# Chapter 31: Testing of DC Machines¶

## Example Number 31.1, Page Number:1092¶

In [1]:
#variable declaration
l=38.1#kg
d=63.53*0.01#cm
v=12#rps
i=49#A
V=220#V

#calculations
r=d/2
torque=l*r*9.81
power=torque*2*3.14*v
motor_input=i*V
efficiency=power*100/motor_input

#result
print "Output power=",round(power),"W"
print "Efficiency=",round(efficiency),"%"

Output power= 8947.0 W
Efficiency= 83.0 %


## Example Number 31.2(a), Page Number:1093¶

In [9]:
#variable declaration
spring_b1=10.0#kg
spring_b2=35.0#kg
d=40*0.01#m
v=950.0#rpm
V=200.0#V
i=30.0#A

#calculations
F=(spring_b2-spring_b1)*9.81
N=v/60
R=d/2
tsh=F*R
omega=2*3.14*N
output=tsh*omega
motor_input=V*i
efficiency=output/motor_input

#result
print "output power=",output,"W"
print "efficiency=",efficiency*100,"%"

output power= 4877.205 W
efficiency= 81.28675 %


## Example Number 31.2(b), Page Number:1093¶

In [15]:
#variable declaration
t1=2.9#kg
t2=0.17#kg
r=7*0.01#m
i=2.0#A
V=230.0#V
n=1500.0#rpm

#calculations
force=(t1-t2)*9.81
torque=force*r
output=torque*2*3.14*n/60
efficiency=output/(V*i)

#result
print "torque=",torque,"N-m"
print "output",output,"W"
print "efficiency",efficiency*100,"%"

torque= 1.874691 N-m
output 294.326487 W
efficiency 63.984018913 %


## Example Number 31.3, Page Number:1095¶

In [22]:
#variable declaration
V=220.0#V
i=2.5#A
ra=0.8#ohm
rsh=200.0#ohm
I=20.0#A

#calculations
ish=V/rsh
ia0=i-ish
culoss=ia0**2*ra
ia=32-ish
cu_lossa=ia**2*ra
total_loss=cu_lossa+constant_loss
input_=V*I
output=input_-total_loss
efficiency=(output/input_)*100

#result
print "Efficiency=",efficiency,"%"

Efficiency= 70.1754545455 %


## Example Number 31.4, Page Number:1096¶

In [38]:
import math
#variable declaration
V=400.0#V
i=5.0#A
ra=0.5#ohm
r=200.0#ohm
I=50.0#A

#calculations
input_nl=V*i
ish=V/r
ia=i-ish
cu_loss=ia**2*ra
constant_loss=input_nl-cu_loss
Ia=I-ish
cu_lossa=Ia**2*ra
total_loss=constant_loss+cu_lossa
input_nl1=V*I
output=input_nl1-total_loss
efficiency=output/input_nl
Eb1=V-(ia*ra)
Eb2=V-(Ia*ra)
change=math.fabs((Eb1-Eb2)/Eb1)

#result
print "output=",output,"W"
print "efficiency=",efficiency*10,"%"
print "percentage change in speed=",change*100,"%"

output= 16852.5 W
efficiency= 84.2625 %
percentage change in speed= 5.64617314931 %


## Example Number 31.5, Page Number:1096¶

In [15]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
I=Symbol('I')
v=220#V
p=44.76#kW
i=13.25#A
ish=2.55#A
ra=0.032#ohm
bd=2#V

#calculations
p_nl=v*i
ia=i-ish
cu_loss=ia**2*ra
bd_loss=2*ia
variable_loss=bd_loss+cu_loss
w=p_nl-variable_loss
ans=solve([v*(I+ish)-p*1000-w-2*I-ra*I**2],[I])
il=ans[0][0]+ish
pin=il*v
e=p*1000/pin

#result

Full load current= 226.0 A


## Example Number 31.6, Page Number:1097¶

In [23]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
I=Symbol('I')
v=200.0#V
o=17.158#kW
inpt=20.2#KW
rf=50.0#ohm
ra=0.06#ohm
o2=7.46#kW

#calculations
loss1=inpt*1000.0-o*1000.0
ic=inpt*1000.0/v
ish=v/rf
ia=ic-ish
cu_loss=ia**2*ra
const_loss=loss1-cu_loss
ans=solve([v*(I+ish)-o2*1000.0-(ra*I**2)-const_loss],[I])
il=ans[0][0]+ish
pin=il*v/1000.0
e=o2*1000*100/(pin*1000)

#result
print "efficiency=",round(e,1),"%"
print "power input=",round(il),"A"

efficiency= 74.1 %
power input= 50.0 A


## Example Number 31.7, Page Number:1097¶

In [1]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
I=Symbol('I')
v=200.0#V
p=14.92#kW
ia=6.5#A
ish=2.2#A
i=70.0#A
pd=3.0#V

#calculations
ic_nl=ia+ish
pi=v*ic_nl
cu_loss=v*ish
cu_lossa=ia**2*pd/i
const_loss=pi-cu_lossa
ans=solve([v*I+cu_loss-p*1000-const_loss-(pd/i)*I**2],[I])
ic=ans[0][0]+ish
pin=v*ic
e=p*1000*100/pin

#result
print "efficiency=",round(e),"%"

efficiency= 88.0 %


## Example Number 31.8, Page Number:1098¶

In [42]:
#variable declaration
p=200*1000.0#W
v=250.0#V
i1=36.0#A
I1=12.0#A
v1=250.0#V
pd=6.0#V
i2=400.0#A

#calculations
ia=i1-I1
ra=pd/i2
cu_loss=ia**2*ra
input_nl=v*i1
constant_loss=input_nl-cu_loss

output_i=p/v
ia=output_i+I1
cu_lossa=ia**2*ra
total_loss=cu_lossa+constant_loss
efficiency=p/(p+total_loss)
#result

output_i=p/(2*v)
ia=output_i+I1
cu_lossa=ia**2*ra
total_loss=cu_lossa+constant_loss
efficiency=p/((p/2+total_loss)*2)

#result

efficiency at full load= 91.3736344667 %
efficiency at half load= 89.6559292335 %


## Example Number 31.9, Page Number:1098¶

In [48]:
#variable declaration
v=250.0#V
p=14.92*1000#W
e=0.88
n=700.0#rpn
rsh=100.0#ohm
i=78.0#A

#calculations
input_=0.8*p/e
total_loss=input_-0.8*p
input_i=input_/v
ish=v/rsh
ia=input_i-ish
ra=total_loss/(2*(ia**2))
Ia=i-ish
total_loss2=Ia**2*ra+total_loss/2
input__=v*i
efficiency=(input__-total_loss2)*100/input__
Eb1=v-(ia*ra)
Eb2=v-(Ia*ra)
n2=(n*Eb2)/Eb1

#result
print "efficiency=",efficiency,"%"
print "speed=",n2,"r.p.m"

efficiency= 86.9450046554 %
speed= 678.443304738 r.p.m


## Example Number 31.10(a), Page Number:1101¶

In [2]:
import math
#variable declaration
v=220.0#V
p=100*1000.0#W
i2=90.0#A

#calculations
i1=p/v
efficiency=math.sqrt(i1/(i1+i2))*100

#result
print "efficiency=",round(efficiency,1),"%"

efficiency= 91.4 %


## Example Number 31.11, Page Number:1102¶

In [52]:
#variable declaration
i=15#A
v=200#V
motor_i=100#A
shunt_i1=3#A
shunt_i2=2.5#A
ra=0.05#ohm
cu_loss=500#W
cu_lossa=361#W
ia=85#A
#calculations
mech_core_stray_loss=0.5*((v*i)-(motor_i**2*ra)-(ia**2*ra))
cu_motor=v*shunt_i1
generator_motor=v*shunt_i2
total_loss=mech_core_stray_loss+cu_motor+generator_motor
input_=v*i+cu_motor
output=v*ia*10**(-3)
loss=cu_loss*10**(-3)+1.07+0.36
efficiency=output*100/(output+loss)

#result
print "eficiency=",efficiency,"%"

eficiency= 89.8045430534 %


## Example Number 31.12, Page Number:1103¶

In [56]:
#variable declaration
v=110#V
i=48#A
i1=3#a
i2=3.5#A
motor_i=230#A
ra=0.035#ohm

#calculations
#motor
cu_loss=motor_i**2*ra
brush_loss=motor_i*2
totalarm_culoss=cu_loss+brush_loss
shunt_cu=v*i1
total_cu_lossm=totalarm_culoss+shunt_cu
#generator
arm_i=233-i+i2
cu_loss=arm_i**2*ra
brush_loss=arm_i*2
totalarm_culoss=cu_loss+brush_loss
shunt_cu=v*i2
total_cu_lossg=totalarm_culoss+shunt_cu
#set
totalcu_loss=total_cu_lossm+total_cu_lossg
total_input=v*i
stray_loss=total_input-totalcu_loss
strayloss_per=stray_loss/2
#motor efficiency
input_=233*v
output=input_-(total_cu_lossm+strayloss_per)
e=output/input_*100
print "motor efficiency=",e,"%"
#generator efficiency
input_=110*185
output=input_-(total_cu_lossg+strayloss_per)
e=output/input_*100
100
print "generator efficiency=",e,"%"

motor efficiency= 88.4590884705 %
generator efficiency= 88.5893642506 %


## Example Number 31.13, Page Number:1103¶

In [58]:
#variable series
v=500.0#A
p=100*1000.0#w
auxiliary_i=30.0#A
output_i=200.0#A
i1=3.5#A
i2=1.8#A
ra=0.075#ohm
vdb=2.0#V

#calculations
motor_arm=output_i+auxiliary_i
motorarm_culoss=(motor_arm**2*ra)+(motor_arm*2)
motorfield_culoss=v*i2
generatorarm_culoss=(output_i**2*ra)+(output_i*2)
generatoefield_culoss=v*i1
total_culoss=motorarm_culoss+motorfield_culoss+generatorarm_culoss+generatoefield_culoss
power=v*auxiliary_i
stray_loss=power-total_culoss
permachine=stray_loss/2
total_loss=generatorarm_culoss+generatoefield_culoss+permachine
output=v*output_i
e=output/(output+total_loss)

#result
print "efficiency=",e*100,"%"

efficiency= 93.1001175389 %


## Example Number 31.14, Page Number:1104¶

In [77]:
#variable declaration
v=250.0#V
i=50.0#A
motor_i=400.0#A
i1=6.0#A
i2=5.0#A
ra=0.015#ohm

#calculations
motora_culoss=motor_i**2*ra
generatora_culoss=(motor_i-i)**2*ra
power=v*i
stray_loss=power-(motora_culoss+generatora_culoss)
permachine=stray_loss/2
#motor
total_motor_loss=motora_culoss+(v*i2)+permachine
motor_input=(v*motor_i)+v*i2
motor_e=(motor_input-total_motor_loss)/motor_input

#generator
total_gen_loss=generatora_culoss+(v*i1)+permachine
gen_output=v*(motor_i-i)
gen_e=(gen_output-total_gen_loss)/gen_output

#result
print "motor efficiency=",motor_e*100,"%"
print "generator efficiency",gen_e*100,"%"

motor efficiency= 92.3148148148 %
generator efficiency 91.4642857143 %


## Example Number 31.15, Page Number:1105¶

In [81]:
#variable declaration
v=250.0#V
i=50.0#A
ia=380.0#A
i1=5.0#A
i2=4.2#A
ra=0.2#ohm

#calculations
motora_culoss=ia**2*ra
generatora_culoss=(ia-i)**2*ra
power=v*i
stray_loss=power-(motora_culoss+generatora_culoss)
permachine=stray_loss/2
#motor
total_motor_loss=motora_culoss+(v*i2)+permachine
motor_input=(v*ia)+v*i2
motor_e=(motor_input-total_motor_loss)/motor_input

#generator
total_gen_loss=generatora_culoss+(v*i1)+permachine
gen_output=v*(ia-i)
gen_e=(gen_output-total_gen_loss)/gen_output

#result
print "motor efficiency=",motor_e*100,"%"
print "generator efficiency",gen_e*100,"%"

motor efficiency= 88.7038001041 %
generator efficiency 95.2121212121 %


## Example Number 31.16, Page Number:1107¶

In [85]:
#variable declaration
v=220.0#V
v2=190.0#V
t=30#sec
t2=20#sec
i=20.0#A

#calculations
avg_v=(v+v2)/2
avg_i=i/2
power=avg_v*avg_i
W=power*(t2/(t-t2))

#result
print "Stray loss=",W,"W"

Stray loss= 4100.0 W


## Example Number 31.17, Page Number:1107¶

In [3]:
#variabledeclaration
n1=1525.0#rpm
n2=1475.0#ohm
dt=25.0#sec
p=1000.0#W
t2=20.0#sec

#calculations
N=(n1+n2)/2
w=p*(t2/(dt-t2))
dN=n1-n2
I=(w*dt)/((2*3.14/60)**2*N*dN)

#result
print "Moment of Inertia=",I,"kg-m2"

Moment of Inertia= 121.708791432 kg-m2


## Example Number 31.18, Page Number:1108¶

In [97]:
#variable declaration
v=240.0#V
v2=225.0#V
dt=25.0#sec
t2=6.0#ohm
iavg=10.0#A
i2=25.0#A
v3=250.0#V
ra=0.4#ohm
r=250.0#ohm

#calculations
avg_v=(v+v2)/2
w_=avg_v*iavg
W=w_*(t2/(dt-t2))
ish=v3/r
ia=i2-ish
cu_loss=ia**2*ra
cu_shunt=v3*ia
total_loss=W+cu_loss+v3
e=((v*i2)-total_loss)/(v*i2)

#result
print "efficiency=",e*100,"%"

734.210526316
efficiency= 79.7564912281 %


## Example Number 31.19, Page Number:1108¶

In [99]:
#variable declaration
n=1000#rpm
n1=1030#rpm
n2=970#rpm
t1=36#sec
t2=15#sec
t3=9#sec
i=10#A
v=219#V

#calculations
W=v*i*(t2/(dt-t2))
dN=n1-n2
I=(W*t2)/((2*3.14/60)**2*n*dN)
Wm=W*t2/t1
iron_loss=W-Wm

#result
print "i)moment of inertia=",I,"kg.m2"
print "ii)iron loss=",iron_loss,"W"
print "iii)mechanical losses=",Wm,"W"

i)moment of inertia= 74.9650087225 kg.m2
ii)iron loss= 1916.25 W
iii)mechanical losses= 1368.75 W


## Example Number 31.20, Page Number:1110¶

In [115]:
#variable declaration
iam=56.0#A
vam=590.0#V
vdm=40.0#V
iag=44.0#A
vag=400.0#V
vdg=40.0#V
r=0.3#ohm

#calculations
input_total=(vdm+vam)*iam
output=vag*iag
total_loss=input_total-output
rse=vdg/iam
cu_loss=((r+2*rse)*iam**2)+(iag**2*r)
strayloss=total_loss-cu_loss
permachine=strayloss/2
#motor
inputm=vam*iam
culossm=(r+rse)*iam**2
totallossm=culossm+permachine
output=inputm-totallossm
em=output*100/inputm
#generator
inputg=vag*iag
culossg=(r)*iag**2
totalloss=culossg+permachine+(vdm*iam)
output=vag*iag
eg=output*100/(output+totalloss)

print
#result
print "motor efficiency=",em,"%"
print "generator efficiency=",eg,"%"

motor efficiency= 72.6997578692 %
generator efficiency= 67.0220868241 %