path: root/Electric_Machines_by_C._I._Hubert/CHAPTER11.ipynb

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   "source": [
    "# CHAPTER11 : DIRECT CURRENT MOTOR CHARACTERISTICS AND APPLICATIONS "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E01 : Pg 448"
   ]
  },
  {
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     "text": [
      "The armature current = 135.429772662 A\n",
      "The resistance rating = 28.952173913 Ohm\n",
      "The power rating = 101.069646111 W\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.1\n",
    "#  Computation of (a) The armature current when operating at rated conditions \n",
    "#  (b) The resistance and power rating of an external resistance required in \n",
    "#  series with the shunt field circuit to operate at 125 percent rated speed\n",
    "#  Page No. 448\n",
    "#  Given data\n",
    "HP=40.;                  #  hp rating of the device\n",
    "Perratedload=0.902;     #  Percentage rated load\n",
    "VT=240.;                 #  Voltage value of motor\n",
    "RF=99.5;                #  Resistance of shunt motor\n",
    "Nf=1231.;                #  Turns per pole of the shunt motor\n",
    "Ra=0.0680;              #  Armature resistance\n",
    "RIP=0.0198;             #  Interpole winding resistance\n",
    "Rs=0.00911;             #  Resistance of series field winding\n",
    "Bp1=0.70;               #  Flux density for a net mmf\n",
    "n1=1150.;                #  Speed of shunt motor\n",
    "\n",
    "#  (a) The armature current when operating at rated conditions\n",
    "P=HP*746./Perratedload;\n",
    "IT=P/VT;                #  Total current\n",
    "IF=VT/RF;               #  Field current\n",
    "Ia=IT-IF;\n",
    "\n",
    "#  (b) The resistance and power rating of an external resistance required in \n",
    "#  series with the shunt field circuit to operate at 125 percent rated speed\n",
    "\n",
    "Fnet=Nf*IF;                  #  Corresponding mmf from magnetization curve\n",
    "Racir=Ra+RIP+Rs;\n",
    "n2=n1*1.25;                  #  125 percent rated speed\n",
    "#  Shaft load is adjusted to  value that limits the armature current to 115% \n",
    "#  of rated current\n",
    "Bp2=Bp1*(n1/n2)*((VT-Ia*Racir*1.15)/(VT-Ia*Racir))\n",
    "FF=2.3*1000.;\n",
    "IF1=FF/Nf;\n",
    "Rx=(VT/IF1)-RF;\n",
    "PRx=(IF1**2.)*Rx;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"The armature current =\",Ia,\"A\"\n",
    "print\"The resistance rating =\",Rx,\"Ohm\"\n",
    "print\"The power rating =\",PRx,\"W\"\n",
    "\n",
    "# Note: Answer varies due to round-off errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E02 : Pg 450"
   ]
  },
  {
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   "execution_count": 2,
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    {
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     "text": [
      "\n",
      " Shunt field current = 4.87804878049 A\n",
      "\n",
      " Armature current = 450.088774014 A\n",
      "\n",
      " Developed torque = 853.589546189 lb-ft\n",
      "\n",
      " Armature current if a resistor inserted in series = 476.56458425 A\n",
      "\n",
      " External resistance required = 17.7013485007 Ohm\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.2\n",
    "#  Computation of (a) Shunt field current (b) Armature current (c) Developed \n",
    "#  torque (d) Armature current if a resistor inserted in series with the shunt \n",
    "#  field circuit caused the speed to increase to 900 r/min (e) External \n",
    "#  resistance required in series with the shunt field circuit to operate \n",
    "#  at 900 r/min\n",
    "#  Page No. 450\n",
    "#  Given data\n",
    "HP=125.;\n",
    "perratedload=0.854;          #  Percentage rated load\n",
    "VT=240.;                      #  Voltage value of motor\n",
    "RF=49.2;                     #  Resistance of shunt motor\n",
    "Nf=577.;                      #  Turns per pole of the shunt motor\n",
    "Ns=4.5;\n",
    "Ra=0.0172;                   #  Armature resistance\n",
    "RIP=0.005;                   #  Interpole winding resistance\n",
    "Rs=0.0023;                   #  Resistance of series field winding\n",
    "n1=850.;                      #  Speed of shunt motor\n",
    "n2=900.;\n",
    "F2=4000.;\n",
    "\n",
    "#  (a) Shunt field current\n",
    "\n",
    "IF=VT/RF;                    #  Field current\n",
    "\n",
    "#  (b) Armature current \n",
    "Pin=HP*746./perratedload;    #  Input power \n",
    "IT=Pin/VT;                  #  Total current\n",
    "Ia1=IT-IF;\n",
    "\n",
    "#  (c) Developed torque \n",
    "\n",
    "Racir=Ra+RIP+Rs;\n",
    "Ea=VT-Ia1*Racir;            #  Armature emf\n",
    "Pmech=Ea*Ia1;               #  Mechanical power\n",
    "TD=Pmech*5252./n1/746.;            #  Torque developed\n",
    "\n",
    "#  (d) Armature current if a resistor inserted in series with the shunt field \n",
    "#  circuit caused the speed to increase to 900 r/min\n",
    "\n",
    "Ia2=Ia1*n2/n1;\n",
    "\n",
    "# (e) External resistance required in series with the shunt field circuit to \n",
    "#  operate at 900 r/min\n",
    "IF2=(F2-0.90*Ns*Ia2)/Nf;\n",
    "Rx=(VT/IF2)-RF;\n",
    "\n",
    "\n",
    "#  Display result on command window\n",
    "print\"\\n Shunt field current =\",IF,\"A\"\n",
    "print\"\\n Armature current =\",Ia1,\"A\"\n",
    "print\"\\n Developed torque =\",TD,\"lb-ft\"\n",
    "print\"\\n Armature current if a resistor inserted in series =\",Ia2,\"A\"\n",
    "print\"\\n External resistance required =\",Rx,\"Ohm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E03 : Pg 453"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Speed of the motor = 1713.81 r/min\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.3\n",
    "#  Computation of Speed if the load is reduced to a value that causes the \n",
    "#  armature current to be 30 percent of the rated current\n",
    "#  Page No.453\n",
    "#  Given data\n",
    "HP=100.;\n",
    "perratedload=0.896;     #  Percentage rated load\n",
    "VT=240.;                 #  Voltage value of motor\n",
    "Ns=14.;                  #  Number of turns/pole in series field\n",
    "Ra=0.0202;              #  Armature resistance\n",
    "RIP=0.00588;            #  Interpole winding resistance\n",
    "Rs=0.00272;             #  Resistance of series field winding\n",
    "n1=650.;                 #  Speed of shunt motor\n",
    "Bp2=0.34;               #  Air gap flux density from magnetization curve\n",
    "Bp1=0.87;               #  Air gap flux density from magnetization curve\n",
    "\n",
    "#  Computation of Speed if the load is reduced to a value that causes the \n",
    "#  armature current to be 30 percent of the rated current\n",
    "\n",
    "Pin=HP*746./perratedload;       #  Input power\n",
    "IT=Pin/VT;                     #  Total current\n",
    "Ia=IT;                         #  Armature current\n",
    "\n",
    "Racir=Ra+RIP+Rs;               #  Resistance of armature circuit\n",
    "Fnet1=Ns*Ia*(1.-0.080);         #  Net mmf\n",
    "Fnet2=0.30*Fnet1;              #  Net mmf from magnetization curve\n",
    "n2=n1/((VT-(Ia*Racir))/Bp1 * Bp2/(VT-(0.30*Ia*Racir)));\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Speed of the motor =\",round(n2,2),\"r/min\""
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## Example E04 : Pg 456"
   ]
  },
  {
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   "execution_count": 4,
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     "text": [
      "The resistance rating of an external resistance = 25.9636748422 Ohm\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.4\n",
    "#  Computation of resistance using linear approximation and values are \n",
    "#  compared with results obtained in example 11.1\n",
    "#  Page No. 456\n",
    "#  Given data\n",
    "HP=40.;                   #  hp rating of the device\n",
    "percentratedload=0.902;        #  Percentage rated load\n",
    "VT=240;                  #  Voltage value of motor\n",
    "RF=99.5;                 #  Resistance of shunt motor\n",
    "Nf=1231.;                 #  Turns per pole of the shunt motor\n",
    "Ra=0.0680;               #  Armature resistance\n",
    "RIP=0.0198;              #  Interpole winding resistance\n",
    "Rs=0.00911;              #  Resistance of series field winding\n",
    "Bp1=0.70;                #  Flux density for a net mmf\n",
    "n1=1150.;                 #  Speed of shunt motor\n",
    "n2=1.25*n1;\n",
    "IT=137.84; \n",
    "#  Computation of resistance using linear approximation and values are \n",
    "#  compared with results obtained in example 11.1\n",
    "\n",
    "IF=VT/RF;                #  Field current\n",
    "Ia1=IT-IF;               #  Armature current\n",
    "Fnet1=Nf*IF;             #  Net mmf\n",
    "Racir=Ra+RIP+Rs;         #  Armature circuit resistance\n",
    "Fnet2=Fnet1*(n1/n2)*((VT-Ia1*Racir*1.15)/(VT-Ia1*Racir));\n",
    "IF1=Fnet2/Nf;           #  Field current\n",
    "Rx=(VT/IF1)-RF;         #  External resistance required\n",
    "\n",
    "\n",
    "#  Display result on command window\n",
    "print\"The resistance rating of an external resistance =\",Rx,\"Ohm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E05 : Pg 456"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "outputs": [
    {
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     "output_type": "stream",
     "text": [
      "External resistance required in series = 7.74291596939 Ohm\n",
      "Error introduced by linear approximation = 56.5004720821 Percent\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.5\n",
    "#  Computation  using linear approximation to show the gross error that occurs \n",
    "#  when a linear assumption is applied to compound motors operating at overload \n",
    "#  conditions\n",
    "#  Page No. 456\n",
    "#  Given data\n",
    "Nf=577.;                  #  Turns per pole of the shunt motor\n",
    "IF=4.88;                 #  Field current\n",
    "Ns=4.5;                 \n",
    "IA=450.09;               #  Armature current\n",
    "F2=4367.8;               #  mmf\n",
    "VT=240.;                  #  Voltage value of motor\n",
    "RF=49.2;                 #  Resistance of shunt motor\n",
    "HP=125.;\n",
    "perratedload=0.854;      #  Percentage rated load\n",
    "Rx1=17.8;                #  Value of resistance in Example 11.2\n",
    "\n",
    "\n",
    "Fnet1=(Nf*IF)+ (0.90 * Ns*IA);   \n",
    "Ia2=Fnet1*IA/F2;         #  Armature current\n",
    "\n",
    "If2=(F2 - Ns*Ia2*0.90)/Nf;\n",
    "Rx=(VT/If2)-RF;         #  External resistance required\n",
    "\n",
    "#  Error introduced by linear approximation\n",
    "PE=(17.8-Rx)/17.8*100;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"External resistance required in series =\",Rx,\"Ohm\"\n",
    "print\"Error introduced by linear approximation =\",PE,\"Percent\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E06 : Pg 460"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Torque developed when operating at rated speed = 9062.45895316 lb-ft\n",
      "Developed torque required at half rated speed = 2265.61473829 lb-ft\n",
      "Armature voltage required for half rated speed = 370.98 V\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.6\n",
    "#  Determine (a) Torque developed when operating at rated speed (b) Developed \n",
    "#  torque required at half rated speed (c) Armature voltage required for half \n",
    "#  rated speed \n",
    "#  Page No. 460\n",
    "#  Given data\n",
    "VT=750.;                   #  Voltage value of motor\n",
    "Nf=1231.;                  #  Turns per pole of the shunt motor\n",
    "Ra=0.00540;               #  Armature resistance\n",
    "RIPcw=0.00420;            #  Interpole winding resistance\n",
    "N=955.;                    #  Speed of shunt motor\n",
    "Ia1=1675.;                 #  Armature current\n",
    "\n",
    "#  (a) Torque developed when operating at rated speed \n",
    "\n",
    "Racir=Ra+RIPcw;\n",
    "Ea=VT-Ia1*Racir;\n",
    "Pmech=Ea*Ia1;\n",
    "TD=Pmech*5252./N/746.;\n",
    "\n",
    "#  (b) Developed torque required at half rated speed \n",
    "\n",
    "T2=TD*(0.5*N/N)**2.;\n",
    "\n",
    "#  (c) Armature voltage required for half rated speed \n",
    "\n",
    "Ia2=T2*Ia1/TD;\n",
    "V2=(0.5*N/N)*(VT-Ia1*Racir) + Ia2*Racir ;\n",
    "\n",
    "#  Shaft load is adjusted to  value that limits the armature current to 115 % of rated current\n",
    "\n",
    "# Display result on command window\n",
    "print\"Torque developed when operating at rated speed =\",TD,\"lb-ft\"\n",
    "print\"Developed torque required at half rated speed =\",T2,\"lb-ft\"\n",
    "print\"Armature voltage required for half rated speed =\",V2,\"V\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E07 : Pg 464"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resistance of the dynamic braking resistor = 0.56222252364 Ohm\n"
     ]
    }
   ],
   "source": [
    "#  Example 11.7\n",
    "#  Computation of the resistance of a dynamic braking resistor that will be \n",
    "#  capable of developing 500 lb-ft of braking torque at a speed of 1000 r/min.\n",
    "#  Page No. 464\n",
    "#  Given data\n",
    "T1=910.;                          #  Torque load\n",
    "Pshaft=199.257*746.;              #  Power of shaft\n",
    "eeta=0.940;                      #  Efficiency\n",
    "VT=240.;                          #  Rated voltage\n",
    "T2=500.;                          #  Braking torque\n",
    "n1=1000.;                         #  Windage and friction speed\n",
    "n2=1150.;                         #  Speed of motor\n",
    "Rf=52.6;                         #  Field resistance\n",
    "Racir=0.00707;                   #  Combined armature,compensating winding and                                                               #  interpolar resistance\n",
    "\n",
    "#  Resistance of a dynamic braking resistor\n",
    "Pshaft=T1*n2/5252.;             #  Shaft power \n",
    "Pin=Pshaft*746./eeta;           #  Input power\n",
    "IT=Pin/VT;                     #  Total current \n",
    "If=VT/Rf;                      #  Field current\n",
    "Ia1=IT-If;                     #  Armature current\n",
    "Ea1=VT-Ia1*Racir;              #  Armature emf\n",
    "\n",
    "Ia2=Ia1*T2/T1;                 #  Armature current\n",
    "Ea2=Ea1*n1/n2;\n",
    "RDB=(Ea2-Ia2*Racir)/Ia2;       #  Resistance\n",
    "\n",
    "# Display result on command window\n",
    "print\"Resistance of the dynamic braking resistor =\",RDB,\"Ohm\""
   ]
  }
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