Contacts to Force the Motion of the High Current, Columnar Vacuum Arc
As I have discussed in Section 2.6.2 in this volume, the high current, columnar vacuum arc moves in the Amperian manner when a transverse magnetic field (TMF) is impressed across it . This finding has led to some very practical high current contact designs for vacuum interrupters. Each of these designs accepts the occurrence of the columnar vacuum arc, but this arc is forced to move across the contact face through the interaction between the current flowing in the arc and a transverse magnetic field (TMF) resulting from the current flowing in the contact itself. The earliest design for this type of contact, the spiral contact, was patented by H. N. Schneider  in 1960 and is illustrated in Figure 3.20(b). Also, in 1960 Smith patented a cup TMF design shown in Figure 3.20(c) . Other typical designs are shown in Figures 3.20(a), (d), and (e). The mode of operation with a columnar vacuum arc is illustrated in Figure 3.21(a) and (b). When opening usual load currents (i.e., < 4kA), however, the vacuum arc will be in the diffuse mode with cathode spots running over the whole spiral cathode’s surface.
FIGURE 3.20 (a) An example of the “Transverse Magnetic Field” (TMF) contact structure for vacuum interrupters, (b) H.N. Schneider’s original spiral contact design , (c) and (d) variations on the TMF design, (e) Smith’s cup TMF design.
Feng et al.  have investigated the performance of the shape of the spirals shown in Figure 3.22 when interrupting currents up to 24kA peak. Seven arc modes are observed in these experiments: the bridge column, the diffuse column arc, the constricted column arc, the plasma jet arc, the anode jet arc the high and low current diffuse arcs. Only minor differences are observed in current interruption performance between the two designs for contact diameters of 40mm and 46mm. The
FIGURE 3.21 The motion of the high current columnar vacuum arc on the TMF contact structure; (a) spiralshaped contacts and (b) the contrate cup shaped contacts.
FIGURE 3.22 The spiral and straight cut Transverse Magnetic Field (TNF) contact designs.
effective contact area eroded by the spiral contacts is between 73% and 79% and between 91% and 97% for the straight cut design.
Figure 3.22 shows the design parameters for the spiral contact. They are, the width and thickness of the spiral arms, the width of the gap between the spiral arms and the notch depth in the contact’s center. For most designs the contacts make closed contact at position (1). The spiral arms radiate from this region. As will be shown in Chapter 6 in this volume, the closing velocity and closing force are very high for vacuum interrupters that are designed to interrupt high fault currents. Thus, when the contacts touch the arms will have built up considerable inertia. The spiral arms experience high stress each time the contacts open and close. It is important to control the mass of these arms. This is done by optimizing the slot width and the arm thickness and width. Feng et al.  have investigate the TMF design in Figure 3.20(a) for slot width (1.5mm to 2.5mm), arm thickness (5mm to 7mm), contact diameter 40mm and initial column arc position (1), (2), and (3) when interrupting ac currents (5kA to 20kA). They conclude that when the initial arc column is at position (1) (i.e., at the contact’s center), magnetic force is much lower that at positions (2) and (3). When the contact gap increases the magnetic force on the column arc increases. However, when the contact thickness increases the magnetic force decreases. The notch depth has little influence.
A second contact structure that uses a TMF to drive the columnar vacuum arc is shown in Figures 3.20(c) nd 3.21(b). This design is the contrate cup contact [96 ,99, 100]. It can be seen from Figures 3.21(b) that the slanted slots cut into the cup’s side provide a transverse component to the magnetic field, which drives the arc around the cup’s surface. It has been found that the arc runs best in this design if the slots do not extend all the way to the rim, i.e. there is a rim of solid contact material. When the slots do extend through the contact’s surface a more or less continuous surface develops after a few mechanical operations. The impact from these mechanical operations will cause the slots at the contact’s surface to collapse and touch each other. One way of preventing the slots from collapsing is suggested by Wang et al.  and is shown in Figure 3.23(a). Liu et al.  in Figure 3.23(b) show another way of enhancing the magnetic field strength. Lamara et al.  propose the raised central spiral and a fixed contrate cup design shown in Figure 3.23(c). The high current column vacuum arc is initiated on the central spiral contacts and migrates to the fixed cup
FIGURE 3.23 Examples of extensions to thecupTMF contact: (a) iron pillars inside the cup design , (b) Spiral cuts into the cup’s base  and (c) spiral moving contacts inside a fixed cup .
structure. The authors of these designs each claim a somewhat improved interruption performance over the simpler designs shown in Figure 3.20.
Many variations of the TMF contact design have been proposed. For example, Figure 3.24 illustrates some TMF design variations proposed by Altof . Most of the vacuum interrupter manufacturers who use this contact design to control the high current columnar arc have developed their own “optimum” designs. The optimum design will depend upon the shape of the spiral or the cup, the width of the slots, the length of the slots, the number of slots, the width of the spiral, the shape of the cup wall, and the slot angle in the cup’s wall as well as the contact material used. Each manufacturer has developed its own optimized design and a benchmark review of available vacuum interrupters shows that there are as many variations of the TMF contact structure as there are manufacturers. Finally, the cost to manufacture a particular design to achieve a given interruption performance rating is, in practice, an important criterion for a commercial product. The spiral TMF contact has traditionally been produced by machining a disc of C-Cr material. Kowanda et al.  show that it is possible to produce a net-shape contact directly witli the press and solid phase sinter technique given in Table 3.4(a).
Figure 3.21(a) shows a columnar arc between the spiral arms. As I have already discussed in Section 2.6.2 in this volume, the current path generates a transverse magnetic field with the magnetic flux Br perpendicular to the page. This TMF, together with the current, produces a Lorentz force FT, which is directed towards the right and tends to enlarge the area of the loop, thus making the arc move. Thus, when the arc is in the columnar mode, the self-magnetic field generated by the current flowing in the spiral arms interacts with the current flowing in the arc to force the arc to move between the spirals. When the arc roots reach the end of the spiral arm, they are forced to jump the gap to the next spiral arm by the arc column continuing to move around the circumference of the contacts. Figure 3.25 shows the typical arc voltage characteristic for spiral, TMF contacts opening a high-current ac circuit. After the initial column arc formation there is a dwell time when the column arc does not move. Once the contacts open far enough (in this example, after 2ms)
FIGURE 3.24 Examples of possible TMF structures for power vacuum interrupters .
FIGURE 3.25 The voltage across spiral contacts as they open a high-current circuit showing the stages of the columnar arc motion and transition to a diffuse vacuum arc as the current approaches zero.
FIGURE 3.26 The column arc behavior between opening spiral contacts as a function of current .
the interaction with the lengthened arc column and the magnetic field comes into play. This initiates a rapid motion of the columnar arc around the periphery of the spiral arms. Figure 3.26 from Niwa et al.  shows the typical durations of the stationary arc column and the rotating arc column as a function of current. As the current approaches zero the column arc dissipates into a diffuse vacuum arc.
The force on the arc column is given by:
where i is the current flowing in the arc and the spiral arms, La is the arc length, B, is the transverse magnetic flux between the spiral arms is some distance behind the arc, and n* « 0.5 (see Section 2.6.2 in this volume). The arc’s velocity will be governed by this driving force and the forces that oppose the arc’s motion. Dullni  assumes that the mechanism limiting the columnar arcs motion is the time it takes for the energy from the arc to heat the contact material at the arc’s roots to the boiling point. This then would permit enough material to enter the arc and maintain its high- pressure columnar nature. He uses an energy balance equation where the energy loss is described by a one-dimensional heat conduction equation at the contact’s surface to calculate the arc velocity varc as a function of the current i. He assumes that a lower bound for the heat flux into the contact can be estimated from an equivalent contact fall voltage drop tyand the electron current density j. He also assumes that the increase of the contact surface temperature produces a sufficient evaporation rate to achieve the gas density necessary for the current transport in the arc plasma column, i.e., the columnar vacuum arc is maintained. He determines the arc velocity to be:
where К, C, and c are the thermal conductivity, mass density, and specific heat of the contact material, respectively; i is the total discharge current in the plasma column,) = i/nr2 (r is the mean radius of the arc column), Th is the final contact temperature, and T0 is the initial surface temperature. The resulting dependence of varc on the arc current is shown in Figure 3.27 for an equivalent contact fall voltage drop of Uf = 17 V. Except in a narrow range of currents the model overestimates the arc velocity that has been measured by experiment. One drawback of this model is that the energy balance equation is not solved for the arc column.
FIGURE 3.27 The speed of the columnar vacuum arc between TMF contacts (experimental data, from Westinghouse Д, О from [Ш]. V from , □ from ; • from  A from , and ■ from ), -----calculated from Teichmann et al’s model  and---calculated from Dullni’s model .
Experimental measurements show that the total arc voltage of a 40kA rms, columnar vacuum arc moving between spiral (TMF) contacts is 100V-200V . Approximately 40% of the total arc power is dissipated in each contact. This corresponds to an equivalent anode fall voltage drop (equivalent particle energy) of the order of 40V. Teichmann et al. have further developed this model  by including the momentum loss from neutral metal vapor leaving the arc column by diffusion. The arc experiences a permanent loss of momentum, FN:
Where TN is the neutral vapor flux out of the plasma column in units of atoms.s"1 and /% is the corresponding atomic mass. (It is assumed that the mass loss is balanced by a corresponding evaporation rate of contact material, F(J. The energy balance equation solved simultaneously with the momentum balance equation (Lorentz force = momentum loss rate) yields a relation for the arc velocity, which is then solved numerically:
Here, у is the total current density, hev is the enthalpy of evaporation, bT is the normalized B-field (BT* / i » 5 pT/A), and L„ is the arc length. The result provides a good agreement between experimental values and theory assuming a realistic equivalent voltage drop Ueq for the contact heating term of 40V. They conclude that the propagation of columnar vacuum arcs between spiral contacts is dominated by neutral vapor loss from the arc column. As can be seen from Figure 3.27, this model agrees quite well with experimental data.
Dullni et al.  have developed their model further by including in the total energy balance an evaporation term:
where a is some fraction of the total energy given by the total arc voltage (in the range 100V-150V) times the current, i, flowing through the arc column. They also assume that in equilibrium:
They then obtained a new expression for varc:
where L(, is the arc length (or contact gap). This equation is shown in Figure 3.28 for L(, =8mm and for j= 1.5 x 10s Am-2. They then determine that for arcs with currents greater than a given value and for La greater than a few millimeters, the number of revolutions N around the periphery of a spiral contact, diameter D, can be given by:
where Atarc is the time during which the columnar arc exists and the contacts have a large enough gap [114,115]. Comparison of their model with experimental data is shown in Figure 3.29. While there is a lot of scatter in the experimental data, the model does seem to fit, to some extent, w'ith the maximum value of N for a given contact diameter. It also shows that at lower currents when the arc is not necessarily in the full columnar mode, it will not move as quickly. They conclude that the maximum rms current imax that could be interrupted by a given spiral contact with a diameter D is:
FIGURE 3.28 The speed of the columnar vacuum arc between spiral, TMF contacts for a contact gap of
8mm and for a current density of 1.5 x 10s A.nr- (-----calculated from Equation (3.20)  and I----1
experimental data .
FIGURE 3.29 The number of rotations of a high current, columnar vacuum arc between spiral, TMF, vacuum interrupter, contacts opening at 1.5 ms4 and a 50 Hz rms current, (1. Д 40mm contact diameter, 2. О 62mm contact diameter and 3. □ 82mm contact diameter)  and (• 68mm contact diameter and ■ 90mm contact diameter) .
Their data as well as my own data for imax as a function of contact diameter is given in Figure 3.30. The relationship given in Equation (3.22) is close to what might be an intuitive expectation for a columnar vacuum arc traveling around the periphery of a TMF contact: i.e., the imax w'ould depend upon the contact’s circumference лО. Looking at the data given in Figure 3.30:
FIGURE 3.30 An example for two vacuum interrupter designs of the interruption ability of TMF contacts as a function of contact diameter for three-distribution circuit, voltage values (Д 12kV, О 24kV and □ 36kV ) and (A 12kV, • 24kV [Eaton Corporation]).
The scatter in the data is such that over the current range shown imax could be proportional to either D or D6/5. It is interesting to note that there is also a strong dependence of imax on the circuit’s system voltage, Us. One example of such dependence over a system voltage range of lkV to 27kV is shown in Figure 3.31. Here the empirical relationship is:
For the columnar arc to rotate around the periphery of the spiral TMF contacts the arc roots have to cross the slots between one spiral arm and the next. Schulman et al.  show that rotating one spiral contact with respect to the other one assists the column arc’s transit across the slots. Models of the columnar arc motion [113, 117] show that the plasma plume from the anode that precedes the arc motion (See Figure 2.58) can easily cross the slot between the spiral arms.
I will discuss the interruption of the vacuum arc in Chapter 4 in this volume. In Chapters 5 and 6 in this volume, I will discuss the effect of Us on the voltage that appears across the vacuum interrupter’s open contacts when interrupting high fault currents. Care must be taken when interpreting Figures 3.30 and 3.31. It does show an interesting correlation between two sets of experimental data and a model of the arc motion in determining the interruption ability of a vacuum interrupter with a TMF contact.
However, the interruption ability of a given vacuum interrupter design does not solely depend upon the contact structure. It is also dependent upon the exact composition of the contact material and the overall internal design of the vacuum interrupter. Thus, the two data sets shown in Figure 3.30 should not be assumed to be the absolute limit of interruption for all vacuum interrupters with the contact diameters given there. Figure 3.32 shows a sequence of photographs of a 30kA rms columnar vacuum arc between 64mm diameter spiral contacts. Here the arc velocity is about 320m. s_l, which is about what you would expect from Figure 3.27. The break-up of the arc column just before current zero is shown in Figure 3.33. At 1ms before the current zero the arc column shows
FIGURE 3.31 An example of the interruption ability of a TMF contact (62mm diameter) as a function of the system voltage.
FIGURE 3.32 The columnar vacuum arc between 62mm diameter, spiral contacts with a circuit current of 30kA (rms).
FIGURE 3.33 The transition from the moving columnar vacuum arc on spiral contacts to the diffuse vacuum arc as the circuit current approaches zero.
that it is breaking up and cathode spots can be seen spreading across the cathode. The decay of the anode spot continues until 0.5ms before current zero after which it is no longer visible.
In Section 2.4 in this volume, I have already presented an account of the “Appearance Diagram” development (Figure 2.45) for butt contacts opening with an ac current and the formation of the columnar vacuum arc between them. Schulman [114, 115] has studied the appearance of the vacuum arc between opening spiral contacts using a similar experimental technique and has shown how complex it can be. His “Appearance Diagrams” for contacts opening on the rise of an ac current wave and at the peak of the ac current wave are shown in Figure 3.34 and Figure 3.35, respectively. The interaction of the columnar vacuum arc with the spiral contacts is quite complex. In each diagram, two dashed curves of gap vs. current are plotted to show the low- and high-current envelopes of the gap-current curves from which the diagrams are made. The arrows show the directions of the changing gap and current for which each diagram is valid. The solid lines indicate approximate boundaries between arc modes. There are no observable changes in the diagrams over the ranges of average contact opening speed of 1.6 ms-1 to 2.1 ms-1.1 will describe these arcing modes using the terminology presented in Section 2.4 in this volume.
Figures 3.34 and 3.35 have some similarities. Firstly, two parallel columns form before the transition to a single column. Perhaps this indicates the formation and rupture of two molten metal bridges and the formation of parallel bridge column arcs. When the second column does not form at contact separation, it can appear on another spiral petal before the gap reaches ~lmm. If not, it can form at a 1 to 2mm gap by the first column splitting at a spiral slot. Except in the case of splitting, both the initial parallel columnar arcs are in the central contact region with one of their arc roots anchored at the edge of a slot.
The parallel columns can be either diffuse columns or constricted columns, depending on whether the separation current is below or above ~15kA. As the gap contact increases, there is a short transition (usually less than 0.14 ms) from two columns to a single running plasma jet column for instantaneous currents above ~20kA. The instantaneous gap at this point depends on current and the separation delay, which, for a given current, falls within a 1 to 1.5mm wide transition region.
FIGURE 3.34 Columnar arc appearance diagram between spiral TMF, spiral contacts for an opening speed 1.6 ms-1, opening delays of 0.48-2.3 ms into the current half cycle and final contact gaps of 4-8mm .
FIGURE 3.35 Columnar arc appearance diagram between spiral TMF, spiral contacts for an opening speed 2.0 ms-1, opening delays of 2.4-4.4 ms into the current half cycle and final contact gaps of 7-8mm .
The threshold gap for formation of the single jet column approaches a range of 3 to 4mm for both diagrams at high currents. Once the single jet column forms, it quickly moves outward and begins running on the spiral arms along the periphery of the contacts. As the current decreases, the arc enters the break-up stage as it passes over the spiral slots. Anode footprints  are still present throughout the break-up stage. The final mode of fully diffuse arcing (no anode involvement seen in Figure 3.33) at the end of the half-cycle is indicated in the region at the top left of the diagrams, corresponding to the current approaching zero at maximum gap.
The differences in the arc behavior shown in Figures 3.34 and 3.35 result from the initiation and maintenance of the columnar vacuum arc’s motion. In these experiments, when the contacts part early in the current half cycle, the running arcs make from 2.5 to 5 vigorous rotations (i.e., a speed between 150 and 300 ms'1) along the periphery of the contacts before going diffuse. They also rarely become anchored long enough to develop intense erosion at the arc roots. Above ~40kA, the transition to single arc motion depends only on gap, with a threshold of 3.6 ± 0.8mm. At a gap of 8mm, the running column transforms to a diffuse arc as the ac current drops to zero without sticking or breaking up. When the contacts open close to the peak current, there is a marked effect on the motion of the columnar vacuum arc. At the current peak, the initial stationary arc results in copious melting and vapor production at the arc roots. This results in a longer contact gap before the arc begins to run around the spiral contact structure. Once the arc does move, it has a lower speed. There is also a greater tendency for the arc roots to stick briefly at the spiral tips. Sometimes the arc splits into two columns at the spiral tips for contact gaps greater than 4mm. The vacuum arc still goes fully diffuse before the current zero. The effect on interruption performance of a vacuum interrupter when it opens at the maximum of a high ac current will be discussed in Section 6.3.4 in this volume.
One obvious design criterion when applying this type of contact structure is that a minimum contact gap is required before a vigorous motion of the columnar arc is achieved. Schulman  has studied the effect of the interaction of columnar vacuum arcs with spiral contacts and small contact gaps (<3mm). For the range of currents investigated (7.7kA peak to 36kA peak), the appearance diagram shown in Figure 3.36 shows that the columnar arcs, if they move at all, only move a minimum distance of one half of the contacts perimeter. He observes that one or two bridge column
FIGURE 3.36 (a) Ranges of peak current for observed appearance of various arcing modes with a full gap of 2mm and a single, high current, vacuum arc column, (b) Ranges of peak current for observed appearance of various arcing modes with a full gap of 2mm and two parallel, high current, vacuum arc columns .
arcs form on contact separation and then become anchored at nearby spiral slots. If only one column forms initially, a second column will sometimes appear and stick at another slot before the gap reaches about 1mm. In other instances, part of the arc will expand across the slot, split off, and move away from the original column to the next slot. His results show that for contact gaps up to 3mm the spiral contacts interact with the arc essentially as butt-type contacts, and the spiral petals do not induce the column instability required for the arc to maintain motion over the slots. When the current is high enough, there is intense erosion at the arc roots. Thus, the conclusion from these experiments is that when applying a TMF contact design, a contact gap of at least 4mm is required and 6mm is preferable.
One advantage of the spiral TMF design is that the contacts are structured such that the last point of contact and hence the point of arc initiation as they open is towards the center of the contacts. Thus, the initial bridge column and the period of little or no arc motion when the contacts are close is away from the periphery of the contact where the arc will eventually run. Once the arc has moved to the periphery of the contact and begins to run around it, the region of arc initiation will have a chance to cool down and evaporation of metal vapor into the contact gap from that region will cease.
The arc voltage for the columnar vacuum arc between spiral contacts has some distinctive features that are illustrated in Figure 3.37. Schulman  correlates the arc voltage with the arc appearance at different stages of the contact opening sequence. Thus, he is able to correlate the arc voltage characteristics to the modes of arc behavior that he observed. It is interesting to note that while the arc is in motion, the vacuum arc voltage is generally about 100V. I would expect that the sooner the columnar vacuum arc breaks up and transitions to the diffuse mode, the better the high current interruption performance of a vacuum interrupter would be. Liu et al.  have shown that the residual axial magnetic field from the spiral contacts plays a role in this transition. Spiral contacts similar to those shown in Figure 3.22(a) with the slots continuing close to the contacts’ center experience the transition to the diffuse mode sooner than the slot structure shown in Figure 3.22(b). Li et al.  have studied the high current interruption performance of TMF contacts with two,
FIGURE 3.37 Arc voltage and current characteristics for an opening TMF contact with a 6mm full contact gap, opening with a speed of - 1.5 ms~' and a peak current of 35kA .
three, four, five, and six spiral arms. Their experiment used two interruption circuits; 36kV/40kA and 17.5kV/63kA. They conclude that the four-arm spiral contact appears to be the best compromise between mechanical robustness and current interruption ability.
Paulus  has investigated the motion of the columnar arc with the contrate cup TMF contact structure shown in Figures 3.20(c) and 3.21(b). In his experiments he shows that the columnar arc does not run on the cup’s rim for contact gaps < 2mm. He also observes that, after the initial arc ignition, parallel, multiple constricted columnar arcs can occasionally occur. Again, these eventually merge into one columnar arc that proceeds to run intermittently or stay motionless on the cup’s rim. He observes running speeds of up to 200ms~‘, but the typical speed is 20-60ms"'. Wolf et al.  also show the initial parallel arc columns. They also show that the high-current arc can be both diffuse column as well as constricted column. This is quite different from the appearance of the arc with the spiral contacts, where once the constricted column forms, it alone moves across the contact surfaces. Figure 3.38 shows the constricted column arc
FIGURE 3.38 Column arc speed on a contrate cup TMF design as a function of circuit current .
speed on a contrate cup TMF design as a function of circuit currents ranging from 25kA to 35kA presented by Wolf et al. . The values agree with those given by Paulus and are much slower than those seen for the columnar vacuum arcs motion on spiral TMF contacts: See, for example, Figure 3.27. Their 3-D simulation model for the cup and spiral contacts showed that the Lorentz force on the arc column explains, to some extent, the difference in the arc rotation speeds. This contact structure has the advantage of a continuous cap on top of the cup’s slots. Thus, the arc roots do not have to jump a gap as they do with the spiral structure. It does, however, have the disadvantage that the region of arc initiation and dwell time as the contacts part is also on this cap. This melted arc ignition region with its high metal evaporation rate will be exposed to the running arc and will be unable to cool down as effectively as will the arc initiation region for the spiral contact. Janiszewski et al.  in a photographic study show that more than one columnar vacuum arc moving in the Amperian direction can exist on the cup’s rim for currents in the range 7.2kA to 24kA. They also show that occasionally the anode attachment can form at the base of the cup. When this happens intense anode melting occurs resulting in the evaporation of the Cu from which the cup is manufactured. This in turn can limit the contact’s ability to interrupt the ac current at current zero. Another possible consequence of this intense stationary anode is that the molten metal inside the cup can flow into the slots cut into its side walls thereby reducing the effect of the TMF.