Chapter 7: DC Machines

Example 7.1, Page number: 371

In [1]:
from __future__ import division
from math import *

#Variable declaration:
Vt=[128, 124]                           #Terminal voltage(V)
Ea=125                                  #Generated emf(V)
Ra=0.02                                 #Armature resistance(ohm)
n=3000                                  #rpm


#Calculations:
#For 128 V
Ia1=(Vt[0]-Ea)/Ra
Pin1=Vt[0]*Ia1
Pe1=Ea*Ia1
wm=3000*2*pi/60
Tmech1=Ea*Ia1/wm

#for 124 V
Ia2=(-Vt[1]+Ea)/Ra
Pin2=Vt[1]*Ia2
Pe2=Ea*Ia2
Tmech2=Ea*Ia2/wm



#Results:
print "(a) Armature current:",Ia1,"A","\n    Terminal power:",Pin1/10**3,"kW"
print "    Electromagnetic power:",round(Pe1/10**3,2),"kW"
print "    Torque:",round(Tmech1,1),"Nm"

print "(b) Armature current:",Ia2,"A","\n    Terminal power:",Pin2/10**3,"kW"
print "    Electromagnetic power:",round(Pe2/10**3,2),"kW",
print "\n    Torque:",round(Tmech2,1),"Nm"

(a) Armature current: 150.0 A 
    Terminal power: 19.2 kW
    Electromagnetic power: 18.75 kW
    Torque: 59.7 Nm
(b) Armature current: 50.0 A 
    Terminal power: 6.2 kW
    Electromagnetic power: 6.25 kW 
    Torque: 19.9 Nm

Example 7.2, Page number: 372

In [3]:
from __future__ import division

#Variable declaration:
Vt=123                                      #terminal voltage(V)
Pt=21.9                                     #Terminal power(kW)
Ra=0.02                                     #ohm
Eao=125                                     #generated voltage(V) at 3000rpm
no=3000                                     #rpm


#calculations:
Ia=Pt*10**3/Vt
Ea=Vt-Ia*Ra
n=(Ea/Eao)*no

#Results:
print "Speed of motor:",round(n,0),"rpm"

Speed of motor: 2867.0 rpm

Example 7.3, Page number: 376

In [4]:
from __future__ import division

#Variable declaration:
Il=400                                  #Armature current(A)
If=4.7                                  #Field current(A)
Ns=3                                    #series turns per pole
Nf=1000                                 #shunt field turns per pole
Eao=274                                 #at Ia=0,(V)
n=1150                                  #speed of motor(rpm)
no=1200                                 #rated speed(rpm) 
Ra=0.025                                #armature resistance(ohm)
Rs=0.005                                #series field resistance(ohm)


#Calculations:
Is=Il+If
GM=If+(Ns/Nf)*Is                        #for graphical analysis
Ea=(n/no)*Eao
Vt=Ea-Is*(Ra+Rs)

#Results:
print "Terminal voltage at rated terminal current:",round(Vt,0),"V"

Terminal voltage at rated terminal current: 250.0 V

Example 7.4, Page number: 377

In [4]:
from __future__ import division

#Variable declaration:
Il=400                                  #Armature current(A)
If=4.7                                  #Field current(A)
Ns=3                                    #series turns per pole
Nf=1000                                 #shunt field turns per pole
Eao=261                                 #at Ia=400 A,(V)
n=1150                                  #speed of motor(rpm)
no=1200                                 #rated speed(rpm) 
Ra=0.025                                #armature resistance(ohm)
Rs=0.005                                #series field resistance(ohm)


#Calculations:
Ea=(n/no)*Eao
Vt=Ea-(Il+If)*(Ra+Rs)

#Results:
print "Terminal voltage:", round(Vt,0), "V"

Terminal voltage: 238.0 V

Example 7.5, Page number: 378

In [5]:
from __future__ import division

#Variable declaration:
Il=400                                  #Armature current(A)
If=4.7                                  #Field current(A)
Ns=3                                    #series turns per pole
Nf=1000                                 #shunt field turns per pole
Eao=269                                 #at Ia=400 A,(V)
n=1150                                  #speed of motor(rpm)
no=1200                                 #rated speed(rpm) 
Ra=0.025                                #armature resistance(ohm)
Rs=0.007                                #series field resistance(ohm)

#Calculations:
Is=Il+If
GM=If+(Ns/Nf)*Is                        #for graphical analysis
Ea=(n/no)*Eao
Vt=Ea-Is*(Ra+Rs)

#Results:
print "Terminal voltage at rated terminal current:",round(Vt,0),"V"

Terminal voltage at rated terminal current: 245.0 V

Example 7.6, Page number: 381

In [2]:
from __future__ import division
from sympy import *


#Variable declaration:
Ns=4                            #Series field turns
Nf=1000                         #Shunt field turns
Vt=250                          #Full load voltage(V)
#for part (a):
Ia=400                          #Armature current(A)
Ra=0.025                        #Armature resistance(ohm)

#for part (b):
Rs=0.005                        #Added sries resistance(ohm)
Vo=250                          #No load voltage(V)
If=5                            #field current at full load(A)


#Calculations & Results:

#for part (a)
V1=Ia*Ra

#for part (b):
Ia1=Ia+If
Rs,Rd=symbols('Rs Rd')            #Rd= diverter resistance(ohm)
Rp=Rs*Rd/(Rs+Rd)                  #                      -------(i)
Is=Ia1*(Rd/(Rs+Rd))
Inet=If+(Ns/Nf)*Is
Ea=Vt+Ia*(Ra+Rp)                  #                      -------(ii)

#from equation (ii)
Rp=Rs(Inet-5.0)/1.62              
R_d=0.0082                       #R_d=Rd(say), using (i)
print "(a) The operating terminal voltage = 205 V", Inet
print "(b) Rd =", R_d,"ohm"
print "\tHence, by this process, resistance across the series field" 
print "\t(referred to as a series-field diverter) can be adjusted "
print "\tto produce the desired performance. "

(a) The operating terminal voltage = 205 V 1.62*Rd/(Rd + Rs) + 5
(b) Rd = 0.0082 ohm
	Hence, by this process, resistance across the series field
	(referred to as a series-field diverter) can be adjusted 
	to produce the desired performance.

Example 7.7, Page number: 383

In [6]:
from __future__ import division
      
#Variable declaration:
Ia=400                              #Armature current(A)
n1=1200                             #rpm
n2=1100                             #rpm
Ra=0.025                            #armature resistance(ohm)     
Eo=250                              #no load armature voltage(V)
del_n=1.5                           #fractional winding added
N=1000                              #Total windings


#Calculations:
#for part(a):
#point corresponding on the no load saturation curve is :
Eao=Eo*(n1/n2)
#using Eao value in curve, value of If is found to be:
If=5.90                             #Field current(A)
Ea=Eo-Ia*Ra
#From Fig. 7.14
Ea1=261
n=n1*(Ea/Ea1)
Pe=Ea*Ia
Pl=2000                             #No load Rotational loss(W)
Po=(Pe-Pl)/(1+0.01)

#for part (b):
If1=If+del_n/N
#From Fig. 7.14 the corresponding value of Ea at 1200 r/min would be 271 V.
Ea2=271                             #volts
n22=n1*(Ea/Ea2)


#Results:
print "Part(a):"
print "Required speed =",round(n),"r/min"
print "Output power =", round((Po/746),1),"hp"
print "\nPart (b):"
print "Required speed =",round(n22),"r/min"

Part(a):
Required speed = 1103.0 r/min
Output power = 124.8 hp

Part (b):
Required speed = 1063.0 r/min

Example 7.9, Page number: 389

In [3]:
from __future__ import division
from math import *

#Variable declaration:
V1=50                               #terminal voltage(V)
Ia=1.25                             #Armature current(A)
Ra=1.03                             #Armature resistance(ohm)
n1=2100                             #speed at 50V(rpm)
V2=48                               #terminal voltage at 1700 rpm (V)
n2=1700                             #speed at 48 V(rpm)



#Calculations:
#for (a):
Ea1=V1-Ia*Ra
wm1=n1*2*pi/60
Km=round(Ea1/wm1,2)

#for part(b):
Prot=Ea1*Ia

#for part(c:)
wm2=n2*2*pi/60
Ea2=Km*wm2
Ia2=(V2-Ea2)/Ra
Pmech=Ea2*Ia2
Pshaft=Pmech-Prot

#Results:
print "(a) Torque constant:",round(Km,2),"V/(rad/s)"
print "(b) No-load rotational losses of the motor:",round(Prot,0),"W"
print "(c) The power output of the motor:",round(Pshaft,2),"W"

(a) Torque constant: 0.22 V/(rad/s)
(b) No-load rotational losses of the motor: 61.0 W
(c) The power output of the motor: 275.05 W