{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 9 - D C Motors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1 - pg 9_14" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "e.m.f for lap wound (V) = 462.0\n", "e.m.f for wave wound (V) = 924.0\n" ] } ], "source": [ "#Chapter-9,Example9_1,pg 9_14\n", "#calculate the emf for lap and wave wounds\n", "#given\n", "P=4.\n", "Z=440.\n", "phi=0.07#flux(in Wb)\n", "N=900.\n", "#for lap-wound\n", "#calculations\n", "A=P\n", "E=phi*P*N*Z/(60*A)\n", "#results\n", "print\"e.m.f for lap wound (V) = \",E\n", "#for wave wound\n", "A=2.\n", "E=phi*P*N*Z/(60*A)\n", "print\"e.m.f for wave wound (V) = \",E\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2 - pg 9_15" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "e.m.f for lap wound (V) = 263.424\n", "speed of generator for wave wound (rpm) = 560.0\n" ] } ], "source": [ "#Chapter-9,Example9_2,pg 9_15\n", "#calculate the speed and emf\n", "#given\n", "P=4.\n", "phi=21.*10**-3#flux(in Wb)\n", "N=1120.\n", "C=42.#coils\n", "tpC=8.#turns per coil\n", "#calculations and results\n", "t=C*tpC#total turns\n", "Z=2*t\n", "#for lap wound\n", "A=P\n", "E=phi*P*N*Z/(60*A)\n", "print\"e.m.f for lap wound (V) = \",E\n", "#for wave wound\n", "A=2.\n", "E=263.424\n", "N=E*60*A/(phi*P*Z)\n", "print\"speed of generator for wave wound (rpm) = \",N" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3 - pg 9_20" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "back e.m.f of motor (V) = 197.5\n" ] } ], "source": [ "#Chapter-9,Example9_3,pg 9_20\n", "#calculate the back emf \n", "#given\n", "V=220.\n", "Ia=30.\n", "Ra=0.75\n", "#calculations\n", "Eb=V-Ia*Ra\n", "#results\n", "print\"back e.m.f of motor (V) = \",Eb\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4 - pg 9_21" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "back e.m.f (V) = 206.0\n", "speed of motor (rpm) = 1648.0\n" ] } ], "source": [ "#Chapter-9,Example9_4,pg 9_21\n", "#calculate the back emf and speed of motor\n", "P=4.\n", "A=P\n", "V=230.\n", "Ra=0.6\n", "Z=250.\n", "phi=30.*10**-3#flux(in Wb)\n", "Ia=40.\n", "#calculations\n", "Eb=V-Ia*Ra\n", "N=Eb*60*A/(phi*P*Z)\n", "#results\n", "print\"back e.m.f (V) = \",Eb\n", "print\"speed of motor (rpm) = \",N\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5 - pg 9_24" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gross torque (N-m) = 76.32\n" ] } ], "source": [ "#Chapter-9,Example9_5,pg 9_24\n", "#calculate the gross torque\n", "#given\n", "P=4.\n", "A=P\n", "Z=480.\n", "phi=20.*10**-3#flux(in Wb)\n", "Ia=50.\n", "#calculations\n", "Ta=0.159*phi*Ia*(P*Z/A)\n", "#results\n", "print\"gross torque (N-m) = \",Ta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6 - pg 9_25" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "induced e.m.f (V) = 225.0\n", "armature current (A) = 6.25\n", "stray losses (W) = 1406.25\n", "loss torque (Nm) = 13.429\n" ] } ], "source": [ "#Chapter-9,Example9_6,pg 9_25\n", "#calculate the induced emf, armature current, stray losses and loss torque\n", "import math\n", "#given\n", "P=4.\n", "A=P\n", "No=1000.#speed of motor\n", "Z=540.\n", "V=230.\n", "phi=25.*10**-3#flux(In Wb)\n", "Ra=0.8\n", "#calculations\n", "Ebo=phi*P*No*Z/(60*A)#induced e.m.f\n", "Iao=(V-Ebo)/Ra#armature current\n", "SL=Ebo*Iao#stray losses\n", "wo=2*math.pi*No/60#angular velocity\n", "Tf=Ebo*Iao/wo#loss torque\n", "#results\n", "print\"induced e.m.f (V) = \",Ebo\n", "print\"armature current (A) = \",Iao\n", "print\"stray losses (W) = \",SL\n", "print\"loss torque (Nm) = \",round(Tf,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 7 - pg 9_37" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor (rpm) = 1374.0\n" ] } ], "source": [ "#Chapter-9,Example9_7,pg 9_37\n", "#calculate the speed of motor\n", "#given\n", "P=4.\n", "Z=200.\n", "V=250.\n", "A=2.\n", "phi=25.*10**-3\n", "Ia=60.\n", "#calculations\n", "Il=Ia\n", "Ra=0.15\n", "Rse=0.2\n", "Eb=V-Ia*(Ra+Rse)\n", "N=Eb*60*A/(phi*P*Z)\n", "#results\n", "print\"speed of motor (rpm) = \",N\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 8 - pg 9_38" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "back e.m.f (V) = 244.375\n" ] } ], "source": [ "#Chapter-9,Example9_8,pg 9_38\n", "#calculate the back emf\n", "#given\n", "V=250.\n", "Il=20.\n", "Ra=0.3\n", "Rsh=200.\n", "#calculations\n", "Ish=V/Rsh\n", "Ia=Il-Ish\n", "Eb=V-Ia*Ra\n", "#results\n", "print\"back e.m.f (V) = \",Eb\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 9 - pg 9_38" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed at full load (rpm) = 939.67\n" ] } ], "source": [ "#Chapter-9,Example9_9,pg 9_38\n", "#calculate the speed at full load\n", "#given\n", "No=1000.\n", "V=220.\n", "Rsh=110.\n", "Ra=0.3\n", "#calculations\n", "Ish=V/Rsh\n", "Ilo=6.\n", "Iao=Ilo-Ish\n", "Rao=0.3\n", "Ebo=V-Iao*Ra\n", "#on full load\n", "Il=50\n", "IaFL=Il-Ish\n", "EbFL=V-IaFL*Ra\n", "#N=k*Eb/phi\n", "NFL=No*EbFL/Ebo\n", "#results\n", "print\"speed at full load (rpm) = \",round(NFL,2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10 - pg 9_39" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor on new load (rpm) = 300.0\n" ] } ], "source": [ "#Chapter-9,Example9_10,pg 9_39\n", "#calculate the speed of motor on new load\n", "#given\n", "N1=800.\n", "I1=20.\n", "V=250.\n", "Ia1=I1\n", "I2=50.\n", "Ia2=I2\n", "Ra=0.2\n", "Ise1=I1\n", "Ise2=I2\n", "Rse=0.3\n", "#calculations\n", "Eb1=V-Ia1*Ra-Ise1*Rse\n", "Eb2=V-Ia2*Ra-Ise2*Rse\n", "#from speed equation\n", "N2=N1*(Eb2/Eb1)*(Ia1/Ia2)\n", "#results\n", "print\"speed of motor on new load (rpm) = \",N2\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11 - pg 9_45" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "new current (A) = 40.0\n", "new speed (rpm) = 2938.776\n" ] } ], "source": [ "#Chapter-9,Example9_11,pg 9_45\n", "#calculate the new current and speed\n", "#given\n", "V=250.\n", "Rsh=250.\n", "Ra=0.25\n", "Rx=Rsh\n", "Ia1=20.\n", "#calculations\n", "Ish1=V/Rsh\n", "Ish2=V/(Rsh+Rx)\n", "N1=1500.\n", "Eb1=V-Ia1*Ra\n", "#phi=k*Ish\n", "#T1=T2\n", "Ia2=Ish1*Ia1/Ish2#new current\n", "Eb2=V-Ia2*Ra\n", "#from speed equation\n", "N2=N1*(((Eb1/Eb2)*(Ish2/Ish1))**-1)#new speed\n", "#results\n", "print\"new current (A) = \",Ia2\n", "print\"new speed (rpm) = \",round(N2,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 12 - pg 9_46" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resistance in shunt field (ohm) = 88.313\n" ] } ], "source": [ "#Chapter-9,Example9_12,pg 9_46\n", "#calculate the resistance in shunt field\n", "#given\n", "import math\n", "V=250.\n", "Ra=0.5\n", "Rsh=250.\n", "Ia1=20.\n", "Ish1=V/Rsh\n", "Eb1=V-Ia1*Ra\n", "N1=600.\n", "N2=800.\n", "#T1=T2\n", "#Ish1*Ia1=Ish2*Ia2\n", "#Ish2*Ia2=20............(1)\n", "#(N1/N2)=(Eb1/Eb2)*(Ish2/Ish1)...........(2)\n", "#using (1) and (2)\n", "#240*(Ish2^2)-187.5*Ish2+7.5=0.........(3)\n", "b=-187.5\n", "a=240\n", "c=7.5\n", "#calculations\n", "Ish2=(-b+math.sqrt(((b**2)-4*a*c)))/(2*a)#neglecting lower value\n", "Rx=(V/Ish2)-Rsh\n", "#results\n", "print\"resistance in shunt field (ohm) = \",round(Rx,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 13 - pg 9_51" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor (rpm) = 912.743\n" ] } ], "source": [ "#Chapter-9,Example9_13,pg 9_51\n", "#calculate the speed of motor\n", "#given\n", "import math\n", "V=250.\n", "Ra=0.15\n", "Rx=0.1\n", "Rse=0.1\n", "N1=800.\n", "Ise1=30.\n", "Ia1=30.#Ia1=Ise1\n", "I1=Ia1\n", "#phi=k*Ise\n", "#T2=T1+0.5*T1(increased by 50%)..........(1)\n", "#Ise2=Ia2*Rx/(Rx+Rse)\n", "#putting values of Rx and Rse Ise2=0.5*Ia2.........(2)\n", "#putting (1) and (2) in torque equation\n", "#calculations\n", "Ia2=math.sqrt(2700)\n", "Ise2=0.5*Ia2#from (2)\n", "Eb1=V-Ia1*Ra-Ise1*Rse\n", "Eb2=V-Ia2*Ra-Ise2*Rse\n", "#using speed equation\n", "N2=N1*Eb2*Ise1/(Eb1*Ise2)\n", "#results\n", "print\"speed of motor (rpm) = \",round(N2,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 14 - pg 9_52" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor (rpm) = 1119.5122\n" ] } ], "source": [ "#Chapter-9,Example9_14,pg 9_52\n", "#calculate the speed of motor\n", "#given\n", "V=220.\n", "Ise1=15.\n", "Ia1=Ise1\n", "Ia2=10.\n", "Ise2=Ia2\n", "I2=Ia2\n", "N1=900.\n", "Ra=0.5\n", "Rse=0.5\n", "Rx=4.\n", "#calculations\n", "Eb1=V-Ia1*Ra-Ise1*Rse\n", "Eb2=V-Ia2*Ra-Ise2*Rse-I2*Rx\n", "N2=N1*Eb2*Ise1/(Eb1*Ise2)\n", "#results\n", "print\"speed of motor (rpm) = \",round(N2,4)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 15 - pg 9_64" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "useful torque (Nm) = 185.26\n", "efficiency at load (percent) = 79.38\n" ] } ], "source": [ "#Chapter-9,Example9_15,pg 9_64\n", "#calculate the useful torque and efficiency at load\n", "#given\n", "import math\n", "P=6.\n", "V=500.\n", "A=2.#wave wound\n", "Z=1200.\n", "phi=20*10**-3#flux\n", "Ra=0.5\n", "Rsh=250.\n", "Il=20.\n", "#calculations\n", "Ish=V/Rsh\n", "Ia=Il-Ish\n", "Eb=V-Ia*Ra\n", "N=Eb*60*A/(phi*P*Z)\n", "Pm=Eb*Ia#mechanical power\n", "w=2*math.pi*N/60#angular velocity\n", "Tg=Pm/w\n", "ML=900#mechanical losses\n", "Pout=Pm-ML\n", "Tsh=Pout/w#usefull torque\n", "Pin=V*Il\n", "n=Pout*100/Pin#efficiency at load\n", "#results\n", "print\"useful torque (Nm) = \",round(Tsh,2)\n", "print\"efficiency at load (percent) = \",n\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 16 - pg 9_65" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor (rpm) = 1860.85\n" ] } ], "source": [ "#Chapter-9,Example9_16,pg 9_65\n", "#calculate the speed of motor\n", "#given\n", "V=120.\n", "Ra=0.2\n", "Rsh=60.\n", "#for full load\n", "Il1=40.\n", "N1=1800.\n", "#for shunt motor\n", "#calculations\n", "Ish=V/Rsh\n", "Ia1=Il1-Ish\n", "Eb1=V-Ia1*Ra\n", "#for half load T2=T1/2\n", "Ia2=Ia1*0.5#T=k*Ia\n", "Eb2=V-Ia2*Ra\n", "N2=N1*Eb2/Eb1#from torque equation\n", "#results\n", "print\"speed of motor (rpm) = \",round(N2,2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 17 - pg 9_66" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed as generator (rpm) = 1592.7\n" ] } ], "source": [ "#Chapter-9,Example9_17,pg 9_66\n", "#calculate the speed of generator\n", "#given\n", "Ra=0.08\n", "Eb1=242.\n", "V=250.\n", "Ia=87.\n", "Vt=V#generator supply\n", "Nm=1500.\n", "#calculations\n", "Ia1=(V-Eb1)/Ra\n", "#at start N=0, Eb=0\n", "Ias=V/Ra#Ia(start)\n", "Ia2=120\n", "Eb2=V-Ia2*Ra\n", "Eg=Vt+Ia*Ra#generator e.m.f\n", "Ng=Nm*Eg/Eb1#speed as generator\n", "#results\n", "print\"speed as generator (rpm) = \",round(Ng,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 18 - pg 9_67" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gross mechanical power (kW) = 70.812\n", "stray losses (W) = 11132.13\n", "no load speed (rpm) = 1250.9121\n" ] } ], "source": [ "#Chapter-9,Example9_18,pg 9_67\n", "#calculate the gross mechanical power,stray losses and no load speed\n", "#given\n", "import math\n", "V=250.\n", "Po=59680.\n", "Rsh=250.\n", "Ra=0.04\n", "n=80.#efficiency\n", "N1=1200.\n", "#calculations and results\n", "Il=Po*100/(V*n)#Pi=V*Il\n", "Ish=V/Rsh\n", "Ia=Il-Ish\n", "Eb=V-Ia*Ra\n", "Pm=Eb*Ia#gross mechanical power\n", "SL=Pm-Po#stray losses\n", "print\"gross mechanical power (kW) = \",round(Pm/1000.,3)\n", "print\"stray losses (W) = \",round(SL,2)\n", "#on no load\n", "#Pg=S, Ebo*Iao=SL..........(1)\n", "#Ebo=V-Iao*Ra............(2)\n", "#putting (2) in (1)\n", "#(Iao^2)-6250*Iao+278303.24=0\n", "b=-6250.\n", "a=1.\n", "c=278303.24\n", "Iao=(-b-math.sqrt((b**2)-4*a*c))/(2*a)\n", "I=Iao-Ish#current drawn on no load\n", "Ebo=V-Iao*Ra\n", "No=N1*Ebo/Eb\n", "print\"no load speed (rpm) = \",round(No,4)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 19 - pg 9_69" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "full load speed (rpm) = 1234.102\n" ] } ], "source": [ "#Chapter-9,Example9_19,pg 9_69\n", "#calculate the full load speed\n", "#given\n", "V=250.\n", "P=4.\n", "Ra=0.1\n", "Rsh=125.\n", "Vbr=2.#brush drop\n", "#no load condition\n", "Ilo=4.\n", "No=1200.\n", "Il1=61.\n", "#calculations\n", "Ish=V/Rsh\n", "Iao=Ilo-Ish\n", "Ebo=V-Iao*Ra-Vbr\n", "#full load condition\n", "#phi1=phio-o.o5*phio (weakened by 5%)\n", "#phi=phi1/phio\n", "phi=0.95\n", "Ia1=Il1-Ish\n", "Eb1=V-Ia1*Ra-Vbr\n", "N1=No*Eb1/(Ebo*phi)\n", "#results\n", "print\"full load speed (rpm) = \",round(N1,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 20 - pg 9_70" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "full load speed (rpm) = 1233.396\n", "speed regulation (percent) = 3.64\n", "hp rating of machine (hp) = 19.42\n", "full load efficiency (percent) = 86.48\n", "The answer differs from the textbook due to rounding off error\n" ] } ], "source": [ "#Chapter-9,Example9_20,pg 9_70\n", "#calculate the full load speed, speed regulation, hp rating and efficiency\n", "#given\n", "V=250.\n", "Ra=0.15\n", "Rsh=166.67\n", "No=1280.\n", "Il1=67.\n", "#calculations\n", "Ish=V/Rsh\n", "Ia1=Il1-Ish\n", "Eb1=V-Ia1*Ra\n", "#on no load\n", "Ilo=6.5\n", "Ish=1.5\n", "Iao=Ilo-Ish\n", "Ebo=V-Iao*Ra\n", "N1=Eb1*No/Ebo\n", "Sr=(No-N1)*100/No#speed regulation\n", "SL=Ebo*Iao\n", "Po=Eb1*Ia1-SL#full load shaft output\n", "hp=Po/746.#horse power rating\n", "Pi=V*Il1\n", "n=Po*100./Pi\n", "#results\n", "print\"full load speed (rpm) = \",round(N1,3)\n", "print\"speed regulation (percent) = \",round(Sr,2)\n", "print\"hp rating of machine (hp) = \",round(hp,2)\n", "print\"full load efficiency (percent) = \",round(n,2)\n", "print \"The answer differs from the textbook due to rounding off error\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 21 - pg 9_71" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor (rpm) = 976.389\n" ] } ], "source": [ "#Chapter-9,Example9_21,pg 9_71\n", "#calculate the speed of motor\n", "import math\n", "#given\n", "Ra=0.1\n", "V=110.\n", "P=4.\n", "Ia1=50.\n", "I1=Ia1\n", "Rse=0.02\n", "N1=700\n", "#calculations\n", "Eb1=V-Ia1*Ra-Ia1*Rse\n", "#using torque equation T=k*phi*Ia\n", "Ia2=math.sqrt(2)*Ia1\n", "Eb2=V-Ia2*Ra-Ia2*Rse/4#parallel speed groups\n", "#using speed equation N=k*Eb/phi\n", "N2=N1*Eb2*2*Ia1/(Eb1*Ia2)\n", "#results\n", "print\"speed of motor (rpm) = \",round(N2,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 22 - pg 9_73" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "new speed of motor (rpm) = 2378.414\n" ] } ], "source": [ "#Chapter-9,Example9_22,pg 9_73\n", "#calculate the new speed of motor\n", "#given\n", "P=4.\n", "Ia1=50.\n", "N1=2000.\n", "V=230.\n", "#calculations\n", "#coils connected in series\n", "#phi1=k*Ia1*(4*n)=k*200*n\n", "#coils connected in parallel groups of series coils\n", "#phi2=k*((Ia2*2*n/2)+(Ia2*2*n/2))=k*2*n*Ia2\n", "#phi1/phi2=100/Ia2........(1)\n", "#N1/N2=phi2/phi1........(2)\n", "#T=kN**2..........(3)\n", "Ia2=(Ia1*(100**3))**(1./4)#using (1) in (3)\n", "N2=(((N1**3)*Ia2)/Ia1)**(1./3)\n", "#results\n", "print\"new speed of motor (rpm) = \",round(N2,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 24 - pg 9_76" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "extra resistance to reduce speed (ohm) = 9.744\n" ] } ], "source": [ "#Chapter-9,Example9_24,pg 9_76\n", "#calculate the extra resistance to reduce speed\n", "import math\n", "#given\n", "V=200.\n", "Ia1=30.\n", "Ra=0.75\n", "Rse=0.75\n", "#calculations\n", "R=Ra+Rse\n", "Eb1=V-Ia1*R\n", "#N2=0.6*N1\n", "N=0.6#N=N2/N1\n", "#using T=k*Ia**2 and T=k*N**3\n", "Ia2=math.sqrt(((0.6**3)*30**2))\n", "#using speed equation N=k*Eb/Ia\n", "Eb2=N*Eb1*Ia2/Ia1\n", "#Eb2=V-Ia2*(R+Rx)\n", "Rx=-(Eb2-V+Ia2*R)/Ia2\n", "#results\n", "print\"extra resistance to reduce speed (ohm) = \",round(Rx,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 25 - pg 9_77" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "new supply voltage (V) = 354.6875\n" ] } ], "source": [ "#Chapter-9,Example9_25,pg 9_77\n", "#calculate the new supply voltage\n", "#given\n", "R=1.\n", "V1=230.\n", "N1=300.\n", "Ia1=15.\n", "N2=375.\n", "#calculations\n", "#using torque equation T=k*N^2\n", "Ia2=N2*Ia1/N1\n", "#using speed equation N=k*Eb/Ia........(1)\n", "Eb1=V1-Ia1*R\n", "#case-2\n", "#Eb2=V2-Ia2*R=V2-18.75......(2)\n", "#putting (2) in (1)\n", "V2=(N2*Eb1*Ia2/(N1*Ia1))+18.75\n", "#results\n", "print\"new supply voltage (V) = \",V2\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 26 - pg 9_78" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "power input in case-2 (kW) = 12.145\n", "efficiency of motor = 74.107\n" ] } ], "source": [ "#Chapter-9,Example9_26,pg 9_78\n", "#calculate the power input and efficiency of motor\n", "#given\n", "import math\n", "V=400.\n", "Po1=18.5*10**3\n", "Pi1=22.5*10**3\n", "Rsh=200.\n", "Ra=0.4\n", "Po2=9.*10**3\n", "#calculations\n", "I1=Pi1/V\n", "Ish=V/Rsh\n", "Ia1=I1-Ish\n", "Acl=(Ia1**2)*Ra#armature copper loss\n", "Scl=(Ish**2)*Rsh#shunt feild copper loss\n", "TL=Pi1-Po1#total losses\n", "SFl=TL-(Acl+Scl)#stray and friction loss\n", "#case-2\n", "Pm=Po2+SFl#mechanical power\n", "#Pm=Eb2*Ia2.........(1)\n", "#Eb2=V-Ia2*Ra.......(2)\n", "#using (1) and (2)\n", "#0.4*(Ia2**2)-400*Ia2+11022.75=0\n", "a=0.4\n", "b=-400\n", "c=11022.775\n", "Ia2=(-b-math.sqrt((b**2)-4*a*c))/(2*a)#neglecting higher value\n", "Pi2=Po2+(Ia2**2)*Ra+(Ish**2)*Rsh+SFl\n", "n=Po2*100/Pi2#efficiency\n", "#results\n", "print\"power input in case-2 (kW) = \",round(Pi2/1000.,3)\n", "print\"efficiency of motor = \",round(n,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 27 - pg 9_79" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum efficiency = 75.59\n" ] } ], "source": [ "#Chapter-9,Example9_27,pg 9_79\n", "#calculate the maximum efficiency\n", "#given\n", "import math\n", "V=250.\n", "Ilo=4.\n", "Ra=1.\n", "Rsh=250.\n", "Il1=20.\n", "#calculations\n", "Ish=V/Rsh\n", "Iao=Ilo-Ish\n", "Ia1=Il1-Ish\n", "Ebo=V-Iao*Ra\n", "Po=Ebo*Iao\n", "Eb1=V-Ia1*Ra\n", "P1=Eb1*Ia1\n", "Pout=P1-Po\n", "Pi=V*Il1\n", "n=Pout*100/Pi\n", "#fro max. efficiency\n", "#const. losses=variable losses\n", "Ia=math.sqrt(Po+(Ish**2)*Rsh)\n", "Ebm=V-Ia*Ra\n", "Pm=Ebm*Ia\n", "Pout=Pm-Po\n", "Pi=V*(Ia+Ish)\n", "nm=Pout*100/Pi\n", "#results\n", "print\"maximum efficiency = \",round(nm,2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 28 - pg 9_81" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "back e.m.f (V) = 83.33\n" ] } ], "source": [ "#Chapter-9,Example9_28,pg 9_81\n", "#calculate the back emf\n", "#given\n", "V=250.\n", "FLo=16.*10**3#full scale output\n", "n=80.\n", "#calculations\n", "I=FLo*100/n#input\n", "Il=I/V\n", "Il=Il\n", "Ia=1.5*Il\n", "#at start\n", "Ra=V/Ia\n", "Rac=0.18#Ra actual\n", "Ras=Ra-Rac#Ra starter\n", "Ia=Il#Ia drops as motor starts\n", "Eb=V-Ia*(Ra)\n", "#results\n", "print\"back e.m.f (V) = \",round(Eb,2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 29 - pg 9_82" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "electromagnetic torque (Nm) = 122.148\n", "flux per pole (mWb) = 11.9316\n", "efficiency of motor (percent) = 85.733\n" ] } ], "source": [ "#Chapter-9,Example9_29,pg 9_82\n", "#calculate the electromagnetic torque, flux and efficiency\n", "#given\n", "import math\n", "Po=20.*735.5#(in W)\n", "V=230.\n", "N=1150.\n", "P=4.\n", "A=P\n", "Z=882.\n", "Ia=73.\n", "Ish=1.6\n", "#calculations\n", "T=60*Po/(2*math.pi*N)\n", "phi=T*A/(0.159*Ia*P*Z)#flux per pole\n", "Il=Ia+Ish\n", "Pin=V*Il\n", "n=Po*100/Pin\n", "#results\n", "print\"electromagnetic torque (Nm) = \",round(T,4)\n", "print\"flux per pole (mWb) = \",round(phi*1000.,4)\n", "print\"efficiency of motor (percent) = \",round(n,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 30 - pg 9_83" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor (rpm) = 785.478\n" ] } ], "source": [ "#Chapter-9,Example9_30,pg 9_83\n", "#calculate the speed of motor\n", "#given\n", "Pr=12.*10**3#rated output\n", "V=200.\n", "Rsh=80.\n", "N1=800.\n", "n=0.9#efficiency\n", "#calculations\n", "Out=0.8*Pr#output is 80% of rated\n", "In=Out/n#input\n", "TL=In-Out\n", "#for max. efficiency\n", "Iln=70#new current\n", "#TL=Wc+(Ia1^2)*Ra\n", "#bur Wc=(Ia1^2)*Ra\n", "Wc=TL/2\n", "Il=In/V\n", "Ish=V/Rsh\n", "Ia1=Il-Ish\n", "Ra=Wc/(Ia1**2)\n", "Ia2=Iln-Ish\n", "Wcn=Wc#const. losses remain same\n", "TL=(Ia2**2)*Ra+Wcn\n", "Pi=V*Iln\n", "n=(Pi-TL)*100/Pi\n", "Eb1=V-Ia1*Ra\n", "Eb2=V-Ia2*Ra\n", "N2=N1*Eb2/Eb1\n", "#results\n", "print\"speed of motor (rpm) = \",round(N2,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 31 - pg 9_85" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "efficiency of motor (percent) = 84.896\n" ] } ], "source": [ "#Chapter-9,Example9_31,pg 9_85\n", "#calculate the efficiency of motor\n", "#given\n", "Po=8.952*10**3\n", "V=440.\n", "Ra=1.1\n", "Rsh=650\n", "Rint=0.4\n", "Rreg=50.\n", "Ml=450.\n", "Vbr=2.#brush drop\n", "Il=24.\n", "#calculations\n", "Rat=Ra+Rint#series connection\n", "Rsht=Rsh+Rreg#series connection\n", "Ish=V/Rsht\n", "Ia=Il-Ish\n", "Acl=(Ia**2)*Rat#armature copper loss\n", "Fcl=(Ish**2)*Rsht#feild copper loss\n", "Bdl=Vbr*Ia#brush drop loss\n", "TL=Acl+Fcl+Bdl+Ml\n", "n=Po*100/(Po+TL)\n", "#results\n", "print\"efficiency of motor (percent) = \",round(n,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 32 - pg 9_85" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motors (rpm) = 334.816\n" ] } ], "source": [ "#Chapter-9,Example9_32,pg 9_85\n", "#calculate the speed of motors\n", "#given\n", "#for first motor\n", "N1=700.\n", "R=0.5#Ra+Rse\n", "I1=70.\n", "V=500.\n", "#calculations\n", "Eb1=V-I1*R\n", "K1=Eb1/(N1*I1)\n", "#for second motor\n", "N2=750.\n", "R=0.5\n", "I2=70.\n", "V=500.\n", "Eb2=V-I2*R\n", "K2=Eb2/(N2*I2)\n", "#motors in series\n", "It=70.\n", "Rt=2*R\n", "Eb=V-It*Rt\n", "N=Eb/(K1*It+K2*It)\n", "#results\n", "print\"speed of motors (rpm) = \",round(N,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 33 - pg 9_86" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum efficiency output (W) = 10225.936\n" ] } ], "source": [ "#Chapter-9,Example9_33,pg 9_86\n", "#calculate the maximum efficiency output\n", "#given\n", "import math\n", "Po=7.46*10**3\n", "V=250\n", "Ilo=5.\n", "Ra=0.5\n", "Rsh=250.\n", "#calculations\n", "Ish=V/Rsh\n", "Iao=Ilo-Ish\n", "Acl=(Iao**2)*Ra\n", "Fcl=(Ish**2)*Rsh\n", "Pi=V*Ilo\n", "FWl=Pi-Acl-Fcl#friction and windage loss\n", "#Pin=Eb*Ia=(V-Ia*Ra)*Ia\n", "#0.5*(Ia**2)-250*Ia+8452=0\n", "b=-250\n", "a=0.5\n", "c=8452\n", "Ia=(-b-math.sqrt((b**2)-4*a*c))/(2*a)#neglecting higher value\n", "TL=(Ia**2)*Ra+(Ish**2)*Rsh+FWl\n", "n=Po*100/(Po+TL)\n", "#for max. efficiency\n", "Ia=math.sqrt((FWl+Fcl)/Ra)\n", "Eb=V-Ia*Ra\n", "Pm=Eb*Ia\n", "#Po at nmax\n", "Po=Pm-FWl\n", "#results\n", "print\"maximum efficiency output (W) = \",round(Po,3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 34 - pg 9_87" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "speed of motor case-1 (rpm) = 946.817\n", "speed of motor case-2 (rpm) = 830.983\n", "speed of motor case-3 (rpm) = 1101.3554\n" ] } ], "source": [ "#Chapter-9,Example9_33,pg 9_87\n", "#calculate the speed of motor in both cases\n", "#given\n", "V=500.\n", "Ra=1.2\n", "Rsh=500.\n", "#calculations\n", "Ish=V/Rsh\n", "Ilo=4.\n", "Iao=Ilo-Ish\n", "Ebo=V-Iao*Ra\n", "Il1=26.\n", "Ish1=1.\n", "Ia1=Il1-Ish1\n", "Eb1=V-Ia1*Ra\n", "No=1000.\n", "N1=No*Eb1/Ebo\n", "print\"speed of motor case-1 (rpm) = \",round(N1,3)\n", "Rx=2.3#connected in series with armature\n", "Eb2=V-Ia1*(Ra+Rx)\n", "N2=N1*Eb2/Eb1\n", "#results\n", "print\"speed of motor case-2 (rpm) = \",round(N2,3)\n", "Ish3=Ish1-0.15*Ish1#reduced by 15%\n", "Ia3=Ish1*Ia1/(Ish3)\n", "Eb3=V-Ia3*Ra\n", "N3=N1*Eb3*Ish1/(Eb1*Ish3)\n", "print\"speed of motor case-3 (rpm) = \",round(N3,4)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }