# CHAPTER20 : DC MACHINES¶

## Example E02 : Pg 770¶

In :
# a
import math
Vt = 230.; # (in volts)
Ia = 73.; # armature current (in amps)
If = 1.6; # feild current (in amps)
Ra = 0.188; # armature circuit resistance(in ohms)
n = 1150.; # rated speed of the rotor(in rpm)
Po = 20.*746.; # output power (in watts)

Ea = Vt - (Ia*Ra); # armature voltage
wm = 2.*math.pi*n/60.; # rated speed of the rotor (in rad/sec)
T = Ea*Ia/wm ; # electromagnetic torque

print '%s' %("a")
print '%s %.2f' %("electromagnetic torque = ",T)

# b
a = 4.; # no. of parallel armature paths
p = 4.; # no. of poles
z = 882.; # no. of armature conductors
flux = Ea*60.*a/(p*z*n); # flux per pole (in Wb)

print '%s' %("b")
print '%s %.2f' %("flux per pole = ",flux)

# c
Prot = (Ea*Ia) - Po; # rotational loss (in watt)
print '%s' %("c")
print '%s %.2f' %("rotational losses = ",Prot)

# d
losses = Prot + (Ia**2. * Ra) + (Vt * If) ;
Pi = (Ea*Ia) + (Ia**2. * Ra) + (Vt * If); # input power
efficiency = 1. - (losses/Pi);

print '%s' %("d")
print '%s %.2f' %("efficiency = ",efficiency)

a
electromagnetic torque =  131.10
b
flux per pole =  0.01
c
rotational losses =  868.15
d
efficiency =  0.87


## Example E03 : Pg 771¶

In :
#  final flux = 0.8*initial flux
Ia1 = 73.; # initial armature current (in amps)
Vt = 230.; # (in volts)
Ra = 0.188; # armature circuit resistance
n1 = 1150.; # initial rotor speed (in rpm)
Ea1 = 216.3; # initial armature voltage

Ia2 = (1./0.8)*Ia1 ; # final armature current
Ea2 = Vt - (Ia2*Ra); # final armature voltage

n2 = (Ea2/Ea1)*(1./0.8)*n1; # final rotor speed

print '%s %.2f' %("final rotor speed(in rpm) = ",n2)

final rotor speed(in rpm) =  1414.54


## Example E04 : Pg 780¶

In :
# a
rop = 0.4; # ratio of ON time T0 to cycle time Tp
Vb =550.; # rated terminal voltage of the dc motor
Ia = 30.; # current drawn by the motor (in amps)
Ra = 1.; # armature circuit resistance (in ohms)
ts = 5.94; # torque and speed parameter of the motor (in N-m/A)

Vm = rop*Vb; # average value of the armature terminal voltage
Ea = Vm - (Ia*Ra); # induced armature voltage

wm = Ea/ts; # motor speed (in rad/s)
print '%s' %("a")
print '%s %.2f' %("motor speed (in rad/s) = ",wm)

# b
deltaI = 5.; # change of armature current during the ON period
La = 0.1; # armature winding inductance (in H)
To = La*deltaI/(Vb - Ea); # ON time
Tp = To/rop; # cycle time

f = 1./Tp ; # required pulses per second
print '%s' %("b")
print '%s %.2f' %("required pulses per second = ",f)

# c
rop = 0.7; # new ratio of ON time T0 to cycle time Tp
Vm = rop*Vb; # average value of the armature terminal voltage
Ea = Vm - (Ia*Ra); # induced armature voltage

wm = Ea/ts; # motor speed (in rad/s)
print '%s' %("c")
print '%s %.2f' %("motor speed with To/Tp equal to 0.7 (in rad/s) = ",wm)

To = La*deltaI/(Vb - Ea); # ON time
Tp = To/rop; # cycle time

f = 1./Tp ; # required pulses per second
print '%s %.2f' %("required pulses per second with To/Tp equal to 0.7 = ",f)

a
motor speed (in rad/s) =  31.99
b
required pulses per second =  288.00
c
motor speed with To/Tp equal to 0.7 (in rad/s) =  59.76
required pulses per second with To/Tp equal to 0.7 =  273.00