# CHAPTER05 : DIRECT CURRENT MACHINES¶

## Example E01 : Pg 82¶

In [1]:
from math import sqrt,pi
B=0.78 # flux density in tesla
A=200.*(10.**(-4.))# cross sectional area in centimetre square
print"Flux per pole O=B.A=",B*A,"Wb"
C=95. # no of coils
Nc=2. # no of turns in each coil
Z=2.*C*Nc
print"Z=2*C*Nc=",Z,"conductors"
n=1200. # rotating speed in rev/min
w=(n/60.)*(2.*pi)
print"w=",w,"rad/s"# ans may vary due to rounof error
a=2. # no of paths
p=4. # no of poles
Ka=(Z*p)/(2.*pi*a)
print"Ka=",Ka,"V-s/Wb"# ans may vary due to rounof error
Eg=Ka*B*A*w
print"Eg=Ka*O*w=",Eg,"V"# ans may vary due to rounof error
VT=250. # terminal voltage in volts
ra=0.2 # armture resistance in ohms
Ia=(VT-Eg)/ra
print"Ia=",Ia,"A"# ans may vary due to rounof error
Pin=VT*Ia
print"Pin=",Pin,"W"# ans in textbook is wrong
print"Armature copper loss=",((Ia*Ia)*ra),"W"# ans in textbook is wrong
Pd=Pin-((Ia*Ia)*ra)# ans in textbook is wrong
print"Pd=Pin-coper loss=",Pd,"W"
print"td=Pd/w=",Pd/w,"N-m"
cf=0.7376 # conversion factor for conversion from N-m to lb-ft
print"or",(Pd/w)*cf,"lb-ft"# ans may vary due to roundoff error

Flux per pole O=B.A= 0.0156 Wb
Z=2*C*Nc= 380.0 conductors
Ka= 120.95775675 V-s/Wb
Eg=Ka*O*w= 237.12 V
Ia= 64.4 A
Pin= 16100.0 W
Armature copper loss= 829.472 W
Pd=Pin-coper loss= 15270.528 W
td=Pd/w= 121.519000741 N-m
or 89.6324149467 lb-ft


## Example E02 : Pg 82¶

In [2]:
from math import sqrt,pi
I=100. # current drawn in amperes
ra=0.07 # armature resistance in ohms
Vt=230. # terminal voltage of motor in volts
print"Eg*=VT*-Iara*=",Vt-(I*ra),"V"
n=1200. # speed of rotation in rev/min
print"KaO=Eg*/w*=",(Vt-(I*ra))/((n/60.)*2.*pi),"V-s/rad"# ans may vary due to roundoff error
Ia=100. # armature current in ampere
print"td=KaOIa=",(Ia*(Vt-(I*ra))/((n/60.)*2.*pi)),"N-m"# ans may vary due to roundoff error
Td=300. # torque in N-m
Ia=Td/((Vt-(I*ra))/((n/60.)*2.*pi))# ans may vary due to roundoff error
print"Ia=td/KaO=",Ia,"A"
ra=0.07 # resistance in ohms
VT=230. # voltage in volts
w=(VT-Ia*ra)/((Vt-(I*ra))/((n/60.)*2.*pi))
print"w=(VT-Iara)/KaO=",w,"rad/sec"# ans may vary due to roundoff error

Eg*=VT*-Iara*= 223.0 V
td=KaOIa= 177.457761547 N-m
Ia=td/KaO= 169.054313198 A


## Example E03 : Pg 83¶

In [3]:
from math import sqrt,pi
# Ex5_3 uses a magnetization curve given in textbook
print"At 1200 rev/min and shunt field current of 0.7A Eg*=90V" # from magnetization curve
n=1200. # speed of rotation in rev/min
Eg1=90. # voltage in volts
wB=(n/60.)*2.
print"KaO*=Eg*/wB=",Eg1/(wB*pi),"V-s/rad"# ans may vary due to roundoff error
Td=30. # torque in N-m
Ia=Td/(Eg1/(wB*pi))
print"Ia=td/KaO*=",Ia,"A"# ans may vary due to roundoff error
VT=125. # voltage in volts
ra=0.2 # resistance in ohms
Eg=VT-(Ia*ra)
print"Eg=",Eg,"V"# ans may vary due to roundoff error
w=Eg/((Eg1/(wB*pi)))
print"w=Eg/KaO*=",w,"rad/s"# ans may vary due to roundoff error
n=(w*60.)/(2.*pi)
print"n=",n,"rev/min"# ans may vary due to roundoff error
# other two techniques
# first technique
nB=1200. # speed in rev/min
n=nB*(Eg/Eg1)# ans may vary due to roundoff error
print"n=",n,"rev/min"
# second technique
print"td=",Td*0.738,"lb-ft"# ans may vary due to roundoff error
print"KaO=Eg*/nB=",Eg/nB,"V-min/rev"
Ia=(Td*0.738)/(7.04*(Eg1/nB))# ans may vary due to roundoff error
print"Ia=td/(7.04*Ka*O)=",Ia,"A"
n=Eg/(Eg1/nB)
print"n=Eg/KaO=",n,"rev/min"# ans may vary due to roundoff error

At 1200 rev/min and shunt field current of 0.7A Eg*=90V
Ia=td/KaO*= 41.8879020479 A
Eg= 116.62241959 V
n= 1554.96559454 rev/min
n= 1554.96559454 rev/min
td= 22.14 lb-ft
KaO=Eg*/nB= 0.0971853496587 V-min/rev
Ia=td/(7.04*Ka*O)= 41.9318181818 A
n=Eg/KaO= 1554.96559454 rev/min


## Example E04 : Pg 89¶

In [4]:
from math import sqrt,pi
# Ex5_4 uses a figure given in textbook
Ia=50. # current in amperes
IB=50. # current in amperes
nB=1200. # speed in rev/min
ratio=0.01 # ratio of Nsc/Nf ,unit less
Isc=0.6*Ia # equation given in textbook
print"Isc=",Isc,"A"
If=1.3 # field current in amperes
print"If*=If+(Nsc/Nf)*Isc=",If+(ratio*Isc),"A"
Eg1=132.5 # voltage in volts
print"KaO=Eg*/nB=",Eg1/nB,"V-min/rev"# ans may vary due to roundoff error
n=1140. # speed in rev/min
Eg=n*(Eg1/nB)
print"Eg=Kan=",Eg,"V"# ans may vary due to roundoff error
ra=0.2 # resistance in ohms
Ra=0.03+ra # by kirchodff's law and parallel combination or resistances
print"Ra=",Ra,"ohm"
VTfl=Eg-(Ia*Ra)
print"VTfl=",VTfl,"V"# ans may vary due to roundoff error
print"If*=If+0=",If,"A"
Eg2=125. # voltage in volts
VTnl=Eg*(n/nB)
print"Eg=Eg*(n/nB)=",VTnl,"V"# ans may vary due to roundoff error
print"Voltage Regulation=(VTnl-VTfl)/VTfl=",((VTnl-VTfl)/VTfl)*100.,"%" # ans may vary due to roundoff error

Isc= 30.0 A
If*=If+(Nsc/Nf)*Isc= 1.6 A
KaO=Eg*/nB= 0.110416666667 V-min/rev
Eg=Kan= 125.875 V
Ra= 0.23 ohm
VTfl= 114.375 V
If*=If+0= 1.3 A
Eg=Eg*(n/nB)= 119.58125 V
Voltage Regulation=(VTnl-VTfl)/VTfl= 4.55191256831 %


## Example E05 : Pg 89¶

In [5]:
from math import sqrt,pi
V=250. # voltage rating in volts
Pout=125000. # output power in watts
ra=0.025 # armature resistance in ohms
rsc=0.01 # resistance in ohms
rf=30. # field resistance in ohms
If=5. # field current in amperes
print"Shunt field copper loss=",If*If*rf,"W"
print"Seires filed copper losses=",Isc*Isc*rsc,"W"
print"ACL=",Ia*Ia*ra,"W"# ans in textbook is wrong
print"Brush copper loss=2Ia=",2*Ia,"W"
Prot=5000. # rotational loss in watts
print"Efficiency=",(Pout/(Pout+losses))*100.,'%'# ans may vary due to roundoff eror
rlosses=500. # rheostat losses in watts
Pin=Pout+losses+rlosses
print"Pin required=",Pin,"W" # ans in the textbook is wrong
Ia1=sqrt((Prot+(If*If*rf))/(ra+rsc))
print"Ia1=",Ia1,"A"

Shunt field copper loss= 750.0 W
Seires filed copper losses= 2550.25 W
ACL= 6375.625 W
Brush copper loss=2Ia= 1010.0 W
Stray load loss=1 % of 125Kw= 1250.0 W
Efficiency= 88.067939131 %
Pin required= 142435.875 W
Ia1= 405.321741689 A