Eddy current effects on the dynamic response of high-speed solenoid valve for common rail injector

Abstract

A high-speed solenoid valve (HSV) with high dynamic responses is a key component of the common rail injector, where it provides accurate and flexible control of the injection. In this study, finite element methods were used to investigate the eddy current inside an HSV. The results demonstrated that the appearance and change in the eddy current were related to the driving current, and significantly influenced the HSV dynamics, particularly the opening response. By considering the eddy current effect, the calculations were seen to match the experimental data effectively during the opening response, but did not match them strongly during the closing response. During the HSV opening process, the eddy current at the surface of the magnetic materials impeded the magnetization; during the closing stage, it prevented the magnetic flux inside the magnetic material from spreading out and delayed demagnetization. An eddy current was proven to always block the magnetic field change and worsen the HSV dynamic response. Slotting on the yoke can significantly reduce the open response time, while hardly influence the close response. It was deemed necessary to optimize the HSV structure to weaken the eddy current effect on the opening and closing response.

Keywords

eddy current effect dynamic response high-speed solenoid valve common rail injection system diesel engine

1. Introduction

The common rail injection system with an electronic control unit has the ability to vary injection timing, pressure, and quantity depending on system working conditions, and is an essential, energy-saving, and emission-reducing component of modern diesel engines. The opening and closing responses of an HSV for a common rail injector are limited to a maximum value of 0.2 ms. Therefore; the high dynamic response of an HSV plays an important role in ensuring flexible injection control [1–4].

Coppo et al. [5] established a mathematical HSV model for a common rail injector using the zero-dimension method, and studied the influences of the driving current on the HSV electromagnetic force under different air gaps. Meanwhile, Cheng et al. [6] investigated the effect of soft magnetic materials on the electromagnetic force, and improved the force by optimizing the magnetic circuit. Sun et al. [7] developed a mathematical model based on the static electromagnetic force of an electronic control pump’s HSV and studied the effects of different structural parameters on the force. Zhao et al. [8] developed another mathematical HSV model, which considered the nonlinearity and magnetic saturation effects on the electromagnetic force. These studies showed that the opening and closing responses of an HSV under system working conditions are influenced by the coupling of the electric and magnetic fields, as well as the mechanical field.

To reduce the opening response time, certain ‘smart’ materials, such as giant magneto strictive materials and piezoelectric crystals, with rapid response times, are used to design HSVs [9–11]. However, these materials exhibit certain disadvantages, such as high costs and excessively small strokes. On the other hand, some traditional soft magnetic materials are relatively feasible approach, as them are inexpensive, well processed, and can be optimized by adjusting the structural parameters and changing the driving strategies. Maiti et al. [12] developed a nonlinear HSV model using Simulink modules, established a detailed mathematical model according to practical experience, and verified the model by experimental data. Ye et al. [13] developed a dynamic HSV model to study the dynamic characteristics of a pilot-operated two-stage solenoid valve, which coupled the motion of the valve spindle with the fluid in the system. Cvetkovic et al. [14] investigated the multi-field coupling relations using a theoretical HSV model. Cheng et al. [15] analyzed the influence of four different driving circuits on the HSV dynamic response, and stressed the importance of a driving strategy on the working response characteristics of HSVs. Zhao et al. [16] investigated the relationship between boost voltage and HSV opening response time, and pointed out that magnetic saturation limited the boost voltage effect on the opening response, i.e., a high boost voltage could lead to a stronger electromagnetic force only in a limited voltage range. Andadi et al. [17,18] tested the impact of temperature and driving current, established a theoretical model to improve dynamic characteristics and predict reliability of the HSV. Wu et al. [19] designed an equivalent magnetic circuit model for a proposed solenoid, and applied an iterative method to obtain an accurate value for the permeability of the nonlinear magnetic material and proposed a multi-objective optimization design for the HSV parameters.

The studies mentioned above focused on the static electromagnetic forces of HSVs at different driving and structural parameters, and dynamic simulation models considering multi-field coupling. Core losses (including hysteresis, eddy current, and excess losses.) of the magnetic materials are relevant to the magnetic flux density B and permeability, and with an increase in the magnetization frequency, core loss increases, and the skin effect is more significant [20–22]. Previously, the yoke of an electromagnet was manufactured using lamination magnetic material, but it is now made from an entire piece of magnetic material. This piece is known as a solid conductor. The lamination construction effectively resisted the eddy current; therefore, a solenoid valve with its yoke manufactured using this technique is insignificantly influenced by an eddy current. Contrarily, a yoke made of solid magnetic material can lead to a strong eddy current when the HSV is operating under high-speed and high-frequency conditions. Investigations on the eddy current in a solenoid valve and its effect on the opening and closing responses of an HSV were inefficient. The magnetic field calculation forms the foundation for the HSV optimization. This can be obtained by the finite element method (FEM) and analytical model calculation. The FEM can directly and accurately calculate the flux pattern and is usually applied for detailed design [23]. In this paper, the FEM was used to study the eddy current mechanism in an HSV for a common rail injector, as well as the eddy current effect on the dynamic response. The results were used to provide a foundation to improve the dynamic response characteristics of the HSV.

2. Description of models and methodology

2.1. Mathematical model of eddy current loss within solenoid

Commonly, calculations for the eddy current loss were obtained from the Steinmetz equation and loss separation models, based on the statistical theory of losses [24,25] and the driving current is sinusoidal excitation. However, in the case here, a peak-hold driving strategy was applied to rapidly open the HSV, which was not sinusoidal.

For an HSV with a yoke made of solid magnetic material, when a time-varying excitation current flows through the conductor, transient magnetic fields will be produced at the plane vertical to the conductor, and an eddy current will inevitably appear in the conductor owing to the change in magnetic fields, Eq. (1) provides the field equation [26]: $\begin{eqnarray}\displaystyle {\nabla}\cdot \frac{1}{{\mu}}({\nabla}\cdot A)=({\sigma}+j{\omega}{\varepsilon})(-j{\omega}A-{\nabla}{\phi}). & & \displaystyle\end{eqnarray}$ (1)

Where A is the vector magnetic potential, φ is the scalar electric potential, μ is the relative permeability, σ is the conductivity, and ϵ is the dielectric coefficient. The total current density consists of the source current density, which is related to the scalar electric potential, and the induced current density, which arises from the time-variant magnetic field. According to Ampere’s law, the total current density J can be calculated as $\begin{eqnarray}\displaystyle J=-{\sigma}\frac{dA}{dt}-{\sigma}{\nabla}V. & & \displaystyle\end{eqnarray}$ (2)

For solid conductors with a voltage source, the total voltage may be known, while the total current density is unknown. The transient solver computes the unknown quantities based on the following electrical circuit equation, which is derived from the solid conductor equations. The electrical circuit equation is expressed as $\begin{eqnarray}\displaystyle \iint _{{\Omega}_{C}}\left({\sigma}\frac{dA}{dt}+J\right)d{\Omega}=\iint _{{\Omega}_{C}}\frac{{\sigma}}{l}V_{b}d{\Omega}. & & \displaystyle\end{eqnarray}$ (3)

Where Ω_C is the cross-sectional width of the conductor, V _b is the voltage difference between the conductor ends, l is the model thickness, and A is the vector magnetic potential. The eddy current loss represents the resistive loss of a solid volume. Accurate prediction of the eddy current loss is important for an HSV. There are two main contributors to the eddy current loss: the on-load solid eddy current loss, resulting from the harmonics of the magnetomotive force of the windings, also known as space harmonics; and the on-load solid eddy current loss caused by the time harmonics of the phase currents, owing to pulse width modulation. The eddy current loss is calculated as $\begin{eqnarray}\displaystyle W_{\text{eddy current loss}}=\int _{VOL}{\sigma}E^{2}dV=\int _{VOL}\frac{J^{2}dV}{{\sigma}}. & & \displaystyle\end{eqnarray}$ (4)

Where V is the material volume. Using the transient solver with motion, the actual measured motor/generator current waveforms applied is helpful for simulating the eddy current [27].

2.2. Simulation model setting

The FEM is a common method for investigating complex energy conversion and analyzing an HSV in detail. Figure 1 illustrates the real part and simulation model of an HSV and its assembly location in a common rail injector. The dynamic simulation model of an HSV consists of the yoke, armature, and winding. The detailed parameters and their values were listed in Table 1. Armature and yoke of the HSV were made from magnetic material, and B-H curve of this material is shown in Fig. 2, which is a necessary boundary condition for Maxwell to calculate the electromagnetic force, with considering the nonlinearity and saturation of the magnetization. The B-H curve is tested by the type of MATS-2010SD, measurement equipment for static B-H magnetic curve. This equipment was produced by China Hunan Linkjoin Technology Co., Ltd. The size of the test ring specimen is consistent with the Chinese standard GB/T 13012-2008 and the International standard IEC 60404-4.

Fig. 1.

Simulation FEM model of HSV.

Table 1

Detailed information of 3D simulation model

Parameters	value
Pre-load force of spring/N	70
Stiffness of spring/(N/mm)	57
Mass of moving components/g	5.3
Number of coil turns	52
Maximum moving displacement of armature/μm	70
Total air gap between yoke and armature/μm	120
Inductance/mH	0.2
Resistance/Ω	0.38

Fig. 2.

B-H curve of the magnetic material.

To measure the dynamic response of HSV, as shown in Fig. 3(a), a test bench is employed, which contains power control unit, driving current control unit and armature displacement measurement unit. As shown in Fig. 3(b), a two-order driving strategy (peak-hold-hold) was set to drive the HSV. The parameters of driving current such as boost voltage, hold current I and hold current II can be flexible set on the test bench. To faster open solenoid valve, a boost voltage is supplied on the HSV coil, and a peak current is obtained. The boost voltage is supplied by a boost circuit, and two hold currents are produced by Pulse Width Modulation (PWM) on the 24 V voltage source. Hold current I is used to ensure the armature can reach its maximum displacement. Hold current II is much lower than hold current I, it is used to maintain the armature at its maximum displacement position and reduce the heat of HSV.

Fig. 3.

Test bench for the dynamic response of HSV and the driving strategy [16].

3. Results and discussion

3.1. Characteristics of eddy current in an HSV

As shown in Fig. 4, for every single cycle, the eddy current appeared three times, and the distributions of the eddy current loss at the first instance differed from those of the following two instances. The eddy current appearance was related to the driving current change. While the HSV was driven by the peak current, with the driving current increasing from 0 to 22 A, the eddy current power loss rapidly increased from 0 to 420 W, and the increase time coincided with the peak current time.

With increases in the peak current, the eddy current increased constantly. As the driving current transited from the peak current to hold current I, the eddy current loss decreased rapidly and slowly fell to zero. While the driving current transited from hold current I to II, the rapid decrease in the driving current led to the appearance of the eddy current for a second time, then drop to zero. During this stage, the duration of the eddy current was very short; it was the same as the transition time from hold current I to II. The eddy current loss at this stage was 141 W, which was lower than the first time. When the driving currents decreased from hold current II to zero, the eddy current appeared for a third time. The third eddy current change regulation was similar to that of the second time, and the eddy current loss was 87 W, which was the lowest value for one cycle.

Fig. 4.

Change in Eddy current loss in HSV yoke and armature with driving current.

3.2. Effects of eddy current on opening and closing response of HSV

As illustrated in Fig. 5, when the eddy current effect was considered in the opening response of the HSV, calculations of the lift, opening time (the factor that could directly determine the injection timing of a common rail injector), and maximum lift matched the experimental data. For the closing response of the HSV, the start closing time of the calculations was consistent with the experimental data, while the end closing time was ahead of the time from the experimental data. The reason is that the influence of the mechanical friction factors of moving parts, such as the armature, on their movement was ignored when conducting the dynamic 3D simulation of the HSV. Therefore, without considering the friction, the armature would drop to its initial position faster.

Without considering the eddy current effect, the calculated start opening time of the HSV was 0.15 ms, while the experimental value was 0.2 ms. Moreover, from Fig. 5, the armature lift velocity for the HSV opening response was quicker, and a shorter time was required to reach its maximum position. For the closing response, the calculated closing time without the eddy current was ahead of the closing time with the eddy current. However, neither calculation matched the experiment effectively, as they were both ahead of the times from the experiment. The error exits in close response. Actually, the completely close time of HSV in calculation is 2.21 ms, while it is 2.25 ms in experiment data. The relative error is 1.7% and match the calculation requirement. This error is due to the mechanical friction between the valve stem and valve sleeve. The eddy current influenced the opening response more significantly than the closing response. For the HSV opening response, with increases in the driving current, the eddy current loss increased to 400 W, which was higher than the loss in the HSV closing response (less than 100 W). 3D cloud images could further aid in the analysis of eddy current distribution in the HSV’s opening and closing responses, and could also help investigate the influence mechanism.

Fig. 5.

Comparison between FEM calculations and experimental data.

3.3. Interrelation of eddy current and magnetic field at opening and closing processes of HSV

For the software Maxwell Ansoft, the current density could describe the eddy current. As shown in Fig. 6, in the open process of an HSV, magnetizations of the yoke and armature were different. The yoke would be magnetized from the surface to the interior. Distribution range of the magnetic field expanded, and the surface had the strongest B. For the armature, magnetization process was from the top surface of the armature to the bottom. At 0.06 ms, although B at this time was not strong, the eddy current appeared, and first at the yoke surface and top armature. At 0.12 ms, with increases in B, eddy current rapidly increased, and spread to the yoke interior and armature bottom. The eddy current mainly existed at the yoke surface. Therefore, according to above analysis, at the open process of an HSV, rapid increases in the driving current could magnetize the yoke and armature quickly, however, eddy current appeared, which mainly existed at the surface of the magnetic material like a wall, and resist the B spread into the interior. Finally, the magnetization process was delayed by the eddy current effects and the open response time was longer.

Fig. 6.

Change in magnetic field distribution and eddy current with time at opening and closing processes of HSV.

The eddy current and B distribution in the HSV closing process differed from those in the opening process. As demonstrated in Fig. 7, at 2.0 ms, the driving current was in the period of hold current II. As the driving current did not change at this point, the eddy current did not appear, and most of the B gathered at the yoke and top of the armature. At 2.1 ms, the magnetic field in the yoke decreased and demagnetization began from the interior of the yoke to its surface; however, owing to the decrease in the driving current, the eddy current appeared at the yoke surface and resisted the spreading of the internal magnetic field. With the development of the demagnetization process, the eddy current decreased and its effect on the demagnetization weakened. This resistance from eddy current effects could delay the decrease of the electromagnetic force of an HSV to zero, causing it to take longer time to close, thus implying a negative effect on the HSV closing response.

Fig. 7.

Distribution of magnetic flux density and eddy current density at the HSV closing process.

For the open and close process of an HSV, the characteristic that the eddy current spreads on the surface of an HSV could negatively influence the response. During the open response, a boost voltage is generally used to rapidly open an HSV; however, a transient peak current could also induce a high eddy current and worsen the HSV dynamic response. In general, for a higher boost voltage, effects of improving the open dynamic response by enhancing the boost voltage would be lower. A high eddy current could result in a large energy loss and temperature increase in an HSV, which finally worsen the working characteristics of the HSV. Therefore, it is necessary to consider the effects of both the boost voltage and eddy current on the HSV dynamic response.

3.4. Effects of slotting on the yoke

According to study above, the eddy current effects in yoke can directly influence the open and close response of an HSV for common rail injector, especially for its open dynamic response. Previously, the HSV is manufactured by laminations of material, and the eddy current effects can be restrained. However, now the HSV is manufactured by a whole block of solid material to reduce the cost, once driven by high-frequency currents, the eddy current is more significant. Slotting on the surface of yoke can reduce the eddy current effects. As shown in Fig. 8, the yoke is slotted on with two different width, 0.5 mm and 1 mm, and the calculation results are shown in Fig. 9. Slotting on the yoke can significantly optimum the open dynamic response of HSV, the open time reduces about 0.08 ms, however, the slotting effects on the close response is not significant. Besides, the width of slot hardly influences the dynamic response, therefore, the width of slot should be as narrow as possible to prevent the deformation of yoke and improve the reliability and service life of HSV.

Fig. 8.

Diagram of two different width of slot on yoke of HSV.

Fig. 9.

Slot effects on the dynamic response of HSV.

4. Conclusion

In this study, a FEM was used to investigate the HSV eddy current distribution and dynamic characteristics. The following conclusions were drawn.

(1) The eddy current in an HSV was related to the driving current change. For the peak current stage, with increases in the peak current, the eddy current was seen to increase; for the transition processes from hold current I to II and from hold current II to zero, the eddy current appeared and quickly dropped to zero. The eddy current directly influenced the HSV dynamic response, and its effect on the opening response was more significant. By considering the eddy current effect, the calculations strongly matched the experimental data for the HSV opening response; however, for the closing response, deviations remained between the calculations and experimental data as the friction was not considered during calculation.

(2) During the HSV opening process, the eddy current on the magnetic material surface resisted the magnetization process of from the surface to the inside. During the HSV closing process, the eddy current resisted the demagnetization process of from the interior to the surface. Resistance of the eddy current could delay the HSV dynamic response; therefore, structural optimization was believed to be necessary to reduce the eddy current effect on the HSV magnetic material.

(3) The boost voltage should not be as high as possible, because the eddy current would appear and strengthen with an increase in boost voltage. Choice of the boost voltage must consider both eddy current and open dynamic response. Slotting on yoke significantly reduces the eddy current effect in HSV and improves the dynamic response characteristics of HSV, especially the opening response time.

Footnotes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No: 51879054).

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