Can I buy or make an adapter to connect 2 generators together to get more amps for my 220 Arc Welder?
No way. The two generators won't generate the same voltage, and even more importantly will be out of phase with each other. The result will be they'll spend all their energy fighting each other. Hopefully this would throw a breaker, but if not it could easily cause a fire.
Of course it's possible! We went to the moon nearly 50 years ago, merging 2 generators is simple.
You will need to get yourself 2 sets of full-wave bridge rectifiers to turn the generator output into DC. And a rather large capacitor to smooth it out. Connect the combined output of the generators to either a large DC-AC inverter or a similarly large DC motor coupled to an AC motor (effectively an analog inverter). The output will be AC power of somewhat less capacity than the sum of both generators. This setup is not all that efficient, you will be lucky to get a 50% increase in capacity for your efforts.
Also of course: the necessary semiconductors, commercial high-capacity inverters and/or motors and associated framing are all going to cost much, much more than buying a new generator of the capacity you need.
If it's something you don't need weekly, call the local rental places. You can get rather large generators for not that large an amount of money.
Obviously, the phases would be out of sync (unless by some miracle you started the engines with perfect timing. So you need a kind of frequency changer or syncronizer or phase corrector.
This apparatus us used for combining power from multiple generators (solar, wind, hydro, etc.) into a "smart" grid. I'm not aware of any hand-held, home-user type of equipment. That sort of equipment is typically mounted on the wall. Absence of evidence is not proof of non-existence, but I generally don't think that such a device would be easy to sell, so I couldn't imagine anyone investing in making such a product. This might be a real DIY build. And I would suggest asking for help from the electrical engineering SE.
As a side note, phase sequence checkers (or synchronoscopes) can be hand held. And I feel confident that you could retrofit something from an old solar panel type of system.
edit- often synchronizing is accomplished through synchronizing the motors. Source: http://ieeecss.org/sites/ieeecss.org/files/documents/IoCT-Part1-06RESG.pdf
edit 2- just a little more relevant reading: Doubly-fed electric machine
edit3- I think one answer to this, is that the electricity from both generators could be converted to DC then back into AC; but the easier answer (for me anyway) would be to mechanically synchronize two generator-motors. Mounting two generator motors on/near one gas-motor, then using a phase checker or volt-meter to calibrate the generator-motors seems pretty straight forward (120V + 120V should be 240V). Belts which slip could not be used between them. Chains would be necessary to keep the positions of the generator-motors timed correctly. A belt could be used to drive generator-motor 1; which is linked with a chain to generator motor 2. edit 3.1- This idea would be like attaching two alternators to one gas-engine. The alternators would need to be mechanically synchronized with a voltmeter.
Linking up generators is a practice done all the time. The fear spoken of, has been overcame. The key things required before the two generators are physically connected to provide the power as one larger double size generator (ignoring losses) are matching of voltage level and phase.
Generator have internal control feed back. When the power tools consume at a steady rate, the generator's engine runs at steady rpm. When the tools demand more power, this demand results in higher magnetic force causing the engine to be loaded and therefore slows down. The generator internal control feedback sense this condition and rev up the engine to recondition the power phase cycle.
Paralleling two or more generator (easier with like kind and capability) requires the generator to play well together. No two engine will run exactly the same, hence the worry of one running ahead of the other. The worry however, are already designed into the generator themselves.
Consider generator A and generator B which have been phase-aligned and parallel connected through a resistive connection. When A's phases are creeping faster than B's phases, at the leading edge and for the time until B's leading edge, A carries the total load and engine A revs up. At 60Hz, that attempt will be for approximately 4 mS (quarter lambda). At the trailing edge, likewise, B will be carrying the load and will react by reving up. During this 1/4 period, A senses that it has no load and will coast its engine.
Case 1: Primary and secondary generator setup (Straight connection w/o governor) Having analyzed that, the resistive connection can be greatly reduced by using a low resistance cables. This forces the two generators to theoretically experience the same identical output. Here is the electrical concern. As A becomes "lazy" and B having to pickup the load, the output maintained by B, A will not know any better and will continue to coast until B can not handle the load by itself and the output start to drop. At which time, A will sense that condition and will rev up its engine. A and B will continue to oscillate with B - in this case - caries the load most of the time and A only join in when B is overworked. The case the B becoming lazy is the same.
Case 2: Load equalizing Adding a governor circuit which senses the load being carries by each generator and sending the feedback to the appropriate engine will load-level the generators.