.... Nothing will happen that's what they are built for.
And as simple as that: that's not true!
fact is, a governor is very well capable to be adjusted to arount 4000-4500 rpm and still remain intakt IF NO SUDDEN LOAD CHANGE hits it.
that can already break it apart...
anyways, loosening the screw effectively bypasses the governor;
it can ask to set the rpms, but it'll be ignored.
The engine can rev up to ~5500 rpm, worst case that's 30% more than the governors intended rpm band...
And here's the thing...
I don't say it'll fail immediately;
with little to no sudden load changes I see no reason for it to fail either...
but if it fails (and a bump in the road can do that at speed)
it's not just the governor that'll be destroyed..
from about nothing (small dents in the oil sump)
over minor issues (dent's in the cylinderbore and or on the piston)
up to total loss (metal shrapnel locking the piston, cracking the con rod which then shreds the crank case)
about anything could happen!
The question now is:
Does it make sense to be afraid of 15mins of work to remove it completely,
just to risk a total loss?
it's up to you; but a governor is a plastic gear with metal weights, running on a bushing with lousy lubrication driven by a hardened steel gear..and it's made to run BELOW 4k rpm at constant speeds.
seeing what it costs to buy a gx340 and what it takes to remove the governor instead of just bypassing it;
to me the answer is very simple...
either let it do it's work, or remove it;
nothing in between!
'sid
PS Metal Rott has a different opinion, fair enough... but he's the only one
and quit having a pissing match (couldn't find that emoticon) about governors.
