DEPENDENCE OF THE MAGNITUDE OF ESG CURRENT PULSATIONS ON THE WIDTH OF THE INDUCTORS

A. M. KUPTSOV, V. A. LUKUTIN, V. M. FEDYAKIN

(Presented by the joint scientific seminar of the Department of TEE and the RESG Division of the Research Institute of Nuclear Physics)

The renewed interest in recent years in electrostatic generators is explained primarily by the merits of these inexpensive and sufficiently universal sources of high dc voltage. In comparison with other high-voltage sources, the principal advantages of electrostatic generators with a dielectric conveyor (ESGD), according to data from foreign firms, are as follows: compactness, low weight, safety of operation under short-circuit conditions, high stability of the output voltage (up to 0.001%), and the practical absence of pulsations [1].

At present, the question has been raised of creating a more efficient industrial ESG. Such an ESG may be a generator with conducting conveyors (ESGP). Its principle of operation as a whole does not differ from that of an ESGD; however, owing to the discrete structure of the charge conveyor in an ESGP, there are a number of specific features [1, 2]. One of these features is a somewhat greater magnitude of current pulsations than in an ESGD [1, 2].

The practical absence of current pulsations is of decisive importance for a number of fields of science and technology, such as, for example, large-screen television, X-ray engineering, and nuclear physics. In this connection, it is of interest to consider those factors which, in generators with conducting conveyors, lead to a reduction in the amplitude of pulsations.

In this article, some results are presented of an experimental investigation whose purpose was to provide practical recommendations for obtaining, in an ESGP, a current with minimal pulsations and to clarify the main causes that determine them.

The results of the investigation were obtained on the basis of statistical processing of oscillograms of the current in the load circuit of the generator. The oscillography procedure is set forth in sufficient detail in [3].

The experiments were carried out on a disk ESGP with a large number of conveyors per pole pitch for a series of interchangeable rotors differing from one another in the number and shape of the conveyors. The minimum number of rotor conveyors was 14, the maximum 52. The diameter of the rotor disks was 140 mm. The conveyors were embedded in compound epoxy resin. The thickness of the resin coating over the conveyors for all

the rotors was the same and was 1.5 mm. The rotor speed was 2700 rpm. The working medium was air at atmospheric pressure.

Experimental results

Fig. 1 shows typical oscillograms of the current in the load circuit of the generator for one of the rotors, corresponding to the short-circuit mode—a—and to the load mode—b. The oscillograms were obtained at the same value of the average current, as recorded by the instrument. Multi-range magnetoelectric microammeters M-135 were used for measuring the currents. The oscillographing conditions were identical in all cases.

Fig. 1

Fig. 2

It is immediately evident from the oscillograms shown that the magnitude of the current pulsations (the pulsation amplitude) in the short-circuit mode is maximal and exceeds the pulsation amplitude in the load mode severalfold. This circumstance was noted in [3]; however, how rapidly the pulsations decrease and, most importantly, what the conditions for their reduction are had not been considered up to the present.

Since the pulsations are maximal in the short-circuit mode, most of the experiments were carried out for the short-circuit mode.

In all experiments, the charging conditions of the carriers were identical and optimal [4]. The generator brushes were installed strictly symmetrically with respect to the inductors.

a) Dependence of the magnitude of the pulsations on the width of the inductors

The shape of the current pulses or, in other words, the shape of the pulsations does not change when the width of the inductors is varied. However, the quantitative relation between the pulsations and the constant (slowly varying) component depends substantially on this circumstance. The maximum pulsations occur in the absence of high-voltage inductors. In this case the constant component is completely absent.

With an unchanged rotor–stator gap, increasing the width of the inductor leads to a substantial decrease in the magnitude of the pulsa-

If the magnitude of the pulsations (A) in the absence of the high-voltage inductor is taken as 100% (in this case the constant component of the current is absent), then the percentage decrease in the pulsations can be represented by the curve shown in Fig. 2. The curve was obtained for a rotor with the number of transporters \(m = 52\).

For rotors with the number of transporters \(m < 52\), the curves of the dependence of the magnitude of the pulsations on the width of the inductors are depicted similarly to curve 1, but lie higher. The percentage content of pulsations in the short-circuit current does not depend on the mean value of the current. The width of the inductors in the graph is denoted by the letter \(S\) and, as in [4], is characterized by the number of transporters that it covers.

b) Influence of the grounded elements of the generator on the magnitude of the pulsations

The work considered the influence of grounding the rotor shaft, grounding the generator housing, and also an artificially increased partial capacitance to ground. The latter was effected by replacing one of the two poorly conducting stator disks with a grounded metal disk. For a rotor with \(m = 52\), the experimental results are presented in Fig. 2. Here curve 2 was obtained under the same conditions as curve 1, but with the shaft grounded. Curve 3 was obtained for the current when the rotor shaft and the generator housing were grounded; curve 4—with an artificially increased partial capacitance to ground.

In all cases the mean value of the current, recorded by the microammeter, is constant, while the qualitative structure of the current changed substantially, as can be judged from Fig. 2. With an increase in the width of the inductor in the presence of grounded elements of the generator, the decrease in pulsations is less significant than in the case when they were not grounded.

The minimum magnitude of the pulsations that can be obtained by increasing the width of the inductor is the greater, the more grounded elements there are in the generator. In the presence of a conducting grounded disk instead of one of the stator disks, this magnitude is the greatest and for the given rotor was about 50%, i.e., in this case the amplitude of the pulsations decreased only by half in comparison with the current pulsations in a generator without a high-voltage inductor.

For rotors with a different number or shape of transporters, the observed regularities are qualitatively similar.

c) Dependence of the magnitude of the pulsations on the load resistance

In order to estimate the degree to which the magnitude of the pulsations decreases with increasing load resistance, oscillograms of the load current were taken while varying the load resistance. As the load resistance was increased, in order to maintain a constant value of the current recorded by the microammeter, the excitation voltage was increased (the curve was obtained at a current equal to 20 μA). For a rotor with 52 transporters and with inductors covering no fewer than 4 transporters, the degree of decrease in the magnitude of the pulsations with increasing load resistance is characterized by the curve shown in Fig. 3. The pulsations decrease most rapidly when the load resistance is increased from 0 to 100 MΩ. Further increase in resistance reduces the magnitude of the pulsations only slightly. The character of the curve, show-

given in Fig. 3, does not change also in the case when the inductors overlap not four, but some other number of conveyors. The analogy is also preserved for a rotor with a different number of conveyors.

Fig. 3

Fig. 4

Discussion of the Results

In [2], when considering commutation processes in generators of this type, the assumption was made that the presence of a pulse component in the load current is due to a part of the charge of the conveyor connected with ground, i.e., to the presence of a partial capacitance of the conveyor to ground. Analysis of the results obtained confirms this assumption.

Thus, it is seen from Fig. 2 that increasing the width of the inductor leads to a decrease in pulsations. If one adheres to the assumption cited above from [2], then this decrease in pulsations should be explained by a decrease in the part of the charge connected with ground. In generators in which there is no weakly conducting stator and no natural recharging of the conveyors, this explanation would hardly give rise to doubt, since increasing the width of the inductors leads to an increase in the degree of shielding of the commutating conveyor from ground, as follows from Fig. 4, a. The latter corresponds to a decrease in capacitive coupling with ground and, as a consequence, leads to a decrease in the magnitude of the pulsations.

In generators with a weakly conducting stator, the relationship between the width of the inductor and the degree of shielding of the commutating conveyor from ground depends substantially on the conductivity of the stator material and on the rate at which the commutation processes proceed. For a static process in the presence of a weakly conducting stator, the degree of shielding of the conveyor should not depend at all on the width of the inductor and, for a given rotor–stator gap, should always be constant, ensuring a constant magnitude of the pulsations. Since in generators with a glass stator this is not achieved, it must be assumed that here, too, increasing the width of the inductor leads to improved shielding of the commutating conveyor from ground; the main cause of the pulsations is the presence of partial capacitance to ground.

Additional confirmation of this assumption can be obtained on the basis of an analysis of Fig. 2. It is known [5, 6] that grounding the rotor shaft or the generator casing leads to an increase in the partial

capacitance of the carriers, including that of the switching carrier, to ground. In this case, when the rotor shaft is grounded, the pulsations should be greater than when it is ungrounded; and when both the shaft and the casing are grounded, greater than when only the shaft is grounded. This is fully confirmed by curves 2 and 3 in Fig. 2.

The most noticeable increase in pulsations is observed with an artificial increase in the partial capacitance to ground (curve 4, Fig. 2).

Taking the above into account, in order to obtain a current with minimal pulsations in the short-circuit mode it is necessary to design the commutation zones in such a way as to ensure the greatest possible shielding of the switching carrier from ground. In the general case this requirement is met by a Faraday cage. In an ESG, however, it is impossible to implement it because of the very design of the rotor. Therefore, for an ESG one should speak only of a certain similarity of such a device, considering the inductors as an imperfect Faraday cage. It is quite obvious that increasing the width of the inductors promotes more complete shielding of the carrier from ground. This has an especially pronounced effect when the inductor width is changed up to a value corresponding to 3–4 overlapped rods. A further increase in the width of the inductors has practically no effect on the degree of shielding of the carriers and practically does not reduce the pulsations.

The dependence of the magnitude of the pulsations on the load resistance can be explained by considering the $RC$ circuit shown in Fig. 4, b, formed by the load resistances and the partial capacitances to ground. It follows from this that, as the load resistance increases, the pulsations decrease. For the given generator, the most significant decrease in pulsations occurs when $R_{\mathrm{н}}$ is increased from 0 to 100 MΩ. A further increase in $R_{\mathrm{н}}$ reduces the pulsations only very slightly (Fig. 3).

Conclusions

1. The presence of pulsations in generators with conducting carriers is due mainly to the partial capacitance of the switching carriers to ground.

2. In a generator whose working gap is reduced within the range 0–1 mm, in order to obtain a current with minimal pulsations the expedient width of the inductors of the discharge system should correspond to 3–4 overlapped carriers.

3. The presence of a grounded shaft and generator casing leads to an increase in pulsations, since the partial capacitance of the carrier to ground increases.

4. Increasing the load resistance sharply reduces the pulsations.

References

1. V. I. Levitov, A. G. Lyapin. Electrostatic Generators with a Rigid Rotor. “Tsintipriboelektroprom,” Part 1, 1963.

2. A. M. Kuptsov, V. V. Patsevich. “Elektrichestvo,” No. 7, 1968.

3. A. M. Kuptsov. Electron Accelerators. “Energiya,” 1968.

4. N. J. Felici. “J. Physique et Radio,” vol. 9, p. 66, 1948.

5. V. V. Patsevich. Electron Accelerators. Atomizdat, 1964.

6. V. A. Lukutin, V. D. Eskov. “Energetika i transport,” 1967, No. 2, p. 94.