path: root/Theory_Of_Machines_by__B._K._Sarkar/Chapter5.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter5-Inertia Force Analysis in Machines"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "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": {}
  }
 ]
}