My father built this thing that is basically a big capacitor that charges up then when you discharge the cap it burns away several small particles of metal. The Gear is sitting in diesel fuel that immediately cools the surface of the metal and carries the metal particles burnt away out and out of the way.(In several of the pictures you can see a black cloud in the fuel)
The arc only happens VERY close to the surface and can't happen when the copper rod is actually touching the gear. The mechanism you see is made out of a DVD player motor and hooked to a little controller that reverses and drives the motor.
When the voltage is high (capacitor has built up a charge) it slowly turns the copper rod down into the metal you want to burn a hole in. When the arc jumps (or the rod comes in contact with the metal) the voltage drops low, so the controller reverses the motor and pulls it back.
Basically the thing works very fast with its "up-down-up-down-up-down-up-down" and slowly burns a hole through... whatever... using electricity. When it is working is has a slight wurring noise and the satisfactory sound of the arc super heating the fuel. When running smoothly it almost sounds about like bacon fat frying.
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