Systems and methods for vector hysteresis analysis
Systems and methods are provided for analyzing magnetic hysteresis. A reversible component associated with an applied magnetic field is determined for establishing a series-distributed model. One or more hysteresis loops are generated for analyzing magnetic hysteresis of a magnetic material.
1. A processor-implemented system for analyzing magnetic hysteresis of a magnetic material, the system comprising:
one or more data processors configured to:
determine an initial reversible component of a magnetic field applied to a magnetic material based on physical characteristics of the magnetic material that is to be built or modified;
determine a first reversible component based at least in part on the initial reversible component using a vector play model by selecting a specific vector play operator that (1) limits a magnitude of an irreversible component of the magnetic field to a maximum value to ensure that a rotational loss property is maintained in saturation and (2) maintains a correct total field for the determined first reversible component;
determine a flux density; and
generate one or more hysteresis loops based at least in part on the flux density for analyzing magnetic hysteresis of the magnetic material;
a non-transitory computer-readable storage medium configured to store data related to the first reversible component, data related to the flux density, and data related to the hysteresis loops for performing a simulation of behavior of the magnetic material, wherein a physical version of the magnetic material is built or modified based on the simulation.
2. The system of claim 1 , wherein the one or more data processors are further configured to determine the first reversible component using the specific vector play operator as follows:
h
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=
{
h
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0
if
h
k
-
h
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0
<
r
k
(
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)
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-
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where h k represents the magnetic field, h rek0 represents the initial reversible component, h rek represents the first reversible component, h s represents the saturation threshold, and r k represents a radius associated with the irreversible component.
3. The system of claim 2 , wherein:
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k
(
h
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)
=
{
1
1
-
k
μ
σ
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if
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≤
(
h
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)
1
1
-
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if
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;
where σ k represents an intrinsic coercivity for a k-th play hysteron, and k μ represents a parameter associated with slopes of one or more recoil lines.
4. The system of claim 3 , wherein the one or more hysteresis loops include a major hysteresis loop and one or more minor hysteresis loops, the minor hysteresis loops being formed based at least in part on the major hysteresis loop and the one or more recoil lines.
5. The system of claim 3 , wherein the one or more data processors are further configured to determine a slope of a recoil line to be a linear function of a slope of a tangent line of a reversible curve at an intersection with the recoil line, the reversible curve being associated with the first reversible component.
6. The system of claim 3 , wherein the slopes of the one or more recoil lines are the same if k μ is equal to 0.
7. The system of claim 3 , wherein the slopes of the one or more recoil lines are different.
8. The system of claim 2 , wherein the one or more data processors are further configured to determine the first reversible component using an iteration algorithm based at least in part on the specific vector play operator.
9. The system of claim 8 , wherein the iteration algorithm comprises:
1) assuming h rek =h rek0 ;
2) obtaining h irk from r k and a direction of (h k −h rek0 );
3) calculating Δh=h k −(h rek +h irk );
4) letting h rek =h rek +αΔh; and
5) repeating operations 2)-4) until |Δh|/h s <ε,
wherein h irk represents the irreversible component.
10. The system of claim 2 , wherein the one or more data processors are further configured to determine the magnetic field based at least in part on the flux density using the specific vector play operator.
11. The system of claim 2 , wherein the one or more data processors are further configured to determine an irreversible component based at least in part on the first reversible component.
12. The system of claim 11 , wherein the one or more data processors are further configured to determine the irreversible component in the direction of h k −h rek0 with a length of r k .
13. The system of claim 11 , wherein the irreversible component is approximately equal to zero when the magnetic field exceeds a saturation threshold.
14. The system of claim 11 , wherein:
the magnetic field corresponds to a rotating magnetic field; and
a magnetic hysteresis loss of the magnetic field is approximately equal to zero when the magnetic field exceeds the saturation threshold.
15. The system of claim 1 , wherein a maximum value of the irreversible component is selected to equal an intrinsic coercivity value when the reversible component is substantially zero, and wherein the maximum value of the irreversible component is selected to decrease to zero as the reversible component approaches saturation.
16. A processor-implemented system for analyzing magnetic hysteresis of a magnetic material, the system comprising:
one or more data processors configured to:
determine a plurality of flux densities associated with a magnetic material based on physical characteristics of the magnetic material that is to be built or modified;
determine a plurality of first magnetic fields based at least in part on the flux densities;
determine a total magnetic field based on a weighted sum of the first magnetic fields, wherein the total magnetic field is determined according to a series distributed model that indicates fluctuations in the total magnetic field over time as a function of weighted (w) flux densities (b) according to:
h
(
t
)
=
∑
k
=
1
n
w
k
h
k
(
b
)
;
generate one or more hysteresis loops based at least in part on the total magnetic field for analyzing magnetic hysteresis of the magnetic material;
a non-transitory computer-readable storage medium configured to store data related to the flux densities, data related to the first magnetic fields, and data related to the total magnetic field for performing a simulation of behavior of the magnetic material, wherein a physical version of the magnetic material is built or modified based on the simulation.
17. The system of claim 16 , wherein the one or more data processors are further configured to determine the first magnetic fields using an iteration algorithm based on the flux densities.
18. The system of claim 16 , wherein the one or more hysteresis loops include a major hysteresis loop and one or more minor hysteresis loops, the minor hysteresis loops being formed by the major hysteresis loop and one or more recoil lines.
19. The system of claim 18 , wherein the recoil lines correspond to different slopes.
20. The system of claim 18 , wherein the data processors are further configured to identify one or more parameters based at least in part on an input flux density curve and an input hysteresis loop.
21. The system of claim 20 , wherein the one or more parameters include: a simulation flux density curve, information associated with slopes of the recoil lines, and a plurality of weighting factors associated with the first magnetic fields.
22. A processor-implemented method for analyzing magnetic hysteresis of a magnetic material, the method comprising:
determining, using one or more data processors, an initial reversible component of a magnetic field applied to a magnetic material based on physical characteristics of the magnetic material that is to be built or modified;
determining, using the one or more data processors, a first reversible component based at least in part on the initial reversible component using a vector play model by selecting a specific vector play operator that (1) limits a magnitude of an irreversible component of the magnetic field to a maximum value to ensure that a rotational loss property is maintained in saturation and (2) maintains a correct total field for the determined first reversible component;
determining, using the one or more data processors, a flux density; and
generating, using the one or more data processors, one or more hysteresis loops based at least in part on the flux density for analyzing magnetic hysteresis of the magnetic material for performing a simulation of behavior of the magnetic material, wherein a physical version of the magnetic material is built or modified based on the simulation.
23. A processor-implemented method for analyzing magnetic hysteresis of a magnetic material, the method comprising:
determining, using one or more data processors, a plurality of flux densities associated with a magnetic material based on physical characteristics of the magnetic material that is to be built or modified;
determining, using the one or more data processors, a plurality of first magnetic fields based at least in part on the flux densities;
determining, using the one or more data processors, a total magnetic field based on a weighted sum of the first magnetic fields, wherein the total magnetic field is determined according to a series distributed model that indicates fluctuations in the total magnetic field over time as a function of weighted (w) flux densities (b) according to:
h
(
t
)
=
∑
k
=
1
n
w
k
h
k
(
b
)
;
and
generating, using the one or more data processors, one or more hysteresis loops based at least in part on the total magnetic field for analyzing magnetic hysteresis of the magnetic material for performing a simulation of behavior of the magnetic material, wherein a physical version of the magnetic material is built or modified based on the simulation.
24. A non-transitory computer readable storage medium comprising programming instructions for analyzing magnetic hysteresis of a magnetic material, the programming instructions being configured to cause one or more data processors to execute operations comprising:
determining an initial reversible component of a magnetic field applied to a magnetic material based on physical characteristics of the magnetic material that is to be built or modified;
determining a first reversible component based at least in part on the initial reversible component using a vector play model by selecting a specific vector play operator that (1) limits a magnitude of an irreversible component of the magnetic field to a maximum value to ensure that a rotational loss property is maintained in saturation and (2) maintains a correct total field for the determined first reversible component;
determining a flux density; and
generating one or more hysteresis loops based at least in part on the flux density for analyzing magnetic hysteresis of the magnetic material for performing a simulation of behavior of the magnetic material, wherein a physical version of the magnetic material is built or modified based on the simulation.
25. A non-transitory computer readable storage medium comprising programming instructions for analyzing magnetic hysteresis of a magnetic material, the programming instructions being configured to cause one or more data processors to execute operations comprising:
determining a plurality of flux densities associated with a magnetic material based on physical characteristics of the magnetic material that is to be built or modified;
determining a plurality of first magnetic fields based at least in part on the flux densities;
determining a total magnetic field based on a weighted sum of the first magnetic fields, wherein the total magnetic field is determined according to a series distributed model that indicates fluctuations in the total magnetic field over time as a function of weighted (w) flux densities (b) according to:
h
(
t
)
=
∑
k
=
1
n
w
k
h
k
(
b
)
;
generating one or more hysteresis loops based at least in part on the total magnetic field for analyzing magnetic hysteresis of the magnetic material for performing a simulation of behavior of the magnetic material, wherein a physical version of the magnetic material is built or modified based on the simulation.