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|
{
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"name": "",
"signature": "sha256:29b5ec9b20f222bcfeb31d6e80f55e5d32272a4cce1e9227a6328e93313e209d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 1:Introduction to Magnetic Circuits<h1>"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.1, Page number: 9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import *\n",
"#Variable declaration:\n",
"Ac=9 #Cross-sectional area of the core(cm**2)\n",
"Ag=9 #Cross-sectional area of the air-gap(cm**2)\n",
"g=0.050 #Air-gap length(cm) \n",
"lc=30 #Mean Length of the core(cm)\n",
"N=500 #No. of windings\n",
"ur=70000 #Relative permeability of the core material\n",
"Bc=1.0 # Magnetic Flux Density of the core(T)\n",
"uo=4*pi*10**-7 #Permeability of free space\n",
"\n",
"#Calculation\n",
"Rc=lc*10**-2/((ur*uo*Ac)*10**-4)\n",
"Rg=g*10**-2/((uo*Ag)*10**-4)\n",
"Q=Bc*Ac*10**-4\n",
"i=Q*(Rc+Rg)/N\n",
"\n",
"#Results\n",
"print \"a.Reluctance of the core,Rc:\",round(Rc,2), \"A.turns/Wb\" \n",
"print \" Reluctance of the air-gap,Rg:\", round(Rg,2), \"A.turns/Wb\"\n",
"print \"b.The flux, Q:\", round(Q,4), \"Wb\"\n",
"print \"c.The current,i:\", round(i,2), \"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"a.Reluctance of the core,Rc: 3789.4 A.turns/Wb\n",
" Reluctance of the air-gap,Rg: 442097.06 A.turns/Wb\n",
"b.The flux, Q: 0.0009 Wb\n",
"c.The current,i: 0.8 A\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.2, Page number: 10"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import *\n",
"#Variable declaration:\n",
"I=10 #Current in the coil(A)\n",
"N=1000 #No of turns in the rotor\n",
"g=1 #Air gap length(cm)\n",
"Ag=2000 #Cross-section of the air-gap(cm**2)\n",
"uo=4*pi*10**-7 #Permeability of free space\n",
"\n",
"#Calculation:\n",
"Q=(N*I*uo*Ag*10**-4)/(2*g*10**-2)\n",
"Bg=round(Q,2)/(Ag*10**-4)\n",
"\n",
"#Results\n",
"print \"The air-gap flux, Q:\", round(Q,2), \"Wb\"\n",
"print \"The flux density, Bg:\", round(Bg,4), \"T\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The air-gap flux, Q: 0.13 Wb\n",
"The flux density, Bg: 0.65 T\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.4, Page number: 13"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import *\n",
"#Variable declaration\n",
"lc=0.3 #length of the core(cm)\n",
"ur1=72300 #Relative permeablity for case(a)\n",
"ur2=2900 #Relative permeablity for case(b)\n",
"Ac=9 #Cross-section of the core(cm**2)\n",
"Rg=4.42*10**5 #Reluctance of the air-gap(A.turns/Wb)\n",
"N=500 #No of coil turns\n",
"uo=4*pi*10**-7 #Permeability of free space(H/m)\n",
"\n",
"#Calculations:\n",
"Rt1=(lc/(ur1*uo*Ac*10**-4))+Rg\n",
"L1=N**2/Rt1\n",
"Rt2=(lc/(ur2*uo*Ac*10**-4))+Rg\n",
"L2=N**2/Rt2\n",
"\n",
"\n",
"\n",
"#Results:\n",
"print \"(a)Inductance,L:\",round(L1,2),\"H\"\n",
"print \"(b)Inductance,L:\",round(L2,2),\"H\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Inductance,L: 0.56 H\n",
"(b)Inductance,L: 0.47 H\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.5, Page number: 15"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from pylab import *\n",
"from matplotlib import *\n",
"from math import *\n",
"%matplotlib inline\n",
"#Variable declaration:\n",
"Ac=9e-4 #Cross-section of the core(m)\n",
"Ag=9e-4 #Cross-section of the air-gap(m)\n",
"g=5e-4 #Air-gap length(m)\n",
"lc=0.3 #Mean length of the core(m)\n",
"N=500 #No. of turns of the core(m)\n",
"uo=4*pi*10**-7 #Permeability of free space(H/m)\n",
"\n",
"#Calculations:\n",
"Rg=g/(uo*Ag) #Reluctance of the air-gap(A.turns/Wb)\n",
"ur=[0]*200 #Initialising array\n",
"L=[0]*200\n",
"\n",
"for n in range(1,101,1):\n",
" ur[n-1]=100+(10000-100)*(n-1)/100\n",
" Rc=lc/(ur[n-1]*uo*Ac) #Reluctance of the core(A.turns/Wb)\n",
" Rtot=Rg+Rc\n",
" L[n-1]=(N**2)/Rtot #Inductance(H)\n",
" \n",
"\n",
"#Results:\n",
"print \"The reqired plot is shown below:\"\n",
"plot(ur, L,'g.')\n",
"xlabel('Core relative permeability, ur')\n",
"ylabel('Inductance,L (H) ')\n",
"title('plot of inductance vs. relative permeability for Example 1.5.')\n",
"show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The reqired plot is shown below:\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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pKQn37t27zNPTM0kkEikuXLjwkL29/YOwsLAQQggJCQkJO3Xq1Mz9+/cvVVJS\nEqqqqtZERkb6ySse6NokE0Vb+h0aezQ0kgNA+8PNfdBhmjuDkLyMtbk7nOn54PJUgOZ1u/s02guS\nRvcmyxmE9IPwWup3AICWIWlAtyB9FVNbziCQHADeHpIGdFlNnU3gDAKg8yBpQJfSVKKQfpQGXRbJ\nAaBjIWlAp5K12akjX3APAE1D0oAO15ZmJyQKgK4BSQM6BJqdAN4NSBogF2h2Ang3IWlAu0GzE8C7\nD0kD3gqanQB6FiQNeCvcI1w0OwH0IEga0GqSZxcN4oZmH+4HAO8WJA1oUXOd2t623kRZURmJAqCH\n6HbvCIeOJ/muCenHiB+ZegTJAgDeGpJGNyd5dsFUZBJCGn8RERIGALQHNE91c5Id3GiCAgAamqfg\nH02dXaAJCgDkDWca3QA6uAGgtXCm0YOhgxsAugokjS4KHdwA0BWheaqLQgc3ALwNNE/1AOjgBoCu\nDmcaXQjOLgCgveBMowdABzcAdHU40+hE0pfS0t/h7AIA3hYeWPgOkmyO8nHwIdE+0Z0cEQC8K9A8\n9Y5o6VJaAICuDGcaHQyd3QDQEeR1pqHQ3jOUlJiYON7Ozu6hjY1N1o4dO1Y1Ve7mzZuuSkpKwjNn\nzkyXZzxdgXRnd7RPNBIGAHQbzTZPNTQ0MJOTk8ddvnx5BJ/P5zAYDMrCwiJ3xIgRlz09PZOUlJSE\nTU0rEokUly1btjclJWUMi8XKd3V1venl5RVrb2//QLrcqlWrdowfPz5RHlmxK5Bskto/aT/emgcA\n3VaTZxqbN29e7+rqejM+Pn6ynZ3dwwULFhwOCgo6amtr+yguLm6Ki4vLrS1btqxravq0tDQ3a2vr\nbA6Hw2cymQ1+fn6RMTEx3tLlfvjhh49mzpx5ysDAoLi9VqqroZ8dlZCdQFb+vhJnFwDQbTV5puHs\n7Pz32rVrv1ZQUBBL/7ZgwYLDYrFYIT4+fnJT0+fn57PMzMwE9Dibzc5LTU11ly4TExPjfeHChVE3\nb950ZTAYjXZehIaG/vOZy+USLpfb7Ep1NZJNUujwBgB54PF4hMfjyX05TSYNLy+v2OYmVFBQEDdX\npqkEIGn58uXfbd++ffX/d3Yzmmqekkwa3YH0/RfhM8Jx/wUAyJX0AfXGjRvlspwmk8aUKVPi6M/0\nTl1yPDY21qu5GbNYrHyBQGBGjwsEAjM2m50nWeb27duD/fz8Igkh5OXLl/oJCQkTmExmQ0sJq6uT\nfpR5tE+piCozAAAgAElEQVQ07sEAgHdCk0ljxYoVu+lksXjx4oM///zzIjpxyHIW4eLicisrK8uG\nz+dzTE1NC6KionwjIiL8Jcs8ffq0D/15/vz5v0yZMiWuuycMQtAcBQDvriaTBpfL5dGf1dXVq0aO\nHHmpVTNWUhLu3bt3maenZ5JIJFJcuHDhIXt7+wdhYWEhhBASEhIS1uaouyBcIQUAPYFMN/cNHDgw\nIyMjY2AHxPM/usvNfXgkCAB0JR3+GJHS0lJdQgihKIohEokU6XGarq5uaXsH052hSQoAeoImzzQ4\nHA6f7rugKIoh2Y/BYDAoyf4IuQbYTc40yuvKcYUUAHQZeMptFyR9aS2SBQB0FR3+7ClZziSePHli\n1b7hdC+Sd3oHxwV3djgAAHLXZJ/GmjVrtlVXV6t5eXnFuri43DIxMSmkKIpRWFhocuvWLZfY2Fgv\nDQ2NysjISL+ODLgrQT8GAPQ0zTZPZWdnW0dGRvpdvXp1WG5urgUhhFhYWOS+9957f/r7+0f06dPn\nqdwD7MLNU+jHAICuCn0aXQD6MACgu+iW79N416APAwB6OiSNVkAfBgD0dG1KGgUFBabtHUh3ED4j\nnPg4+JDkwGQ0TQFAj9SmPg1zc/Nnz549M5dDPP+jK/VpAAB0Fx3+GJHmvKuvZW0MOr8BAP6FPo0W\noPMbAOBfTZ5pfPTRRz809Vt5eXmPOdxG5zcAwL+aTBqDBw++3djLliiKYri4uNySb1hdB17VCgDw\nL9zcBwDwDuoyHeFffvnlVi0trVeLFi36WU9Pr6S9A+oK0PkNANC4VneEu7q63lRUVBQtX778O3kE\n1BWg8xsAoHGtPtOYNm3aWXkE0pWg8xsAoHEtnmk8evTIdvTo0X/069fvPiGE3Llzx2nLli3r5B9a\n58Gd3wAAjWuxI3zEiBGXd+7cuXLJkiU/ZWRkDKQoiuHo6Hjv/v37/TokQHSEAwC0Wqc95bampkbV\n3d09VSIQislkNrR3IAAA0PW12KdhYGBQnJ2dbU2Pnzp1aqaJiUmhfMPqWLhaCgBANi02Tz158sQq\nODj4wPXr1z20tbXLLS0tc06cODGbw+HwOyTADmie4h7hkku5lwghhPg4+JBon2i5Lg8AQN46/c19\nVVVV6mKxWEFTU7OivYNoTkckjYknJpKE7ATiauqKzm8AeCd0Wp/GmjVrtpWXl2urq6tXaWpqVpSV\nlemsW7duS3sH0plwtRQAgGxaPNMYMGDAX3/99dcAye8GDhyYkZGRMVCukf0/XD0FANB6nXamIRaL\nFerq6nrT47W1tSr19fXK7R0IAAB0fS0mjdmzZ58YPXr0H4cOHVr4888/LxozZkzK3Llzf5Vl5omJ\niePt7Owe2tjYZO3YsWOV9O8xMTHezs7Ofw8cODBj8ODBty9cuDCqLSsBAAAdQ6aO8ISEhAkpKSlj\nGAwGNXbs2N89PT2TWppGJBIp2traPkpJSRnDYrHyXV1db0ZERPjb29s/oMtUV1erqampVRNCyN27\nd/tPmzbtrOTlvYTIr3kKl9kCwLusU59yO2HChIQJEyYktGbGaWlpbtbW1tn0pbl+fn6RMTEx3pJJ\ng04YhLy5OktfX/9la5bxNuiHEhLyJoHgMlsAgJa1mDROnz49Y/Xq1dufP39uRGctBoNBVVRUaDY3\nXX5+PsvMzExAj7PZ7LzU1FR36XLnzp2bumbNmm2FhYUmycnJ4xqbV2ho6D+fuVwu4XK5LYXdIjyU\nEADeJTwej/B4PPkviKKoZoc+ffo8yczMtG+pnPRw6tSpGYsWLTpIjx87dmzOsmXLfmiq/OXLl4f3\n7dv3kfT3b0Jsf2W1ZZRPtA9VVlsml/kDAHSm/993tmq/LcvQYke4sbFxkWSTkqxYLFa+QCAwo8cF\nAoEZm83Oa6r88OHDrwiFQqWSkhK91i6rLbR7a5Non2j0ZQAAtEKLzVMuLi63fH19o6ZOnXpOWVm5\nnpA3zVPTp08/09J0WVlZNnw+n2NqaloQFRXlGxER4S9Z5smTJ1Z9+vR5ymAwqPT09EGEEPKuvg0Q\nAOBd0GLSePXqlZaKikqtdH9DS0lDSUlJuHfv3mWenp5JIpFIceHChYfs7e0fhIWFhRBCSEhISNjp\n06dn/Prrr3OZTGaDurp6VWRkpN/brQ4AAMiTzM+e6iy4IxwAoPU67ZLb2tpalUOHDi3MzMx0qK2t\nVWEwGBQhhBw+fHhBewcjb7g3AwDg7bTYER4YGHjs+fPnRomJieO5XC5PIBCYqaurV3VEcO2Nvjcj\nITuBBMcFd3Y4AADdTotJIzs723rz5s3r1dXVq4KCgo6eP39+YmP3W3QHuDcDAODttJg06CumtLS0\nXt29e7d/eXm5dnFxsYH8Q2t/eAQ6AMDbabFPY/HixQdLS0t1t2zZss7Lyyu2qqpKffPmzes7Irj2\nRt+bAQAAbdPi1VNPnz7t06dPn6ctfScvuHoKAKD1Ou19GjNnzjwl/Z2Pj8/J9g4EAAC6viabpx48\neGCfmZnpUF5ern3mzJnpFEUx6AcVSr6UCQAAeo4mk8bjx4/7xsXFTXn16pVWXFzcFPp7DQ2NyoMH\nDy7umPAAAKArabFP4/r16x4eHh7XOyie/4E+DQCA1uu0Po39+/cvLS8v/+f61LKyMp0FCxYcbu9A\n5CU4Lphwj3DJxBMTSXldeWeHAwDQrbWYNO7cueOkra39z95WR0enjH4ibXeAu8ABANpPi0mDoihG\naWmpLj1eWlqqKxKJFOUbVvvBXeAAAO2nxZv7VqxYsdvDw+P6rFmzoimKYpw8edJn7dq1X3dEcO0h\nfEY4CY4LJgemHMBd4AAAb0mmR6Pfv3+/34ULF0YxGAxq1KhRFxwcHDI7IDZCCDrCAQDaQl4d4S0m\njWfPnpkTQv5ZOP1odHNz82ftHUxjkDQAAFqv05KGo6PjPTpR1NXV9c7JybG0tbV9dP/+/X7tHUyj\nASJpAAC0Wqe9hOnevXuOkuPp6emD9u3b92F7BwIAAF1fm1736ujoeE86mcgLzjQAAFqv0840du/e\nvYL+LBaLFdLT0wexWKz89g4EAAC6vhaTRmVlpQbdp6GkpCScPHly/IwZM07LPzQAAOhq2tQ81ZFa\n2zwVHBdMHpc8JqpMVRI+Ixz3ZgBAj9ThzVNTpkyJk1g4JblwBoNBxcbGerV3MO2BfmwIIW8SCN7U\nBwDQfppMGitWrNhNCCFnz56dVlRUZDxnzpzjFEUxIiIi/I2MjJ53XIitg8eGAADIT4vNU4MHD759\n+/btwS19Jy+tbZ4qryvHY0MAoMfrtEej19TUqD558sSKHn/69Gmfmpoa1fYOpL1o99Ym0T7RSBgA\nAHLQ4tVT//nPfz59//33L1paWuYQQgifz+ccOHAAzxgHAOiBZLp6qq6urvfDhw/tGAwGZWdn97BX\nr16vOyA2Qghu7gMAaItOe/YUIYRcu3ZtaE5OjqVQKFSi79mYO3fur+0dTGOQNAAAWq/T+jTmzJlz\n/PPPP9919erVYbdu3XK5efOm682bN11lmXliYuJ4Ozu7hzY2Nlk7duxYJf37iRMnZjs7O//t5OR0\nZ9iwYVfv3Lnj1JaVAACAjtHimYa9vf2DzMxMB/oMQ1YikUjR1tb2UUpKyhgWi5Xv6up6MyIiwt/e\n3v4BXeb69eseDg4OmVpaWq8SExPHh4aGht64cWPIfwWIMw0AgFbrtGdPOTo63issLDQxNTUtaM2M\n09LS3KytrbM5HA6fEEL8/PwiY2JivCWThoeHx3X6s7u7e2peXh67sXmFhob+85nL5RIul9uaUAAA\n3nk8Ho/weDy5L6fFpFFcXGzg4OCQ6ebmlkZ3gMtyR3h+fj7LzMxMQI+z2ey81NRU96bKHzp0aOHE\niRPPN/abZNIAAID/JX1AvXHjRrksp8WkEdrGPXZrmrMuXrz4/uHDhxdcvXp1WFuWBQAAHaPFpMHl\ncnltmTGLxcoXCARm9LhAIDBjs9l50uXu3LnjtHjx4oOJiYnjdXR0ytqyLAAA6BhNJg11dfWqps4W\nGAwGVVFRodncjF1cXG5lZWXZ8Pl8jqmpaUFUVJRvRESEv2SZZ8+emU+fPv3M8ePH51hbW2e3bRXw\nZFsAgI7SZNKoqqpSf6sZKykJ9+7du8zT0zNJJBIpLly48JC9vf2DsLCwEEIICQkJCdu0adNXZWVl\nOkuXLt1PCCFMJrMhLS3NrbXLwpNtAQA6xjvxPo2JJyaShOwE4mrqSpIDk3GmAQA9XqfeEd6ZZEka\neLItAMB/Q9IAAACZddpjRAAAAGhIGgAAIDMkDQAAkBmSBgAAyAxJAwAAZIakAQAAMkPSAAAAmSFp\nAACAzJA0AABAZkgaAAAgMyQNAACQGZIGAADIrMU393VVePESAEDH67ZnGvSLlxKyE0hwXHBnhwMA\n0CN026ShylQlhBDiaupKDkw50MnRAAD0DN32fRp48RIAQNPwEiYAAJAZXsIEAACdDkkDAABkhqQB\nAAAyQ9IAAACZIWkAAIDMkDQAAEBmSBoAACAzJA0AAJAZkgYAAMhMrkkjMTFxvJ2d3UMbG5usHTt2\nrJL+/eHDh3YeHh7Xe/fuXbd79+4V8owFAADentwejS4SiRSXLVu2NyUlZQyLxcp3dXW96eXlFWtv\nb/+ALqOnp1fyww8/fHTu3Lmp8ooDAADaj9zONNLS0tysra2zORwOn8lkNvj5+UXGxMR4S5YxMDAo\ndnFxucVkMhvkFQcAALQfuZ1p5Ofns8zMzAT0OJvNzktNTXVvy7xCQ0P/+czlcgmXy33r+AAA3iU8\nHo/weDy5L0duSYPBYLTbo2klkwYAAPwv6QPqjRs3ymU5cmueYrFY+QKBwIweFwgEZmw2O09eywMA\nAPmTW9JwcXG5lZWVZcPn8zn19fXKUVFRvl5eXrGNlZXHM98BAKD9yfUlTAkJCROWL1/+nUgkUly4\ncOGhNWvWbAsLCwshhJCQkJCwoqIiY1dX15sVFRWaCgoKYg0NjcrMzEwHdXX1qn8CxEuYAABaDW/u\nAwAAmckracitI7y9BccFk8clj4kqU5WEzwjHe8EBADpBt3mMyOOSx+RS7iWSkJ1AguOCOzscAIAe\nqdskDVWmKiGEEFdTV3JgyoFOjgYAoGfqNn0a5XXlJDgumByYcgBNUwAALUBHOAAAyExeSaPbNE8B\nAEDnQ9IAAACZIWkAAIDMkDQAAEBmSBoAACAzJA0AAJAZkgYAAMgMSQMAAGSGpAEAADJD0gAAAJkh\naQAAgMyQNAAAQGZIGgAAIDMkDQAAkBmSBgAAyAxJAwAAZIakAQAAMkPSAAAAmSFpAACAzJA0AABA\nZkgaAAAgMyQNAACQGZJGN8Lj8To7hC4DdfEv1MW/UBfyJ9ekkZiYON7Ozu6hjY1N1o4dO1Y1Vubj\njz/+3sbGJsvZ2fnvjIyMgfKMp7vDBvEv1MW/UBf/Ql3In9yShkgkUly2bNnexMTE8ZmZmQ4RERH+\nDx48sJcsc/78+YnZ2dnWWVlZNgcOHAheunTpfnnFAwAAb09uSSMtLc3N2to6m8Ph8JlMZoOfn19k\nTEyMt2SZ2NhYr6CgoKOEEOLu7p5aXl6u/fz5cyPpeTE2MghjI0NeoQIAgIyU5DXj/Px8lpmZmYAe\nZ7PZeampqe4tlcnLy2MbGRk9/6+Zhb75hxGKxLFx48bODqHLQF38C3XxL9SFfMktaTAYDEqWchRF\n/VcmkJ5O+ncAAOg8cmueYrFY+QKBwIweFwgEZmw2O6+5Mnl5eWwWi5Uvr5gAAODtyC1puLi43MrK\nyrLh8/mc+vp65aioKF8vL69YyTJeXl6xv/7661xCCLlx48YQbW3t8v9pmgIAgC5Dbs1TSkpKwr17\n9y7z9PRMEolEigsXLjxkb2//ICwsLIQQQkJCQsImTpx4/vz58xOtra2z1dTUqn/55Zf58ooHAADa\nAUVRXXZISEgYb2tr+9Da2jpr+/btqzo7nvYenj17Zsblci86ODjc79ev3709e/Z8TFEUKSkp0R0z\nZszvNjY2j8eOHZtcVlamTU+zdevWNdbW1lm2trYPk5KSxtHf37p1a7Cjo+Nda2vrrI8//nhPZ69b\nWwehUKg4YMCAjMmTJ8f15LooKyvTnjFjxik7O7sH9vb2mTdu3HDvqXWxdevWNQ4ODvcdHR3v+vv7\nh9fV1fXqKXUxf/78w4aGhs8dHR3v0t+157rX1dX1mjVrVpS1tXWWu7v7DT6fb9FSTJ1eKU0NQqFQ\n0crKKjsnJ4dTX1/PdHZ2/iszM9O+s+Nqz6GwsNA4IyNjAEVRpLKyUr1v376PMjMz7VeuXPnNjh07\nvqAoimzfvn3VqlWrtlMURe7fv+/g7Oz8V319PTMnJ4djZWWVLRaLGRRFEVdX17TU1FQ3iqLIhAkT\nzickJIzv7PVry7B79+7PAgICTkyZMiWWoijSU+ti7ty5Rw8dOrSAoijS0NCgVF5ertUT6yInJ4dj\naWn5tK6urhdFUWTWrFlRR44cCeopdXH58uXh6enpAyWTRnuu+759+z5YunTpjxRFkcjISF9fX9/I\nlmLq9Epparh27ZqHp6dnIj2+bdu21du2bVvd2XHJc/D29j73+++/j7G1tX1YVFRkRFFvEoutre1D\ninpzFCF5xuXp6Zl4/fr1IQUFBSZ2dnYP6O8jIiL8QkJCfurs9WntIBAI2KNHj065cOHC+/SZRk+s\ni/Lyci1LS8un0t/3xLooKSnR7du376PS0lKdhoYGpcmTJ8clJyeP7Ul1kZOTw5FMGu257p6enok3\nbtxwp6g3Byf6+vrFLcXTZZ891dg9HPn5+azOjEme+Hw+JyMjY6C7u3vq8+fPjegLAoyMjJ7TNzwW\nFBSYSl6BRteJ9PcsFiu/O9bVp59++p+dO3euVFBQENPf9cS6yMnJsTQwMCieP3/+L4MGDUpfvHjx\nwerqarWeWBe6urqlK1as2G1ubv7M1NS0QFtbu3zs2LG/98S6oLXnukvuZ5WUlIRaWlqvSktLdZtb\nfpdNGrLe5/EuqKqqUp8xY8bpPXv2fKKhoVEp+RuDwaB6Ql3Ex8dPNjQ0fDFw4MAMqol7c3pKXQiF\nQqX09PRBH3zwwY/p6emD1NTUqrdv375askxPqYsnT55Yfffdd8v5fD6noKDAtKqqSv348eNzJMv0\nlLpoTGese5dNGrLc5/EuaGhoYM6YMeN0YGDgsalTp54j5M3RQ1FRkTEhhBQWFpoYGhq+IKTx+1rY\nbHYei8XKz8vLY0t+393ud7l27drQ2NhYL0tLyxx/f/+ICxcujAoMDDzWE+uCzWbnsdnsPFdX15uE\nEDJz5sxT6enpg4yNjYt6Wl3cunXLZejQodf09PRKlJSUhNOnTz9z/fp1j55YF7T22CbofSmLxcp/\n9uyZOSFvDlZevXqlpaurW9rc8rts0pDlPo/ujqIoxsKFCw85ODhkLl++/Dv6ey8vr9ijR48GEULI\n0aNHg+hk4uXlFRsZGelXX1+vnJOTY5mVlWXj5uaWZmxsXKSpqVmRmprqTlEU49ixY4H0NN3F1q1b\nvxQIBGY5OTmWkZGRfqNGjbpw7NixwJ5YF8bGxkVmZmaCx48f9yWEkJSUlDH9+vW7P2XKlLieVhd2\ndnYPb9y4MaS2tlaFoihGSkrKGAcHh8yeWBe09tgmvL29Y6TnderUqZmjR4/+o8UAOruTp7nh/Pnz\nE/r27fvIysoqe+vWrWs6O572Hq5cufIeg8EQOzs7/zVgwICMAQMGZCQkJIwvKSnRHT16dEpjl9R9\n/fXXX1pZWWXb2to+TExM9KS/py+ps7Kyyv7oo4++7+x1e5uBx+ONpK+e6ql18ddffzm7uLjcdHJy\n+nvatGlnysvLtXpqXezYseML+pLbuXPnHq2vr2f2lLrw8/OLMDExKWAymfVsNltw+PDh+e257nV1\ndb18fHyi6Utuc3JyOC3FxKCoHtkUCAAAbdBlm6cAAKDrQdIAAACZIWkAAIDMkDQAAEBmSBrQrKKi\nImM/P79Ia2vrbBcXl1uTJk36LSsry6az4lFXV69q7vdXr15p7d+/fyk9XlBQYOrj43NS/pF1nqbq\nZMOGDRsvXLgwihBCuFwuLz09fRAhhEyaNOm3iooKTem6ApBJZ19ShqHrDmKxmDFkyJDrYWFhwfR3\nf//9t9OVK1fek2X6hoYGpbYsk37IWmODurp6ZXPTSz+np6sMIpFIQV7zbqlOKIoiXC734u3btwd1\nRl0JhULFzq5/DO034EwDmnTx4sX3lZWV64ODgw/Q3zk5Od157733/iSEkJUrV+7s37//XScnpzvR\n0dGzCCGEx+Nxhw8ffsXb2zvG0dHxnlgsVli5cuVONze3NGdn578PHDgQLL0cPp/PsbW1fRQUFHS0\nf//+dwUCgdnOnTtX0tOEhoaGSk9TVVWlPmbMmJTBgwffdnJyuhMbG+tFCCGrV6/e/uTJE6uBAwdm\nrFq1akdubq5F//797xJCyJAhQ25kZmY60POgj76rq6vVFixYcNjd3T110KBB6fS8JPF4PO6IESMu\nT548Od7Ozu7h0qVL91P//7iT5OTkcUOHDr02ePDg27NmzYqurq5WI4QQDofDX7169fbBgwffPnny\npA+Hw+F/+eWXWwcOHJjh4uJyKz09fdC4ceOSra2ts+n3zBBCSFPrPm3atLMuLi63HB0d7x08eHCx\nZHyfffbZt46OjvfGjBmT8vLlS31CCJk3b96R06dPz5BeFw6Hwy8pKdGTrKsvvvjim6CgoKMxMTHe\ndLnZs2efaKwuJP/f6LolhJBdu3Z9vnHjxg103X766af/cXV1vfn9999/3NQ8oBvq7KyFoesOe/bs\n+fjTTz/9trHfTp06NWPs2LHJYrGY8fz5c0Nzc/PcwsJC44sXL3LV1NSq6Ofyh4WFBW/ZsmUtRb25\nkcjFxeWm9A1EOTk5HAUFBRH96OakpKRxwcHBYRT15gh90qRJ8ZcvXx5OUf8eVQuFQsWKigoNiqJI\ncXGxvrW1dRZFUYTP51tIHj1LHk3/5z//Wb5hw4ZQiqJIQUGBCf100DVr1mw9fvz4bIp68x6Lvn37\nPqqurlaVjPHixYvc3r171+bk5HBEIpHC2LFjk0+dOjWjuLhYf8SIEZdqampUKOrNo6o3bdq0nqIo\nwuFwcnbu3Pk5PQ8Oh5Pz008/hVAURT799NNv+/fvf6eqqkqtuLhY38jIqKixdZ88eXIcve6lpaU6\nFEWRmpoaFUdHx7v0OIPBEIeHh/tTFEU2bdq0ftmyZT9QFEXmzZv3y+nTp6dT1H+faXA4nJySkhJd\n6bq6dOnSiKlTp56lqH+ftNvcGZL0mcquXbtWbNy48St6eR9++OHezv4bxtD+g9ze3AfdX3MPQrt6\n9eqwgICAcAaDQRkaGr4YOXLkpZs3b7pqampWuLm5pVlYWOQS8uYo/O7du/1PnTo1kxBCKioqNLOz\ns605HA5fcn4WFha5bm5uafQ0ycnJ4wYOHJhBCCHV1dVq2dnZ1sOHD79ClxeLxQpr1qzZduXKleEK\nCgrigoIC0xcvXhhSTTzskBBCfHx8Tnp6eiaFhoaGRkdHz6L7OpKTk8fFxcVN2bVr1+eEEPL69ete\nAoHAzNbW9pHk9G5ubml03P7+/hF//vnne717967LzMx0GDp06DVCCKmvr1emPxNCiK+vb5TkPOhH\n4fTv3/9udXW1mpqaWrWamlp1r169Xr969UqruXXfs2fPJ+fOnZtKyJtnsdGPiVBQUBDTy5kzZ87x\n6dOnn2mqDiRJ19WIESMuf/DBBz++fPlS/9SpUzNnzpx5SvKJw62dp/S6w7sBSQOa1K9fv/v0zr4x\n0jsdOsmoqalVS36/d+/eZWPHjv29uWVJT7NmzZptks1i0k6cODH75cuX+unp6YMUFRVFlpaWOXV1\ndb2bWwaLxcrX09MruXv3bv/o6OhZkk1CZ86cmW5jY5PV3PSSSZSiKAaDwaAoimKMHTv29/Dw8ABZ\n1qtXr16vCSFEQUFBrKysXE9/r6CgIBYKhUpNrTuPx+P+8ccfo2/cuDGkd+/ede+///7FxtaXjqu5\n9WjO3Llzfz127FhgVFSU75EjR+Y1V1ZJSUkoFov/aeKura1VkVy29LrDuwF9GtCkUaNGXXj9+nUv\nyfbzO3fuOP3555/vDR8+/EpUVJSvWCxWKC4uNrh8+fIINze3NOlE4unpmfTjjz9+QO8QHz9+3Lem\npka1ueV6enomHT58eAHdN5Cfn88qLi42kCxTUVGhaWho+EJRUVF08eLF93Nzcy0IIURDQ6OysrJS\no6l5+/r6Ru3YsWNVRUWFpqOj4z16eZLt7hkZGQMbmzYtLc2Nz+dzxGKxQnR09Kzhw4dfGTJkyI2r\nV68Oe/LkiRUhb84MZLm6rLEzIgaDQTW17hUVFZo6OjplvXv3rnv48KHdjRs3htDTicVihZMnT/oQ\nQkh4eHiA5BlZcxqrq3nz5h357rvvljMYDMrOzu4hHcOYMWNSpKc3MjJ6/uLFC8PS0lLd169f94qP\nj58sy3Khe0PSgGadPXt2WkpKyhhra+tsR0fHe2vXrv3axMSkcNq0aWednJzuODs7/z169Og/du7c\nudLQ0PCF9PP9Fy1a9LODg0PmoEGD0vv373936dKl++kEIklymrFjx/4eEBAQ7uHhcd3JyemOj4/P\nyaqqKnXJcrNnzz5x69YtFycnpzvHjh0LtLe3f0AIIXp6eiXDhg272r9//7urVq3aIR3PzJkzT0VF\nRfnOmjUrmv5u/fr1mxsaGphOTk53HB0d723YsGFjY/G5urreXLZs2V4HB4fMPn36PJ02bdpZfX39\nl0eOHJnn7+8f4ezs/PfQoUOvPXr0yLaxupSMQzou+rP0us+aNSu6qqpKffz48YlCoVDJwcEhc82a\nNds8PDyu09OqqalVp6WlufXv3/8uj8fjfvXVV5ta/p/937oihBBDQ8MXDg4OmfPnz/+FLldYWGii\npLHZU3wAAACpSURBVKQklJ6eyWQ2fPXVV5vc3NzSxo0bl+zg4JApy3Khe8MDCwFkwOPxuLt3714R\nFxc3pbNjkaeamhpVJyenOxkZGQPpF4Lt27fvQwsLi9zJkyfHd3Z80PnQpwEgg57wdriUlJQxixYt\n+vmzzz77VvINkh9++OG+zowLuhacaQAAgMzQpwEAADJD0gAAAJkhaQAAgMyQNAAAQGZIGgAAIDMk\nDQAAkNn/ASu6P4PfImgPAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x2a2ba10>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.6, Page number: 19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"\n",
"#Variable declaration:\n",
"Bc=1.0 #Magnetic field induction in the core\n",
"w=377 #Angular frequency of magnetic field(rad/s)\n",
"Rc=3791.33 #Reluctance of the core(A.turns/Wb)\n",
"Rg=442321.3 #Reluctance of the air-gap(A.turns/Wb)\n",
"N=500 #No. of windings\n",
"i=0.80 #Current in the coil\n",
"Ac=9*10**-4 #Cross-section of the core\n",
"\n",
"\n",
"#Calculations:\n",
"L=N**2/(Rc+Rg)\n",
"W=(1./2)*L*i**2\n",
"t = symbols('t')\n",
"Bc = 1.0*sin(w*t)\n",
"e=N*Ac*diff(Bc,t)\n",
"\n",
"#Results:\n",
"print \"The Inductance, L:\", round(L,2), \"H\"\n",
"print \"The magntic stored energy, W:\", round(W,2), \"J\"\n",
"print \"Induced voltage, e:\",e,\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Inductance, L: 0.56 H\n",
"The magntic stored energy, W: 0.18 J\n",
"Induced voltage, e: 169.65*cos(377*t) V\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.7, Page number: 22"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import *\n",
"#Variable declaration:\n",
"Bc=1 #Magnetic field in the core\n",
"Hc=11 #Magnetising force(A.turns/m)\n",
"lc=0.3 #length of the core(m)\n",
"N=500 #No of windings\n",
"g=0.050 #Air-gap length(cm)\n",
"uo=4*pi*10**-7 #Permeability of free space(H/m)\n",
"\n",
"\n",
"#Calculation:\n",
"Fc=Hc*lc #mmf drop for the core path(A.turns)\n",
"Fg=Bc*g*10**-2/uo #mmf drop across the air gap(A.turns)\n",
"i=(Fc+Fg)/N\n",
"\n",
"\n",
"#Results:\n",
"print \"The required current,i:\" ,round(i,2) ,\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required current,i: 0.8 A\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.8, Page number: 28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"\n",
"#Variable declaration:\n",
"N=200 #No. of turns\n",
"Ac=4 #Cross-section of the core(in**2)\n",
"w=377 #Angular frequency of the magnetic field(rad/s)\n",
"Hm=36 #Max value magnetising force(A.turns/m)\n",
"Pc=1.2 #Core loss density(W/kg)\n",
"\n",
"\n",
"#Calculations:\n",
"t=symbols('t')\n",
"Bc=1.5*sin(w*t)\n",
"e=(round(N*Ac*0.94/(39.4**2),2)*diff(Bc,t))\n",
"Erms=275*0.707\n",
"lc=(6+6+8+8)/39.4 #Mean length of the core(m)\n",
"I=Hm*lc/N\n",
"Vc=4*0.94*28 #Core volume(m**3)\n",
"Wc=105.5*(2.54**3)*7.65*10**-3 #Core weight(kg)\n",
"Pa=1.5*13.2 #Watts per Kg\n",
"Irms=Pa/Erms #Current (A)\n",
"Pct=Pc*Wc #Total core loss(W)\n",
"\n",
"\n",
"#Results:\n",
"print \"The applied voltage,e:\", e, \"V\"\n",
"print \"The peak current,I:\", round(I,2), \"A\"\n",
"print \"The total rms current. Irms:\", round(Irms,2), \"A\"\n",
"print \"Total Core loss, Pct:\",round(Pct,2),\"W\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The applied voltage,e: 271.44*cos(377*t) V\n",
"The peak current,I: 0.13 A\n",
"The total rms current. Irms: 0.1 A\n",
"Total Core loss, Pct: 15.87 W\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.9, Page number: 32"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"from math import *\n",
"\n",
"#Variable Declaration:\n",
"g=0.2 #air-gap length(cm)\n",
"lm=1.0 #length of magnetic section(cm)\n",
"Am=4 #Cross-section of the core(cm**2)\n",
"Ag=4 #Cross-section of the air-gap(cm**2)\n",
"\n",
"#Constants used:\n",
"uo=4*pi*10**-7 #Permeability of free space(H/m)\n",
"\n",
"#Calculations:\n",
"Hm=symbols('Hm')\n",
"def Bg(Hm):\n",
" return -uo*Ag*lm*Hm/(Am*g) \n",
"\n",
"Hm1=-49*10**3 #Coercivity of ALNICO 5 (A/m)\n",
"Hm2=-6 #Coercivity of M-5 electrical steel (A/m) \n",
"\n",
"\n",
"#Results:\n",
"print \"Flux Density of air gap:\", round(Bg(Hm1),2),\"T\"\n",
"print \"\\nFlux Density of air gap:\", round(Bg(Hm2*10**4),2),\"gauss\"\n",
"print \"\\nwhere value of Hm for different material.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flux Density of air gap: 0.31 T\n",
"\n",
"Flux Density of air gap: 0.38 gauss\n",
"\n",
"where value of Hm for different material.\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.10, Page number: 34"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"from math import *\n",
"\n",
"#Variable declaration:\n",
"Ag=2 #Cross-section of air-gap(cm**2) \n",
"Bg=0.8 #Air-gap flux density(t)\n",
"Bm=1.0 #Core-flux density(T)\n",
"Hm=-40 #Magnetising force in the core(kA/m)\n",
"uo=4*pi*10**-7 #permeability of free space(H/m)\n",
"g=0.2 #Air-gap length(cm)\n",
"\n",
"#Calculations:\n",
"Am=Ag*Bg/Bm\n",
"lm=-g*Bg/(Hm*uo*10**3)\n",
"Vm=Am*lm\n",
"\n",
"\n",
"#Results:\n",
"print \"The minimum magnet volume,Vm:\",round(Vm,2),\"cm**3\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The minimum magnet volume,Vm: 5.09 cm**3\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1.11, Page number: 39"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"from math import *\n",
"\n",
"#Variable Declaration:\n",
"Am = 2 #magnetic material cros-section(cm^2)\n",
"g=0.2 #air gap length(cm)\n",
"uo=4*pi*10**-7 #permeability of free space(H/m)\n",
"N=100 #No. of windings\n",
"\n",
"#Calculations and results:\n",
"#for part (a)\n",
"Bma = 1.0 #Tesla\n",
"Hma = - 4 #kA/m\n",
"Ag1 = 2 #cm**2\n",
"Ag2 = 4 #cm**2\n",
"\n",
"lm=g*(Am/Ag1)*(Bma/(-uo*Hma*10**4))\n",
"print \"(a) The Requied magnet length = \",round(lm,2),\"cm\"\n",
"\n",
"\n",
"#for part (b):\n",
"i,Hm=symbols('i Hm')\n",
"Bm=-uo*(Ag1/Am)*(lm/g)*Hm+(uo*N/g)*(Ag1/Am)*i\n",
"H_max=200 #kA/m\n",
"B_max=2.1 #Tesla\n",
"i_max=(B_max+2.50*10**-5*H_max)/(6.28*10**-2)\n",
"\n",
"print \"(b) Thus with the air-gap area set to 2 cm^2,\"\n",
"print \" increasing the current to i_max = 45.2 A and then reducing\"\n",
"print \" it to zero will achieve the desired magnetization.\"\n",
"\n",
"#for part (c):\n",
"Bm1=1.00 #Tesla\n",
"Bm2=1.08 #Tesla\n",
"Bg1=(Am/Ag1)*Bm1\n",
"Bg2=(Am/Ag2)*Bm2\n",
"print \"(c) The flux densities when plunger moves at two extremes are:\"\n",
"print \" Bg1 =\",Bg1,\"T and Bg2 =\",Bg2,\"T\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The Requied magnet length = 3.98 cm\n",
"(b) Thus with the air-gap area set to 2 cm^2,\n",
" increasing the current to i_max = 45.2 A and then reducing\n",
" it to zero will achieve the desired magnetization.\n",
"(c) The flux densities when plunger moves at two extremes are:\n",
" Bg1 = 1.0 T and Bg2 = 0.54 T\n"
]
}
],
"prompt_number": 12
}
],
"metadata": {}
}
]
}
|
