Investigation of the Dynamic Characteristics of a Two-Stage High-Speed On/Off Valve with Adjustable Maximum Opening

Abstract

The effective way to improve the reliability of the fuel metering system in an aero-engine is to use a high-speed on/off valve (HSV) instead of a servo valve as the pilot stage of the fuel metering valve. However, the dynamic performance of the fuel metering valve is easily affected by the HSV, so a novel two-stage high-speed on/off valve with adjustable maximum opening (AMOHSV) is proposed in which the maximum stroke of the main valve is regulated with an adjustable rod. Firstly, the structure and working principle of the proposed valve are presented. Then, an entire mathematical model is established and verified based on a multi-physical field coupling mechanism. Finally, simulations and experiments prove that when the maximum opening is 0.2 mm, the total opening time and total closing time of the AMOHSV are within 5 ms. In addition, an upward inflection point and a downward inflection point on the pressure curve of the control chamber can be used to identify the total opening time and total closing time, respectively. The research results also prove that the proposed structure solves the conflict between the maximum flow rate and the dynamic performance of the traditional HSV.

1. Introduction

Aero-engine is the power and heart of the aircraft [1]. Nowadays, as the performance of the aero-engine continues to improve, full authority digital engine control (FADEC) has become the key technology in the field of the aero-engine [2]. In the FADEC system, a fuel metering valve (FMV) regulated by the control unit transmits the fuel flow rate into the combustor [3,4]. The precise control of the fuel flow rate is a guarantee of optimal performance for aero-engines [5], thus the accuracy of the FMV’s output flow rate needs to be improved. To improve the accuracy and dynamic performance of the FMV, an electro-hydraulic servo valve (EHSV) is usually selected to be the pilot stage due to its quick response and high precision [6]. For example, Bertin et al. [7] proposed a nozzle-flapper servo valve actuated with a dual lane piezoelectric ring bender to control the position of the FMV, in which the pilot stage obtains ±50 μm stroke. Due to the large size and low integration of the conventional EHSV, Li et al. [8] designed a new two-dimensional three-way constant pressure differential fuel flow servo valve. The results prove that the frequency response of the servo valve is 38 Hz, and the weight is only 801.5 g. To achieve the high precision opening control of the FMV, the pilot stage consisting of an EHSV, a main valve with double control chambers, and a pressure difference compensated valve was designed and tested [9].

However, due to the perfectly symmetrical structure and extremely tight tolerances of the EHSV, its accuracy and reliability are brittle in extreme environments with long-span temperature variation and strong vibration [10]. Zhang et al. [11] studied the relationships between the flow force, friction, and temperature using the proposed analytical model of the temperature-sensitive operating force of the EHSV. Ma et al. [12] proposed a mathematical model to describe the temperature-zero-drift characteristics of the EHSV. In this research, the simulation results show that the control error of the EHSV increases by 15% when the oil temperature varies between 20 and 270 °C. A monte carlo method considering the independent random parameters was proposed to analyze the reliability of the jet pipe servo valve under the condition of random vibration [13]. Moreover, intelligent fault diagnosis methods based on deep learning can be used to improve fault identification accuracy and reliability for hydraulic components [14,15].

Compared to the EHSV based on the analog flow regulation, the high-speed on/off valve (HSV) based on the discrete flow regulation only works in a fully open or fully closed state, which has several advantages including high reliability (insensitive to oil contamination), quick response, high efficiency, good repeatability, and low cost [16,17]. Therefore, the use of the HSV as the pilot stage has become a hot research topic in academia [18]. For example, Tamburrano et al. [19] proposed a nozzle flapper servo valve driven with two piezoelectric valves in which the output displacement of the piezoelectric valve is only within 0.2 mm, which could not meet the demand of a large flow rate. To improve the reliability of the two-stage proportional valve, two two-position two-way HSVs are used as the pilot stage [20]. However, due to the low flow rate of the pilot HSV, it is difficult to increase the frequency response of the main valve. To solve this issue, parallel-connected HSVs technology is often used to improve the flow rate of the pilot stage, but it simultaneously sacrifices the size [21,22,23].

Therefore, it is necessary to investigate the HSV with a large flow rate. The multi-objective optimization method, such as the non-dominated sorting genetic algorithm II, is used to achieve the Pareto optimal solution of the main structure parameters for the HSV with a large flow rate [24,25]. In addition, in previous studies [26,27,28], once the structure of the two-stage or three-stage HSVs with a large flow rate is determined, its dynamic characteristics and maximum output flow capacity cannot be changed. Since the dynamic performance and maximum output flow capacity are inherently contradictory, this would lead to low robustness of the existing HSVs, which means that the dynamic characteristics and maximum output flow capacity cannot be adjustable according to the working conditions. To address this issue, a two-stage high-speed on/off valve with adjustable maximum opening (AMOHSV) is proposed in this paper, which can regulate the maximum flow rate and the dynamic characteristics by adjusting the position of the rod.

The rest of this article is organized as follows. The structure and working principle of the AMOHSV are introduced in Section 2. Section 3 shows the mathematical model of the AMOHSV. A simulation analysis of the dynamic characteristics of the AMOHSV is presented in Section 4. Comparative experimental results are obtained in Section 5. Finally, Section 6 concludes this article.

2. Structure and Working Principle

In this research, a two-stage high-speed on/off valve with adjustable maximum opening (AMOHSV) is proposed which consists of a pilot HSV, a main valve, a spring, an adjustable rod, and an end cap, as shown in Figure 1.

As shown in Figure 1, the pilot HSV is a two-position and three-way normally open on/off valve actuated with a solenoid. The main valve (poppet) has a processed out pressure groove on its side surface to prevent oil leakage from the control chamber to port A of the main valve. The outlet of the pilot HSV is connected to the control chamber of the main valve. The adjustable rod is used to regulate the maximum opening of the main valve.

The working principle of the AMOHSV is as follows: when the coil of the pilot HSV is de-energized (initial condition), the pilot valve moves to the top side by the high pressure from the supply line, so the port T is blocked, and the control chamber connects to the supply line, which causes the pressure in control chamber to be equal to the supply line. However, the main valve maintains closed states because the effective area of the control chamber is bigger than that of the supply chamber of the main valve. Conversely, when the coil is energized (working condition), the pilot valve moves to the bottom side by electromagnetic force, so the port P is blocked, and the control chamber connects to the return line, which leads to the pressure in the control chamber being smaller than that of the supply line. Then, the pressure difference between the supply chamber and the control chamber pushes the main valve to open.

The bigger the maximum opening of the main valve, the larger the volume of the control chamber, which leads to the attenuation of the main valve’s dynamic characteristic. Therefore, output flow capacity and dynamic performance are inherently contradictory, and it is a wise choice to improve the dynamic performance using a control strategy.

3. Mathematical Model of the AMOHSV

Before establishing the mathematical model of the AMOHSV, it is necessary to understand the motion mechanism and energy conversion of the AMOHSV, as shown in Figure 2. Under the driving voltage, the electro-mechanical converter (solenoid) converts electrical energy into mechanical energy and pushes the pilot valve to move. Then, the pilot valve outputs the flow rate to regulate the pressure of the control chamber for controlling the opening and closing of the main valve.

As it can be seen from Figure 2, it is easy to find that the action mechanism of the multi-physical field coupling of the pilot valve is as follows:

(a)

The coupling of the electric field and the magnetic field is reflected in the fact that the excitation current generates the magnetic field; conversely, the variation in the magnetic field generates the induced electromotive force, which impedes the change in the excitation current.

(b)

The coupling of the magnetic field and mechanical motion is reflected in the fact that the electromagnetic force produces the motion of the armature; conversely, the motion of the armature changes the air gap of the magnetic circuit, which in turn affects the magnetic flux density.

(c)

The coupling of the mechanical motion and the flow field is reflected in the fact that an increase in the pilot valve’s opening leads to an increase in the output flow rate of the pilot valve; conversely, the steady flow force affects the motion of the pilot valve.

The coupling of the main valve is reflected in the mechanical motion and the flow field. Specifically, the variation of the main valve’s opening determines the output flow rate of the main valve, but the increase of the steady flow force in turn affects the motion of the main valve.

The coupling between the pilot valve and the main valve determines the pressure of the control chamber. The pressure variation of the control chamber not only affects the motion of the main valve but also changes the output flow rate of the pilot valve.

3.1. Mathematic Model of the Pilot Valve

The pilot HSV driven by a solenoid converts electrical energy to mechanical energy and then to flow energy. Thus, the mathematical model of the pilot HSV includes an electro-magnetic model, a dynamic model, and a fluid model.

3.1.1. Electro-Magnetic Model

Based on the principle of Kirchhoff Voltage, the balance equation of the coil voltage is defined as [29]:

$$U=IR+L\frac{\mathrm{d}I}{\mathrm{d}t}+I\frac{\mathrm{d}L}{\mathrm{d}t}$$

(1)

where U and I denote the driving voltage and the driving current of the coil, respectively. R and L denote the resistance and the equivalent inductance of the coil, respectively.

Assuming that the magnetic flux is uniformly distributed, a magnetic circuit equation is defined as:

$$NI=H_{\mathrm{c}}{l}_{\mathrm{c}}+H_{\mathrm{a}}{l}_{\mathrm{a}}=H_{\mathrm{c}}{l}_{\mathrm{e}}$$

(2)

where N denotes the number of coil turns; H_c and H_a denote the equivalent magnetic field intensity in the core and the air gap, respectively; l_c and l_a denote the equivalent length of the magnetic circuit inside the core and air gap, respectively; and l_e denotes the equivalent length of the whole magnetic circuit.

The expression of l_e is defined as:

$$l_{\mathrm{e}}=l_{\mathrm{c}}+u_{\mathrm{r}}(l_0-x_{\mathrm{p}})$$

(3)

where u_r denotes the core relative permeability; and l₀ and x_p denote the initial length of the air gap and the displacement of the ball valve, respectively.

The relationships among H_c, φ, and L are given as [30]:

$$H_{\mathrm{c}}=\frac{B}{u_{\mathrm{c}}}=\frac{\phi }{u_{\mathrm{c}}{S}_{\mathrm{e}}}$$

(4)

$$LI=N\phi =\psi$$

(5)

where φ denotes the magnetic flux; B denotes the magnetic flux density; S_e denotes the effective sectional area of the armature; u_c denotes the core permeability; and ψ denotes the flux linkage.

Combining Equations (2)–(5), the coil inductance L is obtained using:

$$L=\frac{N^2{u}_{\mathrm{c}}{S}_{\mathrm{e}}}{l_{\mathrm{eq}}}=\frac{N^2{u}_0{S}_{\mathrm{e}}}{l_{\mathrm{a}}/u_{\mathrm{r}}+(l_0-x_{\mathrm{p}})}$$

(6)

The electromagnetic force F_e is written as:

$$F_{\mathrm{e}}=\frac{{\phi }^2}{2k_{\mathrm{f}}{u}_0{S}_{\mathrm{e}}}$$

(7)

where k_f denotes the coefficient related to magnetic leakage; and u₀ denotes the air permeability.

3.1.2. Dynamic Model of the Pilot Valve

The force balance equation of the pilot valve can be described as:

$$m_{\mathrm{p}}{\ddot{x}}_{\mathrm{p}}=F_{\mathrm{e}}-p_{\mathrm{s}}{A}_{\mathrm{p}}-B_{\mathrm{p}}{\dot{x}}_{\mathrm{p}}-F_{\mathrm{py}}$$

(8)

where m_p denotes the moving mass of the pilot valve; B_p denotes the movement damping of the pilot valve; p_s denotes the supply pressure; A_p denotes the effective area of Port P; and F_py denotes the steady flow force of the pilot valve.

The steady flow force of the pilot valve is written as [31]:

$$F_{\mathrm{py}}=2C_{\mathrm{pv}}{C}_{\mathrm{pd}}{A}_{\mathrm{h}}\Delta p\cos {\theta }_{\mathrm{h}}$$

(9)

where C_pv and C_pd denote the fluid velocity coefficient and the flow coefficient of the pilot valve, respectively; A_h denotes the flow area of the pilot valve; Δp denotes the pressure difference across the variable orifice; and θ_h denotes the flow angle of the pilot valve.

3.1.3. Fluid Model of the Pilot Valve

The flow area of the pilot valve is described as:

$$A_{\mathrm{h}}=\mathsf{\pi }{x}_{\mathrm{p}}\cos {\theta }_{\mathrm{p}}(D_{\mathrm{p}}\sin {\theta }_{\mathrm{p}}+x_{\mathrm{p}}\sin {\theta }_{\mathrm{p}}\cos {\theta }_{\mathrm{p}})$$

(10)

where θ_p denotes the half-cone angle of the pilot valve’s seat; and D_p denotes the diameter of the pilot valve.

Taking a PWM cycle as an example, when the coil is de-energized, the pilot valve remains in the initial station (normally open), and the flow rate from port P to port C is written as:

$$Q_{\mathrm{pc}}=C_{\mathrm{pd}}{A}_{\mathrm{hmax}}(1-\tau )\sqrt{\frac{2}{\rho }(p_{\mathrm{s}}-p_{\mathrm{c}})}$$

(11)

where τ denotes the duty cycle of the driving PWM signal; A_hmax denotes the maximum flow area of the pilot HSV; and p_c denotes the pressure of the control chamber.

Conversely, when the coil is energized, the pilot valve closes, which results in port C being connected to port T. The flow rate from port C to port T is written as:

$$Q_{\mathrm{ct}}=C_{\mathrm{pd}}{A}_{\mathrm{hmax}}\tau \sqrt{\frac{2}{\rho }(p_{\mathrm{c}}-0)}$$

(12)

3.2. Mathematic Model of the Main Valve

The main valve is driven by the pressure in the control chamber, which is regulated by the output flow rate of the pilot valve. Thus, the mathematical model of the main valve includes a fluid model and a dynamic model.

3.2.1. Fluid Model of the Control Chamber

When port P connects to port C, the pressure in the control chamber increases, and the corresponding dynamic pressure model can be defined as:

$${\dot{p}}_{\mathrm{c}}=\frac{{\beta }_{\mathrm{e}}}{V_{01}+A_{\mathrm{m}}{}_{\mathrm{c}}{x}_{\mathrm{m}}}(-A_{\mathrm{m}}{}_{\mathrm{c}}{\dot{x}}_{\mathrm{m}}+Q_{\mathrm{pc}})$$

(13)

where x_m denotes the displacement of the main valve; A_mc denotes the effective area of the main valve’s control chamber; V₀₁ denotes the initial volume of the control chamber when the opening of the main valve is maximum; and β_e denotes the bulk modulus of the fluid.

Conversely, when port C connects to port T, the pressure in the control chamber decreases, and the corresponding dynamic pressure model is given as:

$${\dot{p}}_{\mathrm{c}}=\frac{{\beta }_{\mathrm{e}}}{V_{02}-A_{\mathrm{m}}{}_{\mathrm{c}}{x}_{\mathrm{m}}}(A_{\mathrm{m}}{}_{\mathrm{c}}{\dot{x}}_{\mathrm{m}}-Q_{\mathrm{ct}})$$

(14)

where V₀₂ denotes the initial volume of the control chamber when the opening of the main valve is minimum.

According to Equations (13) and (14), it is easy to find that when the main valve reaches the maximum and minimum positions, the derivative of the x_m changes abruptly, which leads to a sudden change in the pressure (p_c), so that the position of the main valve spool can be identified by the particular variation in the pressure curve.

According to the annular gap flow theory, the leakage flow of the main valve’s annular gap is described as follows:

$$Q_{\mathrm{ca}}=\frac{\mathsf{\pi }{D}_{\mathrm{m}}{h}^3(p_{\mathrm{c}}-p_{\mathrm{a}})}{12\mu l_{\mathrm{m}}}$$

(15)

where D_m denotes the diameter of the main valve; μ denotes the oil dynamic viscosity; h and l_m denote the gap and the length of the annular pressure groove, respectively; and p_a denotes the pressure in port A.

3.2.2. Dynamic Model of the Main Valve

According to the analysis above, the forces on the two sides of the main valve are not equal and act as the power source of the valve motion. Therefore, based on Newton’s laws of motion and kinetic equations in general, the force balance equation of the main valve can be described as:

$$m_{\mathrm{m}}{\ddot{x}}_{\mathrm{m}}=A_{\mathrm{ms}}{p}_{\mathrm{s}}+A_{\mathrm{ma}}{p}_{\mathrm{a}}-A_{\mathrm{mc}}{p}_{\mathrm{c}}-F_{\mathrm{my}}-k_{\mathrm{m}}(x_0+x_{\mathrm{m}})-B_{\mathrm{m}}{\dot{x}}_{\mathrm{m}}$$

(16)

where m_m denotes the moving mass of the main valve; A_ms and A_ma denote the effective area of the inlet port and outlet port of the main valve, respectively; k_m and x₀ denote the stiffness and the preload length of the spring, respectively; and B_m and F_my denote the damping coefficient and the steady flow force of the main valve, respectively.

The steady flow force of the main valve is written as:

$$F_{\mathrm{my}}=2C_{\mathrm{mv}}{C}_{\mathrm{md}}{A}_{\mathrm{m}}\Delta p_{\mathrm{m}}\cos {\theta }_{\mathrm{m}}$$

(17)

where C_mv and C_md denote the fluid velocity coefficient and the flow coefficient of the main valve, respectively; A_m denotes the flow area of the main valve; Δp_m denotes the pressure difference across the main valve; and θ_m denotes the flow angle of the main valve.

3.3. Simulation Model and Main Parameters

Based on Equations (1)–(17), a simulation model of the AMOHSV is established using MATLAB/Simulink as shown in Figure 3, in which a Runge–Kutta algorithm is selected as the type of solver and the fixed-step size is set as 0.05 ms. The main parameters are listed in

Table 1. Main parameters of the AMOHSV.

Name	Symbol	Value
Number of coil turns	N	900
Resistance of the coil (relative to temperature)	R	9 Ω
Air permeability	u0	12.56 × 10−7 H/m
Effective sectional area of the armature	Se	45 × 10−6 m2
Initial length of the air gap	l0	0.45 × 10−3 m
Moving mass of the pilot valve	mp	0.0075 kg
Damping coefficient of the pilot valve	Bp	0.6 N/(m/s)
Supply pressure	ps	6 MPa
Effective area of Port P	Ap	1.37 × 10−6 m2
Half cone angle of pilot valve’s seat	θp	20°
Diameter of the pilot valve’s inlet	Dp	2.4 × 10−3 m
Moving mass of the main valve	mm	0.046 kg
Effective area of main valve’s inlet port	As	1.54 × 10−4 m2
Effective area of the control chamber	Amc	3.14 × 10−4 m2
Stiffness of the spring	km	15,000 N/m
Preload length of the spring	x0	6.8 × 10−3 m
Initial volume of the control chamber when the opening of the main valve is maximum	V01	6.2 × 10−6 m3
Initial volume of the control chamber when the opening of the main valve is zero	V02	6.268 × 10−6 m3

. In Table 1, the resistance of the coil (R) is measured using a digital multimeter; the supply pressure (p_s) is measured using a pressure sensor; and the number of coil turns (N), the damping coefficient (B_p), and the effective sectional area of armature (S_e) are identified using experimental data [29], which are different from the data used to determine the valve response. Other parameters can be found in the design and manufacture stages.

4. Simulation Analysis

Based on the simulation model established above, in this section, the dynamic characteristics of the AMOHSV are studied using simulation under different control strategies and different adjustable maximum openings. Firstly, the PWM control strategy used in this study is introduced in the following section.

4.1. PWM Control Strategy

The conventional PWM control signal has difficulty meeting the growing needs of the HSVs for high dynamic performance and low power consumption because the conventional PWM control signal cannot overcome the hysteresis of coil inductance as well as mechanical hysteresis. Therefore, a compound PWM control signal was proposed by reference [32] and used to improve the dynamic performance and simultaneously reduce the power consumption of the HSVs, as shown in Figure 4.

Figure 4 shows that, compared to the conventional PWM signal, the compound PWM signal consists of four different digital signals, including reference PWM, excitation PWM, high-frequency PWM, and reverse PWM [32]. According to the previous study, it is easy to see that the compound PWM control signal can improve the dynamic performance of the HSV because the added negative voltage changes the passive demagnetization of the armature to active demagnetization during the closing stage.

4.2. Validation of the Simulation Model

To validate the accuracy of the simulation model, the value of the coil current is measured in real-time during experiments. Comparisons of the coil current between the simulations and experimental results under different frequencies are shown in Figure 5.

As can be seen from Figure 5, the simulation results of the coil current are basically consistent with the experimental results under different frequencies, which proves the accuracy of the simulation model can be used to analyze the dynamic characteristics of AMOHSV. Only small errors exist in the energized stage, which may be caused by some factors, such as the residual magnetism of the soft magnetic material, the resistance affected by a temperature rise, the accuracy of the functional model, and the identification errors of the main parameters.

In addition, based on the frequency analysis of the experiment data, we find the following phenomena: (a) the frequency corresponding to the maximum amplitude is the working frequency of the pilot HSV, which is 20 Hz (frequency multiplication: 40 Hz, 60 Hz, 80 Hz, 100 Hz, and 120 Hz); (b) in addition, the amplitudes of 1 kHz, 2 kHz, and 3 kHz are higher than the nearby frequencies because the high-frequency component of PWM signal is 1 kHz; (c) other noise frequency components with small amplitude may be caused by the ripple of a DC power supply and the parasitic parameters in the circuit, which almost have no effect on the results.

4.3. Dynamic Characteristics Analysis

In some practical applications, the position of the valve cannot be measured because the valve is usually mounted in a hydraulic valve block. To indirectly obtain the opening and closing time of the AMOHSV, the relationship between the pressure in the control chamber and the main valve’s position is analyzed using simulations during the opening and closing stages respectively, as shown in Figure 6.

Figure 6 shows that, in the opening stage, when the main valve reaches the maximum position, an upward inflection point occurs on the pressure curve which can be explained using Equation (13). The total opening time of the main valve is 3.52 ms. In the closing stage, when the main valve reaches the minimum position, a downward inflection point occurs on the pressure curve which can be explained using Equation (14). The total closing time of the main valve is 3.57 ms.

A comparison of the simulation and experiment of the pressure is shown in Figure 7.

Figure 7 indicates that the error between the simulation curve and the experimental curve gradually increases after 52 ms because the simulation model does not take into account the water hammer effect at the moment of valve closing. However, this does not affect the validity of the conclusions of this study because this study only focuses on the time when the valve is fully open and when it is fully closed.

Therefore, in the following experiments, the inflection points on the pressure curve can be used to estimate the dynamic performance of the AMOHSV during the opening stage and closing stages.

5. Experimental Results and Analysis

To study the dynamic characteristics of the proposed two-stage high-speed on/off valve with adjustable maximum opening (AMOHSV), comprehensive performance tests are conducted on a hydraulic test platform. A prototype of the proposed AMOHSV is designed, fabricated, and assembled, as shown in Figure 8.

The performance testing bench for the AMOHSV is established, including an xPC target controller, a hydraulic power supply, a porotype of AMOHSV, and so on. The xPC target controller consists of a master computer, a slave computer, a data acquisition and control card (PCI 6251), and a voltage amplifier. A high-frequency pressure sensor (Kunshan Shuanqiao CYG1401F, accuracy is 0.5%, response frequency is 20 kHz, range: 0–10 MPa, flush type) installed in the control chamber is used to measure the pressure of the main valve’s control chamber. The position of the main valve is measured using a laser displacement sensor (Thinkfocus Co, range: −5 mm~5 mm, accuracy is 0.16%) during the assembly of the main valve. All of the above sensors are powered with a linear DC power supplier (Chaoyang Power 4NIC-X24, the maximum output voltage is 24 V, and the ripple wave of the voltage is less than 1 mV).

The PCI 6251 integrated into the slave computer is used to collect the pressure of the main valve’s control chamber with a differential transfer module. The PWM control signal generated using the Simulink model in the master computer is amplified to control the AMOHSV with the power amplifier.

5.1. Dynamic Characteristics during Energized Stage

To study the opening characteristic of the AMOHSV, a comparative study is carried out where the control pressure is analyzed between the conventional PWM and the compound PWM under the supply pressure of 6 MPa. The duty ratio of the PWM signal is 0.5 and the carrier frequencies are set to be 10 Hz, 20 Hz, and 50 Hz.

Figure 9 shows the compared results under different carrier frequencies and different adjustable maximum openings in which the pressure in the control chamber is used to evaluate the opening dynamic characteristics of the main valve during the energized stage.

Figure 9a shows that, when the adjustable maximum opening is set to 0.2 mm, the total opening time of the main valve is 4.5 ms under conventional PWM control; conversely, when the compound PWM control is implemented, the variations of the total opening time are less than 0.2 ms because the driving voltage is same during the energized stage. As can be seen from Figure 9b, compared with that in Figure 9a, the total opening time of the main valve significantly increases since the adjustable maximum opening of the main valve is doubled.

Indeed, the initial voltage (24 V) of the compound PWM is the same as that of the conventional PWM, which means that the total opening time should theoretically remain the same. However, in Figure 9a,b, the total opening time shows irregular variations, which may be caused by several factors, such as pressure fluctuation, adjustment error of the main valve’s maximum displacement, and resistance variation due to the temperature rise.

In order to analyze the influences of the frequencies and adjustable maximum openings on the opening characteristics of the AMOHSV, comprehensive tests are carried out, and a comparison of the results of the total opening time of the AMOHSV during the energized stage is given in

Table 2. Comparison of the total opening time during the energized stage.

Dynamic Characteristics		Maximum Opening = 0.2 mm			Maximum Opening = 0.4 mm
Frequency	Item	Conventional PWM	Compound PWM	Results	Conventional PWM	Compound PWM	Results
10 Hz	Total opening time	4.5 ms	4.35 ms	↓ 3.3%	5.6 ms	6.0 ms	↑ 7.1%
20 Hz	Total opening time	4.45 ms	4.45 ms	=	5.4 ms	5.4 ms	=
50 Hz	Total opening time	4.5 ms	4.95 ms	↑ 10%	5.25 ms	5.75 ms	↑ 9.5%

.

As shown in Table 2, both the frequency and the maximum opening have small effects on the total opening time of the AMOHSV because the driving voltage remains constant during the energized stage. The existing errors in the total opening time of the AMOHSV may be caused by the pressure fluctuations in the control chamber and supply port, which directly affect the force characteristics of the main valve. In addition, the duty ratio of the excitation PWM signal may also lead to errors at different carrier frequencies if it is not set properly.

5.2. Dynamic Characteristics during De-Energized Stage

Figure 10 shows the compared results under different carrier frequencies and different adjustable maximum openings in which the control pressure is used to evaluate the closing dynamic characteristics of the main valve during the de-energized stage.

As shown in Figure 10a, when the adjustable maximum opening is set to 0.2 mm, the total closing time of the main valve is 20.6 ms under conventional PWM control; conversely, the total closing time of the main valve reduces to 4.1 ms under the compound PWM control, which means the closing performance of the main valve is improved significantly. Figure 10b shows that the total closing time increases because the maximum opening of the main valve is doubled, resulting in an increase in the closing movement time of the main valve.

In order to analyze the influences of the frequencies and adjustable maximum openings on the closing characteristics of the AMOHSV, comprehensive tests are carried out, and a comparison of the results of the total closing time of the AMOHSV during the de-energized stage is listed in

Table 3. Comparison of the total closing time during the de-energized stage.

Dynamic Characteristics		Maximum Opening = 0.2 mm			Maximum Opening = 0.4 mm
Frequency	Item	Conventional PWM	Compound PWM	Results	Conventional PWM	Compound PWM	Results
10 Hz	Total closing time	20.6 ms	4.1 ms	↓ 80.1%	23.6 ms	7.15 ms	↓ 69.7%
20 Hz	Total closing time	20.65 ms	4.25 ms	↓ 79.4%	23.25 ms	7.4 ms	↓ 68.2%
50 Hz	Total closing time	can’t close	2.95 ms	↓↓	cannot close	7.55 ms	↓↓

.

As shown in Table 3, when the frequency is set to 10 Hz and 20 Hz, compared with the conventional PWM control, the total closing time of the main valve is reduced by at least 68.2% under the compound PWM control. When the frequency is set to 50 Hz, one period is only 20 ms, and the main valve does not close normally under the conventional PWM control because the electromagnetic force decreases slowly due to the lag of the big coil inductance, and the off-time exceeds half of one period.

Therefore, it is easy to find that, the compound PWM control strategy can significantly improve the closing dynamic performance of the AMOHSV due to the addition of the inverse PWM signal, which accelerates the demagnetization of the soft magnetic material during the de-energized stage.

6. Conclusions

In this research, a two-stage high-speed on/off valve with adjustable maximum opening (AMOHSV) is proposed in which the maximum stroke of the main valve is regulated using an adjustable rod with thread. During the assembly process, the adjustment accuracy of the maximum stroke of the AMOHSV is determined using the laser displacement sensor. The main conclusions are as follows:

(1)

The structure and working principle of the proposed AMOHSV are analyzed. Then, the mathematical model of the AMOHSV is determined based on the action mechanism of the multi-physical field coupling. Subsequently, a simulation model of the entire AMOHSV system is established and verified using the experiments of the coil current.

(2)

Extensive simulations and experiments demonstrate that an upward inflection point and a downward inflection point on the pressure curve of the control chamber can be used to identify the total opening time and total closing time of the AMOHSV.

(3)

The opening dynamic performance of the AMOHSV can be improved by increasing the driving voltage, and the closing dynamic performance of the AMOHSV is significantly improved by the compound PWM control.

In the future, our work shall focus on how to adjust the maximum opening of the main valve in real-time according to the load conditions.