{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter7-GOVERNORS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg196"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 1 PAGE NO 196\n",
"##TITLE:GOVERNORS\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"L=.4## LENGTH OF UPPER ARM IN m\n",
"THETA=30.## INCLINATION TO THE VERTICAL IN degrees\n",
"K=.02## RISED LENGTH IN m\n",
"##============================================================================================\n",
"h2=L*math.cos(THETA/57.3)## GOVERNOR HEIGHT IN m\n",
"N2=(895./h2)**.5## SPEED AT h2 IN rpm\n",
"h1=h2-K## LENGTH WHEN IT IS RAISED BY 2 cm\n",
"N1=(895./h1)**.5## SPEED AT h1 IN rpm\n",
"n=(N1-N2)/N2*100.## PERCENTAGE CHANGE IN SPEED\n",
"##==========================================================================================\n",
"print'%s %.1f %s'%('PERCENTAGE CHANGE IN SPEED=',n,' PERCENTAGE')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"PERCENTAGE CHANGE IN SPEED= 3.0 PERCENTAGE\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 2 PAGE NO 197\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.5(A),7.5(B)\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"OA=.3## LENGTH OF UPPER ARM IN m\n",
"m=6.## MASS OF EACH BALL IN Kg\n",
"M=18.## MASS OF SLEEVE IN Kg\n",
"r2=.2## RADIUS OF ROTATION AT BEGINING IN m\n",
"r1=.25## RADIUS OF ROTATION AT MAX SPEED IN m\n",
"##===========================================================================================\n",
"h1=(OA**2.-r1**2.)**.5## HIEGHT OF GOVERNOR AT MAX SPEED IN m\n",
"N1=(895.*(m+M)/(h1*m))**.5## MAX SPEED IN rpm\n",
"h2=(OA**2.-r2**2.)**.5## HEIGHT OF GONERNOR AT BEGINING IN m\n",
"N2=(895.*(m+M)/(h2*m))**.5## MIN SPEED IN rpm\n",
"##===========================================================================================\n",
"print'%s %.1f %s %.1f %s %.1f %s'%('MAX SPEED = ',N1,' rpm'' MIN SPEED = ',N2,' rpm''RANGE OF SPEED = ',N1-N2,' rpm')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"MAX SPEED = 146.9 rpm MIN SPEED = 126.5 rpmRANGE OF SPEED = 20.4 rpm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 3 PAGE NO 197\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.6\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"OA=.25## LENGHT OF UPPER ARM IN m\n",
"CD=.03## DISTANCE BETWEEN LEEVE AND LOWER ARM IN m\n",
"m=6.## MASS OF BALL IN Kg\n",
"M=48.## MASS OF SLEEVE IN Kg\n",
"AE=.17## FROM FIGURE 7.6\n",
"AE1=.12## FROM FIGURE 7.6\n",
"r1=.2## RADIUS OF ROTATION AT MAX SPEED IN m\n",
"r2=.15## RADIUS OF ROTATION AT MIN SPEED IN m\n",
"##============================================================================================\n",
"h1=(OA**2-r1**2)**.5## HIEGHT OF GOVERNOR AT MIN SPEED IN m\n",
"TANalpha=r1/h1\n",
"TANbeeta=AE/(OA**2-AE**2)**.5\n",
"k=TANbeeta/TANalpha\n",
"N1=(895.*(m+(M*(1.+k)/2.))/(h1*m))**.5## MIN SPEED IN rpm\n",
"h2=(OA**2-r2**2)**.5## HIEGHT OF GOVERNOR AT MAX SPEED IN m\n",
"CE=(OA**2-AE1**2)**.5\n",
"TANalpha1=r2/h2\n",
"TANbeeta1=(r2-CD)/CE\n",
"k=TANbeeta1/TANalpha1\n",
"N2=(895.*(m+(M*(1.+k)/2.))/(h2*m))**.5## MIN SPEED IN rpm\n",
"##========================================================================================================\n",
"print'%s %.1f %s %.1f %s %.1f %s'%('MAX SPEED = ',N1,' rpm'' MIN SPEED = ',N2,' rpm''RANGE OF SPEED = ',N1-N2,' rpm')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"MAX SPEED = 215.5 rpm MIN SPEED = 188.2 rpmRANGE OF SPEED = 27.2 rpm\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 4 PAGE NO 199\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.7\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"g=9.81## ACCELERATION DUE TO GRAVITY \n",
"OA=.20## LENGHT OF UPPER ARM IN m\n",
"AC=.20## LENGTH OF LOWER ARM IN m\n",
"CD=.025## DISTANCE BETWEEN AXIS AND LOWER ARM IN m\n",
"AB=.1## RADIUS OF ROTATION OF BALLS IN m\n",
"N2=250## SPEED OF THE GOVERNOR IN rpm\n",
"X=.05## SLEEVE LIFT IN m\n",
"m=5.## MASS OF BALL IN Kg\n",
"M=20.## MASS OF SLEEVE IN Kg\n",
"##===========================================================\n",
"h2=(OA**2.-AB**2.)**.5## OB DISTANCE IN m IN FIGURE\n",
"h21=(AC**2.-(AB-CD)**2.)**.5## BD DISTANCE IN m IN FIGURE\n",
"TANbeeta=(AB-CD)/h21## TAN OF ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL\n",
"TANalpha=AB/h2## TAN OF ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n",
"k=TANbeeta/TANalpha\n",
"c=X/(2.*(h2*(1.+k)-X))## PERCENTAGE INCREASE IN SPEED \n",
"n=c*N2## INCREASE IN SPEED IN rpm\n",
"N1=N2+n## SPEED AFTER LIFT OF SLEEVE\n",
"E=c*g*((2.*m/(1.+k))+M)## GOVERNOR EFFORT IN N\n",
"P=E*X## GOVERNOR POWER IN N-m\n",
"\n",
"print'%s %.1f %s %.2f %s %.1f %s '%('SPEED OF THE GOVERNOR WHEN SLEEVE IS LIFT BY 5 cm = ',N1,' rpm'' GOVERNOR EFFORT = ',E,' N' 'GOVERNOR POWER = ',P,' N-m')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"SPEED OF THE GOVERNOR WHEN SLEEVE IS LIFT BY 5 cm = 275.6 rpm GOVERNOR EFFORT = 25.95 NGOVERNOR POWER = 1.3 N-m \n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg200"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 5 PAGE NO 200\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.8\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"g=9.81## ACCELERATION DUE TO GRAVITY \n",
"OA=.30## LENGHT OF UPPER ARM IN m\n",
"AC=.30## LENGTH OF LOWER ARM IN m\n",
"m=10.## MASS OF BALL IN Kg\n",
"M=50.## MASS OF SLEEVE IN Kg\n",
"r=.2## RADIUS OF ROTATION IN m\n",
"CD=.04## DISTANCE BETWEEN AXIS AND LOWER ARM IN m\n",
"F=15.## FRICTIONAL LOAD ACTING IN N\n",
"##============================================================\n",
"h=(OA**2-r**2)**.5## HIEGTH OF THE GOVERNOR IN m\n",
"AE=r-CD## AE VALUE IN m\n",
"CE=(AC**2-AE**2)**.5## BD DISTANCE IN m\n",
"TANalpha=r/h## TAN OF ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n",
"TANbeeta=AE/CE## TAN OF ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL\n",
"k=TANbeeta/TANalpha\n",
"N=((895./h)*(m+(M*(1.+k)/2.))/m)**.5## EQULIBRIUM SPEED IN rpm\n",
"N1=((895./h)*((m*g)+(M*g+F)/2.)*(1.+k)/(m*g))**.5## MAX SPEED IN rpm\n",
"N2=((895./h)*((m*g)+(M*g-F)/2.)*(1.+k)/(m*g))**.5## MIN SPEED IN rpm\n",
"R=N1-N2## RANGE OF SPEED\n",
"print'%s %.1f %s %.1f %s '%('EQUILIBRIUM SPEED OF GOVERNOR = ',N,' rpm'' RANGE OF SPEED OF GOVERNOR= ',R,' rpm')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"EQUILIBRIUM SPEED OF GOVERNOR = 145.1 rpm RANGE OF SPEED OF GOVERNOR= 3.4 rpm \n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg202"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 6 PAGE NO 202\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.9\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"g=9.81## ACCELERATION DUE TO GRAVITY \n",
"OA=.30## LENGHT OF UPPER ARM IN m\n",
"AC=.30## LENGTH OF LOWER ARM IN m\n",
"m=5.## MASS OF BALL IN Kg\n",
"M=25.## MASS OF SLEEVE IN Kg\n",
"X=.05## LIFT OF THE SLEEVE\n",
"alpha=30.## ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n",
"##==============================================\n",
"h2=OA*math.cos(alpha/57.3)## HEIGHT OF THE GOVERNOR AT LOWEST POSITION OF SLEEVE\n",
"h1=h2-X/2.## HEIGHT OF THE GOVERNOR AT HEIGHT POSITION OF SLEEVE\n",
"F=((h2/h1)*(m*g+M*g)-(m*g+M*g))/(1.+h2/h1)## FRICTION AT SLEEVE IN N\n",
"N1=((m*g+M*g+F)*895./(h1*m*g))**.5## MAX SPEEED OF THE GOVVERNOR IN rpm\n",
"N2=((m*g+M*g-F)*895./(h2*m*g))**.5## MIN SPEEED OF THE GOVVERNOR IN rpm\n",
"R=N1-N2## RANGE OF SPEED IN rpm\n",
"\n",
"print'%s %.1f %s %.1f %s'%('THE VALUE OF FRICTIONAL FORCE= ',F,' F'' RANGE OF SPEED OF THE GOVERNOR = ',R,' rpm')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"THE VALUE OF FRICTIONAL FORCE= 14.9 F RANGE OF SPEED OF THE GOVERNOR = 14.9 rpm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7-pg203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 7 PAGE NO 203\n",
"##TITLE:GOVERNORS\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"PI=3.147\n",
"m=3## MASS OF EACH BALL IN Kg\n",
"a=.12## LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n",
"b=.08## LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n",
"r2=.12## RADIUS OF ROTATION OF THE BALL FOR LOWEST POSITION IN m\n",
"N2=320.## SPEED OF GOVERNOR AT THE BEGINING IN rpm\n",
"S=20000.## STIFFNESS OF THE SPRING IN N/m\n",
"h=.015## SLEEVE LIFT IN m\n",
"##==================================================\n",
"Fc2=m*(2.*PI*N2/60.)**2*r2## CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N\n",
"L=2*a*Fc2/b## INITIAL LOAD ON SPRING IN N\n",
"r1=a/b*h+r2## MAX RADIUS OF ROTATION IN m\n",
"Fc1=(S*(r1-r2)*(b/a)**2/2)+Fc2## CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N\n",
"N1=(Fc1/(m*r1)*(60./2./PI)**2)**.5\n",
"print'%s %.1f %s %.1f %s '%('INITIAL LOAD ON SPRING =',L,' N'' EQUILIBRIUM SPEED CORRESPONDING TO LIFT OF 15 cm =',N1,' rpm')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INITIAL LOAD ON SPRING = 1217.0 N EQUILIBRIUM SPEED CORRESPONDING TO LIFT OF 15 cm = 327.9 rpm \n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7-pg204"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 8 PAGE NO 204\n",
"##TITLE:GOVERNORS\n",
"\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"PI=3.147\n",
"m=3## MASS OF BALL IN Kg\n",
"r2=.2## INITIAL RADIUS OF ROTATION IN m\n",
"a=.11## LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n",
"b=.15## LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n",
"h=.004## SLEEVE LIFT IN m\n",
"N2=240.## INITIAL SPEED IN rpm\n",
"n=7.5## FLUCTUATION OF SPEED IN %\n",
"##===================================\n",
"w2=2.*PI*N2/60.## INITIAL ANGULAR SPEED IN rad/s\n",
"w1=(100.+n)*w2/100.## FINAL ANGULAR SPEED IN rad/s\n",
"F=2.*a/b*m*w2**2.*r2## INITIAL COMPRESSIVE FORCE IN N\n",
"r1=r2+a/b*h## MAX RDIUS OF ROTATION IN m\n",
"S=2.*((m*w1**2.*r1)-(m*w2**2.*r2))/(r1-r2)*(a/b)**2.\n",
"print'%s %.1f %s %.1f %s'%('INITIAL COMPRESSIVE FPRCE = ',F,' N'' STIFFNESS OF THE SPRING = ',S/1000,' N/m')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INITIAL COMPRESSIVE FPRCE = 557.8 N STIFFNESS OF THE SPRING = 24.1 N/m\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9-pg204"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 9 PAGE NO 204\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.3(C)\n",
"\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"g=9.81## ACCELERATION DUE TO GRAVITY \n",
"PI=3.147\n",
"r=.14## DISTANCE BETWEEN THE CENTRE OF PIVOT OF BELL CRANK LEVER AND AXIS OF GOVERNOR SPINDLE IN m\n",
"r2=.11## INITIAL RADIUS OF ROTATION IN m\n",
"a=.12## LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n",
"b=.10## LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n",
"h=.05## SLEEVE LIFT IN m\n",
"N2=240## INITIAL SPEED IN rpm\n",
"F=30## FRICTIONAL FORCE ACTING IN N\n",
"m=5## MASS OF EACH BALL IN Kg\n",
"##==========================================\n",
"r1=r2+a/b*h## MAX RADIUS OF ROTATION IN m\n",
"N1=41.*N2/39.## MAX SPEED OF ROTATION IN rpm\n",
"N=(N1+N2)/2.## MEAN SPEED IN rpm\n",
"Fc1=m*(2.*PI*N1/60.)**2.*r1## CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N\n",
"Fc2=m*(2.*PI*N2/60.)**2.*r2## CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N\n",
"c1=r1-r## FROM FIGURE 7.3(C) IN m\n",
"a1=(a**2.-c1**2.)**.5## FROM FIGURE 7.3(C) IN m\n",
"b1=(b**2.-(h/2.)**2.)**.5## FROM FIGURE 7.3(C) IN m\n",
"c2=r-r2## FROM FIGURE 7.3(C) IN m\n",
"a2=a1## FROM FIGURE 7.3(C) IN m\n",
"b2=b1## FROM FIGURE 7.3(C) IN m\n",
"S1=2.*((Fc1*a1)-(m*g*c1))/b1## SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS\n",
"S2=2.*((Fc2*a2)-(m*g*c2))/b2## SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS\n",
"S=(S1-S2)/h## STIFFNESS OF THE SPRING IN N/m\n",
"Is=S2/S## INITIAL COMPRESSION OF SPRING IN m\n",
"P=S2+(h/2.*S)## SPRING FORCE OF MID PORTION IN N\n",
"n1=N*((P+F)/P)**.5## SPEED,WHEN THE SLEEVE BEGINS TO MOVE UPWARDS FROM MID POSITION IN rpm\n",
"n2=N*((P-F)/P)**.5## SPEED,WHEN THE SLEEVE BEGINS TO MOVE DOWNWARDS FROM MID POSITION IN rpm\n",
"A=n1-n2## ALTERATION IN SPEED IN rpm\n",
"print'%s %.1f %s %.1f %s '%('INTIAL COMPRESSION OF SPRING= ',Is*100,' cm''ALTERATION IN SPEED = ',A,' rpm')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INTIAL COMPRESSION OF SPRING= 6.8 cmALTERATION IN SPEED = 6.7 rpm \n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10-pg206"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 10 PAGE NO 206\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.10\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"PI=3.147\n",
"AE=.25## LENGTH OF UPPER ARM IN m\n",
"CE=.25## LENGTH OF LOWER ARM IN m\n",
"EH=.1## LENGTH OF EXTENDED ARM IN m\n",
"EF=.15## RADIUS OF BALL PATH IN m\n",
"m=5.## MASS OF EACH BALL IN Kg\n",
"M=40.## MASS OF EACH BALL IN Kg\n",
"##===================================================================\n",
"h=(AE**2.-EF**2.)**.5## HEIGHT OF THE GOVERNOR IN m\n",
"EM=h\n",
"HM=EH+EM## FROM FIGURE 7.10\n",
"N=((895./h)*(EM/HM)*((m+M)/m))**.5\n",
"print'%s %.1f %s'%('EQUILIBRIUM SPEED OF GOVERNOR =',N,' rpm')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"EQUILIBRIUM SPEED OF GOVERNOR = 163.9 rpm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex11-pg207"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 11 PAGE NO 207\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.11\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"PI=3.147\n",
"g=9.81## ACCELERATION DUE TO GRAVITY IN N/mm**2\n",
"AE=.25## LENGTH OF UPPER ARM IN m\n",
"CE=.25## LENGTH OF LOWER ARM IN m\n",
"ER=.175## FROM FIGURE 7.11\n",
"AP=.025## FROM FIGURE 7.11\n",
"FR=AP## FROM FIGURE 7.11\n",
"CQ=FR## FROM FIGURE 7.11\n",
"m=3.2## MASS OF BALL IN Kg\n",
"M=25.## MASS OF SLEEVE IN Kg\n",
"h=.2## VERTICAL HEIGHT OF GOVERNOR IN m\n",
"EM=h## FROM FIGURE 7.11\n",
"AF=h## FROM FIGURE 7.11\n",
"N=160.## SPEED OF THE GOVERNOR IN rpm\n",
"HM=(895.*EM*(m+M)/(h*N**2.*m))\n",
"x=HM-EM## LENGTH OF EXTENDED LINK IN m\n",
"T1=g*(m+M/2.)*AE/AF## TENSION IN UPPER ARM IN N\n",
"print'%s %.3f %s %.1f %s'%('LENGTH OF EXTENDED LINK = ',x,' m''TENSION IN UPPER ARM =',T1,' N')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"LENGTH OF EXTENDED LINK = 0.108 mTENSION IN UPPER ARM = 192.5 N\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex12-pg208"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"##CHAPTER 7 ILLUSRTATION 12 PAGE NO 208\n",
"##TITLE:GOVERNORS\n",
"##FIGURE 7.12,7.13\n",
"import math\n",
"##===========================================================================================\n",
"##INPUT DATA\n",
"PI=3.147\n",
"EF=.20## MINIMUM RADIUS OF ROTATION IN m\n",
"AE=.30## LENGTH OF EACH ARM IN m\n",
"A1E1=AE## COMPARING FIRUES 7.12&7.13\n",
"EC=.30## LENGTH OF EACH ARM IN m\n",
"E1C1=EC## LENGTH OF EACH ARM IN m\n",
"ED=.165## FROM FIGURE 7.12 IN m\n",
"MC=ED## FROM FIGURE 7.12\n",
"EH=.10## FROM FIGURE 7.12 IN m\n",
"m=8.## MASS OF BALL IN Kg \n",
"M=60.## MASS OF SLEEVE IN Kg\n",
"DF=.035## SLEEVE DISTANCE FROM AXIS IN m\n",
"E1F1=.25## MAX RADIUS OF ROTATION IN m\n",
"g=9.81\n",
"##=========================================================\n",
"alpha=math.asin((EF/AE))*57.3## ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL IN DEGREES\n",
"beeta=math.asin((ED/EC))*57.3## ANGLE OF INCLINATION OF THE ARM TO THE HORIZONTAL IN DEGREES\n",
"k=math.tan(beeta/57.3)/math.tan(alpha/57.3)\n",
"h=(AE**2.-EF**2.)**.5## HEIGHT OF GOVERNOR IN m\n",
"EM=(EC**2.-MC**2.)**.5## FROM FIGURE 7.12 IN m\n",
"HM=EM+EH\n",
"N2=(895.*EM*(m+(M/2.*(1.+k)))/(h*HM*m))**.5## EQUILIBRIUM SPEED AT MAX RADIUS\n",
"HC=(HM**2.+MC**2.)**.5## FROM FIGURE 7.13 IN m\n",
"H1C1=HC\n",
"gama=math.atan((MC/HM))*57.3\n",
"alpha1=math.asin((E1F1/A1E1))*57.3\n",
"E1D1=E1F1-DF## FROM FIGURE 7.13 IN m\n",
"beeta1=math.asin((E1D1/E1C1))*57.3\n",
"gama1=gama-beeta+beeta1\n",
"r=H1C1*math.sin(gama1/57.3)+DF## RADIUS OF ROTATION IN m\n",
"H1M1=H1C1*math.cos((gama1/57.3))\n",
"I1C1=E1C1*math.cos(beeta1/57.3)*(math.tan(alpha1/57.3)+math.tan(beeta1/57.3))## FROM FIGURE IN m\n",
"M1C1=H1C1*math.sin(gama1/57.3)\n",
"w1=(((m*g*(I1C1-M1C1))+(M*g*I1C1)/2.)/(m*r*H1M1))**.5## ANGULAR SPEED IN rad/s\n",
"N1=w1*60./(2.*PI)## ##SPEED IN m/s\n",
"print'%s %.1f %s %.1f %s '%('MINIMUM SPEED OF ROTATION =',N2,' rpm'' MAXIMUM SPEED OF ROTATION = ',N1,' rpm')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"MINIMUM SPEED OF ROTATION = 146.6 rpm MAXIMUM SPEED OF ROTATION = 156.3 rpm \n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}