Moment-Frequency Characteristics of Limited-Angle Torque Motors for Direct-Drive Servo Rotary Valve

Abstract

Direct-drive rotary valve (DDRV) is directly driven by a limited-angle torque motor (LATM), which is characterized by anti-pollution, high efficiency and high frequency response. A LATM is designed for the DDRV. The main dimensions and electromagnetic parameters of the motor are calculated by analytical expression of electromagnetic torque. The torque–angle characteristics and torque characteristics of LATM were analyzed by using finite element method for ensure that the motor can have stable torque output in a wide range of turning angle, the results of theoretical and simulation agree well. On the basis, the motor was improved. The results show that the motor has a working angle of ≥±20°, the torque fluctuation within the working angle is less than 5%, and is suitable for driving the DDRV.

1 Introduction

With the characteristics of fast response and high accuracy, electro-hydraulic servo valve is widely used in the aerospace field and engineering machinery. It is basically composed of a torque motor and a hydraulic amplifier, and can drive the high-power hydraulic energy through electronic signals. At present, the most widely used domestic product are nozzle flapper valve and jet pipe valve. The nozzle flapper valve has small flow channel, sensitive to oil pollution. The pre-stage hydraulic amplifier structure of jet pipe valve is complex, difficult to manufacture, and has large internal leakage. In recent years, the demand for miniaturization and high-frequency response of servo valves has led to rapid development of direct drive valves (DDV) [1]. DDV includes slide valve and rotary valve. The rotary valve uses the rotary movement of the valve spool relative to the valve body or valve sleeve to realize the opening and closing, reversing and flow regulation of the oil circuit. Compared with the slide valve, the rotary valve has better high-frequency response characteristics, can realize the control of small flow, and has higher resolution; It can be directly connected with the driving device, which greatly simplifies the mechanism and improves the anti-pollution performance; And the valve spool movement has no acceleration zero drift, and the control accuracy is high [2].

With the development of new materials, the driving structure of DDV is more diversified, such as piezoelectric ceramics, giant magnetostrictive material driven servo valve has been widely used, but its limitations are also very obvious, the disadvantage of small strain makes it can only be used in small flow field. Yu et al. developed a piezoelectric ceramic DDV with a hydraulic micro-displacement amplification. It can be applied to servo systems with large flow and high-frequency [3]. In view of the poor tensile capacity of the pressure ceramic actuator, which affects the performance of the DDV, Guan and Jiao proposed a piezoelectric ceramic DDV with a new multi-body contacting valve spool-driving mechanism [4]. Giant magnetostrictive materials have excellent properties such as large magnetostrictive strain, high output force, high electromechanical coupling coefficient, and fast response speed. They are widely used in electro-hydraulic servo valves. When applied to DDV, the valves have a high-frequency response. However, due to the limited magnetostrictive strain, the output flow rate is relatively small. If they are to be used in large flow applications, an amplification mechanism is required [5]. Yuan et al. has developed a DDV by LATM. The rotational motion of the motor is transformed into the linear motion of the valve spool through the eccentric mechanism at the end of the motor shaft, and the corresponding flow is output. The control of the output flow is transformed into the control of the angular displacement of the motor, but the design of the conversion mechanism is relatively complex [6]. Some DDVs also use voice coil motor as driving mechanism. Wu et al. developed a DDV using high-frequency voice coil motor and advanced digital controller, which further improved the performance of the DDV in steady and transient states [7]. Shih et al. developed a fuzzy self-tuning controller for the DDV driven by voice coil linear force motor. After verification, the controller is superior to the PID controller, making the response of the DDV faster than the general servo valve [8].

The development of rotary valves has a long history in countries such as the United Kingdom, the United States, and Germany. The related technological and products are already mature. Rotary valve is commonly found in patents and company product introductions. In 2015, MOOG Inc developed a DDRV, valve spool can be driven by a torque motor, and the control of the oil circuit is achieved by changing the position of the valve spool relative to the valve sleeve. This valve has a simple principle, is easy to manufacture, and effectively balances the hydraulic forces on the valve spool [9]. In 2018, Zhu et al. proposed a novel servo valve which is driven by two servo motors. The valve sleeve and valve plate can rotate. It can increase the operating frequency and effectively balance the hydrodynamic forces [10]. In 2022, DOMIN Inc developed a mini rotary valve. The valve spool can rotate and the valve sleeve is omitted [11]. Research on rotary valves in China started relatively late. Cui developed rotary valve is driven by an electromagnet. The geometric shapes of the valve spool and the valve sleeve are symmetric, which offsets the radial unbalanced force on the valve spool and greatly reduces the driving torque [2]. Wang et al. proposed a theoretical model to calculate the flow torque in rotary valve which is driven by a servo motor. The experimental results showed that the model is effective [12].

In practical applications, DDVs driven by LATM mainly utilize a conversion mechanism to transform the rotational motion of the LATM into linear motion of the valve spool. However, this design increases the volume of the valve and complexity of the structure, and difficult to manufacturing. LATM is a kind of motor that can rotate within a certain angle range around their axis without additional mechanical devices. They had advantages such as convenient control, high torque density, simplicity, and reliability. However, because of cogging torque is existence, they had torque fluctuations. These fluctuations can affect the high accuracy and smoothness of DDVs. This article developed a LATM for DDRV and conducted simulation analysis using the finite element method. This approach significantly reduces torque fluctuations and enhances the accuracy and stability of the rotary valve.

2 Method

In this article, LATM is used to drive the rotary valve, the motor shaft is directly connected to the valve spool, and the valve spool and the motor shaft are rotate synchronously within a certain range. Linear Hall will rotor position feedback to the controller to realize the valve spool position closed-loop control. Structure shown in Fig. 1. Eliminated the motion conversion device, the valve spool and valve sleeve are relative rotate, make the valve had ability of low friction, anti-pollution.

Fig. 1

DDRV structure schematic

LATM on a similar principle to permanent magnet brushless DC motors, both based on ampere forces. Structurally, the windings are embedded at the stator and the permanent magnets are placed at the rotor, the difference is that the latter has multi-phase winding, while the former only has single-phase winding [13]. Cogging torque is one of the unique problems of permanent magnet motor, which must be considered and solved in the design and manufacture of permanent magnet motor.

Cogging torque is a pulsating torque generated by the interaction between the permanent magnets and the tooth slots in the core when the winding is not energized. The cogging torque varies with the position of the rotor. It arises from the tangential force between the permanent magnets and the tooth of the stator, which always tries to align the magnetic field axis of the permanent magnets with the axis of the stator tooth, thereby causing the rotor to have a tendency to be positioned at a certain location [14].

From an energy perspective, the cogging torque is caused by the changes in magnetic field energy generated by the permanent magnets. The magnetic field energy is related to the angular position of the rotor. In fact, the cogging torque ${T}_{cog}$ can be approximated as the rate of change of the static magnetic field energy W in the motor air gap with respect to the rotor angle. Therefore, the cogging torque can be defined as the negative reciprocal of the magnetic field energy W with respect to the relative position angle $\alpha$ between the stator and rotor when the motor is not energized. This relationship is given by Eq. (1).

$${T}_{cog}=-\frac{\partial W}{\partial \alpha }$$

(1)

In surface-mounted permanent magnet brushless DC motors, assuming the relative permeability ${\mu }_{r}$ of the armature iron core is infinite, and the permeability of the permanent magnet material is the same as air, which is ${\mu }_{0}$, the magnetic field energy can be approximately considered as the sum of the energy of the permanent magnet and the energy of the air gap.

$$W=\frac{1}{2{\mu }_{0}}\int\limits_{v}^{ }{B}_{r}^{2}(\theta ){\left(\frac{{h}_{m}}{{h}_{m}+g(\theta ,\alpha )}\right)}^{2}dV$$

(2)

In the above equation: ${B}_{r}(\theta )$ is the distribution of permanent magnet residual magnetism along the circumference; ${\text{g}}(\uptheta ,\mathrm{\alpha })$ is the distribution of the effective air gap length along the circumference when the angle between the pole centerline and the tooth centerline is $\mathrm{\alpha }$; ${h}_{m}$ is the length of permanent magnet magnetization direction.

Fourier decomposition of ${B}_{r}^{2}(\theta )$:

$${B}_{r}^{2}={B}_{r0}+\sum_{n=1}^{\infty }{B}_{rn}\cos\left(2np\theta \right)$$

(3)

In the above equation: p is the number of pole pairs; n is the positive number that makes $\frac{nz}{2p}$ an integer.

Fourier decomposition of ${(\frac{{h}_{m}}{{h}_{m}+g(\theta ,\alpha )})}^{2}$:

$${\left(\frac{{h}_{m}}{{h}_{m}+g\left(\theta , \alpha \right)}\right)}^{2}={G}_{0}+\sum_{n=1}^{\infty }{G}_{n}\cos\left(nz\left(\theta +\alpha \right)\right)$$

(4)

The final expression for the cogging torque is given by

$${T}_{cog}\left(\alpha \right)=\frac{\pi z{L}_{a}}{4{\mu }_{0}}\left({R}_{2}^{2}-{R}_{1}^{2}\right)\sum_{n=1}^{\infty }n{G}_{n}{B}_{r\frac{nz}{2p}}\sin\left(nz\alpha \right)$$

(5)

In the above equation: ${R}_{1}$ is the outer diameter of armature; ${R}_{2}$ is the inner diameter of stator; ${L}_{a}$ is the length of armature core.

The expression of the cogging torque can be seen that the cogging torque is mainly related to ${B}_{rn}$ and ${G}_{n}$. Therefore, from reducing the amplitude and number of Fourier decomposition coefficients, weakening the cogging torque is mainly achieved by reasonable pole-slot fits, changing the pole parameters and changing the armature parameters [15].

A reasonable pole-slot fit can change the number and amplitude of ${B}_{rn}$ and ${G}_{n}$ to weaken the cogging torque. The concentrated winding LATM can significantly reduce the effect of cogging torque on motor performance [16]. The concentrated winding LATM has an equal number of poles and slots, and there is only one cogging torque cycle within one electromagnetic torque cycle, and the amplitude of the cogging torque is very small within the constant torque interval of the LATM, so the cogging torque has little influence on the constant torque range. The use of a concentrated winding makes the winding end length smaller than that of the conventional cogging type, which effectively reduces the use of copper. Meanwhile, due to the relatively small number of slots in the concentrated winding LATM, the slot area utilization is high and the winding coefficient is higher than that of the distributed winding, resulting in a higher power density.

In addition, changing the pole parameters can change the amplitude of ${{\text{B}}}_{{\text{rn}}}$. Therefore, the design of unequal thickness of permanent magnets can also reduce the impact of cogging torque on the motor performance. The shape of the permanent magnets affects the distribution of the air-gap magnetic density, which affects the amplitude of the cogging torque, in the design of this article, the rotor is of conventional surface-mounted type, but the shape of the permanent magnets is in the shape of a bread-like, which reduces amplitude of cogging torque and thus improves the performance of the motor [17].

Based on the above analysis, the general structure of the motor was determined to be a new structure combining a concentrated winding and a bread-like shape of permanent magnets, as shown in Fig. 2. Subsequently, the motor was further designed based on the design parameters. The specific design parameters are listed in Table 1.

Fig. 2

LATM structure schematic

Table 1 Design parameters

The specific design process is as follows:

First, based on Eq. (6) [16], select the materials for each component and estimate the size of the motor;

$${T}_{e}=\frac{2P{\mu }_{0}{\mu }_{r}{H}_{c}{h}_{m}I{N}_{c}{l}_{ef}}{ln({r}_{2}/{r}_{1})+{\mu }_{r}ln({r}_{3}/{r}_{2})}$$

(6)

In the above equation: P is the number of pole pairs, ${\mu }_{0}$ is the permeability of air, ${\mu }_{r}$ is the permeability of permanent magnet, ${H}_{c}$ is the coercivity of permanent magnet, ${h}_{m}$ is the thickness of permanent magnet, $I$ is the current, ${N}_{c}$ is the number of windings, ${l}_{ef}$ is the effective length of the motor, ${r}_{1}$ is the inner diameter of the permanent magnet, ${r}_{2}$ is the outer diameter of the permanent magnet, ${r}_{3}$ is the inner diameter of the stator.

Secondly, according to the design requirements, the outer diameter of stator and the number of windings are determined, and the slot full factor of the motor is calibrated; the rated torque and constant torque range of the motor under the initial scheme are obtained by using the finite element method.

Then, under the premise of meeting the design requirements, the simulation results were analyzed and compared using the finite element method. The analysis primarily focused on the fluctuation and mean values of the cogging torque and electromagnetic torque under different tooth parameters and magnetic pole parameters (such as tooth width, slot width, tooth tip thickness, and permanent magnet width). By comparing the results, the parameter combinations that minimized the fluctuation and maximized the mean values can be determined.

Finally, the overall assembly scheme of the motor is designed, and a sealing structure is specifically designed for the working environment of the LATM to ensure that the motor armature is not affected by hydraulic oil.

By calculating and calibrating the slot full factor, the motor parameters obtained are shown in Table 2.

Table 2 Motor parameters

3 Simulation Results and Comparisons

Torque fluctuation not only affects the positioning accuracy of the motor, but also triggers vibration and noise, so in the process of motor design, it is necessary to use finite element method to simulate and analyze the motor, and through the comparative of various parameters, minimize the torque fluctuation of the motor as much as possible.

Improvement target: Motor with less torque fluctuation in the ±20° torque range of the motor.

The parameters of the motor tooth and magnetic poles are shown in Table 3. During the improvement process, it is important to ensure both the motor performance and outer diameter dimensions while also ensuring sufficient slot area. Considering these factors together, the following ranges for the tooth parameters can be determined: tooth width range of 5–6 mm, slot width range of 1–2 mm, tooth tip thickness range of 1–2 mm, and permanent magnet width range of 9–11 mm.

Table 3 Initial parameters

3.1 Tooth Width

First of all, to determine the appropriate tooth width parameters, when the current with an RMS value of 1.5 A is passed, the electromagnetic torque varies with the ${T}_{w}$ as shown in Fig. 3, and the cogging torque varies with the tooth width as shown in Fig. 4.

Fig. 3

Variation of electromagnetic torque with tooth width

Fig. 4

Variation of cogging torque with tooth width

From the simulation curves of electromagnetic torque, it can be observed that the three curves obtained are essentially identical when the tooth width varies between 5 and 6 mm. Regarding the simulation curves of cogging torque, it is evident that the tooth width affects the crest value of the cogging torque. As the tooth width increases, the crest value of the cogging torque decreases. In order to achieve a desired slot fill factor while ensuring that the motor has strong saturation resistance capability, the tooth width is selected as 5.5 mm.

3.2 Slot Width

Then, the slot width of the LATM is analyzed. The variation of electromagnetic torque and cogging torque with the slot width is shown in Figs. 5 and 6.

Fig. 5

Variation of electromagnetic torque with slot width

Fig. 6

Variation of cogging torque with slot width

As shown in the Fig. 5, the slot width affects the asymmetry of electromagnetic torque on the left and right sides of the rotor position, and the symmetry of electromagnetic torque is optimal at mm. As the slot width varies from 1 to 1.5 mm, the amplitude of the cogging torque decreases. However, as the slot width further increases from 1.5 to 2 mm, the amplitude of the cogging torque increases in the opposite direction. After comprehensive consideration, the slot width is selected as 1.5 mm.

3.3 Tooth Tip Thickness

The tooth tip thickness is further analyzed. The variation of electromagnetic torque and cogging torque with tooth tip thickness is shown in Figs. 7 and 8.

Fig. 7

Variation of electromagnetic torque with tooth tip thickness

Fig. 8

Variation of cogging torque with tooth tip thickness

When the tooth tip thickness changes from 1 to 1.5 mm, it affects the asymmetry of the electromagnetic torque on the left and right sides of the rotor position $\theta =0^\circ$ and the average value in the working range; when the tooth tip thickness changes from 1.5 to 2 mm, there is no significant change in the curve. And with the change of tooth tip thickness, the change of cogging torque is very small and basically overlapped. The final value of tooth tip thickness is 1.5 mm.

3.4 Permanent Magnet Width

Finally, based on the determined tooth width, slot width, and tooth tip thickness, a comparison is made of the electromagnetic torque curves obtained from different permanent magnet widths to determine the optimal permanent magnet width parameter. The variation of electromagnetic torque and cogging torque with the width of permanent magnet is shown in Figs. 9 and 10. As can be seen from the figures, the width of permanent magnet has a greater influence on the electromagnetic torque and cogging torque. When the width of permanent magnet changes from 9 to 10 mm, the electromagnetic torque curve is smoother and the average value is larger. When the width of permanent magnet changes from 10 to 11 mm, the electromagnetic torque curve changes little. The permanent magnet width also affects the crest value of the cogging torque. It can be seen that when the permanent magnet width is 9.5 mm, the fluctuation is smaller. The permanent magnet width is selected as 9.5 mm.

Fig. 9

Variation of electromagnetic torque with permanent magnet width

Fig. 10

Variation of cogging torque with permanent magnet width

After the above comparative analysis, the final parameter results are ${T}_{w}$ = 5.5 mm, ${t}_{1}$ = 1.5 mm, ${t}_{2}$ = 1.5 mm, ${b}_{m}$ = 9.5 mm.

The general assembly of the LATM developed in this article is shown in Fig. 11, which mainly consists of stator, rotor, coil winding, end-cap assembly, angular displacement sensor, steel sleeve, and shell. The rotor consists of a rotor shaft, a magnetic yoke and permanent magnet, and the end-cap assembly includes an inner end cap, an outer end cap and an angular displacement sensor. The rotor shaft transmits the angular displacement to the valve spool. The steel sleeve and O-ring ensure that the hydraulic oil can only enter the inside of the steel sleeve, providing cooling for the rotor portion and lubrication for the bearings without affecting the coil [18]. The comparison of the results before and after the improvement is shown in Fig. 12. The average value of the improved torque within the working angle ±20° is 93.5 mNm, and the torque fluctuation rate is 4.27%, which meets the requirements for use as a rotary valve driving mechanism.

Fig. 11

LATM overall assembly diagram

Fig. 12

Improvement before and after comparison

4 Conclusion

A LATM is developed for rotary valve with simple overall structure, strong anti-pollution ability and high frequency response. The finite element simulation results show that the motor can output torque (>90 mNm) stably in the operating range of ±20°, and the torque fluctuation is <5% (4.27%), which meets the design requirements.

By combining the concentrated winding and the permanent magnet of bread-like design, the amplitude of the cogging torque is reduced to near zero within the working range, thereby weakening the effect of the cogging torque on the motor's performance.

The sealing structure composed of steel sleeve and O-ring avoids the influence of hydraulic oil on the coil, so that the working process of the motor is not disturbed. At the same time, hydraulic oil can lubricate the bearings, rotor part of the cooling, compact structure.