I don't see why not.
Thinking about the gear-up from 1500 (engine) to 3600 (generator), I wonder how tall of an overdrive you can get in an automotive transmission? I'm guessing it's not
that much. Or maybe you could manage to turn a transmission around so that 1st gear has the engine practically idling, and what used to be overdrive has it close to redline for the same generator speed?
Or maybe you could just do a single-stage fixed-speed arrangement by sourcing your own two pulleys and a belt. That'd be a lot easier! And it would disconnect the shaft requirements from each other as well. And the mounting requirements.
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For a governor, the cost and complexity depend on how tightly you want to control it. A single-purpose lawnmower engine might simply have a vane in the airflow of the mechanical cooling fan, which acts against a spring to control the throttle. You probably want something better than that! The John Deere 140 that my family had for a LONG time (Kohler 14hp single-cylinder) had flyweights on the camshaft, that acted against a spring. The other end of that spring went to the operator's throttle control.
I'd thought for a while about making a DIY cruise control for my '97 Jeep (Inline 6 with a manual 5-speed) out of the assumed-good actuator from a failed aftermarket cruise control (possibly bad assumption, never tried it) and the tachometer. Never actually did it, but one of my potential uses, allowed by using the tach instead of the speedo, was to be a stationary electric generator as well. (disconnect the rear driveshaft and hook it up to the generator; then use 4-wheel-drive, which would now be front-only, to drive with that arrangement)
Just letting my mind run with that for a while, got me the idea to use an ammeter and/or torque sensor as a feedforward component. (put load cells in either the engine mounts or the generator mounts, to be that torque sensor) The idea being that the rotating mass takes a while to change speed, but that doesn't help at all with long-term trends. So if I can tune it so that the average throttle is well matched to the immediate load, and make that work in real-time, then the actual control loop simply does an offset around that average in response to speed. Should allow for tighter control that way. Probably would have used an 8-bit PIC or AVR running all custom code, to actually do it.
Caveat:
The "immediate load" feedforward component is essentially positive feedback. Too much of that, and the system becomes unstable, especially if the AC load has a net-positive impedance. (it'll just run up to redline or down to idle, and stay there) The speed control loop provides negative feedback, so if that's "stronger", then it can still be okay overall. Several things to tune here, all of which lead to runaway or oscillation if the combination isn't good, so you have to watch very carefully and simulate it in your head, to know what to adjust and how.
Once you get it all right though, it can be amazing! Switching a massive load on and off results in only a volume change from the exhaust, and not a speed change at all...
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I had also thought about the engine speed itself. My 4th gear, in a 5-speed, is 1:1, so I do have an overdrive. That would allow me to run the engine a little bit slower for a 1:1 tailshaft-to-generator connection at 3600rpm, but with a redline of 5k, that speed is also inside of the normal operating range for this engine. (my experience with highway entrance ramps tells me that it's about in the middle of the "power band"
) So...does it actually hurt anything to let it sit at 3600 all day with varying load???