Analysis of Factors Influencing Peak Torques and Peak Losses of Rotary Voice Coil Actuators Used in Aerospace

Rotary voice coil actuators (RVCAs) are commonly used for precision servo drive systems working within limited angle range in some fields including aerospace. In this paper, expressions of RVCAs' peak torque and peak loss are derived based on a simple magnetic circuit model, and influences of wire diameter and equivalent area on peak torque and peak loss are analyzed. Especially, two unique influences of installing dimension and environment temperature for this type of motor are researched as well. Armature reaction and its restraining for this type of actuator are also studied. Finally, several effective measures of improving RVCAs' torques are summarized, which are of important value in practical engineering applications.

SECTION I. Introduction

Voice coil actuators (VCAs) are special electrical machines which operate only within a range of stroke lengths or angles. Compared with traditional electrical machines, VCAs have many outstanding advantages, such as small volume, direct driving without gears, high precision and low inertia [1]–​[5], and so used for driving light weight and low inertia loads. VCAs can be classified into single magnetic circuit VCAs and dual magnetic circuit VCAs from aspect of magnetic circuit structure; or classified into linear VCAs (LVCAs) and rotary VCAs (RVCAs) from aspect of motion type [6], [7]. In this paper, dual magnetic circuit RVCAs are mainly studied, whose typical applications include scanning mirror drive in space cameras, mirror positioning in laser technique and swing type valve brake, etc [8].

Generally, the main performance of a RVCA includes peak torque, peak loss, angular stroke, electrical time constant, torque sensitivity, thermal resistance of coil, etc., among which peak torque of the actuator is most important [9]–​[11]. The factors influencing peak torque in this type of motors need to be further studied, because there is a significant difference between the structures of RVCAs and general motors.

In this paper, expressions of peak torque and peak loss of RVCAs are derived in a simplified magnetic circuit model, and influences of main structure parameters are fully analyzed. Especially different from other motors, influences of installing dimension and environment temperature are also studied. Also, armature reaction and its influence of this type actuator are analyzed, and some restraining measures to improve torque are also studied. At the end, several feasible measures for improving RVCA’s torque are given. The work of this paper is of good value to the practical application of RVCAs.

SECTION II. Theoretical Analysis of Peak Torque and Peak Loss

The structure and working principle of a dual magnetic circuit RVCA are shown in FIGURE 1. The RVCA is composed of two components, a stator assembly containing permanent magnet, and a rotor assembly containing coil. In most cases, movable coil installation is adopted where the stator assembly is fixed to a stationary frame and the rotor assembly is connected to the moving load at one end. In some special cases, movable stator installation is also adopted where the rotor is fixed stationary and the magnets are movable. This manner is more suitable for RVCAs with large torque and has two benefits, the motor assembly can be installed more steadily at two ends, and heat in the stationary coil can be easily conducted to external metal frame.

FIGURE 1.

Structure of dual magnetic circuit RVCA.

The rotor of the motor can only swing within a certain range of angle instead of circular motion in 360 degrees because of mechanical limitation. When current passes through the coil, an electromagnetic torque will be generated relatively to the rotating center and drives the RVCA to swing. According to fundamental electromagnetic relation and power supply feature, the peak torque $T_{m}$ of a RVCA is expressed as:

$$\begin{align*} T_{m}=&2NB_{g} I_{m} L_{fe} R_{av} =k_{T} I_{m} \tag{1}\\ I_{m}=&\frac {U_{dc}}{r_{a}}\tag{2}\end{align*}$$ where $N$ represents wire turns of the coil, $B_{g}$ represents magnetic flux density in air gap, $I_{m}$ represents peak current, $L_{fe}$ represents average effective coil length, $R_{av}$ represents average rotating radius of the rotor, $k_{T}$ represents torque sensitivity, $U_{dc}$ represents DC supply voltage, and $r_{a}$ represents resistance of the coil [12].

Key structure parameters of a RVCA are shown in FIGURE 2 (front view of FIGURE 1). Since the yoke is wide enough, the magnetic potential drops in ferric yokes can be ignored. The simplified magnetic circuit of half of the magnet is shown in FIGURE 3, in which $R_{2}$ is reluctance caused by magnet-to-yoke flux leakage and $R_{\mathrm {g}}$ is the air gap reluctance [13]. The reluctance of flux leakage and leakage coefficient can be described as:

$$\begin{align*} \begin{cases} F_{PM} =\dfrac {B_{r} h_{m}}{\mu _{0} \mu _{r}},\;\;R_{1} =\dfrac {2h_{m} }{\mu _{0} \mu _{r} A_{m}} \\ R_{2} =\left[{\dfrac {\mu _{0} L_{fe}}{\pi }\ln \left({1+\dfrac {\pi \delta }{h_{m} }}\right)}\right]^{-1} \\ \sigma =\dfrac {\psi _{g}}{\psi _{1}}=\dfrac {R_{2}}{R_{g} +R_{2}} \\ \end{cases}\tag{3}\end{align*}$$

FIGURE 2.

Key structure parameters of a RVCA.

FIGURE 3.

Simplified magnetic circuit model.

According to the expression of magnetomotive force of permanent magnet, the air gap flux density can be expressed as [14]:

$$\begin{equation*} B_{g} =\frac {h_{m} \sigma }{h_{m} +\mu _{r} \sigma \delta }B_{r} =\frac {\sigma }{1+\mu _{r} \sigma \delta ^{\ast }}B_{r}\tag{4}\end{equation*}$$ where $A_{\mathrm {m}}$ is area of the magnet, is thickness of permanent magnets, $\sigma$ is leakage coefficient, $\mu _{r}$ is the relative permeability of permanent magnets, $\delta$ is the total gap length composed of coil height $a$ and twice $\delta _{0}$ , $\delta ^{\ast }$ is the relative gap length which is $\delta /h_{m}$ , and $B_{r}$ is the remanent flux density of the magnet.

The wire turns of the coil $N$ is determined by sectional area of the coil, and will be

$$\begin{equation*} N=\frac {S_{f} ab}{{\pi d_{Cu}^{2}} \mathord {\left /{ {\vphantom {{\pi d_{Cu} ^{2}} 4}} }\right. } 4}=\frac {4A_{ec}}{\pi d_{Cu} ^{2}}\tag{5}\end{equation*}$$ where $S_{f}$ is slot coefficient, $a,b$ are the height and width of the coil respectively, $A_{ec}$ is the effective area of coil, and $d_{Cu}$ is the copper wire diameter.

The resistance of coil $r_{a}$ can be expressed as

$$\begin{equation*} r_{a} =N\rho \frac {L}{A}=\frac {16\rho LA_{ec}}{\pi ^{2}d_{Cu}^{4}}\tag{6}\end{equation*}$$ where $\rho$ represents the electrical resistivity of copper and $L$ is the average length of one turn.

Therefore, the expressions of torque sensitivity, peak torque and peak loss of the motor can be derived as:

$$\begin{align*} \begin{cases} k_{T} =\textrm {2}NB_{g} L_{fe} R_{av} =\dfrac {8B_{r} L_{fe} R_{av} A_{ec} \sigma }{\pi d_{Cu}^{2}(1+\mu _{r} \sigma \delta ^{\ast })} \\ T_{m} =k_{T} I_{m} =\dfrac {\pi d_{Cu}^{2}B_{r} L_{fe} R_{av} U_{dc} \sigma }{2\rho L(1+\mu _{r} \sigma \delta ^{\ast })} \\ P_{m} =I_{m}^{2}r_{a} =\dfrac {\pi ^{2}d_{Cu}^{4}U_{dc} ^{2}}{16\rho LA_{ec}} \\ \end{cases}\tag{7}\end{align*}$$

It can be seen from the equation that the peak torque of a RVCA relates to not only supply voltage $U_{\mathrm {dc}}$ and structure parameters of the motor (such as effective area of coil $A_{\mathrm {ec}}$ , relative gap length $\delta ^{\ast }$ , average effective coil length $L_{\mathrm {fe}}$ , etc.), but also installation size (average rotating radius of rotor $R_{\mathrm {av}}$ ) and environment temperature (the electrical resistivity $\rho$ ), this is the uniqueness of RVCAs [15].

SECTION III. Influences of Structure Parameters

The parameters of analysis model are: Samarium Cobalt (Sm-Co) magnets, $h_{m}=7$ mm, $d_{Cu}=0.49$ mm, $a=4$ mm, $b=40$ mm, $L_{fe}=50$ mm, $L=175$ mm, $R_{av}=120$ mm, $\delta =$ 7 mm, $S_{f}=0.8$ , and $U_{dc}=12\text{V}$ .

A. Influence of Copper Wire Diameter

According to equation (6) and (7), while structure parameters are unchanged, increasing of copper wire diameter will result in decreasing of wire turns of coil and torque sensitivity at the same time. Secondly, significant decreasing of coil resistance leads to dramatic growth of peak current. At last, both peak torque and peak loss increase as well. The variation curves of main performance are shown in FIGURE 4. If copper wire diameter increases by 10%, the peak torque will increase by 20% but peak loss will increase by 46%, which is an adverse impact on thermal control system and it should be noticed in poor heat dissipation environment.

FIGURE 4.

Variation curves of main performance as the copper wire diameter varies: (a) current and power; (b) torque and torque sensitivity.

B. Influence of Effective Area of Coil

The variation curve of each index is shown in FIGURE 4. It is interesting that the peak torque is independent from the effective area of coil which only influences the torque sensitivity and peak loss. A larger effective area of coil will definitely increase the number of turns and the torque sensitivity, and meanwhile, the peak loss will decrease because of a larger coil resistance. This means, for a RVCA with constant structure parameters, whether the winding is full or not has no impact on the peak torque, and simply increasing the width of coil (the height of coil is limited by the air gap length) cannot improve the peak torque either. Moreover, larger coil width will result in shorter angular stroke under same motor size, or larger motor volume under same angular stroke, thus it is not an optimal choice.

SECTION IV. Influence of Installation Sizes

Compared with simple motors with cylindrical shapes, RVCAs are easier to be installed and the installation is adjustable. As shown in FIGURE 6 (top view of FIGURE 1), relation between the average effective coil length $L_{fe}$ and the average rotating radius $R_{av}$ is:

$$\begin{align*} \begin{cases} L_{fe} =R_{\max } -R_{\min } \\ R_{av} =\dfrac {R_{\max } +R_{\min }}{2} \\ \end{cases}\tag{8}\end{align*}$$ where $R_{\mathrm {min}}$ , $R_{\mathrm {max}}$ are the minimum and maximum rotating radius of rotor respectively within the magnetic field.

FIGURE 5.

Variation curves of main performance as the equivalent area varies: (a) current and power; (b) torque and torque sensitivity.

FIGURE 6.

The relation between minimum rotating radius and maximum rotating angle.

For a finished RVCA, $L_{fe}$ is unchangeable, but $R_{av}$ can be adjusted by changing $R_{\min }$ . According to equation (7), if $R_{\min }$ becomes larger, the torque sensitivity and peak torque will increase while the peak loss stays unchanged.

The disadvantage of this measure is the angular stroke will become shorter as $R_{\min }$ increases, because rotor motion is limited by the two top corners in FIGURE 6. If the $R_{\min }$ increases by $\Delta R_{\min +}$ or decreases by $\Delta R_{\min -}$ as shown in FIGURE 6, the maximum rotating angle can be calculated as:

$$\begin{align*} \beta=&\arctan \left [{ {\frac {\left ({{R_{\min } +L_{fe}} }\right)\sin \theta }{\left ({{R_{\min } +L_{fe}} }\right)\cos \theta +\Delta R_{\min +}}} }\right] \tag{9}\\ \alpha=&\arctan \left [{ {\frac {\left ({{R_{\min } +L_{fe}} }\right)\sin \theta }{\left ({{R_{\min } +L_{fe}} }\right)\cos \theta -\Delta R_{\min -} }} }\right]\tag{10}\end{align*}$$ where $\theta$ is the maximum rotating angle corresponding to $R_{\min }$ , $\beta$ is the maximum rotating angle corresponding to $R_{\min } +\Delta R_{\min +}$ , $\alpha$ is the maximum rotating angle corresponding to $R_{\min } -\Delta R_{\min -}$ .

The variation curve of every index is shown in FIGURE 7. When $R_{\min }$ increases by 10%, the peak torque of RVCA increases by 7.73% and the stroke decreases by 5.89%.

FIGURE 7.

Variation curves of main performance as the minimum rotating radius varies.

SECTION V. Influence of Environment Temperature

RVCAs are usually used in space, where environment temperature impacts their performance significantly. Two parameters of a RVCA will be affected directly by the temperature, the property of permanent magnet material, and coil resistance. Their variation principles are:

$$\begin{align*} \begin{cases} B_{rt} =B_{r20} [1-0.0003(t-20)] \\ \rho _{t} =\rho _{20} [1+0.004(t-20)] \\ \end{cases}\tag{11}\end{align*}$$ where $B_{r20}$ and $\rho _{20}$ are rest flux density and resistivity of copper wire corresponding to 20 °C.

With equation (7) and (11), the variation trends of RVCAs’ key parameters with different environment temperatures can be obtained, as shown in FIGURE 8. Apparently, the coil resistance will increase rapidly as the temperature increases, which will lead to a sharp decline of the peak torque. When the temperature increases from 20 °C to 120 °C, the remainder of the peak torque is only 69.3% of its original value, less than 70%. This is an important problem that the users should be noticed, the impact of environment temperature must be considered when choosing an appropriate RVCA for engineering application.

FIGURE 8.

Variation curves of main performance as the environment temperature varies: (a) current and power; (b) torque and torque sensitivity.

SECTION VI. Influence of Armature Reaction to Torque Uniformity

RVCAs are widely used in precise position control, so the linearity of their output characteristics is very important. The air gap magnetic field in a RVCA is uniform and symmetry when the coil has no current, but when the coil is fed with current, an armature reaction will be generated because one side of the magnetic field is enhanced and the other side is weakened, as shown in FIGURE 9 (the average one is proportional to the no load magnetic flux density in air gap). The reactance will cause a variation of output torque during the movement of the rotor. Torque uniformity (or torque coefficient uniformity) is used to express the distortion, defied as:

$$\begin{equation*} \Delta T=\frac {\Delta T_{\max } -T_{av}}{T_{av}}\times 100\%\tag{12}\end{equation*}$$ where $T_{av}$ is the average torque within the whole scope, $\Delta T_{\max }$ is the maximum difference between the actual torque and the average torque.

FIGURE 9.

Variation of output torques corresponding to different armature currents.

It is very clear that the torque uniformity is directly related to quantity of coil current, direction of coil current and rotor position [16].

The main magnetic field and armature magnetic field of a dual magnetic field RVCA are shown in FIGURE 10, where the main magnetic field is symmetry between left and right, the armature magnetic field is symmetry between top and bottom layers. The physical difference of the two fields is that the armature magnetic flux only closes its loop in the stator without passing air gap. Therefore, main flux does not exist in three saturated areas shown in FIGURE 10, this provides us a new idea for the armature magnetic field restraining.

FIGURE 10.

Magnetic routes of a dual magnetic circuit RVCA.

It is obvious that the direct way to restrain the armature reaction is to cut off the loop of the armature flux, as shown in FIGURE 11. The stator upper plate is broken at middle (gap width is $w$ ), and some permanent magnet (which height is $h$ ) is inserted in the gap to compensate drop of the magnetic flux density caused by the gap.

FIGURE 11.

Structure of broken gap in stator upper plate and inserted.

The output torque and uniformity of the actuator are calculated and shown in FIGURE 12 where w varies from 2 to 20mm and h from 1 to 6mm. According to the contour lines, w = 12mm and h = 1.5mm seem to be an optimal choice. In this case, torque uniformity varies from 6.5% to 1.7% within ±10° moving scope, thus the effect of armature reaction restraining cannot be ignored.

FIGURE 12.

Calculation results of torque uniformity corresponding to different broken gap width and inserted magnet height.

SECTION VII. Experiment

A. Experiments of Environment Temperature Influences

In order to verify the variation of peak torque under different environment temperatures, a RVCA prototype is placed in a test pot where the temperature can be varied from -30 °C to 180 °C and the vacuum degree can be controlled under $5.0\times 10 ^{\mathrm {-4}}$ Pa, as shown in FIGURE 13. The measured peak torque and its variation are listed in TABLE I, whose varying principle is closely coincident with the analysis in FIGURE 8. At 130 °C, the remainder of the peak torque decreases to only 66.0% because of the temperature coefficient in (12).

TABLE 1 Peak Torques Under Different Environment Temperatures

FIGURE 13.

Experiments of environment temperature influences: (a) temperatures test pot; (b) RVCA prototype in test.

B. Experiments of Armature Reaction Influences

Another RVCA prototype is used to verify the effect of armature reaction. Similar structures like FIGURE 10 and FIGURE 11 are used in the prototype according to the optimum parameters.

Torque uniformities are measured before and after the gap is cut at stator yoke. The results are shown in FIGURE 14, and listed in TABLE 2 after calculation.

TABLE 2 Torque Uniformities of Different Stator Yokes

FIGURE 14.

Output peak torques measured corresponding to broken stator yoke structure.

According to the results, new structure can achieve a significant improvement in torque uniformity. Gap structure can reduce the maximum ripple torque (at maximum stroke 8.0 degree) by nearly 50%.

SECTION VIII. Conclusion

Compared with traditional induction motors and DC motors, RVCAs have many special properties. In this paper, factors influencing peak torques and peak losses of RVCAs are analyzed in detail, following conclusions can be obtained:

(1) If structure parameters are constant, increasing the copper wire diameter can increase the peak torque, which is an effective way to improve RVCAs’ torque performance.

(2) Considering a certain RVCA, peak torque can be increased by increasing the distance between the actuator and rotating axis. It is another effective measure to improve RVCAs’ torque performance, but the decrease in angular stroke is an inevitable disadvantage.

(3) The peak torque of a RVCA is independent from the slot coefficient and the effective area of coil. Increasing of the coil width will not affect the peak torque, but it can slightly reduce the peak current and peak loss.

(4) The increase of environment temperature will result in a rapid decline of peak torque. When the temperature grows to 120 degrees, the peak torque will decline to less than 70% of its original value, which should be taken into consideration carefully.

(5) Armature reaction is one of the main factors influencing output torque accuracy of a RVCA, cutting off the route of armature reaction flux in stator yoke is the most effective way to restrain this reactance.