An electrostatic induction motor utilizing electrical resonance for torque enhancement

Sensors and Actuators A 173 (2012) 180–189

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

An electrostatic induction motor utilizing electrical resonance for torque enhancement Takuya Hosobata ∗ , Akio Yamamoto, Toshiro Higuchi Department of Precision Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

a r t i c l e

i n f o

Article history: Received 9 February 2011 Received in revised form 16 September 2011 Accepted 13 October 2011 Available online 20 October 2011 Keywords: Electrostatic motor Induction motor Asynchronous motor Electrical resonance

a b s t r a c t An electrostatic induction motor utilizing electrical resonance to enhance its torque is introduced in this paper. The motor has patterned electrodes embedded on both of its stator and rotor, and driven by three-phase excitation voltage applied to its stator electrodes. The rotor electrodes are connected to external inductances and resistances through slip rings. The torque of the motor is maximized at resonant condition, where the slip frequency is equal to the resonance frequency of the system. A working prototype of the motor was constructed with 18-layered film electrodes. The maximum torque of the motor was 20 mNm at 10 rpm with an excitation by three-phase voltage of 0.9 kV/8.25 kHz. The motor could start itself and rotate in balance with frictions at a speed of 75 rpm with 0.9 kV/8.35 kHz excitation.

1. Introduction Demands for compact and light-weight actuators are growing, especially for mechatronic systems with dynamic motion, such as robotic systems. In such systems, actuators serve not only as mechanical power sources, but also as parts of movable members driven by other actuators; hence their sizes and weights have great influence on the systems’ performances. Such demands pose questions to the dominance of magnetic motors, which are intrinsically heavy and bulky due to their ferromagnetic components. To fulfill such demands, a synchronous electrostatic motor named DEMED (dual excitation multi-phase electrostatic drive) was developed by Niino et al. [1]. DEMED incorporated film type stators and sliders/rotors with large number of fine-pitched electrodes embedded in them. The film structure enabled even larger number of electrodes to be integrated within a small volume when they are stacked in layers. Both stators and sliders/rotors of DEMED were fed with three-phase power to realize a high power output. A power-to-weight ratio of 230 W/kg (1.6 W by 7 g) was reported with a single pair of films, and a thrust force of 310 N was realized with a 50-layered motor. With such a high power output with a compact and light-weight structure, DEMED demonstrated a possibility of utilizing electrostatic motors as alternatives to magnetic motors.

∗ Corresponding author. E-mail addresses: [email protected] (T. Hosobata), [email protected] (A. Yamamoto), [email protected] (T. Higuchi). 0924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2011.10.014

© 2011 Elsevier B.V. All rights reserved.

This paper provides a method to realize an electrostatic induction motor inheriting the electrode structure of DEMED. Under fixed frequency excitation, synchronous motors like DEMED operate at their synchronous speed determined by the frequency. Such characteristic is advantageous in open-loop speed control. On the other hand, induction motors are known to have position independent torques, and smooth accelerations are obtained with fixed frequency excitations. Thus, the induction motors are suited for load varying applications. The two types of motors are complementary, thus we believe that providing an induction motor as powerful as DEMED will broaden the choices of actuators for mechatronic systems. Electrostatic induction motors with rotors made from solid dielectric materials and stators equipped with electrodes for polyphase excitation have been studied by various researchers, both from theoretical and experimental aspects[2–6]. These motors utilized charge relaxation to realize a charge distribution on the rotor surface which lags behind the applied electric field. Such motors are also actively studied in the field of MEMS (microelectromechanical systems) [7–11]. The motors are suited for MEMS applications, because their simple rotor structure meets the requirement of MEMS fabrication. The studies on such micromotors have even led to a realization of a micro turbine generator[12]. Even though the dielectric-rotor induction motors are well studied, we took a different approach to realize an electrostatic induction motor: with patterned electrodes on both stator and rotor, and rotor electrodes connected to an external circuit. The idea was inspired by the work by Charpentier et al., in which they provided a lumped model of an electrostatic induction motor

T. Hosobata et al. / Sensors and Actuators A 173 (2012) 180–189

External elements

181

current

Slip speed

Rotor

Rotor speed

Potential wave Electric field Charge wave

Synchronous speed

Stator

Fig. 1. Schematic of an electrostatic induction motor utilizing electrical resonance.

considering the duality with magnetic motors [13]. Their model showed that an electrostatic induction motor can be realized by variable capacitors with resistances connected to them. There are two advantages for this type of induction motor over dielectricrotor motor. First, the characteristics of the motor can be modified by lumped elements, which is easier in comparison to dielectricrotor motors, whose characteristics are dependent on the surface resistance and dielectric properties. Second, the rotor electrodes can be skewed to reduce the torque fluctuation. These advantages together with the structural compatibility with DEMED have motivated us towards the development of a new type of electrostatic induction motor. The electrostatic induction motor introduced in this paper is illustrated in Fig. 1. The motor incorporates the same electrodes as DEMED, with three-phase electrodes embedded in a stator and a rotor. In DEMED, both of the stator and the rotor electrodes are fed with three-phase power, but for the induction motor the rotor electrodes are connected to external elements through slip rings. Induction motors with slip rings can also be found in magnetic motors. The magnetic induction motors can be classified into two types by their rotor structure: squirrel cage motors and wound-rotor motors. The squirrel cage motors have the resistances inherent in their rotor structure, whereas the wound-rotor motors incorporate slip rings, and external resistances can be added to adjust their torque-slip characteristics. The electrostatic induction motor we propose is analogous to the wound-rotor induction motor, with its variable capacitances and adjustable external elements provided separately. Inductors and resistors are chosen as the external elements. The inductors are introduced to the system to utilize electrical resonance, which enhances the torque of the motor. The idea of utilizing electrical resonance was demonstrated by the authors for an electrostatic master-slave mechanism in [14], but its application to an induction motor is presented for the first time. With properly chosen resonance parameters, the maximum torque of the motor is equivalent to that of DEMED when the motor is operating at a resonant condition. An advantage of the proposed motor over magnetic induction motors is that its stator and rotor can be made thin and light. The external inductors may become bulky in size, but are placed outside of the motor. Thus, the motor can be installed in spaces that are too thin for magnetic motors to fit in. For example, such characteristic may improve compactness of direct-drive joints in robotic arms. This article is subdivided into following sections. First, a qualitative overview of the motor’s operation is provided in Section 2.

Three-phase voltage source Fig. 2. An illustration showing the operation of the motor by assuming traveling potential and charge waves.

Section 3 focuses on the modeling and analysis of the motor using an equivalent circuit. Section 4 gives a description of a prototyped electrostatic motor and an external circuit. Results of experiments using the protyped motor are shown in Section 5, followed by a discussion and conclusions in Sections 6 and 7. 2. Overview of the motor’s operation The operation of the motor is qualitatively explained using the illustration in Fig. 2. For simplicity, the motor is illustrated as a linear motor, but the explanation applies to a rotory motor. The three-phase voltage applied to the stator electrodes forms a potential wave on the stator. The wave travels at a speed proportional to the frequency of the voltage, which is called the synchronous speed. The potential wave gives rise to a charge wave on the stator surface which also travels at the same speed. The stator charge wave induces charges across the gap onto the surface of the rotor and drags them in the traveling direction. The induced rotor charges also become a wave that travels at the synchronous speed. As the rotor charge wave travels, charges are exchanged among the rotor electrodes by currents that flow through the external elements: inductors and resistors. These currents alternate with a frequency called the slip frequency, which is proportional to the slip speed: the relative speed of the electric field to the rotor’s actual speed. The currents give rise to voltages across terminals of the external elements, and determines the voltages of the rotor electrodes. Correspondingly, a traveling potential wave is formed on the rotor. The external elements impede the currents and hence obstruct the traveling of the rotor charge wave. Due to this obstruction, the rotor charge wave lags behind the stator charge wave. The two displaced charge waves give rise to a tangential electric field in the gap, and the rotor experiences a motive torque as a resultant of the forces exerted by the field to the rotor charges. Our concern is the relation between the slip frequency and the torque of the motor. In the next section, the torque-slip relation is analyzed using a lumped parameter model with voltages of electrodes as variables of concern, and the torque is determined from the principle of virtual work. This approach was chosen because it is difficult and impractical to calculate the actual electric field and distributions of charges, especially when the structure of

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2 Stator Electrical angle

5

4

1

Rotor Fig. 3. Illustration of a segment of the rotor and the stator electrodes. The rotor electrodes are skewed, whereas the stator electrodes are straight.

6

electrodes are as complicated as the motor we are about to discuss. The lumped model lacks an intuitive image of the motor’s operation, and thus this section was provided for compensation.

3

3. Modeling and analysis Pairs of electrodes

Modeling and analysis of the motor are described in this section. The first part focuses on the construction of an equivalent circuit of the motor. In the second part, characteristics of the motor are analyzed from the equivalent circuit. In the analysis, voltages of the electrodes are determined first, and then the expression of the torque is derived from the principle of virtual work. The last part of the section explains about the utilization of electrical resonance to maximize the torque of the motor. 3.1. Construction of an equivalent circuit Detailed illustration of a segment of the rotor and the stator electrodes are shown in Fig. 3. The rotor and the stator are two coaxial disks, with rotor free to rotate relative to the stator while maintaining a certain gap, guided by bearings that are not shown in the figure. The rotor’s angle and speed are respectively represented by the symbols  R and uR . The rotor and the stator are similar in structure; each of them has strip-like radial electrodes embedded in their insulating substrate, equally spaced with a pitch angle p. The stator electrodes are straight, whereas the rotor electrodes are skewed. The electrodes in the stator are numbered from one to three and those in the rotor from four to six, as shown in Fig. 3. The electrode structure is chosen for two reasons. First, to keep the theory and experimental setup as simple as possible, since three is the least number of phases required to drive this motor. Second, to maintain compatibility with the doubly fed synchronous motor DEMED, so that the two motors can be compared on the same basis. The three-to-three phase configuration is not optimum in terms of space harmonics, which result in large torque ripple. Thus, the rotor electrodes are skewed to reduce the space harmonics (for details on skewing, see [15]). The modeling and identification method for this type of electrodes has already been established in [16], in which the distributed capacitances are represented by lumped capacitances. Using the lumped capacitances, the system in Fig. 1 is represented by an equivalent circuit shown in Fig. 4. All variable capacitances formed in the gap between the rotor and the stator are assumed to be sinusoidal functions of the electrical angle of the rotor  E = (2/3p) R . The variable capacitance Cij ( E ) corresponds to the mutual capacitance between electrodes numbered i and j, which is defined in the table in Fig. 4. The symbols CM and C0 are constants respectively representing the amplitude and the offset of capacitance variation. Parasitic capacitances formed

Variable capacitances

(1,4), (2,5) and (3,6) (1,5), (2,6) and (3,4) (1,6), (2,4) and (3,5)

Fig. 4. Equivalent circuit of the electrostatic induction motor with external circuit elements connected to its rotor electrodes.

between the adjacent pair of electrodes within the rotor or stator are assumed to be independent of the rotor angle. The parasitic capacitances are represented by CR and CS respectively for the rotor and stator. Such assumptions are valid when the electrodes are skewed, as described in [16]. A three-phase excitation voltage is applied to the stator electrodes with an amplitude of vS and a frequency of ω. The rotor electrodes are connected to external circuit elements with impedance Z. The external elements will be defined later, but expressed here as an arbitrary impedance for generalization. Voltages of the electrodes with respect to the ground are represented by symbols vk (k = 1, . . . , 6), with the subscripts corresponding to the numbers given to the electrodes. For simplicity, dielectric losses in the insulators are not considered in this model. As a result, scope of the model is limited to the cases in which the dielectric losses are much less than the losses in the external elements. However, experimental results described in later sections show that the model is sufficient to explain the basic characteristics of the prototyped motor, with small errors due to the omission of dielectric losses. 3.2. Analysis using equivalent circuit The motive torque of the motor can be derived from the virtual work principle as 1  ∂Cij (E ) (vi − vj )2 . 2 ∂R 3

T=

6

(1)

i=1 j=4

The unknown variables are the voltages of the rotor electrodes

v4 , v5 and v6 , which are to be determined through the analyis of the equivalent circuit. As a first step, we simplify the circuit into a balanced threephase circuit. Such simplification is done by assuming a steadystate condition, where the rotor is rotating at a constant speed uR .

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183

Substituting (4) into (1), the expression of the motive torque of the motor is obtained in a simple form T (ωP ) =

3 CM vS vR sin  2p

(6)

T (ωP ) =

3 CM vS Im{VR (jωP )}. 2p

(7)

Hence, the determination of torque-slip characteristic of the motor is reduced to an analysis of a simple analogue circuit. Fig. 5. Transformation of the circuit representing the electrostatic induction across the gap between the rotor and stator, in steady-state condition.

The relation between the electrical angle  E and the rotor speed uR is  E = (2/3p)uR t . For simplicity, we let the angle be null at t = 0, because the same expression of the torque is obtained regardless of the initial value of  E . In steady-state, the charges induced across the gap on the electrode number 4 of the rotor is given as qG4 =

3 

Ck4 (E )(v4 − vk )

(2)

k=1



qG4 = 3C0 v4 −



CM vS sin ωP t , 2C0

(3)

where ωP = ω − (2/3p)uR is the slip frequency, representing the relative speed of the electric field to the rotor’s actual speed. The transformation from (2) to (3) corresponds to the circuit transformation in Fig. 5. With the same procedure applied for the rotor electrodes 5 and 6, together with a delta-wye conversion of the delta-connected capacitances CR , the circuit in Fig. 4 is converted into a balanced three-phase circuit shown in Fig. 6. From the circuit, we know that the voltages of the rotor electrodes are three-phase voltages of frequency ωP , which are expressed as



v4 = vR sin(ωP t + ) v5 = vR sin(ωP t +  − 2/3) . v6 = vR sin(ωP t +  + 2/3)

(4)

Applying a sinusoidal steady-state analysis, the amplitude vR and the phase  is obtained from the complex function VR (jωP ) =

1 CM jωP Z(3C0 + 3CR ) vS 2 C0 + CR 1 + jωP Z(3C0 + 3CR )

(5)

as vR = |VR (jωP )| and  = ∠ VR (jωP ).

Fig. 6. Balanced three-phase circuit model of the electrostatic induction motor in steady-state condition.

3.3. Utilization of electrical resonance for torque maximization The maximum torque of DEMED using the same type of stator and rotor[16] is TSYNC =

3 CM v2S . 2p

(8)

In this case, vS represents the amplitude of the three-phase voltage applied to both of the stator and rotor electrodes. This torque is regarded as the maximum torque, provided that the voltage vS is made as high as possible without causing any dielectric breakdown. The following analysis shows that this maximum torque can be realized by connecting a series of inductor and resistor to each of the rotor electrodes, utilizing electrical resonance. To clarify the necessity of electrical resonance, first we consider the case with only resistors with resistance R. The rotor voltage for such case can be obtained by letting Z = R in (5), which yields VR (jωP ) =

1 CM jωP  vS 2 C0 + CR 1 + jωP 

(9)

where  = 3(C0 + CR )R is the time constant of charge relaxation. The torque of the motor is obtained by substituting (9) into (7) as TR (ωP ) = TRMAX

2ωP  1 + (ωP )2

,

(10)

where TRMAX is the maximum torque defined as TRMAX =

2 3 CM v2 . 8p C0 + CR S

(11)

The expression of the torque (10) has the same form as the idealized models of dielectric-rotor electrostatic induction motors (for example, see [6]). The only difference is that the time constant of this motor is determined by lumped resistances and capacitances, whereas for the dielectric-rotor motors it is determined by the surface resistivity and the dielectric constant. The optimum condition for this motor, is when ωP  = 1. Note that a change in resistance R shifts the optimum slip frequency, but the maximum torque TRMAX is independent of the value of R. To compare TRMAX with TSYNC , capacitances C0 and CR needs to be determined. To generalize the discussion, we assume the most ideal condition where C0 = CM and CR = 0. The former assumption corresponds to a motor with very small gap compared to other dimensions of electrodes, where pair of opposing electrodes can be regarded as an ideal plate capacitor with their overlapping area varying from zero a definite value. The latter corresponds to the case where capacitances formed among adjacent pair of electrodes are negligibly small. Under these assumptions, TRMAX /TSYNC = 1/4. This indicates that amplitude of the excitation voltage needs to be twice as large as DEMED to achieve the maximum torque TSYNC . Practically, C0 and CR cannot be neglected and even higher voltage is required. For example, for the motor described in the next section, TRMAX /TSYNC ≈ 0.026, and the required excitation voltage is about six times higher than DEMED. Hence, we conclude that the maximum torque TSYNC cannot be achieved with only external resistances.

T. Hosobata et al. / Sensors and Actuators A 173 (2012) 180–189

180

Gain

Phase 0.5

90

Normalized torque

0

0

Phase

Voltage gain

1

(degrees)

184

1

0.5 0 0.8

0.9 1 Normalized slip frequency

1.1

1.2

Fig. 7. Example of the rotor voltage and the torque of an optimally designed electrostatic induction motor with external inductances and resistances.

To increase the torque, we add inductors with inductance L in series with the resistors, to form a resonant circuit. Substituting Z = R + jωP L into (5), the rotor voltage is expressed as VR (jωP ) =

2 ) − (jω /ω ) (QωP2 /ωN 1 CM P N vS , 2 2 2 C0 + CR Q (ω /ω − 1) − jωP /ωN P

(12) Fig. 8. Photograph of the electrostatic motor unit.

N

where ωN is the resonance frequency and Q is the quality factor of resonance, respectively defined as ωN =



and Q =

1 R

1

(13)

3(C0 + CR )L



L . 3(C0 + CR )

(14)

The expression of the torque is obtained by substituting (12) into (7) as TRL (ωP ) = TN

ωP /ωN 2 Q 2 (ωP2 /ωN

− 1)2 + (ωP /ωN )2

,

(15)

4. Construction of the motor This section describes the configuration of the prototyped motor and the external circuit. The first part describes the electrostatic motor unit incorporating 18 layers of film-type electrodes and slip rings, whose photograph is shown in Fig. 8. The second part focuses on the external circuit, whose parameters were chosen to satisfy the optimum condition mentioned in the last section. 4.1. Structure of the electrostatic motor unit Fig. 9 shows the cross-sectional illustration of the prototyped electrostatic motor unit. Eighteen films with patterned electrodes:

where TN is the torque at resonant condition when ωP = ωN , which is defined as TN =

2 3 CM v2 Q. 4p C0 + CR S

(16)

Rotary shaft

The value of TN is nearly equal to the maximum torque, when Q is sufficiently high. For example, when Q = 5, TN is only 0.3% smaller than the maximum torque. The torque TN is adjustable with the parameter Q, and thus the maximum torque TSYNC can be realized. From the comparison between equations (16) with (8), the optimum quality factor is QOPT =

TSYNC C0 + CR =2 . TN CM

Wires for rotor electrodes Slip rings

Ball bearing

(17)

Wires for stator electrodes

2  1 and When QOPT is high enough to assume QOPT −1 tan QOPT = /2, the amplitude and phase of the rotor voltage at resonance frequency are respectively approximated as

vRN =

1 CM vS 2 C0 + CR



2 QOPT + 1 ≈ vS ,

(18)

and N = tan−1 QOPT ≈

 , 2

Level of dielectric liquid Fluorinert FC-77 (3M)

Stacked film electrodes (18 layers)

(19)

which indicate that the rotor voltages are optimized with their amplitude equal to the excitation voltages, and with their phase shifted by /2. An example of the torque-slip characteristic of optimally designed motor is shown in Fig. 7.

PTFE bushing Fig. 9. Cross-sectional illustration of the electrostatic motor unit.

T. Hosobata et al. / Sensors and Actuators A 173 (2012) 180–189

185

Fig. 11. Cross-sectional dimensions of a pair of stator and rotor films. Glass beads are scattered in the gap to maintain a constant and small gap.

Q wN /2 vRN /vS

= = =

32 8.36 kHz , 0.98

(20)

which satisfied the optimum condition described in the previous section.

a

Pairs of electrodes

Stator

Pairs of electrodes

(1,4) (1,5) (1,6)

(1,2) (1,3) (2,3)

Rotor

(4,5) (4,6) (5,6)

900 Capacitance (pF)

nine for the stator and the rest for the rotor were stacked in layers to form a single motor. The reason for the stacking is to have a torque large enough with respect to the measurement range of the torque sensor, which are described in the next section. The stator films were fixed to the stator housing, whereas the rotor films were fixed to the rotary shaft. The rotation of the shaft was guided by two radial bearings: one ball bearing on the top side and the other a bushing made from PTFE on the bottom side. The gap between the films were not maintained by these bearings, but by the glass beads with 20 ␮m diameter scattered in the gap. The shaft was made hollow so that the wirings connecting the rotor electrodes to the slip rings could pass through it. Grooves were made on the outer surface of the slip rings, and the sides of needle shaped brushes were pressed against them to establish electrical contacts. Inside the stator housing was filled with dielectric liquid Fluorinert FC-77. The purpose of the liquid was to prevent corona discharge resulting from high voltage, so that experiments can be carried out exceeding the limitation by the breakdown field strength of air. Planar dimensions of a single pair of a stator film and a rotor film is shown in Fig. 10, and cross-sectional dimensions are shown in Fig. 11. The rotor electrodes were skewed by an angle of 1.5 times the electrode pitch, which is the optimum skew ratio as described in [15]. The measured capacitances of this 18-layered electrostatic motor unit are shown in Fig. 12. The capacitances were not perfectly symmetric, thus averaged values are used to represent the capacitance parameters of the motor: CR = 700 pF, CM = 110 pF and C0 = 370 pF.



850 800 750 700 650 600 550

b

(2,4) (2,5) (2,6)

(3,4) (3,5) (3,6)

550 Capacitance (pF)

Fig. 10. Planar dimensions of a single pair of a stator film and a rotor film. Feeding lines from the pads to the electrodes are omitted from the illustration for simplicity.

The inductance and resistance of the air solenoid we prepared for the rotor side were L = 67 mH and R = 110 . From these values, the quality factor was calculated as Q = 41.5, and the voltage amplitude gain of the rotor voltages to the stator voltages at resonant condition was vRN /vS = 2.13. With such a high gain, the maximum field strength in the gap was restricted by the dielectric break down in the rotor film, and the best performance of the motor could not be achieved. The rotor voltage could be reduced by one of the three ways: reducing inductance L, increasing resistance R or adding external capacitors to the system. We chose the third way, which was most convenient in practice. The circuit in Fig. 6 indicates that adding wye-connected capacitors with capacitance CEXT to the rotor side is equivalent to increasing the value of CR by CEXT /3. Thus, we added three high voltage capacitors with capacitance CEXT = 2200 pF to the system. As a result, the equivalent CR became 1430 pF and the corresponding resonance parameters became

500 450 400 350 300 250

4.2. Configuration of the external circuit Fig. 13 shows a schematic diagram of the external circuit. Two differences from the theoretical model are the existence of the externally added capacitors and the three transformers.

200 Fig. 12. Measured capacitances of the 18-layered electrostatic motor: (a) parasitic capacitances and (b) variable capacitances. Capacitances were measured using LCZ meter ZM2372(NF), at 1 Vrms /8 kHz.

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12.5 mm

Air solenoids

Slip rings 25

30

mm

6 5 Rotor terminals 4 2

mm

Wire dia. 0.2 mm Winding 2350 turns

5

4

1

6 Three-phase voltage source 3 Electrostatic motor unit 3 2 Stator terminals 1

Fig. 13. Schematic diagram of the external circuit for the electrostatic induction motor. The three-phase voltage source was realized using a waveform generator 7075 (HIOKI) and three power amplifiers 4020 (NF). The voltages from the amplifiers were in the order of tens of volts, which was further amplified by ten times with three transformers in wye–wye connection. The primary and secondary coils of each transformer were wound coaxially on the ferrite core PQ5050 (TDK).

The use of transformers to obtain high voltages while minimizing reactive currents is described in [17]. For the present system, the transformers were designed so that their inductances referred to the secondary side LS coincide with the inductances of the coils connected to the rotor side. The external capacitances were also added to the stator side, so that the reactive current was minimized at the adjusted resonance frequency. 5. Experimental results 5.1. Experimental setup Fig. 14 shows the measurement setup, whose purpose was to measure the two important characteristics of the motor: the rotor voltage and the motor torque, with different slip frequencies. In order to create a constant slip frequency condition, the rotor of the electrostatic motor unit was forced to rotate at a constant speed. The forced rotation was realized by a dc motor RE40 (maxon motor),

Rotary encoder K-1 (Canon)

Flexible coupling

Motor mount plate (fixed)

DC motor RE40 148877 (maxon motor)

Electrostatic motor unit

Base plate (fixed)

Ball bearings

Rotary table

Force sensor LTS-1KA (Kyowa Electronic Instruments) with moment arm (100 mm) and preloaded ball joint

Fig. 14. Schematic of the experimental setup for torque and voltage measurement.

which was controlled by a PID controller constructed in DSP controller board DS1104 (dSpace), with feedback from an optical rotary encoder K-1 (Canon). The resolution of the rotary encoder was 324,000 pulses per rotation with interpolator CR-16/100 (Canon), which was chosen to be much smaller than the electrode pitch. Under the forced rotation, voltages were measured by an oscilloscope DPO3014 (Tektronix). As for the torque measurement, the stator was mounted on a rotary table, which was connected to a force sensor LTS-1KA (Kyowa Electronic Instruments) through a moment arm of 100 mm and a preloaded ball joint. Hence, the torque of the motor was calculated from the measured reaction force acting on the force sensor. 5.2. Measurement of the rotor voltages As a first step, frequencies of the rotor voltages were measured with different excitation frequencies and rotor speeds, to confirm their correspondence to the slip frequency. An example of the measured voltages is shown in Fig. 15. In short time scale, the voltages appeared to be a three-phase voltage, as shown in Fig. 15a. However, as shown in Fig. 15b, a beating waveform was observed in longer time scale. The beating waveforms are known to be observed when more than one sinusoidal wave with small frequency differences are superimposed. To clarify the origin of each frequency component, the beating wave was analyzed using FFT, and the result is shown in Fig. 15c. The frequency with the largest magnitude coincided with the theoretical value of the slip frequency ωP , whereas the frequency with the second largest magnitude was equal to the excitation frequency ω. These correspondences persisted regardless of the excitation frequency or the rotor speed. Secondly, the amplitude of the rotor voltage was measured with different slip frequencies. The result of the measurement is shown in Fig. 16. Only the voltage amplitude of the phase 4 is shown, because the data for other two phases showed similar trends. The result shows that the amplitude of the slip frequency component was maximized when the slip frequency was about 8.2 kHz, independent of the excitation frequency. This value was lower than the theoretical value of resonance frequency which was 8.36 kHz. One probable cause of the lowered resonance frequency is a small increase in capacitance: for example, increase of 70 pF in C0 . Such increase is likely to be caused by a small decrease of gap between the films, because the voltages during the voltage measurement were much higher than during the capacitance measurement. As for the component with frequency ω, the amplitude stayed below 20% of the excitation voltage. The reason for the presence of this

T. Hosobata et al. / Sensors and Actuators A 173 (2012) 180–189

a

40 Torque mNm

Voltage (kV)

0.6 0.4 0.2 0 -0.2 -0.4 -0.6

b

1

Voltage (kV)

Time (40 μs/div)

0.5

30 20 10

Time (0.5 s/div)

0

Fig. 17. A temporal waveform of the measured torque. The motor was excited with three-phase voltage of 0.9 kV/8.25 kHz, forced to rotate at a constant speed of 10 rpm. Despite the theoretical expectation of position and time invariant torque at constant speed, torque ripple of 33 Hz was observed, which corresponds to an oscillation per rotation of three electrode pitches.

-0.5

Time (10 ms/div)

c Magnitude (kV)

Torque ripple

0

-1

0.6 0.5 0.4 0.3 0.2 0.1 0

: Slip frequency

5.3. Measurement of the output torque : Excitation frequency 8

8.1

8.2 8.3 Frequency (kHz)

8.4

8.5

Fig. 15. An example of the measured voltages of the rotor electrodes: (a) threephase voltage obeserved in short time scale, (b) beating waveform observed in longer time scale and (c) frequency components of the beating wave. The measurement was conducted with a three-phase excitation voltage of 0.9 kV/8.35 kHz, and a constant rotor speed of 10 rpm.

component and also their influence on the torque, has not been clarified. An unexpected finding was that the peak voltage became lower with higher excitation frequency. The drop in the peak voltage indicates that the quality factor Q is lowered, and thus it points out the existence of energy dissipation that we did not consider in the theoretical model. A resonant condition with higher excitation frequency also means faster rotor speed, and thus the unknown source of dissipation is expected to be dependent on either or both of the two parameters.

1 0.8 Voltage Amplitude Gain

187

Excitation freq. 8.25 kHz 8.35 kHz 8.45 kHz

0.6

F

0.4

q re

ue

nc

Frequency

0.2 0 7.7

y

7.8

7.9

8 8.1 8.2 Slip frequency (kHz)

8.3

8.4

8.5

Fig. 16. Voltage amplitude of a rotor electrode plotted against slip frequency. The voltage was approximated as a sum of two sinusoidal voltage with different frequencies: the slip frequency ωP and excitation frequency ω. The solid line shows the theoretical curve calculated from the measured parameters. The amplitude of the three-phase excitation voltage was 0.9 kV, and the rotor speed was swept from 10 rpm to 150 rpm with 10 rpm step.

The motive torque of the motor was deduced from the two available torques: an output torque (a sum of the motive torque and an excited frictional torque) and an unexcited frictional torque. By the term “excited frictional torque”, we are referring to the frictional torque caused by the mechanical contact between the films through glass beads, that are increased by electrostatic attractive forces. To know the motive torque, the excited frictional torque needed to be removed from the output torque. However, the excited frictional torque was indistinguishable from the motive torque, because both of them were dependent on the state of excitation. Therefore, the “unexcited frictional torque”: the frictional torque without applying voltages, was measured instead of the excited frictional torque. The torque obtained by subtracting the unexcited frictional torque from the output torque did not represent the true motive torque, but provided an insight on the trend of the motive torque. An example of the measured output torque at constant rotor speed plotted against time is shown in Fig. 17. Fluctuations in the torque were observed, even though a constant torque was expected in theory. There was a torque ripple with a frequency of (2/3p)uR : an oscillation per rotation of three electrode pitches, with a range of about 5 mNm. By the frequency, it is apparent that the ripple comes from the motive torque of the motor. The slower trend of fluctuations were dependent on the rotor angle, indicating that they come from an angular dependency of friction or a small misalignment in the rotation axis. However, the mean value of the torque remained constant, which agreed with the theoretical expectation. The output torques were measured with different excitation frequencies and rotor speeds, and averaged output torques are plotted against the rotor speed in Fig. 18a. The unexcited frictional torques are also shown in Fig. 18b. The frictional torque was measured with and without the slip rings, and the results show that the friction from the slip rings was minor in comparison to that of the films. The following three can be said from the data. First, the optimum rotor speed: the speed where the torque is maximized is shifted with the excitation frequency, which agrees with the theoretical expectation that the torque is a function of the slip frequency. Second, about half of the motor’s motive torque was used in overcoming the friction. Theoretically, the torque should be positive, but negative torques were observed due to the offset by excited frictional torques. The negative torques exceeded the unexcited frictional torques at rotation speeds higher than 100 rpm, which indicated an increase in the friction by the excitation. Third, the torque diminished with the increase of rotor speed. One reason for this was the viscous torque: an increase of friction with higher speed. Another reason was the

T. Hosobata et al. / Sensors and Actuators A 173 (2012) 180–189

a

30 Excitation freq. 8.25 kHz

Measured torque (mNm)

20

8.35 kHz

8.45 kHz

10 Motive torque 0 Braking torque

−10

No-load rotor speed (rpm)

188

150 125 100 75 50

0

−20

No starting torque

25 8.15

8.25 8.35 8.45 Excitation frequency (kHz)

8.55

−30 −40

0

25

50

75

100

125

Fig. 20. No-load steady-state speeds of the motor measured with different excitation frequencies. With 8.45 kHz and 8.55 kHz excitation, the motor could not start itself because the motive torque at stationary condition was lower than the friction torque. The amplitude of the three-phase excitation voltage was 0.9 kV.

150

Friction Torque (mNm)

b

motive torque was balanced with the friction torque. The noload speed increased linearly with the excitation frequency. With exitation frequencies higher than 8.35 kHz, the motor could not start itself because the motive torque was smaller than the friction torque at stationary condition. Rotations at these frequencies were realized by gradually increasing the excitation frequency from lower frequency where starting torque was available.

30 20 10 0

Without slip rings With slip rings 0

25

50

75

100

125

150

Fig. 18. Averaged torque plotted against the rotor speed: (a) torque measured with three-phase excitation of 0.9 kV amplitude and (b) friction torque measured without excitation.

decrease of the amplitude of the rotor voltage, as was shown in Fig. 16. To compare the measured torques with the theoretical torques, the unexcited frictional torques were subtracted from the measured torques, and they are plotted against the slip frequency in Fig. 19. The results explicitly show that the maximum torque is obtained when the slip frequency is equal to the resonant frequency at 8.2 kHz. From the data, the maximum motive torque of the motor is presumed to be about 37 mNm, which is also in good agreement with the theoretical value. The negative torque still remained at slip frequencies lower than 8 kHz. Comparing the data with the theoretical curve, the increase in friction appears more prominent when the difference of the slip frequency from the resonant frequency is larger. The frequency dependence of the fricitional torques remains to be studied. 5.4. No-load rotor speed

Compensated torque (mNm)

The rotor speeds with no external load was measured and the result is shown in Fig. 20. The rotor rotated at speeds where the

40 30

Excitation freq. 8.25 kHz 8.35 kHz 8.45 kHz

20 10 0

In broad, the results of the experiments agreed with the theory, and the feasibility of constructing an electrostatic induction motor by the proposed method is confirmed. However, some improvements are needed both in modeling and fabrication of the motor. First, in terms of modeling, the model needs to be refined with sources of dissipation taken into consideration. Possible improvements are the consideration of dielectric losses, and flow of dielectric liquid in the gap. Second, other configurations of external circuit needs to be considered as well. The external circuit presented in this paper was designed to utilize electrical resonance to maximize the torque of the motor. However, the torque-slip characteristic becomes sensitive to the slip frequency with this configuration, and it is not optimum in terms of the range of operation speed. Moreover, optimization based on efficiency of the motor should also be considered. As for fabrication of the motor, a reduction of friction is necessary. The motor should be tested with less friction, to explicitly measure its performance. Guides with small friction while maintaining small gap are already established for electrostatic motors with rigid substrates, including air-bearings [18] and coplanar ball bearings [19]. The use of these guides together with the presented method should be considered. The design of electrodes also needs to be reconsidered. The theory of the proposed motor was based on a lumped parameter model, which assumes that the stator and rotor electrodes are given. The electrodes are assumed to have the same design as those of the sychronous motor DEMED; therefore, the design may not be optimum for the proposed electrostatic induction motor. Design parameters such as the number of phases, materials of substrates, and shapes and dimensions of electrodes need to be optimized, using field analyses such as finite element method and surface charge method. 7. Conclusions

-10 7.6

6. Discussion

7.7

7.8

7.9

8 8.1 8.2 8.3 Slip frequency (kHz)

8.4

8.5

8.6

Fig. 19. Compensated torque plotted against the slip frequency. The friction torques measured without excitation are subtracted from the data. The solid line shows the theoretical value. The amplitude of the three-phase excitation voltage was 0.9 kV.

A method to construct an electrostatic induction motor utilizing electrical resonance for torque enhancement is introduced in this paper. The motor is analyzed using an equivalent circuit, and a parameter optimization method to maximize its torque is provided. Experiments were carried out using an electrostatic motor with

T. Hosobata et al. / Sensors and Actuators A 173 (2012) 180–189

18-layered film-type electrodes, and the results of the experiments agreed with the theory in most respects. The maximum output torque generated by the motor was 20 mNm at 10 rpm with excitation by three-phase voltage of 0.9 kV/8.25 kHz, which was greatly reduced by the friction between films. Without the friction, maximum torque of 37 mNm is expected. The maximum speed at which the motor could start itself and rotate in balance with friction was 75 rpm, with excitation by a three-phase voltage of 0.9 kV/8.35 kHz. The motor is an asynchronous counterpart of the already existing synchronous motor DEMED. The two motors with complimentary characteristics provide new choices for dynamic mechatronic systems, with thin and light-weight characteristics of electrostatic motors. References [1] T. Niino, T. Higuchi, S. Egawa, Dual excitation multiphase electrostatic drive, in: Proceedings of IEEE Industry Applications Conference, vol. 2, 1995, pp. 1318–1325. [2] B. Bollée, Electrostatic motors, Philips Technical Review 30 (6/7) (1969) 178–194. [3] C. Kooy, Torque on a resistive rotor in a quasi electrostatic rotating field, Applied Scientific Research 20 (2–3) (1969) 161–172. [4] J. Ubbink, Optimization of the rotor surface resistance of the asynchronous electrostatic motor, Applied Scientific Research 22 (6) (1970) 442–448. [5] S. Choi, D. Dunn, A surface-charge induction motor, Proceedings of the IEEE 59 (5) (1971) 737–748. [6] E. Mognaschi, J. Calderwood, Asynchronous dielectric induction motor, IEE Proceedings A: Physical Science, Measurement and Instrumentation, Management and Education 137 (6) (1990) 331–338. [7] S.F. Bart, J.H. Lang, An analysis of electroquasistatic induction micromotors, Sensors and Actuators 20 (1–2) (1989) 97–106. [8] R. Hagedorn, G. Fuhr, T. Muller, T. Schnelle, U. Schnakenberg, B. Wagner, Design of asynchronous dielectric micromotors, Journal of Electrostatics 33 (2) (1994) 159–185. [9] G.R. Fuhr, R. Hagedorn, J. Gimsa, Analysis of the torque-frequency characteristics of dielectric induction motors, Sensors and Actuators A: Physical 33 (3) (1992) 237–247. [10] C. Livermore, A.R. Forte, T. Lyszczarz, S.D. Umans, A.A. Ayon, J.H. Lang, A high-power mems electric induction motor, Journal of Microelectromechanical Systems 13 (3) (2004) 465–471. [11] S. Nagle, C. Livermore, L. Frechette, R. Ghodssi, J. Lang, An electric induction micromotor, Journal of Microelectromechanical Systems 14 (5) (2005) 1127–1143. [12] J. Steyn, S. Kendig, R. Khanna, S. Umans, J. Lang, C. Livermore, A self-excited mems electro-quasi-static induction turbine generator, Journal of Microelectromechanical Systems 18 (2) (2009) 424–432.

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[13] J. Charpentier, Y. Lefevre, E. Sarraute, B. Trannoy, Synthesis and modelling of an electrostatic induction motor, IEEE Transactions on Magnetics 31 (3) (1995) 1404–1407. [14] T. Hosobata, A. Yamamoto, T. Higuchi, An electrostatic master-slave mechanism with force enhancement by external inductors for cancellation of selfand parasitic capacitances, Sensors and Actuators A: Physical 163 (1) (2010) 333–342. [15] A. Yamamoto, T. Niino, T. Ban, T. Higuchi, High-power electrostatic motor using skewed electrodes, Electrical Engineering in Japan 125 (3) (1998) 50–58. [16] A. Yamamoto, T. Niino, T. Higuchi, Modeling and identification of an electrostatic motor, Precision Engineering 30 (1) (2006) 104–113. [17] T. Niino, A. Yamamoto, T. Higuchi, Operation of a dual excitation multiphase electrostatic drive by amplitude-modulated ac voltage, Electrical Engineering in Japan 131 (4) (2000) 78–84. [18] L. Frechette, S. Nagle, R. Ghodssi, S. Umans, M. Schmidt, J. Lang, An electrostatic induction micromotor supported on gas-lubricated bearings, in: Proceedings of the IEEE Micro Electro Mechanical Systems (MEMS), 2001, pp. 290–293. [19] M. McCarthy, C. Waits, M. Beyaz, R. Ghodssi, A rotary microactuator supported on encapsulated microball bearings using an electro-pneumatic thrust balance, in: Proceedings of IEEE International Conference on Micro Electro Mechanical Systems, 2009, pp. 1095–1098.

Biographies Takuya Hosobata received the BS and MS degrees in mechanical engineering from Waseda University, Japan, in 2002 and 2004, respectively. He worked at Sumitomo Heavy Industries Ltd., from April 2004 to September 2008, on ultra precision positioning stages. He is currently a doctoral student at the University of Tokyo. His research interests include electrostatic actuators, precision engineering and mechatronics. Akio Yamamoto received the BS, MS, and PhD degrees in precision engineering from the University of Tokyo, Japan, in 1994, 1996, and 1999, respectively. He was a research associate in the Department of Precision Engineering, the University of Tokyo, from April 1999 to March 2000, and a lecturer from April 2000 to March 2005. Since April 2005, he has been an associate professor in the same department. His research interests include mechatronics, electrostatic actuators, and human–machine interactions. Toshiro Higuchi received the BS, MS, and PhD degrees in precision machinery engineering from the University of Tokyo, Japan, in 1972, 1974, and 1977, respectively. He was a lecturer at the Institute of Industrial Science (IIS), the University of Tokyo, from April 1977 to March 1978, and an associate professor from April 1978 to November 1991. Since November 1991, he has been a Professor in the department of precision engineering, the University of Tokyo. He was the leader of the Higuchi Ultimate Mechatronics Project, Kanagawa Academy of Science and Technology, from April 1992 to March 1997. His research interests include mechatronics, magnetic bearings, electrostatic actuators, MEMS, robotics, and manufacturing.