the influence of the separation screen on the decay of ... · - initial work in ev, (for copper...

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166 The influence of the separation screen on the decay of electromagnetic field in the area between points of contact Bogdan Kwiatkowski 1 1 , Jacek Bartman 1 , Ewa 2 1 Department of Computer Engineering, University of Rzeszow {bkwiat, pkrut, jbartman}@ur.edu.pl 2 University of Information technology and Management, Faculty of Applied Informatics, Department of Applied Information Systems [email protected] Abstract. In this chapter the principles of the work of the vacuum switch has been described alongside with the idea of emergence of the difussive arch and the technical issues connected with those phenomena. In the subsequent parts the measurements of the decay of the components of the axial, radial and circumferential of the electromagnetic field have been presented for the construction of two systems of contact point generating in the area between contact points both unipolar and bipolar field with or without the so called separation screen. The comparison and interpretation of the measurement results was made. Keywords: contact system, current streams, separation screen, vacuum chamber 1 The issues concerning the switches of vacuum chambers In the high and low voltage switches the physics of turning off the electric arch deserves special attention. Constantly the number of produced and installed switches increases for this type of energy networks. The switches with higher and higher volt- ages rated and easily cut off currents are produced, which considerably exceed the switch-off ability of the constructions. Depending on the power of the switch-off cur- rent the process of turning off the arch is of various intensity. As a result numerous researches has been carried out to explore these phenomena and lead to the increase of the cut-off ability and endurance of the contact systems. 1.1 The mechanisms of the emergence of the arc discharge in the vacuum chamber of the switch Turning off of the electric arc in the vacuum is completely different than in the low-oil, pneumatic or gas-isolated SF6 switches. In vacuum the so called chain devel- opment of the discharge with the following Townsend’s mechanism, cannot be devel- oped due to the lack of loose molecules in the area among the electrons, which could undergo ionization and lead to rapid discharge. In the construction of vacuum switch-

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Page 1: The influence of the separation screen on the decay of ... · - initial work in eV, (for copper equals 4.5 eV), =6.83*109 VJ-1.5m-1.From the equa-tion above it can be assumed that

166

The influence of the separation screen on the decay of electromagnetic field in the area between

points of contact

Bogdan Kwiatkowski1���������� �1, Jacek Bartman1, Ewa ���������2

1Department of Computer Engineering, University of Rzeszow {bkwiat, pkrut, jbartman}@ur.edu.pl

2University of Information technology and Management, Faculty of Applied Informatics, Department of Applied Information Systems [email protected]

Abstract. In this chapter the principles of the work of the vacuum switch has been described alongside with the idea of emergence of the difussive arch and the technical issues connected with those phenomena. In the subsequent parts the measurements of the decay of the components of the axial, radial and circumferential of the electromagnetic field have been presented for the construction of two systems of contact point generating in the area between contact points both unipolar and bipolar field with or without the so called separation screen. The comparison and interpretation of the measurement results was made.

Keywords: contact system, current streams, separation screen, vacuum chamber

1 The issues concerning the switches of vacuum chambers

In the high and low voltage switches the physics of turning off the electric arch deserves special attention. Constantly the number of produced and installed switches increases for this type of energy networks. The switches with higher and higher volt-ages rated and easily cut off currents are produced, which considerably exceed the switch-off ability of the constructions. Depending on the power of the switch-off cur-rent the process of turning off the arch is of various intensity. As a result numerous researches has been carried out to explore these phenomena and lead to the increase of the cut-off ability and endurance of the contact systems.

1.1 The mechanisms of the emergence of the arc discharge in the vacuum chamber of the switch

Turning off of the electric arc in the vacuum is completely different than in the low-oil, pneumatic or gas-isolated SF6 switches. In vacuum the so called chain devel-opment of the discharge with the following Townsend’s mechanism, cannot be devel-oped due to the lack of loose molecules in the area among the electrons, which could undergo ionization and lead to rapid discharge. In the construction of vacuum switch-

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167

es the emergence of arc is usually possible thanks to the release of electrons form the surface of the contact points under the influence of a strong electromagnetic field which develops by electrodes, or under the influence of escapement and ionization of the loose molecules from the area among the electrodes.

The field emission and thermo emission plays a key part here. In the initial phase of the discharge the main role has the field emission, later both mechanisms simulta-neously have a deciding role. The field emission is described by the Fowler-Nordheim equation in which:

��

�������

e

512 ΦΦ

≈ (1)

Where: � – current density, =1.54 * l0-6 AJV-2, � – strength of the electric field in Vm-1, Φ- initial work in eV, (for copper equals 4.5 eV), �=6.83*109 VJ-1.5m-1.From the equa-tion above it can be assumed that the strength of the electric field crucial for the emis-sion of electrons equals 109 Vm-1 and 1010 Vm-1. Those values appear to be higher than the ones which are in the existing vacuum switches and equal 107 Vm-1 =100 kV/cm. Locally the strength of the electric field is amplified by the amplifying coeffi-cient amounting 102 up to 103. This empowerment can be considered as an implica-tions in the area between electrode of the outer molecule. The possibility of appear-ance of the micromolecules among the electrodes reduces considerably the electric durability of the vacuum. Only by conditioning of the vacuum chamber which is based on the sustained contact with electrodes and their voltage, there can be ob-served an increase in the strength of the electric chamber. This process relies on nu-merous discharges which release the loose molecules form the area between elec-trodes. There is also known a phenomena where molecules stick to the walls of the chamber, which after the release get to the area between electrodes and cause the waekening of the electric durability in vacuum. This wakening may result in field emission caused by bombing of the electrodes in the stream of electrones as well as a consequence of pairing of the electrodes due to the high temperature. The mechanism of arc discharge in the vacuum chamber of the switch is different from the one in oil switches. There are no conditions which, under the influence of the strong electric field, could produce free electrons and compose an arc column. The electrons which come from metal of the electrodes, namely the points od contacts, form an arc plasma which is subjected to the influence od electromagnetic field produced by shaped points of contact or outside the vacuum chamber. The spacial positioning of the elec-trones and ions in the vacuum plasma is presented below (fig.1).

Fig. 1. The spacial positioning of the electrones and ione in the vacuum chamber [6], [7]

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168

In the vacuum switches two kinds of arches can be distinguished dependin on the direction of the activity of the electromagnetic field, namely the radial and axial field. Depending on this direction the turning off of the arc in different. The method of the diffusive turning off (made by the axial field) causes the separation of the arc into parallel streams of current. The method in which the arc forms a column (created by radial magnetic field) makes the column swirl on the surface of the electrodes’ points of contact. In the diffusive method form many points on a cathode, streams of electrones and iones sized from 5 to 10 μm are emited. The current in the streams flows parallelly, where in one stream the current equals 1 amp and the arc voltage is very low. It is favourable when considering the amount of enerfy emited in electrodes, because it does not lead to a strong discharge of the surface of the points of contact. On the cathod the usually is a high temperature and the voltage of the electric field of 5000K i 5 x l09 V/m. The points on cathode where there are so high currents, divide theselves into as many pieces as it is needed to enable the current to flow in an appropieate and even value [1]. That is why many strams appeat which comprise the whole area of an electrode [100]. Between a cathode and anode there flows an ion and electron current which comprises only 10% of this current. The speed of the ions is of 104 m/s being this way bigger than the speed of emission. Plasma is then very mobile, so when the point emitting electrons and ions disappear the arc turns off. The dacay od the voltage in the arc is as follows: the cathodal decrese in the voltage of 20V, the minor decrease of the voltage in the arc itself, which increases with the current and negative when close to the anode. In the diffusive method thanks to the decays of the arc on a greater area there is a small usage os the points of contact. In the constructions where there is radial magnetic field, the arc is more dense and pushed externally to electrodes in accordance with the Lorentz force. The anode draws the electrones and is rather passive here. Cations balance the spacial electric charge of the electrones in the neighbourhood of the anode, which causes the positive decrease of the anodal voltage, making the further absorption od electrones by anode. The energy received by anode constantly increases on a small area. This leads to the preheating of the anode and the emission of nautral charges which are ionised creating a big charge of the electrones. Under the influence of their activity the current flows towards the cathode in the reversed direction to the bacis current with lower voltage. This phenomenon causes the creation ofanodal rate which is much bigger than cathodal one, leading to melting of the anode and exhaustion of the material fumes, which the point was made of. In the vacuum, as a result of the unevenness of the surface of the electrodes, the arc kindles in the points, where the local voltage is the highest and with a low current it divides itself into streams which enable the current to flow pararerlly. The radial electromagnetic field causes the movement of the arc towards the electrodes, the surface of the points of contact. This phenomena is called the Hall efect which makes the turning off of the arc more difficult. The dense arc column causes local liquation of the surface of the contact points and lots of fumes of metals. The presence of the big amount of fumes may cause other combustions and weaken the durability. Due to this the constructions of vacuum chambers aim to prevent from creating the dense arc column.

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169

2 The measurement of the decay of the electromagnetic field between the contact points of vacuum switches

The axial magnetic field generated by the coil contact points can be measured by two methods. One is based od measuring the voltage induced in concentricaly placed coils among the contact points. This method is available when measuring the field only in the points generating in the area between the points of contacts a unipolar field. The other method is a measurement of the components of the electromagnetic field by the measuring probe. The researches were made with constructions generating both unipolar and biopolar fields, that is why the authors chose this method and it will be described in details. In this method the contact point overlay was put in the magnetic field generated by the coil (fig.2). The measurement was made by the probe on the surface of the contact point and the measured voltage was compared with whe voltage of the coil of the base system outside the measured system .

Fig. 2. The measurement of the decay of the field by the use of probe [8]

2.1 Description of the experimental system

To a laboratory measurement a HIOKI logger was used of a type ”8841/42 MEMORY HiCORDER”. It a modern, multifunctional, portable appliance with a great technic parameters, made to help in laboratory measurements as well as outside the lab. This appliance can register up to 16 various analogue courses with a 12 bite definition and 16 digital courses (4 probes). In order to measure the electromagnetic induction in the area between the contact points, a probe was constructed with 3 coild. These coils were placed in such an order to make it possible to measure all the components od the electromagnetic induction (fig.3).

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170

Fig. 3. Measuring probe [4], [5]

On each of the measuring coils 50 scrolls have been coiled, the diameter of the coils is ∅9 mm. The measuring probe with is basis was secured to the appliance hold-ing the points of contact. It enabled to lift and wind down the points od contact at an appropriate hight. Moreover, the table where the probe was installed had a special plate allowing to place the probe at every 150 at the perimeter. The measurement system with the probes was put into the Faraday’s cage in order to avoid the influence of the surroundings. While measuring the probes were connected to the logger and a computer. Picture 4 (fig.4) presents the measuring spot.

Fig. 4. A complete measuring spot [4], [5]

2.2 Sampling of the measuring coils

Before the process of measurement, the sampling of measuring coils took place by putting them into a homogenous electromagnetic field. To have this result two Her-molz coils were used, which consist of 13spools each and a diameter of 357 mm. While measurement through the coils a current flew I=66A. By putting the coils in the electromagnetic field created by the coils described above, the measurement was made of the electromagnetic induction by a hallotron gauge of electromagnetic induc-tion. To check the correctness of the measurement two gauges were used. In both

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171

cases the induction equaled to 2,8 mT. After measuring, calculations were made to ensure that it was correct, using the formula 2 to find out the surface of the coils.

�z� �

s∗

= � (2)

Where: s- the substitutional area covered by coils, z-number of spools of coils, B- induction taken by hallotron gauge, u-the voltage on the coils.

Fig. 5. The measuring coils, measurements: D1=8 mm, D2=10 mm, Dsubst=9 mm.

2.3 Description of the measuring method

In the employed method the measured value is voltage induced in the measuring coils. These coils, during the current flows through the contact point system, are in the area between the contact points and are put from the outside to the inside of the con-tact plate. The measurement of the voltage induced on the coils is made by the HIOKI logger with the definition of 100 μs. It enables to get even 25 thousand measuring points for each of the position of the probe. The measuring probe in the initial phase for each of the contact systems was placed in the zero position (00) and then moved successively every 150 around the perimeter of the contact plate.

Fig. 6. The diagram of the experimental measuring system [4], [5].

In case of measuring the contact systems the value measure is the voltage induced in the coils, and the value demanded is the electromagnetic induction, more precisely the

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172

decay of the electromagnetic induction on the surface of the contact plate. Electro-magnetic induction in a u moment u(t0)=0 equals – Bmax whereas when u(t0+0.5T) it qeuals Bmax. Here an integral in the borders 0 to T/2 from the absolute value of the voltage is:

� −=�

�offsetu���Sz

�0

max )(**2

12(3)

Thus the final formula for the electromagnetic induction

))(max(10*50*2*

**4

*)( 3

200

1

I���Sz

foffsetu���� i

��=

−= (4)

2

)(max)(min20012001

uuoffset ÷÷

+= (5)

Where: u- the voltage measured in the measuring coils, z=50 – the number of spools of measuring coil, S=59 mm2 – the surface of the measuring coil, fp – the definition of sampling of the logger, I – current flowing through the contact system [3].

3 The results of the measurments of the contact systems

Two contact points constructions generating a unipolar (point of contact no1) and bipolar (point of contact no2) fiels underwent researches (fig.7).

a) Unipolar point of contact no1 b) ) bipolar point of contact no2

Fig. 7. Constructions of the contact points which underwent the researches.

The aim of the measurements is to prove that there is a possibility of enhancing the evenness of the decay of the electromagnetic field by the choice of an appropriate construction of the points of contact and to show the influence of the separation screen on the decay of the fields in the area between the points of contact. Three com-ponents of the field were measured: axial, peripheral and radial, measuring them by 3 probes at the same time from the peripheral edge of the contact point to its center. While measuring, researchers tried to choose the axial component with as even decay of the fields as possible on the surface of the contact point, which ensures the even ddecay of the diffusive arc. The peripheral component should be possibly small as it focuses the diffusive arc and may cause the exceeded combustion of the contact point in its central part and lead to vast amount of the metal fumes. Radial component in-

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173

fluences the movement of the arc on the peripheral areas and its value are usually big in the centralparts of the points of contact.

3.1 Unipolar point of conract no1

For the construction of the point of contact no 1 measurements were made for the two possible positions of the lower point of contact against the upper one (fig.8) and also there were measurements made with and without the separation screen (fig.9). In odrer to normalize the system, in the picture below some characteristic points are shown which explain the placement of the points of contact against each other.

Fig. 8. Unipolar point of contact with characteristic places for the contact system.

Fig. 9. The separation screen

3.2 The arrangement “crack-crack” without the screen

The crack of the upper point of contact is precisely under the crack of the lower point. Below the course of the particular components of induction for this arrangement of the points of contact against each other.

INPUTS

CRACKS

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174

Paripheral component Radial component

Fig. 10. The components of the electromagnetic induction (without the screen)

Fig. 11. The axial component of the electromagnetic induction (without the screen)

The values of the axial component (fig.11) were increasing when approaching the centre of the contact system. Their values were between 50mT and 300 mT. The regu-lar increase on the whole surface of the contact point of the axial component, the one which enhances the development and maintenance of the diffusive arc is very benefi-cial. Very good decay can be observed in the peripheral component (fig.10). It has smaller values than axial component and they are between 50 mT and 120 mT. The radial component (fig.10) has high values, which is connected with the characteristics of the measuring method. In spite of this its dacay and increase in even on the whole surface of the point of contact.

00 150 300 450 600 750 900 1050 1800

00 150 300 450 600 750 900 1050 1800

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175

3.3 The arrangement “crack-crack” with the screen

The statisctics set identically as in point 3.2, but the separation screen has been place as in the picture 9 (fig. 9).

Peripheral component Radial component

Fig. 12. The components of electromagnetic induction (with the screen)

Fig. 13. The radial component of the electromagnetic induction (with the screen)

After the separation screen was used the character of changes of all the components did not change. The values of the axial component slightly decreased but the decay on the surface of the contact point seems to be even greater in evenness. In a beneficial way have changed the values of the peripheral component, they equal zero. The axial component takes high values in plus for the same reason as it did in the case without the separation screen. Pictures 14 and 15 show exemplary courses of the components of the electromagnetic induction, which illustrate the changes connected with the use of the separation screen (fig.14), (fig.15) [4].

00 150 300 450 600 750 900 1050 1800

00 150 300 450 600 750 900 1050 1800

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176

Axial component without the screen Axial component with the screen

Fig. 14. The axial component of the electromagnetic induction for the angle of 450.

Peripheral component without the screen Peripheral component with the screen

Fig. 15. Peripheral component of the electromagnetic induction for the angle of 600.

3.4 The bipolar point of contact no 2

For the bipolar point of contact measurements were made for four arrangements. In odrer to normalize the system concerning particular arrangements in the icture 16 (fig.16) characteristic indications are shown. For this point of contact measurements both with and aithout a screen were made.

Fig. 16. The bipolar point of contact no 2 with its charact. indications of the contact system

INPUTS

CRACKS

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177

3.5 The “Input-input” arrangement with the screen

This arrangement is characterised by the fact that the input of the upper contact point in right above the input of the lower contact point. The courses indicated in the pictures 17 and 18 show the decay of the components of the electromagnetic induction for all of the measuring angles.

The peripheral component The radial component

Fig. 17. The components of the electromagnetic induction (with the screen)

Fig. 18. The axial component of the electromagnetic induction (with the screen)

From the courses presented in pictures 17 and 18 (fig.17), (fig.18) it can be seen that all the components of the electromagnetic induction raise their values when approach-ing the centre od the contact system. The components’ values are doubled when com-pared with the unipolar point of contact no1, moreover, its decay is evener especially in the middle of the contact point. The peripheral component has rather low values, only in the cetre part of the point of contact there its sharp rise.

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

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178

3.6 The “input-input” arrangement without the screen

The arranegement set as previously, but without the separation screen.

Peripheral component Radial component

Fig. 19. The components of the electromagnetic induction (without the screen)

Fig. 20. The axial component of the electromagnetic induction (without the screen)

Comparing the analogue courses (the same arrangements of the points of contact) in pictures 17 and 18, it can be seen that the values of all components are higher without the screen. It is crucial especially for the axial component, the difference for this component is about 100mT. It should be observed, that the radial component has equal values for both of the considered cases (with and without the screen). The val-ues of the peripheral component rise when the measuring angle changes. The highest values are for angles from 1350 to 1800 and in the centre part of the contact plate where they are about 580mT.

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

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179

Axial component wihout the screen 900 angle Axial component with the screen 750 angle Fig. 21. The axial component of the electromagnetic induction, input-input arrangement

Peripheral component without the screen 750 angle Peripheral component with the screen 900 angle

Fig. 22. Peripheral component of the electromagnetic induction, input-input arrangement

From the courses of the axial component it shows that the separation screen causes the decrease of the value of the electromagnetic induction, which is not beneficial for the conditions of emergence of the diffusive arc.

3.7 The “crack-crack” arrangement with the screen

The crack of the upper point of contact is right above the crack of the lower point of contact (fig.16). Below the courses characterizing this arrangements were shown.

Peripheral component Radial component

Fig. 23. Components of the electromagnetic induction (with the screen)

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

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180

Fig. 24. The axial component of the electromagnetic induction (with the screen).

All courses for this arrangement are similar in their character as they were previously. The values of the axial component increased when approaching the centre of the con-tact plate (fig.22). This component has the highest values at angles from 600 to 900. When comparing peripheral components for both arrangements, namely points 3.7 and 3.6, it can be observed that the courses for the “crack-crack” with the screen ar-rangement are more dense, so the differences in values of the inductions of particular angles are rather small. The biggest density of the characteristics is for angles from 150 to 1200 and for 1800. Their values in the middle of the point of contact are in the range of 200-250 mT.

3.8 The “crack-crack” without the screen arrangement

The crack of the upper point of contact in precisely above the crack of the lower con-tact point (fig.16). Below the courses characterizing this arrangements were present-ed.

Peripheral component Radial component

Fig. 25. The components of the electromagnetic induction (without the screen)

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

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181

Fig. 26. Axial component electromagnetic induction (without the screen)

All the components of the electromagnetic induction for this arrangement stay in the same character as in the previous cases. The values reached by the particular compo-nents are higher when compared with the analogue arrangement with the screen. The axial component has its highest values for measuring angles of 750, 900 having its rising tendency when approaching the centre of the point of contact. Peripheral com-ponent its highest values reaches at angles from 1500 to 1800.

Axial component without the screen 900angle Axial component with the screen 750angle

Fig. 27. Axial component of the electromagnetic induction, “crack-crack” arrangement

Peripheral component without the screen 750 angle

Peripheral component with the screen 900 angle

Fig. 28. Peripheral component of the electromagnetic induction, crack-crack arrangement

00 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800

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182

For the axial component the values received in the “crack-crack” with the screen ar-rangement, are higher about 100 mT than the values received in the “input-input” with the screeen. For both arrangements induction reaches its highest values for the central angles, namely from 600 to 1350. For the “input-input” with the screen ar-rangement the maximum values are reached earlier (for the bigger values of the radi-us) and are kept to the centre of the contact system. Maintaining the constant value of the induction on the surface of the contact point is desired for the emergence of the diffusive arc. The value of the axial component of the induction for angles from 00 to 900 rises both for the arrangement “crack-crack” without the screen and for “input-input” without the screen. For angle 900 in both cases the values of induction are the highest. After crossing this angle the values decrease.

4 Summary

The results of the measurements made in particular points of contact applied in theswitches of vacuum chambers indicated that there is a significant influence of the arrangement of the contact points on the decay of the magnetic fiels between the points of contact. In case of unipolar and bipolar points of contact the influence of the arrangement of the contact points against each other is visible and what is possible is the choice of decay of the magnetic field in the most beneficial way.

Unipolar points of contact (fig.8) The decay of the field was measured for the arrangement “input-input” and “crack-crack”. Measurement proved the existence of significat differences in values of the voltage of the fiels in the “crack-crack” ar-rangement. For this arrangement of points of contact, the voltage of the magnetic field for the axial component is about 50% bigger, which is crucial when turnign off the diffusive arc.

Bipolar points of contact (fig.16). In the beginning the measurements of the decays of the fiels with and without the screen around the contact point were made. While applying the screen, probe to measure the decay of the field on the surface of the contact points was inserted by the hole in the screen. It has been stated that the use of the screen decreses the value of the voltage of the axial magnetic field, which is not beneficial. It happens because the screen forms a dense spool where the flow of cur-rent generates the field in a different direction. The researches made with the screen were conducted in the “input-input” and “crack-crack” arrangements. In the latter arrangement of the contact points the axial component for all angles, on the peripheral edge are higher than the ones occuring in the “input-input” arrangement, also the peripheral component for all angles is lower, which should be considered as more beneficial. The radial component does not show differences and does not change in both arrangements.

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183

5 Bibliography

1. Sikora R.: Teoria pola elektromagnetycznego��Wydawnictwo Naukowo-Techniczne, War-szawa 1985.

2. Harald Fink, Marcus Heimbach, Wenkai Shang: Vacuum Intrerrupters with Axial Magnet-ic Field Contact Based on Bipolar and Quadropolar Design, IEEE 19 International Sympo-sium on Discharges and Electrical Insulation in Vacuum, Xian-2000.

3. Brandt S.: Analiza danych. Metody statystyczne i obliczeniowe, Wydawnictwo NaukowePWN, Warszawa 1998.

4. Kwiatkowski B., P���������������������������� ����������������������������������gnetycznego w przestrzeni mi��� �� �������������� ��czaln��� ��czników pró�niowych- Przegl�d Elektrotechniczny 11’2008 – str. 340-343.

�� �����������!���"��#����$������������������� ����&�'�;��������;��<��>����?�������;the Axial Radial and Circumferential Component of the Magnetic Induction Vector Withinthe Space between Switches on Rupturing Capacity of Vacuum Switches, 8-th AIMS In-ternational Conference on Dynamical Systems, Differential Equations and Applications,Dresden University of Technology, Department of Mathematics, p. 48,

@� >�?�G������Z���\��������"�������^���_������_���$�������$�&��� ���������� ������������������������ ���!�"������#�"�, PWN Warszawa-Pozna� 1983.

`� !��������$���_���������\��cicka-Grzesiak H.: $�" �!%�"���"��� ��#��&����"����!'���� ������� � #������� � �" �!%�"���"�����!'� ��!�&������������!������Zeszyty Na-ukowe Politechniki Pozna��������}���� ������~���� �������������������������� ������pró�ni, Pozna� 1989.

8. Wang Zhongyi: (����!'��"��'�����!���!�)��� ��" �*�&"���!�)��� �+����������"���"�,�&'-����&��-�!����."�����������Xian Jiaotong University PHD. Thesis, Xian, China 1997.