130G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195-t 



or 



G{d - nc) 



ml sin j8 = 



2rn 



where the gravity moment (vil sin (3) must be just ecjual to or smaller 

 than [G(d — pic)]/2riJi to have no chatter occur in the governor. Expres- 

 sing this in terms of the mass of the weight we have the chatter equation 



for the fly-bar governor as 



-^1!^ 



Appendix IV 



DERIVATION OF CHATTER EQUATION FOR DRIVE-BAR TYPE GOVERNOR 



Referring to the schematic, Fig. 4, consider the governor rotating at 

 constant speed o) in the vertical plane. Taking moments about B 



F„J) - Fsb + F, + fxFnC - Fnd - ml sin = 



where m = mass of weight 



/ = distance from C.G. of weight to pivot B 

 (S = operating angle of governor weights 

 Assume that at some angle d the gravity component will be large 

 enough to make the F„ force equal to zero and a condition of equilibrium 

 exists. For this condition 



FJ = 



nFnC = 



and therefore, Fj , the torque component on the weight, must also equal 

 zero. The moment equation becomes 



FJ) = Fsh + ml sin 3 (1) 



Using the equation for centrifugal force 



Fm = mJ^n 



