# Chapter 3 : Magnetic Circuits¶

## Example 1 : pg 42¶

In [1]:
# Example 3.1;ampere-turns
#calculate the ampere turns required
# given :
from math import pi
bt=([[2],[2.5],[3.0]])#making equations from Table
H=([[400],[600],[800]]);#making equations from Tble
fsl=10**-3;#Flux in Wb
cal=4*10**-4;#area in m**2
#calculations
fdl=fsl/cal;#magnetic field in Tesla
hl=H[1][0];#AT/m
pll=0.57;#lenth in meter (path length 2345)
at2345=pll*hl;#ampere turns
fcl=2*10**-3;#magnetic field in Wb
fdcl=fcl/cal;#in Tesla
hcl=H[0][0];#in AT/m
lcl=169;#length in mm
atcl=(lcl*10**-3)*hcl;#ampere turns
l=1;#length mm
Hl=((4*pi))*10**-7;#AT/m
atrg=fcl/Hl;#AT
tat=at2345+atcl+atrg;#total ampere turns
#results
print "total ampere-turns required is, (AT)=",round(tat,2)
total ampere-turns required is, (AT)= 2001.15

## Example 2 : pg 44¶

In [2]:
# Example 3.2;
#calculate the Kb,Ke,hystresis and eddy current loss
import numpy
# given :
f1=50.;#frequency in Hz
f2=25.;#frequency in Hz
p1=30.1;#power in W
p2=12.4;#power in W
#calculations and results
A=([[f1, f1**2],[f2, f2**2]]);#making equations
B=([[p1],[p2]]);##making equations
X=numpy.dot(numpy.linalg.inv(A),B);#calculating parameters
print "part (a) Kb and Ke"
print "Kh is ", X[0,0]
print "Ke is ",X[1,0]
h25=X[0,0]*f2;#calculating parameters
e25=X[1,0]*f2**2;#calculating parameters
h50=X[0,0]*f1;#calculating parameters
e50=X[1,0]*f1**2;#calculating parameters
print "part (b) hystresis and eddy current loss "
print "hysteresis loss at 25 Hz is , (W)=",h25
print "eddy current loss at 25 Hz is ,(W)=",e25
print "hysteresis loss at 50 Hz is ,(W)=",h50
print "eddy current loss at 50 Hz is ,(W)=",e50
W=40;#kg
h50=X[0,0]*f1;#calculating parameters
e50=X[1,0]*f1**2;#calculating parameters
print "part (c) hystresis and eddy current loss "
print "hysteresis loss per kg at 50 Hz is ,(W)=",h50/W
print "eddy current loss per kg at 50 Hz is ,(W)=",e50/W
part (a) Kb and Ke
Kh is  0.39
Ke is  0.00424
part (b) hystresis and eddy current loss
hysteresis loss at 25 Hz is , (W)= 9.75
eddy current loss at 25 Hz is ,(W)= 2.65
hysteresis loss at 50 Hz is ,(W)= 19.5
eddy current loss at 50 Hz is ,(W)= 10.6
part (c) hystresis and eddy current loss
hysteresis loss per kg at 50 Hz is ,(W)= 0.4875
eddy current loss per kg at 50 Hz is ,(W)= 0.265

## Example 3 : pg 46¶

In [3]:
# Example 3.3;
#Calculate the hystresis  loss per Kg
# given :
l=10.;#lengh in mm
atm=200.;#AT/m
a=4800.;#area in m**2
#calculations
loss=atm*(l*10**-2)*(a/100);#loss in J/m**3/cycle
d=7.8*10**3;#kg/m**3
vikg=1/d;#m**3
loss1=loss*vikg;#J/cycle
f=50;#Hz
tl=loss1*f;#J/s
#results
print "hystersis loss is ,(W/kg)=",round(tl,2)
hystersis loss is ,(W/kg)= 6.15

## Example 4 : pg 52¶

In [4]:
# Example 3.4;amper-turns
#calculate the ampere turn required
# given :
from math import sqrt, pi
r=150.;#length in mm
t=12.;#torque in N-m
#calculations
f=t/(r*10**-3);#force in N
np=2;#no. of poles
fp=f/np;#force per pole in N
A=400.;#area mm**2
mu=4*pi*10**-7;#
b=sqrt((fp*2*mu)/(A*10**-6));#magnetic field in Tesla
H=b/mu;#in AT/m
tar=2*0.6*10**-3;#length in meter
atr=H*tar;#AT
#results
print "ampere turn required is, (AT)=",round(atr,3)
#answer is wrong in the textbook
ampere turn required is, (AT)= 478.731