Question

104 AUTOMATIC CONTROL ENGINEERING 2.44 to Fig. 23,44 is shown a speed sensing device in which the position to proportional to the angulur velocity of the gear pump The rate of flower through the pump e proportional to the speed of rotation, y = 0, s. Because of the fixed orifice, the pressure po proportional to the rate of flows. S4. The force balance of the bellow-spring combination is = Ar where is the spring rate and in the area of the bellows. Determine the equation relating the position to the speed Governor spring 5 Hellows Fired orifice P Gear pump Figure P3:44

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Answer 1

DC (displacement of spring). Governo sipsing Bellosos Р Gear Pump fixed Orifice The rate of flow į trought the Pimp is Poopornal to rrotatien (ov), 4 = Con 0 (2) Due to fixed osifice Pressure p is propost- -ional to rate of How (2), P= C₂ x Q From eqn. (1) P = Cex (Gxn) Fs = kill The force balance for bellow - Spring Combination is, F PE & Feping Bellow ka P.R

Sipning constant of bellow, from equ k.x = C₂ x (C,xn). A so displacement G. C₂ A .n k ( C₂ C3 C3 An K Black diagostem for Huis Boblem is as below, a} a. Ghat | P/ P=622 (notational (diaphae speed So here tansfer Fincation IS, nas) 9. C2 (A) G. Ca (BK). m(s)