I'm not too familiar withyour particular gen set but I know a little about generators and a lot about diesels since I used to design them as an engineer.
First, an opinion as to where to start. I assume you are not overloading the engine when running on 240 or 120.
There should never be a swing of 5Hz even if completly unloaded or loaded.
Therefore, there are two avenue to look at in your diagnosis. One is the engine governing system needs adjustment or repair as it cannot maintain the speed when load is applied.
The second is the frequency meter and its transducer and input are messed up or something is wrong with the winding and switching feeding the transducer. Let's explore each possibility.
On the engine side there might be a low idle screw that you can turn up enough to raise and hold the speed at 60 hz without the throttle cable connected. This is the same adjustment used on any gen set that does not have a separate throttle cable. I adjust my low idle for 55Hz and high idle for 65 Hz so the throttle cable only adjust from 55 to 65 Hz. This protects the voltage regulator on the generator which does not like low speed. as long as you have this low idle adjustment screw you do have to fix the throttle cable before proceeding to diagnose the operational problem.
Running at 60 hz load the engine with a similar load in both 120 and 240 and note, by ear, the speed drop. It will be the same for both loads. If the Hz drops more than about 2 to 2-1/2 from high idle no load to full load then the govenor droop function needs adjusted. You will likely need a device or devices that can apply full load to adjust the droop but it probably can be adjusted by yourself if you can find it in the manual. Droop will set the rpm or Hz spread from full load to no load. Note that some droop is needed for speed stability. Again 2 to 2-1/2 Hz drop should still give very good stability. Instability is called hunting and this occures if the linkage is sticky or droop is adjusted too tight. Hunting is charactorized by the unit never settling down to a constant speed under constant load. The frequency meter keeps oscilating a small amount back and forth back and forth. Note a wandering voltage regulator can cause hunting which resembles droop but in that case the volt meter and the frquency meter are swinging.
There is also a max fuel adjustment and that needs to be checked too. Once you learn the procedures it is easy and fun to tune it up. One of my generators had the fuel screws and droop so out of whack that when I adjusted the droop the unit would slow down and die as it could not get enough fuel. Adjustments will fix that. I am making the assumption that your unit is running on all cylinders well and the exhust note sounds evenand no excess smoke and it starts up well when cranked. The governor fuel settings consist of: Shutdown solenoid plunger position, Droop, Max fuel, High Idle, Low Idle. Each setting has a separate screw. The trick is to follow the manual in sequence as some settings effect the others. Usually all you need is a full load, the frequency meter, and small hand tools, and of course, the manual.
The other side of the equation is the frequency meter or where it is getting its information from. The frequency meter gets a signal from the frequency transducer which gets its input from one of the 6 windings in the generator. Since the voltage reconnection switch that is adjusted for 120 and 240 is moved there may be a problem with which winding is used or something causing an error on the feed to the transducer when the switch is repositioned. One of the electrical guys on here will have to run that down for you. I'm an engine guy!
If you start it and see 60Hz unloaded stop it and then move the switch to the other voltage start it unloaded, same throttle position, and see 55Hz but the gen speed sounds the same to the ear then the problem is the frequency gage system and may be pointing at a bigger problem inside the generator. What I'm saying here is that the engine will maintain the same speed at a given load or no load regardless of the generator switch position. Therefore, your first tests are to confirm it is either the engine or the generator causing the issue.
Hope these ideas help.
