# Analysis on Dynamic Response Characteristics of High-Speed Solenoid Valve for Electronic Control Fuel Injection System

Authors: Jianyu Zhang; Peng Liu; Liyun Fan; Yajie Deng
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

A 3D numerical simulation model of high-speed solenoid valve (HSV) for electronic control fuel injection system (ECFIS) has been developed. The model has been validated experimentally with acceptable maximum errors of 2% and 8.7% in closure response time and open response time, respectively. Effect of assembly parameters such as residual air gap, maximum lift of valve stem, mass of the moving parts, spring stiffness, and spring pretightening force on dynamic response characteristics of HSV has been analyzed in detail using the simulation model, and influence rules of various parameters on dynamic response characteristics have been established. Moreover, the correlation between interaction factors of main influence factors and dynamic response characteristics of HSV has also been analyzed. It is concluded that residual air gap, maximum lift of the valve stem, and spring pretightening force are the main influencing factors on dynamic response characteristics of HSV, and there are obvious interaction effects between them; when two or three of these main influencing factors are adjusted at the same time, the interaction effects should be considered.


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## Body

## 1. Introduction

With the continuous development of electronic control technology for diesel engines, the electronic control fuel injection system has become an inevitable trend to meet the requirements of increasingly stringent diesel emission regulations [1–4]. HSV is the most widely used automatic control component in ECFIS for diesel. Its dynamic response characteristics directly affect the control precision of the quantity and timing of fuel injection. Fluctuations in the quantity and timing of fuel injection greatly affect the combustion process in the cylinder of diesel engine in terms of economy, power, and emission performance of diesel engine. Therefore, research in the field of dynamic response characteristics of HSV is of significant importance for ECFIS.At present, there are lots of research materials available regarding this subject mostly focusing on the modeling, magnetic circuit optimization, and control method of HSV. Melgoza and Rodger [5] developed two new kinds of table models of electromagnetic energy conversion devices with one electrical and one mechanical degrees of freedom and performed a closing transient simulation whose results compared well against measurements. Li and Lee [6] presented an adaptive meshless method for magnetic field computation of an actuator, and it offered a technique to estimate the distribution of numerical errors and a scheme that automatically inserts additional nodes to improve computational accuracy and efficiency. Batdorff and Lumkes [7] introduced a high-fidelity magnetic equivalent circuit model for an axisymmetric electromagnetic actuator, and it improved the accuracy of conventional magnetic equivalent circuit. Cai et al. [8] optimized the plunger, plunger sleeve, coil, and magnetic ring structure parameters of the submersible electromagnetic actuator based on the magnetic equivalent circuit method. Yin et al. [9] developed the multiphysical field coupling model of solenoid valve for gasoline direct injection considering the electric, magnetic, and thermal properties employing the finite element method and optimized the armature, core, and coil structure parameters based on the multiobjective-simulated annealing algorithm. In [10, 11], peak and hold current control method for solenoid valve was introduced, and the drive circuit was designed and verified which can improve the dynamic response speed and the reliability and satisfy actual application. Lu et al. [12] investigated different driving circuits and control methods for of solenoid value and applied the preenergizing and reverse-energizing control strategy to speed up the response of the solenoid value.However, very limited research is available on the key assembly parameters of dynamic response characteristics of HSV. These parameters include residual air gap, maximum lift of valve stem, the mass of the moving parts, spring stiffness, and spring pretightening force, which are closely related to the motion state of HSV. Moreover, detailed analysis of interaction effects between different system factors and their influence on dynamic response characteristics of HSV still required to be investigated thoroughly. Interaction effects between different system factors can be understood using Figure1 as an example. In Figure 1, A and B stand for the individual factors, A∗B stands for the interaction factor between A and B, and A∗A and B∗B stand for the interaction factors with itself. It shows impact of two independent variables A and B on the dependent variable Y. Not only the individual factor A and B will affect Y but also the interaction factors A∗B, A∗A, and B∗B may affect Y because it is a common phenomenon that the factors promote or restrain each other. As a result, the influence degree of other relative variables on the dependent variable will change when a variable is at different levels. Therefore, it is necessary to further study the influences of interaction effect between parameters on dynamic response characteristics of HSV. In this research work, we have used the numerical simulations along with lab experiments to analyze in detail the influence of assembly parameters on dynamic response characteristics of HSV. Key influential assembly parameters have been determined, and the interaction effects between them are studied by the correlation analysis method combined with design of experiments. Research work carried out in this paper decisively provides some theoretical guidance for the selection of parameters and optimal match of HSV.Figure 1
Relational graph of two-factor influence.


## 2. Structures and Work Principle of HSV

This paper focuses on HSV of electronic unit pump (EUP) shown in Figure2. EUP mainly includes HSV, pump body, plunger, and its reset spring. HSV mainly includes armature, iron core, coil, valve stem, reset spring, terminal, and plug. After turning the power on, iron core attracts armature, pulls the valve stem, closes the seal cone, cuts off fuel, loop and thus sets up high pressure in the pump chamber which is required for fuel injection, whereas turning power off resets all. Resetting spring forces armature to reset the valve stem, decreasing the high-pressure fuel inside the pump chamber and thus stopping the fuel injection. Controlling of injection timing and injection quantity can be achieved through precisely adjusting the closing time and duration of control valve stem [13].Figure 2
Schematic of EUP and HSV.


## 3. Methodology

The entire process and method of dynamic response characteristics of HSV are shown in Figure3. Firstly, the transient numerical model of HSV was developed and validated. Secondly, the parametric influence on dynamic response characteristics of HSV were analyzed using the numerical model, and the key influential assembly parameters were obtained. Thirdly, design of experiments (DOE) was carried out to get sample points, and the response values of sample points were obtained by simulation. Then the correlation coefficients of interaction effect factors were computed. Finally, the correlation analysis was carried out.Figure 3
Research flowchart.


### 3.1. Numerical Modeling

#### 3.1.1. Mathematical Model

Bulleted Maxwell equations for low frequency transient magnetic field can be simplified as follows:(1)∇×H=σE,∇×E=∂B∂t,∇⋅B=0,where H is the magnetic field, σ is the conductivity of material, E is the electric field intensity, B is the magnetic induction intensity, and t is the time.The electromagnetic force is computed by the virtual work method:(2)Fmag=dWs,ids,where Fmag is the electromagnetic force on the armature in the direction of the displacement, W (s,i) is the magnetic coenergy of the system, s is the virtual displacement of the armature, and i is the current of coil. W (s,i) is given by(3)Ws,i=∫V∫0HB⋅dHdV,where V is the virtually distorted empty area around the armature.After combining equation (2) with equation (3), we get(4)Fmag=∂∂s∫V∫0HB⋅dHdV.The motion equation of the armature is as follows:(5)md2xdt2=Fmag−λdxdt−kx−F,where m is the mass of the moving parts, x is the displacement, λ is the damping coefficient of movement, k is the spring stiffness, and F is the spring pretightening.


#### 3.1.2. Numerical Modeling in Ansoft Maxwell

The above mathematical model is solved by the finite element method in the software Ansoft Maxwell. HSV is the nonaxisymmetrical structure; therefore, the 3D model has been developed to get the high-precision results, and eddy current has been considered in the Ansoft Maxwell environment. The iron core model is shown in Figure4(a). It is made of silicon steel sheets with a lamination coefficient of 0.95. The B-H curve of iron core material is shown in Figure 5. The coil model is shown in Figure 4(b). It is combination of a number of copper coils to build into a coil ring. The longitudinal section of the ring is made for the input terminals of excitation. The excitation type is set to current, and the measured currents are imported as excitation. The armature model is shown in Figure 4(c) whose material is DT4 (electrician pure iron). Since the moving parts in the Ansoft Maxwell modeling environment must be a three-dimensional entity and have a real boundary, the surfaces of moving parts cannot be curved surfaces but a divisible plane. To meet the requirements, an extra polygon cylinder surrounding the armature is built, and its material is set to air. Besides, a moving region was built to separate the static parts from the moving parts. Finally to make magnetic field boundary conditions satisfy the infinite far field boundary conditions, the solution domain was established to surround the entire model with air. The whole model including the solution domain is shown in Figure 4(d).Figure 4
Ansoft simulation model of HSV: (a) Iron core model. (b) Coil model. (c) Armature model. (d) The whole model.
(a)
(b)
(c)
(d)Figure 5
B-H curves of materials.


### 3.2. Numerical Model Validation

Figure6 shows the test bench for dynamic response of HSV. It consists of EUP, HSV, control unit, oscilloscope, eddy current displacement sensor, and current probe. The eddy current displacement sensor is placed suitably at the plug of EUP to measure the displacement of the valve stem. Coil current of HSV is measured in real time by using the current probe and transferred to the oscilloscope. The multiple groups of experimental results at the typical working conditions have been obtained by changing the cam rotational speeds and injection pulse widths to the controller.Figure 6
Test bench for dynamic response of HSV.The evaluation index of dynamic response of HSV includes the closure response timetc and the open response time to (as shown in Figure 7). We imported the measured currents at the typical working conditions to the numerical model as excitation, respectively, and carried out simulations to get the simulated results. Table 1 shows comparisons between the simulated and experimental results.Figure 7
Schematic of the response time of HSV.Table 1
Comparison of simulation and experiment.
Typical working conditions
Simulation
Experiment
Error (%)
Cam rotational speeds (r/min)
Injection pulse widths (°CaA)
t
c (ms)
t
o (ms)
t
c (ms)
t
o (ms)
t
c
t
o
975
3.8
0.658
0.496
0.668
0.543
1.5
8.7
1200
2.1
0.694
0.524
0.698
0.55
0.6
4.7
1200
4.2
0.698
0.520
0.7
0.555
0.3
6.3
1425
4.8
0.72
0.544
0.735
0.593
2.0
8.3
CaA stands for the rotation angle of the cam.According to Table1, the maximum error of the closure response time of HSV is 2%. Moreover, the simulated results of the closure response time are all less than the experimental result. Two reasons for less simulated closure times are because we have ignored the friction in the movement of armature and also not considered the rising of the temperature of the solenoid valve which can lead to the decrease in the magnetic permeability of armature and iron core. The maximum error of the open response time of HSV is 8.7%, and the simulated results of the open response time are also all less than the experimental result. The reason for less open simulation response time is that the initial magnetization curve was employed to describe the entire process of magnetization in simulation, which ignored the hysteresis effect. In fact, the hysteresis loop of soft magnetic material is very narrow. So we can use the initial magnetization curve to describe the entire process of magnetization. The error in simulations is considered within acceptable range when comparing with experiments, therefore validating the numerical model of HSV for next research on dynamic response of HSV.


### 3.3. DOE

DOE is a technology which is used widely, and central composite design (CCD) is one of the most popular DOEs. It can efficiently and reliably provide sample points for computing the correlation coefficients. CCD is a mixture of the traditional interpolation node distribution mode and full-factor or partial-factor design, which can provide more information with as little experiments as possible, including variable effects and test error [14]. Its design points consist of 2n factorial design points or partial-factor design points, 2n axial points or star points, and nc center points. Figure 8 shows the CCD of two factors in which n is 2. The distances are ±1 between center points and high or low level of factors (variables in standardized units). The distances are ±α between center points and axial points or star points. It is called central composite face (CCF) when α takes 1 [15]. CCF has been used in this paper.Figure 8
CCD of two factors.


#### 3.4. Correlation Analysis

Correlation analysis refers to two or more factors. The purpose is to measure how closely their correlativity between two factors is. Correlation coefficientR represented by equation (6) is a quantitative indicator for studying the degree of linear correlation between two factors. In equation (6), x is the studied factor, y is the corresponding response valve, i is the number i design sample point, n is the total number of sample points of DOE, x¯ is the average of this factor, and y¯ is the average of this response. The range of correlation coefficient R is from −1 to 1. R more than zero shows a positive correlation between two factors, whereas R less than zero shows a negative correlation between two factors. The larger the absolute value of correlation coefficient R is, the closer the correlation between the two factors is:(6)R=∑i=1nxi−x¯yi−y¯∑i=1nxi−x¯2∑i=1nyi−y¯2.


## 3.1. Numerical Modeling

### 3.1.1. Mathematical Model

Bulleted Maxwell equations for low frequency transient magnetic field can be simplified as follows:(1)∇×H=σE,∇×E=∂B∂t,∇⋅B=0,where H is the magnetic field, σ is the conductivity of material, E is the electric field intensity, B is the magnetic induction intensity, and t is the time.The electromagnetic force is computed by the virtual work method:(2)Fmag=dWs,ids,where Fmag is the electromagnetic force on the armature in the direction of the displacement, W (s,i) is the magnetic coenergy of the system, s is the virtual displacement of the armature, and i is the current of coil. W (s,i) is given by(3)Ws,i=∫V∫0HB⋅dHdV,where V is the virtually distorted empty area around the armature.After combining equation (2) with equation (3), we get(4)Fmag=∂∂s∫V∫0HB⋅dHdV.The motion equation of the armature is as follows:(5)md2xdt2=Fmag−λdxdt−kx−F,where m is the mass of the moving parts, x is the displacement, λ is the damping coefficient of movement, k is the spring stiffness, and F is the spring pretightening.


### 3.1.2. Numerical Modeling in Ansoft Maxwell

The above mathematical model is solved by the finite element method in the software Ansoft Maxwell. HSV is the nonaxisymmetrical structure; therefore, the 3D model has been developed to get the high-precision results, and eddy current has been considered in the Ansoft Maxwell environment. The iron core model is shown in Figure4(a). It is made of silicon steel sheets with a lamination coefficient of 0.95. The B-H curve of iron core material is shown in Figure 5. The coil model is shown in Figure 4(b). It is combination of a number of copper coils to build into a coil ring. The longitudinal section of the ring is made for the input terminals of excitation. The excitation type is set to current, and the measured currents are imported as excitation. The armature model is shown in Figure 4(c) whose material is DT4 (electrician pure iron). Since the moving parts in the Ansoft Maxwell modeling environment must be a three-dimensional entity and have a real boundary, the surfaces of moving parts cannot be curved surfaces but a divisible plane. To meet the requirements, an extra polygon cylinder surrounding the armature is built, and its material is set to air. Besides, a moving region was built to separate the static parts from the moving parts. Finally to make magnetic field boundary conditions satisfy the infinite far field boundary conditions, the solution domain was established to surround the entire model with air. The whole model including the solution domain is shown in Figure 4(d).Figure 4
Ansoft simulation model of HSV: (a) Iron core model. (b) Coil model. (c) Armature model. (d) The whole model.
(a)
(b)
(c)
(d)Figure 5
B-H curves of materials.


## 3.1.1. Mathematical Model

Bulleted Maxwell equations for low frequency transient magnetic field can be simplified as follows:(1)∇×H=σE,∇×E=∂B∂t,∇⋅B=0,where H is the magnetic field, σ is the conductivity of material, E is the electric field intensity, B is the magnetic induction intensity, and t is the time.The electromagnetic force is computed by the virtual work method:(2)Fmag=dWs,ids,where Fmag is the electromagnetic force on the armature in the direction of the displacement, W (s,i) is the magnetic coenergy of the system, s is the virtual displacement of the armature, and i is the current of coil. W (s,i) is given by(3)Ws,i=∫V∫0HB⋅dHdV,where V is the virtually distorted empty area around the armature.After combining equation (2) with equation (3), we get(4)Fmag=∂∂s∫V∫0HB⋅dHdV.The motion equation of the armature is as follows:(5)md2xdt2=Fmag−λdxdt−kx−F,where m is the mass of the moving parts, x is the displacement, λ is the damping coefficient of movement, k is the spring stiffness, and F is the spring pretightening.


## 3.1.2. Numerical Modeling in Ansoft Maxwell

The above mathematical model is solved by the finite element method in the software Ansoft Maxwell. HSV is the nonaxisymmetrical structure; therefore, the 3D model has been developed to get the high-precision results, and eddy current has been considered in the Ansoft Maxwell environment. The iron core model is shown in Figure4(a). It is made of silicon steel sheets with a lamination coefficient of 0.95. The B-H curve of iron core material is shown in Figure 5. The coil model is shown in Figure 4(b). It is combination of a number of copper coils to build into a coil ring. The longitudinal section of the ring is made for the input terminals of excitation. The excitation type is set to current, and the measured currents are imported as excitation. The armature model is shown in Figure 4(c) whose material is DT4 (electrician pure iron). Since the moving parts in the Ansoft Maxwell modeling environment must be a three-dimensional entity and have a real boundary, the surfaces of moving parts cannot be curved surfaces but a divisible plane. To meet the requirements, an extra polygon cylinder surrounding the armature is built, and its material is set to air. Besides, a moving region was built to separate the static parts from the moving parts. Finally to make magnetic field boundary conditions satisfy the infinite far field boundary conditions, the solution domain was established to surround the entire model with air. The whole model including the solution domain is shown in Figure 4(d).Figure 4
Ansoft simulation model of HSV: (a) Iron core model. (b) Coil model. (c) Armature model. (d) The whole model.
(a)
(b)
(c)
(d)Figure 5
B-H curves of materials.


## 3.2. Numerical Model Validation

Figure6 shows the test bench for dynamic response of HSV. It consists of EUP, HSV, control unit, oscilloscope, eddy current displacement sensor, and current probe. The eddy current displacement sensor is placed suitably at the plug of EUP to measure the displacement of the valve stem. Coil current of HSV is measured in real time by using the current probe and transferred to the oscilloscope. The multiple groups of experimental results at the typical working conditions have been obtained by changing the cam rotational speeds and injection pulse widths to the controller.Figure 6
Test bench for dynamic response of HSV.The evaluation index of dynamic response of HSV includes the closure response timetc and the open response time to (as shown in Figure 7). We imported the measured currents at the typical working conditions to the numerical model as excitation, respectively, and carried out simulations to get the simulated results. Table 1 shows comparisons between the simulated and experimental results.Figure 7
Schematic of the response time of HSV.Table 1
Comparison of simulation and experiment.
Typical working conditions
Simulation
Experiment
Error (%)
Cam rotational speeds (r/min)
Injection pulse widths (°CaA)
t
c (ms)
t
o (ms)
t
c (ms)
t
o (ms)
t
c
t
o
975
3.8
0.658
0.496
0.668
0.543
1.5
8.7
1200
2.1
0.694
0.524
0.698
0.55
0.6
4.7
1200
4.2
0.698
0.520
0.7
0.555
0.3
6.3
1425
4.8
0.72
0.544
0.735
0.593
2.0
8.3
CaA stands for the rotation angle of the cam.According to Table1, the maximum error of the closure response time of HSV is 2%. Moreover, the simulated results of the closure response time are all less than the experimental result. Two reasons for less simulated closure times are because we have ignored the friction in the movement of armature and also not considered the rising of the temperature of the solenoid valve which can lead to the decrease in the magnetic permeability of armature and iron core. The maximum error of the open response time of HSV is 8.7%, and the simulated results of the open response time are also all less than the experimental result. The reason for less open simulation response time is that the initial magnetization curve was employed to describe the entire process of magnetization in simulation, which ignored the hysteresis effect. In fact, the hysteresis loop of soft magnetic material is very narrow. So we can use the initial magnetization curve to describe the entire process of magnetization. The error in simulations is considered within acceptable range when comparing with experiments, therefore validating the numerical model of HSV for next research on dynamic response of HSV.


## 3.3. DOE

DOE is a technology which is used widely, and central composite design (CCD) is one of the most popular DOEs. It can efficiently and reliably provide sample points for computing the correlation coefficients. CCD is a mixture of the traditional interpolation node distribution mode and full-factor or partial-factor design, which can provide more information with as little experiments as possible, including variable effects and test error [14]. Its design points consist of 2n factorial design points or partial-factor design points, 2n axial points or star points, and nc center points. Figure 8 shows the CCD of two factors in which n is 2. The distances are ±1 between center points and high or low level of factors (variables in standardized units). The distances are ±α between center points and axial points or star points. It is called central composite face (CCF) when α takes 1 [15]. CCF has been used in this paper.Figure 8
CCD of two factors.


### 3.4. Correlation Analysis

Correlation analysis refers to two or more factors. The purpose is to measure how closely their correlativity between two factors is. Correlation coefficientR represented by equation (6) is a quantitative indicator for studying the degree of linear correlation between two factors. In equation (6), x is the studied factor, y is the corresponding response valve, i is the number i design sample point, n is the total number of sample points of DOE, x¯ is the average of this factor, and y¯ is the average of this response. The range of correlation coefficient R is from −1 to 1. R more than zero shows a positive correlation between two factors, whereas R less than zero shows a negative correlation between two factors. The larger the absolute value of correlation coefficient R is, the closer the correlation between the two factors is:(6)R=∑i=1nxi−x¯yi−y¯∑i=1nxi−x¯2∑i=1nyi−y¯2.


## 3.4. Correlation Analysis

Correlation analysis refers to two or more factors. The purpose is to measure how closely their correlativity between two factors is. Correlation coefficientR represented by equation (6) is a quantitative indicator for studying the degree of linear correlation between two factors. In equation (6), x is the studied factor, y is the corresponding response valve, i is the number i design sample point, n is the total number of sample points of DOE, x¯ is the average of this factor, and y¯ is the average of this response. The range of correlation coefficient R is from −1 to 1. R more than zero shows a positive correlation between two factors, whereas R less than zero shows a negative correlation between two factors. The larger the absolute value of correlation coefficient R is, the closer the correlation between the two factors is:(6)R=∑i=1nxi−x¯yi−y¯∑i=1nxi−x¯2∑i=1nyi−y¯2.


## 4. Results and Analysis

### 4.1. Individual Assembly Factor Analysis

The main assembly parameters of HSV includes residual air gap, maximum lift of the valve stem, the mass of the moving parts, spring stiffness, and spring pre-tightening force. Table2 shows the studied range of every parameter. In this paper, the measured current at 1200 r/min cam rotational speed with 7.2°CaA injection pulse width was imported to the numerical model as excitation to research the dynamic response of HSV. All other parameters have been considered with their reference values when carrying out single parameter analysis.Table 2
The studied of main assembly parameters.
Factors
Reference value
Range
Residual air gap,d (mm)
0.08
0.04–0.12
Maximum lift of valve stem,S (mm)
0.14
0.1–0.18
Mass of the moving parts,m (g)
12
8–16
Spring stiffness,k (N/mm)
14
6–22
Spring pretightening,F (N)
60
50–70


#### 4.1.1. Residual Air Gap

Residual air gap is the distance from iron core to armature after HSV closure. It has an obvious influence on the dynamic response of HSV as shown in Figure9. With the increase of residual air gap from 0.04 mm to 0.12 mm, actuation trigger time (tc1 as shown in Figure 7) increases from 0.114 ms to 0.156 ms, and the closure response time of HSV increases from 0.478 ms to 0.602 ms; release trigger time (to1 as shown in Figure 7) decreases from 0.126 ms to 0.056 ms, and the open response time of HSV decreases from 0.584 ms to 0.486 ms because the working air gap of HSV consists of residual air gap and valve stem lift. So the increase of residual air gap makes the increase of working air gap, when keeping the valve stem lift unchanged. It leads to the increase of magnetic resistance, and as a result, the electromagnetic force decreases. Consequently, the actuation trigger time and the closure response time of HSV increase. However, for the opening process of HSV, electromagnetic force is resistance. Therefore release trigger time and the open response time of HSV decrease. When comparing the change of release trigger time with the open response time of HSV, it can be found that residual air gap affects the open response time of HSV by release trigger time. Besides, residual air gap makes a greater influence on the closure response time than the open response time. Therefore, a smaller residual air gap is suggested with two potential benefits. Firstly, it can improve the whole response speed of HSV. Secondly, the hold current can be reduced after the HSV closes, which can reduce the power loss and heat production of the coil.Figure 9
Influence of residual air gap on the dynamic response of HSV.


#### 4.1.2. Maximum Lift of Valve Stem

Just like residual air gap, the maximum lift of the valve stem also has an obvious influence on the dynamic response of HSV as shown in Figure10. With the increase of maximum lift of the valve stem from 0.1 mm to 0.18 mm, actuation trigger time increases from 0.114 ms to 0.156 ms, and the closure response time increases from 0.418 ms to 0.676 ms; release trigger time keeps unchanged, and the open response time of HSV decreases from 0.434 ms to 0.598 ms. Movement distance of armature increases with the increase of maximum lift of the valve stem. Moreover, by keeping the residual air gap unchanged, increase of the maximum lift of the valve stem increases the initial working air gap too. This leads to an increase of magnetic resistance and decrease of electromagnetic force. As a result, actuation trigger time and the closure response time of HSV increase. By keeping residual air gap and drive current unchanged, the increase of the movement distance obviously leads to the increase of the open response time of HSV. Therefore, decreasing the maximum lift of the valve stem can effectively improve the response speed of HSV. But sudden and quick discharge of high pressure oil can be a problem with less available drainage area. Therefore, it is recommended that the maximum lift of the valve stem should be considered wisely.Figure 10
Influence of maximum lift of the valve stem on the dynamic response of HSV.


#### 4.1.3. Mass of the Moving Parts

Effect of mass of the moving parts on the dynamic response of HSV is shown in Figure11. It mainly impacts on both the whole closure response and open response time and slightly on the actuation trigger time and release trigger time. With the increase of mass of the moving parts from 8 g to 16 g, the closure response time and open response time increase from 0.5 ms to 0.566 ms and 0.484 ms to 0.544 ms, respectively. The increase of mass of the moving parts inevitably decreases the acceleration of armature, resulting in the increase of response time. Therefore, mass of the moving parts should be designed as light as possible where it meets the structure strength requirements. In the armature processing, generally a groove or a hole can be made in armature at appropriate location. This can weaken the effect of vortex and reduces the mass of the moving parts.Figure 11
Influence of mass of the moving parts on the dynamic response of HSV.


#### 4.1.4. Spring Stiffness

Spring stiffness has little influence on the dynamic response of HSV as shown in Figure12. Because valve stem lift is only 0.16 mm, even with the different values of stiffness, the deformation force is too small as compared to the pretightening and electromagnetic force.Figure 12
Influence of spring stiffness on the dynamic response of HSV.


#### 4.1.5. Spring Pretightening

Spring pretightening also has a defined impact on the dynamic response of HSV as shown in Figure13. With the increase of pretightening from 50 N to 70 N, both actuation trigger time and closure response time increase from 0.12 ms to 0.15 ms and 0.492 ms to 0.592 ms, respectively, whereas release trigger time and open response time decrease from 0.1 ms to 0.068 ms and 0.586 ms to 0.466 ms, respectively. In fact, the bigger the pretightening is, the faster the closure response time changes, and the slower the open response time changes because spring force almost keeps unchanged during the movement process of armature with small valve stem lift. Therefore, pretightening is the main resistance during the closing process of HSV. Any increase in pretightening will increase current required to move armature, and as a result, the actuation trigger time increases. Moreover acceleration of armature also decreases with the increase of pretightening, thereby increasing the closure response time of HSV. On the contrary, pretightening is the main driving force during the opening process of HSV; therefore, the release trigger time and open response time of HSV decrease with the increase of spring pretightening. So when it meets the requirement of the open response time of HSV, it should use a smaller pretightening.Figure 13
Influence of spring pretightening on the dynamic response of HSV.


### 4.2. Correlation Analysis

We have concluded after individual assembly factor analysis that spring stiffness has little influence on dynamic response characteristics of HSV; therefore, the interaction effect has been analyzed between remaining four factors only. Twenty-seven experimental points were designed by CCF, and their response values were obtained by the simulation model as shown in Table3. Correlation coefficients between all factors and the response time of HSV were obtained using equation (6) and are shown in Figure 14.Table 3
Experimental design scheme and results.
Number
d (mm)
S (mm)
m (g)
F (N)
t
c (ms)
t
o (ms)
t (ms)
1
0.04
0.1
8
50
0.322
0.532
0.854
2
0.04
0.1
8
70
0.37
0.42
0.79
3
0.04
0.1
16
50
0.372
0.596
0.968
4
0.04
0.1
16
70
0.426
0.478
0.904
5
0.12
0.1
8
50
0.402
0.424
0.826
6
0.12
0.1
8
70
0.48
0.334
0.814
7
0.12
0.1
16
50
0.456
0.482
0.938
8
0.12
0.1
16
70
0.544
0.388
0.932
9
0.04
0.18
8
50
0.508
0.724
1.232
10
0.04
0.18
8
70
0.618
0.56
1.178
11
0.04
0.18
16
50
0.578
0.796
1.374
12
0.04
0.18
16
70
0.702
0.626
1.328
13
0.12
0.18
8
50
0.638
0.616
1.254
14
0.12
0.18
8
70
0.926
0.474
1.4
15
0.12
0.18
16
50
0.722
0.68
1.402
16
0.12
0.18
16
70
1.064
0.536
1.6
17
0.08
0.14
12
50
0.492
0.586
1.078
18
0.08
0.14
12
70
0.592
0.466
1.058
19
0.08
0.14
8
60
0.5
0.486
0.986
20
0.08
0.14
16
60
0.566
0.546
1.112
21
0.04
0.14
12
60
0.478
0.584
1.062
22
0.12
0.14
12
60
0.602
0.486
1.088
23
0.08
0.1
12
60
0.412
0.434
0.846
24
0.08
0.18
12
60
0.676
0.598
1.274
25
0.08
0.14
12
60
0.534
0.518
1.052
26
0.08
0.14
12
60
0.534
0.518
1.052
27
0.08
0.14
12
60
0.534
0.518
1.052Figure 14
Correlation of each factor with response time.Correlation coefficients of the second-order factors of parameter self-interaction (d∗d, S∗S, m∗m, and F∗F) are almost similar and are around 0.1 as shown in Figure 14. It shows that the factors of parameter self-interaction have little influence on dynamic response characteristics of HSV. Correlation coefficients of interactions between two different parameters including residual gas gap with maximum lift of valve stem (d∗S), residual gas gap with spring pretightening force (d∗F), and maximum lift of the valve stem with spring pretightening force (S∗F) are the main influential factors. Their correlation coefficients are 0.17, 0.14, and 0.18, respectively, for the closure response time, and 0.13, 0.13, and 0.09, respectively, for the total response time t. They have relatively great influence on the closure response time and the open response time of HSV. So the interaction effects should be considered and multiparameter optimization strategy is recommended to do it, when two or three of these parameters—residual air gap, maximum lift of valve stem, and spring pretightening force—are adjusted at the same time. Other factors have no obvious correlation with dynamic response characteristics of HSV.


## 4.1. Individual Assembly Factor Analysis

The main assembly parameters of HSV includes residual air gap, maximum lift of the valve stem, the mass of the moving parts, spring stiffness, and spring pre-tightening force. Table2 shows the studied range of every parameter. In this paper, the measured current at 1200 r/min cam rotational speed with 7.2°CaA injection pulse width was imported to the numerical model as excitation to research the dynamic response of HSV. All other parameters have been considered with their reference values when carrying out single parameter analysis.Table 2
The studied of main assembly parameters.
Factors
Reference value
Range
Residual air gap,d (mm)
0.08
0.04–0.12
Maximum lift of valve stem,S (mm)
0.14
0.1–0.18
Mass of the moving parts,m (g)
12
8–16
Spring stiffness,k (N/mm)
14
6–22
Spring pretightening,F (N)
60
50–70


### 4.1.1. Residual Air Gap

Residual air gap is the distance from iron core to armature after HSV closure. It has an obvious influence on the dynamic response of HSV as shown in Figure9. With the increase of residual air gap from 0.04 mm to 0.12 mm, actuation trigger time (tc1 as shown in Figure 7) increases from 0.114 ms to 0.156 ms, and the closure response time of HSV increases from 0.478 ms to 0.602 ms; release trigger time (to1 as shown in Figure 7) decreases from 0.126 ms to 0.056 ms, and the open response time of HSV decreases from 0.584 ms to 0.486 ms because the working air gap of HSV consists of residual air gap and valve stem lift. So the increase of residual air gap makes the increase of working air gap, when keeping the valve stem lift unchanged. It leads to the increase of magnetic resistance, and as a result, the electromagnetic force decreases. Consequently, the actuation trigger time and the closure response time of HSV increase. However, for the opening process of HSV, electromagnetic force is resistance. Therefore release trigger time and the open response time of HSV decrease. When comparing the change of release trigger time with the open response time of HSV, it can be found that residual air gap affects the open response time of HSV by release trigger time. Besides, residual air gap makes a greater influence on the closure response time than the open response time. Therefore, a smaller residual air gap is suggested with two potential benefits. Firstly, it can improve the whole response speed of HSV. Secondly, the hold current can be reduced after the HSV closes, which can reduce the power loss and heat production of the coil.Figure 9
Influence of residual air gap on the dynamic response of HSV.


### 4.1.2. Maximum Lift of Valve Stem

Just like residual air gap, the maximum lift of the valve stem also has an obvious influence on the dynamic response of HSV as shown in Figure10. With the increase of maximum lift of the valve stem from 0.1 mm to 0.18 mm, actuation trigger time increases from 0.114 ms to 0.156 ms, and the closure response time increases from 0.418 ms to 0.676 ms; release trigger time keeps unchanged, and the open response time of HSV decreases from 0.434 ms to 0.598 ms. Movement distance of armature increases with the increase of maximum lift of the valve stem. Moreover, by keeping the residual air gap unchanged, increase of the maximum lift of the valve stem increases the initial working air gap too. This leads to an increase of magnetic resistance and decrease of electromagnetic force. As a result, actuation trigger time and the closure response time of HSV increase. By keeping residual air gap and drive current unchanged, the increase of the movement distance obviously leads to the increase of the open response time of HSV. Therefore, decreasing the maximum lift of the valve stem can effectively improve the response speed of HSV. But sudden and quick discharge of high pressure oil can be a problem with less available drainage area. Therefore, it is recommended that the maximum lift of the valve stem should be considered wisely.Figure 10
Influence of maximum lift of the valve stem on the dynamic response of HSV.


### 4.1.3. Mass of the Moving Parts

Effect of mass of the moving parts on the dynamic response of HSV is shown in Figure11. It mainly impacts on both the whole closure response and open response time and slightly on the actuation trigger time and release trigger time. With the increase of mass of the moving parts from 8 g to 16 g, the closure response time and open response time increase from 0.5 ms to 0.566 ms and 0.484 ms to 0.544 ms, respectively. The increase of mass of the moving parts inevitably decreases the acceleration of armature, resulting in the increase of response time. Therefore, mass of the moving parts should be designed as light as possible where it meets the structure strength requirements. In the armature processing, generally a groove or a hole can be made in armature at appropriate location. This can weaken the effect of vortex and reduces the mass of the moving parts.Figure 11
Influence of mass of the moving parts on the dynamic response of HSV.


### 4.1.4. Spring Stiffness

Spring stiffness has little influence on the dynamic response of HSV as shown in Figure12. Because valve stem lift is only 0.16 mm, even with the different values of stiffness, the deformation force is too small as compared to the pretightening and electromagnetic force.Figure 12
Influence of spring stiffness on the dynamic response of HSV.


### 4.1.5. Spring Pretightening

Spring pretightening also has a defined impact on the dynamic response of HSV as shown in Figure13. With the increase of pretightening from 50 N to 70 N, both actuation trigger time and closure response time increase from 0.12 ms to 0.15 ms and 0.492 ms to 0.592 ms, respectively, whereas release trigger time and open response time decrease from 0.1 ms to 0.068 ms and 0.586 ms to 0.466 ms, respectively. In fact, the bigger the pretightening is, the faster the closure response time changes, and the slower the open response time changes because spring force almost keeps unchanged during the movement process of armature with small valve stem lift. Therefore, pretightening is the main resistance during the closing process of HSV. Any increase in pretightening will increase current required to move armature, and as a result, the actuation trigger time increases. Moreover acceleration of armature also decreases with the increase of pretightening, thereby increasing the closure response time of HSV. On the contrary, pretightening is the main driving force during the opening process of HSV; therefore, the release trigger time and open response time of HSV decrease with the increase of spring pretightening. So when it meets the requirement of the open response time of HSV, it should use a smaller pretightening.Figure 13
Influence of spring pretightening on the dynamic response of HSV.


## 4.1.1. Residual Air Gap

Residual air gap is the distance from iron core to armature after HSV closure. It has an obvious influence on the dynamic response of HSV as shown in Figure9. With the increase of residual air gap from 0.04 mm to 0.12 mm, actuation trigger time (tc1 as shown in Figure 7) increases from 0.114 ms to 0.156 ms, and the closure response time of HSV increases from 0.478 ms to 0.602 ms; release trigger time (to1 as shown in Figure 7) decreases from 0.126 ms to 0.056 ms, and the open response time of HSV decreases from 0.584 ms to 0.486 ms because the working air gap of HSV consists of residual air gap and valve stem lift. So the increase of residual air gap makes the increase of working air gap, when keeping the valve stem lift unchanged. It leads to the increase of magnetic resistance, and as a result, the electromagnetic force decreases. Consequently, the actuation trigger time and the closure response time of HSV increase. However, for the opening process of HSV, electromagnetic force is resistance. Therefore release trigger time and the open response time of HSV decrease. When comparing the change of release trigger time with the open response time of HSV, it can be found that residual air gap affects the open response time of HSV by release trigger time. Besides, residual air gap makes a greater influence on the closure response time than the open response time. Therefore, a smaller residual air gap is suggested with two potential benefits. Firstly, it can improve the whole response speed of HSV. Secondly, the hold current can be reduced after the HSV closes, which can reduce the power loss and heat production of the coil.Figure 9
Influence of residual air gap on the dynamic response of HSV.


## 4.1.2. Maximum Lift of Valve Stem

Just like residual air gap, the maximum lift of the valve stem also has an obvious influence on the dynamic response of HSV as shown in Figure10. With the increase of maximum lift of the valve stem from 0.1 mm to 0.18 mm, actuation trigger time increases from 0.114 ms to 0.156 ms, and the closure response time increases from 0.418 ms to 0.676 ms; release trigger time keeps unchanged, and the open response time of HSV decreases from 0.434 ms to 0.598 ms. Movement distance of armature increases with the increase of maximum lift of the valve stem. Moreover, by keeping the residual air gap unchanged, increase of the maximum lift of the valve stem increases the initial working air gap too. This leads to an increase of magnetic resistance and decrease of electromagnetic force. As a result, actuation trigger time and the closure response time of HSV increase. By keeping residual air gap and drive current unchanged, the increase of the movement distance obviously leads to the increase of the open response time of HSV. Therefore, decreasing the maximum lift of the valve stem can effectively improve the response speed of HSV. But sudden and quick discharge of high pressure oil can be a problem with less available drainage area. Therefore, it is recommended that the maximum lift of the valve stem should be considered wisely.Figure 10
Influence of maximum lift of the valve stem on the dynamic response of HSV.


## 4.1.3. Mass of the Moving Parts

Effect of mass of the moving parts on the dynamic response of HSV is shown in Figure11. It mainly impacts on both the whole closure response and open response time and slightly on the actuation trigger time and release trigger time. With the increase of mass of the moving parts from 8 g to 16 g, the closure response time and open response time increase from 0.5 ms to 0.566 ms and 0.484 ms to 0.544 ms, respectively. The increase of mass of the moving parts inevitably decreases the acceleration of armature, resulting in the increase of response time. Therefore, mass of the moving parts should be designed as light as possible where it meets the structure strength requirements. In the armature processing, generally a groove or a hole can be made in armature at appropriate location. This can weaken the effect of vortex and reduces the mass of the moving parts.Figure 11
Influence of mass of the moving parts on the dynamic response of HSV.


## 4.1.4. Spring Stiffness

Spring stiffness has little influence on the dynamic response of HSV as shown in Figure12. Because valve stem lift is only 0.16 mm, even with the different values of stiffness, the deformation force is too small as compared to the pretightening and electromagnetic force.Figure 12
Influence of spring stiffness on the dynamic response of HSV.


## 4.1.5. Spring Pretightening

Spring pretightening also has a defined impact on the dynamic response of HSV as shown in Figure13. With the increase of pretightening from 50 N to 70 N, both actuation trigger time and closure response time increase from 0.12 ms to 0.15 ms and 0.492 ms to 0.592 ms, respectively, whereas release trigger time and open response time decrease from 0.1 ms to 0.068 ms and 0.586 ms to 0.466 ms, respectively. In fact, the bigger the pretightening is, the faster the closure response time changes, and the slower the open response time changes because spring force almost keeps unchanged during the movement process of armature with small valve stem lift. Therefore, pretightening is the main resistance during the closing process of HSV. Any increase in pretightening will increase current required to move armature, and as a result, the actuation trigger time increases. Moreover acceleration of armature also decreases with the increase of pretightening, thereby increasing the closure response time of HSV. On the contrary, pretightening is the main driving force during the opening process of HSV; therefore, the release trigger time and open response time of HSV decrease with the increase of spring pretightening. So when it meets the requirement of the open response time of HSV, it should use a smaller pretightening.Figure 13
Influence of spring pretightening on the dynamic response of HSV.


## 4.2. Correlation Analysis

We have concluded after individual assembly factor analysis that spring stiffness has little influence on dynamic response characteristics of HSV; therefore, the interaction effect has been analyzed between remaining four factors only. Twenty-seven experimental points were designed by CCF, and their response values were obtained by the simulation model as shown in Table3. Correlation coefficients between all factors and the response time of HSV were obtained using equation (6) and are shown in Figure 14.Table 3
Experimental design scheme and results.
Number
d (mm)
S (mm)
m (g)
F (N)
t
c (ms)
t
o (ms)
t (ms)
1
0.04
0.1
8
50
0.322
0.532
0.854
2
0.04
0.1
8
70
0.37
0.42
0.79
3
0.04
0.1
16
50
0.372
0.596
0.968
4
0.04
0.1
16
70
0.426
0.478
0.904
5
0.12
0.1
8
50
0.402
0.424
0.826
6
0.12
0.1
8
70
0.48
0.334
0.814
7
0.12
0.1
16
50
0.456
0.482
0.938
8
0.12
0.1
16
70
0.544
0.388
0.932
9
0.04
0.18
8
50
0.508
0.724
1.232
10
0.04
0.18
8
70
0.618
0.56
1.178
11
0.04
0.18
16
50
0.578
0.796
1.374
12
0.04
0.18
16
70
0.702
0.626
1.328
13
0.12
0.18
8
50
0.638
0.616
1.254
14
0.12
0.18
8
70
0.926
0.474
1.4
15
0.12
0.18
16
50
0.722
0.68
1.402
16
0.12
0.18
16
70
1.064
0.536
1.6
17
0.08
0.14
12
50
0.492
0.586
1.078
18
0.08
0.14
12
70
0.592
0.466
1.058
19
0.08
0.14
8
60
0.5
0.486
0.986
20
0.08
0.14
16
60
0.566
0.546
1.112
21
0.04
0.14
12
60
0.478
0.584
1.062
22
0.12
0.14
12
60
0.602
0.486
1.088
23
0.08
0.1
12
60
0.412
0.434
0.846
24
0.08
0.18
12
60
0.676
0.598
1.274
25
0.08
0.14
12
60
0.534
0.518
1.052
26
0.08
0.14
12
60
0.534
0.518
1.052
27
0.08
0.14
12
60
0.534
0.518
1.052Figure 14
Correlation of each factor with response time.Correlation coefficients of the second-order factors of parameter self-interaction (d∗d, S∗S, m∗m, and F∗F) are almost similar and are around 0.1 as shown in Figure 14. It shows that the factors of parameter self-interaction have little influence on dynamic response characteristics of HSV. Correlation coefficients of interactions between two different parameters including residual gas gap with maximum lift of valve stem (d∗S), residual gas gap with spring pretightening force (d∗F), and maximum lift of the valve stem with spring pretightening force (S∗F) are the main influential factors. Their correlation coefficients are 0.17, 0.14, and 0.18, respectively, for the closure response time, and 0.13, 0.13, and 0.09, respectively, for the total response time t. They have relatively great influence on the closure response time and the open response time of HSV. So the interaction effects should be considered and multiparameter optimization strategy is recommended to do it, when two or three of these parameters—residual air gap, maximum lift of valve stem, and spring pretightening force—are adjusted at the same time. Other factors have no obvious correlation with dynamic response characteristics of HSV.


## 5. Conclusions

(1)
A numerical simulation model of HSV has been developed in the Ansoft Maxwell environment, and its accuracy has been validated experimentally. It provides an effective platform for the research on the dynamic response characteristics of HSV.
(2)
These assembly parameters—residual air gap, maximum lift of valve stem, and spring pretightening force—have significant influence on dynamic response characteristics of HSV, and there are obvious interaction effects between these parameters. When two or three of them are adjusted at the same time, the interaction effects should be considered and multiparameter optimization strategy is recommended to do it.



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*Source: 2803545-2020-01-22.xml*