PKHCrSSlVK WKLDIXC 891 



model which will f^how that coiisidcratioii of the maj;iietic forces does 

 yield an explanation \-erifyinji; tlie order of mafj;nitude of the bridf>;in}2; 

 ol)ser\('d ill experiments. 



The model simulates th(> I)ridi2;iiijj; phenomenon by the translational 

 motion of a small cylindrical filament across the f>;ap between the two 

 surfaces. It is argued that the magnetic energy originally stored in the 

 arc should be comparable to the kinetic energy of the mo\ing filament. 



The magnetic energy n^siding within a small cylindi'ical filament of 

 diameter d, length (, carrying a current / is: 



IGtt 



(2) 



If such a filament moves at constant velocity through a distance /' in 

 time / its kinetic energy will be 



8, = XiM^ = -^ , (3) 



wh(>r(> p is the density of the filament material. If the two energies are 

 comparable then the bridging time is roughly. 



( ~ ^'- 4/i (4) 



If we assume the following as reasonable numl)ers: 



/ = 1,000 amperes, 

 ( = 3 mils, 

 d - 20 mils, 

 p = 10 gm cm^ 



then equation (4) gives a transition time of 15 X 10~^ seconds. This 

 figure is of the same order of magnitude as bridging times observed 

 during experiments. 



The rough model used here is only one stage more refined than purely 

 dimensional analysis but seems to give reasonable agreement with ex- 

 periments. Of importance is the design guide offered by equation (4). 

 By means of proper choice of the welding circuit it is possible to select 

 an arbitrary current versus time relationship. In order to avoid bridging 

 effects, which are, of course, very erratic, the bridging time / should be 

 maximized. By ecjuation (4) the ratio of current to separation should, 

 therefore, be minimized. Stated in words this means that if large cur- 

 rents are necessary for the process (this will be shown to be desiiable 



