{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 38: Magnetic materials</h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 1, page no. 694</h3>"
]
},
{
"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": [
"<h3>Example 2, page no. 695</h3>"
]
},
{
"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": [
"<h3>Example 3, page no. 695</h3>"
]
},
{
"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": [
"<h3>Example 4, page no. 696</h3>"
]
},
{
"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": [
"<h3>Example 5, page no. 699</h3>"
]
},
{
"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": [
"<h3>Example 6, page no. 699</h3>"
]
},
{
"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": [
"<h3>Example 7, page no. 700</h3>"
]
},
{
"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": [
"<h3>Example 8, page no. 701</h3>"
]
},
{
"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": [
"<h3>Example 9, page no. 702</h3>"
]
},
{
"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": [
"<h3>Example 10, page no. 703</h3>"
]
},
{
"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": {}
}
]
}