890 THE BELL SYSTEM TECHNICAL JOUKNAL, JULY 1954 



separation means a longer arc duration, pi-oviding a larger energy in- 

 put and hence increased evaporation. This means that the mo^'ing part 

 has to tra\'el further before the arc is extinguished thus further increasing 

 the arc din'ation. 



C. Bridging 



Early experiments indicated a variation in arc duration greater than 

 that which could be explained on the basis of variation of initiation sepa- 

 ration and l)urn-off alone. It was realized that there was a third phenome- 

 non involved. This phenomenon in which metal filaments form and 

 extinguish the arc prematurely will be called bridging. As a demonstra- 

 tion of bridging the two surfaces to be welded were spaced 0.002 inches 

 apart and voltage applied between them. The resultant arc produced a 

 molten filament between them and a weld was formed.* With the ma- 

 terials used the welds produced were somewhat porous and not too 

 strong but tests were much too fragmentary to properly evaluate this 

 process. 



Electrostatic forces are too small to account for the bridging phenome- 

 non. A speculative explanation on the basis of magnetic forces may be 

 attempted. Let us first examine a luiiform liquid filament carrying a 

 current /. Application of the electromagnetic stress tensor demonstrates 

 the presence of radially compressive pressures equal to: 



t2 2 



p = !?4;, (1) 



STT-^a" 



where 



/ equals total current carried by filament. 

 r eciuals radial distance from center of filament. 

 Mo equals permeability of filament material. 

 a equals radius of filament. 



In the presence of these compressive stresses the filament will tend to 

 elongate. Consider now the two surfaces of the parts to be welded covered 

 with a thin film of molten material. If due to the turbulence caused by 

 the arc a small filament forms on one surface it may tend to elongate in 

 the presence of magnetic forces and bridge the gap between the surfaces. 

 A detailed dynamical analysis of the formation and stability of these 

 metal bridges is quite difficult. The following treatment is a very rough 



* This may actually be an alternate method of welding with the advantage of 

 offering excellent dimensional control. 



