JP5228730B2 - Analysis method of eddy current loss in magnet of permanent magnet motor - Google Patents

Description

  The present invention relates to an analysis method for eddy current loss in a magnet of a permanent magnet motor, and more particularly to an analysis method using both a three-dimensional finite element method and a two-dimensional finite element method.

  In order to evaluate the heat generation and demagnetization of the magnet of a PM motor, when calculating the eddy current loss in the magnet by numerical analysis, it is necessary to perform a three-dimensional nonlinear stationary magnetic field analysis considering the three-dimensional eddy current distribution of the magnet. Become. However, when performing analysis that takes into account current harmonics of the carrier frequency component due to inverter drive, etc., calculation with a small step size of the step-by-step method is required, and the calculation time becomes enormous. Therefore, a method for calculating eddy current loss using only three-dimensional analysis is not practical.

  Therefore, assuming that the axial component of the magnetic flux in the iron core is negligible, the entire motor performs a two-dimensional nonlinear steady eddy current analysis, and among the obtained harmonic orders, the major orders are equal to the gap magnetic flux density. A method has been proposed in which the calculation time is reduced by giving a magnetic vector potential as a boundary condition and performing a three-dimensional complex approximation analysis of only the rotor using the obtained magnetic permeability distribution (for example, non-patent) Reference 1).

In addition, as a method of obtaining the magnet eddy current loss of the PM motor in the calculation time equivalent to the two-dimensional analysis, the time change of the magnetic flux density inside the magnet is analyzed by the two-dimensional magnetic field analysis by the finite element method using the two-dimensional model of PM motor. 3D analysis considering the eddy current of the magnet by the finite element method based on the 3D model of the magnet and the temporal change of the magnetic flux density. The applicant of the present application has already proposed a method for calculating the magnet eddy current loss density from the time change of the eddy current density of the magnet obtained by this (see, for example, Patent Document 1).
Katsumi Yamazaki, Yuji Kano “Loss Analysis of IPM Motors Using Three-Dimensional and Two-Dimensional Finite Element Methods” The Institute of Electrical Engineers of Japan, Stationary and Rotating Machine Joint Research Fund, SA-07-79, RM-07-95 (2007) JP 2008-123076 A

  In the analysis method using both the above-mentioned 3D finite element method and 2D finite element method, although the calculation time for the entire rotor increases, 3D eddy current analysis is performed to improve the analysis accuracy. Three-dimensional eddy current analysis considering resistance is not performed.

  Since the eddy current in the magnet affects the stator side as a reaction magnetic field, an error occurs in the calculation of the eddy current loss in the magnet by the above three-dimensional eddy current analysis, and particularly in the analysis of the PM motor having a large eddy current. It becomes large and sufficient analysis accuracy cannot be obtained.

  It is an object of the present invention to provide a method for analyzing eddy current loss in a magnet of a permanent magnet motor that can analyze eddy current loss with reduced calculation time and can perform highly accurate analysis including the magnetic resistance of the entire motor. There is.

  The present invention focuses on the influence of the magnetic flux distribution of the entire motor in consideration of the magnetic flux passing through the stator due to the reaction magnetic field generated by the eddy current in the magnet, and the analysis of the entire motor is a two-dimensional static magnetic field analysis. In the three-dimensional eddy current loss analysis that calculates the current loss, the analysis is performed by the step-by-step method using only the magnet as the analysis area, and the entire motor is applied to the eddy current of the magnet for the analysis considering the reaction magnetic field of the eddy current. The magnetic resistance was also analyzed, and the two-dimensional analysis of the entire motor was performed by changing the magnetization amount of the magnet to calculate this magnetic resistance, and this was analyzed as an equivalent gap. The method is characterized.

(1) A method of analyzing eddy current loss in a magnet of a permanent magnet motor in which the eddy current loss in the magnet of the permanent magnet motor is analyzed by data processing by a computer using a combination of two-dimensional analysis and three-dimensional analysis,
The computer
Using the magnetic vector potential A based on the following equation, perform a two-dimensional static magnetic field analysis of the entire motor,

However, M is the amount of magnetization of the magnet, J ₀ is the current density applied to the coil, ν is the magnetic resistivity, and the distribution of the magnetic flux density B _m in the magnet obtained by the two-dimensional static magnetic field analysis is used. Find the eddy current distribution by three-dimensional eddy current analysis ,

Only the 1/2 region of one magnet divided in the thickness direction is set as the analysis region, and the distribution of the magnetic flux density B _m is given to each layer in the magnet thickness direction,
When considering the reaction magnetic field due to the eddy current of the magnet, using the magnetic vector potential A and the electric scalar potential φ based on the following equation:

However, sigma than conductivity, have row the three-dimensional eddy current analysis of only the magnets,

The reaction magnetic field three-dimensional eddy current analysis considering sets the gap G _a of gap G _t magnets and iron core between divided magnet, the magnet and the gap relative to eddy currents in the magnet G _t and G _The analysis is performed using an analysis model in which a gap G _{l in} which the magnetic resistance of the entire motor excluding _a is equivalently replaced is set.

(2) The length of the gap G _l is determined from the magnetoresistance R _i taking into account the nonlinearity of the entire motor other than the magnet with respect to the current flowing on the magnet surface.

(3) The magnetic resistance R _i is obtained by calculating a magnetic flux change amount Δφ linked to the magnet when the magnetization amount M of the magnet is increased by a minute amount ΔM.

Where L _l is the magnet length, L _w is the magnet width, L _t is the magnet thickness, μ _r is the magnet recoil permeability, R _m is the magnet reluctance, R _t is the total motor reluctance,
It is characterized by more demanding.

  As described above, according to the present invention, the analysis of the entire motor is a two-dimensional static magnetic field analysis, and in the three-dimensional eddy current loss analysis for calculating the eddy current loss in the magnet, only the magnet is set as the analysis region.・ Analyze by the step method, and further analyze the magnetic resistance of the entire motor against the eddy current of the magnet in the analysis considering the reaction magnetic field of the eddy current. This is done by changing the magnetized amount of the magnet and analyzing this as an equivalent gap, so it is possible to analyze the eddy current loss with a reduced calculation time, and in addition, the highly accurate analysis including the magnetoresistance of the stator Can do.

(1) Analysis Method FIG. 1 is an analysis procedure showing an embodiment of the present invention, and the eddy current loss in a magnet is obtained using a two-dimensional / three-dimensional analysis method in combination. In FIG. 1, in step S1, the entire motor is analyzed by two-dimensional static magnetic field analysis. In steps (S2-1) and (S2-2), the three-dimensional analysis for calculating the eddy current loss in the magnet is performed by the step-by-step method using only the magnet as the analysis region, and step (S2-1) Then, three-dimensional analysis ignoring the reaction magnetic field caused by eddy current is performed, and in step (S2-2), the three-dimensional analysis considering the reaction magnetic field caused by eddy current is performed. Furthermore, in the three-dimensional eddy current loss analysis of the magnet, the reluctance of the entire motor against the eddy current of the magnet is calculated by two-dimensional analysis of the entire motor with the magnet magnetization M changed, and this is replaced with an equivalent gap. To analyze.

  The processing functions of step S1 and steps (S2-1) and (S2-2) are realized by data processing by a computer composed of computer resources and software using the same, and detailed processing will be described below. To do.

(S1) Two-dimensional analysis of the whole motor The whole motor is analyzed by a method similar to Non-Patent Document 1, and a two-dimensional static magnetic field analysis is performed by the A method using the magnetic vector potential A having the following equation as a basic equation.

Here, M is the amount of magnetization of the magnet, J ₀ is the current density applied to the coil, and ν is the magnetic resistivity.

(S2) determining the eddy current distribution by a three-dimensional analysis of only the magnets using the distribution of the magnetic flux density B _m in the magnet obtained by the three-dimensional eddy current analysis motor entire two-dimensional static magnetic field analysis of the magnet. This analysis is divided into two cases: when the reaction magnetic field due to eddy current is ignored and when it is considered.

(S2-1) Analysis ignoring reaction magnetic field due to eddy current The three-dimensional eddy current analysis of the magnet when ignoring the reaction magnetic field due to eddy current is performed in consideration of symmetry as shown in FIG. Only the 1/2 region of one magnet divided in the thickness direction is set as the analysis region, and the distribution of the magnetic flux density B _m obtained by the two-dimensional analysis is given to each layer in the magnet thickness direction for analysis. At this time, the formulation is made using Faraday's law and the current continuity formula shown below.

Here, E is the electric field strength and J _e is the eddy current density.

  From equation (3), the current vector potential T shown in the following equation is defined.

  Substituting equation (4) into equation (2) yields the following basic equation: However, (sigma) is electrical conductivity.

As a boundary condition of the current vector potential T, a natural boundary where the eddy current density J _e is perpendicular to the symmetry plane, and a fixed boundary of T = 0 where the eddy current density J _e is parallel to the other planes. give.

(S2-2) Analysis including reaction magnetic field due to eddy current When analysis including reaction magnetic field due to eddy current of magnet is performed, A-φ using magnetic vector potential A and electric scalar potential φ based on the following equation: Use the law.

In addition, when considering the reaction magnetic field of eddy current, it is necessary to consider the magnetic resistance of the whole motor with respect to the magnetic flux which an eddy current produces. Therefore, in the analysis of this case, to set the gap G _a of gap G _t magnets and iron core between divided magnet as shown in FIG. 2 (b) and (c), also, the vortex in the magnet using the analysis model was set gap G _l by replacing the magnetic resistance of the entire motor equivalently except magnet and the gap G _t and G _a parsing for current.

The boundary condition at this time is a fixed boundary condition where A = 0, φ = 0, and the magnetic flux is parallel to the magnet symmetry plane and A = 0, φ = 0, and the magnetic flux is parallel to the upper surface of G _t . The other surface was assumed to be in contact with an iron core with infinite magnetic permeability, and natural boundary conditions were used.

The length of the gap G _l added equivalently is determined from the magnetoresistance R _i considering the non-linearity of the entire motor other than the magnet with respect to the current flowing on the magnet surface.

Hereinafter, the analysis method will be described with reference to FIG. First, in order to grasp the amount of magnetic flux φ that only the current I _m flowing through the magnet surface make analyzes with increased magnetization M of the magnets by a small amount .DELTA.M, I was determined variation Δφ of magnetic flux linking the magnets. At this time, if ΔM is constant in the magnet, the amount of change [Delta] _m and ΔM of I _m, the following expression is established.

Here, L _l is the length of the magnet, and μ _r is the recoil permeability of the magnet. From this the entire motor reluctance R _t can be calculated by the following equation.

Further, since the magnetic resistance R _i other than the magnet is obtained by removing the magnetic resistance R _{m of the} magnet from R _t , the following equation is obtained. However, L _w is the width of the magnet, L _t is the thickness of the magnet.

On the other hand, in the plan view, the perspective view, and the gap relation diagram of the magnet shown in FIG. 3, the magnetic resistance R _i other than the magnet is expressed by the following equation.

By setting these equations (10) and (11) as equal, the length of G _l can be obtained as follows.

The length of the gap G _l varies depending on the armature current and the rotor position.

(2) Example of Eddy Current Loss Analysis Method In order to examine the validity of the above analysis method, an example of an eddy current loss analysis method using an IPM motor (embedded magnet type synchronous motor) model will be described.

  FIG. 3A and Table 1 show the models and specifications of the IPM motor used as the model for study. The purpose of this analysis is to examine the validity, so the armature current of the IPM motor was an ideal sine wave. Moreover, in order to examine the influence of the division of the magnet in the axial direction, the analysis was performed when the magnet was divided into 1, 3, and 5 in the axial direction.

  In this analysis, the eddy current loss obtained by the three-dimensional nonlinear eddy current analysis considering the eddy current of the magnet is assumed to be a true value, and its validity is examined by comparison with the analysis result by this analysis method. The three-dimensional division diagram is shown in FIG. This division diagram was created by stacking two-dimensional division diagrams in the thickness direction, and the analysis region was half the thickness of one magnet divided in consideration of symmetry.

The division diagram for the two-dimensional analysis of the entire motor when this analysis method is used is the two-dimensional division diagram used for stacking. Moreover, the division figure used for the three-dimensional analysis of the magnet by this analysis method is shown in FIG. The magnets and gaps Gt and Ga in these division diagrams are the same as those in the three-dimensional division diagram of FIG. 3B, and in the analysis method (step S2-1) ignoring the reaction magnetic field due to eddy currents, In the analysis method that takes into account the reaction magnetic field (step S2-2), a division diagram including _a magnet and gaps G _t , G _a , and G _l is used. Incidentally, G _t is 0.2 mm, G _a is set to 0.1 mm, G _l is calculated for each analysis step, and fixes the split view.

  In this analysis example, one period is obtained if the rotor rotates 45 degrees, but the analysis was performed by rotating each period by 0.469 deg divided into 96 parts. In the three-dimensional nonlinear eddy current analysis that assumes a true value, a step-by-step method is used to analyze 1.5 periods in which the steady state is obtained. In addition, a two-dimensional static magnetic field analysis of the motor in step S1, and a step In the analysis of the magnet of S2-1, the analysis was performed for one period, and in the analysis of the magnet of Step S2-2, the analysis was performed for 1.5 periods that are almost in a steady state.

(3) Verification of analysis method <3.1> Torque waveform To examine the validity of step S1 (two-dimensional static magnetic field analysis) in FIG. 1, the torque waveform obtained by the two-dimensional static magnetic field analysis is converted into a three-dimensional eddy current. The results were compared with the analysis results. FIG. 4 shows a temporal change in torque converted to the entire region. However, it is normalized by the average torque obtained by the three-dimensional analysis when the magnet is not divided. From this figure, when the magnet is not divided, there is a slight difference between the two-dimensional analysis and the three-dimensional analysis. However, when the magnet is divided into five, the influence of the eddy current of the magnet becomes small, so they are almost the same. It was confirmed.

_3.2 Calculation of Gap G _l The magnetic flux density distribution at the rotor position calculated by applying a normal armature current and the amount of magnetization M to the magnet in FIG. 5A, and the vortex in FIG. The magnetic flux density distribution of only ΔM obtained by changing the magnetization amount of the magnet to M + ΔM and subtracting the magnetic flux density vector calculated by M in order to calculate the gap G _l when considering the reaction magnetic field of the current is shown.

  From these figures, it can be seen that the magnetic flux generated by the eddy current reaction magnetic field passes through the stator due to the magnetic saturation of the rotor, and the stator must be taken into account when calculating the magnetic resistance accurately.

FIG. 6 shows a change in the gap length _Gl obtained by the equation (12) depending on the rotor position. From this figure, it can be seen that the gap length G _l varies depending on the rotor position and the armature current.

<3.3> Eddy Current Loss FIG. 7 shows temporal changes in eddy current loss per magnet obtained by the three-dimensional eddy current analysis and the analysis method according to the present invention. 7A shows a case where the magnet is not divided, FIG. 7B shows a case where the magnet is divided into three, and FIG. 7C shows a case where the magnet is divided into five. In FIGS. 7A to 7C, 3D is an eddy current loss by a three-dimensional eddy current analysis method, Method ₁ is an eddy current loss by a two-dimensional analysis of the entire motor, and Method 2withoutG ₁ is a case where magnetic resistance is ignored. eddy current loss, Method2withG _l shows the eddy current loss in the case of considering the magnetoresistance. However, the figure is normalized with the value of the average eddy current loss obtained by the three-dimensional analysis without dividing the magnet.

From the characteristics shown in FIG. 7, when the magnet is not divided (a), the difference between the analysis methods is large, because the influence of the reaction magnetic field due to the eddy current of the magnet is large. That is, in Method 1 ignoring the reaction magnetic field of eddy current, the decrease of the magnetic flux in the magnet due to the reaction magnetic field is not taken into consideration, so the eddy current increases and the eddy current loss is overestimated. On the other hand, in the case of ignoring the gap G _l in Method2, the large decrease in magnetic flux by the reaction field in the opposite, eddy current loss eddy current is reduced would be underestimated. In addition, Method 2 in consideration of the gap G _l substantially matches the result of the three-dimensional eddy current analysis, and it can be seen that a reasonable result is obtained. As the number of magnet divisions is increased, the reaction magnetic field created by eddy currents decreases, so the difference between the analysis methods also decreases, and in the case of 5 divisions, almost reasonable results are obtained no matter which proposed method is used. I understand that

FIG. 8 shows the average eddy current loss density distribution obtained by each analysis method when the magnet is not divided. The result of Method 2 considering the gap G _l substantially coincides with the distribution obtained by the three-dimensional eddy current analysis (3D).

FIG. 9 shows a statistical diagram of the average eddy current loss per magnet obtained by each analysis method. However, the figure is normalized with the value obtained by the three-dimensional analysis when the magnet is not divided. As is clear from this figure, the error of Method 2 in consideration of the gap G _l is about 5% even when the largest magnet is not divided, confirming the validity of the analysis method of the present invention.

<3.4> Analysis specifications Table 2 shows the analysis specifications when the three-dimensional eddy current analysis of the entire motor and Method 2 are used.

Three-dimensional eddy current analysis (3D) and Method 2 magnet analysis showed a calculation time for 1.5 cycles to reach steady state using the step-by-step method. Further, Method 2 motor analysis (2D) is a static magnetic field analysis, and therefore analysis of only one period is sufficient. However, in order to calculate the gap G _l , 1 again using the magnet magnetization M and its correction amount ΔM. It is necessary to calculate the period, and the total is shown.

  By using the analysis method of the present invention, the calculation time can be reduced to about 1/30, which was confirmed to be useful.

(4) Characteristic matter according to the embodiment In this embodiment, in order to obtain the eddy current loss in the magnet of the PM motor at a high speed, the method uses a combination of the two-dimensional static magnetic field analysis of the motor and the three-dimensional eddy current analysis of the magnet. At the same time, it was applied to a sine wave drive IPM motor, and the validity and usefulness of the analysis method of this embodiment was confirmed. This feature is summarized as follows.

  (A) As a method of analyzing the three-dimensional eddy current in the magnet using the magnetic flux distribution in the magnet obtained by the two-dimensional static magnetic field analysis, there are two methods of ignoring the reaction magnetic field of eddy current and considering it. Can be applied. Further, in the method that considers the reaction magnetic field, since the magnetic resistance against the reaction magnetic field is also taken into account, a method of analyzing by providing an equivalent gap in the magnet can be applied.

  (B) When the analysis method of the embodiment is applied to a model in which the magnet is not divided in the thickness direction, the eddy current loss obtained when the reaction magnetic field of the eddy current is ignored and when the magnetic resistance of the motor with respect to the reaction magnetic field is ignored Is significantly different from the results of the three-dimensional analysis, but it was confirmed that reasonable results can be obtained by considering the reaction magnetic field and the corresponding magnetoresistance. In addition, when the number of magnets is increased, a reasonable result can be obtained even with the proposed method ignoring the influence of the reaction magnetic field.

  (C) The calculation time can be greatly reduced by using the analysis method of the present embodiment.

The analysis procedure which shows embodiment of this invention. An analysis model of a magnet. The top view of an IPM motor, a perspective view, and the gap related figure of a magnet. Example of temporal change of torque by 3D and 2D analysis. An example of a magnetic flux density distribution created by magnetization amounts M and ΔM. Variation of the gap length G _l by the rotor position. Temporal change in eddy current loss per magnet. Average eddy current loss density distribution obtained by each analysis method of non-divided magnets. Statistical chart of average eddy current loss per magnet obtained by each analysis method.

Claims (3)

A method for analyzing eddy current loss in a magnet of a permanent magnet motor, in which the eddy current loss in the magnet of the permanent magnet motor is analyzed by data processing by a computer using a combination of two-dimensional analysis and three-dimensional analysis,
The computer
Using the magnetic vector potential A based on the following equation, perform a two-dimensional static magnetic field analysis of the entire motor,

However, M is the amount of magnetization of the magnet, J ₀ is the current density applied to the coil, ν is the magnetic resistivity, and the distribution of the magnetic flux density B _m in the magnet obtained by the two-dimensional static magnetic field analysis is used. Find the eddy current distribution by three-dimensional eddy current analysis,
Only the 1/2 region of one magnet divided in the thickness direction is set as the analysis region, and the distribution of the magnetic flux density B _m is given to each layer in the magnet thickness direction,
When considering the reaction magnetic field due to the eddy current of the magnet, using the magnetic vector potential A and the electric scalar potential φ based on the following equation:

Where σ is conductivity
From the 3D eddy current analysis of the magnet only,
The reaction magnetic field three-dimensional eddy current analysis considering sets the gap G _a of gap G _t magnets and iron core between divided magnet, the magnet and the gap relative to eddy currents in the magnet G _t and G _An analysis method for eddy current loss in a magnet of a permanent magnet motor, characterized in that the analysis is performed using an analysis model in which a gap _Gl is set in which the magnetic resistance of the entire motor except _a is equivalently replaced . The magnet of the permanent magnet motor according to claim 1 , wherein the length of the gap G _l is determined from a magnetic resistance R _i in consideration of non-linearity of the entire motor other than the magnet with respect to a current flowing on the magnet surface. Internal eddy current loss analysis method. The magnetic resistance R _i is obtained by calculating a change amount Δφ of the magnetic flux linked to the magnet when the magnetization amount M of the magnet is increased by a minute amount ΔM.

Where L _l is the magnet length, L _w is the magnet width, L _t is the magnet thickness, μ _r is the magnet recoil permeability, R _m is the magnet reluctance, R _t is the total motor reluctance,
The method for analyzing eddy current loss in a magnet of a permanent magnet motor according to claim 2 , wherein the eddy current loss analysis method is used.

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