EFFECT OF THE ROTOR–STATOR AND ROTOR–BRUSH GAP SIZES ON THE SHORT-CIRCUIT CURRENT OF A DISK ROD ELECTROSTATIC GENERATOR

A. F. KALGANOV, E. A. PODPLETNEVA, Yu. N. SIVKOV

(Presented by the joint scientific seminar of the Department of Theoretical Foundations of Electrical Engineering and the sector of rotor ESGs of the YaFEA Research Institute)

In many works devoted to the study of rod-type ESGs, the latter are considered only as systems possessing linear characteristics [1—8]. The results of studies, including analytically derived dependences of some parameters on others, do much to clarify the processes occurring in an ESGS. However, they prove insufficient for estimating the maximum output parameters of an ESG, since these parameters are attained under conditions in which the system becomes nonlinear (saturation regime) and can no longer be described analytically.

Because there is no analytical calculation of an ESGS in saturation regimes, the maximum output parameters of an ESGS are usually estimated experimentally [9—11].

Additional nonlinearity is introduced into the ESG system when contact commutation is replaced by gas-discharge commutation.

We have carried out experimental studies of the dependence of the maximum short-circuit current of a single-disk ESGS on the size of the rotor–stator gap \(d_1\) under contact commutation and on the size of the gap \(\delta\) between the collector part of the rotor and the brush under gas-discharge commutation.

The studies were carried out on the generator described in [12], under atmospheric conditions. Contact commutation was performed by means of narrow brushes according to the method of [12], while gas-discharge commutation was performed by means of brushes in the form of steel rods 4 mm in diameter, the ends of which, facing the collector part of the rotor, had a conical shape; the end of the conical part was rounded with a radius of 1 mm and polished. The position of the rod brushes relative to the collector part of the rotor was adjusted by means of a threaded connection of their other ends with the brush holders. The gap size was determined from the thread pitch of the rod brush and from the angle of rotation of the fastening nut.

Effect of the rotor–stator gap

In Fig. 1, curve 1 shows the dependence \(I_{\text{s.c.}\,m}=f(d_1)\) under conditions in which both gaps between the rotor and the disks of the double stator were maintained equal. The current was measured with an M-194 microammeter having an accuracy class of 1.0.

As can be seen from the figure, curve 1 has two characteristic regions. The first of them corresponds to gaps of \(0.2 \div 1\) mm, when, as the gap increases, the short-circuit current decreases sharply. The second region corresponds to gaps \(d_1 > 1\) mm, when the decrease in the short-circuit current with increasing gap becomes insignificant.

The nature of the dependence \(I_{\text{s.c.}m}=f(d_1)\) corresponds to the nature of the change in the breakdown field strength \(E_{\text{br}}\) of a weakly nonuniform electric field as a function of the size of the breakdown gap. Adhering to the initial propositions set forth in [13], with regard to the relation between the maximum short-circuit current and the value of the mean limiting field strength \(E'_{\text{lim}}\) in the rotor–stator gap of the ESG, this strength can be estimated from the relation

Fig. 1. Dependences of the maximum short-circuit current on the sizes of the rotor–stator gaps of a single-disk ESG

Fig. 2. Dependences of the electric-field strength on the interelectrode distance of a standard arrester \((E_{\text{br}})\) and on the rotor–stator gap of the ESG \((E'_{\text{lim}}\) and \(E_{\text{lim}})\)

\[ E'_{\text{lim}}=\frac{\sigma'_m}{\varepsilon_0} =\frac{1}{\varepsilon_0}\cdot\frac{I_{\text{s.c.}m}}{2Sn}, \tag{1} \]

where

\[ \sigma'_m \]

is the maximum value of the mean surface density of the charge transported by the rotor, determined from the maximum short-circuit current;

\(S\) is the two-sided working surface of the rotor;

\(n\) is the number of rotor revolutions per second.

Figure 2 shows the dependence \(E'_{\text{lim}}=f(d_1)\), calculated from (1) using the experimental values of \(I_{\text{s.c.}m}\), and the dependence \(E_{\text{lim}}=f(d_1)\), calculated from the relation

\[ E_{\text{lim}}=\frac{E'_{\text{lim}}}{k_0}, \tag{2} \]

where \(E_{\text{lim}}\) is the amplitude value of the field strength attained; \(k_0\) is a coefficient which, according to [13], characterizes the degree of uniformity of the electric field in the rotor–stator gap of the ESG.

In the case considered, the value of \(k_0\) varies from 0.91 to 0.95 as \(d_1\) changes from 0.2 to 0.8 mm.

For comparison, Fig. 2 gives the dependence of the electric strength \(E_{\mathrm{br}}\) of an air gap formed by spheres 2.5 cm in diameter, according to data from [14].

From the data presented it is evident that both \(E_{\mathrm{rel}}\) and \(E_{\mathrm{lim}}\) are smaller than \(E_{\mathrm{br}}\). In this case the difference between \(E_{\mathrm{br}}\) and \(E'_{\mathrm{lim}}\) is 25–30%, and between \(E_{\mathrm{br}}\) and \(E_{\mathrm{lim}}\) it is 17–27%. Taking into account the presence of a tangential component of the electric field in the rotor–stator gap, which on average is estimated at one tenth of the normal component of the field, one may state that the values of \(E_{\mathrm{br}}\) and \(E_{\mathrm{rel}}\) agree satisfactorily (within 15–20%). The incomplete agreement of these quantities may be due both to the fact that the coefficient \(k_0\) perhaps does not characterize the nonuniformity of the field in the electrostatic generator with sufficient accuracy, and to the failure to ensure the conditions for maintaining breakdown field strengths in the rotor–stator gap because of the influence, for example, of the brush–collector system.

The data obtained clearly indicate the need to maintain very small rotor–stator gaps in the electrostatic generator in order to improve specific energy indices; this imposes special requirements on the precision of manufacture and assembly of the main working elements of the generator.

In multidisk electrostatic generators, each rotor disk is separated from the stator by a double gap. In real electrostatic-generator designs, ensuring strict equality of the two gaps (especially when they are very small) is difficult, if not impossible. In this connection, it is of practical interest to know the degree of change in the value of \(I_{\mathrm{s.c.},m}\) of the generator when one of the two gaps is changed. We carried out an experimental determination of such a change on a single-disk electrostatic generator. The experimental results are given in Fig. 1 in the form of the dependence \(I_{\mathrm{s.c.},m}=f(d'_1)\), \(d''_1=\mathrm{const}\) (curve 2), when one of the gaps (\(d'_1\)) was varied from 0.2 to 4 mm, and the other (\(d''_1\)) remained unchanged and equal to 0.2 mm. As can be seen, curve 2 is analogous in the nature of its variation to curve 1, but is located higher (the short-circuit current for this case is considerably larger).

The behavior of curve 2 may be explained as follows. If the current \(I_{\mathrm{s.c.},m}\) is determined by the attainable value \(E_{\mathrm{lim}}\), which in turn depends on \(d_1\), then for a single-disk generator with a double stator it can be represented as the sum of two currents: \(I'_{\mathrm{s.c.},m}=f(d'_1)\) and \(I''_{\mathrm{s.c.},m}=f(d''_1)\). For \(d'_1=\mathrm{const}\) and increasing \(d''_1\), the current \(I''_{\mathrm{s.c.},m}\) must be constant, while the current \(I'_{\mathrm{s.c.},m}\) and the total current \(I_{\mathrm{s.c.},m}\) must decrease; in this case, owing to the constancy of \(I_{\mathrm{s.c.},m}\), the decreases in \(I_{\mathrm{s.c.},m}\) must be substantially smaller than in the case when both gaps are increased simultaneously. This point is illustrated by curve 3 in Fig. 1. The ordinate of its point is the sum of one half of the ordinate of curve 1 for \(d_1=0.2\) mm and one half of the ordinate of the same curve for the current increased value of \(d_1\). As can be seen, curves 2 and 3 almost coincide; the difference between them does not exceed 6%, which is within the error in estimating the value of \(d_1\). Under these conditions the short-circuit current of the electrostatic generator may be determined as

\[ I_{\mathrm{s.c.}}=Sn\varepsilon_0(E'n+E''n), \]

where \(E'n\) and \(E''n\) are the normal components of the field in the gap; \(d'_1\) and \(d''_1\), respectively.

Effect of the rotor–brush gap

Figure 3 gives the dependences of the maximum short-circuit current under gas-discharge commutation in relative units \(\beta\) (as the ratio

the maximum short-circuit current with gas-discharge commutation to the maximum short-circuit current with contact commutation, all other conditions being equal (as a function of the rotor–brush gap \(\delta\) for two values of the rotor–stator gap \(d_1\) (0.2 and 1 mm, with \(d_1=d'_1=d''_1\)). The values of the short-circuit currents with contact commutation correspond to the data of curve 1 in Fig. 1.

From the data obtained it follows that, as the gap increases, the maximum short-circuit current of the generator decreases; moreover, the degree of current decrease is the greater, the larger the gap between the rotor and the stator. Another characteristic feature of the dependences \(\beta=f(\delta)_{d_1=\mathrm{const}}\) is that, for small values of \(d_1\) (of the order of 0.2 mm), the generator short-circuit current practically does not change when the gap \(\delta\) is varied over the range \(0 \div 0.5\) mm, whereas at a gap \(d_1=1\) mm a sharp decrease in current is observed already at a gap \(\delta=0.2\) mm.

Fig. 3. Dependences of the maximum short-circuit current on the rotor–brush gap for various rotor–stator gaps

Conclusions

1. The calculated, from the maximum short-circuit current, limiting attainable values of the normal component of the electric-field strength in the rotor–stator gap of an electrostatic generator prove to be close to the values of the electric strength of the medium under comparable conditions, which is an additional confirmation of the validity of the initial assumptions stated earlier concerning the method for estimating the maximum short-circuit current of an electrostatic generator.

2. In the presence of a double stator and, accordingly, a double gap between the rotor and the stator, the short-circuit current of a single-disk generator is directly proportional to the sum of the field-strength values attained in each of the gaps.

3. The use of gas-discharge commutation in an electrostatic generator practically does not lead to a reduction of the maximum short-circuit current if sufficiently small gaps are provided both between the rotor and the brush and between the rotor and the stator.

LITERATURE

1. S. A. Bobkovskii. ZhTF, 10, No. 17, 1404, 1940.

2. Yu. S. Korzennikov, V. V. Patsevich, Yu. N. Sivkov. Electron Accelerators (Proceedings of the 5th Interuniversity Conference, Tomsk, 1964), Moscow, 1966.

3. V. A. Lukutin, V. D. Es’kov. Journal Energetika i transport, No. 2, 1967.

4. V. A. Lukutin, V. D. Es’kov. Izv. TPI, vol. 149, 1966.

5. A. P. Kononov, V. A. Lukutin, V. V. Patsevich. Izv. TPI, vol. 149, 1966.

6. V. D. Es’kov. Izv. TPI, vol. 152, 1966.

7. A. P. Kononov, V. V. Patsevich, V. D. Es’kov. Journal Energetika i transport, No. 4, 1967.

8. A. P. Kononov. Investigation of a Disk-Type Electrostatic Generator. Dissertation, Tomsk, 1967.

9. N. J. Felici, J. Phys. et Rad., 9, No. 2, 66, 1948.

10. V. V. Patsevich. Some Questions in the Theory and Calculation of Electrostatic Generators with Conveyor Conductors. Dissertation, Tomsk, 1963.

11. A. F. Kalganov, V. V. Patsevich, Yu. N. Sivkov. Abstracts of Papers of the All-Union Interuniversity Scientific-Technical Conference on Problems of the Creation and Methods of Testing High-Voltage Physical Apparatus, Tomsk, 1967.

12. A. F. Kalganov, E. A. Podpletneva, Yu. N. Sivkov. On the question of comparing experimental and calculated characteristics of the short circuit of a rod-type electrostatic generator. Present collection.

13. A. F. Kalganov. On the energy relation between rod-type electrostatic generators and electrostatic generators with a dielectric conveyor. Present collection.

14. Edited by Prof. A. A. Vorob’ev. High-Voltage Testing Equipment and Measurements, GEI, 1960.