Generac 4000xl runs a few minutes then acts like it's seizing up

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It has run too lean for a while and the piston and rings are damaged. The piston is probably picked up and grows with heat enough to partially seize when hot, frees off when it cools down. It needs a new piston and rings set. If you are lucky the bore is not too badly damaged and may go again with a new piston. When/if you get it fixed make the mixture (air:fuel) richer and check you have enough oil in the fuel.

check that the over load switch is not seized of course then replace

its possible the overspeed is set to sensitive. or your rpm are to high. these are preset in the factory as a safety, check your manual to ensure your rpm speed is in the pre set area. generators will do this under load when you have a big load on them or take a load off. the governor will some times over compensate causing it to trip on overspeed.

if the gerator runs pretty smooth up until then, i would suggest checking/changing your oil as the low oil level switch is picking up on a slight change in the oil level (easier to detect when oil is hot), if it start to give hesitation or reduction of power, check the choke, make sure its off.

Check for low oil or over temp.

You have a problem with the carb float valve. It is no longer sealing causing fuel to continue to flow into the float bowl after it is full. It may be dirty, out of adjustment or just need to be replaced because old and worn out.

check to see if somthing is blocking the movement of the govenor linkage

check the oil sensor circuit. I know when I take out or short out the sensor ckt on mine, it'll keep on running. low oil isn't good for any motor.

there is some problem in your AMF/ATS pannel