JP2008039709A - Vector hysteresis magnetic field analysis method, vector hysteresis magnetic field analysis program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a precise, high-speed vector hysteresis magnetic field analysis method requiring only less amount of memory. <P>SOLUTION: In a magnetic field analysis equation, related to magnetic vector potential with a magnetization vector as a source term, the estimation magnetization vector at certain time, is set, the amount of variation of the magnetic vector potential is obtained, the amount of variations in magnetic flux density is calculated from the amount, and a tensor for relating the amount of variations in an arbitrary scalar hysteresis model and a magnetization vector to that of a magnetic field vector is used together, thus the amount of variations in magnetization and magnetic fields from that of the magnetic flux density are calculated and the magnetization vector is updated. By repeating this process, the convergence solution of the magnetic vector potential that takes into consideration the vector hysteresis characteristics is obtained, and the convergence solution of the magnetization vector, and magnetic field vector is calculated. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for analyzing a hysteresis magnetic field of a magnetic material, and more particularly to a method for analyzing a hysteresis magnetic field in consideration of a rotational hysteresis phenomenon.

As a typical example of a conventional general-purpose hysteresis magnetic field analysis method, there is a Preisach model as a magnetic dipole set model, and a vector Preisach model as a vector hysteresis model considering a rotational hysteresis phenomenon is, for example, Document ID Mayergoyz:
Mathematical Models of Hysteresis and their Applications, Springer-Verlag, New
Shown in York, 2003, etc. The Stoner-Wholfarth model is another typical vector hysteresis model that is a magnetic anisotropic particle model, EC Stoner and EP Wholfarth: A mechanism of magnetic hysteresis in heterogeneous alloys, Phil. Trans. Roy. Soc., Vol. 240A, pp.599-642 (1948) etc. This method is an analysis method based on a statistical model in which a magnetic material is regarded as an assembly of a large number of magnetic dipoles.

I. D. Mayergoyz: Mathematical Models of Hysteresis and theirApplications, Springer-Verlag, New York, 2003 E. C. Stoner and E. P. Wholfarth: A mechanism of magnetic hysteresis in heterogeneous alloys, Phil. Trans. Roy. Soc., Vol. 240A, pp. 599-642 (1948)

  In motors, rotating machines, MRI, etc., magnetic materials such as electromagnetic steel plates and pure iron are used, and the magnetic materials always have hysteresis magnetic characteristics. However, since it is difficult to analyze the hysteresis magnetic characteristics, conventionally, there has been almost no magnetic field analysis in consideration of the hysteresis magnetic characteristics of the magnetic material at the design stage. In motors, rotating machines, MRI, etc., there is a rotating magnetic field or a rotating oscillating magnetic field, and in order to analyze the hysteresis magnetic characteristics, a hysteresis magnetic field analysis using a vector hysteresis model that can take into account the hysteresis effect due to the rotating magnetic field is necessary. is there.

  Literature ID Mayergoyz: Mathematical Models of Hysteresis and their Applications, Springer-Verlag, New York, 2003, EC Stoner and EP Wholfarth: A mechanismof magnetic hysteresis in heterogeneous alloys, Phil. Trans. Roy. Soc., Vol. 240A, pp. As shown in 599-642 (1948), various models for describing vector hysteresis have been proposed. However, since the conventional vector hysteresis model directly extends the idea of the one-dimensional scalar hysteresis model to a three-dimensional space, it requires much more memory and calculation time than the scalar hysteresis model.

  When a magnetic field analysis is performed on a motor, a rotating machine, MRI, or the like, the calculation is generally performed using a finite element method. In the finite element method, an analysis region is divided into many elements, and a solution is obtained by solving a large-scale simultaneous equation. The more complex the analysis system, the greater the number of elements in the finite element model. For example, a magnetic circuit having a complicated shape such as MRI requires one or more elements. In such a case, analysis requires enormous memory and calculation time. When the conventional vector hysteresis model is used in such a situation, a huge amount of memory and calculation time are required for the hysteresis magnetic field analysis, and practical calculation is impossible.

  Further, a common problem in the conventional vector hysteresis model is that it is unclear whether the magnetization has been rotated when the magnitude of the magnetization is reduced. Theoretically, magnetization reversal is a necessary condition that the magnitude of the magnetization becomes zero. However, when analyzing with a computer, the time step has a certain finite width, so when the magnetization direction changes nearly 180 degrees. Therefore, it is difficult to determine whether the magnetization is reversed or the magnetization is rotated. If this discrimination of magnetization reversal is mistaken, it will have a great influence on the subsequent hysteresis behavior, and the calculated value of hysteresis loss will differ greatly. The conventional vector hysteresis magnetic field analysis has a serious problem that the unclearness of the magnetization reversal determination greatly reduces the accuracy of the hysteresis magnetic field analysis.

  One feature of the present invention is that in a vector hysteresis magnetic field analysis method, a second-order or third-order tensor that relates a fluctuation component of a magnetic field strength vector and a fluctuation component of a magnetization vector or a magnetic flux density vector, and an arbitrary scalar hysteresis model, Is to use.

  The other features of the present invention are as described in the claims.

  All scalar hysteresis models can be easily vectorized, and magnetic hysteresis with rotational hysteresis can be analyzed with high speed and accuracy.

  In order to achieve the above object, the hysteresis magnetic field analysis method according to the present invention provides a method of functionally vectorizing an arbitrary scalar hysteresis model. As a premise, how to apply the hysteresis model to the magnetic field analysis will be described first.

  Using magnetic vector potential A, magnetic flux density B and electric field E are

And Ampere's formula is

It is. The relationship between the magnetic flux density B, the magnetic field H, and the magnetization M is determined using the vacuum permeability μ _0.

Can be written. (Equation 1) (Equation 2) (Equation 3) (Equation 4)

Get. If the solution A at a certain time t is obtained, the magnetic flux density B is obtained from (Equation 1). Thereby, the fluctuation amount ΔB of the magnetic flux density with respect to the previous time can be calculated. Here, by using a vector hysteresis model that relates the magnetization fluctuation amount ΔM and the magnetic field fluctuation amount ΔH, the magnetization fluctuation amount ΔM and the magnetic field fluctuation amount ΔH can be obtained from the magnetic flux density fluctuation amount ΔB. When the magnetization variation ΔM and the magnetic field variation ΔH are obtained, the magnetization M and the magnetic field H at each time are obtained.

Here, a vector hysteresis model which is a basic part of the present invention will be described. Consider a coordinate system based on the magnetization M. A unit vector parallel to the magnetization M at time t−Δt before the change is e _1, and a unit vector in the direction of the vector product M × H perpendicular to this plane and perpendicular to this plane is M × H. Is defined as e ₃ , and another unit vector e ₂ is defined as e ₂ = e ₃ × e ₁ . A set of unit vectors e ₁ , e ₂ , and e ₃ constitutes a right-hand system, and the amount of field variation is expressed in this orthogonal coordinate system. At this time, the subscripts //, ⊥1, and ⊥2 are used for the amount of change in the direction of the unit vectors e ₁ , e ₂ , and e ₃ , respectively. Unit vectors e ₁ , e ₂ ,
In the coordinate system of e ₃ , the magnetization M is expressed as (M, 0, 0), and the magnetization amount M can have positive and negative values. On the other hand, the magnitude H of the magnetic field H is a non-negative amount. The aforementioned unit vector e ₁ is oriented in the direction of magnetization when the magnetization amount M is positive. When the angle of the unit vector e ₁ and the magnetic field H is denoted by theta _MH, magnetic field H can be expressed in the coordinate system of the unit vectors e _1, e _2, e ₃ and _{(Hcosθ MH, Hsinθ MH, 0} ).

The magnetic field fluctuation amounts in this coordinate system are set as ΔH _// , ΔH _⊥1 and ΔH _Ｈ2 , and the magnetization fluctuation amounts are set as ΔM _// , ΔM _⊥1 and ΔM _⊥2 . Magnetization M ′ after fluctuation and magnetic field H ′ after fluctuation are

It can be expressed. At this time, since the magnetization direction changes, the unit vectors e ₁ , e ₂ , e ₃ change to e ₁ ′, e ₂ ′, e ₃ ′. The unit vector e ₁ ′ ignores high-order minute quantities,

Can be written. If the secondary minute term is ignored, the // component of the magnetization fluctuation amount can be ΔM _// even in the coordinate system after the fluctuation. The // component of the fluctuation amount of the magnetic field as seen in the coordinate system after fluctuation is ΔH _// '. From (Equation 7) and (Equation 8), the magnetic field component H _// ′ parallel to the magnetization M ′ after the fluctuation ignores the secondary minute term,

Can be written. Therefore, H _// ′ is

It becomes. Here, ΔM _⊥1 and ΔM _⊥2 that cause the rotation of magnetization are magnetic field fluctuation amounts ΔH _// ,
A relation is _made to ΔH _⊥1 and ΔH _⊥2 . For example,

And Here, x is a magnetic susceptibility defined by x = M / H, α, μ, and γ are dimensionless quantities, and are functions such as M, H, θ _{MH, and the} like. From (Equation 11) and (Equation 12),

を用いて It is. Where ΔH _// 'and ΔM _// are the difference susceptibility

Using

From (Equation 13) (Equation 14),

Is obtained.

  When (Equation 11), (Equation 12), and (Equation 15) are expressed in matrix form,

It becomes. Here, if the magnetization fluctuation amounts ΔM _// , ΔM _⊥1 and ΔM _⊥2 shown in ( _Equation 16) are _replaced with magnetic flux density fluctuation amounts ΔB _// , ΔB _⊥1 and ΔB _⊥2 ,

It becomes. When the deformation is performed using ΔM = ΔB−μ ₀ ΔH, the magnetic field fluctuation amount ΔH and the magnetization fluctuation amount ΔM are obtained from the magnetic flux density fluctuation amount ΔB as follows.

Can be written. here,

It is. Using (Equation 5), the magnetic vector potential A is obtained, and the fluctuation amount ΔA is calculated.

Thus, the fluctuation amount ΔB of the magnetic flux density is obtained. Further, the fluctuation amount ΔH of the magnetic field strength can be obtained from (Equation 18) from the fluctuation amount ΔB of the magnetic flux density, and the fluctuation amount ΔM of magnetization can be obtained from (Equation 19). As a result, the magnetic flux density B, magnetic field H, and magnetization M can be obtained. can get.

  Hereinafter, the flow of the hysteresis magnetic field analysis method in the first embodiment of the present invention will be described with reference to a flowchart.

Α, β, and γ appearing in (Equation 17), (Equation 18), and (Equation 19) are dimensionless quantities, and M, H,
An example of this function form is shown as a function such as θ _MH .

Here, h = H / H _s (H > 0), m = M / M _s (−M _s < M < M _s ), θ _MH is an angle formed by the magnetization M and the magnetic field H, and 0 < θ _MH < Π. However, when magnetization M <0, θ _MH is an angle formed by −M and H. a ₁ , a ₂ , a ₃ , b ₁ , b ₂ , b ₃ , c ₁ , c ₂ , c ₃ are magnetic characteristic parameters (positive values) specific to the material. The operator sgn (m) takes a value of 1 when m is non-negative and -1 when it is negative. Min (a, b) means taking the smaller value of a and b. In order to loss rotating hysteresis becomes zero in the magnetic saturation state, it may become a theta _MH = [pi when theta _MH = 0, m <0 when sin [theta _MH = 0 i.e. m> 0. The condition of the variation amount θθ _MH of θ _MH is sgn (m) Δθ _MH <0. Δθ _MH is

Here, Δh _// = ΔH _// / H, Δh _⊥1 = ΔH _⊥1 / H. Sgn (m) Δθ _MH <0 with minimum magnetic field h = 1 in the magnetic saturation state. Therefore, if h = 1,

Considering that sgn (m) Δh _// > 0 when magnetic saturation occurs, the term Δh _// acts so that the magnetization and the magnetic field are parallel. In order to act on the term of Δh _作用 1 in the same way,

is required. When m> 0 and θ _{MH <<} 1,

And to satisfy this,

It becomes. The same result is obtained when m <0 and π−θ _MH << 1. If the normalized magnetic field h = 1 and the magnetization and the magnetic field become parallel, in the magnetic saturation state where h > 1, β = δ = 0, | α | = 1, sinθ _MH = 0 in (Equation 16), and the magnetization There is no delay factor, and magnetization and magnetic field are always parallel.

β includes sgn (ΔH _// ) in the form of ( _Equation 24) and δ includes sgn (ΔH _⊥1 ) in the form of ( _Equation 26), which means that ΔH _// and ΔH _⊥1 vibrate positively or negatively. Then, it means that the direction of the magnetization M gradually approaches the direction of the magnetic field H. However, (Equation 16) is a model in which the direction of the magnetization M approaches the direction of the magnetic field H in any small magnetic field vibration, but in reality, the hysteresis is temporarily constrained by “friction”, and to some extent The direction of magnetization M does not fluctuate unless the activation level is higher than. For this reason, a play area that does not make the change in the angle of magnetization obtained in (Equation 19) effective is provided as necessary. As a result, the finite magnetic field vibration component has a play in which the magnetization direction does not change, which is closer to a more realistic analysis.

Another example of the function form of α and β will be shown. In this model, consider magnetization and the angle theta _MH magnetic field reaches the angle theta _MH ^max corresponding to the maximum friction torque, and the torque and the maximum friction torque acting on the magnetization equal. On the other hand, when θ _MH <θ _MH ^max , it is considered that the magnetization rotation is determined only by the magnetization phenomenon. The amount of change Δθ _MH of the angle θ _MH between the magnetization and the magnetic field is calculated using the amount of change ΔH in the magnitude of the magnetic field and the amount of change ΔH _θ in the rotation direction of the magnetic field.

It expresses. here,

From (Equation 32),

It becomes. Here, for convenience, if s = sin θ _MH and c = cos θ _MH ,

Can be written. From (Equation 10), (Equation 14), (Equation 35), and (Equation 36), considering M = M _//

The torque T acting on the magnetization is

Since the torque fluctuation amount ΔT is

From (Expression 32) and (Expression 38),

Here, the friction torque is T _f and T _f is a function of M and H _// forming a scalar hysteresis space. Fluctuation amount [Delta] T _f of the time T _f is the use of (Expression 36) (number 38)

Can be written. When θ _MH = θ _MH ^max , assuming that the torque fluctuation amount ΔT shown in (Equation 41) is equal to this ΔT _f , the coefficients related to ΔH and ΔH _θ are compared.

Is obtained.

  From (Expression 16), (Expression 35), (Expression 36), and (Expression 37),

Get. Substituting (Equation 43) and (Equation 44),

は０になる。磁気飽和状態でｓ＝０であることを考慮すると、

が得られる。この点を考慮すると、磁気飽和状態でβ＝０になることがわかる。また、このとき、Ｍ＞０でｃ＝１となりα＝１が得られ、Ｍ＜０でｃ＝−１となりα＝−１が得られる。これは、磁気飽和状態において磁界と磁化は平行にふるまうことを意味し、
（数４７）（数４８）は理にかなった式になっている。 Get. Since the friction is zero in the magnetic saturation state, the coefficient of ΔH in (Equation 42)

Becomes 0. Considering that s = 0 in the magnetic saturation state,

Is obtained. Considering this point, it can be seen that β = 0 in the magnetic saturation state. At this time, when M> 0, c = 1 and α = 1 is obtained, and when M <0, c = −1 and α = −1 is obtained. This means that the magnetic field and magnetization behave in parallel in the magnetic saturation state,
(Expression 47) (Expression 48) is a reasonable expression.

Here, when θ _MH = θ _MH ^max , the magnetization will completely follow the rotation of the magnetic field.
G which is a coefficient of Δθ _{H in} (Expression 32) is 0. Therefore, in (Equation 48), T _f ^H = 0, and β in (Equation 48) is

なので、β＝０になるのは自明である。 It becomes. In the magnetic saturation state,

Therefore, it is obvious that β = 0.

The friction torque T _f used here can be obtained from T _f = W _rot / ω by measuring the rotational hysteresis loss W _rot in a rotating magnetic field with an angular frequency ω.

On the other hand, when θ _MH <θ _MH ^max , the torque acting on the magnetization is smaller than the maximum friction torque, so the magnetization rotation effect due to the torque does not work, and only the magnetization phenomenon due to the magnetic field fluctuation component remains. Among the fluctuation components of the magnetic field, ΔH _// contributes only to the fluctuation of the magnitude of magnetization and does not contribute to the magnetization rotation. The only component that contributes to the magnetization rotation is the fluctuation component ΔH _⊥1 perpendicular to the magnetization of the magnetic field. Therefore,

It becomes. Here, x ₀ is the magnetic susceptibility in the ⊥1 direction perpendicular to the magnetization. At this time, F and G are

It becomes. Considering the magnetization phenomenon and the precedence of the magnetic field rotation, 0 <G <1 must be satisfied, and x ₀ <| x | is an essential condition.

  FIG. 1 shows an example of an analysis system according to the present invention. The analysis system includes a computer 100, a display device 101, and a storage medium 102. Here, in order to clearly show the storage medium 102, the storage medium 102 is taken out of the computer 100, but the storage medium 102 may be installed inside the computer 100. For example, the processing described in FIG. 2 is executed as the first embodiment of the present invention using this analysis system.

FIG. 2 shows a flow of a hysteresis magnetic field analysis method using (Equation 5) as a basic analytical expression as a first embodiment of the present invention. In the first step 11, the magnetization at the previous time is called and the data is discretized and assigned to the right side of (Equation 5). In the second step 12, the discretized (Equation 5) is numerically analyzed to obtain the magnetic vector potential A at time t. In the third step 13, the fluctuation amount ΔA of the magnetic vector potential is calculated, and the fluctuation amount ΔB of the magnetic flux density is obtained using (Equation 22). In the fourth step 14, the magnetization fluctuation amount ΔM and the magnetic field fluctuation amount ΔH are obtained from the magnetic flux density fluctuation amount ΔB using (Equation 18) and (Equation 19), and the magnetization M and the magnetic field H are calculated. In the determination step 10, it is determined whether or not the magnetization M has converged. If it has not converged, in the fifth step 15, the magnetization M is substituted into the right side of the discretized (Equation 5), and the second step 12 is returned. The above processing is repeated again. If the magnetization M converges in the determination step 10, the magnetization M and the magnetic field H in the magnetic material are stored in the storage medium 102 in the sixth step 16. Thereafter, the process proceeds to the calculation of the next time.

A second embodiment of the present invention will be described. In this embodiment, an equation different from (Equation 5) is used. When A at the previous time is A ₀ and rot (rotA ₀ ) is subtracted from both sides of (Equation 5),

It becomes. As in the first embodiment of the present invention using (Equation 5), the value at the previous time is used as the initial value of the magnetization M, and the magnetic field H and the magnetization M are obtained while updating the magnetization M.

FIG. 3 shows the flow of the hysteresis magnetic field analysis method in this embodiment. In the first step 21, the magnetization at the previous time is called and the data is substituted into the right side of the discretized (Equation 52). In the second step 22, the discretized (Equation 52) is numerically analyzed to obtain the fluctuation amount ΔA of the magnetic vector potential at time t. In the third step 23, the fluctuation amount ΔB of the magnetic flux density is obtained from the fluctuation amount ΔA of the magnetic vector potential using (Equation 22). In the fourth step 24, the magnetization fluctuation amount ΔM and the magnetic field fluctuation amount ΔH are obtained from the magnetic flux density fluctuation amount ΔB using (Equation 18) and (Equation 19), and the magnetization M and the magnetic field H are calculated. In the determination step 20, it is determined whether or not the magnetization M has converged. If it has not converged, in the fifth step 25, the magnetization M is substituted into the right side of the discretized (Equation 52), and the second step 22 is returned. The above processing is repeated again. If the magnetization M converges in the determination step 20, the magnetization M and the magnetic field H in the magnetic material are stored in the storage medium 102 in the sixth step 26. Thereafter, the process proceeds to the calculation of the next time.

  The effect peculiar to the present embodiment is that the convergence of the solution is relatively fast when the fluctuation amount ΔA of the magnetic vector potential is a value close to the previous time. In the hysteresis magnetic field analysis, the coil current is often fluctuated with time, and when the coil current monotonously increases or decreases, the fluctuation amount ΔA of the magnetic vector potential is often close to the previous time. The effect is great.

  A third embodiment of the present invention will be described. In this embodiment, an equation different from (Equation 5) is used. (Equation 5) is converted into an expression of variation. If both sides of time t and time t−Δt (Equation 5) are subtracted,

It becomes. From Equation 53, the solution ΔA is obtained while updating the magnetization fluctuation amount ΔM, and the magnetic field H and the magnetization M are obtained.

  FIG. 4 shows the flow of the hysteresis magnetic field analysis method in this embodiment. In the first step 31, the magnetization at the previous time is called, and the data is discretized and assigned to the right side of (Equation 53). In the second step 32, the discretized (Equation 53) is numerically analyzed to obtain the fluctuation amount ΔA of the magnetic vector potential at time t. In the third step 33, the fluctuation amount ΔB of the magnetic flux density is obtained from the fluctuation amount ΔA of the magnetic vector potential using (Equation 22). In the fourth step 34, the magnetization fluctuation amount ΔM and the magnetic field fluctuation amount ΔH are obtained from the magnetic flux density fluctuation amount ΔB using (Equation 18) and (Equation 19), and the magnetization M and the magnetic field H are calculated. In the determination step 30, it is determined whether or not the magnetization M has converged. If it has not converged, in the fifth step 35, the magnetization fluctuation amount ΔM is substituted into the right side of the discretized (Equation 53), and the second step 32. Return to the above process and repeat. If the magnetization M converges in the determination step 30, the magnetization M and the magnetic field H in the magnetic material are stored in the storage medium 102 in the sixth step 36. Thereafter, the process proceeds to the calculation of the next time.

  The effect peculiar to the present embodiment is that when the coil current monotonously increases or decreases, if the values of the previous time are used as the initial values of the magnetic vector potential fluctuation amount ΔA and the magnetization fluctuation amount ΔM, the convergence of the solution is achieved. It is extremely fast.

  A fourth embodiment of the present invention will be described. In this embodiment, an equation different from (Equation 5) is used. When two ampere equations at time t and previous time t−Δt are listed,

Here, the subscript 0 indicates an amount at the previous time t−Δt. When (Expression 55) is subtracted from (Expression 54) and ΔH = H−H ₀ is used,

The following two types of equations are obtained. Both left sides are obtained by subtracting the left sides of (Equation 54) and (Equation 55), but regarding the right side, (Equation 56) is obtained by subtracting the right sides of (Equation 54) and (Equation 55). (Equation 57) is obtained by subtracting the left side of (Equation 55) from the right side of (Equation 54). Here, regarding (Equation 57), there are two ways of expressing the handling of rotH ₀ . One uses H ₀ = ν ₀ (B ₀ −M ₀ ),

It can be expressed. Here, ν ₀ is the reciprocal of the vacuum permeability. Also,

Using,

とおくと、 Can be written. Here, the superscript 0 indicates the amount at the initial time t = 0. (Equation 56) (Equation 57)

After all,

は（数１８）右辺のテンソルを（ｘ，ｙ，ｚ）座標系に変換したものであり、 Where the differential magnetic resistivity tensor

(Expression 18) is obtained by converting the right-side tensor to the (x, y, z) coordinate system.

(E _1x , e _1y , e _1z ), (e _2x , e _2y , e _2z ), (e _3x , e _3y , e _3z ) are respectively the unit vectors e ₁ , e ₂ , e _{3 is} an (x, y, z) component. Moreover, any of the following three types may be used for the right side b.

を更新して、第１ステップ４１にもどって、上記の処理を再度繰り返す。判定ステップ
４０で磁化Ｍが収束すれば、第５ステップ４５において、磁性体における磁化Ｍと磁界Ｈを記憶媒体１０２に記憶する。その後、次の時刻の計算に移行する。 FIG. 5 shows the flow of the hysteresis magnetic field analysis method in this embodiment. In the first step 41, the discretized (Equation 62) is numerically analyzed to obtain the fluctuation amount ΔA of the magnetic vector potential at time t. In the second step 42, the fluctuation amount ΔB of the magnetic flux density is obtained from the fluctuation amount ΔA of the magnetic vector potential using (Equation 22). In the third step 43, the magnetization fluctuation amount ΔM and the magnetic field fluctuation amount ΔH are obtained from the magnetic flux density fluctuation amount ΔB using (Equation 18) and (Equation 19), and the magnetization M and the magnetic field H are calculated. In the determination step 40, it is determined whether or not the magnetization M has converged. If not, in the fourth step 44, the differential magnetic resistivity tensor shown in (Equation 61).

, And return to the first step 41 to repeat the above process again. If the magnetization M converges in the determination step 40, the magnetization M and the magnetic field H in the magnetic material are stored in the storage medium 102 in the fifth step 45. Thereafter, the process proceeds to the calculation of the next time.

  This embodiment is also the same as the second and third embodiments described above from the viewpoint of obtaining the magnetic vector potential fluctuation amount ΔA. Is not on the right side. For this reason, as an effect peculiar to the present embodiment, there is an effect that the number of iterations for obtaining the solution ΔA can be reduced.

According to the hysteresis magnetic field analysis method related to the present invention described above, since the relationship between ΔM _// and ΔH _// 'can be expressed by any conventional scalar hysteresis model, any scalar hysteresis model can be easily vectorized and rotated. The magnetic hysteresis phenomenon with hysteresis can be analyzed with high speed and high accuracy.

The figure which shows an example of the analysis system in this invention. The figure which shows the flow of the hysteresis magnetic field analysis which is 1st Example of this invention. The figure which shows the flow of the hysteresis magnetic field analysis which is the 2nd Example of this invention. The figure which shows the flow of the hysteresis magnetic field analysis which is the 3rd Example of this invention. The figure which shows the flow of the hysteresis magnetic field analysis which is the 4th Example of this invention.

Explanation of symbols

10: Convergence determination process in the first embodiment, 11: Step 1, 12 in the first embodiment, 12: Step 2, 13 in the first embodiment, 13: Step 3, 14 in the first embodiment, 1st. Steps 4 and 15 in the embodiment, Steps 5 and 16 in the first embodiment, Steps 6 and 20 in the first embodiment, convergence determination processing in the second embodiment, 21... Step 1 in the second embodiment. , 22 ... step 2 in the second embodiment, 23 ... step 3 in the second embodiment, 24 ... step 4, 25 in the second embodiment, steps 25, 26 in the second embodiment, 26 ... second Steps 6 and 30 in the embodiment ... Convergence determination processing in the third embodiment, 31 ... Steps 1 and 32 in the third embodiment, Steps 2 and 33 in the third embodiment, 3rd Steps 3 and 34 in the example Steps 4 and 35 in the third embodiment Steps 5 and 36 in the third embodiment Steps 36 and 36 in the third embodiment Steps 40 and 40 in the third embodiment Convergence determination processing in the fourth embodiment 41 ... Step 1 in the fourth embodiment, 42 ... Step 2, in the fourth embodiment, 43 ... Step 3, in the fourth embodiment, 44 ... Step 4, 45 in the fourth embodiment, 45 ... Fourth implementation Steps 5 and 100 in the example: a computer in an example of the analysis system, 101: a display device in the example of the analysis system, 102: a storage medium in the example of the analysis system.

Claims (13)

  A vector hysteresis magnetic field analysis method using a second-order or third-order tensor and an arbitrary scalar hysteresis model that relate a fluctuation component of a magnetic field strength vector to a fluctuation component of a magnetization vector or a magnetic flux density vector.   It is characterized in that the magnitude of magnetization is obtained using an arbitrary scalar hysteresis model that correlates the magnitude of magnetization with the projection component of the magnetic field vector onto the magnetization vector, and the change in the direction of the magnetization vector is obtained with the fluctuation component of the magnetic field. Vector hysteresis magnetic field analysis method.   3. The vector hysteresis magnetic field analysis method according to claim 2, wherein a change in the direction of the magnetization vector is obtained by linear combination of fluctuation components of the magnetic field.   4. The vector hysteresis magnetic field analysis method according to claim 1, wherein the magnetic hysteresis magnetic field has a play that does not react to a certain finite magnetic field vibration component.   5. The scalar hysteresis model according to claim 1, wherein a negative value is allowed for a scalar component that characterizes the magnitude of the magnetization vector, and the direction of the magnetization vector is positive when the scalar component is positive. A vector hysteresis magnetic field analysis characterized in that a scalar hysteresis model is formed in a space defined by the direction of the magnetization vector and consisting of two quantities of the projection component of the magnetic field vector in the direction of the magnetization vector and the scalar component related to the magnetization vector. Method.   4. The function according to claim 3, wherein the coefficient in the linear combination of the change in direction of the magnetization vector and the fluctuation component of the magnetic field is a function of the magnitude of the magnetic field, the magnitude of magnetization that allows negative values, and the angle between the magnetization vector and the magnetic field vector. A vector hysteresis magnetic field analysis method characterized by:   7. The vector hysteresis magnetic field analysis method according to claim 1, wherein the magnetic field analysis method is a finite element method.   8. The vector hysteresis magnetic field analysis method according to claim 7, wherein a solution of the magnetic vector potential at each time is obtained while repetitively updating the magnetization vector induced in the magnetic material.   8. The vector hysteresis magnetic field analysis method according to claim 7, wherein the fluctuation amount of the magnetic vector potential at each time is obtained while the fluctuation amount of the magnetization vector induced in the magnetic material is repeatedly updated.   8. The vector hysteresis magnetic field analysis method according to claim 7, wherein the fluctuation amount of the magnetic vector potential at each time is obtained while the fluctuation amount of the magnetization vector is repeatedly updated using a differential magnetic resistivity tensor.   A vector hysteresis magnetic field analysis program for causing a computer to execute the processing according to any one of claims 1 to 10.   12. The vector hysteresis magnetic field analysis program according to claim 11, which requests input of rotational hysteresis loss characteristic data.   A computer-readable recording medium on which the program according to any one of claims 11 to 12 is recorded.

Images