ROD-TYPE CYLINDRICAL ELECTROSTATIC GENERATOR

A. F. Kalganov, Yu. A. Korzennikov, A. F. Korostelev, G. V. Unzhakov

(Presented by the scientific seminar of the Department of Theoretical Foundations of Electrical Engineering and the sector of rotary electrostatic generators of the Scientific Research Institute of Nuclear Physics, Electronics, and Automation)

In accordance with [1], a working model of a rotary electrostatic generator of cylindrical design with rod-type conveyors (RESGC) has been developed. Structurally, the generator consists of three main elements ensuring its operation: a dielectric cup-shaped rotor, in the walls of which, along its generatrices, rod-type metallic conveyors of circular cross section are located; an external stator (with respect to the rotor), made integrally with the low-voltage flange; and an internal stator, made integrally with the high-voltage flange, on which the commutating brushes are located. In the proposed design, the number of seating locations is reduced to a minimum, thereby providing greater rigidity of the system and better coaxiality of the rotor and stators.

Such a structural design became possible owing to the use, as the weakly conducting layer of the stators, of a synthetic material based on epoxy resin. The choice of this material was made on the basis of the data given in [2].

In the generator constructed, the mean diameter of the rotor \(D\) is 100 mm, the rotor wall thickness is 7 mm, and the working length of the rods \(l\) is 162 mm. The sealed generator unit is a steel tube with an internal diameter of 150 mm, sealed at one end by a steel cover with the necessary insulating bushings for the low voltage and excitation voltage, and at the other end by an insulating cover combined with the high-voltage terminal. Both covers are held by nuts screwed onto the tube. The working medium of the generator is hydrogen compressed to 15 atm.

The practical implementation of the design development required the development of an appropriate technology for manufacturing the main working elements of the RESGC. Below is a brief description of the technology used for manufacturing the rotor and stators of the RESGC.

Two variants of the rotor-manufacturing technology were used. In the first variant, a rotor was made with steel rods of comparatively large diameter (1 mm and more). On the outer surface of an insulating blank, whose internal diameter and length corresponded to the dimensions of the future rotor, grooves were milled along the generatrices, into which the rods were then laid. The blank with the rods was placed and centered inside a mold,

made of an anti-adhesion material (with respect to the epoxy resin). The inner diameter of the mold determined the outer diameter of the rotor. The cavity between the mold and the rotor blank was filled with an epoxy compound. After completion of the polymerization process, the rotor was annealed and pressed out of the mold, having the specified dimensions. The cleanliness of the outer surface of the rotor was determined by the finish of the mold surface. To complete preparation of the rotor it was necessary only to face the collector part.

With a two-row arrangement of rods, the operation described above was repeated twice: after fastening and casting the first row of rods with compound, analogous fastening and casting of the second row of rods were carried out.

In the second version, a rotor with copper-wire conveyors was manufactured. In this case, a hollow thin-walled insulating cylinder was first prepared. Its walls (along the generatrices) were wound with wire at the appropriate pitch. The blank was installed and centered in a cylindrical mold with two coaxial walls. The cavity between the walls, together with the blank, was filled with an epoxy compound. The subsequent operations were analogous to those for the rotor with rods.

The technology for manufacturing the stators also differed according to whether it concerned the internal or the external stator.

In manufacturing the internal stator, a blank is prepared in the form of a cylindrical insulating body combined with a flange. Metal inductors are fastened on the insulating body. The blank with the inductors is installed in a cylindrical mold, and the cavity between the blank and the inner surface of the mold is filled with an epoxy compound of special composition, which after curing has the specified conductivity, forming the weakly conducting layer of the stator. After completion of polymerization, the stator body with the weakly conducting layer is pressed out of the mold.

In manufacturing the external stator, the insulating body of the stator performs the role of the external mold. A mandrel of anti-adhesion material is inserted into this body, on which the inductors are installed by means of rings. The space between the mandrel and the stator body is filled with an epoxy compound. After curing of the compound, which becomes the weakly conducting layer of the stator, the mandrel is pressed out.

The mandrels and molds are selected in size so that the finished parts have the specified dimensions and the required surface finish.

Figures 1 and 2 show photographs of the stators and one of the rotors manufactured by the technology described above, and of a sealed ESGG unit.

The electrical calculation of the generator was carried out on the basis of the method set forth in [3]. Since the generator had a two-pole design, the expected output voltage, according to the rotor diameter, was to be 100 kV. If the operating electric-field strength (normal component) in the rotor–stator gap is ensured at 200 kV/cm, close to the electric strength of hydrogen at 15 atm under conditions of a slightly nonuniform field, and with the filling factor of the dielectric body of the rotor by conveyors, \(\kappa_0\), equal to unity, the maximum short-circuit current of the generator would be

\[ I_{\text{k.z.t}} = 2\varepsilon_0 E_n 2S_{\text{geom}} n = 4\varepsilon_0 E_n \pi D l n = 4 \cdot 8.85 \cdot 10^{-12} \cdot 200 \cdot 10^5 \cdot \pi \cdot 0.1 \cdot 0.162 \cdot \]

\[ \cdot 46.7 = 1.69 \cdot 10^{-3}\ \text{A} = 1.69\ \text{mA}, \]

where \(S_{\mathrm{geom}}=\pi Dl\) is the working geometrical surface of one side of the rotor of the ESGG;

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

Such a current would be developed by an ESG with dielectric carriers having a working rotor surface \(S=S_{\mathrm{geom}}\).

In reality, owing to the presence of the carriers, the value of the coefficient \(k_0\) of the ESGG is less than unity. Correspondingly, the short-circuit current must also be smaller. The corresponding calculations for different geometries of the rotor–stator system are given in Table 1. The calculations were made for the case in which the gas gap between the rotors and stators \(d_1\) is \(0.5\ \mathrm{mm}\). Such a gap value was achieved in the generator that was built. It is comparatively large, but this is explained by the fact that, in calculating the required dimensions of the molds used to manufacture the stators and rotors, the allowance for shrinkage of the epoxy compounds was insufficiently taken into account.

Fig. 1. Principal working components of the ESGG: \(a\)—outer stator combined with the low-voltage flange; \(b\)—inner stator combined with the high-voltage flange and the high-voltage insulator; \(c\)—rotor with rod-type carriers

Fig. 2. General view of the sealed ESGG unit

Four rotor variants were investigated: two with a two-row arrangement of rods (A and B) and two with a single-row arrangement (V and G).

For most rotors the coefficient \(k_0\) is considerably less than unity. It is greatest (0.92) for rotor V, which has 60 rods with a radius of \(1.5\ \mathrm{mm}\), and smallest (0.74) for rotor G, which has 45 rods with a radius of \(1\ \mathrm{mm}\). The corresponding difference is also present in the calculated values of the short-circuit currents (see column 10).

Column 11 of the table gives the measured values of the short-circuit currents, and column 12 gives their percentage ratio to the calculated currents. This percentage ratio increases from rotor A to rotor G. Analogous changes also apply to the limiting electric-field strength reached in the rotor–stator gap (see column 13).

Figures 3 give the short-circuit characteristics, and Fig. 4 gives the load characteristics at \(U_{\mathrm{v}}=25\ \mathrm{kV}\) for the ESGG with rotors V and G.

The interpretation of the results obtained reduces to the following.

1. The comparatively low value of the filling coefficient \(k_0\) \((=0.82)\) for the generator with rotor A corresponds to the fact that the rotor carries carriers of small radius (\(0.49\ \mathrm{mm}\)) having a small depth of embedment in the dielectric body of the rotor (\(1\ \mathrm{mm}\)). At the same time, the greatest deviation of the measured current from the calculated one is observed here. Apparently, because of the large number of carriers of small radius (and, correspondingly, because of the comparatively small

distances between them), even at small excitation voltages, because of the large nonuniformity of the field in the plane in which the conveyors are located (including, and especially, in the region of the collector part).

Table 1

Electrical and mechanical parameters of ESGS variants

Note: in calculating the data given in the table, the value of the relative dielectric permittivity of the rotor material \(\varepsilon_{r_2}=4.5\) was used (data from our measurements).

part), electrical flashover occurs between the conveyors in the commutation zone. As a result, premature “saturation” of the current sets in. In this connection, the low value of \(E'_{\mathrm{lim}}\) obtained by calculation \((=152\ \mathrm{kV/cm})\) in fact is not yet critical for the given conditions. The value \(E'_{\mathrm{lim}}\) for this case could have been increased if, with other conditions being different, the number of conveyors had been reduced.

1. A certain increase in the coefficient \(\kappa_0\) for the ESGS with rotor B in comparison with rotor A corresponds to the fact that the rotor here has conveyors of larger radius (1 mm). However, despite the fact that the number of conveyors is somewhat increased and the distances between them have decreased, the change in the measured current in comparison with the calculated one is less significant. Apparently, under these conditions the field between the conveyors is more uniform, and this ensured the attainment of a larger value of \(E'_{\mathrm{lim}}\).

1. The high value of \(k_0\) for rotor B is due to the fact that the rotor carries large transporters (\(r = 1.5\) mm), which, moreover, have a considerable embedding depth (2 mm). For the generator with this rotor, a closer agreement of the measured short-circuit current with the calculated one was also obtained. However, the difference is still significant. Apparently, reducing the number of rods to 60 is still insufficient to ensure the required electrical strength over the surface of the collector.

Fig. 3. Short-circuit characteristics of the ESGS: 1 — for a rotor with \(2m = 60\), \(r = 1.5\) mm; 2 — for a rotor with \(2m = 45\), \(r = 1\) mm. \(\triangle\) — forward stroke; \(\nabla\) — reverse stroke; \(\bigcirc\) — forward stroke; \(\square\) — forward stroke after 20 min.

Fig. 4. Load characteristics of the ESGS: 1 — for a rotor with \(2m = 45\), \(r = 1\) mm, \(U_{\mathrm{в}} = 25\) kV; 2 — for a rotor with \(2m = 60\), \(r = 1.5\) mm, \(U_{\mathrm{в}} = 25\) kV.

1. The generator with rotor G has the smallest value of \(k_0\), since the rotor carries a small number of transporters with \(r = 1\) mm. Its calculated short-circuit current is, correspondingly, also the smallest. However, the measured value of the current, and consequently also the value of \(E'_{\mathrm{pred}}\), are closest to the calculated value (93%).

This can be explained by the fact that, by increasing \(a\) to \(\sim 7\) mm and \(l'\) to \(\sim 5\) mm, conditions are provided for maintaining the existing potential difference between the transporters even at high excitation voltages.

It should be noted here that the values of the measured short-circuit currents given in column 11 for rotors A, B, and V correspond to the time of the generator’s first switching-on. However, with time the currents decrease, and the operation of the generator becomes unstable. After disassembling the generator, it was found each time that in many places of the rotor, insulation breakdowns had occurred between the rods. Only the generator with rotor G operated stably for a long time. Therefore, although, according to Fig. 3, short-circuit characteristic 1 of the ESGS with rotor V is better than characteristic 2 of the ESGS with rotor G, preference should be given to the generator having characteristic 2, since a generator with such a characteristic is serviceable, whereas characteristic 1 was obtained only for the initial operating period of the ESGS and subsequently is not maintained.

Comparison of Figs. 3 and 4 shows that the better short-circuit characteristic corresponds to the worse (in slope) load characteristic. For the generator with rotor G, a voltage multiplication coefficient \(k_u \approx 40\) was obtained. At a voltage of 100 kV, the load current

is 760 μA. In the stabilized regime, 700 μA was obtained at 100 kV.

The experimental results thus confirm the initial premises set forth in [3]: the radius of the carriers and the depth of their embedding in the body of the rotor should not be small. The tendency to increase the number of carriers also proves to be unjustified. The rod-type electrostatic generator can be operable when the level of its short-circuit current differs substantially from the current level of a dielectric-carrier electrostatic generator under equivalent conditions. In other words, operable rod-type electrostatic generators will always correspond to values of \(k_0\) significantly less than unity. However, by using both surfaces of the rotor, the current of a rod-type electrostatic generator is considerably greater than that of a dielectric-carrier electrostatic generator of the same overall dimensions. If a gap \(d_1\) of about 0.3 mm is provided in the rod-type electrostatic generator (instead of the 0.5 mm obtained by us), one may expect to obtain a load current of 1 mA at 100 kV with dimensions \(D = 100\) mm and \(l = 150\) mm.

REFERENCES

1. A. F. Kalganov, Yu. A. Korzennikov. Inventor’s Certificate No. 202291, 1967.

2. L. A. Korshunova, R. M. Kessenikh, A. F. Kalganov. Proceedings of the All-Union Interuniversity Scientific and Technical Conference on Problems of the Development and Methods of Testing High-Voltage Physical Apparatus, Moscow, 1969.

3. A. F. Kalganov. On the energy relationship between rod-type electrostatic generators and electrostatic generators with a dielectric carrier. The present collection.