Problema del “instrumento malicioso no calificado”

As stated earlier, the electrode-fall regions in an arc are extremely short and unlikely to be more than 10−3mm long and therefore the positive column may be taken to occupy the whole gap length between the electrodes. This length is dependent on the power inputs and interchanges which cause erosion of the element and therefore extension of the gap.

3.3.1.1 Power supplied to an anode

An anode receives significant power in the following two ways:

(a) The power used in a cathode to cause electrons to leave its surface is returned to an anode when the electrons reach and enter it. The associated power is equal to the product of the work function (a voltage Vwf) and the current flowing into the anode.

(b) The kinetic energy of the electrons reaching an anode is given up to it. The associated power is made up of two parts, i.e. the thermal power acquired in the column, equivalent to the electrons falling through a voltage drop (VT)of 1 V [24] and that due to the acceleration experienced by the electrons in the anode-fall region.

Power is also given to an anode in other ways including the following:

(c) Radiation and conduction from the positive column. From calculations which have been done, it appears that with the areas and at the temperature differences which exist in practice the power levels associated with these modes of heat transfer are very small compared with those referred to under (a) and (b) above. (d) Joule heating of the anode. Assessments of this effect have also been made [10] and these indicate that the associated power is likely to be small. This confirms the view expressed earlier by other workers.

3.3.1.2 Power lost by an anode

An anode dissipates power in several ways including radiation and heat conduction into the surrounding filling material and also away from the arc into adjacent parts of the element. The levels tend to be small in each case and an example is given in Reference 10 to illustrate the magnitude of the heat conducted along the element.

3.3.1.3 Power supplied to a cathode

A cathode receives significant power in the following ways:

(a) The ions reaching a cathode use some of their energy in overcoming the surface forces and give up the remainder to it. As with an anode, the associated power is made up of two parts, i.e. the thermal power acquired in the column and that due to the acceleration experienced by the ions in the cathode-fall region, equal to the cathode-fall voltage and the ionic currents.

(b) The power given up when ions and electrons recombine at a cathode is equal to the product of the ionisation potential of the atoms, in volts, and the ion current flowing into the cathode.

(c) Power is also given to a cathode in other ways, as outlined in Section 3.3.1.1 (c) and (d), and again these quantities tend to be small.

3.3.1.4 Power lost by a cathode

In addition to dissipating power by the mechanisms described in Section 3.3.1.2 for an anode, a cathode supplies significant power to the electrons emitted by it, this

quantity being equal to the product of the electronic current and the work function (a voltage).

3.3.1.5 Power balance

The difference between the power supplied to and the power dissipated from a pair of electrodes is used in raising their temperatures and in melting and vaporising them. The power available for this purpose at an anode was given by Cobine and Burger [24] as:

power= (Vaf+ Vwf + VT)× i (3.2)

Since the ratio of electronic to ionic currents at a cathode is unknown it is not possible readily to determine the power supplied to it. X-ray photographs of elements which have passed high currents invariably show that associated pairs of anodes and cathodes have burned back almost equally and therefore it is reasonable to assume that the power supplied to a cathode is the same as that given to an anode.

An important factor, which affects the burnback, is that only a fraction of the element material which initially occupies the space in which a gap is ultimately formed is vaporised during the arcing process, the remainder flowing away in liquid form. This fact was revealed by Wright and Beaumont when elements which had cleared large currents were examined microscopically. The elements together with the fused quartz filler, known as fulgurite, were sectioned longitudinally and in a plane orthogonal to that of the element strip, for examination. An example is shown in Figure 3.4 and the metal which flowed out in liquid form can be seen clearly. Further tests showed that the metal which had vaporised was deposited finely in the quartz filling material. This behaviour is presumably caused by the pressure distribution during arcing.

In calculating the arcing performance by taking account of energy requirements and interchanges, it is clearly necessary to determine the proportion of the element which is vaporised as this requires more energy per unit mass than the material which runs away in liquid form. To assess the proportions, Wright and Beaumont used a number of fuselinks containing silver elements and quartz filler to clear large currents. They were subsequently X-rayed to determine the final lengths of the arcs. The time integrals of the currents during the arcing periods were determined from oscillograph records of the currents and the energy available for melting and vaporising was taken to be:

EMV = 2(Vaf+ Vwf + VT)  ta

0

i dt (3.3)

in which tais the duration of the arcing period.

This was equated to the energy needed to remove the electrode material, i.e. EMV = mv(latent heat of vaporisation)+ mt(latent heat of fusion)

d

a

b

c

Figure 3.4 Microscopic picture of fulgurite section Where

a electrode

b electrode material which has flowed away in liquid form c grains of filler

d arc cavity which has been filled with epoxy adhesive to enable the section to be made through the fulgurite

in which mt is the total mass of material removed from the element, a quantity determinable from the X-ray photographs, and mvis the mass of the vaporised metal. It will be noted that this latter expression neglects the energy required to raise the temperature of the element material from the melting to boiling temperature, a quantity which is very small compared with the latent heat of vaporisation. It will also be seen that the bulk temperature of the electrode material is assumed to be raised to 200◦C during the pre-arcing period.

In all the tests which were done it was found that eqns. 3.3 and 3.4 were satisfied when mv 0·40 mt, i.e. the mass of material vaporised was only about 40 per cent of the total mass which was melted. For this condition, it is found that 20 per cent of the total energy supplied is used to provide the latent heat of fusion Lfand consequently the following expression may be used to determine the lengthening of the gap between a pair of electrodes, that is the burnback in an interval of time δt:

l2− l1=

mass of electrode removed in δt Ae× density of electrode material

= 2(Vaf + Vwf+ VT)× {(i1+ i2)/2}δt × (0.2/Lf)

A_e× density of electrode material (3.5) where l1and l2and i1and i2are the gap lengths and currents at the beginning and end of the interval, respectively, and Aeis the cross-sectional area of the electrode at the arc roots over the time being considered.

By continuously calculating the burnback for each time interval the length of the positive column at any instant in the arcing period can readily be determined.