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//CHAPTER 7 ILLUSRTATION 9 PAGE NO 204
//TITLE:GOVERNORS
//FIGURE 7.3(C)
clc
clear
//===========================================================================================
//INPUT DATA
g=9.81// ACCELERATION DUE TO GRAVITY
PI=3.147
r=.14// DISTANCE BETWEEN THE CENTRE OF PIVOT OF BELL CRANK LEVER AND AXIS OF GOVERNOR SPINDLE IN m
r2=.11// INITIAL RADIUS OF ROTATION IN m
a=.12// LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m
b=.10// LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m
h=.05// SLEEVE LIFT IN m
N2=240// INITIAL SPEED IN rpm
F=30// FRICTIONAL FORCE ACTING IN N
m=5// MASS OF EACH BALL IN Kg
//==========================================
r1=r2+a/b*h// MAX RADIUS OF ROTATION IN m
N1=41*N2/39// MAX SPEED OF ROTATION IN rpm
N=(N1+N2)/2// MEAN SPEED IN rpm
Fc1=m*(2*PI*N1/60)^2*r1// CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N
Fc2=m*(2*PI*N2/60)^2*r2// CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N
c1=r1-r// FROM FIGURE 7.3(C) IN m
a1=(a^2-c1^2)^.5// FROM FIGURE 7.3(C) IN m
b1=(b^2-(h/2)^2)^.5// FROM FIGURE 7.3(C) IN m
c2=r-r2// FROM FIGURE 7.3(C) IN m
a2=a1// FROM FIGURE 7.3(C) IN m
b2=b1// FROM FIGURE 7.3(C) IN m
S1=2*((Fc1*a1)-(m*g*c1))/b1// SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS
S2=2*((Fc2*a2)-(m*g*c2))/b2// SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS
S=(S1-S2)/h// STIFFNESS OF THE SPRING IN N/m
Is=S2/S// INITIAL COMPRESSION OF SPRING IN m
P=S2+(h/2*S)// SPRING FORCE OF MID PORTION IN N
n1=N*((P+F)/P)^.5// SPEED,WHEN THE SLEEVE BEGINS TO MOVE UPWARDS FROM MID POSITION IN rpm
n2=N*((P-F)/P)^.5// SPEED,WHEN THE SLEEVE BEGINS TO MOVE DOWNWARDS FROM MID POSITION IN rpm
A=n1-n2// ALTERATION IN SPEED IN rpm
printf('INTIAL COMPRESSION OF SPRING= %.3f cm\n ALTERATION IN SPEED = %.3f rpm',Is*100,A)
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