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diff --git a/Fundamentals_of_Electrical_Machines/CH_2.ipynb b/Fundamentals_of_Electrical_Machines/CH_2.ipynb new file mode 100755 index 00000000..4a1c83c7 --- /dev/null +++ b/Fundamentals_of_Electrical_Machines/CH_2.ipynb @@ -0,0 +1,623 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "CHAPTER 2: BASICS OF MAGNETIC CIRCUITS"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1, Page number 53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "l = 4.0 #Length(m)\n",
+ "w = 2.0 #Width(m)\n",
+ "B = 0.12 #Magnetic flux density(Tesla)\n",
+ "\n",
+ "#Calculation \n",
+ "A = l*w #Area(m^2)\n",
+ "flux = B*A #Magnetic flux(Wb)\n",
+ "\n",
+ "#Result\n",
+ "print('Magnetic flux , \u03a6 = %.2f Wb' %flux)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnetic flux , \u03a6 = 0.96 Wb\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2, Page number 54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "d_in = 3.0 #Inside diameter(cm)\n",
+ "d_out = 6.0 #Outside diameter(cm)\n",
+ "N = 200.0 #Number of turns\n",
+ "I = 3.0 #Current(A)\n",
+ "flux = 0.015 #Flux(Wb)\n",
+ "\n",
+ "#Calculation\n",
+ "d = d_in+(d_out-d_in)/2 #Distance(cm)\n",
+ "l = math.pi*d #Mean length of core(cm)\n",
+ "A = math.pi*d**2/4*10**-4 #Area(m^2)\n",
+ "B = flux/A #Flux density(Wb/m^2)\n",
+ "MMF = N*I #Magnetomotive force(At)\n",
+ "H = N*I/(l*10**-2) #Magnetic field intensity(At/m)\n",
+ "\n",
+ "#Result\n",
+ "print('Flux density , B = %.2f Wb/m^2' %B)\n",
+ "print('Magnetomotive force , MMF = %.1f At' %MMF)\n",
+ "print('Magnetic field intensity , H = %.2f At/m' %H)\n",
+ "print('\\nNOTE : ERROR : Calculation & unit mistakes in textbook')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Flux density , B = 9.43 Wb/m^2\n",
+ "Magnetomotive force , MMF = 600.0 At\n",
+ "Magnetic field intensity , H = 4244.13 At/m\n",
+ "\n",
+ "NOTE : ERROR : Calculation & unit mistakes in textbook\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3, Page number 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "u_r = 625.0 #Relative permeability of rectangular core\n",
+ "N = 25.0 #Number of turns\n",
+ "I = 2.0 #Current(A)\n",
+ "a = 5.5 #Lenght of rectangular core(cm)\n",
+ "b = 1.5 #Width of rectangular core(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "l = 2*(a+b) #Mean length of core(cm)\n",
+ "H = N*I/(l*10**-2) #Magnetic field intensity(At/m)\n",
+ "u_0 = 4*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "u = u_0*u_r #Permeabilty\n",
+ "B = u*H #Magnetic flux density(Wb/m^2)\n",
+ "\n",
+ "#Result\n",
+ "print('Magnetic field intensity , H = %.f At/m ' %H)\n",
+ "print('Permeabilty , \u00b5 = %.2e ' %u)\n",
+ "print('Magnetic flux density , B = %.2f Wb/m^2 ' %B)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnetic field intensity , H = 357 At/m \n",
+ "Permeabilty , \u00b5 = 7.85e-04 \n",
+ "Magnetic flux density , B = 0.28 Wb/m^2 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4, Page number 57"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "N = 6.0 #Number of turns\n",
+ "I = 3.0 #Current(A)\n",
+ "flux = 0.056 #Flux(Wb)\n",
+ "\n",
+ "#Calculation\n",
+ "MMF = N*I #Magnetomotive force(At)\n",
+ "R_m = MMF/flux #Reluctance(At/Wb)\n",
+ "\n",
+ "#Result\n",
+ "print('Magnetomotive force , MMF = %.f At' %MMF)\n",
+ "print('Reluctance , R_m = %.1f At/Wb' %R_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnetomotive force , MMF = 18 At\n",
+ "Reluctance , R_m = 321.4 At/Wb\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.5, Page number 59"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "I = 15.0 #Current through conductor(A)\n",
+ "N = 10.0 #Number of turns\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "u_r = 1.0 #Relative permeability of air medium\n",
+ "r = 0.015 #Distance(m)\n",
+ "\n",
+ "#Calculation\n",
+ "B = u_0*u_r*N*I/(2*math.pi*r) #Magnetic flux density(T)\n",
+ "\n",
+ "#Result\n",
+ "print('Magnetic flux density , B = %.1e T' %B)\n",
+ "print('\\nNOTE : ERROR : Distance is 1.5 cm & not 2.5 cm as given in textbook')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnetic flux density , B = 2.0e-03 T\n",
+ "\n",
+ "NOTE : ERROR : Distance is 1.5 cm & not 2.5 cm as given in textbook\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.6, Page number 60-61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "N = 200.0 #Number of turns \n",
+ "d_in = 7.0 #Inner diameter(cm)\n",
+ "d_out = 10.0 #Outer diameter(cm)\n",
+ "A = 0.005 #Cross sectional area(m^2)\n",
+ "I = 5.0 #Current through coil(A)\n",
+ "\n",
+ "#Calculation\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "R = d_out-d_in\n",
+ "l = round(2*math.pi*R/100,2) #Mean circumference length(m)\n",
+ "#For case(i)\n",
+ "H = N*I/l #Magnetic field intensity(At/m)\n",
+ "#For case(ii)\n",
+ "B = u_0*H*1000 #Flux density(mWb/m^2)\n",
+ "#For case(iii)\n",
+ "flux = B*A*1000 #Flux(\u00b5Wb)\n",
+ "\n",
+ "#Result\n",
+ "print('Magnetic field intensity , H = %.1f At/m' %H)\n",
+ "print('Flux density , B = %.1f mWb/m^2' %B)\n",
+ "print('Flux , \u03a6 = %.f \u00b5Wb' %flux)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Magnetic field intensity , H = 5263.2 At/m\n",
+ "Flux density , B = 6.6 mWb/m^2\n",
+ "Flux , \u03a6 = 33 \u00b5Wb\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.7, Page number 62-63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "l = 0.1 #Length(m)\n",
+ "w = 0.01 #Width(m)\n",
+ "h = 0.1 #Height(m)\n",
+ "N = 450.0 #Number of turns\n",
+ "I = 0.2 #Current(A)\n",
+ "u_r = 850.0 #Relative permeability\n",
+ "\n",
+ "#Calculation\n",
+ "MMF = N*I #Magnetomotive force(At)\n",
+ "l_c = (h-w)*4 #Mean length of the path(m)\n",
+ "A = w*w #Cross sectional area(m^2)\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "R_m = l_c/(u_0*u_r*A) #Reluctance(At/Wb)\n",
+ "flux = MMF/R_m #Flux(Wb)\n",
+ "B = flux/A #Magnetic flux density(Wb/m^2)\n",
+ "H = B/(u_0*u_r) #Magnetic field intensity(At/m)\n",
+ "\n",
+ "#Result\n",
+ "print('Flux , \u03a6 = %.2e Wb' %flux)\n",
+ "print('Flux density , B = %.2f Wb/m^2' %B)\n",
+ "print('Field intensity , H = %.1f At/m' %H)\n",
+ "print('\\nNOTE : Changes in obtained answer from that of textbook is due to more precision')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Flux , \u03a6 = 2.67e-05 Wb\n",
+ "Flux density , B = 0.27 Wb/m^2\n",
+ "Field intensity , H = 250.0 At/m\n",
+ "\n",
+ "NOTE : Changes in obtained answer from that of textbook is due to more precision\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.8, Page number 64-65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "N = 450.0 #Number of turns wound on left side of limb\n",
+ "A = 4.0 #Cross sectional area(m^2)\n",
+ "phi_2 = 3.0 #Flux(Wb) in the right limb\n",
+ "u_r = 500.0 #Relative permeability\n",
+ "l_1 = 0.12 #Length of middle limb(m)\n",
+ "l_2 = 0.24 #Length of right limb(m)\n",
+ "\n",
+ "#Calculation\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "phi_1 = phi_2*l_2/l_1 #Flux in middle limb(Wb)\n",
+ "phi = phi_1+phi_2 #Total flux(Wb)\n",
+ "B = phi/A #Flux density in the left limb(Wb/m^2)\n",
+ "H = B/(u_0*u_r) #Magnetic field intensity(At/m)\n",
+ "MMF = H*l_2 #Magnetomotive force(At)\n",
+ "B_2 = phi_2/A #Flux density in the right limb(Wb/m^2)\n",
+ "H_2 = B_2/(u_0*u_r) #Magnetic field(At/m)\n",
+ "MMF_2 = H_2*l_2 #Magnetomotive force(At)\n",
+ "MMF_t = MMF+MMF_2 #Total magnetomotive force(At)\n",
+ "I = MMF_t/N #Current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('Current , I = %.2f A' %I)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Current , I = 2.55 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.9, Page number 67-68"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "l = 0.45 #Mean length(m)\n",
+ "A = 25.0*10**-4 #Cross sectional area(m^2)\n",
+ "l_g = 0.8*10**-3 #Length of air gap(m)\n",
+ "N = 500.0 #Number of turns \n",
+ "I = 1.25 #Current(A) \n",
+ "flux = 1.5*10**-3 #Flux(Wb)\n",
+ "\n",
+ "#Calculation\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "B = flux/A #Magnetic flux density(Wb/m^2)\n",
+ "MMF = N*I #Magnetomotive force(At)\n",
+ "R_m = MMF/flux #Reluctance(At/Wb)\n",
+ "H = B/u_0 #Magnetizing force(At/m)\n",
+ "MMF_ag = H*l_g #Magnetomotive force(At)\n",
+ "MMF_i = MMF-MMF_ag #Magnetomotive force for iron ring(At)\n",
+ "H_i = MMF_i/l #Magnetic field intensity for iron part(At/m)\n",
+ "u_r = B/(u_0*H_i) #Relative permeability for iron\n",
+ "\n",
+ "#Result\n",
+ "print('Reluctance , R_m = %.2e At/Wb' %R_m)\n",
+ "print('Relative permeability of the iron ring iron , \u00b5_r = %.f ' %u_r)\n",
+ "print('\\nNOTE : Reluctance part is not solved in textbook')\n",
+ "print('ERROR : Current is 1.25A not 2.25A & flux is 1.5 mWb not 2.5 mWb as given in textbook')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reluctance , R_m = 4.17e+05 At/Wb\n",
+ "Relative permeability of the iron ring iron , \u00b5_r = 884 \n",
+ "\n",
+ "NOTE : Reluctance part is not solved in textbook\n",
+ "ERROR : Current is 1.25A not 2.25A & flux is 1.5 mWb not 2.5 mWb as given in textbook\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.10, Page number 68"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "A = 2.0*10**-4 #Cross sectional area(m^2)\n",
+ "N = 200.0 #Number of turns \n",
+ "flux = 1.5*10**-3 #Flux(Wb)\n",
+ "u_r = 4000.0 #Relative permeability of core\n",
+ "l_g = 0.01 #Length of air gap(m)\n",
+ "a = 9.0 #Length(cm)\n",
+ "w = 3.0 #Width(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "R_mg = l_g/(u_0*A) #Reluctance of air gap(At/Wb)\n",
+ "l = 4*(a-w-w+(1.5+1.5))-1 #Mean length of iron(cm)\n",
+ "u = u_0*u_r #Permeability\n",
+ "R_mi = l*10**-2/(u*A) #Reluctance of iron(At/Wb)\n",
+ "R_mt = R_mg+R_mi #Total reluctance(At/Wb)\n",
+ "I = R_mt*flux/N #Current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('Total reluctance , R_mt = %.3e AT/Wb' %R_mt)\n",
+ "print('Current flowing through the coil , I = %.1f A' %I)\n",
+ "print('\\nNOTE : ERROR : Total flux is 1.5 mWB & not 2.5 mWB as given in textbook question')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total reluctance , R_mt = 4.002e+07 AT/Wb\n",
+ "Current flowing through the coil , I = 300.1 A\n",
+ "\n",
+ "NOTE : ERROR : Total flux is 1.5 mWB & not 2.5 mWB as given in textbook question\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.11, Page number 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "I = 150.0 #Current through conductor(A)\n",
+ "l = 2.0 #Conductor length(m)\n",
+ "B = 0.35 #Magnetic flux density(T)\n",
+ "\n",
+ "#Calculation\n",
+ "F = B*l*I #Force(N)\n",
+ "\n",
+ "#Result\n",
+ "print('Force , F = %.f N' %F)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force , F = 105 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.12, Page number 76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "l = 25.0*10**-2 #Length of air-core coil(m)\n",
+ "A = 4.0*10**-4 #Cross sectional area(m^2)\n",
+ "N = 65.0 #Number of turns\n",
+ "\n",
+ "#Calculation\n",
+ "u_0 = 4.0*math.pi*10**-7 #Permeability of free space(H/m)\n",
+ "u_r = 1.0\n",
+ "u = u_0*u_r #Permeability\n",
+ "L = N**2*u*A/l*10**6 #Inductance(\u00b5H)\n",
+ "\n",
+ "#Result\n",
+ "print('Inductance of the coil , L = %.1f \u00b5H' %L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Inductance of the coil , L = 8.5 \u00b5H\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.13, Page number 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "k_h = 110.0 #Hysteresis co-efficient(J/m^3)\n",
+ "V_cvol = 0.005 #Volume of core(m^3)\n",
+ "B_m = 1.12 #Maximum flux density(T)\n",
+ "f = 60.0 #Frequency(Hz)\n",
+ "n = 1.6\n",
+ "\n",
+ "#Calculation\n",
+ "P_h = k_h*V_cvol*B_m**n*f #Hysteresis loss(W)\n",
+ "\n",
+ "#Result\n",
+ "print('Hysteresis loss , P_h = %.2f W' %P_h)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Hysteresis loss , P_h = 39.56 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |