described by the B-H magnetisation curve (hysteresis loop) as shown
in figure 4.6.
The loop is generated by measuring the magnetic flux B of a
ferromagnetic material while the magnetising force H is changed.
A ferromagnetic material that has never been previously magnetised
or has been thoroughly demagnetised will follow the dashed line as H
is increased. As the line demonstrates, the greater the amount of
current applied (H+), the stronger the magnetic field in the component
(B+). At point “a” almost all of the magnetic domains are aligned and
an additional increase in the magnetising force will produce very
little increase in magnetic flux. The material has reached the point of
magnetic saturation. When H is reduced down to zero, the curve will
move from point "a" to point “b”. At this point, it can be seen that some
magnetic flux remains in the material even though the magnetising force
is zero. This is referred to as the point of retentivity on the graph and
indicates the remanence or level of residual magnetism in the material.
(Some of the magnetic domains remain aligned but some have lost
there alignment.) As the magnetising force is reversed, the curve
moves to point “c”, where the flux has been reduced to zero. This
is called the point of coercivity on the curve. (The reversed magnetising
force has flipped enough of the domains so that the net flux within the
material is zero.) The force required to remove the residual magnetism
from the material, is called the coercive force or coercivity of
the material.
As the magnetising force is increased in the negative direction, the
material will again become magnetically saturated but in the opposite
direction (point “d”). Reducing H to zero brings the curve to point “e”.
It will have a level of residual magnetism equal to that achieved
in the other direction. Increasing H back in the positive direction will
return B to zero. Notice that the curve did not return to the origin of the
graph because some force is required to remove the residual magnetism.
The curve will take a different path from point “f” back to the saturation
point where it completes s the loop. The complete close loop abcdefa is
called as a hysteresis loop. Hard magnetic materials have wider
hysteresis loops as compared to that of soft magnetic materials as
shown in figure 4.7.
ferromagnetic material while the magnetising force H is changed.
A ferromagnetic material that has never been previously magnetised
or has been thoroughly demagnetised will follow the dashed line as H
is increased. As the line demonstrates, the greater the amount of
current applied (H+), the stronger the magnetic field in the component
(B+). At point “a” almost all of the magnetic domains are aligned and
an additional increase in the magnetising force will produce very
little increase in magnetic flux. The material has reached the point of
magnetic saturation. When H is reduced down to zero, the curve will
move from point "a" to point “b”. At this point, it can be seen that some
magnetic flux remains in the material even though the magnetising force
is zero. This is referred to as the point of retentivity on the graph and
indicates the remanence or level of residual magnetism in the material.
(Some of the magnetic domains remain aligned but some have lost
there alignment.) As the magnetising force is reversed, the curve
moves to point “c”, where the flux has been reduced to zero. This
is called the point of coercivity on the curve. (The reversed magnetising
force has flipped enough of the domains so that the net flux within the
material is zero.) The force required to remove the residual magnetism
from the material, is called the coercive force or coercivity of
the material.
As the magnetising force is increased in the negative direction, the
material will again become magnetically saturated but in the opposite
direction (point “d”). Reducing H to zero brings the curve to point “e”.
It will have a level of residual magnetism equal to that achieved
in the other direction. Increasing H back in the positive direction will
return B to zero. Notice that the curve did not return to the origin of the
graph because some force is required to remove the residual magnetism.
The curve will take a different path from point “f” back to the saturation
point where it completes s the loop. The complete close loop abcdefa is
called as a hysteresis loop. Hard magnetic materials have wider
hysteresis loops as compared to that of soft magnetic materials as
shown in figure 4.7.
Source (pdf)
http://www1.mmu.edu.my/~wslim/lecture_notes/Chapter4.pdf
Core Losses
Core losses occur in magnetic cores of
ferromagnetic materials under alternating
magnetic field excitations. The diagram on the
right hand side plots the alternating core losses
of M-36, 0.356 mm steel sheet against the
excitation frequency. In this section, we will
discuss the mechanisms and prediction of
alternating core losses.
As the external magnetic field varies at a very low
rate periodically, as mentioned earlier, due to the
effects of magnetic domain wall motion the B-H
relationship is a hysteresis loop. The area enclosed by the loop
is a power loss known as
the hysteresis loss, and can be calculated by
http://www1.mmu.edu.my/~wslim/lecture_notes/Chapter4.pdf
Core Losses
Core losses occur in magnetic cores of
ferromagnetic materials under alternating
magnetic field excitations. The diagram on the
right hand side plots the alternating core losses
of M-36, 0.356 mm steel sheet against the
excitation frequency. In this section, we will
discuss the mechanisms and prediction of
alternating core losses.
As the external magnetic field varies at a very low
rate periodically, as mentioned earlier, due to the
effects of magnetic domain wall motion the B-H
relationship is a hysteresis loop. The area enclosed by the loop
is a power loss known as
the hysteresis loss, and can be calculated by
For magnetic materials commonly used in the construction of
electric machines an
approximate relation is
electric machines an
approximate relation is
where Ch is a constant determined by the nature of theferromagnetic material, f the frequency of excitation, and Bp the
peak value of the flux density.
Example:
A B-H loop for a type of electric steel sheet is shown in the diagram
below. Determine approximately the hysteresis loss per cycle in a
torus of 300 mm mean diameter and a square cross section of 50*50 mm.
Solution:
The are of each square in the diagram represent
If a square that is more than half within the loop is regarded as totallyenclosed, and one that is more than half outside is disregarded, then
the area of the loop is
Source ( pdf )
http://services.eng.uts.edu.au/cempe/subjects_JGZ/ems/ems_ch7_nt.pdf
http://services.eng.uts.edu.au/cempe/subjects_JGZ/ems/ems_ch7_nt.pdf
Hysteresis loss
When a magnetic material is taken through a cycle of
magnetization, energy is dissipated in the material in the form of
heat. This is known as the hysteresis loss.
Transformers and most electric motors operate on alternating
current. In such devices the flux in the iron changes continuously
both in value and direction. The magnetic domains are therefore
oriented first in one direction, then the other, at a rate that depends
upon the frequency. Thus, if the flux has a frequency of 50 Hz, the
domains describe a complete cycle every 1/50 of a second, passing
successively through peak flux densities +Bm and -Bm as the peak
magnetic field intensity alternates between +Hm and -Hm. If we
plot the flux density B as a function of H, we obtain a closed curve
called hysteresis loop (Fig.1.18). The residual induction Br and
coercive force Hc have the same significance as before.
When a magnetic material is taken through a cycle of
magnetization, energy is dissipated in the material in the form of
heat. This is known as the hysteresis loss.
Transformers and most electric motors operate on alternating
current. In such devices the flux in the iron changes continuously
both in value and direction. The magnetic domains are therefore
oriented first in one direction, then the other, at a rate that depends
upon the frequency. Thus, if the flux has a frequency of 50 Hz, the
domains describe a complete cycle every 1/50 of a second, passing
successively through peak flux densities +Bm and -Bm as the peak
magnetic field intensity alternates between +Hm and -Hm. If we
plot the flux density B as a function of H, we obtain a closed curve
called hysteresis loop (Fig.1.18). The residual induction Br and
coercive force Hc have the same significance as before.
Figure 1.18 Hysteresis loop. If B is expressed in tesla and H in
amperes per meter, the area of the loop is the energy dissipated per
cycle, in joules per kilogram.
In describing a hysteresis loop, the flux moves successively
from +Bm, +Br 0, -Bm, -Br, 0, and +Bm, corresponding respectively
to points a, b, c, d, e, f, and a, of Fig.1.18. The magnetic material
absorbs energy during each cycle and this energy is dissipated as
heat. We can prove that the amount of heat released per cycle
(expressed in J/m3) is equal to the area (in T-A/m) of the hysteresis
loop. To reduce hysteresis losses, we select magnetic materials that
have a narrow hysteresis loop, such as the grain-oriented silicon
steel used in the cores of alternating current transformers.
So the net energy losses/cycle/m3= (hystrisi loop area) Jule
Scale factors of B and H should be taken into considration while
calculating the actual loop area. For example if the scale are 1
cm=x AT/m for H and 1cm=y Wb/m2 for B Then,
Wh = xy* (area of BH loop) Joule / m3 / cycle
It may be shown that the energy loss per unit volume for each
cycle of magnetization is equal to the area of the hysteresis loop.
The area of the loop will depend on the nature of the material and
the value of Bmax (Fig.1.18), and an approximate empirical
relationship discovered by Steinmetz is:
amperes per meter, the area of the loop is the energy dissipated per
cycle, in joules per kilogram.
In describing a hysteresis loop, the flux moves successively
from +Bm, +Br 0, -Bm, -Br, 0, and +Bm, corresponding respectively
to points a, b, c, d, e, f, and a, of Fig.1.18. The magnetic material
absorbs energy during each cycle and this energy is dissipated as
heat. We can prove that the amount of heat released per cycle
(expressed in J/m3) is equal to the area (in T-A/m) of the hysteresis
loop. To reduce hysteresis losses, we select magnetic materials that
have a narrow hysteresis loop, such as the grain-oriented silicon
steel used in the cores of alternating current transformers.
So the net energy losses/cycle/m3= (hystrisi loop area) Jule
Scale factors of B and H should be taken into considration while
calculating the actual loop area. For example if the scale are 1
cm=x AT/m for H and 1cm=y Wb/m2 for B Then,
Wh = xy* (area of BH loop) Joule / m3 / cycle
It may be shown that the energy loss per unit volume for each
cycle of magnetization is equal to the area of the hysteresis loop.
The area of the loop will depend on the nature of the material and
the value of Bmax (Fig.1.18), and an approximate empirical
relationship discovered by Steinmetz is:
In this expression Wh is the loss per unit volume for each cycle of
magnetization; the index n has a value of about 1.6 to 1.8 for many
materials; and the coefficient h
λ is a property of the material, with
typical values of 500 for 4 percent silicon steel and 3000 for cast
iron.
When the material is subjected to an alternating magnetic field of
constant amplitude there will be a constant energy loss per cycle,
and the power absorbed is therefore proportional to the frequency.
Assuming the Steinmetz law, we have the following expression for
the hysteresis loss per unit volume
magnetization; the index n has a value of about 1.6 to 1.8 for many
materials; and the coefficient h
λ is a property of the material, with
typical values of 500 for 4 percent silicon steel and 3000 for cast
iron.
When the material is subjected to an alternating magnetic field of
constant amplitude there will be a constant energy loss per cycle,
and the power absorbed is therefore proportional to the frequency.
Assuming the Steinmetz law, we have the following expression for
the hysteresis loss per unit volume
Where f is the frequency in Hertz.
Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/
Source ( pdf )
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/
MAGNETIC%20CIRCUITS.pdf
from : http://electric-transformers.blogspot.com/2009/03/magnetic-hysteresis-loop.html