A GOVERNOR FOR TKLEl'HOXE DIALS 1297 



acts through the center of gravity of the weights radially from the turn- 

 ing center of the governor shaft. The torciue force, F, is applied on the 

 weights by the drive-bar arms. These forces are opposed by the spring 

 force, Fs . A stud-to-case force, F„ , and a frictional component of this 

 force, fiFn , act on the weights when the friction studs are in contact 

 with the case. In deriving the eciuation of motion for speeds in excess of 

 the critical velocity the following symbols will be used as noted on Fig. 4. 

 F — Force applied by tonjue on governor weights 

 F„ ■ — ■ Normal force of case acting on studs 

 Fs — Force exerted by spring when studs touch case 

 Fm — Centrifugal force acting at center of gravity of each 

 weight 

 ju ■ — ■ Coefficient of friction 



7o — Moment of inertia of the governor about center shaft 

 u — Angular velocity of governor 

 m ■ — Critical angular velocity at which studs just touch the 



case 

 m — Mass of each weight 



ro ■ — Radius to the center of gravity of each weight 

 r — Radius of governor case 

 a — Stud angle 

 Neg. Rotation — Rundowai of governor 



From the schematic. Fig. 4, taking moments about B we have 



FJ) - F,h + nF„c - FJ-^ F = (1) 



collecting terms 



b{F^ - Fs) - Fnid - Mc) + Fj = 



b{F^ - Fs) + Fj (2) 



F = 



(d — ixc) 



The driving torque on the governor is G^ = 2Fe; the retarding torciue, 

 2nF„r. The difference between the driving torque and the retarding 

 torcjue is as follows: 



ho: = G - 2nFnr (3) 



where h = Moment of inertia of the governor about the shaft center 



CO = Angular acceleration about shaft center 

 equating 



F^ = ^^_^ (4) 



2nr 



