2016-08-12

2. Coaxial condenser and electrostatic machine

Previously we showed that redistribution of charges on the surface of the capacitor depends on its type, and under certain conditions, affect changes in the efficiency of the second kind. Next, we consider trehapsidny coaxial capacitor, one of capacitor plates Korogocho has an uneven surface, and analyse the scheme of its inclusion, together with the electrostatic machine [1].

The choice of such a capacitor structure due to its simplicity, but its parameters we will discuss below. The figure shows this design (top view) and marking a capacitor with further concepts. In fact, it is three cylinders of different diameters inserted one into the other. The surface of the two inner smooth and outer rough, so it is conditionally shown with a dashed line. The system forms two capacitor — \(C_1\) and \(C_2\), the capacity of which is calculated according to the formulas: \[ C_1 = { 2\,\pi\,\varepsilon\,\ell \over \ln (r_2/r_1) } \] where \(\varepsilon\) — constant dielectric permittivity, \(\ell\) is the length of any of the cylinders, \(r_1, r_2\) are the radii of inner and middle cylinder, respectively. \[ C_2 = { 2\,\pi\,\varepsilon\,\ell \over \ln (r_3/r_2) } \] Here \(r_2, r_3\) are the radii of the middle and outer cylinder. Although the roughness of the surface of the outer cylinder will make minor adjustments, while we will not consider, because you want to show more qualitative than quantitative result.

The figure shows a possible circuit of such a device. High-voltage from the voltage source, through the upper closed contact of switch SW, charging the capacitor \(C_1\). SW key then momentarily closes its lower contact, and a large portion of the charge flows in the \(C_2\), and the throttle \(L_1\) prevents the passage of current to the load at this point. After a period equal to the time constant circuit, the inductor begins to flow the current in \(R_n\).

From previous part we know that the rate of increase in efficiency can be roughly calculated from the formula: \[ K_{\eta2} \approx {C_1 \over \ C_2}, \, g \gg 1 \] where \(g\) is a ratio of shapes of the surfaces of the capacitors. Substituting everything into the previous formula to obtain the final result for this circuit: \[ K_{\eta2} \approx {\ln (r_3/r_2) \over \ \ln (r_2/r_1)}, \, g \gg 1 \] to obtain \(g \gg 1\) you need to make the surface of the external plate of the capacitor is irregular. Alternatively, you can use the mesh: curvature components of its branches, may be sufficient to obtain the desired ratio.

Testatika

Is it possible in the previous scheme to replace the high voltage source HV electrostatic machine (EM)? The difference will be that during each cycle the capacitor will flow a relatively small charge, which the scheme must necessarily be disposed of, otherwise accumulate it can slow down the rotating disk. In addition, for correct operation — you need the switch so in the common form of EM is not suitable, will have to modify it.

On the lower picture on the left shows this approach. There in the form of a sector represented by a petal of EM is removed from the charge by means of brushes. But in this design there are two: the first (in the direction of movement of the sector) resets the charge on the internal capacitor \(C_1\), followed by a short period in which both contacts of the brushes are shorted together, and therefore the charge flows in the external capacitor \(C_2\), and then starts to work the throttle \(L_1\) the charge flowing to the load \(R_n\). As you can see, the difference of this design from classical EM — the presence of one of its poles two brushes instead of one. The diagram to the right symmetric variant of the scheme involving brush the back side of the drive bearing opposite charges. The main difference is the lack of grounding.

You need to stay on the throttle \(L_1\) (\(L_2\)). The fact that the load \(R_n\) in the classical EM stress must be very high impedance that doesn't really suit us. For its reduction it is necessary to transform the voltage generally applied, for example, 220 Volts. This can be done in different ways, we offer this: \(L_1\) (\(L_2\)) should be like the Tesla transformer (TT) [2], which can operate as a throttle and which can easily cope with high input voltage and transformation. Here you need to remember that TT is a quarter-wave long line, but because one end will be a maximum voltage, the other the maximum current. When the actual speed of the machine it will turn out rather cumbersome, but quite acceptable. For example, rpm 1400 rpm, 36 sectors on the disk and the wire is 0.1 mm, TT may have a height of 50 cm and a diameter of 40 cm it Should be noted that for this method you need good matching of circuit parameters with the parameters of the transformer.

Interesting is another variant of the scheme when an internal capacitor accumulates charge from all sectors of EM, but it flows on the outside only once during the entire revolution of the disk. In this case, the removal of charge is only one brush, but additionally need to install the shorting bar in some part of the disc EM. Instead of a contact you can apply discharger that will work to achieve a certain voltage. In any case, in this scheme will need another soglasovat with an output transformer (TV1), in which it makes sense to use a core made of ferrite or from a transformer steel. It is conventionally the upper part works as the inductor, and the bottom — like a transformer. A symmetric variant of the scheme is done by analogichnym way.

Understanding the principle of the creation of such devices you can think of your circuit coaxial capacitor and EM.

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