{ "metadata": { "name": "", "signature": "sha256:7389552750eb30891c831f10215e616f84c75b4bc1c44e309d45236439691034" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 38: Magnetic materials

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 1, page no. 694

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "A = 12.5;# in cm2\n", "x = 500;# horizontal axis 1 cm = 500 A/m\n", "y = 0.2;# vertical axis 1 cm = 0.2 T\n", "f = 50;# in Hz\n", "\n", " #calculation: \n", " #hysteresis loss per cycle\n", "HL = A*x*y\n", " #At 50 Hz frequency, hysteresis loss\n", "HLf = HL*f\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n(a)hysteresis loss per cycle is = \",HL,\" J/m3\"\n", "print \"\\n(b)At 50 Hz frequency, hysteresis loss \",HLf,\" W/m3\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", "(a)hysteresis loss per cycle is = 1250.0 J/m3\n", "\n", "(b)At 50 Hz frequency, hysteresis loss 62500.0 W/m3" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 2, page no. 695

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "n = 1.6;# the Steinmetz index\n", "f1 = 50;# in Hz\n", "f2 = 25;# in Hz\n", "Bm1 = 1.5;# in Tesla\n", "Bm2 = 1.1;# in Tesla\n", "Ph1 = 62500;# in W/m3\n", "v = 1;\n", "\n", "#calculation: \n", " #hysteresis loss Ph = kh*v*f*(Bm)**n\n", "kh = Ph1/(v*f1*(Bm1)**n)\n", " #When f = 25 Hz and Bm = 1.1 T,\n", "Ph2 = kh*v*f2*(Bm2)**n\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n hysteresis loss When f = 25 Hz and Bm = 1.1 T, is = \",round(Ph2,2),\" W/m3\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " hysteresis loss When f = 25 Hz and Bm = 1.1 T, is = 19025.33 W/m3" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 3, page no. 695

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "csa = 0.002;# in m2\n", "l = 1;# in m\n", "a = 400/0.01;# 10 mm = 400 A/m \n", "b = 0.1/0.01;# 10 mm = 0.1 T \n", "A = 0.01;# in m2\n", "f = 80;# in Hz\n", "\n", "#calculation: \n", " #hysteresis loss per cycle\n", "HL = A*a*b\n", " #At a frequency of 80 Hz,\n", " #hysteresis loss\n", "HLf = HL*f\n", " #Volume of ring\n", "v = csa*l\n", " #hysteresis loss\n", "Ph = HLf*v\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n the hysteresis loss at a frequency of 80 Hz is \",Ph,\" W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " the hysteresis loss at a frequency of 80 Hz is 640.0 W" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 4, page no. 696

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Phi1 = 0.01;# in Wb\n", "Phi2 = 0.008;# in Wb\n", "csa = 0.008;# in m2\n", "v = 0.005;# in m3\n", "f = 50;# in Hz\n", "n = 1.7;# the Steinmetz constant\n", "Ph1 = 100;# in Watt\n", "\n", " #calculation: \n", " #maximum flux density\n", "Bm1 = Phi1/csa\n", " #hysteresis loss Ph1 = kh*v*f*(Bm1)**n\n", "kh = Ph1/(v*f*(Bm1)**n)\n", " #When the maximum core flux is 8 mWb,\n", "Bm2 = Phi2/csa\n", " #hysteresis loss, Ph2\n", "Ph2 = kh*v*f*(Bm2)**n\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"value of hysteresis loss when maximum core flux is 8 mWb and the frequency is 50 Hz is \",round(Ph2,2),\" W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "value of hysteresis loss when maximum core flux is 8 mWb and the frequency is 50 Hz is 68.43 W\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5, page no. 699

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Pe1 = 10;# in W/m3\n", "f1 = 50;# in Hz\n", "f2 = 30;# in Hz\n", "\n", " #calculation: \n", " #When the eddy current loss is 10 W/m3, frequency f is 50 Hz.\n", " #constant k\n", "k = Pe1/(f1**2)\n", " #When the frequency is 30 Hz, eddy current loss,\n", "Pe2 = k*(f2**2)\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\neddy current loss per cubic metre is \",Pe2,\" W/m3\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", "eddy current loss per cubic metre is 3.6 W/m3" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 6, page no. 699

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Pe = 100;# in W/m3\n", "f1 = 50;# in Hz\n", "t1 = 0.0005;# in m\n", "x = 1/3;\n", "f2 = 250;# in Hz\n", "Bm1 = 1;\n", " #calculation: \n", " #Pe = ke*(Bm1*f1*t1)**2\n", " #Hence, at 50 Hz frequency\n", "ke = Pe/(Bm1*f1*t1)**2\n", " #At 250 Hz frequency\n", "Bm2 = x*Bm1\n", "t2 = ((Pe/ke)**0.5)/(Bm2*f2)\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\nlamination thickness is \",t2,\"m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", "lamination thickness is 0.0003 m" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 7, page no. 700

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Ph1 = 40;# in W\n", "Pe1 = 20;# in W\n", "f1 = 50;# in Hz\n", "x = 1/2;\n", "f2 = 60;# in Hz\n", "t1 = 1;\n", " #calculation: \n", " #hysteresis loss Ph = kh*v*f*(Bm)**n = k1*f\n", " #Thus when the hysteresis is 40 W and the frequency 50 Hz,\n", "k1 = Ph1/f1\n", " #If the frequency is increased to 60 Hz,\n", "Ph2 = k1*f2\n", " #eddy current loss, Pe = ke*(Bm1*f1*t1)**2 = k2*f**2\n", " #since the flux density and lamination thickness are constant.\n", " #When the eddy current loss is 20 W the frequency is 50 Hz. Thus\n", "k2 = Pe1/(f1**2)\n", " #If the frequency is increased to 60 Hz,\n", "Pe2 = k2*(f2**2)\n", " #hysteresis loss Ph = kh*v*f*(Bm)**n, is independent of the thickness of the laminations. \n", " #Thus, if the thickness of the laminations is halved, the hysteresis loss remains at \n", "Phb2 = Ph1\n", " #eddy current loss, Pe = ke*(Bm1*f1*t1)**2 = k2*t**3\n", "k3 = Pe1/(t1**3)\n", "t2 = 0.5*t1\n", "Peb2 = k3*t2**3\n", " #total core loss when the thickness of the laminations is halved is given by\n", "TL = Phb2 + Peb2\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n(a)If the frequency is increased to 60 Hz,hysteresis loss is \",Ph2,\" W and eddy current loss \", Pe2,\" W\"\n", "print \"\\n(b)the total core loss when the thickness of the laminations is halved \",TL,\" W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", "(a)If the frequency is increased to 60 Hz,hysteresis loss is 48.0 W and eddy current loss 28.8 W\n", "\n", "(b)the total core loss when the thickness of the laminations is halved 42.5 W\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8, page no. 701

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "V1 = 500;# in Volts\n", "V2 = 1000;# in Volts\n", "Ph1 = 400;# in W\n", "Pe1 = 150;# in W\n", "f1 = 50;# in Hz\n", "n = 1.6;# Steinmetz index\n", "f2 = 100;# in Hz\n", "\n", " #calculation: \n", " #hysteresis loss Ph = k1*f*(E/f)**n\n", " #At 500 V and 50 Hz\n", "k1 = Ph1/(f1*(V1/f1)**1.6)\n", " #At 1000 V and 100 Hz,\n", "Ph2 = k1*f2*(V2/f2)**1.6\n", " #eddy current loss, Pe = k2*E**2\n", " #At 500 V,\n", "k2 = Pe1/(V1**2)\n", " #At 1000 V,\n", "Pe2 = k2*(V2**2)\n", " #the new total core loss\n", "TL = Ph2 + Pe2\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n the new total core loss \",TL,\" W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " the new total core loss 1400.0 W" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 9, page no. 702

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#from pylab import *\n", "%matplotlib inline\n", "#initializing the variables:\n", "f1 = 50;# in Hz\n", "f2 = 60;# in Hz\n", "\n", "#calculation:\n", "k1 = 0.5\n", "k2 = 0.032\n", "f = [30, 50, 70,90]\n", "Pcf = [1.5, 2.1, 2.7, 3.4]\n", "fig = plt.figure()\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(f,Pcf,'-')\n", "xlabel('f')\n", "ylabel('Pc/f')\n", "show()\n", "HL1 = k1*f1\n", "ECL1 = k2*f1**2\n", "\n", "HL2 = k1*f2\n", "ECL2 = k2*f2**2\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n (a) at Frequency = 50 Hz, hysteresis loss is\", HL1,\" W and eddy current loss is\", ECL1,\" W\"\n", "print \"\\n (b) at Frequency = 60 Hz, hysteresis loss is\", HL2,\" W and eddy current loss is\", ECL2,\" W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'." ] }, { "metadata": {}, "output_type": "display_data", "png": 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}, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " (a) at Frequency = 50 Hz, hysteresis loss is 25.0 W and eddy current loss is 80.0 W\n", "\n", " (b) at Frequency = 60 Hz, hysteresis loss is 30.0 W and eddy current loss is 115.2 W" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 10, page no. 703

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "TL1 = 400;# in Watt\n", "TL2 = 498;# in Watt\n", "x = 0.25;\n", "y = 0.4;\n", "f1 = 50;# in Hz\n", "n = 1.7;# Steinmetz index\n", "f2 = 60;# in Hz\n", "\n", " #calculation: \n", " #if volume v and the maximum flux density are constant\n", " #hysteresis loss Ph = kh*v*f*(Bm)**n = k1*f\n", " #(if the maximum flux density and the lamination thickness are constant)\n", " #eddy current loss, Pe = ke*(Bm1*f1*t1)**2 = k2*f**2\n", " #At 50 Hz frequency, TL1 = k1*f1 + k2*f1**2\n", " #At 60 Hz frequency, TL2 = k1*f2 + k2*f2**2\n", " #Solving equations gives the values of k1 and k2.\n", "k2 = (5*TL2 - 6*TL1)/(5*(f2**2) - 6*(f1**2))\n", "k1 = (TL1 - k2*f1**2)/f1\n", " #hysteresis loss Ph = k1*f\n", "Ph1 = k1*f1\n", " #eddy current loss\n", "Pe1 = k2*f1**2\n", " #Since at 50 Hz the flux density is increased by 25%, the new hysteresis loss is\n", "Ph2 = Ph1*(1 + x)**1.7\n", " #Since at 50 Hz the flux density is increased by 25%, and the lamination thickness is increased by 40%, \n", " #the new eddy current loss is\n", "Pe2 = Pe1*((1 + x)**2)*(1 + y)**3\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n (a)the hysteresis and eddy current losses at 50 Hz are \",round(Ph1,2),\" W and \",round( Pe1,2),\" W resp.\"\n", "print \"\\n (b)the hysteresis and eddy current losses at 50 Hz after increement are \",round(Ph2,2),\" W and \",round( Pe2,2),\" W resp.\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " (a)the hysteresis and eddy current losses at 50 Hz are 325.0 W and 75.0 W resp.\n", "\n", " (b)the hysteresis and eddy current losses at 50 Hz after increement are 474.93 W and 321.56 W resp.\n" ] } ], "prompt_number": 3 } ], "metadata": {} } ] }