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diff --git a/Theory_Of_Machines/ch16.ipynb b/Theory_Of_Machines/ch16.ipynb new file mode 100755 index 00000000..1bb89129 --- /dev/null +++ b/Theory_Of_Machines/ch16.ipynb @@ -0,0 +1,1466 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:18b62f9d05dddb3fa3e34cb2cfa86e210f5eaa5cdedab202d52d0e65a17b4192" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 16 : Turning Moment Diagrams and Flywheel" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.1 Page No : 573" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import linalg\n", + "\n", + "# Variables:\n", + "m = 6.5*1000 \t\t#kg\n", + "k = 1.8 \t\t\t#m\n", + "deltaE = 56.*1000 \t#N-m\n", + "N = 120. \t\t\t#rpm\n", + "\n", + "#Solution:\n", + "#Calculating the maximum and minimum speeds\n", + "#We know that fluctuation of energy deltaE = math.pi**2/900*m*k**2*N*(N1-N2) or N1-N2 = (deltaE/(math.pi**2/900*m*k**2*N)) .....(i)\n", + "#Also mean speed N = (N1+N2)/2 or N1+N2 = 2*N .....(ii)\n", + "A = [[1, -1],[ 1, 1]]\n", + "B = [deltaE/(math.pi**2/900*m*k**2*N), 2*N]\n", + "V = linalg.solve(A,B)\n", + "N1 = round(V[0]) \t\t\t#rpm\n", + "N2 = round(V[1]) \t\t\t#rpm\n", + "\n", + "#Results:\n", + "print \" Maximum speed N1 = %d rpm.\"%(N1)\n", + "print \" Minimum speed N2 = %d rpm.\"%(N2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Maximum speed N1 = 121 rpm.\n", + " Minimum speed N2 = 119 rpm.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.2 Page No : 573" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "k = 1. \t\t\t#m\n", + "m = 2500. \t\t\t#kg\n", + "T = 1500. \t\t\t#N-m\n", + "\n", + "#Solution:\n", + "#Angular acceleration of the flywheel:\n", + "#Calculating the mass moment of inertia of the flywheel\n", + "I = m*k**2 \t\t\t#kg-m**2\n", + "#Calculating the angular acceleration of the flywheel\n", + "alpha = T/I \t\t\t#rad/s**2\n", + "#Kinetic energy of the flywheel:\n", + "omega1 = 0 \t\t\t#Angular speed at rest\n", + "#Calculating the angular speed after 10 seconds\n", + "omega2 = omega1+alpha*10 \t\t\t#rad/s\n", + "#Calculating the kinetic energy of the flywheel\n", + "KE = 1./2*I*(omega2)**2/1000 \t\t\t#Kinetic energy of the flywheel kN-m\n", + "\n", + "#Results:\n", + "print \" Angular acceleration of the flywheel alpha = %.1f rad/s**2.\"%(alpha)\n", + "print \" Kinetic energy of the flywheel = %.1f kN-m.\"%(KE)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Angular acceleration of the flywheel alpha = 0.6 rad/s**2.\n", + " Kinetic energy of the flywheel = 45.0 kN-m.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.3 Page No : 574" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "P = 300.*1000 \t#W\n", + "N = 90. \t\t#rpm\n", + "CE = 0.1\n", + "k = 2. \t\t\t#m\n", + "\n", + "#Solution:\n", + "#Calculating the mean angular speed\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 1./100\n", + "#Calculating the work done per cycle\n", + "WD = P*60/N \t\t\t#Work done per cycle N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = WD*CE \t\t\t#N-m\n", + "#Calculating the mass of the flywheel\n", + "m = deltaE/(k**2*omega**2*CS) \t\t\t#kg\n", + "#Results:\n", + "print \" Mass of the flywheel, m = %d kg.\"%(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Mass of the flywheel, m = 5628 kg.\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.4 Page No : 574" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "m = 36. \t\t\t#kg\n", + "k = 150./1000 \t\t#m\n", + "N = 1800. \t\t\t#rpm\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.6\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the value of 1 mm**2 on the turning moment diagram\n", + "c = 5*math.pi/180 \t\t\t#Value of 1 mm**2 on turning miment diagram N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "#From the turning moment diagram maximum energy = E+295 and minimum energy = E-690\n", + "deltaE = (285-(-690))*c \t\t\t#N-m\n", + "#Calculating the coefficient of fluctuation of energy\n", + "CS = deltaE/(m*k**2*omega**2)*100 \t\t\t#%\n", + "\n", + "#Results:\n", + "print \" Coefficient of fluctuation of speed CS = %.1f %%.\"%(CS)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Coefficient of fluctuation of speed CS = 0.3 %.\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.5 Page No : 575" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N = 600. \t\t\t#rpm\n", + "R = 0.5 \t\t\t#m\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.7\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 3./100\n", + "#Calculating the value of 1 mm**2 on turning moment diagram\n", + "c = 600*math.pi/60 \t\t\t#Value of 1 mm**2 on turning moment diagram N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "#From the turning moment diagram maximum fluctuation = E+52 and minimum fluctuation = E-120\n", + "deltaE = (52.-(-120))*c \t\t\t#N-m\n", + "#Calculating the mass of the flywheel\n", + "m = deltaE/(R**2*omega**2*CS) \t\t\t#kg\n", + "\n", + "#Results:\n", + "print \" Mass of the flywheel m = %d kg.\"%(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Mass of the flywheel m = 182 kg.\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.6 Page No : 584\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N = 250. \t\t\t#rpm\n", + "m = 500. \t\t\t#kg\n", + "k = 600./1000 \t\t\t#m\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.8\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the torque required for one complete cycle\n", + "T = (6*math.pi*750)+(1./2*math.pi*(3000-750))+(2*math.pi*(3000-750))+(1./2*math.pi*(3000-750)) \t\t\t#N-m\n", + "#Calculating the mean torque\n", + "Tmean = T/(6*math.pi) \t\t\t#N-m\n", + "#Calculating the power required to drive the machine\n", + "P = Tmean*omega/1000 \t\t\t#kW\n", + "#Coefficient of fluctuation of speed:\n", + "#Calculating the value of LM\n", + "LM = math.pi*((3000.-1875)/(3000-750.))\n", + "#Calculating the value of NP\n", + "NP = math.pi*((3000.-1875)/(3000-750))\n", + "#Calculating the value of BM\n", + "BM = 3000-1875. \t\t\t#N-m CN = BM\n", + "#Calculating the value of MN\n", + "MN = 2*math.pi\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = (1./2*LM*BM)+(MN*BM)+(1./2*NP*BM) \t\t\t#N-m\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = deltaE/(m*k**2*omega**2)\n", + "\n", + "#Results:\n", + "print \" Power required to drive the machine P = %.3f kW.\"%(P)\n", + "print \" Coefficient of speed CS = %.3f.\"%(CS)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Power required to drive the machine P = 49.087 kW.\n", + " Coefficient of speed CS = 0.072.\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.7 Page No : 578" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N = 100. \t\t\t#rpm\n", + "k = 1.75 \t\t\t#m\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.9\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 1.5/100\n", + "#Coefficient of fluctuation of energy:\n", + "AB = 2000.\n", + "LM = 1500. \t\t\t#N-m\n", + "#Calculating the work done per cycle\n", + "WD = (1./2*math.pi*AB)+(1./2*math.pi*LM) \t\t\t#Work done per cycle N-m\n", + "#Calculating the mean resisting torque\n", + "Tmean = WD/(2*math.pi) \t\t\t#N-m\n", + "#Calculating the value of CD\n", + "CD = math.pi/2000*(2000-875) \t\t\t#rad\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = 1./2*CD*(2000-875) \t\t\t#N-m\n", + "#Calculating the coefficient of fluctuation of energy\n", + "Ce = deltaE/WD*100 \t\t\t#%\n", + "#Calculating the mass of the flywheel\n", + "m = deltaE/(k**2*omega**2*CS) \t\t\t#kg\n", + "#Crank angles for minimum and maximum speeds:\n", + "#Calculating the value of CE\n", + "CE = (2000.-875)/2000*(4*math.pi/9) \t\t\t#rad\n", + "#Calculating the crank angle for minimum speed\n", + "thetaC = ((4.*math.pi/9)-CE)*180/math.pi \t\t\t#degrees\n", + "#Calculating the value of ED\n", + "ED = (2000.-875)/2000*(math.pi-(4*math.pi/9)) \t\t\t#rad\n", + "#Calculating the crank angle for maximum speed\n", + "thetaD = ((4.*math.pi/9)+ED)*180/math.pi \t\t\t#degrees\n", + "\n", + "#Results:\n", + "print \" Coefficient of fluctuation of energy CE = %d %%.\"%(Ce)\n", + "print \" Mass of the flywheel, m = %.1f kg.\"%(m)\n", + "print \" Crank angle from IDC for the minimum speed, thetaC = %d degrees.\"%(thetaC)\n", + "print \" Crank angle from IDC for the maximum speed, thetaD = %d degrees.\"%(thetaD)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Coefficient of fluctuation of energy CE = 18 %.\n", + " Mass of the flywheel, m = 197.3 kg.\n", + " Crank angle from IDC for the minimum speed, thetaC = 35 degrees.\n", + " Crank angle from IDC for the maximum speed, thetaD = 136 degrees.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.8 Page No : 580" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N = 600. \t\t\t#rpm\n", + "Tmax = 90. \t\t\t#N-m\n", + "m = 12. \t\t\t#kg\n", + "k = 80./1000 \t\t#m\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.10\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Power developed:\n", + "#Calculating the work done per cycle\n", + "WD = 3*1./2*math.pi*90 \t\t\t#Work done per cycle N-m\n", + "#Calculating the mean torque\n", + "Tmean = WD/(2*math.pi) \t\t\t#N-m\\\n", + "#Calculating the power developed\n", + "P = Tmean*omega/1000 \t\t\t#Power developed kW\n", + "#Coefficient of fluctuation of speed:\n", + "#Calculating the maximum fluctuation of energy\n", + "#From the torque-crank angle diagram maximum energy = E+5.89 and minimum energy = E-5.89\n", + "deltaE = 5.89-(-5.89) \t\t\t#N-m\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = round(deltaE/(m*k**2*omega**2)*100) \t\t\t#%\n", + "#Calculating the coefficient of fluctuation of energy\n", + "CE = deltaE/WD*100 \t\t\t#%\n", + "#Calculating the maximum angular acceleration of the flywheel\n", + "alpha = (Tmax-Tmean)/(m*k**2) \t\t\t#rad/s**2\n", + "\n", + "#Results:\n", + "print \" Power developed = %.2f kW.\"%(P)\n", + "print \" Coefficient of fluctuation of speed CS = %d %%.\"%(CS)\n", + "print \" Coefficient of fluctuation of energy CE = %.2f %%.\"%(CE)\n", + "print \" Maximum angular acceleration of the flywheel alpha = %d rad/s**2.\"%(alpha)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Power developed = 4.24 kW.\n", + " Coefficient of fluctuation of speed CS = 4 %.\n", + " Coefficient of fluctuation of energy CE = 2.78 %.\n", + " Maximum angular acceleration of the flywheel alpha = 292 rad/s**2.\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.9 Page No : 582" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "P = 20.*1000 \t\t\t#W\n", + "N = 300. \t\t\t#rpm\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.11\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#ra/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 4./100\n", + "#Calculating the number of working strokes per cycle for a four stroke engine\n", + "n = N/2\n", + "#Calculating the work done per cycle\n", + "WD = P*60/n \t\t\t#Work done per cycle N-m\n", + "#Calculating the work done during expansion cycle\n", + "WE = WD*3./2 \t\t\t#N-m\n", + "#Calculating the maximum turning moment\n", + "Tmax = WE*2/math.pi \t\t\t#N-m\n", + "#Calculating the mean turning moment\n", + "Tmean = WD/(4*math.pi) \t\t\t#N-m\n", + "#Calculating the excess turning moment\n", + "Texcess = Tmax-Tmean \t\t\t#N-m\n", + "#Calculating the value of DE\n", + "DE = Texcess/Tmax*math.pi \t\t\t#rad\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = (1./2*DE*Texcess) \t\t\t#N-m\n", + "#Calculating the moment of inertia of the flywheel\n", + "I = deltaE/(omega**2*CS) \t\t\t#kg-m**2\n", + "\n", + "#Results:\n", + "print \" Moment of inertia of the flywheel I = %.1f kg-m**2.\"%(I)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Moment of inertia of the flywheel I = 255.4 kg-m**2.\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.10 Page No : 584" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "a1 = 0.45*10**-3\n", + "a2 = 1.7*10**-3\n", + "a3 = 6.8*10**-3\n", + "a4 = 0.65*10**-3 \t\t\t#m**2\n", + "N1 = 202.\n", + "N2 = 198. \t\t\t#rpm\n", + "R = 1.2 \t\t\t#m\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.12\n", + "#Calculating the net area\n", + "a = a3-(a1+a2+a4) \t\t\t#Net area m**2\n", + "#Calculating the energy scale constant\n", + "c = 3*10**6 \t\t\t#Energy scale constant N-m\n", + "#Calculating the net work done per cycle\n", + "WD = a*c \t\t\t#Net work done per cycle N-m\n", + "#Calculating the mean torque\n", + "Tmean = round(WD/(4*math.pi)) \t\t\t#N-m\n", + "#Calculating the value of FG\n", + "FG = Tmean \t\t\t#N-m\n", + "#Calculating the work done during expansion stroke\n", + "WDe = a3*c \t\t\t#Work done during expansion stroke N-m\n", + "#Calculating the value of AG\n", + "AG = WDe/(1./2*math.pi) \t\t\t#N-m\n", + "#Calculating the excess torque\n", + "Texcess = round(AG-FG,-1) \t\t\t#N-m\n", + "#Calculating the value of AF\n", + "AF = Texcess \t\t\t#N-m\n", + "#Calculating the value of DE\n", + "DE = round(AF/AG*math.pi,1) \t\t\t#rad\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = 1./2*DE*AF \t\t\t#N-m\n", + "#Mass of the rim of a flywheel:\n", + "#Calculating the mean speed of the flywheel\n", + "N = (N1+N2)/2 \t\t\t#rpm\n", + "#Calculating the mass of the rim of a flywheel\n", + "m = deltaE/(math.pi**2/900*R**2*N*(N1-N2)) \t\t\t#kg\n", + "\n", + "#Results:\n", + "print \" Mass of the rim of the flywheel m = %.f kg.\"%(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Mass of the rim of the flywheel m = 1381 kg.\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.11 page no : 585" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "from scipy.integrate import quad\n", + "\n", + "# variables\n", + "w = math.pi*2*180./60 # rad/s\n", + "T = 180 # rpm\n", + "Cs = 0.01 # speed\n", + "\n", + "# Calculations\n", + "work_done_r = 20000 * 2 # pi N-m\n", + "Tmean = work_done_r/2 # N-m\n", + "power = round(Tmean * w,-3)/1000\n", + "deltaE = 11078 \n", + "energy = deltaE/round((w**2*Cs),2)\n", + "excess = 9500*math.sin(math.radians(90)) - 5700*math.cos(math.radians(90))\n", + "alpha = excess/energy\n", + "\n", + "# results\n", + "print \"power developed by the engine : %.f kW\"%power\n", + "print \"maximum fluctuation of energy : %.f kg-m**2\"%energy\n", + "print \"Alpha a = %.3f rad/s**2\"%alpha" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "power developed by the engine : 377 kW\n", + "maximum fluctuation of energy : 3121 kg-m**2\n", + "Alpha a = 3.044 rad/s**2\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.12 Page No : 587" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables:\n", + "m = 500. \t\t\t#kg\n", + "k = 0.4 \t\t\t#m\n", + "N = 150. \t\t\t#rpm\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.14\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Fluctuation of energy:\n", + "#Equating the change in torque to zero and calculating the value of theta\n", + "thetaA = math.sin(math.radians(0))\n", + "thetaC = math.sin(math.radians(0))+180\n", + "thetaE = math.sin(math.radians(0))+360 \t\t\t#degrees\n", + "thetaB = 65.4\n", + "thetaD = 294.6\n", + "\n", + "#Calculating the maximum fluctuation of energy\n", + "def f4(theta): \n", + " return (5000+600*math.sin(2*theta))-(5000+500*math.sin(theta))\n", + "\n", + "deltaE = round( quad(f4 ,thetaC*math.pi/180,thetaD*math.pi/180)[0])\n", + "\n", + "#Calculating the total percentage fluctuation of speed\n", + "CS = deltaE/(m*k**2*omega**2)*100 \t\t\t#%\n", + "#Maximum and minimum angular acceleration of the flywheel and the corresponding shaft positions:\n", + "#Calculating the maximum or minimum values of theta\n", + "#Differentiating (600*math.sin(2*theta))-500*math.sin(theta) = 0 with respect to theta and equating to zero\n", + "#we get 12*2*(math.cos(theta))**2-5*math.cos(theta)-12 = 0\n", + "a = 12.*2\n", + "b = -5.\n", + "c = -12.\n", + "costheta1 = (-b+math.sqrt(b**2-4*a*c))/(2*a)\n", + "costheta2 = (-b-math.sqrt(b**2-4*a*c))/(2*a)\n", + "theta1 = math.degrees(math.acos(costheta1))\n", + "theta2 = math.degrees(math.acos(costheta2)) \t\t\t#degrees\n", + "#Calculating the maximum torque\n", + "Tmax = 600*math.sin(math.radians(2*theta1))-500*math.sin(math.radians(theta1)) \t\t\t#N-m\n", + "#Calculating the minimum torque\n", + "Tmin = 600*math.sin(math.radians(2*theta2))-500*math.sin(math.radians(theta2)) \t\t\t#N-m\n", + "#Calculating the maximum acceleration\n", + "alphamax = Tmax/(m*k**2) \t\t\t#rad/s**2\n", + "#Calculating the minimum acceleration\n", + "alphamin = abs(Tmin)/(m*k**2) \t\t\t#rad/s**2\n", + "\n", + "\n", + "#Results:\n", + "print \" Fluctuation of energy deltaE = %d N-m.\"%(deltaE)\n", + "print \" Total percentage fluctuation of speed CS = %.1f %%.\"%(CS)\n", + "print \" Shaft position corresponding to maximum and minimum accelerations\\\n", + " theta = %d degrees and %.1f degrees.\"%(theta1,theta2)\n", + "print \" Maximum acceleration, alphamax = %.2f rad/s**2.\"%(alphamax)\n", + "print \" Minimum acceleration alphamin = %.1f rad/s**2.\"%(alphamin)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Fluctuation of energy deltaE = 1204 N-m.\n", + " Total percentage fluctuation of speed CS = 6.1 %.\n", + " Shaft position corresponding to maximum and minimum accelerations theta = 35 degrees and 127.6 degrees.\n", + " Maximum acceleration, alphamax = 3.46 rad/s**2.\n", + " Minimum acceleration alphamin = 12.2 rad/s**2.\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.13 Page No : 589" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables:\n", + "I = 1000. \t\t\t#kg-m**2\n", + "N = 300. \t\t\t#rpm\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.15 and Fig. 16.16\n", + "#Calculating the angular speed of the crank\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Power of the engine:\n", + "#Calculating the work done per revolution\n", + "def f0(theta): \n", + " return 5000+1500*math.sin(3*theta)\n", + "\n", + "WD = quad(f0,0,2*math.pi)[0]\n", + "\n", + "#Calculating the mean resisting torque\n", + "Tmean = WD/(2*math.pi) \t\t\t#N-m\n", + "#Calculating the power of the engine\n", + "P = Tmean*omega/1000 \t\t\t#kW\n", + "#Maximum fluctuation of the speed of the flywheel when resisting torque is consmath.tant:\n", + "#Calculating the value of theta \n", + "theta = (5000-5000)/1500\n", + "theta = 1./3*(math.sin(math.radians((theta)))+180) \t\t\t#degrees\n", + "#Calculating the maximum fluctuation of energy\n", + "def f1(theta): \n", + " return 5000+1500*math.sin(3*theta)-5000\n", + "\n", + "deltaE = quad(f1,0,60*math.pi/180)[0]\n", + "\n", + "#Calculating the maximum fluctuation of speed of the flywheel\n", + "CS1 = deltaE/(I*omega**2)*100 \t\t\t#%\n", + "#Maximum fluctuation of speed of the flywheel when resisting torque (5000+600*math.sin(theta)) N-m:\n", + "#Calculating the values of theta thetaB and thetaC\n", + "thetaB = math.sin(math.radians(math.sqrt((1./4*(3-600./1500))))) \t\t\t#degrees\n", + "thetaC = 180-thetaB \t\t\t#degrees\n", + "#Calculating the maximum fluctuation of energy\n", + "\n", + "def f2(theta): \n", + " return (5000+1500*math.sin(3*theta))-(5000+600*math.sin(theta))\n", + "\n", + "deltaE = round( quad(f2,thetaB*math.pi/180,thetaC*math.pi/180)[0])\n", + "\n", + "#Calculating the maximum fluctuation of speed of the flywheel\n", + "CS2 = abs(deltaE)/(I*omega**2)*100 \t\t\t#%\n", + "\n", + "#Results:\n", + "print \" Power of the engine P = %.1f kW.\"%(P)\n", + "print \" Maximum fluctuation of the speed of the flywheel when resisting torque\\\n", + " is constant, CS = %.1f %%.\"%(CS1)\n", + "print \" Maximum fluctuation of speed of the flywheel when resisting torque \\\n", + " 5000+600*sintheta N-m CS = %.3f %%.\"%(CS2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Power of the engine P = 157.1 kW.\n", + " Maximum fluctuation of the speed of the flywheel when resisting torque is constant, CS = 0.1 %.\n", + " Maximum fluctuation of speed of the flywheel when resisting torque 5000+600*sintheta N-m CS = 0.020 %.\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.14 Page No : 592" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N = 800. \t\t\t#rpm\n", + "stroke = 300. \t\t\t#mm\n", + "sigma = 7.*10**6 \t\t\t#N/m**2\n", + "rho = 7200. \t\t\t#kg/m**3\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.18\n", + "#Calculating the angular speed of the engine\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 4./100\n", + "#Diameter of the flywheel rim:\n", + "#Calculating the peripheral velocity of the flywheel rim\n", + "v = math.sqrt(sigma/rho) \t\t\t#m/s\n", + "#Calculating the diameter of the flywheel rim\n", + "D = v*60/(math.pi*N) \t\t\t#m\n", + "#Cross-section of the flywheel rim:\n", + "#Calculating the value of 1 mm**2 on the turning moment diagram\n", + "c = 500.*math.pi/30 \t\t\t#Value of 1 mm**2 on the turning moment diagram N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = round((420.-(-30))*c) \t\t\t#N-m\n", + "#Calculating the mass of the flywheel rim\n", + "m = deltaE/(v**2*CS) \t\t\t#kg\n", + "#Calculating the thickness of the flywheel rim\n", + "t = math.sqrt(m/(math.pi*D*5*rho))*1000 \t\t\t#mm\n", + "#Calculating the width of the flywheel rim\n", + "b = 5*t \t\t\t #mm\n", + "\n", + "#Results:\n", + "print \" Diameter of the flywheel rim D = %.3f m.\"%(D)\n", + "print \" Thickness of the flywheel rim t = %d mm.\"%(t)\n", + "print \" Width of the flywheel rim b = %d mm.\"%(b)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Diameter of the flywheel rim D = 0.744 m.\n", + " Thickness of the flywheel rim t = 84 mm.\n", + " Width of the flywheel rim b = 424 mm.\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.15 Page No : 594" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "P = 150.*1000 \t\t\t#W\n", + "N = 80. \t\t\t#rpm\n", + "CE = 0.1\n", + "D = 2.\n", + "R = D/2. \t\t\t#m\n", + "rho = 7200. \t\t\t#kg/m**3\n", + "\n", + "#Solution:\n", + "#Calculating the angular speed of the engine\n", + "omega = round(2*math.pi*N/60,1) \t\t\t#rad/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 4./100\n", + "#Mass of the flywheel rim:\n", + "#Calculating the work done per cycle\n", + "WD = P*60/N \t\t\t#Work done per cycle N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = WD*CE \t\t\t#N-m\n", + "#Calculating the mass moment of inertia of the flywheel\n", + "I = deltaE/(omega**2*CS) \t\t\t#kg-m**2\n", + "#Calculating the mass moment of inertia of the flywheel rim\n", + "Irim = 0.95*I \t\t\t#kg-m**2\n", + "#Calculating the mass of the flywheel rim\n", + "k = R \t\t\t#Radius of gyration m\n", + "m = Irim/k**2 \t\t\t#kg\n", + "#Calculating the cross-sectional area of the flywheel rim\n", + "A = m/(2*math.pi*R*rho) \t\t\t#m**2\n", + "\n", + "#Resilts:\n", + "print \" Mass of the flywheel rim m = %.f kg.\"%(m)\n", + "print \" Cross-sectional area of the flywheel rim A = %.3f m**2.\"%(A)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Mass of the flywheel rim m = 3787 kg.\n", + " Cross-sectional area of the flywheel rim A = 0.084 m**2.\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.16 Page No : 595" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N = 600. \t\t\t#rpm\n", + "rho = 7250. \t\t\t#kg/m**3\n", + "sigma = 6.*10**6 \t\t\t#N/m**2\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.19\n", + "#Calculating the angular speed of the engine\n", + "omega = 2.*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the total fluctuation of speed\n", + "CS = 2./100\n", + "#Moment of inertia of the flywheel:\n", + "#Calculating the value of 1 mm**2 of turning moment diagram\n", + "c = 250.*math.pi/60 \t\t\t#Value of 1 mm**2 of turning moment diagram N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = round((162.-(-35))*c) \t\t\t#N-m\n", + "#Calculating the moment of inertia of the flywheel\n", + "I = deltaE/(omega**2*CS) \t\t\t#kg-m**2\n", + "#Dimensions of the flywheel rim:\n", + "#Calculating the peripheral velocity of the flywheel\n", + "v = math.sqrt(sigma/rho) \t\t\t#m/s\n", + "#Calculating the mean diameter of the flywheel\n", + "D = v*60/(math.pi*N) \t\t\t#m\n", + "#Calculating the maximum fluctuation of energy of the flywheel rim\n", + "deltaErim = 0.92*deltaE \t\t\t#N-m\n", + "#Calculating the mass of the flywheel rim\n", + "m = deltaErim/(v**2*CS) \t\t\t#kg\n", + "#Calculating the thickness of the flywheel rim\n", + "t = math.sqrt(m/(math.pi*D*2*rho))*1000 \t\t\t#mm\n", + "#Calculating the breadth of the flywheel rim\n", + "b = 2*t \t\t\t#mm\n", + "\n", + "#Results:\n", + "print \" Moment of inertia of the flywheel I = %.1f kg-m**2.\"%(I)\n", + "print \" Thickness of the flywheel rim t = %.1f mm.\"%(t)\n", + "print \" Breadth of the flywheel rim b = %.1f mm.\"%(b)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Moment of inertia of the flywheel I = 32.7 kg-m**2.\n", + " Thickness of the flywheel rim t = 58.6 mm.\n", + " Breadth of the flywheel rim b = 117.2 mm.\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.17 Page No : 596" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "a1 = 5.*10**-5 #m**2\n", + "a2 = 21.*10**-5 #m**2\n", + "a3 = 85.*10**-5 #m**2\n", + "a4 = 8.*10**-5 \t\t\t#m**2\n", + "N2 = 98.\n", + "N1 = 102. \t\t\t#rpm\n", + "rho = 8150. \t\t\t#kg/m**3\n", + "sigma = 7.5*10**6 \t\t\t#N/m**2\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.20\n", + "#Calculating the net area\n", + "a = a3-(a1+a2+a4) \t\t\t#Net area m**2\n", + "#Calculating the value of 1 m**2 on the turning moment diagram in terms of work\n", + "c = 14*10**6 \t\t\t#Value of 1 m**2 on the turning moment diagram N-m\n", + "#Calculating the net work done per cycle\n", + "WD = a*c \t\t\t#Net work done per cycle N-m\n", + "#Calculating the mean torque on the flywheel\n", + "Tmean = round(WD/(4*math.pi)) \t\t\t#N-m\n", + "FG = Tmean \t\t\t#N-m\n", + "#Calculating the work done during expansion stroke\n", + "WDe = int(a3*c) \t\t\t#Work done during expansion stroke N-m\n", + "#Calculating the value of AG\n", + "AG = int(WDe/(1./2*math.pi)) \t\t\t#N-m\n", + "#Calculating the excess torque\n", + "Texcess = AG-FG \t\t\t#Excess torque N-m\n", + "AF = Texcess \t\t\t#N-m\n", + "#Calculating the value of DE\n", + "DE = round(AF/AG*math.pi,1) \t\t\t#rad\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = 1./2*DE*AF \t\t\t#N-m\n", + "#Moment of inertia of the flywheel:\n", + "#Calculating the mean speed during the cycle\n", + "N = (N1+N2)/2 \t\t\t#rpm\n", + "#Calculating the corresponding angular mean speed\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = (N1-N2)/N\n", + "#Calculating the moment of inertia of the flywheel\n", + "I = deltaE/(omega**2*CS) \t\t\t#kg-m**2\n", + "#Size of flywheel:\n", + "#Calculating the peripheral velocity of the flywheel\n", + "v = math.sqrt(sigma/rho) \t\t\t#m/s\n", + "#Calculating the mean diameter of the flywheel\n", + "D = v*60/(math.pi*N) \t\t\t#m\n", + "#Calculating the mass of the flywheel rim\n", + "m = deltaE/(v**2*CS) \t\t\t#kg\n", + "#Calculating the thickness of the flywheel rim\n", + "t = math.sqrt(m/(math.pi*D*4*rho))*1000 \t\t\t#mm\n", + "#Calculating the width of the flywheel rim\n", + "b = 4*t \t\t\t#mm\n", + "\n", + "#Results:\n", + "print \" Moment of inertia of the flywheel I = %.f kg-m**2.\"%(I)\n", + "print \" Thickness of the flywheel rim t = %.1f mm.\"%(t)\n", + "print \" Width of the flywheel rim b = %.1f mm.\"%(b)\n", + "\n", + "# rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Moment of inertia of the flywheel I = 2316 kg-m**2.\n", + " Thickness of the flywheel rim t = 21.6 mm.\n", + " Width of the flywheel rim b = 86.3 mm.\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.18 Page No : 599" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "P = 50.*1000 \t\t\t#W\n", + "N = 150. \t\t\t#rpm\n", + "n = 75.\n", + "sigma = 4.*10**6 \t\t\t#N/m**2\n", + "rho = 7200. \t\t\t#kg/m**3\n", + "\n", + "#Solution:\n", + "#Refer Fig. 16.21\n", + "#Calculating the angular speed of the engine\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the mean torque transmitted by the flywheel\n", + "Tmean = P/omega \t\t\t#N-m\n", + "FG = Tmean \t\t\t#N-m\n", + "#Calculating the work done per cycle\n", + "WD = Tmean*4*math.pi \t\t\t#Work done per cycle N-m\n", + "#Calculating the work done during power stroke\n", + "WDp = 1.4*WD \t\t\t#Work done during power stroke N-m\n", + "#Calculating the maximum torque transmitted by the flywheel\n", + "Tmax = WDp/(1./2*math.pi) \t\t\t#N-m\n", + "BF = Tmax \t\t\t#N-m\n", + "#Calculating the excess torque\n", + "Texcess = Tmax-Tmean \t\t\t#N-m\n", + "BG = Texcess \t\t\t#N-m\n", + "#Calculating the value of DE\n", + "DE = BG/BF*math.pi \t\t\t#N-m\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = 1./2*DE*BG \t\t\t#N-m\n", + "#Mean diameter of the flywheel:\n", + "#Calculating the peripheral velocity of the flywheel\n", + "v = math.sqrt(sigma/rho) \t\t\t#m/s\n", + "#Calculating the mean diameter of the flywheel\n", + "D = v*60./(math.pi*N) \t\t\t#m\n", + "#Cross-sectional dimensions of the rim:\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 1./100\n", + "#Calculating the total energy of the flywheel\n", + "E = deltaE/(2*CS) \t\t\t#N-m\n", + "#Calculating the energy of the rim\n", + "Erim = 15./16*E \t\t\t#N-m\n", + "#Calculating the mass of the flywheel rim\n", + "m = Erim/(1./2*v**2) \t\t\t#kg\n", + "#Calculating the thickness of the rim\n", + "t = round(math.sqrt(m/(math.pi*D*4*rho))*1000) \t\t\t#mm\n", + "#Calculating the width of the rim\n", + "b = 4*t \t\t\t#mm\n", + "\n", + "#Results:\n", + "print \" Mean diameter of the flywheel D = %d m.\"%(D)\n", + "print \" Thickness of the flywheel rim t = %d mm.\"%(t)\n", + "print \" Width of the flywheel rim b = %d mm.\"%(b)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Mean diameter of the flywheel D = 3 m.\n", + " Thickness of the flywheel rim t = 170 mm.\n", + " Width of the flywheel rim b = 680 mm.\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.19 Page No : 603" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "N1 = 225.\n", + "N2 = 200. \t\t\t#rpm\n", + "k = 0.5 \t\t\t#m\n", + "E1 = 15.*1000 \t\t\t#N-m\n", + "HolePunched = 720. \t\t\t#per hour\n", + "\n", + "#Solution:\n", + "#Power of the motor:\n", + "#Calculating the total energy required per second\n", + "E = E1*HolePunched/3600 \t\t\t#N-m/s\n", + "#Calculating the power of the motor\n", + "P = E/1000 \t\t\t#kW\n", + "#Minimum mass of the flywheel:\n", + "#Calculating the energy supplied by the motor in 2 seconds\n", + "E2 = E*2 \t\t\t#N-m\n", + "#Calculating the energy supplied by the flywheel during punching\n", + "deltaE = E1-E2 \t\t\t#N-m\n", + "#Calculating the mean speed of the flywheel\n", + "N = (N1+N2)/2 \t\t\t#rpm\n", + "#Calculating the minimum mass of the flywheel\n", + "m = round(deltaE*900/(math.pi**2*k**2*N*(N1-N2))) \t\t\t#kg\n", + "\n", + "#Results:\n", + "print \" Power of the motor P = %d kW.\"%(P)\n", + "print \" Minimum mass of the flywheel m = %d kg.\"%(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Power of the motor P = 3 kW.\n", + " Minimum mass of the flywheel m = 618 kg.\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.20 Page No : 603" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "d = 38. #mm\n", + "t = 32. #mm\n", + "s = 100. \t\t\t#mm\n", + "E1 = 7. \t\t\t#N-m/mm**2 of sheared area\n", + "v = 25. \t\t\t#m/s\n", + "\n", + "#Solution:\n", + "#Power of the motor required:\n", + "#Calculating the sheared area\n", + "A = round(math.pi*d*t) \t\t\t#mm**2\n", + "#Calculating the total energy required per hole\n", + "E1 = E1*A \t\t\t#N-m\n", + "#Calculating the energy required for punching work per second\n", + "E = E1/10 \t\t\t#Energy required for punching work per second N-m/s\n", + "#Calculating the power of the motor required\n", + "P = E/1000 \t\t\t#Power of the motor required kW\n", + "#Mass of the flywheel required:\n", + "#Calculating the time required to punch a hole in a 32 mm thick plate\n", + "t32 = 10/(2*s)*t \t\t\t#Time required to punch a hole in 32 mm thick plate seconds\n", + "#Calculating the energy supplied by the motor in t32 seconds\n", + "E2 = E*t32 \t\t\t#N-m\n", + "#Calculating the energy to be supplied by the flywheel during punching\n", + "deltaE = E1-E2 \t\t\t#N-m\n", + "#Calculating the coefficient of fluctuation of speed\n", + "CS = 3/100.\n", + "#Calculating the mass of the flywheel required\n", + "m = round(deltaE/(v**2*CS)) \t\t\t#kg\n", + "\n", + "#Results:\n", + "print \" Power of the motor required P = %.3f kW.\"%(P)\n", + "print \" Mass of the flywheel required m = %d kg.\"%(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Power of the motor required P = 2.674 kW.\n", + " Mass of the flywheel required m = 1198 kg.\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.21 Page No : 604" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "P = 3. \t\t\t#kW\n", + "m = 150. \t\t\t#kg\n", + "k = 0.6 \t\t\t#m\n", + "N1 = 300. \t\t\t#rpm\n", + "\n", + "#Solution:\n", + "#Calculating the angular speed of the flywheel before riveting\n", + "omega1 = 2*math.pi*N1/60 \t\t\t#rad/s\n", + "#Speed of the flywheel immediately after riveting:\n", + "#Calculating the energy supplied by the motor\n", + "E2 = P*1000 \t\t\t#N-m/s\n", + "#Calculating the energy absorbed during one riveting operation which takes 1 second\n", + "E1 = 10000 \t\t\t#N-m\n", + "#Calculating the energy to be supplied by the flywheel for each riveting operation per second\n", + "deltaE = E1-E2 \t\t\t#N-m\n", + "#Calculating the angular speed of the flywheel immediately after riveting\n", + "omega2 = math.sqrt(omega1**2-(2*deltaE/(m*k**2))) \t\t\t#rad/s\n", + "#Calculating the corresponding speed in rpm\n", + "N2 = omega2*60/(2*math.pi) \t\t\t#rpm\n", + "#Calculating the number of rivets that can be closed per minute\n", + "n = E2/E1*60 \t\t\t#Number of rivets that can be closed per minute\n", + "\n", + "#Results:\n", + "print \" Speed of the flywheel immediately after riveting N2 = %.1f rpm.\"%(N2)\n", + "print \" Number of rivets that can be closed per minute = %d rivets.\"%(n)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Speed of the flywheel immediately after riveting N2 = 257.6 rpm.\n", + " Number of rivets that can be closed per minute = 18 rivets.\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.22 Page No : 605" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "d = 40. #mm\n", + "t = 15. \t\t\t#mm\n", + "NoofHoles = 30. \t\t\t#per minute\n", + "EnergyRequired = 6. \t\t\t#N-m/mm**2\n", + "Time = 1./10 \t\t\t#seconds\n", + "N1 = 160.\n", + "N2 = 140. \t\t\t#rpm\n", + "k = 1. \t\t\t#m\n", + "\n", + "#Solution:\n", + "#Calculating the sheared area per hole\n", + "A = round(math.pi*d*t) \t\t\t#Sheared area per hole mm**2\n", + "#Calculating the energy required to punch a hole\n", + "E1 = EnergyRequired*A \t\t\t#N-m\n", + "#Calculating the energy required for punching work per second\n", + "E = E1*NoofHoles/60 \t\t\t#Energy required for punching work per second N-m/s\n", + "#Calculating the energy supplied by the motor during the time of punching\n", + "E2 = E*Time \t\t\t#N-m\n", + "#Calculating the energy to be supplied by the flywheel during punching a hole\n", + "deltaE = E1-E2 \t\t\t#N-m\n", + "#Calculating the mean speed of the flywheel\n", + "N = (N1+N2)/2 \t\t\t#rpm\n", + "#Calculating the mass of the flywheel required\n", + "m = round(deltaE*900/(math.pi**2*k**2*N*(N1-N2))) \t\t\t#kg\n", + "\n", + "#Results:\n", + "print \" Mass of the flywheel required m = %d kg.\"%(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Mass of the flywheel required m = 327 kg.\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.23 Page No : 606" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables:\n", + "n = 25.\n", + "d1 = 25./1000 #m\n", + "t1 = 18./1000 #m\n", + "D = 1.4\n", + "R = D/2 \t\t\t#m\n", + "touu = 300.*10**6 \t\t\t#N/m**2\n", + "etam = 95./100\n", + "CS = 0.1\n", + "sigma = 6.*10**6 \t\t\t#N/m**2\n", + "rho = 7250. \t\t\t#kg/m**3\n", + "\n", + "#Solution:\n", + "#Power needed for the driving motor:\n", + "#Calculating the area of the plate sheared\n", + "AS = math.pi*d1*t1 \t\t\t#m**2\n", + "#Calculating the maximum shearing force required for punching\n", + "FS = AS*touu \t\t\t#N\n", + "#Calculating the energy required per stroke\n", + "E = 1./2*FS*t1 \t\t\t#Energy required per stroke N-m\n", + "#Calculating the energy required per minute\n", + "E1 = E*n \t\t\t#Energy required per minute N-m\n", + "#Calculating the power required for the driving motor\n", + "P = E1/(60*etam)/1000 \t\t\t#Energy required for the driving motor kW\n", + "#Dimensions for the rim cross-section:\n", + "#Calculating the maximum fluctuation of energy\n", + "deltaE = 9./10*E \t\t\t#N-m\n", + "#Calculating the maximum fluctuation of energy provided by the rim\n", + "deltaErim = 0.95*deltaE \t\t\t#N-m\n", + "#Calculating the mean speed of the flywheel\n", + "N = 9.*25 \t\t\t#rpm\n", + "#Calculating the mean angular speed\n", + "omega = 2*math.pi*N/60 \t\t\t#rad/s\n", + "#Calculating the mass of the flywheel\n", + "m = round(deltaErim/(R**2*omega**2*CS)) \t\t\t#kg\n", + "#Calculating the thickness of rim\n", + "t = math.sqrt(m/(math.pi*D*2*rho))*1000 \t\t\t#mm\n", + "#Calculating the width of rim\n", + "b = 2*t \t\t\t#mm\n", + "\n", + "#Results:\n", + "print \" Power needed for the driving motor = %.3f kW.\"%(P)\n", + "print \" Thickness of the flywheel rim t = %d mm.\"%(t)\n", + "print \" Width of the flywheel rim b = %d mm.\"%(b)\n", + "#Answers vary due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Power needed for the driving motor = 1.674 kW.\n", + " Thickness of the flywheel rim t = 43 mm.\n", + " Width of the flywheel rim b = 86 mm.\n" + ] + } + ], + "prompt_number": 32 + } + ], + "metadata": {} + } + ] +}
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