is shown in Figure 10. It can be seen from the figure that the speed of the valve spool becomes 0 after 30 ms, that is, the action of the spool is basically completed within 30 ms. At 30 ms, the valve spool reaches the fastest speed, approximately 1.4 m/s, and the response speed is quick. After 30 ms, due to reaching the end of the journey, the speed of the valve spool decreases to 0 m/s. Next, according to the contrast of the change of the electromagnetic force and the linear item of the valve spool movement resistance, the opening and closing movement characteristics of the valve spool can be verified. In order to obtain the valve spool inertia force—$F_{si}$, the valve spool acceleration must be obtained. The first derivative of the velocity to the response time in Figure 10 is the valve spool acceleration. The acceleration change curve of the valve spool is shown in Figure 11.

As shown in Figure 12, overlaying each resistance, the sum of the valve spool movement resistance is calculated. From Figure 11, it can be seen that with the increase in the valve spool movement displacement, the movement resistance also increases.

According to the analysis of the influence of the coil size and the size of the moving iron core on the magnetic force size, in order to ensure that the electromagnetic force is enough, the moving iron core with a smaller radius and the coil with a smaller height can be adopted in the design to provide sufficient electromagnetic force. Considering the existence of the actual coil insulation layer, the magnetic insulation layer, and other protective layers, the radius of the moving iron core is selected as 3 mm, and the coil outer radius is 8.5 mm. The maximum diameter of the corresponding coil is 17 mm, and the coil height is 18.23 mm. As shown in Figure 13, the corresponding electromagnetic force and action resistance to this size are analyzed and compared.

As can be seen from Figure 13, the axial electromagnetic force curve is all above the action resistance, indicating that the electromagnetic force under the design is always greater than the action resistance of the solenoid valve. Therefore, the design meets the requirements of the electromagnetic force and can complete the action change of the valve spool.

4. Experimental Research

In this chapter, the response experiment of the electromagnetic cartridge valve is designed and completed. The experimental data are organized and analyzed. It is concluded that the left coil and right coil can be opened normally when they are energized, and the response time of the valve spool meets the application requirements of the solenoid valve.

4.1. Experimental Purpose

According to the electromagnetic cartridge valve designed in this paper, the response experiment of the electromagnetic cartridge valve is designed to verify and analyze the matching effect and reliability among the electromagnetic cartridge valve, software, and mechanical and electrical liquid components.

4.2. Experimental Principle

The schematic diagram of the electromagnetic cartridge valve experiment is shown in Figure 14, which mainly includes three parts: hydraulic system, data acquisition system, and load. The motor of the hydraulic system drives the oil pump to drive the hydraulic oil into the three-bit four-way electromagnetic cartridge valve. The command signals are send to the three-bit four-way electromagnetic cartridge valve through the data processing center. By observing whether the sensor reading is stable, it can be determined whether the solenoid valve is functioning properly.

Figure 15 shows the experimental devices of the electromagnetic cartridge valve. The hydraulic system serves as the power source to load the load (fluid control valve), which includes components such as hydraulic pump, motor, one-way valve, and electromagnetic cartridge valve. The data acquisition system is used to collect the data of the pressure sensors, including the terminal computer, data acquisition card, and pressure sensors. The key experimental equipment parameters are shown in

Table 2. Parameter table of the key test equipment.

Name	Model Number	Specifications	Manufacture Factory
Hydraulic pump	CBN-320	0–16 MPa	Xin Mingyao Hydraulic Technology (Taizhou, China)
Electric motor	77S-RA/CW	7000 r/min 680 W	Zhongyuan Tools (Anyang, China)
Data acquisition card	HK-USB-DAQ V1.2	16-ways 0–10 V	HengKai Technology (Luoyang, China)
Pressure sensor	SUP-P300	0–20 MPa	Hangzhou Meikong (Hangzhou, China)
Flow sensor	LWYC-15 L	0.6–6 m3/h	Hui Xiang (Shenzhen, China)

. Figure 16 shows the physical diagram of some experimental devices, including three-bit four-way solenoid valve, coils, pressure sensors, power supply, hydraulic pump, and electric motor. The software for processing the data collected by the data acquisition card is ANSYS Fluent, and the collected data were simulated and analyzed.

4.3. Experimental Steps

(1)

As shown in Figure 14, the oil tank, motor pump, one-way valve, three-bit four-way electromagnetic cartridge valve, pressure sensors, and load (fluid control valve) are connected.

(2)

The motor pump acts as the hydraulic power source to pump the oil from the oil tank to the three-bit four-way electromagnetic cartridge valve.

(3)

The voltage instruction signals are input to the left coil of the three-bit four-way electromagnetic cartridge valve.

(4)

We observe whether the power source and the valve group operate smoothly, and observe whether the pressure sensor reading is stable through the data processing center.

(5)

We stop the experiment and collect data.

(6)

We input the voltage instruction signals to the right coil of the three-bit four-way solenoid valve and repeat steps (4) and (5).

(7)

We sort out the experimental data and analyze the experimental results.

4.4. Analysis of the Experimental Results

4.4.1. Analysis of the Experimental Results of the Left Coil of the Solenoid Valve

The pressure sensor is used to measure the pressure of the fluid control valve, and the deformation of the mechanical structure of the sensor is measured through the fluid pressure. Here, the transient pressure measurement method is used to sample and analyze the fluid pressure in real time by using the pressure sensors with the high-frequency sampling. As shown in Figure 17, when the left coil is powered on or off, the pressure data of the pressure sensor 1 are obtained by the data acquisition card.

It can be seen from Figure 17 that the variation trends of the pressure and the flow rate are roughly the same. When the time is around 0–20,000 ms, the pressure curve is almost horizontal indicating that the pressure changes little over time and is in a stable state. At this time, the solenoid valve pushes the fluid control valve to move to the right. When the time is around 20,000–24,000 ms, the pressure rises gradually, and the analysis of the reason is that the fluid control valve has moved to the right to the limit position, resulting in a gradual rise in the pressure of the hydraulic pump. Thus, the value measured by the pressure gauge gradually increases. At 24,000–38,000 ms, the pressure curve is the horizontal section again; the analysis of the reason is that the pressure of the hydraulic pump rises to the limit pressure, and the value of the pressure gauge is the limit pressure. After 38,000 ms, the pressure gradually decreases. This is because the hydraulic pump and the left coil of the solenoid valve are powered off, and the pressure gradually reduces to 0 MPa. The data for 200–300 ms when the electromagnetics are on, 15,000–15,100 ms when the fluid control valve moves to the right, and 30,000–30,100 ms when the fluid control valve is in the limit position are extracted, respectively. The pressure curves are shown in Figure 18, Figure 19 and Figure 20.

As can be seen from Figure 18, at 200–232 ms, the pressure fluctuates above and below 0 MPa, indicating that the pressure is very small, and the valve spool of the solenoid is not opened at this time. At 232–284 ms, the pressure begins to increase rapidly, and the opening process of the solenoid valve spool is about 52 ms. The difference with the theoretical calculated value of 30 ms in the Section 3.3 above is 22 ms. The reason may be the power loss of the wound coils of the solenoid valve, resulting in a longer opening time. After 284 ms, the pressure tends to be stable, and the solenoid valve is in the open state at this time.

When the fluid control valve moves to the right, the pressure data diagram is shown in Figure 19. As can be seen from Figure 19, the pressure curve is a fluctuation curve, and the pressure curve is fitted. According to the fitting curve, the average pressure of the fluid control valve is about 3.75 MPa. Figure 20 shows the pressure data of the fluid control valve in the limit position. Similarly, as can be seen from Figure 20, the pressure curve is also a fluctuation curve, and the pressure curve is fitted. From the fitting curve, when the fluid control valve is in the extreme position (moving to the far right end), the average pressure detected is about 15.30 MPa. The known maximum working pressure of the hydraulic pump is 16 MPa. The difference in the pressure data of the hydraulic pump may be caused by the pressure loss when the oil moves through the solenoid valve and the tubing.

4.4.2. Analysis of the Experimental Results of the Right Coil of the Solenoid Valve

As shown in Figure 21, when the right coil is powered on or off, the pressure data of the pressure sensor 2 are obtained by the data acquisition card.

It can be seen from Figure 21 that the changes in the pressure and the flow rate are the same as the trend of the left coil. At about 0–24,000 ms, the pressure curve is almost horizontal, indicating that the pressure at this time changes little with time and is in a stable state. At this time, the solenoid valve is pushing the fluid control valve to move to the left and the pressure is gradually rising at about 24,000–30,000 ms. The reason is that the fluid control valve has moved to the left to the limit position, causing the pressure of the hydraulic pump to rise gradually. Thus, the value measured by the pressure gauge gradually rises, and at 30,000–42,000 ms, the pressure curve is once again the horizontal section. The reason is that the pressure of the hydraulic pump rises to the limit pressure. The value of the pressure gauge is the value at which the maximum pressure is reached. After 42,000 ms, the pressure decreases gradually; the reason for this is that the pressure of the hydraulic pump rises to the limit pressure, and the pressure gauge value is the value at the limit pressure. The reason is that the hydraulic pump and the left coil of the solenoid valve are powered off, and the pressure gradually reduces to 0 MPa. As shown in Figure 22, Figure 23 and Figure 24, the data of 400–500 ms when the solenoid valve is opened, 15,000–15,100 ms when the fluid control valve is opened, and 35,000–35,100 ms when the fluid control valve is in the limit position are, respectively, extracted to draw the pressure curves.

As can be seen from Figure 22, at 400–420 ms, the pressure fluctuates above and below 0 MPa, indicating that the pressure is very small, and the solenoid valve spool is not opened at this time. At 420–464 ms, the pressure begins to increase rapidly, and the opening process of the solenoid valve spool is about 44 ms. The difference with the theoretical calculated value of 30 ms in the Section 3.3 above is 14 ms, which may be caused by the existence of the power loss in the wound coils of the solenoid valve, resulting in longer opening time. After 464 ms, the pressure tends to be stable, and the solenoid valve is in the open state at this time.

Figure 23 shows the pressure data of the fluid control valve moving to the left. As can be seen in Figure 23, the pressure curve is a fluctuation curve, and the pressure curve is fitted. According to the fitting curve, the average pressure of the fluid control valve is about 3.72 MPa. Figure 24 shows the pressure data of the fluid control valve in the limit position. Similarly, it can be seen from Figure 24 that the pressure curve is a fluctuation curve, and the pressure curve is fitted. According to the fitting curve, when the fluid control valve is in the extreme position (moving to the far left end), the average value of the detected pressure data is about 15.25 MPa. The known maximum working pressure of the hydraulic pump is 16 MPa. The difference in the pressure data may be caused by the pressure loss when the oil moves through the solenoid valve and the tubing.

Through the above experiments, when the left and right coil is powered on, the left coils and right coils can be opened normally. When the left coil is electrified, the opening time of the solenoid valve is about 52 ms, and when the right coil is electrified, the opening time of the solenoid valve is about 44 ms. These have errors with the previous theoretical values. The reason may be the power loss of the wound coils of the solenoid valve, resulting in a longer opening time.

5. Conclusions

In this paper, in order to change the size of the downhole robot, the size of the electromagnetic cartridge valve was reduced. Two optimization methods were proposed for the size reduction of the solenoid valve. The mechanical model of the three-bit four-way cartridge valve was established. The influence of the coil diameter and iron core diameter on the electromagnetic force of the three-bit four-way cartridge solenoid valve was analyzed. Subsequently, the finite element analysis of the electromagnetic field of the model was conducted, and it was found that the electromagnetic force increases with the increase in the coil diameter and iron core diameter. But if the moving magnetic core is too small, the magnetic flux can be saturated, leading to the damage to the magnetic core. According to the changes in the electromagnetic force with the outer diameter of the coil and the radius of the moving iron core, the moving core radius of 3 mm and the outer coil radius of 8.5 mm were selected for the numerical simulation. The results show that the action of the valve spool is basically completed within 30 ms. The acceleration of the valve spool increases with the response time, and the action resistance increases with the displacement of the valve core. It shows that the electromagnetic force under this design is always greater than the action resistance of the solenoid valve. That is, the maximum outside diameter of the solenoid valve is successfully reduced without affecting the movement of the spool. Then, the response experiment of the solenoid valve was designed. Through the on–off and off–power experiments on the left and right side coils of the solenoid valve, the matching effect and reliability between the solenoid valve, software and electromechanical hydraulic components were verified and analyzed. In these two experiments, the actual response time of the solenoid valve spool was 52 ms and 44 ms, respectively, which is slightly larger than the theoretical calculated value of 30 ms, while the experimental average pressure of the fluid control valve when it moves to the limit position is 15.30 MPa and 15.25 MPa, respectively, which is lower than the theoretical maximum working pressure value of the fluid control valve of 16 MPa. According to the data results, the three-bit four-way solenoid valve can meet the requirements of practical application after the size optimization design. The dimensional optimization of the three-position four-way solenoid valve can help to reduce the radial size of downhole robots. This research provides a possibility for downhole robots to operate in more confined spaces. This study is of great significance to the research and application of downhole robots in drilling engineering.