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diff --git a/_Theory_Of_Machines/Chapter6.ipynb b/_Theory_Of_Machines/Chapter6.ipynb new file mode 100755 index 00000000..895e2c68 --- /dev/null +++ b/_Theory_Of_Machines/Chapter6.ipynb @@ -0,0 +1,486 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:a0a25762305b1c74ca417d46a7390eaac10578c3f22cb04bddc542c61d85667c"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter6-Turning Moment Diagram and Flywheel"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg175"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 1 PAGE NO 175\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "\n",
+ "k=1.## radius of gyration of flywheel in m\n",
+ "m=2000.## mass of the flywheel in kg\n",
+ "T=1000.## torque of the engine in Nm\n",
+ "w1=0.## speedin the begining\n",
+ "t=10.## time duration\n",
+ "##==============================\n",
+ "I=m*k**2.## mass moment of inertia in kg-m**2\n",
+ "a=T/I## angular acceleration of flywheel in rad/s**2\n",
+ "w2=w1+a*t## angular speed after time t in rad/s\n",
+ "K=I*w2**2/2.## kinetic energy of flywheel in Nm\n",
+ "##==============================\n",
+ "print'%s %.1f %s %.1f %s '%('Angular acceleration of the flywheel=',a,' rad/s**2'' Kinetic energy of flywheel= ',K,' N-m')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular acceleration of the flywheel= 0.5 rad/s**2 Kinetic energy of flywheel= 25000.0 N-m \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 2 PAGE NO 176\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "import math\n",
+ "pi=3.141\n",
+ "N1=225.## maximum speed of flywheel in rpm\n",
+ "k=.5## radius of gyration of flywheel in m\n",
+ "n=720.## no of holes punched per hour\n",
+ "E1=15000.## energy required by flywheel in Nm\n",
+ "N2=200.## mimimum speedof flywheel in rpm\n",
+ "t=2.## time taking for punching a hole\n",
+ "##==========================\n",
+ "P=E1*n/3600.## power required by motor per sec in watts\n",
+ "E2=P*t## energy supplied by motor to punch a hole in N-m\n",
+ "E=E1-E2## maximum fluctuation of energy in N-m\n",
+ "N=(N1+N2)/2.## mean speed of the flywheel in rpm\n",
+ "m=E/(pi**2./900.*k**2.*N*(N1-N2))\n",
+ "print'%s %.1f %s %.1f %s'%('Power of the motor= ',P,' watts''Mass of the flywheel required= ',m,' kg')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power of the motor= 3000.0 wattsMass of the flywheel required= 618.2 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 3 PAGE NO 176\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "import math\n",
+ "pi=3.141\n",
+ "d=38.## diameter of hole in cm\n",
+ "t=32.## thickness of hole in cm\n",
+ "e1=7.## energy required to punch one square mm\n",
+ "V=25.## mean speed of the flywheel in m/s\n",
+ "S=100.## stroke of the punch in cm\n",
+ "T=10.## time required to punch a hole in s\n",
+ "Cs=.03## coefficient of fluctuation of speed\n",
+ "##===================\n",
+ "A=pi*d*t## sheared area in mm**2\n",
+ "E1=e1*A## energy required to punch entire area in Nm\n",
+ "P=E1/T## power of motor required in watts\n",
+ "T1=T/(2.*S)*t## time required to punch a hole in 32 mm thick plate\n",
+ "E2=P*T1## energy supplied by motor in T1 seconds\n",
+ "E=E1-E2## maximum fluctuation of energy in Nm\n",
+ "m=E/(V**2.*Cs)## mass of the flywheel required\n",
+ "print'%s %.1f %s'%('Mass of the flywheel required= ',m,' kg')\n",
+ "\n",
+ "\t\t"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of the flywheel required= 1197.8 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg177"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 4 PAGE NO 177\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "##figure 6.4\n",
+ "import math\n",
+ "##===================\n",
+ "pi=3.141\n",
+ "N=480.## speed of the engine in rpm\n",
+ "k=.6## radius of gyration in m\n",
+ "Cs=.03## coefficient of fluctuaion of speed \n",
+ "Ts=6000.## turning moment scale in Nm per one cm\n",
+ "C=30.## crank angle scale in degrees per cm\n",
+ "a=[0.5,-1.22,.9,-1.38,.83,-.7,1.07]## areas between the output torque and mean resistance line in sq.cm\n",
+ "##======================\n",
+ "w=2.*pi*N/60.## angular speed in rad/s\n",
+ "A=Ts*C*pi/180.## 1 cm**2 of turning moment diagram in Nm\n",
+ "E1=a[0]## max energy at B refer figure\n",
+ "E2=a[0]+a[1]+a[2]+a[3]\n",
+ "E=(E1-E2)*A## fluctuation of energy in Nm\n",
+ "m=E/(k**2.*w**2*Cs)## mass of the flywheel in kg\n",
+ "print'%s %.1f %s'%('Mass of the flywheel= ',m,' kg')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of the flywheel= 195.8 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg178"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 5 PAGE NO 178\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "##==============\n",
+ "pi=3.141\n",
+ "P=500.*10**3.## power of the motor in N\n",
+ "k=.6## radius of gyration in m\n",
+ "Cs=.03## coefficient of fluctuation of spped \n",
+ "OA=750.## REFER FIGURE\n",
+ "OF=6.*pi## REFER FIGURE\n",
+ "AG=pi## REFER FIGURE\n",
+ "BG=3000.-750.## REFER FIGURE\n",
+ "GH=2.*pi## REFER FIGURE\n",
+ "CH=3000.-750.## REFER FIGURE\n",
+ "HD=pi## REFER FIGURE\n",
+ "LM=2.*pi## REFER FIGURE\n",
+ "T=OA*OF+1./2.*AG*BG+BG*GH+1./2.*CH*HD## Torque required for one complete cycle in Nm\n",
+ "Tmean=T/(6.*pi)## mean torque in Nm\n",
+ "w=P/Tmean## angular velocity required in rad/s\n",
+ "BL=3000.-1875.## refer figure\n",
+ "KL=BL*AG/BG## From similar trangles\n",
+ "CM=3000.-1875.## refer figure\n",
+ "MN=CM*HD/CH##from similar triangles\n",
+ "E=1./2.*KL*BL+BL*LM+1./2.*CM*MN## Maximum fluctuaion of energy in Nm\n",
+ "m=E*100./(k**2*w**2.*Cs)## mass of flywheel in kg\n",
+ "print'%s %.1f %s'%('Mass of the flywheel= ',m,' kg')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of the flywheel= 1150.3 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg179"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 6 PAGE NO 179\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "import math\n",
+ "pi=3.141\n",
+ "PI=180.##in degrees\n",
+ "theta1=0.\n",
+ "theta2=PI\n",
+ "m=400.## mass of the flywheel in kg\n",
+ "N=250.## speed in rpm\n",
+ "k=.4## radius of gyration in m\n",
+ "n=2.*250./60000.## no of working strokes per minute\n",
+ "W=1000.*pi-150.*math.cos((2*theta2)/57.3)-250.*math.sin((2*theta2)/57.3)-(1000.*theta1-150.*math.cos((2*theta1)/57.3)-250.*math.sin((2*theta1)/57.3))## workdone per stroke in Nm\n",
+ "P=W*n## power in KW\n",
+ "Tmean=W/pi## mean torque in Nm\n",
+ "twotheta=math.atan((500/300)/57.3)## angle at which T-Tmean becomes zero\n",
+ "THETA1=twotheta/2.\n",
+ "THETA2=(180.+twotheta)/2.\n",
+ "E=-150.*math.cos((2.*THETA2)/57.3)-250.*math.sin((2.*THETA2)/57.3)-(-150*math.cos((2.*THETA1)/57.3)-250.*math.sin((2*THETA1)/57.3))## FLUCTUATION OF ENERGY IN Nm\n",
+ "w=2.*pi*N/60.## angular speed in rad/s\n",
+ "Cs1=E*100./(k**2.*w**2.*m)## fluctuation range\n",
+ "Cs=Cs1/2.## tatal percentage of fluctuation of speed\n",
+ "Theta=60.\n",
+ "T1=300.*math.sin((2*Theta)/57.3)-500.*math.cos((2*Theta)/57.3)## Accelerating torque in Nm(T-Tmean)\n",
+ "alpha=T1/(m*k**2.)## angular acceleration in rad/s**2\n",
+ "print'%s %.1f %s %.3f %s %.3f %s '%('Power delivered=',P,' kw''Total percentage of fluctuation speed=',Cs,' ''Angular acceleration=',alpha,'rad/s**2')\n",
+ "#in book ans is given wrong \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered= 26.2 kwTotal percentage of fluctuation speed= 0.342 Angular acceleration= 7.965 rad/s**2 \n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg181"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 7 PAGE NO 181\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "\n",
+ "pi=3.141\n",
+ "m=200.## mass of the flywheel in kg\n",
+ "k=.5## radius of gyration in m\n",
+ "N1=360.## upper limit of speed in rpm\n",
+ "N2=240.## lower limit of speed in rpm\n",
+ "##==========\n",
+ "I=m*k**2.## mass moment of inertia in kg m**2\n",
+ "w1=2.*pi*N1/60.\n",
+ "w2=2.*pi*N2/60.\n",
+ "E=1./2.*I*(w1**2.-w2**2.)## fluctuation of energy in Nm\n",
+ "Pmin=E/(4.*1000.)## power in kw\n",
+ "Eex=Pmin*12.*1000.## Energy expended in performing each operation in N-m\n",
+ "print'%s %.1f %s %.1f %s '%('Mimimum power required= ',Pmin,' kw' ' Energy expended in performing each operation= ',Eex,' N-m')\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mimimum power required= 4.9 kw Energy expended in performing each operation= 59195.3 N-m \n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg182"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 8 PAGE NO 182\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "import math\n",
+ "pi=3.141\n",
+ "b=8.## width of the strip in cm\n",
+ "t=2.## thickness of the strip in cm\n",
+ "w=1.2*10**3.## work required per square cm cut\n",
+ "N1=200.## maximum speed of the flywheel in rpm\n",
+ "k=.80## radius of gyration in m\n",
+ "N2=(1.-.15)*N1## minimum speed of the flywheel in rpm\n",
+ "T=3.## time required to punch a hole\n",
+ "##=======================\n",
+ "A=b*t## area cut of each stroke in cm**2\n",
+ "W=w*A## work required to cut a strip in Nm\n",
+ "w1=2.*pi*N1/60.## speed before cut in rpm\n",
+ "w2=2.*pi*N2/60.## speed after cut in rpm\n",
+ "m=2.*W/(k**2.*(w1**2.-w2**2.))## mass of the flywheel required in kg\n",
+ "a=(w1-w2)/T## angular acceleration in rad/s**2\n",
+ "Ta=m*k**2.*a## torque required in Nm\n",
+ "print'%s %.1f %s %.1f %s '%('Mass of the flywheel= ',m,' kg'' Amount of Torque required=',Ta,'Nm')\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Mass of the flywheel= 493.1 kg Amount of Torque required= 330.4 Nm \n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9-pg182"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 9 PAGE NO 182\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "\n",
+ "pi=3.141\n",
+ "P=5.*10**3.## power delivered by motor in watts\n",
+ "N1=360.## speed of the flywheel in rpm\n",
+ "I=60.## mass moment of inertia in kg m**2\n",
+ "E1=7500.## energy required by pressing machine for 1 second in Nm\n",
+ "##========================\n",
+ "Ehr=P*60.*60.## energy sipplied per hour in Nm\n",
+ "n=Ehr/E1\n",
+ "E=E1-P## total fluctuation of energy in Nm\n",
+ "w1=2.*pi*N1/60.## angular speed before pressing in rpm \n",
+ "w2=((2.*pi*N1/60.)**2.-(2.*E/I))**.5## angular speed after pressing in rpm \n",
+ "N2=w2*60./(2.*pi)\n",
+ "R=N1-N2## reduction in speed in rpm\n",
+ "print'%s %.1f %s %.1f %s '%('No of pressings that can be made per hour= ',n,' Reduction in speed after the pressing is over= ',R,' rpm ')\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "No of pressings that can be made per hour= 2400.0 Reduction in speed after the pressing is over= 10.7 rpm \n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex10-pg183"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 6 ILLUSRTATION 10 PAGE NO 183\n",
+ "##TITLE:Turning Moment Diagram and Flywheel\n",
+ "import math\n",
+ "pi=3.141\n",
+ "Cs=.02## coefficient of fluctuation of speed \n",
+ "N=200.## speed of the engine in rpm\n",
+ "\n",
+ "theta1=math.acos(0/57.3)\n",
+ "theta2=math.asin((-6000/16000)/57.3)\n",
+ "theta2=180.-theta2\n",
+ "##===============================================\n",
+ "##largest area,representing fluctuation of energy lies between theta1 and theta2\n",
+ "E=6000.*math.sin(theta2/57.3)-8000./2.*math.cos((2*theta2)/57.3)-(6000.*math.sin((theta1)/57.3)-8000./2.*math.cos((2*theta1)/57.3))## total fluctuation of energy in Nm\n",
+ "Theta=180## angle with which cycle will be repeated in degrees\n",
+ "Theta1=0\n",
+ "Tmean=1/pi*((15000*pi+(-8000*math.cos((2*Theta)/57.3))/2.)-((15000*Theta1+(-8000*math.cos((2*Theta1)/57.3))/2.)))## mean torque of engine in Nm\n",
+ "P=2*pi*N*Tmean/60000.## power of the engine in kw\n",
+ "w=2*pi*N/60.## angular speed of the engine in rad/s\n",
+ "I=E/(w**2.*Cs)## mass moment of inertia of flywheel in kg-m**2\n",
+ "print'%s %.1f %s %.1f %s '%('Power of the engine= ',P,' kw'' minimum mass moment of inertia of flywheel=',-I,' kg-m**2'' E value calculated in the textbook is wrong. Its value is -15,124. In textbook it is given as -1370.28')\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power of the engine= 314.1 kw minimum mass moment of inertia of flywheel= 19.5 kg-m**2 E value calculated in the textbook is wrong. Its value is -15,124. In textbook it is given as -1370.28 \n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |