Precise positioning using electrostatic glass motor

Precision Engineering Journal of the International Societies for Precision Engineering and Nanotechnology 26 (2002) 162–167

Precise positioning using electrostatic glass motor R. Moser a,b,∗ , T. Higuchi b b

a Institute of Robotic Systems, EPFL, 1015 Lausanne, Switzerland Department of Precision Engineering, The University of Tokyo, 113-8656 Tokyo, Japan

Received 13 March 2001; received in revised form 9 August 2001; accepted 6 September 2001

Abstract This paper reports the application of electrostatic glass motors to precise positioning. It will be shown that by drawing advantage of a property of glasses, the relatively stable charge arrangements on its surface induced by an electrostatic field, sub-micrometric and sub-arc sec displacements can be achieved. Based on this principle, a stage featuring two linear and one rotative degree-of-freedom will be proposed. Its potential is experimentally determined on one rotative degree-of-freedom. The main advantages of the proposed novel form of positioning are its long stroke, compactness and simplicity. © 2002 Elsevier Science Inc. All rights reserved. Keywords: Electrostatic motor; Glass motor; Electrostatic forces; Electrostatic induction; Positioning

1. Introduction Precise positioning over a long stroke is required in various fields. Important advances in the field of electromagnetic motors, piezoelectric actuators and bearing technology allow nanometric resolution. Alas, these devices are rather complex, therefore expensive, and require sophisticated assembly techniques for the delicate components. For some applications the stiffness of the positioning stage is of minor importance. Compactness, temperature resistance and the absence of magnetic fields are the design objectives. This paper presents a novel approach to drive such stages, by exploiting the electrical properties of glasses. Charges due to ionic bulk conductivity and surface charges are arranged by application of an electrostatic field. These arrangements have an extraordinary long rise and decay time constant in the order or several tens of seconds and can be used to drive the glass. It was verified experimentally that what we call the electrostatic glass motor is operating at the speed of the applied field, although being a kind of induction motor. The principle of the electrostatic glass motor for fast moving rotors, typically fast turning disc shaped rotors, was described by Higuchi and coworkers [1–5]. Similar electrostatic motors were investigated by Ubink [6], Kooy [7] and Bollee [8], but they focused on asynchronous machines or ∗

Corresponding author. Fax: +41-21-693-3866. E-mail address: [email protected] (R. Moser).

they equipped both, rotor and stator with electrodes to ensure synchronous movements. These concepts find adequate applications, but for precise positioning, neither asynchronous behavior, nor stepping motor-like cogging (due to electrodes on the rotor) are realistic options. Using the relatively stable charge distribution on glasses induced by an applied electrostatic field, very slow and smooth synchronous propulsion is possible and the principle of its application to positioning is presented in this paper. The main advantages of the proposed devices over their electromagnetic and piezoelectric counterparts are its simplicity (the motor part being reduced to two electrodes, manufactured by standard PCB etching processes), its compactness and its broad speed range.

2. Concept 2.1. Proposed apparatus Fig. 1 depicts the principle of the proposed three DOF positioning apparatus. The stage is based on linear and rotational frictionless bearings like air bearings or magnetic bearings (1), which keep the glass rotors at constant gap above the electrodes (2). A moving electrostatic field is created by strip shaped electrodes (2), which interacts with glass plates (3), mounted on the moving parts. The rotational degree-of-freedom (4) is based on a spindle, which supports a glass disc covered by the plate for the object to

0141-6359/02/$ – see front matter © 2002 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 6 3 5 9 ( 0 1 ) 0 0 1 1 2 - X

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Fig. 1. Concept of three degree-of-freedom positioning stage using electrostatic glass motors.

be positioned. Each degree-of-freedom can be controlled open loop by observing the position of its electrostatic field, generated by a three channel function generator and three high voltage amplifiers. 2.2. Force generation During glass fabrication, alkalis and alkaline-earth oxides are added to the glass-blend. The result is a more open glass structure where these ions are able to migrate more freely through the polyhedra and produce ionic conductivity. This phenomenon allows the creation of charge arrangements close to the surface with a net polarization, once they interact with a strong electric field. These arrangements have a time constant in the order of several tens of seconds, as shown in Fig. 2. The plot suggests a hyperbolically governed charge/discharge, as it is often the case in describing the decay of charges from highly insulated surfaces.

Fig. 2. Non-contact charge induction on a glass plate. Charge and discharge. Applied field strength 2.5 MV/m.

Fig. 3. (a) Arrangement of charges on a glass surface due to two electrodes and (b) occurring drag forces if the field moves.

If the applied field is due to two parallel electrodes of opposite polarity, then the charge distribution has two distinctive maximums at the location of the most intense field, which is the region between the electrodes. It is important to note that we deal here with contact-less charge induction, the glass rotor is never in contact with the electrodes. If the field is moving (the electrodes are displaced, for example), the glass charges are not mobile enough to follow and therefore apply a drag force on the glass. Fig. 3 depicts the mentioned situation. The parameters that determine the location and amplitude of the charge distribution are: the air gap ∆, the inter-electrode gap d and the electrode width w, as well as the applied potential V = V+ − V− . In order to displace the glass without moving the electrodes, a moving electrostatic field is required, created by three sinusoidal excitations, mutually phase shifted by 120◦ . Numerical simulation using the surface charge method [9] reveals that, as Gauss’ law states, the induced net charge density is effectively highest between terminals (Fig. 4). Similar simulations varying the geometrical parameters reveal that the electrode width w is of little importance

Fig. 4. Schematic plot of the glass charge distribution due to a three phase electrostatic field (no scale). The encircled signs indicate the positive and negative net polarization.

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Fig. 5. Variation of the locations of peak charge densities for a rotor displacement of one terminal, 2π /3 advancement of the field. Phasor in the first two quadrants indicates a positive voltage. Accordingly, charge distributions ‘below’ the glass surface represent negative net polarization of the glass.

for the force generation. So the obtainable force per glass surface unit increases with an increasing electrode density. We observed and reported already the contact-less suspension of glass [1], where the charges, once induced, remain in their locations on the glass disc. Also, if a moving electrostatic field is applied to a previously charged glass disc and the movement of the field is fast compared to the charge time constant shown in Fig. 1, amplitude and location of the charge arrangements remain constant. The resulting synchronous propulsion is possible over a very broad speed range. Even if the field moves slow enough to give the charges the possibility to rearrange themselves, a usable force was observed. Fig. 5 sketches the variation of charge densities for a slow moving field. The charge densities are modeled after Fig. 4, with peak amplitudes twice higher between plus and minus electrodes than in all the other possible cases. Indicated at the left-hand side are the phase evolution of the three channels, at the right-hand side is the corresponding position of the glass rotor. The absence of grooves or electrodes on the glass ensures ripple free displacement.

Fig. 6. Open loop control scheme. F.G indicates a three channel function generator with mutually locked phases. The arrow indicates the direction of motion.

the clock, therefore the speed of the glass rotor. The rotor position is controlled via the parameter k, which, function of the desired displacement and the geometric dimensions of the electrode. The parameter k is the number of desired displacement steps. Once the desired number of clock k impulses is delivered to the function generator, the clock will be interrupted. Doing so, the system is brought to rest by freezing the sinusoidal excitations into dc voltage. For the determination of k, consider Fig. 7. Let n [bit] be the resolution of the function generators output. The output voltage will then have 2n distinct voltage levels if the function generator is driven at its full range. The distance D denotes the width of one set of electrodes (Fig. 6). If the applied field moves 360◦ , the rotor follows and makes a displacement of D, since the movement is synchronous. During this displacement, 2 × 2n voltage steps are applied by the function generator. By approximating the sine wave with a ramp wave, we may write for the resolution r (m): r≈

D 2 × 2n

(1)

Let v (m/s) the speed of the glass rotor, and f the clocks’ frequency in Hertz, so v = rf

(2)

2.3. Control The advancement of the moving electrostatic field can easily be observed. Consider a digital function generator that is triggered by an external clock, in the absence of which he holds the last output voltage at dc level. Assuming that the rotor follows exactly the field, it is sufficient to count the clock impulses for knowing the rotors location. The rotor speed is function of the clock frequency. Fig. 6 presents the open loop control scheme for the proposed device. The parameter f stands for the frequency of

Fig. 7. Geometric electrode parameters for a three phase excitation, used for the determination of the displacement unit parameter k.

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Let δ be the intended rotor displacement. The coefficient k (steps) follows from (1) k=

δ r

(3)

The electrodes can be realized by photolithography, so the precision of the geometrical dimensions (Fig. 7) is ensured. The position overshoot is function of the rotor inertia and approaching speed. The absence of grooves (variable capacitance motor) or fixed charges (electret motor) ensure that the motor has no other equilibrium positions than those dictated by the applied moving field.

3. Experimental work and discussion Fig. 8. Picture of the experimental rotative stage.

3.1. Experimental set-up The experimental evaluation was done using a standard 65 mm diameter hard-disc glass ceramic disc, mounted on an air bearing (Canon AB-30R). The electrode consists of 180 stripes, subdivided into three phases. Fig. 8 shows a photograph of the set-up. The electrode was manufactured using standard printed circuit board techniques. The interelectrode gap d and the electrode width w (at the outermost radius) being both 400 ␮m, the electrode (Fig. 9) supports three phase sinusoidal voltages up to 600 V zero-to-peak before breakdown. 3.2. Measurements The used displacement sensor was a capacitive probe (ADE Microsens 5410). Applying a frequency correspond-

ing to a field displacement rate of 10.3 arc sec/s, only little speed ripple was observed within the range of the sensor (Fig. 10). Also in the order of hundreds and thousands of arc sec (using a laser displacement probe), very smooth rotation was observed. By ‘unfreezing’ the dc voltage for a 0.003 Hz moving field during 0.1 s, the transient response to a step excitation can be observed. Fig. 11 shows the measurement result. The plot shows the unfiltered response of the capacitive displacement probe. Depending on the aimed application, a restrictive low pass filter can be used. The sensor target was fixed at the outermost radius of the 6.5 cm glass disc. Under the prescribed conditions, sub-arc sec rotations seem possible. By increasing the disc radius, therefore increasing the number of electrode stripes, the smallest possible displacement would be further reduced.

Fig. 9. Picture of the electrode. Copper on glass-epoxy.

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It was observed that the rotor could be accelerated up to 97 rpm with a voltage close to the breakdown potential. The top speed is limited by the inertia of the rotor (our air bearing has a considerable inertia), the applied voltage and humidity. Using a ball bearing, the same disc was rotated over 4,000 rpm, using the same electrode, indicating other possible applications of the electrostatic glass motor [3–5].

4. Conclusion

Fig. 10. Smooth rotation of the rotor, powered by a 10.3 arc sec/s moving electrostatic field.

A new concept for positioning has been proposed in this paper. Using a seldom used electrical property of glasses, the relatively stable charge distributions arranged by an applied electrostatic field, very slow and smooth synchronous rotation is possible. Based on this principle, linear and rotative positioning devices can be designed. A three degree-of-freedom stage has been proposed, and a rotative stage has been realized and tested. An appropriate electrode pattern has been developed and, by applying three phase sinusoidal voltages in the order of the kilovolt, rotations under one arc sec have been observed. The resolution is function of the patterns geometric dimensions, as well as of the function generators resolution. For very precise positioning, interpolated incremental rotation and displacement sensors should be used, because of the drives’ susceptibility to static errors. The proposed concept of motoring a stage produces weak forces that require low rotor inertia. However, it seems to find promising applications in the in-line positioning of optical devices, laser machining or electron-beam operations. Its main advantages are the absence of speed ripple, unlimited rotational and large linear stroke, a very large speed range (fast for transportation, slow for approaching the desired position) and its compact outline together with its cost effective simplicity. Very slow and precise rotation under one arc sec together with a very broad speed range (up to 100 rpm for the presented experimental set-up) and unlimited rotation range are features unmatched by conventional electromagnetic and piezoelectric actuators. The systems drawback is the weak forces/torque it produces, but stacking multiple glass–electrode pairs can increase those. The authors expect the proposed concept to be widely applied to the mentioned fields, as well as for the transportation and positioning of silicium-on-insulator (SOI) wafers.

References

Fig. 11. Transient response to a step excitation. The function generator incremented the three sine waves for a few bits during 0.1 s. The principle of ‘unfreezing’ the dc voltage into ac sine waves is depicted below.

[1] Jeon UJ, Higuchi T. Electrostatic suspension of dielectrics. IEEE Trans Ind Electron 1998;6:938–46. [2] Jeon UJ, Higuchi T. Induction motors with electrostatic suspension. J Electrostat 1998:45157–73. [3] Hori S, Moser R, Poh FL, Higuchi, T. Development of electrostatic dielectric disc drive. In: Proceedings of the 12th Symposium on Electromagnetics and Dynamics. Okinawa, 2000. p. 559–64.

R. Moser, T. Higuchi / Precision Engineering 26 (2002) 162–167 [4] Moser R, Higuchi T. Electrostatic motor bearing combination for glass disc. In: Proceedings of the 12th Symposium on Electromagnetics and Dynamics. Okinawa, 2000. p. 555–58. [5] Moser R, Hori S, Poh FL, Higuchi T. Electrostatic motor-bearing combination for glass disc. In: Proceedings of ICMA, 2000. p. 243–8. [6] Ubink J. Optimization of the rotor surface resistance of the asynchronous electrostatic motor. Appl Sci Res 1969;22:442–8.

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