Keywords

1 Introduction

The electrification of automotive powertrains is actively promoted from the perspective of reducing environmental impact. Nevertheless, internal combustion engines are expected to continue to be used, including those utilizing biofuels or hydrogen, and those incorporated in hybrid vehicles. Therefore, improvements in engine performance are necessary. Furthermore, to improve the aerodynamic performance of the entire vehicle, compactness of the powertrain is increasingly required. However, enhancing performance requires improving the combustion conditions of the engines. The combustion state of an engine is influenced by multiple parameters of the valve-train system. Engine valves operated by cam mechanisms can significantly affect fuel efficiency and power output depending on the operating conditions. To address this issue, variable valve mechanisms have been developed [1,2,3]. However, conventional variable valve mechanisms face technical challenges in achieving direct control at all engine speeds. Therefore, this study proposes an electromagnetic valve drive system. This system employs a linear actuator to drive the valve, allowing for continuous variations in valve lift and timing. Consequently, the valve control can be optimized according to the engine speed, thereby enhancing the environmental performance of the engine and suppressing backfire in the manifold of hydrogen engines. Other studies have proposed actuators for intake and exhaust systems. However, the seesaw-type electromagnetic valve drive proposed by Fuse et al. has significant issues such as the inclusion of large armatures and springs, leading to increased complexity and mass [4, 5]. Similarly, Okazaki et al. proposed a solenoid method that did not use permanent magnets. However, when coils are used in a stator, electrical resistance increases during high-speed motion, resulting in increased power requirements in high-speed engines [6]. Furthermore, the linear actuator proposed by Uchida et al. controls a valve with stator coils, making it disadvantageous for high-speed motion [7]. Thus, existing linear actuators face challenges related to their increased size, complex structure, and insufficient thrust. In light of these issues, we propose a voice coil motor-type linear actuator utilizing the Lorentz force [8,9,10]. This actuator simplifies the structure using a coil in the mover and achieves high responsiveness through operation at low AC frequencies. The voice coil motor type is particularly suitable for position control, enabling highly precise operation. The motion of the valve being a short reciprocating movement, the influence of the coil wiring on the movement of the mover is considered minimal. Moreover, a direct-drive system facilitates precise operation. This study focuses on the issues of actuator enlargement and the associated increases in volume and mass that arise when generating the thrust necessary for engine valve operation. Automotive engines face significant spatial constraints, necessitating the use of small actuators to drive the valves. To address this problem, we aimed to enhance the thrust per unit volume of the actuator at the foundational stage and prototype three models. These models vary the ratio of the permanent magnets within the actuator to examine their impact and evaluate the thrust characteristics through electromagnetic field analysis.

2 Enhancing Thrust Density with Dual Halbach Array

We applied a dual Halbach array to the linear actuator to enhance the thrust per unit volume. Figure 1 shows a schematic of the configuration of a dual Halbach array. This figure depicts the arrangement of the permanent magnets and coils, with the magnetization directions represented as N-S. By placing permanent magnets as shown, a magnetic circuit can be formed solely with permanent magnets, avoiding the generation of large external magnetic fields. This configuration reduces the yoke volume required for the magnetic circuit formation, thereby decreasing the overall volume of the actuator. Previous studies conducted electromagnetic field analyses on models with dual Halbach arrays using three-dimensional computer-aided design software to investigate the magnetic field and thrust characteristics. The magnetic flux generated by the permanent magnets did not sufficiently intersect the coils orthogonally, resulting in a thrust of approximately 48.8 N, thereby limiting the performance of the actuator to low engine speed operations [11]. To address this, we developed three new models, maintaining the same external dimensions as the previous model (100 mm in diameter and 100 mm in height), but varying the ratio of the permanent magnets. Figure 2 shows a schematic of the newly prototype linear actuator. These actuators consist of permanent magnets and coils, with the coils serving as the mover and the permanent magnets serving as the stator. When electric current passes through the coils, the Lorentz force drives the coils in the axial direction, as indicated in the figure. Five permanent magnets magnetized in the same direction but with different orientations were arranged to concentrate the magnetic flux on the coils. Figure 3 shows a cross-sectional view of the actuator. As shown, the widths of the permanent magnets on either side of the coil (W1) and the outermost permanent magnets (W2) varied. W2 was reduced from 10 mm to 0 mm in 5 mm increments, with a corresponding increase in W1's width. The dimensions for each model are: Model A with W1:9.5 mm, W2:10 mm; Model B with W1:12 mm, W2:5 mm; and Model C with W1:14.5 mm, W2:0 mm. The three models were compared and analyzed. The analytical conditions are listed in Table 1. We used a neodymium-sintered magnet, NMX-S52, for permanent magnets, and the temperature was set at 20 ℃. The displacement of the coil (mover) was set to 10 mm, with a displacement of 1 mm every 0.1 s, resulting in one reciprocating motion over 2 s. The coil windings were set at 461 turns to maintain a fill factor below 45%, and the coil resistance was set to 1 Ω with a power supply voltage of 5 V, ensuring a current density below 10 A/mm2. We applied 5 V from 0 to 1 s to measure the thrust during the upward movement from 0 to 10 mm, and −5 V from 1.1 to 2 s to evaluate the thrust during the downward movement from 10 to 0 mm. Based on these conditions, we conducted a transient response analysis using the finite element method. We used the electromagnetic field analysis software JMAG to investigate the thrust characteristics during the reciprocating motion of the mover.

Fig. 1.
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Dual Halbach array applied to linear actuators.

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Fig. 2.
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Schematic of the linear actuator.

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Table 1. Analysis conditions.
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Fig. 3.
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Linear actuator dimensions

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3 Lorentz Force Density and Thrust Analysis Results

The contour plot of the axial Lorentz force density acting on each model’s coil and the vector plot of the magnetic flux density over the entire actuator are shown in Fig. 4. The axial Lorentz force density on the coil increased from model A to model C. Comparing the magnetic flux near the coil, model A exhibited a predominantly axial flux, whereas model C showed an increase in flux intersecting the coil vertically.

Consequently, the Lorentz force density reveals that while most of the coil in model A experiences a Lorentz force density of 0.5 × 106 N/mm2, regions indicating a 1.5 × 106 N/mm2 Lorentz force density increase in models B and C as the magnet ratios change. Figure 5 shows the average thrust of the moving coil for each model, with the vertical axis representing the average thrust and the horizontal axis denoting the model names. The coils, which are the movers in each model, ascend from the 0 mm point to the 10 mm point, stop at the 10 mm point, and then descend back to the 0 mm point. Figure 5 shows the average absolute values of each displacement point during this reciprocating motion. Notably, model A exhibited an average thrust of approximately 68.6 N, while models B and C yielded approximately 84.8 N and 107 N, respectively, indicating a difference of approximately 38.4 N between models A and C. This discrepancy is attributed to the flux density being perpendicular to the current flowing through the coil, resulting in a low Lorentz force density in Model A. By eliminating the permanent magnets at the ends of the dual-Halbach array (as shown in Fig. 1) and increasing the volume of the permanent magnets sandwiching the coil, we achieved an improved thrust per unit volume. At a cam actuation angle of 250° and a displacement of 10 mm, the engine rotational speeds corresponding to the thrust of models A, B, and C were approximately 5987, 6351, and 6838 rpm, respectively. Despite having the same volume, adjusting the permanent magnet ratios resulted in a maximum difference of 851 rpm in the engine rotational speeds each model could accommodate.

Fig. 4.
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Plot of Lorentz force density vs. magnetic flux density.

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Fig. 5.
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Average thrust of each model.

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4 Conclusion

In this study, we developed three linear actuator models with varying ratios of permanent magnets by applying a dual Halbach array to improve the thrust per unit volume. These models were compared and analyzed using electromagnetic field analysis. The results revealed that reducing the permanent magnets at both ends of the dual Halbach array and increasing the volume of the other permanent magnets effectively enhanced the thrust. Specifically, the maximum thrust was achieved by eliminating the permanent magnets at both ends and increasing the number of permanent magnets at the ends of the coil. Future investigations will focus on further enhancing the thrust by exploring different ratios of permanent magnets. When we are able to prototype a more efficient actuator, we plan to make a detailed comparison with standard valve and cam mechanisms to determine their performance and energy-saving advantages and limitations.