WO2015092865A1

WO2015092865A1 - Vector hysteresis analysis method, program therefor, and vector hysteresis analysis device

Info

Publication number: WO2015092865A1
Application number: PCT/JP2013/083719
Authority: WO
Inventors: 李　燦; 宮田　健治; 長谷川　学
Original assignee: 株式会社日立製作所
Priority date: 2013-12-17
Filing date: 2013-12-17
Publication date: 2015-06-25

Abstract

This vector hysteresis analysis method is characterized by using a model that assumes a magnetic material to be an aggregate of micro-magnets, wherein the hysteresis of the magnetic material is analyzed by inputting magnetic characteristic data represented by vectors along a plurality of easy magnetization axes and a plurality of hard magnetization axes and further inputting the proportion of each of the easy magnetization axes and the proportion of each of the hard magnetization axes. This makes it possible to obtain the vector magnetization path corresponding to the history of a given vector magnetic field path.

Description

Vector hysteresis analysis method, program thereof, and vector hysteresis analysis apparatus

The present invention relates to a method for analyzing vector hysteresis of a magnetic material, a program thereof, and a vector hysteresis analyzing apparatus.

The hysteresis phenomenon is a representative physical phenomenon that memorizes past history and governs the behavior after the present. There are two physical movements of A and A 'with different past histories, and A and A' drag past past histories even if they have the same physical quantity and external force works under the same conditions for the future. It is a phenomenon that shows different movements.

In electrical equipment, magnetic materials, especially electromagnetic steel sheets, are often used. Most magnetic materials have hysteresis. In this hysteresis, if the magnetic field is not one-dimensional and has a degree of freedom of the vector, the magnetization appears as a vector. Therefore, the hysteresis is also vector hysteresis.

The details of this vector hysteresis solution are described in Non-Patent Document 1, but until now, it has been used for magnetization analysis using the finite element method and applied to actual equipment. is there.

Patent Documents

1 and 2 disclose magnetic field analysis methods related to vector hysteresis.

Among these, in Patent Document 1, in the modeling of the two-dimensional magnetic characteristics for performing the magnetic field analysis by taking the relationship between the magnetic field strength and the magnetic flux density as a vector quantity, the magnetic flux density, the inclination angle, and the A method is disclosed in which interpolation around a predetermined angle is handled separately when performing coefficient interpolation with respect to the axial ratio.

Patent Document 2 discloses a magnetic field analysis method using two-dimensional magnetic property modeling including a term representing a change due to frequency of a term representing a temporal change in magnetic flux density.

Patent Document 3 discloses a method for analyzing a hysteresis magnetic field in consideration of a minor loop.

Furthermore, Non-Patent Document 2 discloses a method of analyzing hysteresis when a compressive stress and an external magnetic field are applied in the rolling direction of a non-oriented electrical steel sheet using a grain magnetics model (GM model). .

JP 2004-184234 A JP 2004-184233 A Japanese Patent Laid-Open No. 2005-83764

Conventionally, analysis of vector hysteresis appearing in electrical devices including magnetic materials has been complicated and difficult. Even the techniques described in Patent Documents 1 to 3 and

Non-Patent Documents

1 and 2 were not sufficient.

An object of the present invention is to provide a vector hysteresis solution that can analyze the vector hysteresis magnetic characteristics of a magnetic material and can be easily incorporated into a magnetic field analysis.

The vector hysteresis analysis method of the present invention uses a model in which a magnetic material is regarded as an assembly of micro magnets, magnetic property data represented by a vector of a plurality of easy magnetization axes and hard magnetization axes, a magnetization easy axis, and a magnetization difficulty. The distribution ratio of the shaft is input, and the hysteresis of the magnetic material is analyzed.

According to the present invention, when one vector magnetic field trajectory is given, the vector magnetization trajectory corresponding to the history can be obtained from the history of the trajectory. Moreover, since the above transition probability or its cumulative function is expressed in the form of a function, it is suitable for a computer. Therefore, high speed calculation can be realized.

Further, according to the present invention, since vector hysteresis can be predicted, it is possible to optimally design or optimally control an electric device using a magnetic material.

It is a schematic diagram which shows the demagnetization state of the micro magnet in a magnetic body. FIG. 1B is a schematic diagram of a four-axis model in which the micromagnet of FIG. 1A is divided for each direction. It is a graph which shows the transition probability of 180 degree inversion of a micro magnet. It is a graph which shows the accumulation function which is integral of the transition probability of FIG. 2A. It is a graph which shows the transition probability of 90 degree rotation in the case of defining a hard magnetization axis in a direction orthogonal to the easy magnetization axis. It is a graph which shows the accumulation function which is integral of the transition probability of FIG. 3A. It is a graph which shows the transition probability that the magnetization direction of a micro magnet turns to a magnetic field direction when a magnetic field acts strongly in directions other than an easy magnetization axis or a difficult axis. It is a graph which shows the accumulation function which is integral of the transition probability of FIG. 4A. It is a schematic diagram which shows the magnetization easy axis | shaft and its magnetization difficult axis | shaft in a 4-axis model. It is a graph which shows the major loop obtained by the two-dimensional vector hysteresis solution method. It is a graph which shows the whole magnetic field track in an example. FIG. 7B is a graph showing, from the orbit around the origin to the farthest point in the first quadrant, after the orbit around the origin and reaching the farthest point in the third quadrant of the magnetic field trajectory shown in FIG. 7A. FIG. 7B is a graph showing, from the magnetic field trajectory shown in FIG. 7A, after the process of FIG. 7B, after the orbit around the origin from the farthest point in the third quadrant to the farthest point in the first quadrant. 8 is a graph showing a magnetization trajectory obtained from the magnetic field trajectories of FIGS. 7A to 7C. It is a schematic diagram showing a magnetization easy axis and a magnetization difficult axis of a two-dimensional 8-axis model. FIG. 5 is a schematic diagram showing an easy axis of magnetization in the XY plane and its hard axis of magnetization when three two-dimensional four-axis models are overlapped and expanded to three dimensions. It is a schematic diagram showing an easy axis of magnetization in the YZ plane and its hard axis of magnetization when three two-dimensional four-axis models are overlapped and expanded to three dimensions. FIG. 6 is a schematic diagram showing an easy magnetization axis and a hard magnetization axis of a ZX plane when three two-dimensional four-axis models are overlapped and expanded to three dimensions. FIG. 10A is a schematic diagram showing a state in which the easy magnetization axis and the hard magnetization axis of FIGS. 10A to 10C are superimposed. It is a flowchart which shows the procedure which determines the analysis function of the magnetic body data in a vector hysteresis analysis. It is a schematic block diagram which shows the analysis apparatus of vector hysteresis.

In the vector hysteresis solution of the present invention, it is assumed that the magnetic properties of the magnetic material are determined by the collective motion of a group (group) of micro magnets (magnetic domains). And, the easy axis of magnetization of this micromagnet (the most stable state is that the micromagnet is oriented along this axis. Hereinafter, also simply referred to as “easy axis”) has a finite number of directions (for example, four directions). And

Suppose that a micro magnet belongs to one of the representative n easy magnetization axes, so that n magnetic bodies can be handled as a group. In addition, each easy axis has an orthogonal hard axis (hereinafter, also simply referred to as “hard axis”).

Here, the change in magnetization due to the magnetic field includes 180 ° reversal on the easy axis of the micromagnet, 90 ° rotation from the easy axis to the hard axis, or 90 ° from the hard axis to the easy axis, and the magnetic field in the magnetic field direction. Suppose that it consists only of changes by three processes of parallel rotation. Here, the parallel rotation of the magnetic field means that the direction of magnetization of the micro magnet is directed to the direction of the magnetic field when the magnetic field acts strongly in a direction other than the easy magnetization axis or the hard magnetization axis. This is because when the magnetic field is strong, the direction of the magnetic field is energetically stable.

When there is no magnetic field, the micro magnets are in a stable state, so they line up in the positive direction of the easy axis or in the opposite direction (negative direction).

FIG. 1A is a schematic diagram showing a demagnetization state of a micro magnet in a magnetic body. FIG. 1B is a schematic diagram of a four-axis model in which the micromagnet of FIG. 1A is divided into directions.

In FIG. 1A, the micro magnets 1 have magnetization, and the magnetization directions of the respective micro magnets 1 are not determined and are randomly distributed in all directions. This is referred to as a demagnetized state, and the total magnetization of the micro magnets is 0, that is, the macro is a state in which the magnetic material has no magnetization.

In FIG. 1B, the micro magnets 1 of FIG. 1A are grouped into four easy axes 2 (four axes) to form a micro magnet group 101. In each of the micro magnet groups 101, the number of micro magnets 1 having positive and negative magnetizations is theoretically equal. Therefore, also in each easy magnetization axis 2, the total magnetization cancels each other and becomes zero.

When a magnetic field is applied in the direction of the easy magnetization axis, repulsive energy is generated between the micro magnet facing in the opposite direction and the magnetic field, resulting in an unstable state. As instability increases, the micromagnet flips 180 ° and enters a stable state.

180 ° inversion by magnetic field is given as transition probability by magnetic field. When a magnetic field is applied in the direction of the hard magnetization axis, which is perpendicular to the easy magnetization axis, initially it is energetically better to line up in the easy axis direction because of the energy generated from the repulsive force between the magnetic field and the micro magnet. However, when the magnetic field is increased, the micromagnet rotates 90 ° because it rotates 90 ° and becomes more energetically stable toward the hard axis. This is given as the transition probability due to this 90 ° rotating magnetic field. Further, when a strong magnetic field is applied in an arbitrary direction, a micro magnet oriented toward the easy axis and the difficult axis is more energetically stable when oriented in the direction of the magnetic field. This rotation is defined as a parallel magnetic field rotation and given as a transition probability.

It is possible to obtain a magnetization vector for a magnetic field vector in one easy magnetization axis among n easy magnetization axes by giving a transition probability or a cumulative function that is an integral function thereof. Thereby, the magnetization vector in each of n easy magnetization axes is calculated | required, and the sum total becomes a magnetization vector of a magnetic body.

従う Following the above procedure gives a solution for vector hysteresis.

More specific description will be given below.

When a magnetic material is magnetized, there is an upper limit for no further magnetization, and the magnetization is called saturation magnetization (hereinafter referred to as Ms). The magnetic field at that time is a saturation magnetic field (Hs). Here, when it is not necessary, (Hs, Ms) = (1, 1) is standardized and an embodiment will be described.

FIG. 2A is a graph showing the transition probability of the 180 ° inversion of the micro magnet.

In this figure, it is considered that there are two typical states for one of the easy magnetization axes shown in FIG. 1B. One state is a state in which the magnetic field is -1 and works in the negative direction of the easy axis, and the micro magnets are aligned in the negative direction. This state is set to -1. The other state is a state where the magnetic field is 1 and works in the positive axis direction, and the micro magnets are aligned in the positive direction.

In this case, when the magnetic field continuously changes from −1 to 1, the micro magnet is reversed by 180 °, and the magnetization changes from −1 to 1. The transition probability in this case is indicated by a solid line in FIG. 2A.

On the other hand, when the magnetic field changes from 1 to −1, the magnetization of the micromagnet reverses 180 ° in the easy axis negative direction. That is, the magnetization changes from 1 to -1. The transition probability in this case is indicated by a broken line in FIG. 2A.

FIG. 2B shows the process of FIG. 2A as a sum of the ratios of the micro magnets.

The solid line shown in this figure is also called ascending curve, and the broken line is also called descending curve. Here, if a function representing an ascending curve is defined as fD (h), the descending curve becomes −fD (−h).

The situation at 90 ° rotation is different from 180 ° inversion.

FIG. 3A is a graph showing the transition probability of 90 ° rotation when a hard magnetization axis is defined in a direction orthogonal to the easy magnetization axis. FIG. 3B is a graph showing a cumulative function that is an integral of the transition probability of FIG. 3A.

As shown in FIG. 3A, a hard magnetization axis 4 is defined in a direction orthogonal to the easy magnetization axis 2. When a magnetic field 3 (magnetic field is -1) is applied in the direction opposite to the hard axis 4, the micro magnet faces the direction of the magnetic field 3. This state is set to -1. When the magnetic field 3 is changed to 1 which is the positive direction from here, the micro magnet rotates 90 ° and faces the direction of the easy magnetization axis 2. A state in which all the micro magnets are in the easy axial direction is defined as a zero state.

From this state, when the magnetic field 3 is increased in the hard axis direction, the micro magnet starts to rotate 90 ° in the hard axis direction. When the value of the magnetic field 3 becomes 1, the entire micro magnets are aligned in the hard axis direction. This state is set to 1.

The cumulative function that is the result of integrating such a process is the solid line in FIG. 3B. On the other hand, when the opposite process is followed, the process becomes a broken line in FIG. 3A, and the cumulative function in this case is the broken line in FIG. 3B. If the rising curve function in FIG. 3B is defined as fDt (h), the falling curve is again −fDt (−h).

FIG. 4A shows the transition probability of the parallel rotation of the magnetic field. In the parallel rotation of the magnetic field, when the magnetic field works strongly in a direction other than the easy axis or the hard axis, the micro magnet is energetically oriented in the magnetic field direction because the magnetic field is stronger than the easy axis or the hard axis. Is more stable.

The solid line shown in this figure is the probability of rotating in the magnetization direction when the magnetic field increases, and the broken line is the probability of rotating in the easy axis direction from the state 1 where the magnetic field decreases.

FIG. 4B shows a cumulative function of the transition probability of FIG. 4A.

Unlike the 180 ° reversal or 90 ° rotation, the ascending curve and the descending curve of the magnetic field parallel rotation are not point-symmetric and are defined respectively. The rising curve function is defined as frotR (h), and the falling curve function is defined as frotL (h).

As described above, the transition probabilities of 180 ° reversal, 90 ° rotation, and magnetic field parallel rotation, and their cumulative functions could be prepared. In the following, a solution method for vector hysteresis is constructed when four easy magnetization axes are used.

FIG. 5 shows the unit vector dD _i of the i-magnetization easy axis and the unit vector dDt _i of the hard axis of the 4-axis model. dD _i is given as the following formula (1) and the hard axis is rotated 90 ° to the easy axis in the counterclockwise direction. This example is a 4-axis model, where i is an integer from 1 to 4.

Determine the distribution ratio of each easy axis. When the distribution ratio is cO _i , the following formula (2) must be satisfied.

The magnetic saturation field and the saturation magnetization (Hs, Ms), 2-dimensional magnetic field trajectories _{_{... H j-1, H j}} , H j + 1, when given as ..., the i- easy axis in the magnetic field _{H j} The magnetization _mi is obtained according to the following equations (3) to (16).

Here, MEMO (hD, hDpst _i , mDpst _i ) is calculated from the past magnetic field, magnetization (hDpst _i , mDpst _i ), and current magnetic field hD (HiDt _i , MiDt _i ), (HfDt _i ). , MfDt _i ) and dirDt _i = 1 if the magnetic field increase direction (hDtpst _i <hDt) and dirDt _i = −1 if the magnetic field decrease direction (hDtpst _i > hDt) is there. When there is no change in the magnetic field, the magnetization value at the previous time may be given.

FD and FDt of the above equation (11) are given by the following equations (17) and (18) by using the information on the branch point and the cumulative function.

The coefficients a, b, α, and β in the above formulas (14) and (15) are derived from the following physical requirements.

The micro-magnetization that faces the easy axis and the magnetization that faces the hard axis must satisfy the following formula (19). This equation is necessary to match the actual magnetization.

The remaining parallel rotation of the magnetic field is given by the following equations (20) to (24).

The parallel rotation of the magnetic field is a ratio that is directed to the direction of the magnetic field, and thus is related only to the magnitude of the magnetic field regardless of the direction of the magnetic field. Therefore, it is the same as scalar hysteresis.

The function FR (hrot, Hi, Mi, Hf, Mf, dir) is given by the following equation (25).

By calculating these equations, the magnetization M _j is obtained by the following equation (26) using the current magnetic field H _j from the past magnetic fields H _j−1 and M _j−1 .

When the magnetic body is isotropic, the distribution ratio cO _i of each easy axis is the same, so cO _i = 0.25 is substituted. For the coefficients a, b, α, and β in the equations (14) and (15), a = 0, b = 1, α = 1, and β = 1 are substituted. Further, (6000 (A / m), 1.8 (T)) is used as the saturation magnetic field Hs and the saturation magnetization Ms.

Here, the magnetic field trajectory starts from (Hx, Hy) = (0, 0), reaches the saturation point (Hx, Hy) = (6000, 0) in the x-axis positive direction, and returns to the saturation point in the negative x-axis direction ( The magnetic field trajectory is moved to Hx, Hy) = (− 6000,0) and returned to the saturation point (Hx, Hy) = (6000,0).

The magnetization trajectory on the magnetic field trajectory can be obtained using the above equations (2) to (18) and (20) to (26) and coefficients.

FIG. 6 shows the relationship between Hx and Mx described above. In this figure, a magnetization curve (major loop) including a saturation point of magnetization due to a magnetic field is shown.

Next, the results of studying whether the above solution represents a past history under the above conditions will be shown.

FIG. 7A shows the entire magnetic field trajectory. FIG. 7B starts from (Hx, Hy) = (0, 0), turns back at (285.83, 39.45), rotates around (0, 0), and then (−2858.83, −39. 45) shows the trajectory to reach. 7C moves from (−2858.83, −39.45) to the vicinity of (0,0) after passing through the trajectory of FIG. 7B, and after rotating, traces to (285.83, 39.45). It shows the trajectory to arrive.

FIG. 8 shows the magnetization trajectories corresponding to the trajectories shown in FIGS. 7A to 7C, using the above calculation formulas and conditions. In FIG. 8, the solid line corresponds to FIG. 7B, and the broken line corresponds to FIG. 7C.

In FIG. 8, Mx = 1.5T, and the magnetic field rotated near (0,0) rotates around (0.75,0), and Mx = −1.5T. It can be seen that a magnetic field rotated in the vicinity of (0,0) rotates the magnetization around (−0.75, 0). The rotation of both magnetic field trajectories is near (0, 0), but the former rotates around (0.75, 0) because of the history of reaching Mx = 1.5T, and the latter is Mx = −. Rotate around (-0.75, 0) by the history up to 1.5T. This shows that the solution of the present invention is effective.

In Example 1, four axes of easy magnetization were used, but here the case of eight axes is shown.

FIG. 9 shows the easy axis and the hard axis in the 8-axis model. dD _i is given by the following equation (27).

Also in this model, since the above equation (2) holds, when the magnetic material is isotropic, the distribution ratio is cO _j = 0.125 which is half of the 4-axis model.

The application of other mathematical expressions is the same as in the first embodiment.

Next, the 3D model will be described.

In the two-dimensional model, the easy magnetization axis and the hard magnetization axis are on a two-dimensional space (plane). The limitation is the same in three dimensions. Therefore, in order to expand to three dimensions, three planes XY, YZ, and XZ must be prepared.

In this embodiment, three two-dimensional four-axis models shown in FIGS. 10A to 10C are overlapped and expanded to a three-dimensional space shown in FIG. 10D.

In this case, the above formula (2) is also applied. Therefore, the distribution ratio must satisfy the following formula (28).

To summarize the above explanation, the outline of the process of the vector hysteresis analysis method is as follows.

容易 Classify the easy axis of the micro magnet into a finite number of directions (step 1).

Suppose the distribution ratio or transition probability of the easy axis or its cumulative function (step 2).

If the transition probability is assumed, the cumulative function is calculated by integration (step 3).

In step 3, with respect to the change in magnetization due to the magnetic field, 180 ° inversion on the easy axis of the micromagnet, 90 ° rotation from the easy axis to the hard axis, or 90 ° from the hard axis to the easy axis, and in the magnetic field direction. Assuming that the change is due to three processes of parallel rotation of the magnetic field, a cumulative function is calculated from the transition probabilities for these processes.

The three cumulative functions are combined and a magnetization curve (major loop) including a saturation point of magnetization due to the magnetic field is calculated by fitting or function processing S104 of FIG. 11 described later (step 4).

マイナー Calculate the minor loop based on the major loop (step 5).

In step 5, a minor loop that does not include the origin (0, 0) can also be calculated.

These steps may be a computer readable program.

Also, these steps can be processed using an analysis device. Specifically, the analysis device includes a data holding unit and a calculation unit. Here, the data holding unit records numerical data of a model in which a magnetic body is regarded as an assembly of micro magnets, and magnetic characteristic data represented by vectors of a plurality of easy magnetization axes and hard magnetization axes. This analyzes the hysteresis of a magnetic substance from magnetic characteristic data and the distribution ratio of the easy magnetization axis and the hard magnetization axis.

The process of determining a vector hysteresis analysis function for analyzing vector hysteresis will be described with reference to a flowchart.

FIG. 11 is a flowchart for determining an analysis function of magnetic material data in vector hysteresis analysis.

In this figure, when starting the vector hysteresis analysis, first, the magnetic data and the number of axes of the magnetic material to be analyzed are input (S101). In the case of magnetic steel sheets, magnetic data must have major loops in the RD (rolling direction) and TD (rolling orthogonal direction) directions. Enter the trajectory. If it is not a magnetic steel sheet, it is possible with a single major loop in the case of an isotropic magnetic body, but in the case of a magnetic body with anisotropy, if it is a two-dimensional body, the x-axis and y-axis are defined, Enter the major loop for those axes. If it is 3D, enter the z-axis major loop. If there is a magnetization trajectory for the rotating magnetic field, the data is also input.

Next, the input data is processed (S102) and displayed on the display (S103). Processing the input data includes, for example, determining the saturation magnetic field and magnetization in each direction, or allowing the user to determine whether to confirm the input by input, and the saturation magnetic field and magnetization as shown in FIGS. 1B, 2B, and 3B. Use to standardize. In the rotating magnetic field, processing is performed so that the delay angle of magnetization with respect to each rotating magnetic field can be displayed.

When the data is confirmed, proceed to the next stage.

In S104, each function is called from the storage device 50 that has previously stored the probability function shown in FIGS. 1A to 3B or a cumulative function group thereof, 180 ° reversal, 90 ° rotation and magnetic field parallel rotation function, The cO _{i in} 28) and (26) and the correlation coefficients a and b in the above equations (14) and (15) are calculated according to a preprogrammed routine so as to match the input data as much as possible.

In this case, a function determinant is prepared in the input data. The deterministic coefficient is a numerical value input by the user. If the value calculated from the measure function that digitizes the difference of the decision function from the input data is smaller than the deterministic coefficient, the next step will be taken. If larger, the error function will contribute to the error. Measure the degree, readjust the decision function in the direction of decreasing its contribution, and repeat until it becomes smaller than the deterministic coefficient (S105).

Next, calculation is performed from the decision function such as the major loop and the delay angle displayed on the display (S103) by the input data processing (S106).

The calculated result is displayed on the display in comparison with the input data (S107). The user compares with the display and determines whether or not the vector hysteresis function is valid (S108).

If it is determined that it is sufficient, a decision function is output (S109), and the analysis is terminated (S110). On the other hand, if it is determined that it is insufficient, the user returns to S104, prepares a routine for redefining and calculating the deterministic coefficient, or a routine for readjusting the error contribution, and performs the processing from S105 onward.

In the process shown in the figure, a vector hysteresis function according to the model of the present invention corresponding to one magnetic material is defined.

In this way, it becomes possible to incorporate into the model the vector hysteresis magnetic characteristics of the magnetic material used for the intended dynamic magnetic field analysis.

After this, as in Patent Document 3, the dynamic magnetic field analysis incorporating the above model may be used to perform analysis with a system desired to be analyzed.

FIG. 12 is a schematic configuration diagram showing a vector hysteresis analyzing apparatus.

In this figure, the analysis device 200 includes a central processing unit 201 (CPU), a storage device 202, an input interface 203, a display device 204, and an input device 205 (for example, a keyboard or a mouse). The central processing unit 201 and the storage device 202 are connected to the display device 204 and the input device 205 via the input interface 203.

In the storage device 202, the processing procedure of the vector hysteresis analysis method shown in FIG. 11, the equations used to calculate the physical quantity to be analyzed, and control data for controlling the analysis process are stored in advance. The processing procedure of the vector hysteresis analysis is programmed and stored in the storage device 202. The storage device 202 is a recording medium that can be read by the central processing unit 201.

If the vector hysteresis solution of the present invention is used, the vector hysteresis can be predicted in the design of an electric device using a magnetic material, for example, a transformer, a motor, a generator, etc., so that optimum design or optimum control becomes possible.

1: Micro magnet, 2: Easy magnetization axis, 3: Magnetic field, 4: Hard magnetization axis.

Claims

Using a model in which a magnetic material is regarded as an assembly of micro magnets, magnetic property data represented by a vector of a plurality of easy magnetization axes and hard magnetization axes, and a distribution ratio of the easy magnetization axes and the hard magnetization axes are input. An analysis method of vector hysteresis characterized by analyzing hysteresis of a magnetic material.
The magnetic property data includes a magnetization curve including a saturation point of magnetization due to a magnetic field in at least one direction, and further includes a step of correcting the distribution ratio or transition probability of the easy axis or a cumulative function thereof. The method of analyzing vector hysteresis according to claim 1.
The magnetic characteristic data includes a magnetization trajectory for a rotating magnetic field trajectory having at least one constant magnitude, and further includes a step of correcting the distribution ratio or transition probability of the easy axis or a cumulative function thereof. The vector hysteresis analysis method according to claim 1, wherein:
4. The method for analyzing vector hysteresis according to claim 1, wherein the magnetic characteristic data includes a magnetic field that is an independent variable and magnetization that is a dependent variable.
A program used for analysis of vector hysteresis, wherein the computer uses a model in which a magnetic body is regarded as an assembly of micromagnets, magnetic property data represented by vectors of a plurality of easy magnetization axes and hard magnetization axes, and the magnetization A program for executing a procedure for inputting an easy axis and a distribution ratio of the hard-to-magnetize axis, and a procedure for analyzing hysteresis of a magnetic material.
The magnetic property data includes a magnetization curve including a saturation point of magnetization caused by a magnetic field in at least one direction, and the computer further includes a procedure for correcting the distribution ratio or transition probability of the easy axis or a cumulative function thereof. The program according to claim 5 for execution.
The magnetic property data includes a magnetization trajectory with respect to a rotating magnetic field trajectory having at least one constant magnitude, and further executes a procedure for correcting the distribution ratio or transition probability of the easy axis or a cumulative function thereof. The program according to claim 5 for causing the program to occur.
The program according to any one of claims 5 to 7, wherein the magnetic characteristic data includes a magnetic field as an independent variable and magnetization as a dependent variable.
A data holding unit that records numerical data of a model in which a magnetic body is regarded as an assembly of micromagnets and a vector of a plurality of easy magnetization axes and hard magnetization axes, the magnetic characteristic data, and the easy magnetization axis And a calculation unit for analyzing the hysteresis of the magnetic material from the distribution ratio of the hard magnetization axis.
The magnetic property data includes a magnetization curve including a saturation point of magnetization due to a magnetic field in at least one direction, and the calculation unit further corrects the distribution ratio or transition probability of the easy axis or a cumulative function thereof. The vector hysteresis analyzing apparatus according to claim 9, wherein:
The magnetic property data includes a magnetization trajectory for a rotating magnetic field trajectory having at least one constant magnitude, and the calculation unit further corrects the distribution ratio or transition probability of the easy magnetization axis or a cumulative function thereof. The vector hysteresis analyzing apparatus according to claim 9.
12. The vector hysteresis analyzing apparatus according to claim 9, wherein the magnetic property data includes a magnetic field as an independent variable and magnetization as a dependent variable.