# Chapter 29: D.C. Motor¶

## Example Number 29.1, Page Number:999¶

In [3]:
#variable declaration
v=220#V
r=0.5#ohm
i=20#A

#calculation
#as generator
eg=v+i*r
#as motor
eb=v-i*r

#result
print "as generator:eg=",eg,"V"
print "as motor:eb=",eb,"V"

as generator:eg= 230.0 V
as motor:eb= 210.0 V


## Example Number 29.2, Page Number:999¶

In [1]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
ia=Symbol('ia')
r=0.1#ohm
brush_drop=2#V
n=1000#rpm
i=100#A
v=250#V
n2=700#rpm

#calculations
rl=v/i
eg1=v+i*r+brush_drop
eg2=eg1*n2/n
ia=solve(eg2-2-ia*r-2.5*ia,ia)

#result
print "current delivered to the load=",ia[0],"A"

current delivered to the load= 69.7692307692308 A


## Example Number 29.3, Page Number:999¶

In [10]:
#variable declaration
v=440#V
ra=0.8#ohm
rf=200#ohm
output=7.46#kW
efficiency=0.85

#calculations
input_m=output*1000/efficiency
im=output*1000/(efficiency*v)
ish=v/rf
ia=im-ish
eb=v-ia*ra

#results
print "back emf=",eb,"V"

back emf= 425.642780749 V


## Example Number 29.4, Page Number:1000¶

In [11]:
#variable declaration
v=250#V
ra=0.06#ohm
rf=100#ohm

#calculations
#as generator
ish=v/rf
ia=i+ish
eb=v+ia*ra
power=eb*ia/1000

print "As generator: power=",power,"kW"

#as motor
ish=v/rf
ia=i-ish
eb=v-ia*ra
power=eb*ia/1000

print "As generator: power=",power,"kW"

As generator: power= 26.12424 kW
As generator: power= 23.92376 kW


## Example Number 29.5, Page Number:1000¶

In [14]:
import math
#variable declaration
p=a=4
z=32
v=200.0#V
i=12.0#A
ra=2.0#ohm
rf=200.0#ohm
n=1000.0#rpm
i2=5.0#A
#calculations
ia=i+v/rf
eg=v+ia*ra
phi=eg*a*60/(z*n*p)
#as motor
ia=i2-v/rf
eb=v-ia*ra
n=60*eb/(phi*z)

#result
print "flux per pole=",phi,"wb"
print "speed of the machine=",math.ceil(n),"rpm"

flux per pole= 0.42375 wb
speed of the machine= 850.0 rpm


## Example Number 29.6, Page Number:1002¶

In [18]:
#variable declaration
ia=110#A
v=480#V
ra=0.2#ohm
z=864
p=a=6
phi=0.05#Wb

#calculations
eb=v-ia*ra
n=60*eb/(phi*z)
ta=0.159*phi*z*ia*p/a

#result
print "the speed=",math.floor(n),"rpm"
print "the gross torque=",ta,"N-m"

the speed= 636.0 rpm
the gross torque= 755.568 N-m


## Example Number 29.7, Page Number:1003¶

In [21]:
#variable declaration
v=250#V
z=782
ra=rf=0.5#ohm
ia=40#A
phi=25*0.001#Wb
p=4
a=2
#calculation
eb=v-ia*ra
n=60*eb/(phi*z)
ta=0.159*phi*z*ia*p/a

print "the speed=",math.floor(n),"rpm"
print "the gross torque=",ta,"N-m"

the speed= 705.0 rpm
the gross torque= 248.676 N-m


## Example Number 29.8, Page Number:1003¶

In [24]:
#variable declaration
eb=250.0#V
n=1500.0#rpm
ia=50.0#A

#calculations
pm=eb*ia
ta=9.55*eb*ia/n

#result
print "torque=",ta,"N-m"
print "machanical power=",pm,"W"

torque= 79.5833333333 N-m
machanical power= 12500.0 W


## Example Number 29.9, Page Number:1003¶

In [32]:
#variable declaration
v=220#V
p=4
z=800
ia=45#A
phi=25*0.001#Wb
ra=0.6#ohm
a=p/2

#calculation
ta=0.159*phi*z*ia*p/a
eb=v-ia*ra
n=eb*a/(phi*z*p)

#result
print "developed torque=",ta,"N-m"
print "shaft torque=",tsh,"N-m"

developed torque= 286.2 N-m
shaft torque= 270.618131415 N-m


## Example Number 29.10, Page Number:1003¶

In [38]:
#variable declaration
v=220.0#V
n=500.0#rpm
i=50.0#A
ra=0.2#ohm

#calculation
ia2=2*i
fb1=v-(i*ra)
eb2=v-(ia2*ra)
n2=eb2*n/fb1
#result
print "speed when torque is doubled=",n2,"N-m"

speed when torque is doubled= 476.19047619 N-m


## Example Number 29.11, Page Number:1003¶

In [40]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
r=Symbol('r')
v=500#V
n=1000#rpm
efficiency=0.90
ra=0.24#ohm
vd=2#v
i=1.8#A
ratio=1.5

#calculation
il=input_m/v
il=ratio*il
ia=il-i
r=solve(ia*(r+ra)+vd-v,r)

#result
print "full-load line current=",il,"A"
print "full-load shaft torque",tsh,"N-m"
print "total resistance=",r[0],"ohm"

full-load line current= 124.333333333 A
full-load shaft torque 356.215 N-m
total resistance= 3.82420021762787 ohm


## Example Number 29.12, Page Number:1004¶

In [43]:
#variable declaration
p=a=4
v=220#V
z=540
i=32#A
output=5.595#kW
ra=0.09#ohm
i_f=1#A
phi=30*0.001#Wb

#calculation
ia=i-i_f
eb=v-ia*ra
n=eb*a*60/(phi*z*p)
tsh=9.55*output/n

#result
print "speed=",n,"rpm"
print "torque developed=",tsh*1000,"N-m"

speed= 804.481481481 rpm
torque developed= 66.4182473183 N-m


## Example Number 29.13(a), Page Number:1004¶

In [58]:
#variable declaration
v=220.0#V
i=5.0#A
ra=0.04#ohm
phi=0.04#Wb
z=160
il=95.0#A
inl=9.0#A
p=4
a=2
#calculation
ea0=v-(inl-i)*ra
n0=ea0*a*60/(phi*z*p)
ea=v-(il-i)*ra
n=ea*n0/ea0

#result

no-load speed= 1030.5 rpm
load speed= 1014.375 rpm


## Example Number 29.13(b), Page Number:1004¶

In [66]:
#variable declaration
p=a=6
i=400#A
n=350#rpm
phi=80*0.001#Wb
z=600*2
loss=0.03#percentage

#calculation
e=phi*z*n*p/(60*a)
pa=e*i
t=pa/(2*3.14*n/60)
t_net=0.97*t
bhp=t_net*36.67*0.001/0.746
#result
print "brake-horse-power",bhp,"HP"

brake-horse-power 291.551578696 HP


## Example Number 29.13(c), Page Number:1004¶

In [67]:
#variable declaration
p=4
z=774
phi=24*0.001#Wb
ia=50#A
a=2
#calculations
t=0.159*phi*z*ia*p/a

#result
print "torque=",t,"N-m"

torque= 295.3584 N-m


## Example Number 29.13(d), Page Number:1005¶

In [81]:
#variable declaration
v=500.0#V
i=5.0#A
ra=0.15#ohm
rf=200.0#ohm
il=40.0#A

#calculations
ih=v/rf
pi=v*i
cu_loss_f=cu_loss=v*ih
output=v*il
cu_loss_a=(il+ih)**2*ra
total_loss=cu_loss+cu_loss_a+cu_loss_f
efficiency=output/(output+total_loss)
#result
print "efficiency=",efficiency*100,"%"

efficiency= 87.8312542029 %


## Example Number 29.13(e), Page Number:1006¶

In [88]:
#variable delcration
ia=40#A
v=220#V
n=800#rpm
ra=0.2#ohm
rf=0.1#ohm
loss=0.5#kW

#calculations
eb=v-ia*(ra+rf)
ta=9.55*eb*ia/n
cu_loss=ia**2*(ra+rf)
total_loss=cu_loss+loss*1000
input_m=v*ia
output=input_m-total_loss

#result
print "output of the motor=",output/1000,"kW"

output of the motor= 7.82 kW


## Example Number 29.14, Page Number:1006¶

In [2]:
#variable declaration
f=400.0#N
d=10.0#cm
n=840#rpm
v=220.0#V
n1=1800#rpm
efficiency=.80
d2=24.0#cm

#calculations
tsh=f*d*0.01/2
output=tsh*2*3.14*n/60
input_m=output/efficiency
i=input_m/v
d1=n*d2/n1

#calculation
print "current taken by the motor=",round(i),"A"
print "size of motor pulley=",d1,"cm"

current taken by the motor= 10.0 A
size of motor pulley= 11.2 cm


## Example Number 29.15, Page Number:1006¶

In [102]:
#variable declaration
v=200.0#V
p=4
z=280
ia=45.0#A
phi=18*0.001#Wb
ra=0.5+0.3#ohm
loss=800.0#W
d=0.41
a=4
#calculation
eb=v-ia*ra
n=eb*60*a/(phi*z*p*4)
inpt=v*ia
cu_loss=ia**2*ra
total_loss=loss+cu_loss
output=inpt-total_loss
tsh=9.55*output/n
f=tsh*2/d

#result
print "pull at the rim of the pulley=",f,"N-m"

pull at the rim of the pulley= 628.016180845 N-m


## Example Number 29.16, Page Number:1007¶

In [106]:
#variable declaration
p=4
v=240#V
output=11.19#kW
n=1000#rpm
ia=50#A
i=1#A
z=540
ra=0.1#ohm
vd=1#V
a=2
#calculation
eb=v-ia*ra
ta=9.55*eb*ia/n
tsh=9.55*output*1000/n
phi=eb*60*a*1000/(z*n*p)
input_a=v*ia
cu_loss=ia**2*ra
brush_loss=ia*2
power=input_a-(cu_loss+brush_loss)
rotational_loss=power-output*1000
input_m=v*(ia+i)
efficiency=output*1000/input_m

#result
print "total torque=",ta,"N-m"
print "useful torque=",tsh,"N-m"
print "flux/pole=",phi,"mWb"
print "rotational losses=",rotational_loss,"W"
print "efficiency=",efficiency*100,"%"

total torque= 112.2125 N-m
useful torque= 106.8645 N-m
flux/pole= 13.0555555556 mWb
rotational losses= 460.0 W
efficiency= 91.4215686275 %


## Example Number 29.17, Page Number:1007¶

In [111]:
#variable declaration
v=460.0#v
n=500.0#rpm
i=40.0#A
i2=30.0#A
ra=0.8#ohm

#calculation
t2_by_t1=i2**2/i**2
change=(1-t2_by_t1)*100#percentage
eb1=v-i*ra
eb2=v-i2*ra
n2=eb2*i*n/(eb1*i2)
#result
print "speed=",n2,"rpm"
print "percentage change in torque=",change,"%"

speed= 679.127725857 rpm
percentage change in torque= 43.75 %


## Example Number 29.18, Page Number:1008¶

In [129]:
#variable declaration
v=460.0#V
output=55.95#kW
n=750#rpm
I=252.8#kg-m2
ia1=1.4
ia2=1.8

#calculations
ia=(ia1+ia2)/2
n=n/60.0
tsh=output*1000/(2*3.14*n)
torque_avg=(ia-1)*tsh
dt=(I*2*3.14*n)/torque_avg

#result
print "approximate time to attain full speed=",dt,"s"

approximate time to attain full speed= 46.4050282991 s


## Example Number 29.19, Page Number:1008¶

In [138]:
#variable declaration
output=14.92#kW
v=400.0#V
n=400.0#rpm
i=40.0#A
I=7.5#kg-m2
ratio=1.2

#calculations
n=n/60
t=output*1000/(2*3.14*n)
torque=(ratio-1)*t
dt=(I*2*3.14*n)/torque

print "time to attain full speed=",dt,"s"

time to attain full speed= 4.4055406613 s


## Example Number 29.20, Page Number:1009¶

In [143]:
#variable declaration
p=4
z=944
phi=34.6*0.001#Wb
ta=209.0#N-m
v=500.0#V
ra=3.0#ohm
a=2
#calculation
ia=ta/(0.159*phi*z*(p/a))
ea=v-ia*ra
n=ea/(phi*z*(p/a))

#result
print "line current=",ia,"A"
print "speed=",n*60,"rpm"

line current= 20.1219966813 A
speed= 403.798260345 rpm


## Example Number 29.21, Page Number:1010¶

In [144]:
#variable declaration
v=250#v
n=1000#rpm
ia=8#A
ra=0.2#ohm
rf=250#ohm
i2=50#A

#calculation
ish=v/rf
eb0=v-(ia-ish)*ra
eb=v-(i2-ish)*ra
n=eb*n/eb0

#result
print "speed when loaded=",n,"rpm"

speed when loaded= 966.21078037 rpm


## Example Number 29.22, Page Number:1010¶

In [148]:
#variable declaration
n=800#rpm
ia=100#A
v=230#V
ra=0.15#ohm
rf=0.1#ohm
ia2=25#A
ratio=0.45

#calculation
eb1=v-(ra+rf)*ia
eb2=v-ia2*(ra+rf)
n2=eb2*n/(eb1*ratio)

#result
print "speed at which motor runs=",n2,"rpm"

speed at which motor runs= 1940.37940379 rpm


## Example Number 29.23, Page Number:1010¶

In [158]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
ia2=Symbol('ia2')
#variable declaration
v=230.0#V
ra=0.5#ohm
rf=115.0#ohm
n1=1200#rpm
ia=2.5#A
n2=1120#rpm

#calculation
eb1=v-ra*ia
x=n2*eb1/n1
ia2=solve((v-ra*ia2)-x,ia2)
ia=ia2[0]+(v/rf)
input_m=v*ia

#result
print "line current=",round(ia,1),"A"
print "power input=",round(input_m,1),"W"

line current= 35.0 A
power input= 8050.0 W


## Example Number 29.24, Page Number:1010¶

In [174]:
#variable declaration
power=100.0#kW
n1=300#rpm
v=220.0#V
ra=0.025#ohm
rf=60.0#ohm
vd=1.0#V

#calculation
i=power*1000/v
ish=v/rf
ia=i+ish
eb=v+ia*ra+2*vd
ia2=i-ish
eb2=v-ia2*ra-2*vd
n2=eb2*n1/eb

#result
print "speed=",n2,"rpm"

speed= 278.796797778 rpm


## Example Number 29.25, Page Number:1011¶

In [190]:
import math
#variable declaration
v=250.0#V
n=1000.0#rpm
ra=0.5#ohm
rf=250.0#ohm
ia=4.0#A
i=40.0#A
ratio=0.04#percentage by whih armature reaction weakens field

#calculations
ish=v/rf
ia2=ia-ish
eb0=v-ia2*ra
n0=n*eb0/v
ia=i-ish
eb=v-ia*ra
n=eb*n0/(eb0*(1-ratio))

#result
print "speed of machine=",math.floor(n),"rpm"

speed of machine= 960.0 rpm


## Example Number 29.26, Page Number:1011¶

In [191]:
#variable declaration
v=250#V
ooutput=14.92#kW
n=1000#rpm
i=75#A
ra=0.25#ohm
ratio=0.20

#calculation
eb1=v-i*ra
eb_inst=eb1*(1-ratio)
ia_inst=(v-eb_inst)/ra
t_inst=9.55*eb_inst*ia_inst/n
ia2=i/(1-ratio)
eb2=v-ia2*ra
n2=eb2*n/(eb1*(1-ratio))

#result
print "armature current=",ia2,"A"
print "speed=",n2,"rpm"

armature current= 93.75 A
speed= 1224.66216216 rpm


## Example Number 29.27, Page Number:1012¶

In [197]:
#variable declaration
v=200.0#V
i=4.0#A
n=700.0#rpm
rf=100.0#A
v2=6.0#V
i2=10.0#A
input_m=8.0#kW

#calculation
ish=v/rf
il=input_m*1000/v
ia=il-ish
ra=v2/i2
eb0=v-ish*ra
eb=v-ia*ra
n=eb*n/eb0
ta=9.55*eb*ia/n
inpt=v*i
cu_loss=ish**2*ra
constant_loss=inpt-cu_loss
cu_loss_arm=ia**2*ra
total_loss=constant_loss+cu_loss_arm
output=input_m*1000-total_loss
efficiency=output/(input_m*1000)
print
#result
print "speed on load=",n,"rpm"
print "torque=",ta,"N-m"
print "efficiency=",efficiency*100,"%"

speed on load= 623.943661972 rpm
torque= 103.0636 N-m
efficiency= 79.2 %


## Example Number 29.28, Page Number:1012¶

In [200]:
#variabe declaration
v=220#V
inl=5#A
n_nl=1150#rpm
ra=0.5#ohm
rsh=110#ohm

#calculations
input_nl=v*inl
ish=v/rsh
ia0=inl-ish
cu_loss_nl=ia1**2*ra
constant_loss=input_nl-cu_loss_nl
ia=i-ish
cu_loss_a=ia**2*ra
total_loss=cu_loss_a+constant_loss
eb_nl=v-(ia0*ra)
eb=v-ia*ra
n=n_nl*eb/eb_nl
ta=9.55*eb*ia/n

#result
print "torque developed=",ta,"N-m"
print "efficiency=",efficiency,"%"
print "the speed=",n,"rpm"

torque developed= 87.096 N-m
efficiency= 79.5361818182 %
the speed= 1031.57894737 rpm


## Example Number 29.29, Page Number:1013¶

In [1]:
#variable declaration
v=250.0#V
ra=0.1#ohm
vb=3#V
rf=0.05#ohm
ia=80.0#A
n=600.0#rpm
i2=100.0#A

#calculation
eb1=v-ia*(ra+rf)
eb2=v-i2*(ra+rf)
n2=eb2*ia*n/(eb1*i2)

#result
print "speed when current is 100 A=",n2,"rpm"

speed when current is 100 A= 473.949579832 rpm


## Example Number 29.30, Page Number:1013¶

In [2]:
import math
#variable declaration
v=220.0#V
n=800.0#rpm
i=100.0#A
ra=0.1
ratio=1.0/2.0
#calculation
ia1=i*math.sqrt(ratio)
eb1=v-i*ra
eb2=v-ia1*ra
n2=eb2*i*n/(eb1*ia1)
#result
print "speed when motor will run when developing half the torque=",round(n2,0),"rpm"

speed when motor will run when developing half the torque= 1147.0 rpm


## Example Number 29.31, Page Number:1013¶

In [224]:
import math
#variable declaration
p=a=4
n=600#rpm
ia=25#A
v=450#V
z=500
phi=1.7*0.01*math.pow(ia,0.5)

#calculation
eb=n*phi*z*p/(60*a)
iara=v-eb
ra=iara/ia
i=math.pow((phi*ia*math.sqrt(ia)/(phi*2)),2.0/3.0)
eb2=v/2-i*ra
phi2=1.7*0.01*math.pow(i,0.5)
n2=eb2*phi*n/(eb*phi2)

#result
print "speed at which motor will run=",round(n2,0),"rpm"

speed at which motor will run= 372.0 rpm


## Example Number 29.32, Page Number:1017¶

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import math
#variable declaration
v=460.0#V
ra=0.5#ohm

def f(ia,t):
n=(v*ia-ia**2*ra)*60/(2*3.14*t)
return(n)

n1=f(20.0,128.8)
n2=f(30.0,230.5)
n3=f(40.0,349.8)
n4=f(50.0,469.2)
T=[128.8,230.5,349.8,469.2]
N=[n1,n2,n3,n4]
plt.plot(T,N)
plt.xlabel("Torque(NM.m)")
plt.ylabel("Speed(rpm)")
plt.xlim((0,500))
plt.ylim((0,800))
plt.show()


## Example Number 29.33, Page Number:1017¶

In [2]:
%matplotlib inline
import matplotlib.pyplot as plt
import math
#variable declaration
output=5.968#kW
n=700#rpm
v1=500#V
n2=600#rpm
ra=3.5#ohm
loss=450#W

#calculation

def fp(i,v):
p=5.968*((n2*(v1-i*ra)/(v*n))**2)
return(p)

def fm(i,v):
m=((v1-i*ra)*i-loss)/1000
return(m)

p1=fp(7.0,347.0)
p2=fp(10.5,393.0)
p3=fp(14.0,434.0)
p4=fp(27.5,468.0)

m1=fm(7.0,347.8)
m2=fm(10.5,393.0)
m3=fm(14.0,434.0)
m4=fm(27.5,468.0)

#plot
I=[7,10.5,14,27.5]
P=[p1,p2,p3,p4]
M=[m1,m2,m3,m4]
plt.plot(I,P)
plt.plot(I,M)
plt.xlabel("Current")
plt.ylabel("Power(kW)")
plt.xlim((0,30))
plt.ylim((0,12))
plt.show()


## Example Number 29.34, Page Number:1022¶

In [3]:
#variable declaration
v=500#V
i=3#A
ia=3.5#A
ib=4.5#A

#calculation
loss=v*i
#B unexcited
loss1=v*(ia-i)
#B excited
loss2=v*(ib-i)
loss=loss2-loss1

#result
print "iron losses of B=",loss,"W"

iron losses of B= 500.0 W


## Example Number 29.35, Page Number:1023¶

In [ ]:
#variable declaration
v=220.0#V
ra=0.2#ohm
rf=110.0#ohm
ia=5.0#A
n=1500#rpm
i2=52.0#A

#calculation
ish=v/rf
ia1=ia-ish
ia2=i2-ish
eb1=v-ia1*ra
eb2=v-ia2*ra
n2=round(eb2*n/eb1,0)
input_nl=v*ia
cu_loss_nl=ia1**2*ra
constant_loss=input_nl-cu_loss_nl
cu_loss_l=ia2**2*ra
total_loss=constant_loss+cu_loss_l
input_l=v*i2
output=input_l-total_loss
tsh=9.55*output/n2

#result
print "speed=",n2,"rpm"
print "shaft torque=",tsh,"N-m"


## Example Number 29.36, Page Number:1023¶

In [ ]:
#variable declaration
v=250#V
n=1000#rpm
ia=5#A
ra=0.2#ohm
rf=250#ohm
i=50#A
ratio=0.03#percentage by which armature reaction weakens field

#calculations
ish=v/rf
ia1=ia-ish
ia2=i-ish
eb1=v-ia1*ra
eb2=v-ia2*ra
n2=eb2*n/(eb1*(1-ratio))

#result
print "speed=",round(n2,0),"rpm"


## Example Number 29.37, Page Number:1023¶

In [244]:
#variable declaration
v=500#V
ia=5#A
ra=0.22#A
rf=250#ohm
i=100#A

#calculations
ish=v/rf
ia0=ia-ish
eb0=v-ia0*ra
cu_loss=ia0**2*ra
input_m=v*ia
constant_loss=input_m-cu_loss
ia=i-ish
eb=v-ia*ra
cu_loss=ia**2*ra
total_loss=cu_loss+constant_loss
input_m=v*i
output=input_m-total_loss
efficiency=output*100/input_m
per=(eb-eb0)*100/eb0

#result
print "efficiency=",round(efficiency,1),"%"
print "percentage change in speed=",round(per,2),"%"

efficiency= 90.8 %
percentage change in speed= -4.19 %


## Example Number 29.38, Page Number:1024¶

In [247]:
#variable declaration
v=250#V
n=1000#rpm
i=25#A
i2=50#A
ratio=0.03#percentage by which the armature reaction weakens field
ra=0.2#ohm
rf=250#ohm
vd=1
#calculation
ish=v/rf
ia1=i-ish
ebh=v-ia1*ra-2*vd
ia2=i2-ish
eb2=v-ia2*ra-2*vd
n2=eb2*n/(ebh*(1-ratio))
ta1=9.55*eb1*ia1/n
ta2=9.55*eb2*ia2/n2

#result
print "speed=",round(n2,0),"rpm"
print "torque in first case=",ta1,"N-m"
print "torque in second case=",ta2,"N-m"

speed= 1010.0 rpm
torque in first case= 57.11664 N-m
torque in second case= 110.3912768 N-m


## Example Number 29.39, Page Number:1024¶

In [254]:
#variable declaration
v=250.0#V
n1=1000.0#rpm
ra=0.5#ohm
rf=250.0#ohm
ia=4.0#A
i=40.0#A
ratio=0.04#percentage by which the armature reaction weakens field
eb1=250.0#V

#calculation
ish=v/rf
eb2=v-(i-ish)*ra
n2=eb2*n/(eb1*(1-ratio))
cu_loss=(ia-ish)**2*ra
input_m=v*ia
constant_loss=input_m-cu_loss
cu_loss_a=(i-ish)**2*ra
total_loss=constant_loss+cu_loss_a
inpt=v*i
output=inpt-total_loss
efficiency=output*100/inpt

#result
print "speed=",round(n2,0),"rpm"
print "efficiency=",efficiency,"%"

speed= 960.0 rpm
efficiency= 82.44 %


## Example Number 29.40, Page Number:1025¶

In [256]:
#variable declaration
p=4
v=250#V
z=120*8
a=4
phi=20*0.001#Wb
i=25#A
ra=0.1#ohm
rf=125#ohm
loss=810#W

#calculations
ish=v/rf
ia=i-ish
eb=v-ia*ra
n=eb*a*60/(p*z*phi)
ta=9.55*eb*ia/n
cu_loss=ia**2*ra
cu_loss_shunt=v*ish
total_loss=loss+cu_loss+cu_loss_shunt
input_m=v*i
output=input_m-total_loss
tsh=9.55*output/n
efficiency=output*100/input_m

#result
print "gross torque=",ta,"N-m"
print "useful torque=",tsh,"N-m"
print "efficiency=",efficiency,"%"

gross torque= 70.288 N-m
useful torque= 60.2946209124 N-m
efficiency= 78.1936 %


## Example Number 29.41, Page Number:1025¶

In [263]:
#variable declaration
output=14.92#kW
n=1150#rpm
p=4
a=2
z=620
ra=0.2#ohm
i=74.8#A
i2=3#A
v=230#V
#calculation
ia=i-i2
eb=v-ia*ra
phi=eb*a*60/(p*z*n)
ta=9.55*eb*ia/n
power=eb*ia
loss_rot=power-output*1000
input_m=v*i
total_loss=input_m-output*1000
per=total_loss*100/input_m

#result
print "flux per pole=",phi*1000,"mWb"
print "torque developed=",ta,"N-m"
print "rotational losses=",loss_rot,"W"
print "total losses expressed as a percentage of power=",per,"%"

flux per pole= 9.07321178121 mWb
torque developed= 128.575818783 N-m
rotational losses= 562.952 W
total losses expressed as a percentage of power= 13.2759823297 %


## Example Number 29.42, Page Number:1025¶

In [271]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
ia1=Symbol('ia1')
output=7.46#kW
v=250#V
i=5#A
ra=0.5#ohm
rf=250#ohm

#calculation
input_m=v*i
ish=v/rf
ia=i-ish
cu_loss=v*ish
cu_loss_a=ra*ia**2
loss=input_m-cu_loss
ia1=solve(ra*ia1**2-v*ia1+output*1000+loss,ia1)
i2=ia1[0]+ish
input_m1=v*i2
efficiency=output*100000/input_m1
ia=math.sqrt((input_m-cu_loss_a)/ra)
input_a=v*ia
cu_loss=ia**2*ra
output_a=input_a-(cu_loss+loss)

#result
print "efficiency=",efficiency,"%"
print "output power at which efficiency is maximum=",output_a/1000,"kW"

efficiency= 79.5621535016683 %
output power at which efficiency is maximum= 10.2179357944 kW


## Example Number 29.43, Page Number:1026¶

In [272]:
#variable declaration
n2_by_n1=1.0/2.0
ia2_by_ia1=phi1_by_phi2=1.0/2.0
v2_by_v1=n2_by_n1*phi1_by_phi2
reduction_v=(1-v2_by_v1)*100
reduction_i=(1-ia2_by_ia1)*100

#result
print "percentage reduction in the motor terminal voltage=",reduction_v,"%"
print "percentage fall in the motor current=",reduction_i,"%"

percentage reduction in the motor terminal voltage= 75.0 %
percentage fall in the motor current= 50.0 %


## Example Number 29.44, Page Number:1026¶

In [275]:
#variable declaration
p=6
v=500#V
z=1200
phi=20*0.001#Wb
ra=0.5#ohm
rf=250#ohm
i=20#A
loss=900#W
a=2
#calculation
ish=v/rf
ia=i-ish
eb=v-ia*ra
n=eb*a*60/(p*z*phi)
ta=9.55*eb*ia/n
cu_loss=ia**2*ra
cu_loss_f=v*ish
total_loss=cu_loss+cu_loss_f+loss
input_m=v*i
output=input_m-total_loss
tsh=9.55*output/n
efficiency=output*100/input_m

#result
print "useful torque=",ta,"N-m"
print "output=",output/1000,"Kw"
print "efficiency==",efficiency,"%"

useful torque= 206.28 N-m
output= 7.938 Kw
efficiency== 79.38 %


## Example Number 29.45, Page Number:1027¶

In [280]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
ia1=Symbol('ia1')
output=37.3*1000#W
v=460#V
i=4#A
n=660#rpm
ra=0.3#ohm
rf=270#ohm

#calculations
ish=v/rf
cu_loss=v*ish
ia=i-ish
cu_loss_a=ia**2*ra
input_a=loss=v*ia
ia1=solve(ra*ia1**2-v*ia1+output+loss,ia1)
i=ia1[0]+ish
eb1=v-(ia*ra)
eb2=v-(ia1[0]*ra)
n2=n*eb2/eb1
ia=math.sqrt((cu_loss+input_a)/ra)

#result
print "the current input=",i,"A"
print "speed=",round(n2,0),"rpm"
print "armature current at which efficiency is maximum=",ia,"A"

the current input= 90.2860908863713 A
speed= 623.0 rpm
armature current at which efficiency is maximum= 78.3156008298 A

In [ ]: