There's really no interaction between the two welders at all (assuming that the outputs of the welding machines are galvanically isolated). No current flows in the part of the workpiece between the two welders, so the workpiece behaves the same way that two completely separate pieces of metal would behave.
Assume both are configured for 10VDC, 10A. When they start welding, I see the power sources connected in parallel, 10VDC, so, total voltage seen by both is 10V. Amps, on the other hand, are added, so, 20A total (split across each welder, 10A? Does it work like that?)
That's preeeeeeetty much correct.
If both machines are set to 10 V, 10 A, then:
- The arc on the left will have a voltage of 10 V and will conduct 10 A.
- The part of the workpiece on the left will conduct 10 A.
- The arc on the right will have a voltage of 10 V and will conduct 10 A.
- The part of the workpiece on the right will conduct 10 A.
(Actually, either the voltage or the current will probably drop below the set value, but I don't know which or how much. Throughout the rest of this answer, I'm going to make the (false) simplifying assumption that each arc behaves like a 1 ohm resistor.)
You can add up these two currents and conclude that there's a total of 20 A going from the two electrodes through the workpiece into the two return connections. However, this number isn't particularly meaningful, since the two 10 A currents are flowing in completely separate parts of the workpiece.
Now assume Left adjusts to 20VDC, and 20A. The amps climbs to 30 across... each? What's the total voltage across both?
If the left machine is set to 20 V, 20 A, and the right machine is set to 10 V, 10 A, then:
- The arc on the left will have a voltage of 20 V and will conduct 20 A.
- The part of the workpiece on the left will conduct 20 A.
- The arc on the right will have a voltage of 10 V and will conduct 10 A.
- The part of the workpiece on the right will conduct 10 A.
It's as simple as that. (Again, I'm making the almost-certainly-false simplifying assumption that each arc acts like a 1 ohm resistor.)
The "total voltage across both" is a physically meaningless concept. It is possible to type "20 + 10" into a calculator and press the = key, and the calculator will give you a number, but that number will be meaningless.
(Voltage is a little bit like height. If there were 10 airplanes all flying 35,000 feet above the ground, would you say that they have a total height of 350,000 feet? Probably not, because "total height" isn't really a meaningful concept here.)
Now assume Left reverts back to 10VDC/10A, but switches to DCEN. Now I see the voltages connected serially, and so the voltages are added (10+10=20VDC), and amps are added I think 1/x = 1/10 + 1/10, or 10A apiece?
I'm not sure where you're getting that 1/x formula from. What will happen is:
- The arc on the left will have a voltage of 10 V (in the opposite direction) and will conduct 10 A (in the opposite direction).
- The part of the workpiece on the left will conduct 10 A (in the opposite direction as the right).
- The arc on the right will have a voltage of 10 V and will conduct 10 A.
- The part of the workpiece on the right will conduct 10 A.
At this point, you could take a voltmeter and connect the red lead to the left electrode and the black lead to the right electrode. There's no practical reason to do that, and the result doesn't tell you anything useful, but in any case, the voltmeter is going to read -20 V. The reason for this is that the left electrode is 10 V below the workpiece, and the workpiece is 10 V below the right electrode, so the left electrode is 20 V below the right electrode.
You could also add the -10 A on the left to the 10 A on the right to get 0 A, but this quantity is totally meaningless, since the reality is that the workpiece has 10 A going through it in one place and another 10 A going through it in another place.
Assume Left changes again to 20VDC/20A, and DCEN. serial voltages added for 30VDC split between them. Amps are distributed similarly, 1/20 + 1/10 = 3/20, or about 6A apiece?
Nope. The situation is analogous:
- The arc on the left will have a voltage of 20 V (in the opposite direction as the right) and will conduct 20 A (in the opposite direction as the right).
- The part of the workpiece on the left will conduct 20 A (in the opposite direction as the right).
- The arc on the right will have a voltage of 10 V and will conduct 10 A.
- The part of the workpiece on the right will conduct 10 A.
Finally, assume Left switches over to AC. How are these calculations made?
Again, it's analogous:
- The arc on the left will have a voltage of 20 V AC and will conduct 20 A AC.
- The part of the workpiece on the left will conduct 20 A AC.
- The arc on the right will have a voltage of 10 V DC and will conduct 10 A DC.
- The part of the workpiece on the right will conduct 10 A DC.
The amps climbs to 30 across
... there would have to be 30 A between the two orange boxes in the diagram \$\endgroup\$