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Is there an adjustable jet on the bottom of your carberator that looks like this?
The metal disk is connected to the gas cap as it should be.
Ok So we know the fuel is not getting blocked off and that you are getting spark after the engine dies, that leaves the carburetor. You are going to need to clean out the carburetor and main jet, hopefully this will fix your hot (lean) running condition.
First turn of your fuel or pinch off the fuel line.
Turn you machine on its snout so that the handles are facing straight up in the air.
On the side of the engine you will see the carburetor float bowl with your main jet in the center. Remove this jet by unscrewing it and gently remove the bowl inspecting to see if there is any debris inside it. Clean the bowl and spray some carb cleaner straight up and into the hole the jet was unscrewed from.
you will also need to clean the jet thoroughly including the little hole not just the big one (see picture) Once everything is clean set the machine back on it's wheels and turn the fuel on allowing fuel to run through into a drip pan for about 10 seconds.
Stand the machine back up and reassemble. This should get you going.
So. I forgot to mention that I already cleaned the carb. Here is the background . . . I have had the blower for three years. The first year it ran great. The second year it ran well, but I had to keep the choke on all the time to get the engine to run right. After some reading, I reasoned that the carb was dirty. I bought a gallon can of "chem dip" carb cleaner. I disassembled the carb (removed all plastic and rubber parts) and submerged the carb in the chem dip for 30 minutes. After removing from the chem-dip, I washed the carb with water and cleaned all the orifaces with compressed air. Then I reassembled the carb, attached it to the motor and restarted the blower to check to see if it would warm up and run with the choke off. I repeated this chem dip process five times before the engine would run with the choke off. I also replaced the gasket between the carb and intake manifold.
How can I tell if the engine is running lean?
A lean running engine will run much hotter then a normal engine. If your muffler is starting to glow that is a good indicator. Also if you remove the spark plug the tip will appear white if the engine is running lean.
In all accounts this does sound like a classic ignition problem. When an ignition coil starts to go bad, it will stop producing spark when it gets hot. After it cools down it will begin to spark. As time goes on it will loose it's ability to create spark all together. Because you are immediately getting spark this is throwing me off.
I still believe that your problem is in the carb. Just because it has been dipped and cleaned does not guarantee that it will function correctly.
Does this engine run smooth when it is running?
You most definitely have a carburation issue. The osculating is the engines governor trying to compensate for the lack of fuel being delivered. Using the choke to smooth out the engine is the same as changing the jets inside the carburetor. By lessening the amount of air being drawn into the carburetor you are increasing the fuel ratio (the amount of fuel does not change, just the air fuel ration) At this point after cleaning your carburetor this many times and as thoroughly as you have I would probably replace it. The only other option is to bring the carb to a shop that has a sonic cleaner. These little machines are what jewelers use to clean jewelery and are extremely effective in cleaning out the hidden orifices in these carburetors. You also have welch plugs in the carburetor that if not sealed properly will allow the low and high speed circuits to cross and mix the two air fuel ratio's at the wrong time.
My professional opinion would be to replace the carb if cost effective.
Just put the new carb on and the blower runs great. The "osscilating from slow to fast" engine speed problem is gone, and now the engine runs smoothly. Also, the engine RPM's were much higher before the carb change, and now they seem much more reasonable.
Thanks again for your help!