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diff --git a/_Theory_Of_Machines/Chapter5.ipynb b/_Theory_Of_Machines/Chapter5.ipynb new file mode 100755 index 00000000..f5d72d04 --- /dev/null +++ b/_Theory_Of_Machines/Chapter5.ipynb @@ -0,0 +1,413 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:a109b0284cb0a4fc44bb60197ec78d6f24860fb5b5091b8f3432975ce1e08de6"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Chapter5-Inertia Force Analysis in Machines"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Ex1-pg160"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 1 PAGE NO 160\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "import math\n",
+ "pi=3.141\n",
+ "r=.3## radius of crank in m\n",
+ "l=1.## length of connecting rod in m\n",
+ "N=200.## speed of the engine in rpm\n",
+ "n=l/r\n",
+ "##===================\n",
+ "w=2.*pi*N/60.## angular speed in rad/s\n",
+ "\n",
+ "teeta=math.acos((-n+((n**2)+4*2*1)**.5)/(2*2))*57.3## angle of inclination of crank in degrees\n",
+ "Vp=w*r*(math.sin(teeta/57.3)+(math.sin((2*teeta)/57.3)/n))## maximum velocity of the piston in m/s\n",
+ "print'%s %.1f %s'%('Maximum velocity of the piston = ',Vp,' m/s')\n",
+ "print'%s %.2f %s'%('teeta',teeta,'')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum velocity of the piston = 7.0 m/s\n",
+ "teeta 74.96 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg161"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 2 PAGE NO 161\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "import math\n",
+ "PI=3.141\n",
+ "r=.3## length of crank in metres\n",
+ "l=1.5## length of connecting rod in metres\n",
+ "N=180.## speed of rotation in rpm\n",
+ "teeta=40.## angle of inclination of crank in degrees\n",
+ "##============================\n",
+ "n=l/r\n",
+ "w=2.*PI*N/60## angular speed in rad/s\n",
+ "Vp=w*r*(math.sin(teeta/57.3)+math.sin((2.*teeta/57.3)/(2.*n)))## velocity of piston in m/s\n",
+ "fp=w**2.*r*(math.cos(teeta/57.3)+math.cos(2.*teeta/57.3)/(2.*n))## acceleration of piston in m/s**2\n",
+ "costeeta1=(-n+(n**2.+4.*2.*1.)**.5)/4.\n",
+ "teeta1=math.acos(costeeta1)*(57.3)## position of crank from inner dead centre position for zero acceleration of piston\n",
+ "##===========================\n",
+ "print'%s %.1f %s %.1f %s %.1f %s'%('Velocity of Piston = ',Vp,' m/s'' Acceleration of piston =',fp,' m/s**2'' position of crank from inner dead centre position for zero acceleration of piston=',teeta1,' degrees')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity of Piston = 4.4 m/s Acceleration of piston = 83.5 m/s**2 position of crank from inner dead centre position for zero acceleration of piston= 79.3 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg161"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 3 PAGE NO 161\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "import math\n",
+ "pi=3.141\n",
+ "D=.3## Diameter of steam engine in m\n",
+ "L=.5## length of stroke in m\n",
+ "r=L/2.\n",
+ "mR=100.## equivalent of mass of reciprocating parts in kg\n",
+ "N=200.## speed of engine in rpm\n",
+ "teeta=45## angle of inclination of crank in degrees\n",
+ "p1=1.*10**6## gas pressure in N/m**2\n",
+ "p2=35.*10**3## back pressure in N/m**2\n",
+ "n=4.## ratio of crank radius to the length of stroke\n",
+ "##=================================\n",
+ "w=2.*pi*N/60## angular speed in rad/s\n",
+ "Fl=pi/4.*D**2.*(p1-p2)## Net load on piston in N\n",
+ "Fi=mR*w**2*r*(math.cos(teeta/57.3)+math.cos((2*teeta)/57.3)/(2*n))## inertia force due to reciprocating parts\n",
+ "Fp=Fl-Fi## Piston effort\n",
+ "T=Fp*r*(math.sin(teeta/57.3)+(math.sin((2*teeta)/57.3))/(2.*(n**2-(math.sin(teeta/57.3))**2)**.5))\n",
+ "print'%s %.1f %s %.1f %s '%('Piston effort = ',Fp,' N' 'Turning moment on the crank shaft = ',T,' N-m')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Piston effort = 60447.0 NTurning moment on the crank shaft = 12604.2 N-m \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg162"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 4 PAGE NO 162\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "import math\n",
+ "pi=3.141\n",
+ "D=.10## Diameter of petrol engine in m\n",
+ "L=.12## Stroke length in m\n",
+ "l=.25## length of connecting in m\n",
+ "r=L/2.\n",
+ "mR=1.2## mass of piston in kg\n",
+ "N=1800.## speed in rpm\n",
+ "teeta=25.## angle of inclination of crank in degrees\n",
+ "p=680.*10**3## gas pressure in N/m**2\n",
+ "n=l/r\n",
+ "g=9.81## acceleration due to gravity\n",
+ "##=======================================\n",
+ "w=2.*pi*N/60.## angular speed in rpm\n",
+ "Fl=pi/4.*D**2.*p## force due to gas pressure in N\n",
+ "Fi=mR*w**2.*r*(math.cos(teeta/57.3)+math.cos((2*teeta)/57.3)/(n))## inertia force due to reciprocating parts in N\n",
+ "Fp=Fl-Fi+mR*g## net force on piston in N\n",
+ "Fq=n*Fp/((n**2-(math.sin(teeta/57.3))**2.)**.5)## resultant load on gudgeon pin in N\n",
+ "Fn=Fp*math.sin(teeta/57.3)/((n**2-(math.sin(teeta/57.3))**2.)**.5)## thrust on cylinder walls in N\n",
+ "fi=Fl+mR*g## inertia force of the reciprocating parts before the gudgeon pin load is reversed in N\n",
+ "w1=(fi/mR/r/(math.cos(teeta/57.3)+math.cos((2*teeta)/57.3)/(n)))**.5\n",
+ "N1=60.*w1/(2.*pi)\n",
+ "print'%s %.1f %s %.1f %s %.1f %s %.1f %s '%('Net force on piston = ',Fp,' N'' Resultant load on gudgeon pin = ',Fq,' N'' Thrust on cylinder walls = ',Fn,' N'' speed at which other things remining same,the gudgeon pin load would be reversed in directionm= ',N1,' rpm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Net force on piston = 2639.3 N Resultant load on gudgeon pin = 2652.9 N Thrust on cylinder walls = 269.1 N speed at which other things remining same,the gudgeon pin load would be reversed in directionm= 2528.4 rpm \n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 5 PAGE NO 163\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "##Figure 5.3\n",
+ "import math\n",
+ "pi=3.141\n",
+ "N=1800.## speed of the petrol engine in rpm\n",
+ "r=.06## radius of crank in m\n",
+ "l=.240## length of connecting rod in m\n",
+ "D=.1## diameter of the piston in m\n",
+ "mR=1## mass of piston in kg\n",
+ "p=.8*10**6## gas pressure in N/m**2\n",
+ "x=.012## distance moved by piston in m\n",
+ "##===============================================\n",
+ "w=2.*pi*N/60.## angular velocity of the engine in rad/s\n",
+ "n=l/r\n",
+ "Fl=pi/4.*D**2.*p## load on the piston in N\n",
+ "teeta=32.## by mearument from the figure 5.3\n",
+ "Fi=mR*w**2.*r*(math.cos(teeta/57.3)+math.cos((2*teeta)/57.3)/n)## inertia force due to reciprocating parts in N\n",
+ "Fp=Fl-Fi## net load on the gudgeon pin in N\n",
+ "Fq=n*Fp/((n**2.-(math.sin(teeta/57.3))**2.)**.5)## thrust in the connecting rod in N\n",
+ "Fn=Fp*math.sin(teeta/57.3)/((n**2-(math.sin(teeta/57.3))**2)**.5)## reaction between the piston and cylinder in N\n",
+ "w1=(Fl/mR/r/(math.cos(teeta/57.3)+math.cos((2*teeta)/57.3)/(n)))**.5\n",
+ "N1=60.*w1/(2.*pi)## \n",
+ "print'%s %.1f %s %.1f %s %.1f %s %.1f %s'%('Net load on the gudgeon pin= ',Fp,' N''Thrust in the connecting rod= ',Fq,' N'' Reaction between the cylinder and piston= ',Fn,' N'' The engine speed at which the above values become zero= ',N1,' rpm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Net load on the gudgeon pin= 4241.2 NThrust in the connecting rod= 4278.9 N Reaction between the cylinder and piston= 566.8 N The engine speed at which the above values become zero= 3158.0 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 6 PAGE NO 165\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "import math\n",
+ "pi=3.141\n",
+ "D=.25## diameter of horizontal steam engine in m\n",
+ "N=180.## speed of the engine in rpm\n",
+ "d=.05## diameter of piston in m\n",
+ "P=36000.## power of the engine in watts\n",
+ "n=3.## ration of length of connecting rod to the crank radius\n",
+ "p1=5.8*10**5## pressure on cover end side in N/m**2\n",
+ "p2=0.5*10**5## pressure on crank end side in N/m**2\n",
+ "teeta=40.## angle of inclination of crank in degrees\n",
+ "m=45.## mass of flywheel in kg\n",
+ "k=.65## radius of gyration in m\n",
+ "##==============================\n",
+ "Fl=(pi/4.*D**2.*p1)-(pi/4.*(D**2.-d**2.)*p2)## load on the piston in N\n",
+ "ph=(math.sin(teeta/57.3)/n)\n",
+ "phi=math.asin(ph)*57.3## angle of inclination of the connecting rod to the line of stroke in degrees\n",
+ "r=1.6*D/2.\n",
+ "T=Fl*math.sin((teeta+phi)/57.3)/math.cos(phi/57.3)*r## torque exerted on crank shaft in N-m\n",
+ "Fb=Fl*math.cos((teeta+phi)/57.3)/math.cos(phi/57.3)## thrust on the crank shaft bearing in N\n",
+ "TR=P*60./(2.*pi*N)## steady resisting torque in N-m\n",
+ "Ts=T-TR## surplus torque available in N-m\n",
+ "a=Ts/(m*k**2)## acceleration of the flywheel in rad/s**2\n",
+ "print'%s %.1f %s %.1f %s %.1f %s '%('Torque exerted on the crank shaft= ',T,' N-m'' Thrust on the crank shaft bearing= ',Fb,'N''Acceleration of the flywheel= ',a,' rad/s**2')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Torque exerted on the crank shaft= 4233.8 N-m Thrust on the crank shaft bearing= 16321.0 NAcceleration of the flywheel= 122.2 rad/s**2 \n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg166"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 7 PAGE NO 166\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "import math\n",
+ "pi=3.141\n",
+ "D=.25## diameter of vertical cylinder of steam engine in m\n",
+ "L=.45## stroke length in m\n",
+ "r=L/2.\n",
+ "n=4.\n",
+ "N=360.## speed of the engine in rpm\n",
+ "teeta=45.## angle of inclination of crank in degrees\n",
+ "p=1050000.## net pressure in N/m**2\n",
+ "mR=180.## mass of reciprocating parts in kg\n",
+ "g=9.81## acceleration due to gravity\n",
+ "##========================\n",
+ "Fl=p*pi*D**2./4.## force on piston due to steam pressure in N\n",
+ "w=2.*pi*N/60.## angular speed in rad/s\n",
+ "Fi=mR*w**2.*r*(math.cos(teeta/57.3)+math.cos((2*teeta)/57.3)/(n))## inertia force due to reciprocating parts in N\n",
+ "Fp=Fl-Fi+mR*g## piston effort in N\n",
+ "phi=math.asin((math.sin(teeta/57.3)/n))*57.3## angle of inclination of the connecting rod to the line of stroke in degrees\n",
+ "T=Fp*math.sin((teeta+phi)/57.3)/math.cos(phi/57.3)*r## torque exerted on crank shaft in N-m\n",
+ "print'%s %.1f %s'%('Effective turning moment on the crank shaft= ',T,' N-m')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effective turning moment on the crank shaft= 2366.2 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg166"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 5 ILLUSRTATION 8 PAGE NO 166\n",
+ "##TITLE:Inertia Force Analysis in Machines\n",
+ "##figure 5.4\n",
+ "import math\n",
+ "pi=3.141\n",
+ "D=.25## diameter of vertical cylinder of diesel engine in m\n",
+ "L=.40## stroke length in m\n",
+ "r=L/2.\n",
+ "n=4.\n",
+ "N=300.## speed of the engine in rpm\n",
+ "teeta=60.## angle of inclination of crank in degrees\n",
+ "mR=200.## mass of reciprocating parts in kg\n",
+ "g=9.81## acceleration due to gravity\n",
+ "l=.8## length of connecting rod in m\n",
+ "c=14.## compression ratio=v1/v2\n",
+ "p1=.1*10**6.## suction pressure in n/m**2\n",
+ "i=1.35## index of the law of expansion and compression \n",
+ "##==============================================================\n",
+ "Vs=pi/4.*D**2.*L## swept volume in m**3\n",
+ "w=2.*pi*N/60.## angular speed in rad/s\n",
+ "Vc=Vs/(c-1.)\n",
+ "V3=Vc+Vs/10.## volume at the end of injection of fuel in m**3\n",
+ "p2=p1*c**i## final pressure in N/m**2\n",
+ "p3=p2## from figure\n",
+ "x=r*((1.-math.cos(teeta/57.3)+(math.sin(teeta/57.3))**2/(2.*n)))## the displacement of the piston when the crank makes an angle 60 degrees with T.D.C\n",
+ "Va=Vc+pi*D**2.*x/4.\n",
+ "pa=p3*(V3/Va)**i\n",
+ "p=pa-p1## difference of pressues on 2 sides of piston in N/m**2\n",
+ "Fl=p*pi*D**2./4.## net load on piston in N\n",
+ "Fi=mR*w**2.*r*(math.cos(teeta/57.3)+math.cos(2.*teeta/57.3)/(n))## inertia force due to reciprocating parts in N\n",
+ "Fp=Fl-Fi+mR*g## piston effort in N\n",
+ "phi=math.asin((math.sin(teeta/57.3)/n))*57.3## angle of inclination of the connecting rod to the line of stroke in degrees\n",
+ "T=Fp*math.sin((teeta+phi)/57.3)/math.cos(phi/57.3)*r## torque exerted on crank shaft in N-m\n",
+ "print'%s %.1f %s'%('Effective turning moment on the crank shaft= ',T,' N-m')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Effective turning moment on the crank shaft= 8850.3 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |