{ "metadata": { "name": "", "signature": "sha256:cc4f342391bb51dd1544d3ff7e470e05be79bafb54959e6b5c13aa0d16dbd712" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 29: D.C. Motor" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.1, Page Number:999" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=220#V\n", "r=0.5#ohm\n", "i=20#A\n", "\n", "#calculation\n", "#as generator \n", "eg=v+i*r\n", "#as motor\n", "eb=v-i*r\n", "\n", "#result\n", "print \"as generator:eg=\",eg,\"V\"\n", "print \"as motor:eb=\",eb,\"V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "as generator:eg= 230.0 V\n", "as motor:eb= 210.0 V\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.2, Page Number:999" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from sympy.solvers import solve\n", "from sympy import Symbol\n", "#variable declaration\n", "ia=Symbol('ia')\n", "r=0.1#ohm\n", "brush_drop=2#V\n", "n=1000#rpm\n", "i=100#A\n", "v=250#V\n", "n2=700#rpm\n", "\n", "#calculations\n", "rl=v/i\n", "eg1=v+i*r+brush_drop\n", "eg2=eg1*n2/n\n", "ia=solve(eg2-2-ia*r-2.5*ia,ia)\n", "\n", "#result\n", "print \"current delivered to the load=\",ia[0],\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "current delivered to the load= 69.7692307692308 A\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.3, Page Number:999" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=440#V\n", "ra=0.8#ohm\n", "rf=200#ohm\n", "output=7.46#kW\n", "efficiency=0.85\n", "\n", "#calculations\n", "input_m=output*1000/efficiency\n", "im=output*1000/(efficiency*v)\n", "ish=v/rf\n", "ia=im-ish\n", "eb=v-ia*ra\n", "\n", "#results\n", "print \"back emf=\",eb,\"V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "back emf= 425.642780749 V\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.4, Page Number:1000" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "load=25#kW\n", "v=250#V\n", "ra=0.06#ohm\n", "rf=100#ohm\n", "\n", "#calculations\n", "#as generator\n", "i=load*1000/v\n", "ish=v/rf\n", "ia=i+ish\n", "eb=v+ia*ra\n", "power=eb*ia/1000\n", "\n", "print \"As generator: power=\",power,\"kW\"\n", "\n", "#as motor\n", "i=load*1000/v\n", "ish=v/rf\n", "ia=i-ish\n", "eb=v-ia*ra\n", "power=eb*ia/1000\n", "\n", "print \"As generator: power=\",power,\"kW\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "As generator: power= 26.12424 kW\n", "As generator: power= 23.92376 kW\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.5, Page Number:1000" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#variable declaration\n", "p=a=4\n", "z=32\n", "v=200.0#V\n", "i=12.0#A\n", "ra=2.0#ohm\n", "rf=200.0#ohm\n", "n=1000.0#rpm\n", "i2=5.0#A\n", "#calculations\n", "ia=i+v/rf\n", "eg=v+ia*ra\n", "phi=eg*a*60/(z*n*p)\n", "#as motor\n", "ia=i2-v/rf\n", "eb=v-ia*ra\n", "n=60*eb/(phi*z)\n", "\n", "#result\n", "print \"flux per pole=\",phi,\"wb\"\n", "print \"speed of the machine=\",math.ceil(n),\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "flux per pole= 0.42375 wb\n", "speed of the machine= 850.0 rpm\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.6, Page Number:1002" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "ia=110#A\n", "v=480#V\n", "ra=0.2#ohm\n", "z=864\n", "p=a=6\n", "phi=0.05#Wb\n", "\n", "#calculations\n", "eb=v-ia*ra\n", "n=60*eb/(phi*z)\n", "ta=0.159*phi*z*ia*p/a\n", "\n", "#result\n", "print \"the speed=\",math.floor(n),\"rpm\"\n", "print \"the gross torque=\",ta,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the speed= 636.0 rpm\n", "the gross torque= 755.568 N-m\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.7, Page Number:1003" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=250#V\n", "z=782\n", "ra=rf=0.5#ohm\n", "ia=40#A\n", "phi=25*0.001#Wb\n", "p=4\n", "a=2\n", "#calculation\n", "eb=v-ia*ra\n", "n=60*eb/(phi*z)\n", "ta=0.159*phi*z*ia*p/a\n", "\n", "print \"the speed=\",math.floor(n),\"rpm\"\n", "print \"the gross torque=\",ta,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the speed= 705.0 rpm\n", "the gross torque= 248.676 N-m\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.8, Page Number:1003" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "eb=250.0#V\n", "n=1500.0#rpm\n", "ia=50.0#A\n", "\n", "#calculations\n", "pm=eb*ia\n", "ta=9.55*eb*ia/n\n", "\n", "#result\n", "print \"torque=\",ta,\"N-m\"\n", "print \"machanical power=\",pm,\"W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "torque= 79.5833333333 N-m\n", "machanical power= 12500.0 W\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.9, Page Number:1003" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=220#V\n", "p=4\n", "z=800\n", "load=8.2#kW\n", "ia=45#A\n", "phi=25*0.001#Wb\n", "ra=0.6#ohm\n", "a=p/2\n", "\n", "#calculation\n", "ta=0.159*phi*z*ia*p/a\n", "eb=v-ia*ra\n", "n=eb*a/(phi*z*p)\n", "tsh=load*1000/(2*3.14*n)\n", "\n", "#result\n", "print \"developed torque=\",ta,\"N-m\"\n", "print \"shaft torque=\",tsh,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "developed torque= 286.2 N-m\n", "shaft torque= 270.618131415 N-m\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.10, Page Number:1003" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=220.0#V\n", "n=500.0#rpm\n", "i=50.0#A\n", "ra=0.2#ohm\n", "\n", "#calculation\n", "ia2=2*i\n", "fb1=v-(i*ra)\n", "eb2=v-(ia2*ra)\n", "n2=eb2*n/fb1\n", "#result\n", "print \"speed when torque is doubled=\",n2,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed when torque is doubled= 476.19047619 N-m\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.11, Page Number:1003" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from sympy.solvers import solve\n", "from sympy import Symbol\n", "#variable declaration\n", "r=Symbol('r')\n", "v=500#V\n", "load=37.3#kW\n", "n=1000#rpm\n", "efficiency=0.90\n", "ra=0.24#ohm\n", "vd=2#v\n", "i=1.8#A\n", "ratio=1.5\n", "\n", "#calculation\n", "input_m=load*1000/efficiency\n", "il=input_m/v\n", "tsh=9.55*load*1000/n\n", "il=ratio*il\n", "ia=il-i\n", "r=solve(ia*(r+ra)+vd-v,r)\n", "\n", "#result\n", "print \"full-load line current=\",il,\"A\"\n", "print \"full-load shaft torque\",tsh,\"N-m\"\n", "print \"total resistance=\",r[0],\"ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "full-load line current= 124.333333333 A\n", "full-load shaft torque 356.215 N-m\n", "total resistance= 3.82420021762787 ohm\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.12, Page Number:1004" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=a=4\n", "v=220#V\n", "z=540\n", "i=32#A\n", "output=5.595#kW\n", "ra=0.09#ohm\n", "i_f=1#A\n", "phi=30*0.001#Wb\n", "\n", "#calculation\n", "ia=i-i_f\n", "eb=v-ia*ra\n", "n=eb*a*60/(phi*z*p)\n", "tsh=9.55*output/n\n", "\n", "#result\n", "print \"speed=\",n,\"rpm\"\n", "print \"torque developed=\",tsh*1000,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed= 804.481481481 rpm\n", "torque developed= 66.4182473183 N-m\n" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.13(a), Page Number:1004" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=220.0#V\n", "load=20.0#kW\n", "i=5.0#A\n", "ra=0.04#ohm\n", "phi=0.04#Wb\n", "z=160\n", "il=95.0#A\n", "inl=9.0#A\n", "p=4\n", "a=2\n", "#calculation\n", "#no load\n", "ea0=v-(inl-i)*ra\n", "n0=ea0*a*60/(phi*z*p)\n", "#load\n", "ea=v-(il-i)*ra\n", "n=ea*n0/ea0\n", "\n", "#result\n", "print \"no-load speed=\",n0,\"rpm\"\n", "print \"load speed=\",n,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "no-load speed= 1030.5 rpm\n", "load speed= 1014.375 rpm\n" ] } ], "prompt_number": 58 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.13(b), Page Number:1004" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=a=6\n", "i=400#A\n", "n=350#rpm\n", "phi=80*0.001#Wb\n", "z=600*2\n", "loss=0.03#percentage\n", "\n", "#calculation\n", "e=phi*z*n*p/(60*a)\n", "pa=e*i\n", "t=pa/(2*3.14*n/60)\n", "t_net=0.97*t\n", "bhp=t_net*36.67*0.001/0.746\n", "#result\n", "print \"brake-horse-power\",bhp,\"HP\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "brake-horse-power 291.551578696 HP\n" ] } ], "prompt_number": 66 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.13(c), Page Number:1004" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=4\n", "z=774\n", "phi=24*0.001#Wb\n", "ia=50#A\n", "a=2\n", "#calculations\n", "t=0.159*phi*z*ia*p/a\n", "\n", "#result\n", "print \"torque=\",t,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "torque= 295.3584 N-m\n" ] } ], "prompt_number": 67 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.13(d), Page Number:1005" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=500.0#V\n", "i=5.0#A\n", "ra=0.15#ohm\n", "rf=200.0#ohm\n", "il=40.0#A\n", "\n", "#calculations\n", "ih=v/rf\n", "pi=v*i\n", "cu_loss_f=cu_loss=v*ih\n", "output=v*il\n", "cu_loss_a=(il+ih)**2*ra\n", "total_loss=cu_loss+cu_loss_a+cu_loss_f\n", "efficiency=output/(output+total_loss)\n", "#result\n", "print \"efficiency=\",efficiency*100,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency= 87.8312542029 %\n" ] } ], "prompt_number": 81 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.13(e), Page Number:1006" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable delcration\n", "ia=40#A\n", "v=220#V\n", "n=800#rpm\n", "ra=0.2#ohm\n", "rf=0.1#ohm\n", "loss=0.5#kW\n", "\n", "#calculations\n", "eb=v-ia*(ra+rf)\n", "ta=9.55*eb*ia/n\n", "cu_loss=ia**2*(ra+rf)\n", "total_loss=cu_loss+loss*1000\n", "input_m=v*ia\n", "output=input_m-total_loss\n", "\n", "#result\n", "print \"output of the motor=\",output/1000,\"kW\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "output of the motor= 7.82 kW\n" ] } ], "prompt_number": 88 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.14, Page Number:1006" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "f=400.0#N\n", "d=10.0#cm\n", "n=840#rpm\n", "v=220.0#V\n", "n1=1800#rpm\n", "efficiency=.80\n", "d2=24.0#cm\n", "\n", "#calculations\n", "tsh=f*d*0.01/2\n", "output=tsh*2*3.14*n/60\n", "input_m=output/efficiency\n", "i=input_m/v\n", "d1=n*d2/n1\n", "\n", "#calculation\n", "print \"current taken by the motor=\",round(i),\"A\"\n", "print \"size of motor pulley=\",d1,\"cm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "current taken by the motor= 10.0 A\n", "size of motor pulley= 11.2 cm\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.15, Page Number:1006" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=200.0#V\n", "p=4\n", "z=280\n", "ia=45.0#A\n", "phi=18*0.001#Wb\n", "ra=0.5+0.3#ohm\n", "loss=800.0#W\n", "d=0.41\n", "a=4\n", "#calculation\n", "eb=v-ia*ra\n", "n=eb*60*a/(phi*z*p*4)\n", "inpt=v*ia\n", "cu_loss=ia**2*ra\n", "total_loss=loss+cu_loss\n", "output=inpt-total_loss\n", "tsh=9.55*output/n\n", "f=tsh*2/d\n", "\n", "#result\n", "print \"pull at the rim of the pulley=\",f,\"N-m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "pull at the rim of the pulley= 628.016180845 N-m\n" ] } ], "prompt_number": 102 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.16, Page Number:1007" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=4\n", "v=240#V\n", "output=11.19#kW\n", "n=1000#rpm\n", "ia=50#A\n", "i=1#A\n", "z=540\n", "ra=0.1#ohm\n", "vd=1#V\n", "a=2\n", "#calculation\n", "eb=v-ia*ra\n", "ta=9.55*eb*ia/n\n", "tsh=9.55*output*1000/n\n", "phi=eb*60*a*1000/(z*n*p)\n", "input_a=v*ia\n", "cu_loss=ia**2*ra\n", "brush_loss=ia*2\n", "power=input_a-(cu_loss+brush_loss)\n", "rotational_loss=power-output*1000\n", "input_m=v*(ia+i)\n", "efficiency=output*1000/input_m\n", "\n", "#result\n", "print \"total torque=\",ta,\"N-m\"\n", "print \"useful torque=\",tsh,\"N-m\"\n", "print \"flux/pole=\",phi,\"mWb\"\n", "print \"rotational losses=\",rotational_loss,\"W\"\n", "print \"efficiency=\",efficiency*100,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total torque= 112.2125 N-m\n", "useful torque= 106.8645 N-m\n", "flux/pole= 13.0555555556 mWb\n", "rotational losses= 460.0 W\n", "efficiency= 91.4215686275 %\n" ] } ], "prompt_number": 106 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.17, Page Number:1007" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=460.0#v\n", "n=500.0#rpm\n", "i=40.0#A\n", "i2=30.0#A\n", "ra=0.8#ohm\n", "\n", "#calculation\n", "t2_by_t1=i2**2/i**2\n", "change=(1-t2_by_t1)*100#percentage\n", "eb1=v-i*ra\n", "eb2=v-i2*ra\n", "n2=eb2*i*n/(eb1*i2)\n", "#result\n", "print \"speed=\",n2,\"rpm\"\n", "print \"percentage change in torque=\",change,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed= 679.127725857 rpm\n", "percentage change in torque= 43.75 %\n" ] } ], "prompt_number": 111 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.18, Page Number:1008" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=460.0#V\n", "output=55.95#kW\n", "n=750#rpm\n", "I=252.8#kg-m2\n", "ia1=1.4\n", "ia2=1.8\n", "\n", "#calculations\n", "ia=(ia1+ia2)/2\n", "n=n/60.0\n", "tsh=output*1000/(2*3.14*n)\n", "torque_avg=(ia-1)*tsh\n", "dt=(I*2*3.14*n)/torque_avg\n", "\n", "#result\n", "print \"approximate time to attain full speed=\",dt,\"s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "approximate time to attain full speed= 46.4050282991 s\n" ] } ], "prompt_number": 129 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.19, Page Number:1008" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "output=14.92#kW\n", "v=400.0#V\n", "n=400.0#rpm\n", "i=40.0#A\n", "I=7.5#kg-m2\n", "ratio=1.2\n", "\n", "#calculations\n", "n=n/60\n", "t=output*1000/(2*3.14*n)\n", "torque=(ratio-1)*t\n", "dt=(I*2*3.14*n)/torque\n", "\n", "print \"time to attain full speed=\",dt,\"s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "time to attain full speed= 4.4055406613 s\n" ] } ], "prompt_number": 138 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.20, Page Number:1009" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=4\n", "z=944\n", "phi=34.6*0.001#Wb\n", "ta=209.0#N-m\n", "v=500.0#V\n", "ra=3.0#ohm\n", "a=2\n", "#calculation\n", "ia=ta/(0.159*phi*z*(p/a))\n", "ea=v-ia*ra\n", "n=ea/(phi*z*(p/a))\n", "\n", "#result\n", "print \"line current=\",ia,\"A\"\n", "print \"speed=\",n*60,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "line current= 20.1219966813 A\n", "speed= 403.798260345 rpm\n" ] } ], "prompt_number": 143 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.21, Page Number:1010" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=250#v\n", "n=1000#rpm\n", "ia=8#A\n", "ra=0.2#ohm\n", "rf=250#ohm\n", "i2=50#A\n", "\n", "#calculation\n", "ish=v/rf\n", "eb0=v-(ia-ish)*ra\n", "eb=v-(i2-ish)*ra\n", "n=eb*n/eb0\n", "\n", "#result\n", "print \"speed when loaded=\",n,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed when loaded= 966.21078037 rpm\n" ] } ], "prompt_number": 144 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.22, Page Number:1010" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "n=800#rpm\n", "ia=100#A\n", "v=230#V\n", "ra=0.15#ohm\n", "rf=0.1#ohm\n", "ia2=25#A\n", "ratio=0.45\n", "\n", "#calculation\n", "eb1=v-(ra+rf)*ia\n", "eb2=v-ia2*(ra+rf)\n", "n2=eb2*n/(eb1*ratio)\n", "\n", "#result\n", "print \"speed at which motor runs=\",n2,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed at which motor runs= 1940.37940379 rpm\n" ] } ], "prompt_number": 148 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.23, Page Number:1010" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from sympy.solvers import solve\n", "from sympy import Symbol\n", "#variable declaration\n", "ia2=Symbol('ia2')\n", "#variable declaration\n", "v=230.0#V\n", "ra=0.5#ohm\n", "rf=115.0#ohm\n", "n1=1200#rpm\n", "ia=2.5#A\n", "n2=1120#rpm\n", "\n", "#calculation\n", "eb1=v-ra*ia\n", "x=n2*eb1/n1\n", "ia2=solve((v-ra*ia2)-x,ia2)\n", "ia=ia2[0]+(v/rf)\n", "input_m=v*ia\n", "\n", "#result\n", "print \"line current=\",round(ia,1),\"A\"\n", "print \"power input=\",round(input_m,1),\"W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "line current= 35.0 A\n", "power input= 8050.0 W\n" ] } ], "prompt_number": 158 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.24, Page Number:1010" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "power=100.0#kW\n", "n1=300#rpm\n", "v=220.0#V\n", "load=10.0#kW\n", "ra=0.025#ohm\n", "rf=60.0#ohm\n", "vd=1.0#V\n", "\n", "#calculation\n", "i=power*1000/v\n", "ish=v/rf\n", "ia=i+ish\n", "eb=v+ia*ra+2*vd\n", "i=load*1000/v\n", "ia2=i-ish\n", "eb2=v-ia2*ra-2*vd\n", "n2=eb2*n1/eb\n", "\n", "#result\n", "print \"speed=\",n2,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed= 278.796797778 rpm\n" ] } ], "prompt_number": 174 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.25, Page Number:1011" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#variable declaration\n", "v=250.0#V\n", "n=1000.0#rpm\n", "ra=0.5#ohm\n", "rf=250.0#ohm\n", "ia=4.0#A\n", "i=40.0#A\n", "ratio=0.04#percentage by whih armature reaction weakens field\n", "\n", "#calculations\n", "ish=v/rf\n", "ia2=ia-ish\n", "eb0=v-ia2*ra\n", "n0=n*eb0/v\n", "ia=i-ish\n", "eb=v-ia*ra\n", "n=eb*n0/(eb0*(1-ratio))\n", "\n", "#result\n", "print \"speed of machine=\",math.floor(n),\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed of machine= 960.0 rpm\n" ] } ], "prompt_number": 190 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.26, Page Number:1011" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=250#V\n", "ooutput=14.92#kW\n", "n=1000#rpm\n", "i=75#A\n", "ra=0.25#ohm\n", "ratio=0.20\n", "\n", "#calculation\n", "eb1=v-i*ra\n", "eb_inst=eb1*(1-ratio)\n", "ia_inst=(v-eb_inst)/ra\n", "t_inst=9.55*eb_inst*ia_inst/n\n", "ia2=i/(1-ratio)\n", "eb2=v-ia2*ra\n", "n2=eb2*n/(eb1*(1-ratio))\n", "\n", "#result\n", "print \"armature current=\",ia2,\"A\"\n", "print \"speed=\",n2,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "armature current= 93.75 A\n", "speed= 1224.66216216 rpm\n" ] } ], "prompt_number": 191 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.27, Page Number:1012" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=200.0#V\n", "i=4.0#A\n", "n=700.0#rpm\n", "rf=100.0#A\n", "v2=6.0#V\n", "i2=10.0#A\n", "input_m=8.0#kW\n", "\n", "#calculation\n", "ish=v/rf\n", "il=input_m*1000/v\n", "ia=il-ish\n", "ra=v2/i2\n", "eb0=v-ish*ra\n", "eb=v-ia*ra\n", "n=eb*n/eb0\n", "ta=9.55*eb*ia/n\n", "inpt=v*i\n", "cu_loss=ish**2*ra\n", "constant_loss=inpt-cu_loss\n", "cu_loss_arm=ia**2*ra\n", "total_loss=constant_loss+cu_loss_arm\n", "output=input_m*1000-total_loss\n", "efficiency=output/(input_m*1000)\n", "print \n", "#result\n", "print \"speed on load=\",n,\"rpm\"\n", "print \"torque=\",ta,\"N-m\"\n", "print \"efficiency=\",efficiency*100,\"%\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "speed on load= 623.943661972 rpm\n", "torque= 103.0636 N-m\n", "efficiency= 79.2 %\n" ] } ], "prompt_number": 197 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.28, Page Number:1012" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variabe declaration\n", "v=220#V\n", "load=11#kW\n", "inl=5#A\n", "n_nl=1150#rpm\n", "ra=0.5#ohm\n", "rsh=110#ohm\n", "\n", "#calculations\n", "input_nl=v*inl\n", "ish=v/rsh\n", "ia0=inl-ish\n", "cu_loss_nl=ia1**2*ra\n", "constant_loss=input_nl-cu_loss_nl\n", "i=load*1000/v\n", "ia=i-ish\n", "cu_loss_a=ia**2*ra\n", "total_loss=cu_loss_a+constant_loss\n", "output=load*1000-total_loss\n", "efficiency=output*100/(load*1000)\n", "eb_nl=v-(ia0*ra)\n", "eb=v-ia*ra\n", "n=n_nl*eb/eb_nl\n", "ta=9.55*eb*ia/n\n", "\n", "#result\n", "print \"torque developed=\",ta,\"N-m\"\n", "print \"efficiency=\",efficiency,\"%\"\n", "print \"the speed=\",n,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "torque developed= 87.096 N-m\n", "efficiency= 79.5361818182 %\n", "the speed= 1031.57894737 rpm\n" ] } ], "prompt_number": 200 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.29, Page Number:1013" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "load=18.65#kW\n", "v=250.0#V\n", "ra=0.1#ohm\n", "vb=3#V\n", "rf=0.05#ohm\n", "ia=80.0#A\n", "n=600.0#rpm\n", "i2=100.0#A\n", "\n", "#calculation\n", "eb1=v-ia*(ra+rf)\n", "eb2=v-i2*(ra+rf)\n", "n2=eb2*ia*n/(eb1*i2)\n", "\n", "#result\n", "print \"speed when current is 100 A=\",n2,\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed when current is 100 A= 473.949579832 rpm\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.30, Page Number:1013" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#variable declaration\n", "v=220.0#V\n", "n=800.0#rpm\n", "i=100.0#A\n", "ra=0.1\n", "ratio=1.0/2.0\n", "#calculation\n", "ia1=i*math.sqrt(ratio)\n", "eb1=v-i*ra\n", "eb2=v-ia1*ra\n", "n2=eb2*i*n/(eb1*ia1)\n", "#result\n", "print \"speed when motor will run when developing half the torque=\",round(n2,0),\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed when motor will run when developing half the torque= 1147.0 rpm\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.31, Page Number:1013" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#variable declaration\n", "p=a=4\n", "n=600#rpm\n", "ia=25#A\n", "v=450#V\n", "z=500\n", "phi=1.7*0.01*math.pow(ia,0.5)\n", "\n", "#calculation\n", "eb=n*phi*z*p/(60*a)\n", "iara=v-eb\n", "ra=iara/ia\n", "i=math.pow((phi*ia*math.sqrt(ia)/(phi*2)),2.0/3.0)\n", "eb2=v/2-i*ra\n", "phi2=1.7*0.01*math.pow(i,0.5)\n", "n2=eb2*phi*n/(eb*phi2)\n", "\n", "#result\n", "print \"speed at which motor will run=\",round(n2,0),\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed at which motor will run= 372.0 rpm\n" ] } ], "prompt_number": 224 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.32, Page Number:1017" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import math\n", "#variable declaration\n", "v=460.0#V\n", "ra=0.5#ohm\n", "\n", "def f(ia,t):\n", " n=(v*ia-ia**2*ra)*60/(2*3.14*t)\n", " return(n)\n", "\n", "n1=f(20.0,128.8)\n", "n2=f(30.0,230.5)\n", "n3=f(40.0,349.8)\n", "n4=f(50.0,469.2)\n", "T=[128.8,230.5,349.8,469.2]\n", "N=[n1,n2,n3,n4]\n", "plt.plot(T,N)\n", "plt.xlabel(\"Torque(NM.m)\") \n", "plt.ylabel(\"Speed(rpm)\") \n", "plt.xlim((0,500))\n", "plt.ylim((0,800))\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.33, Page Number:1017" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import math\n", "#variable declaration\n", "output=5.968#kW\n", "n=700#rpm\n", "v1=500#V\n", "n2=600#rpm\n", "ra=3.5#ohm\n", "loss=450#W\n", "\n", "#calculation\n", "\n", "def fp(i,v):\n", " p=5.968*((n2*(v1-i*ra)/(v*n))**2)\n", " return(p)\n", "\n", "def fm(i,v):\n", " m=((v1-i*ra)*i-loss)/1000\n", " return(m)\n", "\n", "p1=fp(7.0,347.0)\n", "p2=fp(10.5,393.0)\n", "p3=fp(14.0,434.0)\n", "p4=fp(27.5,468.0)\n", "\n", "m1=fm(7.0,347.8)\n", "m2=fm(10.5,393.0)\n", "m3=fm(14.0,434.0)\n", "m4=fm(27.5,468.0)\n", "\n", "#plot\n", "I=[7,10.5,14,27.5]\n", "P=[p1,p2,p3,p4]\n", "M=[m1,m2,m3,m4]\n", "plt.plot(I,P)\n", "plt.plot(I,M)\n", "plt.xlabel(\"Current\") \n", "plt.ylabel(\"Power(kW)\") \n", "plt.xlim((0,30))\n", "plt.ylim((0,12))\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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WnK3c8v4tjM4azYtdXqRdvXZhlyRSZlat2vlMpKwsOOignc9Eql8/tVsLCgAp\nli9Wf8FFoy/i4H0OZtjZw6hepXrYJYnEXV5rYcfpL9avL/hMpD33DLviolEASJGNnDeSARMGcGfG\nnfRo3UPn9kvkrV6989jC4sVBa2HHsYVkbC0oAKRQ67eup+d7Pfnsx88Ydf4omtVsFnZJIkkrJwe+\n+GLnsYV164LWwo5jC2G2FhQAsluzf5rNRa9fxIn1TuThjg9TrVIajoSJJMDq1TuPLSxeDLVr/x4I\n55wDRx+duJoUAFIgd+fhTx/m7ql382inR7mwyYVhlySSdvJaC3mB0LYtnHFG4tavAJCdrNy4ksv/\nezkrN63k5fNe5tD9Dg27JBGJg+IGgCZxT3NTvp5Ci6dacNT+R/HR5R/p4C8iv0n4DWEkMXJyc7gz\n806GzRnGC51f4LQGp4VdkogkGQVAGvru1++4ZPQlVKtUjTnd51Bzz5phlyQiSUhdQGnmjaw3OOaZ\nYzi74dmM/dtYHfxFZJfUAkgTm7M3c/2E6xn35Tjeuugtjq1zbNgliUiSUwCkiVk/zWLtlrXM6T6H\nffbYJ+xyRCQF6DRQEZE0odNARUSkSBQAIiIRpQAQEYkoBYCISEQpAEREIkoBICISUQoAEZGIUgCI\niESUAkBEJKIUACIiEZXwADCzumY2xcwWmdlCM+uT6BpERCSEuYDMrBZQy93nmtmewCygs7tn5XuN\n5gISESmmpJ8LyN1/dve5sccbgCygdqLrEBGJulDHAMysPtAC+DTMOkREoii0AIh1/7wO9I21BERE\nJIFCuSGMmVUERgMvuvubBb1m0KBBvz3OyMggIyMjIbWJiKSKzMxMMjMzS/z+MAaBDRgOrHb3/rt4\njQaBRUSKqbiDwGEEQFvgQ2A+kLfyW9x9XL7XKABERIop6QOgKBQAIiLFl/SngYqISHJQAIiIRJQC\nQEQkohQAIiIRpQAQEYkoBYCISEQpAEREIkoBICISUQoAEZGIUgCIiESUAkBEJKIUACIiEaUAEBGJ\nKAWAiEhEKQBERCJKASAiElEKABGRiFIAiIhElAJARCSiFAAiIhGlABARiSgFgIhIRCkAREQiSgEg\nIhJRCgARkYhSAIiIRJQCQEQkohQAIiIRFUoAmFlHM1tiZl+Y2U1h1CAiEnUJDwAzKw88BnQEGgMX\nm9mRia4jTJmZmWGXEFfpvH3pvG2g7YuaMFoAfwa+dPdv3D0bGAWcE0IdoUn3/wnTefvSedtA2xc1\nYQTAQcC/vEDRAAAFQElEQVT3+Z7/EFsmIiIJFEYAeAjrFBGRHZh7Yo/HZnYcMMjdO8ae3wLkuvu/\n871GISEiUgLubkV9bRgBUAH4HOgA/AjMAC5296yEFiIiEnEVEr1Cd88xs17AeKA8MEwHfxGRxEt4\nC0BERJJD0l0JnO4XiZnZN2Y238zmmNmMsOspDTN7zsyWm9mCfMuqm9lEM1tqZhPMbN8wayyNXWzf\nIDP7Ibb/5phZxzBrLA0zq2tmU8xskZktNLM+seVpsQ93s30pvw/NbA8z+9TM5sa2bVBsebH2XVK1\nAGIXiX0OnAIsA2aSZuMDZvY10Mrdfwm7ltIys3bABmCEuzeNLRsMrHL3wbEA38/dbw6zzpLaxfbd\nAax39wdCLa4MmFktoJa7zzWzPYFZQGfgctJgH+5m+/5KGuxDM6vq7pti46ofAX2B8yjGvku2FkBU\nLhIr8ih9MnP3qcCaHRafDQyPPR5O8A8uJe1i+yB99t/P7j439ngDkEVwTU5a7MPdbB+kwT50902x\nh5WAigSn2Bdr3yVbAEThIjEHJpnZZ2Z2ddjFxEFNd18ee7wcqBlmMXHS28zmmdmwVO0e2ZGZ1Qda\nAJ+Shvsw3/Z9EluU8vvQzMqZ2VyCfTTB3WdQzH2XbAGQPP1R8XOCu7cAOgE9Y90MacmD/sV026dP\nAIcARwM/AfeHW07pxbpHRgN93X19/r+lwz6Mbd/rBNu3gTTZh+6e6+5HA3WAY82syQ5/L3TfJVsA\nLAPq5ntel6AVkDbc/afY75XAGIJur3SyPNb3ipkdCKwIuZ4y5e4rPAZ4lhTff2ZWkeDgP9Ld34wt\nTpt9mG/7XszbvnTbh+7+KzAFOJ1i7rtkC4DPgMPNrL6ZVQIuBN4KuaYyY2ZVzWyv2ONqwGnAgt2/\nK+W8BXSLPe4GvLmb16ac2D+qPF1I4f1nZgYMAxa7+0P5/pQW+3BX25cO+9DMauR1XZlZFeBUgjGO\nYu27pDoLCMDMOgEP8ftFYveEXFKZMbNDCL71Q3AR3n9SefvM7GWgPVCDoL/xduC/wKvAwcA3wF/d\nfW1YNZZGAdt3B5BB0HXgwNdA93x9rinFzNoCHwLz+b2r4BaCq/NTfh/uYvsGAheT4vvQzJoSDPKW\nJ/gi/4q732Vm1SnGvku6ABARkcRIti4gERFJEAWAiEhEKQBERCJKASAiElEKABGRiFIAiIhElAJA\nIsPMapnZKDP7MjYX07tmdngC19/ezI5P1PpECqMAkEiIXRU6Bpjs7oe5e2uCi56KNNGZmZXb3fMi\nOgloU4L3icSFAkCi4iRgm7s/nbfA3ecDFczs7bxlZvaYmXWLPf7GzO41s1nABQU8P83MppvZLDN7\nNTa9R977BsWWzzezhrHZKLsD/WM3IWmbuE0XKZgCQKKiCcENQQqTfwZFJ7i5Rit3fyX/c+B94Fag\nQ+z5LGBAvvetjC1/ArjB3b8BngQecPcW7v5RGW2XSIkl/KbwIiEp6Zwnr+zi+XFAY2B60LtEJWB6\nvte9Efs9Gzg33/KUvxGJpA8FgETFIuD8Apbn8MeWcJUd/r5xN88nuvslu1jf1tjv7ejfmSQpdQFJ\nJLj7ZKBy/ruwmVkzgm/kjc2sUmx63ZOL+JGfAieYWYPYZ1UrwhlF64G9il+9SHwoACRKugCnxE4D\nXQj8i+COUK8CCwm6d2bv5v2/dSPFbujzd+BlM5tH0P3TcBfvyXvf20CX2CDwCaXcFpFS03TQIiIR\npRaAiEhEKQBERCJKASAiElEKABGRiFIAiIhElAJARCSiFAAiIhGlABARiaj/D6p919PNp3KzAAAA\nAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.34, Page Number:1022" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=500#V\n", "i=3#A\n", "ia=3.5#A\n", "ib=4.5#A\n", "\n", "#calculation\n", "loss=v*i\n", "#B unexcited\n", "loss1=v*(ia-i)\n", "#B excited\n", "loss2=v*(ib-i)\n", "loss=loss2-loss1\n", "\n", "#result\n", "print \"iron losses of B=\",loss,\"W\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "iron losses of B= 500.0 W\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.35, Page Number:1023" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=220.0#V\n", "ra=0.2#ohm\n", "rf=110.0#ohm\n", "ia=5.0#A\n", "n=1500#rpm\n", "i2=52.0#A\n", "\n", "#calculation\n", "ish=v/rf\n", "ia1=ia-ish\n", "ia2=i2-ish\n", "eb1=v-ia1*ra\n", "eb2=v-ia2*ra\n", "n2=round(eb2*n/eb1,0)\n", "input_nl=v*ia\n", "cu_loss_nl=ia1**2*ra\n", "constant_loss=input_nl-cu_loss_nl\n", "cu_loss_l=ia2**2*ra\n", "total_loss=constant_loss+cu_loss_l\n", "input_l=v*i2\n", "output=input_l-total_loss\n", "tsh=9.55*output/n2\n", "\n", "#result\n", "print \"speed=\",n2,\"rpm\"\n", "print \"shaft torque=\",tsh,\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.36, Page Number:1023" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=250#V\n", "n=1000#rpm\n", "ia=5#A\n", "ra=0.2#ohm\n", "rf=250#ohm\n", "i=50#A\n", "ratio=0.03#percentage by which armature reaction weakens field\n", "\n", "#calculations\n", "ish=v/rf\n", "ia1=ia-ish\n", "ia2=i-ish\n", "eb1=v-ia1*ra\n", "eb2=v-ia2*ra\n", "n2=eb2*n/(eb1*(1-ratio))\n", "\n", "#result\n", "print \"speed=\",round(n2,0),\"rpm\"" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.37, Page Number:1023" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=500#V\n", "ia=5#A\n", "ra=0.22#A\n", "rf=250#ohm\n", "i=100#A\n", "\n", "#calculations\n", "ish=v/rf\n", "ia0=ia-ish\n", "eb0=v-ia0*ra\n", "cu_loss=ia0**2*ra\n", "input_m=v*ia\n", "constant_loss=input_m-cu_loss\n", "ia=i-ish\n", "eb=v-ia*ra\n", "cu_loss=ia**2*ra\n", "total_loss=cu_loss+constant_loss\n", "input_m=v*i\n", "output=input_m-total_loss\n", "efficiency=output*100/input_m\n", "per=(eb-eb0)*100/eb0\n", "\n", "#result\n", "print \"efficiency=\",round(efficiency,1),\"%\"\n", "print \"percentage change in speed=\",round(per,2),\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency= 90.8 %\n", "percentage change in speed= -4.19 %\n" ] } ], "prompt_number": 244 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.38, Page Number:1024" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=250#V\n", "n=1000#rpm\n", "i=25#A\n", "i2=50#A\n", "ratio=0.03#percentage by which the armature reaction weakens field\n", "ra=0.2#ohm\n", "rf=250#ohm\n", "vd=1\n", "#calculation\n", "ish=v/rf\n", "ia1=i-ish\n", "ebh=v-ia1*ra-2*vd\n", "ia2=i2-ish\n", "eb2=v-ia2*ra-2*vd\n", "n2=eb2*n/(ebh*(1-ratio))\n", "ta1=9.55*eb1*ia1/n\n", "ta2=9.55*eb2*ia2/n2\n", "\n", "#result\n", "print \"speed=\",round(n2,0),\"rpm\"\n", "print \"torque in first case=\",ta1,\"N-m\"\n", "print \"torque in second case=\",ta2,\"N-m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed= 1010.0 rpm\n", "torque in first case= 57.11664 N-m\n", "torque in second case= 110.3912768 N-m\n" ] } ], "prompt_number": 247 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.39, Page Number:1024" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "v=250.0#V\n", "n1=1000.0#rpm\n", "ra=0.5#ohm\n", "rf=250.0#ohm\n", "ia=4.0#A\n", "i=40.0#A\n", "ratio=0.04#percentage by which the armature reaction weakens field\n", "eb1=250.0#V\n", "\n", "#calculation\n", "ish=v/rf\n", "eb2=v-(i-ish)*ra\n", "n2=eb2*n/(eb1*(1-ratio))\n", "cu_loss=(ia-ish)**2*ra\n", "input_m=v*ia\n", "constant_loss=input_m-cu_loss\n", "cu_loss_a=(i-ish)**2*ra\n", "total_loss=constant_loss+cu_loss_a\n", "inpt=v*i\n", "output=inpt-total_loss\n", "efficiency=output*100/inpt\n", "\n", "#result\n", "print \"speed=\",round(n2,0),\"rpm\"\n", "print \"efficiency=\",efficiency,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed= 960.0 rpm\n", "efficiency= 82.44 %\n" ] } ], "prompt_number": 254 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.40, Page Number:1025" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=4\n", "v=250#V\n", "z=120*8\n", "a=4\n", "phi=20*0.001#Wb\n", "i=25#A\n", "ra=0.1#ohm\n", "rf=125#ohm\n", "loss=810#W\n", "\n", "#calculations\n", "ish=v/rf\n", "ia=i-ish\n", "eb=v-ia*ra\n", "n=eb*a*60/(p*z*phi)\n", "ta=9.55*eb*ia/n\n", "cu_loss=ia**2*ra\n", "cu_loss_shunt=v*ish\n", "total_loss=loss+cu_loss+cu_loss_shunt\n", "input_m=v*i\n", "output=input_m-total_loss\n", "tsh=9.55*output/n\n", "efficiency=output*100/input_m\n", "\n", "#result\n", "print \"gross torque=\",ta,\"N-m\"\n", "print \"useful torque=\",tsh,\"N-m\"\n", "print \"efficiency=\",efficiency,\"%\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "gross torque= 70.288 N-m\n", "useful torque= 60.2946209124 N-m\n", "efficiency= 78.1936 %\n" ] } ], "prompt_number": 256 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.41, Page Number:1025" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "output=14.92#kW\n", "n=1150#rpm\n", "p=4\n", "a=2\n", "z=620\n", "ra=0.2#ohm\n", "i=74.8#A\n", "i2=3#A\n", "v=230#V\n", "#calculation\n", "ia=i-i2\n", "eb=v-ia*ra\n", "phi=eb*a*60/(p*z*n)\n", "ta=9.55*eb*ia/n\n", "power=eb*ia\n", "loss_rot=power-output*1000\n", "input_m=v*i\n", "total_loss=input_m-output*1000\n", "per=total_loss*100/input_m\n", "\n", "#result\n", "print \"flux per pole=\",phi*1000,\"mWb\"\n", "print \"torque developed=\",ta,\"N-m\"\n", "print \"rotational losses=\",loss_rot,\"W\"\n", "print \"total losses expressed as a percentage of power=\",per,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "flux per pole= 9.07321178121 mWb\n", "torque developed= 128.575818783 N-m\n", "rotational losses= 562.952 W\n", "total losses expressed as a percentage of power= 13.2759823297 %\n" ] } ], "prompt_number": 263 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.42, Page Number:1025" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from sympy.solvers import solve\n", "from sympy import Symbol\n", "#variable declaration\n", "ia1=Symbol('ia1')\n", "output=7.46#kW\n", "v=250#V\n", "i=5#A\n", "ra=0.5#ohm\n", "rf=250#ohm\n", "\n", "#calculation\n", "input_m=v*i\n", "ish=v/rf\n", "ia=i-ish\n", "cu_loss=v*ish\n", "cu_loss_a=ra*ia**2\n", "loss=input_m-cu_loss\n", "ia1=solve(ra*ia1**2-v*ia1+output*1000+loss,ia1)\n", "i2=ia1[0]+ish\n", "input_m1=v*i2\n", "efficiency=output*100000/input_m1\n", "ia=math.sqrt((input_m-cu_loss_a)/ra)\n", "input_a=v*ia\n", "cu_loss=ia**2*ra\n", "output_a=input_a-(cu_loss+loss)\n", "\n", "#result\n", "print \"efficiency=\",efficiency,\"%\"\n", "print \"output power at which efficiency is maximum=\",output_a/1000,\"kW\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency= 79.5621535016683 %\n", "output power at which efficiency is maximum= 10.2179357944 kW\n" ] } ], "prompt_number": 271 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.43, Page Number:1026" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "n2_by_n1=1.0/2.0\n", "ia2_by_ia1=phi1_by_phi2=1.0/2.0\n", "v2_by_v1=n2_by_n1*phi1_by_phi2\n", "reduction_v=(1-v2_by_v1)*100\n", "reduction_i=(1-ia2_by_ia1)*100\n", "\n", "#result\n", "print \"percentage reduction in the motor terminal voltage=\",reduction_v,\"%\"\n", "print \"percentage fall in the motor current=\",reduction_i,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "percentage reduction in the motor terminal voltage= 75.0 %\n", "percentage fall in the motor current= 50.0 %\n" ] } ], "prompt_number": 272 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.44, Page Number:1026" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#variable declaration\n", "p=6\n", "v=500#V\n", "z=1200\n", "phi=20*0.001#Wb\n", "ra=0.5#ohm\n", "rf=250#ohm\n", "i=20#A\n", "loss=900#W\n", "a=2\n", "#calculation\n", "ish=v/rf\n", "ia=i-ish\n", "eb=v-ia*ra\n", "n=eb*a*60/(p*z*phi)\n", "ta=9.55*eb*ia/n\n", "cu_loss=ia**2*ra\n", "cu_loss_f=v*ish\n", "total_loss=cu_loss+cu_loss_f+loss\n", "input_m=v*i\n", "output=input_m-total_loss\n", "tsh=9.55*output/n\n", "efficiency=output*100/input_m\n", "\n", "#result\n", "print \"useful torque=\",ta,\"N-m\"\n", "print \"output=\",output/1000,\"Kw\"\n", "print \"efficiency==\",efficiency,\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "useful torque= 206.28 N-m\n", "output= 7.938 Kw\n", "efficiency== 79.38 %\n" ] } ], "prompt_number": 275 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example Number 29.45, Page Number:1027" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from sympy.solvers import solve\n", "from sympy import Symbol\n", "#variable declaration\n", "ia1=Symbol('ia1')\n", "output=37.3*1000#W\n", "v=460#V\n", "i=4#A\n", "n=660#rpm\n", "ra=0.3#ohm\n", "rf=270#ohm\n", "\n", "#calculations\n", "ish=v/rf\n", "cu_loss=v*ish\n", "ia=i-ish\n", "cu_loss_a=ia**2*ra\n", "input_a=loss=v*ia\n", "ia1=solve(ra*ia1**2-v*ia1+output+loss,ia1)\n", "i=ia1[0]+ish\n", "eb1=v-(ia*ra)\n", "eb2=v-(ia1[0]*ra)\n", "n2=n*eb2/eb1\n", "ia=math.sqrt((cu_loss+input_a)/ra)\n", "\n", "#result\n", "print \"the current input=\",i,\"A\"\n", "print \"speed=\",round(n2,0),\"rpm\"\n", "print \"armature current at which efficiency is maximum=\",ia,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the current input= 90.2860908863713 A\n", "speed= 623.0 rpm\n", "armature current at which efficiency is maximum= 78.3156008298 A\n" ] } ], "prompt_number": 280 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }