n8 PHILlPS TECHNICAL REVIEW VOLUME 30 Electrostatic motors B. Bollée The magnetic forces between moving electric charges, which underlie the operation of all present-day electric motors, are much smaller than the electrostatic forces between the same charges. As electrostatic motors are based on the second effect it appears surprising, at first sight, that they are not in common use. This article explains why, under ordinary conditions, the electrostatic motor is at a disadvantage compared with the electromagnetic motor. The most likely area of application appears to lie in the construction of very small motors. It is shown that, by using the precision techniques available in a modern laboratory, it is possible to make various types of electrostatic motors with torques of practical interest. Introduetion One aspect of the present trend towards miniaturiza- studied both types. A brief outline of the principles of tion is the search for methods of making smaller electric operation is given below, followed.by a more detailed motors which are still able to deliver a useful mechanical discussion of particular aspects. power output. Ifthe motor is used in an apparatus with a built-in energy source (dry cells, storage battery, Principles of the synchronous and asynchronous electro- static motor energy paper [ij, solar cell), then the efficiency of the motor is of great importance as this will determine the The synchronous motor we considered is shown in size and usefullife of the source. In assessing the per- its most elementary form in fig. 1. It is a variable formance of miniaturized motors the power per unit (rotary) capacitor with a square-wave voltage applied volume and the efficiency are the two most important across the plates. When the motor is running at the criteria. In the case of the traditional electromagnetic correct speed (i.e. synchronously), the rotor turns half motorwith all its modern variants, both the power per unit volume and the efficiency are reduced when the same design is produced in a scaled-down version. This comes about because the energy dissipation in the magnet coils relative to the electric power consumed becomes greater as the motor becomes smaller. The .. g operation of the electrostatic motor is based on the forces which electric fields exert on electric charges. It contains no coils, and the dissipation is very low, being that due to charge transport in an arrangement of short electrodes connected in parallel, and to dielectric losses. It is therefore to be expected that the ratio of dissipation to power consumption in a very small electrostatic motor will compare favourably with that in an electro- magnetic motor of the same size. With this idea in mind we instituted a fresh investigation into the possibilities of making electrostatic motors. Like, electromagnetic motors, electrostatic motors can be synchronous and asynchronous and we have Fig. 1. The principle of the synchronous electrostatic motor is .illustrated by a variable (rotary) capacitor connected to a voltage Jr. B. Bollée, formerly with Philip; Research Laboratories, of rectangular waveform. Between {}= 0 and {}= n/2 there is Eindhoven, is now in charge of the University Workshops ill Utrecht. a voltage between the rotor and the stator. The rotor blade J is then attracted by the stator blade 3, and 2 by 4. In the next [IJ P. A. Boter and M. D. Wijnen, Energy paper, Philips tech. quarter-revolution the voltage is zero and the rotor continues Rev. 28, 298-299, 1967. turning under its own inertia. 1969, No. 6/7 ELECTROSTATIC MOTORS 179 a revolution in one cycle of the voltage. In the quarter- revolution when the rotor and stator blades are ap- proaching each other there is a voltage between them and they attract each other. During the next quarter- revolution the voltage is zero, and the rotor ,continues to rotate by its own inertia. Although the torque in one period shows a marked fluctuation, this motor is syn- chronous in the sense that it rotates in step with the v supply voltage. The choice of electrode configuration and number of electrodes can be varied considerably. Fig. 2 shows a small motor we have made which has sixty axially orien ted electrodes. The operation of the asynchronous electrostatic Fig. 3. The operation of the asynchronous electrostatic motor motor is based on the fact that a cylinder of a material depends on the fact that a cylinder A which is slightly conductive which is slightly electrically conducting (a "poor insu- (or shows dielectric hysteresis) experiences a torque when placed lator") is subjected to a torque when placed in a rotat- in a rotating electric field E. ing electric field. This is illustrated schematically in fig. 3. When a voltage is applied to the capacitor and v, cos wt the capacitor is rotated about the axis of the cylinder A, a torque is exerted on the cylinder. The explanation is that the field gives rise to induced charges on the cylin- der. Owing to the resistance these lag behind the rotat- ing field. Consequently the field exerts a torque on the V,sin wt Fig. 4. An arrangement of stationary electrodes and two alter- nating voltages differing 90° in phase, used for generating a rotating field. charges and hence on the cylinder. A cylinder made of a material which is not electrically conductive but which shows dielectric hysteresis also experiences a torque in a rotating field. In order to use this effect to make an electric motor, the rotating field must of course be obtained by elec- trical rather than mechanical means. This can be done by using phase-shifted voltages on a number of station- ary electrodes. The simplest arrangement is that shown in fig. 4, where two pairs of electrodes are connected to voltages which differ in phase by 90°. An arrange- ment which we have actually constructed is shown in Fig. 2. An electrostatic synchronous motor with 60 electrodes. fig. 5. It consists of three electrodes connected to three Length of the rotor 10 mm, diameter 4.5 mm, gap between stator and rotor electrodes 10 fJ.m. The rotor and stator are hollow different voltages with a mutual phase difference of aluminium cylinders in which rectangular grooves have been cut. 120°. The shaft runs in sapphire bearings. The maximum power is about lOO fJ.W at 220 V and 50 Hz. The motors shown in figs. 4 and 5 are called bipolar; Fig. 5. A configuration of three electrodes for connection to a three-phase voltage. a) Successive configurations of the electric field corresponding to phase increments of 60°. b) The voltages on the three b electrodes as a function of time. 180 PHILIPS TECHNICAL REVIEW VOLUME 30 the fields generated by the electrodes are such that the the asynchronous motor again came up for discussion, rotor will have one pair of poles. If a motor is built with in a thesis by Strobl [7l. He checked his theoretical cal- a ring of N electrodes, with the successive electrodes culation on a 2000 V motor built for that purpose, but energized by voltages of successive phases, then the an operational motor was never constructed. After this number of pole-pairs is p = Njm; where m is the the asynchronous motor also fell into oblivion. number of phases. As previously mentioned, there is now a need for The torque on the cylinder in fig. 3 is present because miniature motors in a wide variety of devices ranging the rotating field has an angular velocity with respect to from toys to satellites. The electrostatic motor has the cylinder. When the motor is operating, the angular features that make it of interest for such purposes, velocity of the rotor must be smaller than that of the especially as many new materials and technologies have rotatingfield (i.e.the operation is "asynchronous"), and become available since the thirties which could be turned the torque and efficiency depend on the ratio between to good use in the manufacture of such small motors. these angular velocities. It will be apparent from the work discussed below that The performance that can be obtained from an it is in fact possible to produce electrostatic motors with electrostatic motor is limited by the breakdown that a volume of no more than a few cubic centimetres which occurs if too high a voltage is applied to a given motor have torques of practical interest (of the order of (or, for a given voltage, if the distance between the 5 [LNm, i.e. about 50 mg-force X cm). plates is made too small). A "normal" breakdown field strength (in air of atmospheric pressure with a gap of The synchronous electrostatic motor 1 mm) is about 3 X 106 V/m, so that for a synchronous Our investigations into the synchronous electrostatic motor with a plate spacing of 100 [Lm the voltage must motor relate mainly to obtaining an optimum design. remain below 300 V. One way of raising this limiting The essential features to be considered are the capaci- value is to operate the motor in a vacuum, in which tance variation (and hence the form and arrangement field strengths of 3 X lOB V/m are possible. The break- of the electrodes) and the waveform of the alternating down field strength also depends on the distance be- voltage (sinusoidal, square-wave, etc.). First the torque tween the electrodes. As the electrode spacing decreases, and power are calculated as a function of the capaci- the breakdown field strength in air at atmospheric tance variation and the voltage. Initially the losses are pressure begins to increase sharply at about 7.5 [Lm, left out of account, and are dealt with in a separate and at 2 [Lm it reaches a value of 1.7 X lOB V/m, which section.