I described the propeller governor, and the way it lets more oil into the hub if the propeller is going too slowly and cuts off supply if the propeller is going too fast. You now know that if the propeller isn't going fast enough, and the governor allows too much oil pressure into the hub, that the beta reverse valve will keep blade angle above eleven degrees. And you know that if the beta reverse valve fails, and the blade angle drops below nine degrees, that the beta backup valve will close to keep the blade angle no lower than about nine degrees. Pilots always ask of every system, "what if it fails?"
If the pilot valve in the governor were to fail open in cruise, the beta system would prevent the blades from going into beta, but the oil pressure would still hold a propeller in the eleven degree blade angle position, even though it was turning too fast. If the propeller speed continued to increase the overspeed could destroy the propeller, and produce vibrations (or shed propeller blades!) that damaged the airframe. One governor is not enough to guard against this highly undesirable situation, so there is also an overspeed governor.
Normally, the valve to the overspeed governor remains closed, and oil bypasses it going straight from the primary governor to the propeller dome. But the overspeed governor is very similar to the primary governor, with flyweights and a pilot valve, but for the overspeed governor, the flyweights will open its pilot valve if the propeller speed is too high, defined as 101.5% Np. (That is, the propeller is spinning at a rate that is 101.5 per cent of an arbitrary number that doesn't mean anything). The open valve dumps oil pressure through the overspeed governor back to the sump, bypassing the hub and allowing the propeller blades to return to a coarser pitch, slowing their rotation.
A test switch for the overspeed governor temporarily resets the overspeed governor limit to 70% Np. The pilot tests both overspeed governors at once by pressing and holding the test switch with a high rpm selected, and the power at idle, then advancing both power levers to a position that supplies enough torque to achieve full rpm. The Np should not rise above 70%.
Think that's enough? Yeah, right. If the backup system doesn't have a backup system it's not much of a backup system, is it? The overspeed governor is backed up by the NF governor which slows the propeller by cutting off the fuel supply if Np exceeds the selected value by more than 6%. As max Np is 96% (I warned you that 100% was an arbitrary, meaningless number), that means that with the propeller levers full forward, the NF governor takes action at 102% Np. Interestingly, during reverse thrust operations, the NF governor limit is reset to 5% below the selected value--always 96% in reverse--so that the NF governor keeps Np down to 91%. This ensures that the primary governor never cuts off the oil supply, leaving control of the blade angle to the beta valve.
And if all that stuff fails, the pilot (not one of the pilot valves, the woman in the seat) can pull a lever to shut off the fuel to the engine. When inflight engine shutdown emergency checklist is complete, she'll turn to her co-pilot, roll her eyes and say, "It's your turn to tell the passengers they're not going to where they thought they were going." I hate doing those PAs.