{ "metadata": { "name": "", "signature": "sha256:f03a268884ccacb4d0b4a4e0ccceeba1a58caa51f0cbd85024ffaf9d558c0182" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 2 : D.C. Motors" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.1 page no : 5" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "V = 220.\n", "I_a = 30. \t\t\t#armature currnet\n", "R_a = 0.75 \t\t\t#Armature resistance\n", "\n", "# Calculations\n", "E_b = V - I_a*R_a \t\t\t# Since V = E_b+ I_a*R_a\n", "\n", "\n", "# Results\n", "print 'Induced EMF or back EMF in the motor is %.1f V'%(E_b)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Induced EMF or back EMF in the motor is 197.5 V\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.2 page no : 6" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Pole = 4.\n", "A = Pole \t\t\t#for lap winding\n", "V = 230.\n", "Z = 250. \t\t\t#number of armature conductors\n", "phi = 30.*10**-3 \t\t\t#flux per pole in weber\n", "I_a = 40.\n", "R_a = 0.6 \t\t\t#Armature resistance\n", "\n", "# Calculations \n", "E_b = V - I_a*R_a \t\t\t# Since V = E_b+ I_a*R_a\n", "N = E_b * 60*A/(phi*Pole*Z) \t\t\t#because E_b = phi*P*N*Z/(60*A)\n", "\n", "# Results\n", "print 'Back emf is %.0f V and running speed is %.0f rpm'%(E_b,N)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Back emf is 206 V and running speed is 1648 rpm\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.3 page no : 9" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Pole = 4.\n", "A = Pole \t\t\t#for lap winding\n", "Z = 480.\t\t\t#number of armature conductors\n", "phi = 20.*10**-3 \t\t\t#flux per pole in weber\n", "I_a = 50. \t\t\t#Armature current\n", "\n", "# Calculations\n", "T_a = 0.159*phi*I_a*Pole*Z/A \t\t\t#Gross torque developed by armature\n", "\n", "# Results\n", "print 'Gross torque developed by armature is %.3f N-m'%(T_a)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Gross torque developed by armature is 76.320 N-m\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.4 page no : 10" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "Pole = 4.\n", "A = Pole \t\t\t#for lap winding\n", "V = 230.\n", "R_a = 0.8 \t\t\t#Armature resistance\n", "N_0 = 1000. \t\t\t#no load speed in rpm\n", "Z = 540. \t\t\t#number of armature conductors\n", "phi = 25.*10**-3 \t\t\t#flux per pole in weber\n", "\n", "# Calculations and Results\n", "E_b0 = phi*Pole*N_0*Z/(60*A) \t\t\t#induced emf\n", "\n", "#part(i)\n", "print 'i)Induced e.m.f = %.0f V'%(E_b0)\n", "\n", "#part(ii)\n", "I_a0 = (V- E_b0)/R_a \t\t\t#because V = E_b0+ I_a0*R_a\n", "print 'ii)Armature current = %.2f A'%(I_a0)\n", "\n", "#part(iii)\n", "stray_losses = E_b0*I_a0 \t\t\t#on no load ,power developed is fully power required to overcome strya losses\n", "print 'iii)Stray loss = %.2f W'%(stray_losses)\n", "\n", "#part(iv)\n", "T_f = E_b0*I_a0/(2*math.pi*N_0/60) \t\t\t#lost torque\n", "print 'iv)Lost torque = %.3f N-m'%(T_f)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)Induced e.m.f = 225 V\n", "ii)Armature current = 6.25 A\n", "iii)Stray loss = 1406.25 W\n", "iv)Lost torque = 13.429 N-m\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.5 page no : 21" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Pole = 4.\n", "Z = 200. \t\t\t #No of armature conductors\n", "A = 2. \t\t\t #wave connected armature\n", "V = 250.\n", "phi = 25.*10**-3 \t\t\t#flux per pole in weber\n", "I_a = 60.\n", "I_L = I_a \t \t\t#armature current\n", "R_a = 0.15\n", "R_se = 0.2 \t\t\t#resistances of armature and series field winding\n", "\n", "# Calculations\n", "E_b = V - I_a*(R_a+R_se) \t\t\t#induced emf\n", "N = E_b * 60*A/(phi*Pole*Z) \t\t\t#because E_b = phi*P*N*Z/(60*A)\n", "\n", "# Results\n", "print 'Required speed is %.0f r.p.m'%(N)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Required speed is 1374 r.p.m\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.6 page no : 22" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 250.\n", "I_L = 20. \t\t\t#load current\n", "R_a = 0.3\n", "R_sh = 200. \t\t\t#Armature and shunt field winding\n", "\n", "# Calculations\n", "I_sh = V/R_sh \t\t\t#shunt current\n", "I_a = I_L-I_sh \t\t\t#armature current\n", "E_b = V - I_a*R_a \t\t\t#emf generated\n", "\n", "# Results\n", "print 'Armature current is %.2f A'%(I_a)\n", "print 'Back e.m.f is %.3f V'%(E_b)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Armature current is 18.75 A\n", "Back e.m.f is 244.375 V\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.7 page no : 22" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 220.\n", "R_a = 0.3\n", "R_sh = 110. \t\t\t#resistance of armature and shunt field winding\n", "\n", "#no load\n", "N_0 = 1000. \t\t\t#no load speed in r.p.m\n", "I_L0 = 6. \t\t\t#line current on no load\n", "I_sh = V/R_sh \t\t\t#no load shnt current\n", "I_a0 = I_L0 - I_sh \t\t\t#no load armature current\n", "E_b0 = V - I_a0*R_a \t\t\t#no load induced emf\n", "\n", "# Calculations\n", "#full load\n", "I_sh_FL = V/R_sh\n", "I_L_FL = 50 \t\t\t#line current at full load\n", "I_a_FL = I_L_FL - I_sh_FL\t\t\t#full load armature current\n", "E_b_FL = V - I_a_FL * R_a \t\t\t#full load induced emf\n", "\t\t\t#using speed equation as treating phi as constant\n", "N_FL = N_0 * (E_b_FL/E_b0)\n", "\n", "# Results\n", "print 'Speed on full load is %.2f r.p.m'%(N_FL)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Speed on full load is 939.67 r.p.m\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.8 page no : 23" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "R_a = 0.2\n", "R_se = 0.3 \t\t\t#resistance of armature and series field winding\n", "#following variables correspond to load 1\n", "V = 250.\n", "N_1 = 800.\n", "I_1 = 20.\n", "I_a1 = I_1\n", "I_se1 = I_a1\n", "\n", "# Calculations\n", "E_b1 = V - I_a1*(R_a+R_se)\n", "#following variables correspond to load 2\n", "I_2 = 50.\n", "I_a2 = I_2\n", "E_b2 = V - I_a2*(R_a+R_se)\n", "\n", "#from speed equation it can be derived that\n", "\n", "N_2 = N_1 * (E_b2/E_b1) * (I_a1/I_a2)\n", "\n", "# Results\n", "print 'Speed on motor on no load is %.0f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Speed on motor on no load is 300 r.p.m\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.9 page no : 31" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 250.\n", "R_a = 0.3\n", "R_sh = 200. \t\t\t#resistance of armature and shunt field winding\n", "R_x = 150. \t\t\t#additional resistance added in series to field winding\n", "I_L1 = 22.\n", "I_sh1 = V/R_sh \t\t\t#initial shunt current before adding 150 ohms resistance\n", "I_a1 = I_L1 - I_sh1 \t\t\t#initial armature current before adding 150 ohms resistance\n", "N_1 = 1500. \t\t\t#initial speed before adding 150 ohms resistance\n", "\n", "# Calculations\n", "#T (prop.) phi*I_a (prop.) I_sh*I_a and T_1 = T_2 and simplifying further \n", "I_sh2 = V/(R_sh + R_x) \t\t\t#new shunt current\n", "I_a2 = I_sh1*I_a1/I_sh2 \t\t\t#New armature current\n", "\n", "E_b1 = V - I_a1*R_a \t\t\t#induced emf before adding 150 ohms resistance\n", "E_b2 = V - I_a2*R_a \t\t\t#new emf\n", "\n", "N_2 = N_1 * (E_b2/E_b1) * (I_sh1/I_sh2) \t\t\t#new speed\n", "\n", "# Results\n", "print 'New armature current and speed are %.4f A and %.f r.p.m respectively'%(I_a2,N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "New armature current and speed are 36.3125 A and 2575 r.p.m respectively\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.10 page no : 36" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "V = 250.\n", "R_a = 0.15\n", "R_se = 0.1\n", "R_x = 0.1 \t\t\t#Resimath.tance of armature , series field winding and extra resistance\n", "N_1 = 800. \t\t\t#initial speed before load torque is increased\n", "I_1 = 30.\n", "I_a1 = I_1\n", "I_se1 = I_1 \t\t\t#initial currents\n", "\n", "# Calculations\n", "T_2_by_T_1 = 1 + (50./100) \t\t\t#50 percent increase as mentioned in question\n", "I_se2_by_I_a2 = R_x/(R_x + R_se) \t\t\t#from the figure\n", "\n", "#T (prop.) phi*I_a (prop.) I_sh*I_a and T_1 = T_2 and simplifying ,solving further \n", "I_a2 = math.sqrt(I_a1*I_se1*T_2_by_T_1/I_se2_by_I_a2) \t\t\t#new armature current\n", "I_se2 = I_se2_by_I_a2 *I_a2 \t\t\t#new series field current\n", "\n", "E_b1 = V - I_a1*R_a - I_se1*R_se \t\t\t#indiced emf initially\n", "E_b2 = V - I_a2*R_a - I_se2*R_se \t\t\t#new induced emf\n", "N_2 = N_1 * (E_b2/E_b1) * (I_se1/I_se2) \t\t\t#required speed\n", "\n", "# Results\n", "print 'The required running speed of motor is %.3f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The required running speed of motor is 912.743 r.p.m\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.11 page no : 38" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "V = 220.\n", "I_1 = 50.\n", "I_a1 = I_1 \t\t\t#Currents before adding extra resistance\n", "T_2_by_T_1 = 0.5\n", "R_t = 0.15 \t\t\t#R_e + R_se = 0.15\n", "\n", "# Calculations\n", "I_a2 = I_a1 * math.sqrt(T_2_by_T_1) \t\t\t#Because T (prop.) I_a**2\n", "E_b1 = V-I_a1*(R_t) \t\t\t#induced emf before adding extra resistance\n", "N_1 = 500.\n", "N_2 = 300. \t\t\t#speeds before and adding extra resistance\n", "\n", "#N (prop.) E_b/phi (prop.) E_b/I_a\n", "E_b2 = E_b1 *(I_a2/I_a1)*(N_2/N_1) \t\t\t#induced emf after adding resistance\n", "R_x = (V-E_b2)/I_a2 -R_t \t\t\t#because E_b2 = V - I_a2*(R_a + R_se + R_x)\n", "\n", "# Results\n", "print 'Desired extrea resistance = %.4f ohms '%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Desired extrea resistance = 3.5225 ohms \n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.12 page no : 43" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "R_a = 1.\n", "I_a = 1.2 \n", "V = 50.\n", "\n", "# Calculations and Results\n", "#part(i)\n", "E_b = V - I_a*R_a\n", "rot_loss_NL = E_b*I_a \t\t\t#no load rotational loss \n", "print 'i)No load rotational losses = %.2f W'%(rot_loss_NL)\n", "\n", "#part(ii)\n", "omega_2000 = 2*math.pi*2000/60 \t\t\t#angular velocity when speed of motor = 2000 rpm\n", "K_m = E_b/omega_2000 \t\t\t#to determine K_m\n", "V = 48.\n", "omega_1800 = 2*math.pi*1800/60 \t\t\t#angular velocity when speed of motor = 1800 rpm\n", "E_b = K_m*omega_1800\n", "I_a = (V-E_b)/R_a \t\t\t#armature current\n", "P_dev = E_b*I_a\t\t\t#power developed\n", "motor_output = P_dev - rot_loss_NL\n", "print 'ii)Motor output = %.f W'%(motor_output)\n", "\n", "#part(iii)\n", "E_b = 0. \t\t\t#when motor stalls\n", "V_stall = 20. \t\t\t#voltage during stalling\n", "I_a = V_stall/R_a \t\t\t#armature current during stalling\n", "T_stall = K_m*I_a \t\t\t#stalling torque\n", "print 'iii)Stalling torque = %.2f N-m'%(T_stall)\n", "print 'partii answer is slightly different due to inaccurate calculation of Power developed'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)No load rotational losses = 58.56 W\n", "ii)Motor output = 121 W\n", "iii)Stalling torque = 4.66 N-m\n", "partii answer is slightly different due to inaccurate calculation of Power developed\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.13 page no : 49" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 120.\n", "R_a = 0.2 \n", "R_sh = 60. \t\t\t#armature and field resistance\n", "I_L1 = 40.\n", "N_1 = 1800. \n", "\n", "# Calculations\n", "I_sh = V/R_sh\n", "\n", "I_a1 = I_L1 - I_sh \n", "E_b1 = V -I_a1*R_a \t\t\t#Induced emf at half load\n", "T2_by_T1 = 1./2 \n", "I_a2 = I_a1*(T2_by_T1) \t\t\t#T (prop.)I_a\n", "E_b2 = V- I_a2*R_a\t\t\t#induced emf at half load\n", "N_2 = N_1 *(E_b2/E_b1) \t\t\t#N (prop.) E_b as phi is constant\n", "\n", "# Results\n", "print 'Speed on half load condition is %.2f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Speed on half load condition is 1860.85 r.p.m\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.14 page no : 50" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "R_a = 0.08\n", "E_b1 = 242. \n", "V = 250.\n", "\n", "# Calculations and Results\n", "#part(i)\n", "I_a1 = (V-E_b1)/R_a\n", "print 'i)Armature current = %.0f A'%(I_a1)\n", "\n", "#part(ii)\n", "N = 0.\n", "E_b = 0. \t\t\t#because N = 0\n", "I_a_start = V/R_a\n", "print 'ii)Starting armature current = %.0f A'%(I_a_start)\n", "\n", "#part(iii)\n", "I_a2 = 120.\n", "E_b2 = V-I_a2*R_a\n", "print 'iii)Back emf if armature current is changed to 120 A = %.1f V'%(E_b2)\n", "\n", "#part(iv)\n", "I_a = 87.\n", "N_m = 1500.\n", "E_g = V + I_a*R_a \t\t\t#induced emf\n", "N_g = N_m*(E_g/E_b1)\t\t\t#as E (prop.) N\n", "print 'iv)Generator speed to deliver 87 A at 250 V = %.1f rpm'%(N_g)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)Armature current = 100 A\n", "ii)Starting armature current = 3125 A\n", "iii)Back emf if armature current is changed to 120 A = 240.4 V\n", "iv)Generator speed to deliver 87 A at 250 V = 1592.7 rpm\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.15 page no : 51" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from numpy import roots\n", "\n", "# Variables\n", "shaft_output = 80.*746 \t\t\t#coverted to watts\n", "eta = 80./100 \t\t\t#efficiency\n", "V = 250.\n", "N_1 = 1200.\n", "R_a = 0.04\n", "R_sh = 250. \t\t\t #armature and shunt field resistance\n", "\n", "# Calculations and Results\n", "power_input = shaft_output/eta\n", "I_L = power_input /V\n", "I_sh = V / R_sh\n", "I_a = I_L - I_sh\n", "E_b1 = V - I_a*R_a\n", "\n", "gross_mechanical_power = E_b1*I_a \t\t\t#electrical equivalent of mechanical power developed\n", "stray_losses = gross_mechanical_power - shaft_output\n", "print 'Mechanical power developed on full load = %.3f kW'%(gross_mechanical_power/1000)\n", "\n", "#on no load shaft_output = 0 and entire gross power is used to overcome stray losses\n", "Eb0_Ia0 = stray_losses\n", "#E_b0 = V - I_a0*R_a ... solving for I_0\n", "p = [R_a, -V, Eb0_Ia0]\n", "ans = roots(p)\n", "I_a0 = ans[1] \t\t\t#first root is ignored math.since its too large\n", "I_L0 = I_sh+I_a0 \t\t\t#current drawn from supply\n", "E_b0 = V - I_a0*R_a \n", "\n", "#From speed equation N (prop.) E_b\n", "N_0 = N_1*(E_b0/E_b1)\n", "print 'No load speed and current are %.4f rpm and %.2f A respectively'%(N_0,I_L0)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mechanical power developed on full load = 70.812 kW\n", "No load speed and current are 1250.9121 rpm and 45.85 A respectively\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.16 page no : 53" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 250.\n", "P = 4. \n", "R_a = 0.1 \n", "R_sh = 124. \t\t\t#armature and shunt field resistance \n", "I_L0 = 4.\n", "N_0 = 1200.\n", "I_L_1 = 61.\n", "\n", "# Calculations\n", "I_sh = V/R_sh\n", "I_a0 = I_L0-I_sh\n", "V_brush = 2 \t\t\t#voltage loss due to brush\n", "E_b0 = V - I_a0*R_a- V_brush\n", "\n", "I_a1 = I_L_1 - I_sh\n", "E_b1 = V - I_a1*R_a -V_brush\n", "\n", "phi1_by_phi0 = 1-(5./100) \t\t\t#weakened by 5 %\n", "N_1 = N_0 *(E_b1/E_b0) /phi1_by_phi0\n", "\n", "# Results\n", "print 'Full load speed is %.3f r.p.m'%(N_1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Full load speed is 1234.102 r.p.m\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.17 page no : 54" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 250.\n", "R_a = 0.15 \n", "R_sh = 167.67 \t\t\t#armature and shunt field resistance\n", "N_0 = 1280. \t\t\t#speed at no load\n", "\n", "#full load\n", "I_L1 = 67. \t\t\t#current drawn on full load\n", "I_sh = V / R_sh \t\t\t#as shunt motor\n", "I_a1 = I_L1- I_sh\n", "E_b1 = V - I_a1*R_a\n", "\n", "#on no load\n", "I_L0 = 6.5\n", "I_a0 = I_L0 - I_sh\n", "E_b0 = V - I_a0*R_a\n", "\n", "# Calculations and Results\n", "#part(i) USING SPEED EQUATION\n", "#N (prop.) E_b/phi (prop.)E_b \t\t\t#as phi is constant\n", "N_1 = N_0 * (E_b1 / E_b0)\n", "print 'i)Full load speed = %.3f r.p.m'%(N_1)\n", "\n", "#part(ii)\n", "speed_regulation = 100* ((N_0-N_1)/N_1)\n", "#N_1 is full load speed and N_0 = No load speed \n", "print 'ii)Speed regulation = %.2f percent '%(speed_regulation )\n", "\n", "#part(iii)\n", "shaft_output_FL = E_b1*I_a1 - E_b0*I_a0 \t\t\t#full load power developed - stray losses\n", "hp_rating = shaft_output_FL /746\n", "print 'iii)HP rating of machine = %.2f h.p'%(hp_rating)\n", "\n", "#part(iv)\n", "power_input = V*I_L1\n", "eta = 100*(shaft_output_FL/power_input) \t\t\t#full load efficiency\n", "print 'iv)Full load efficiency = %.2f percent'%(eta)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)Full load speed = 1233.396 r.p.m\n", "ii)Speed regulation = 3.78 percent \n", "iii)HP rating of machine = 19.42 h.p\n", "iv)Full load efficiency = 86.48 percent\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.18 page no : 55" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 200.\n", "R_a = 0.5\n", "R_se = 0.2\n", "R_x = 0.2 \t\t\t#armature and series field resistance; extra resistance\n", "I_a1 = 20.\n", "I_1 = I_a1 \n", "I_se1 = I_a1\n", "I_a2 = 20.\n", "I_2 = I_a2\n", "I_se2 = I_2 *(R_x/(R_se+R_x))\n", "\n", "# Calculations\n", "E_b1 = V -I_a1*R_a - I_a1*R_se\n", "E_b2 = V -I_a2*R_a - I_se2*R_se\n", "\n", "phi2_by_phi1 = 70./100\n", "N_1 = 1000\n", "N_2 = N_1*(E_b2/E_b1) /phi2_by_phi1 \t\t\t#N (prop.) E_b/phi\n", "\n", "# Results\n", "print 'Required speed is %.2f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Required speed is 1443.93 r.p.m\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.19 page no : 57" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "V = 110.\n", "P = 4.\n", "R_a = 0.1\n", "R = 0.01 \t\t\t#A resistance of 0.01 ohms\n", "R_se = R+R\n", "\n", "# Calculations\n", "#case(i)\n", "I_1 = 50.\n", "I_a1 = I_1\n", "N_1 = 700.\n", "E_b1 = V -I_a1*(R_a + R_se)\n", "\n", "#T (prop) phi*I_a from torque equation (1)\n", "\n", "#phi_1 (prop.) I_a1 (2)\n", "#case(ii) when I_a2 gets divided to half\n", "#phi_2 (prop.) I_a2/2 (3)\n", "\n", "#combining (1)(2)(3) and T1 = T2\n", "I_a2 = math.sqrt(2*I_a1**2)\n", "R_se_eqvt = (R*R)/(R+R) \t\t\t#Equavalent of parallel combination\n", "E_b2 = V - I_a2*R_a - I_a2* R_se_eqvt\n", "\n", "#using speed equation N (prop.) E_b / phi and using (2) and (3)\n", "N_2 = N_1 *( E_b2/E_b1) *(I_a1/(I_a2/2))\n", "\n", "# Results\n", "print 'Speed after reconnection = %.3f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Speed after reconnection = 976.389 r.p.m\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.20 page no : 58" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "P = 4.\n", "I_a1 = 50.\n", "N_1 = 2000.\n", "V = 230.\n", "\n", "\n", "# Calculations and Results\n", "#phi_1 is proportioanl to total ampere-turns produced by field coils\n", "#phi_1 (prop.) I_a1*P*n (prop.) 200*n (1)\n", "\n", "#After reconnection ,phi_2 proportional to ampere turns divided as follows\n", "#phi_2 (prop.) [I_a2/2*2*n + I_a2/2*2*n] (prop.) 2*n*I_a2 (2)\n", "\n", "# Dividing (1) and (2) ,(phi_1/phi_2) = 100 / I_a2 (3)\n", "\n", "#T (prop.) phi*I_a AND T (prop.) N**2 (4)(5)\n", "#therefore N**2 (prop.) phi*I_a (6)\n", "\n", "#N (prop.) E_b/phi (prop.) 1/phi ..\n", "#Because drops across windings can be neglected , E_b1 = E_b2\n", "#therefore N (prop.) 1/phi (7)\n", "\n", "#using (7) and (6) phi**3 (prop.) 1/I_a (8)\n", "\n", "#combining (3) and (8)\n", "I_a2 = (50.*100**3)**(1./4) \t\t\t#new armature current\n", "print 'New armature current = %.3f A'%(I_a2)\n", "#combining (6) and (7) N**3 (prop.) I_a1\n", "N_2 = N_1 *(I_a2/I_a1)**(1./3)\n", "print 'New motor speed = %.3f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "New armature current = 84.090 A\n", "New motor speed = 2378.414 r.p.m\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ " Example 2.22 page no : 61" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "V = 200.\n", "I_a1 = 30.\n", "R_t = 1.5 \t\t\t#R_a + R_se\n", "E_b1 = V - I_a1*R_t\n", "N2_by_N1 = (60./100)\n", "\n", "# Calculations\n", "#T (prop.) I_a**2 and T (prop.) N_3....therefore I_a**2 (prop.) N**3\n", "I_a2 = I_a1*math.sqrt(N2_by_N1**3)\n", "\n", "#N (prop.) E_b/I_a\n", "N2_by_N1\n", "E_b2 = E_b1 *(I_a2/I_a1)*N2_by_N1\n", "R_x = (V- E_b2)/I_a2 - R_t \t\t\t#because E_b2 = V - I_a2*(R_x+R_t)\n", "\n", "# Results\n", "print 'Additional resistance to be added in series with motor circuit = %.3f ohms'%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Additional resistance to be added in series with motor circuit = 9.744 ohms\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.23 page no : 63" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from numpy import array,roots\n", "\n", "# Variables\n", "V = 250.\n", "R_a = 0.4 \n", "R_sh = 100. \t\t\t#armature and shunt field resistance\n", "I_sh1 = V / R_sh\n", "P_out_FL = 10 * 735.5\n", "eta = 85./100 \t\t\t#efficiency\n", "P_in = P_out_FL/eta\n", "I_L1 = P_in /V\n", "I_a1 = I_L1 - I_sh1\n", "\n", "# T (prop.) phi*I_a (prop.) I_sh*I_a because phi (prop.) I_sh\n", "#Bu torque is constant.. \n", "Ia2_Ish2 = I_a1*I_sh1\n", "E_b1 = V - I_a1*R_a\n", "\n", "#N (prop.) E_b/I_sh\n", "#put E_b2 = V - I_a2*R_a and solving further for I_sh2 we get ,I_sh2**2 - 1.8824 I_sh2 +0.2417 = 0\n", "p = array([1, -1.8824, 0.2417])\n", "ans = roots(p) \n", "I_sh2 = ans[0]\n", "#root 1 was considered because its always easier to attain root(1) because less resistacne is needeed\n", "#R_x in series with field\n", "R_x = (V/I_sh2) -R_sh \t\t\t#because I_sh2 = V/(R_sh + R_x)\n", "print 'Extra resistance to be added = %.2f ohms'%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Extra resistance to be added = 43.37 ohms\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.24 page no : 64" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "R_t = 1. \t\t\t#R_t = R_se + R_a\n", "V_1 = 230.\n", "N_1 = 300.\n", "N_2 = 375.\n", "I_1 = 15.\n", "I_a1 = I_1\n", "\n", "# Calculations\n", "#T (prop.) I_a**2 and T (prop.) N_2....therefore I_a**2 (prop.) N**2\n", "I_a2 = I_a1 *(N_2/N_1)\n", "E_b1 = V_1 - I_a1*(R_t)\n", "\n", "#N (prop.) E_b/I_a\n", "E_b2 = E_b1*(I_a2/I_a1)*(N_2/N_1)\n", "V_2 = E_b2 + I_a2* (R_t) \t\t\t#because E_b2 = V_2 - I_a2*(R_a+R_se)\n", "\n", "# Results\n", "print 'Voltage supply needed = %.4f V'%(V_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Voltage supply needed = 354.6875 V\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.25 page no : 66" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "I_L1 = 30.\n", "V = 230.\n", "R_sh = 230.\n", "R_a = 1.\n", "I_sh = V / R_sh\n", "I_a1 = I_L1 - I_sh\n", "E_b1 = V - I_a1*R_a\n", "\n", "# Calculations\n", "#T (prop.) phi*I_a (prop.) I_a as phi is constant\n", "#and torque is constant\n", "I_a2 = I_a1\n", "N2_by_N1 = 1./2\n", "#N (prop.) E_b/phi (prop.) E_b\n", "E_b2 = E_b1 *(N2_by_N1)\n", "R_x = (V- E_b2)/I_a2 - R_a \t\t\t#Because E_b2 = V - I_a2*(R_a + R_x)\n", "\n", "# Results\n", "print 'resistance to be inserted in series = %.4f ohms '%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance to be inserted in series = 3.4655 ohms \n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.26 page no : 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "T_1 = 40. \t\t\t#initial torque\n", "#phi_1 is initial flux\n", "#phi_2 is new flux\n", "#T_2 is new torque\n", "#I_a1 is initial current\n", "#I_a2 is new current\n", "phi2_by_phi1 = 1- (30./100) \t\t\t#decrease by 30 percent\n", "Ia2_by_Ia1 = 1+(15./100) \t\t\t#increase by 15 percent\n", "\n", "# Calculations\n", "#T (prop.)phi*I_a\n", "T_2 = T_1*(phi2_by_phi1)*(Ia2_by_Ia1)\n", "\n", "# Results\n", "print 'New torque is %.1f N-m'%(T_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "New torque is 32.2 N-m\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.27 page no : 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# Variables\n", "V = 230.\n", "N_1 = 1000.\n", "N_2 = 950.\n", "R_a = 0.5\n", "R_sh = 230. \t\t\t#armature and shunt field resistance\n", "I_L1 = 10.\n", "\n", "# Calculations\n", "I_sh = V/R_sh\n", "I_a1 = I_L1 - I_sh\n", "\n", "#T (prop.) phi*I_a (prop.) I_a with phi constant and T is constant due to full-load\n", "I_a2 = I_a1\n", "\n", "E_b1 = V - I_a1*R_a\n", "E_b2 = E_b1*(N_2/N_1) \t\t\t#N (prop.) E_b /phi (prop.) E_b as phi is constant\n", "\n", "R_x = (V-E_b2)/I_a2 -R_a \n", "\n", "# Results\n", "print 'resistance to be inserted in series with armature = %.4f ohms'%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance to be inserted in series with armature = 1.2528 ohms\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.28 page no : 68" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 250.\n", "N_0 = 1000.\n", "I_0 = 5.\n", "R_a = 0.2\n", "R_sh = 250. \t\t\t#armature and shunt field resistance\n", "I_L = 50. \t\t\t#on no load\n", "I_sh = V / R_sh\n", "I_a0 = I_0 - I_sh\n", "I_a = I_L - I_sh\n", "E_b0 = V- I_a0*R_a\n", "E_b1 = V- I_a *R_a\n", "\n", "# Calculations\n", "phi1_by_phi0 = 1-(3./100) \t\t\t#weakens by 3 percent\n", "#N (prop.) E_b/phi\n", "N_1 = N_0 *(E_b1/E_b0) /phi1_by_phi0\n", "\n", "# Results\n", "print 'Speed when loaded and drawing 50A current is %.3f r.p.m'%(N_1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Speed when loaded and drawing 50A current is 993.695 r.p.m\n" ] } ], "prompt_number": 31 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.29 page no : 69" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "V = 230.\n", "I_a0 = 3.3\n", "R_a = 0.3\n", "R_sh = 160. \t\t\t#armature and shunt field resistance \n", "I_L1 = 40.\n", "N_0 = 1000.\n", "E_b0 = V - I_a0*R_a\n", "I_sh = V/ R_sh\n", "I_a1 = I_L1 - I_sh\n", "E_b1 = V - I_a1*R_a\n", "phi1_by_phi0 = 1- (4./100) \t\t\t#weakening by 4 percent \n", "\n", "# Calculations and Results\n", "N_1 = N_0 *(E_b1/E_b0)/(phi1_by_phi0) \t\t\t#because N (prop.) E_b/phi\n", "print 'Full load speed is %.4f rpm'%(N_1)\n", "T_0 = E_b0*I_a0/(2*math.pi*N_0/60)\n", "T_1 = T_0*(I_a1/I_a0)*phi1_by_phi0 \t\t\t# because T (prop.) phi*I_a\n", "print 'Full load developed torque is %.4f N-m'%(T_1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Full load speed is 993.5485 rpm\n", "Full load developed torque is 80.9585 N-m\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.30 page no : 70" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 220.\n", "I_L = 52.\n", "N_1 = 750.\n", "N_2 = 600.\n", "R_a = 0.2\n", "R_sh = 110. \t\t\t#armature and shunt field resistance\n", "\n", "# Calculations and Results\n", "I_sh = V/ R_sh\n", "I_a1 = I_L - I_sh\n", "I_a2 = I_a1\t\t\t#T (prop.) I_a and T is constant\n", "E_b1 = V - I_a1*R_a\n", "\n", "#N (prop.) E_b/phi (prop.) E_b\n", "E_b2 = E_b1*(N_2/N_1)\n", "R_x = (V- E_b2)/I_a2 -R_a \t\t\t#Because E_b2 = V - I_a2*(R_a+R_x)\n", "print 'resistance to be connected in series = %.2f ohms'%(R_x)\n", "\n", "#After R_x gets connected in series with armature and 110 ohms in series with field winding\n", "N_1 = 600.\n", "I_sh2 = V /(R_sh+110)\n", "I_a1 = 50.\n", "I_sh1 = 2.\n", "I_sh2 = 1.\n", "#T (prop.) I_a*I_sh and T doesn't vary\n", "I_a2 = I_a1*(I_sh1/I_sh2)\n", "E_b1 = V - I_a1*(R_a+R_x)\n", "E_b2 = V - I_a2*(R_a+R_x)\n", "N_2 = N_1*(E_b2/E_b1)*(I_sh1/I_sh2) \t\t\t#Because N (prop.) E_b/I_sh\n", "print 'New speed = %.3f rpm'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance to be connected in series = 0.84 ohms\n", "New speed = 828.571 rpm\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.31 page no : 72" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 230.\n", "R_a = 0.15\n", "R_sh = 250. \t\t\t#armature and shunt field resistance\n", "I_a1 = 50.\n", "I_a2 = 80.\n", "N_1 = 800.\n", "N_2 = 1000.\n", "I_sh1 = V / R_sh\n", "\n", "# Calculations\n", "E_b1 = V - I_a1*R_a\n", "E_b2 = V - I_a2*R_a\n", "\n", "I_sh2 = I_sh1*(E_b2/E_b1)*(N_1/N_2) \t\t\t#Because N (prop.) E_b/ I_sh\n", "R_x = (V/I_sh2 ) - R_sh \t\t\t#because I_sh2 = V /(R_x+ R_sh)\n", "\n", "# Results\n", "print 'resistance to be added is R_x = %.0f ohms'%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance to be added is R_x = 69 ohms\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.32 page no : 74" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 230.\n", "R_a = 0.5\n", "N_1 = 800.\n", "N_2 = 600.\n", "I_a2 = 20. \n", "I_a1 = I_a2\n", "E_b1 = V - I_a1*R_a\n", "\n", "# Calculations\n", "#N (prop.) E_b/phi (prop.) E_b as phi is constant\n", "E_b2 = E_b1 *(N_2/N_1)\n", "#additional resistance required\n", "R_x = (V -E_b2)/I_a2 - R_a \t\t\t#because E_b2 = V - I_a2*(R_a+R_x)\n", "\n", "# Results\n", "print 'Additional resistance required = %.2f ohms '%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Additional resistance required = 2.75 ohms \n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.33 page no : 74" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 220.\n", "R_a = 0.5\n", "R_x = 5. \t\t\t#armature resistacne and extra resistance\n", "I_1 = 15.\n", "I_se1 = I_1\n", "I_se2 = I_se1 \n", "I_2 = I_se2\n", "N_1 = 800.\n", "\n", "# Calculations\n", "E_b1 = V - I_1*R_a\n", "E_b2 = V - I_2*(R_a+R_x)\n", "\n", "N_2 = N_1*(E_b2/E_b1)*(I_se1/I_se2) \t\t\t#because N (prop.) E_b/I_se\n", "\n", "# Results\n", "print 'New speed of rotor = %.3f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "New speed of rotor = 517.647 r.p.m\n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.34 page no : 75" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "V = 250.\n", "I_a1 = 20.\n", "R_a = 0.5\n", "N_1 = 1000.\n", "N_2 = 500.\n", "\n", "# Calculations and Results\n", "#T (prop.) I_a and T_1 = T_2\n", "I_a2 = I_a1\n", "E_b1 = V - I_a1*R_a\n", "\n", "#N (prop.) E_b\n", "E_b2 = E_b1 *(N_2/N_1)\n", "R_x = (V-E_b2)/I_a2 - R_a \t\t\t#because E_b2 = V - I_a2*(R_a+R_x)\n", "print 'Additional resistance = %.0f ohms'%(R_x)\n", "T3_by_T2 = 0.5 \t\t\t#torque is halved\n", "I_a3 = I_a2 *(T3_by_T2) \t\t\t#new armature current\n", "E_b3 = V - I_a3*(R_x + R_a)\n", "N_3 = E_b3*N_2 / E_b2 \t\t\t#N (prop.) E_b\n", "print 'New speed = %.3f rpm'%(N_3)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Additional resistance = 6 ohms\n", "New speed = 770.833 rpm\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.35 page no : 76" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "P_out = 100*735.5\n", "V = 500.\n", "P = 4.\n", "A = 2.\t\t\t# due to wave winding\n", "Z = 492. \t\t\t#no of conductors\n", "phi = 50.*10**-3 \t\t\t#flux per pole\n", "eta = 92./100 \t\t\t#efficiency\n", "P_in = P_out/eta\n", "R_a = 0.1 \n", "R_sh = 250. \t\t\t#amature and shunt field resistance\n", "\n", "# Calculations\n", "I_L = P_in/V\n", "I_sh = V/ R_sh\n", "I_a = I_L - I_sh\n", "E_b = V - I_a*R_a\n", "N = E_b*60*A/(phi*P*Z) \t\t\t#because E_b = phi*P*N*Z/(60*A)\n", "\n", "T_sh = P_out/(2*math.pi*N/60) \t\t\t#Useful torque\n", "\n", "# Results\n", "print 'i)Speed at full load = %.4f rpm'%(N)\n", "print 'ii)Useful torque = %.2f N-m'%(T_sh)\n", "print 'Answer mismatches due to improper approximation'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)Speed at full load = 590.5011 rpm\n", "ii)Useful torque = 1189.41 N-m\n", "Answer mismatches due to improper approximation\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.36 page no : 77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import roots\n", "import math \n", "\n", "# Variables\n", "N_1 = 1000.\n", "I_1 = 50.\n", "I_a1 = I_1\n", "V = 250.\n", "R_x = 4.4\n", "R_t = 0.6 \t\t\t#R_t = R_a+R_se\n", "E_b1 = V - I_a1*(R_t)\n", "\n", "# Calculations\n", "#T (prop.)I_a**2 T (prop.) N**2 .... hence N (prop.) I_a\n", "#N (prop.) E_b /I_a \n", "#combining both E_b (prop.) I_a**2\n", "#using E_b2 = V - I_a2*(R_a + R_se + R_x) and solving for I_a2 we get 0.088 I_a2**2 +5 I_a2 -250 = 0\n", "p = [0.088 ,5, -250] \n", "ans = roots(p)\n", "I_a2 = ans[1] \t\t\t#root(1) is ignored as it is -ve\n", "E_b2 = V - I_a2*(R_t + R_x) \n", "N_2 = N_1*(E_b2/E_b1)*(I_a1/I_a2)\n", "\n", "# Results\n", "print 'Motor speed = %.2f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Motor speed = 639.79 r.p.m\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.37 page no : 78" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import roots\n", "import math \n", "\n", "# Variables\n", "V = 250.\n", "I_a1 = 20.\n", "R_sh = 250.\n", "R_a = 0.5 \t\t\t#shunt field and armature resistance\n", "I_sh1 = V / R_sh\n", "E_b1 = V - I_a1*R_a\n", "\n", "#T (prop.) phi*I_a (prop.) I_sh*I_a\n", "#math.since T_1 = T_2\n", "I_sh2_I_a2 = I_sh1*I_a1 \n", "I_sh2_I_a2 = I_sh1*I_a1 \t\t\t# = 20\n", "\n", "# Calculations\n", "#N (prop.) E_b/I_sh\n", "#E_b1 = V - I_a1*R_a\n", "#Solving further for I_a2 we get I_a2**2 -500 I_a2 + 12800\n", "p = [1, -500, 12800]\n", "ans = roots(p)\n", "I_a2 = ans[1] \t\t\t#higher root is neglected\n", "I_sh2 = I_sh2_I_a2 / I_a2\n", "R_x = (V / I_sh2) - R_sh \t\t\t#resistance to be inserted in shunt field\n", "\n", "# Results\n", "print 'resistance to be inserted = %.4f ohms '%(R_x)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance to be inserted = 88.3129 ohms \n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.38 page no : 79" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "# Variables\n", "V = 250.\n", "N_1 = 1000.\n", "I_L1 = 25.\n", "R_a = 0.2\n", "R_sh = 250. \t\t\t#armature and shunt field resistance\n", "V_brush = 1. \t\t\t#voltage drop due to brushes\n", "\n", "# Calculations and Results\n", "I_sh1 = V/R_sh\n", "I_a1 = I_L1 - I_sh1\n", "E_b1 = V- I_a1*R_a - 2 *V_brush\n", "\n", "#when loaded\n", "I_L2 = 50.\n", "I_sh2 = I_sh1 \t\t\t#as flux weakensby armature reaction shunt field current remains same \n", "I_a2 = I_L2 - I_sh2\n", "E_b2 = V- I_a2*R_a - 2 *V_brush\n", "\n", "phi2_by_phi1 = 1- (3./100) \t\t\t#weakens by 3 percent\n", "N_2 = N_1*(E_b2/E_b1)/ phi2_by_phi1 \t\t\t#N (prop.) E_b/phi\n", "print 'New speed = %.3f rpm'%(N_2)\n", "T_1 = E_b1*I_a1/(2*math.pi*N_1/60)\n", "T_2 = E_b2*I_a2/(2*math.pi*N_2/60)\n", "print 'Torque before field weakening = %.4f N-m'%(T_1)\n", "print 'Torque after field weakening = %.4f N-m'%(T_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "New speed = 1009.733 rpm\n", "Torque before field weakening = 55.7373 N-m\n", "Torque after field weakening = 110.3831 N-m\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.39 page no : 80" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "# Variables\n", "V = 220.\n", "R_a = 0.5\n", "R_x = 1. \t\t\t#armature resistance and extra resistance\n", "N_FL = 500. \t\t\t#full load speed in r.p.m\n", "I_a_FL = 30.\n", "\n", "# Calculations and Results\n", "#part(i) Full load \n", "E_b_FL = V- I_a_FL * R_a\n", "#T (prop.) I_a... T is constant\n", "I_a_dash_FL = I_a_FL \n", "E_b_dash_FL = V- I_a_dash_FL * (R_a+R_x)\n", "#N (prop.) E_b/phi (prop.) E_b\n", "N_dash_FL = N_FL*(E_b_dash_FL/E_b_FL)\n", "print 'i)Speed at full load torque = %.4f r.p.m'%(N_dash_FL)\n", "\n", "#part(ii)\n", "T2_by_T1 = 2\n", "I_a_dash_FL = I_a_FL *(T2_by_T1)\n", "E_b_dash_FL = V- I_a_dash_FL * (R_a+R_x)\n", "N_dash_FL = N_FL*(E_b_dash_FL/E_b_FL)\n", "print 'ii)Speed at double full load torque = %.3f r.p.m'%(N_dash_FL)\n", "\n", "#part(iii) ...stalling\n", "E_b = 0 \t\t\t#as speed is zero in case of stalling torque\n", "I_a_stall = (V-E_b)/(R_a+R_x)\n", "T_FL = E_b_FL * I_a_FL/(2*math.pi*N_FL/60)\n", "T_stall = T_FL *(I_a_stall/ I_a_FL)\n", "print 'iii)Stalling torque = %.3f Nm'%(T_stall)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)Speed at full load torque = 426.8293 r.p.m\n", "ii)Speed at double full load torque = 317.073 r.p.m\n", "iii)Stalling torque = 574.231 Nm\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.40 page no : 81" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "V = 230.\n", "I_a1 = 30.\n", "R_a = 0.4\n", "R_x = 1.1\t\t\t#armature resistance and extra resistance\n", "N_1 = 500.\n", "\n", "\n", "# Calculations and Results\n", "#part(i)\n", "E_b1 = V - I_a1*R_a\n", "I_a2 = I_a1 \t\t\t#I_a is constant as T , phi are constant\n", "E_b2 = V - I_a2*(R_a+R_x)\n", "N_2 = N_1 *(E_b2/E_b1) \t\t\t#Because N (prop.) E_b/phi (prop.) E_b\n", "print 'i)Speed at full load torque = %.3f r.p.m'%(N_2)\n", "\n", "#part(ii)\n", "T2_by_T1 = 1.5\n", "I_a2 = I_a1 * T2_by_T1\n", "E_b2 = V - I_a2*(R_a+R_x)\n", "N_2 = N_1 *(E_b2/E_b1) \t\t\t#Because N (prop.) E_b/phi (prop.) E_b\n", "print 'ii)Speed at 1.5 times full load torque = %.3f r.p.m'%(N_2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "i)Speed at full load torque = 424.312 r.p.m\n", "ii)Speed at 1.5 times full load torque = 372.706 r.p.m\n" ] } ], "prompt_number": 43 } ], "metadata": {} } ] }