# Chapter 4 DC Machines¶

## Example 4.1,Page number 139¶

In [57]:
import math
from math import pi
#given
P=4      #power
A=2
Z=462     #impedance
#calculations
Wn=(16.66)*(2*pi)
z=0.0276
Icoil=100      #current in the coil
Ka=(Z*P)/(2*2*pi)
Ea=(Ka*0.0276*Wn)
Ia=2*Icoil
T=(Ka*z*Ia)
Pa=Ea*Ia*10**-3
Ka=round(Ka,2)
Ea=round(Ea,1)
T=round(T,1)
Pa=round(Pa,1)
print 'Armature constant,Ka=',Ka
print 'Induced armature voltage=',Ea,'V'
print 'Electromagnetic torque developed=',T,'N-m'
print 'power developed by the armature=',Pa,'kW'

Armature constant,Ka= 147.06
Induced armature voltage= 424.9 V
Electromagnetic torque developed= 811.8 N-m
power developed by the armature= 85.0 kW


## Example 4.2,Page number 151¶

In [58]:
import math
#given
Ia=120        #real armature current
Vt=100
Ea=100        #real armature voltage
Ra=0.1
Ar=0.06
EA=98
Ifeff=1.4
#calculations
Vt1=Ea-(Ia*Ra)    #terminal voltage neglecting armature reaction effect
Ifeff1=1-Ar
V=EA-(Ia*Ra)
Ea=(Vt)+(Ia*Ra)
Ifactual=Ifeff+Ar
print 'terminal voltage neglecting armature effect=',Vt1,'volts'
print 'required field current',Ifactual,'Amperes'

terminal voltage neglecting armature effect= 88.0 volts
required field current 1.46 Amperes


## Example 4.3,Page number 154¶

In [59]:
import math
#given
Eaa=111          #maximum generated voltage
Ia=120           #current
Ra=0.1           #resistance
Rfw=80           #field resistance
Eac=85
If=0.5
v=100
#calculations
Vt=Eaa -(Ia*Ra)     #max. value of generated voltage
Rf=v/1
Rfc=Rf-Rfw
Rfcrit=Eac/If
Rfc=Rfcrit -Rfw
print 'critical field circuit resistance is',Rfc,'ohms'

critical field circuit resistance is 90.0 ohms


## Example 4.4,Page number 159¶

In [60]:
import math
#given
Ia=120
Ra=0.1
Vt=80
Vt1=75
AB=17
Ea=6
#calculations
V=Ia*Ra   #Ohm's law
Ia=AB/Ra
Ia1=Ea/Ra
print 'short-circuit current of the generator=',Ia1,'A'

short-circuit current of the generator= 60.0 A


## Example 4.5,Page number 163¶

In [61]:
import math
#given
Ia=120
Vt=100          #terminal voltage
Rsr=0.01        #series winding Resistance
Ra=0.1
Ia=120
Rf=100
Ifeff=1.45
If=1.01
Nf=1200           #no.of turns per pole
Ifar=0.06
#calculations
It=Ia-If
If=(Vt+It*Rsr)/Rf
Ea=Vt+(It*Rsr)+(Ia*Ra)
Nsr=(Ifeff -If+Ifar)*(1200)/(It)
Nsr=round(Nsr,2)
print 'No. of series turns=',Nsr,'turns per pole'

No. of series turns= 5.02 turns per pole


## Example 4.6,Page number 170¶

In [62]:
import math
#given
Vt=100.0          #supply voltage
Ra=0.1          #Armature resistance
Ia=6.0            #Armature current
If=0.99
Rfw=80.0
Ia1=5.0
Iarated=120.0
N=1000.0           #No of rpms of the motor
Afl=0.95
Prot=497.5       #rotational power
#calculations
Eanl=Vt-(Ia*Ra)
Rf=Vt/If
Rfc=Rf-Rfw
Prot=Ea*5.0
Eanl=Vt-(Ia*Ra)
Eafl=Vt-(Iarated*Ra)
Wfl=(Eafl/Eanl)*N
Wm=(Wfl/60)*2*pi
T=(Eafl*Iarated)/Wm
Pout=(Eafl*Iarated)-(Prot)
Pin=(Vt)*(Iarated+If)
Eff=(Pout/Pin)*100.0
Wfl1=(Eafl/Eanl)*(1/Afl)*N
Wm1=(Wfl1/60)*(2*pi)
T=(Eafl*Iarated)/(Wm1)
Eff1=(Pout/Pin)*100.0
Wm=(100/6)*(2*pi)
Ka=Eanl/Wm
Ia=1.5*120
Tstart=(Ka*Ia)
Ifeff=If-Ifar
Ea1=93.5
Ka1=(Ea1/Wm)
Tstart1=(Ka1*Ia)
Eff=round(Eff,2)
Eff1=round(Eff1,2)
Tstart=round(Tstart,2)
Tstart1=round(Tstart1,2)
print 'effeciency at no armature reaction is',Eff,'%'
print 'effeciency with armature reaction is',Eff1,'%'
print 'starting torque neglecting armature reaction is',Tstart,'N-m'
print 'starting torque with armature reaction is',Tstart1,'N-m'

effeciency at no armature reaction is 82.6 %
effeciency with armature reaction is 82.6 %
starting torque neglecting armature reaction is 177.98 N-m
starting torque with armature reaction is 167.41 N-m


## Example 4.7,Page number 172¶

In [63]:
import math
#given
If=0.99
Vt=100.0
Ia=120.0        #current in amperes
Ra=0.1
Rpm2=1000.0
Ifeff=0.86
Nf=1200.0
rpm1=1000.0
Ifeff1=1.32      #effective field current
Rpm3=800.0
EA=65.0
#calculations
Ea=Vt-(Ia*Ra)
Ea1=Rpm2/Rpm1*Ea
Ifar=If-Ifeff
At=Nf*Ifar
Ea2=Rpm2/Rpm3*Ea
Nsr=(Ifeff1 -If+Ifar)*(Nf)/(Ia+If)
Ifeff2=If-(Nsr*(Ia+If))/Nf-Ifar
N=(Ea/EA)*Rpm2
Nsr=round(Nsr,2)
N=round(N,2)
print 'No.of ampere-turns',At,'At/pole'
print 'Nw=',Nsr,'turns/pole'
print 'Speed of the motor=',N,'rpm'

No.of ampere-turns 156.0 At/pole
Nw= 4.56 turns/pole
Speed of the motor= 1353.85 rpm


## Example 4.8,Page number 180¶

In [64]:
import math
from math import pi
#given
Nb=1500.0             #in rpm
Vt=500.0              #armature voltage
T=300.0               #torque
k=(Vt/(Nb*0.1047))
Ia=T/k                #armature current
n=3000.0              #in rpm
T=(Vt/(n*0.1047))*94.2477
T=round(T,0)
print 'motor armature current=',Ia,'A'
print 'Torque at speed of 3000 rpm=',T,'N-m'

motor armature current= 94.23 A
Torque at speed of 3000 rpm= 150.0 N-m


## Example 4.9,Page number 180¶

In [65]:
from math import sqrt
#given
Vt=220.0                #dc supply
Ia=25.0                 #current drawn in amperes
Ra=0.6                #resistance
Rsr=0.4
Rae=0
N=300.0                 #in rpm
N1=200.0
Wm=(2*pi/60)
Hp=746.0
#calculations
Ea=Vt-Ia*(Ra+Rsr+Rae)
P=Ea*Ia
a=P/Hp
T=(Ea*Ia)/(N*Wm)
Ksr=T/Ia**2
T1=(N1/N)**2*T
P=(T1*N1*Wm)
P=P/746
P=round(P,2)
print 'power delivered=',P,'hp'

power delivered= 1.94 hp


## Example 4.10,Page number 185¶

In [66]:
from math import sqrt
#given
Iarated=100
Vt=100                  #dc supply voltage
Ra=0.1                  #armature resistance
Ia1=200
#calculations
Iastart=Vt/Ra
Rae=(Vt-20)/(200)        #0.4
Ea2=Vt-Iarated*(Ra+Rae)
Rae2=(Vt-Ea2-20)/(200)   #0.15
Ea3=Vt-(Ia*(Ra+Rae2))
Ea3=Vt-Iarated*(Ra+Rae2)
Rae3=0.025     #(Vt-Ea3 -20)/200
Ea4=Vt-(Iarated*(Ra+Rae3))
Rae4=-0.0375   #(Vt-Ea4 -20)/200
Ia=(Vt-Ea4)/Ra
R1=0.4-0.15
R2=0.15-0.025
R3=0.025-0
print 'current is',Ia,'A'
print 'resistance R1=',R1,'ohms'
print 'resistance R2=',R2,'ohms'
print 'resistance R3=',R3,'ohms'

current is 125.0 A
resistance R1= 0.25 ohms
resistance R2= 0.125 ohms
resistance R3= 0.025 ohms


## Example 4.11,Page number 191¶

In [67]:
import math
from math import pi,sqrt
#given
Ia=40                  #current
Ra=0.25                #resistance
La=10                  #impedance
ACv=265
Angle=30
Ka=0.18                #motor constant
#calculations
A=math.cos(pi*Angle/180)
Vt=(2*sqrt(2)*ACv*A)/(pi)   #average termminal voltage
Ea=Vt-(Ia*Ra)               #back emf
N=Ea/Ka                     #speed in rom
Sec=(Ka*60)/(2*pi)
T=Sec*Ia
P=Vt*Ia
P=(Ia**2*Ra)+Ea*Ia
T=round(T,2)
P=round(P,0)
print 'Motor torque is',T,'N-m'
print 'power to the motor is',P,'W'

Motor torque is 68.75 N-m
power to the motor is 8265.0 W


## Example 4.12, Page number 192¶

In [68]:
import math
from math import pi,sqrt
#given
V=480           #voltage
RPM=1800         #revolutions per minute
Ia=16.5          #current
Ra=0.0874         #resistance
Ka=0.33
Angle=30
N=1800
#calculations
Vp=(V/sqrt(3))              #supply phase voltage
Vt=(3*sqrt(6)*Vp)/(pi)      #motor terminal voltage
Ea=Vt-(Ia*Ra)
No=(Ea/Ka)
A=math.cos(pi*Angle/180)
Vt1=Vt*A
Ea1=Vt1 -(Ia*Ra)
Eaf=Ka*N
Vtf=Eaf+(Ia*Ra)
Angle=0.94   #Vtf/Vt
a=math.acos(Angle)
Alfa=a*180/pi
Eas=Vtf-(Ia*Ra)
Eas=606.96
Nos=Eas/Ka
SpeedReg=(Nos-N)/N*100
No1=round(No1,2)
Alfa=round(Alfa,2)
SpeedReg=round(SpeedReg,2)
print 'no-load speed at firing angle 30 is',No1,'rpm'
print 'Alfa=',Alfa
print 'Speed regulation is',SpeedReg,'%'

no-load speed at firing angle 30 is 1696.79 rpm
Alfa= 19.95
Speed regulation is 2.18 %


## Example 4.13,Page number 195¶

In [69]:
import math
#given
Supv=120            #dc supply voltage
Ia=20               #armature circuit inductance
Ra=0.5              #armature circuit resistance
Ka=0.05             #motor constant
#calculations
Vt=Ia*Ra
A=(Vt/Supv)
Ea=Supv -(Ia*Ra)
N=Ea/Ka
print 'The range of the speed is 0<N<',N,'rpm'

The range of the speed is 0<N< 2200.0 rpm