JP7057235B2 - Divided magnet eddy current loss analysis method - Google Patents

Description

The present invention relates to a method for analyzing split magnet eddy current loss.

Permanent magnet-driven motors have become widespread due to the progress in miniaturization and higher efficiency of motors. High-performance rare earth sintered magnets represented by neodymium magnets, which have high magnetic properties, are often used as magnets used in motors, but these magnets are higher than general ferrite magnets. Has conductivity.

Further, the magnet installed in the motor is fixed to the rotor of the motor and rotates together with the rotor.

In the case of a synchronous motor, the magnet rotates in synchronization with the rotational fundamental wave component of the magnetic field, so that the rotational fundamental wave component is regarded as a static magnetic field when viewed in the rotating coordinate system mounted on the magnet.

However, since the stator of the motor has a slot structure, the magnetic resistance changes due to the rotation of the rotor, and the rotating magnetic field rotates while being distorted in time. Therefore, in addition to the rotational fundamental wave component, a temporal and spatial harmonic flux component is applied to the magnet, and an eddy current is generated in the magnet.

Further, in the case of a synchronous motor driven by an inverter, the coil current flowing through the stator has many time harmonic components, which also causes eddy current generation.

The heat generated by the magnet caused by the eddy current generated in the magnet leads to thermal demagnetization of the magnet, deterioration of magnetic characteristics, and deterioration of motor operating efficiency.

Therefore, in order to suppress the generation of eddy current, the magnet used for the motor is divided into the circumferential direction and the rotation axis direction of the motor.

The motor has substantially the same structure in the direction of the rotation axis, and the magnetic flux flows in the in-plane direction perpendicular to the rotation axis. Therefore, when the magnet is divided in the circumferential direction of the motor, the eddy current field generated in the magnet can be grasped by performing the two-dimensional magnetic field analysis on the plane perpendicular to the rotation axis. However, when the magnet is divided in the direction of the rotation axis of the motor, it is necessary to grasp the three-dimensional eddy current field, and the three-dimensional magnetic field analysis is required.

However, if all three-dimensional magnetic field analysis is performed on the entire analysis system, the analysis scale becomes large and the analysis time becomes enormous.

As a background technique in this technical field, there is Japanese Patent Application Laid-Open No. 2010-72773 (Patent Document 1).
This publication describes a method for analyzing the eddy current loss in a magnet of a permanent magnet type motor with a shortened calculation time. In particular, an analysis method using both the three-dimensional finite element method and the two-dimensional finite element method is described. It is described that the analysis of the entire motor is a two-dimensional magnetic field analysis, and the three-dimensional analysis for calculating the eddy current loss in the magnet is performed by the step-by-step method with only the magnet as the analysis region.

Japanese Unexamined Patent Publication No. 2010-72773

Patent Document 1 describes a method for analyzing an eddy current loss in a magnet of a permanent magnet type motor. However, in the eddy current loss analysis method described in Patent Document 1, when the magnet region is taken out and three-dimensional analysis is performed, it is necessary to set an air layer for modeling the magnetoresistance around the magnet region. Therefore, it is necessary to change the thickness of the air layer as the rotor of the motor rotates.

Therefore, in the eddy current loss analysis method described in Patent Document 1, it is necessary to carry out a two-dimensional transient magnetic field analysis in order to obtain a time change in the thickness of the air layer.

Therefore, the present invention provides a split magnet eddy current loss analysis method capable of analyzing a magnet eddy current loss by performing a simple two-dimensional transient magnetic field analysis. For example, the present invention provides a split magnet eddy current loss analysis method capable of analyzing the eddy current field and eddy current loss of a magnet split in the rotation axis direction of a rotating machine at high speed.

In order to solve the above problems, in the split magnet vortex current loss analysis method of the present invention, a plane perpendicular to the rotation axis of a rotating machine having a magnet and a magnetic material is divided into elements, and two-dimensional magnetic field analysis is performed. Then, the partial region including the magnet was extracted from the region of the two-dimensional magnetic field analysis performed as a partial two-dimensional mesh, and the time-series data of the magnetic permeability in each element of the partial two-dimensional mesh and the boundary region of the partial two-dimensional mesh. The time-series data of the magnetic vector potential value in the above is stored, and the extracted partial two-dimensional mesh is stacked in the direction of the rotation axis to half the length in the axial direction of the magnet to form a partial three-dimensional mesh. The magnetic permeability at each time in the transient analysis is assigned to each element of the original mesh, and the magnetic vector potential value at each time and the rotation axis direction of each element are on the side in the rotation axis direction in the boundary region of each element of the partial three-dimensional mesh. A series of these processes, in which the product of the length of the side of the magnet is set as the boundary condition information, the three-dimensional magnetic field analysis is performed using the assigned magnetic permeability and the boundary condition information, and the vortex current loss of the magnet is calculated. Is characterized by being executed by a computer .

According to the present invention, it is possible to provide a split magnet eddy current loss analysis method capable of analyzing a magnet eddy current loss by performing a simple two-dimensional transient magnetic field analysis. For example, according to the present invention, it is possible to provide a split magnet eddy current loss analysis method for analyzing the eddy current field and eddy current loss of a magnet split in the rotation axis direction of a rotating machine at high speed.

Issues, configurations and effects other than those mentioned above will be clarified by the description of the following examples.

It is explanatory drawing which shows the analysis process of the first half of Example 1. FIG. It is explanatory drawing which shows the analysis process of the latter half of Example 1. FIG. It is explanatory drawing which shows the specific example in Example 1, and is explanatory drawing which shows that the partial 2D mesh is extracted from the 2D mesh, and the partial 3D mesh is generated based on the partial 2D mesh. It is a eddy current density vector distribution map in a magnet obtained by three-dimensional analysis. It is explanatory drawing which shows the analysis process of the first half of Example 2. It is explanatory drawing which shows the analysis process of the latter half of Example 2. It is explanatory drawing which shows the specific example in Example 2, and is explanatory drawing which shows that the partial 2D mesh is extracted from the 2D mesh, and the partial 3D mesh is generated based on the partial 2D mesh. It is explanatory drawing which shows the 1st analysis process of the first half in Example 3. FIG. It is explanatory drawing which shows the 2nd analysis process of the first half in Example 3. FIG. It is explanatory drawing which shows the analysis process of the latter half in Example 3. FIG. It is explanatory drawing which shows the relationship between the magnet shaft length / magnet width, and the compounding ratio. It is explanatory drawing which shows the relationship between the time step and the eddy current loss in a magnet (when the reaction magnetic field by a magnet eddy current is small). It is explanatory drawing which shows the relationship between the time step and the eddy current loss in a magnet (when the reaction magnetic field by a magnet eddy current is large). It is explanatory drawing which shows the analysis process of the latter half in Example 4. FIG. It is a block diagram of the hardware for mounting this invention. It is a functional block diagram of the analysis system for embodying this invention.

Hereinafter, examples of the present invention will be described with reference to the drawings.

FIG. 1 is an explanatory diagram showing an analysis process in the first half of Example 1.

The two-dimensional analysis process 101 has an input data file 10. The input data file 10 contains two-dimensional mesh data 11 for numerically solving the differential equation, control data 12 for describing analysis conditions for controlling the analysis process, and the magnet and the periphery of the magnet to be analyzed for eddy current loss. Element number data 31 corresponding to the partial two-dimensional mesh element including the region (partial region consisting of the magnet to be analyzed for eddy current loss and the peripheral region adjacent to the magnet), and the node corresponding to the boundary node of the partial two-dimensional mesh. It has number data 32. The input data file 10 composed of these data (11, 12, 31, 32) is input to the computer.

A transient two-dimensional magnetic field analysis 21 is executed by the analysis execution module based on the two-dimensional mesh data 11 which is the input data and the control data 12 which describes the analysis conditions.

That is, in this embodiment, a rotating machine having a magnet and a magnetic material (described by using a "motor" in the following embodiment), that is, a plane perpendicular to the rotation axis of the motor is used as a mesh element. Divide and perform two-dimensional magnetic field analysis.

The time series data 41 of the magnetic permeability of each partial two-dimensional mesh element with respect to the element number data 31 corresponding to the partial two-dimensional mesh element input to the computer is stored in the storage device. This is because the magnetic permeability of a non-linear magnetic material changes with time, so that the magnetic permeability distribution obtained by the two-dimensional analysis is diverted to the three-dimensional analysis.

Further, the time-series data 42 of the magnetic vector potential value at the boundary node of each partial two-dimensional mesh with respect to the node number data 32 corresponding to the boundary node of the partial two-dimensional mesh input to the computer is stored in the storage device.

FIG. 2 is an explanatory diagram showing an analysis process in the latter half of the first embodiment.

The three-dimensional analysis process 102 first includes partial three-dimensional mesh data (a thin insulating layer is placed at one end) 51 in which partial two-dimensional meshes are stacked in the direction of rotation axis (perpendicular to the two-dimensional mesh) and an analysis process. The control data 52 that describes the analysis conditions for controlling the above and the control data 52 are input to the computer.

Then, at each time of the three-dimensional transient analysis using the data obtained by the two-dimensional analysis, (1) the magnetic permeability of the corresponding element of the partial three-dimensional mesh is set, and (2) the boundary of the partial three-dimensional mesh. Set the product of the magnetic vector potential value at the corresponding time and the length of the side on the side in the direction of the rotation axis on the surface, and (3) set the zero value on the remaining side on the boundary surface of the 3D mesh. To carry out. The transient in the transient magnetic field analysis includes the time derivative item.

A transient three-dimensional magnetic field analysis 61 is performed by the analysis execution module using the partial three-dimensional mesh data 51, the control data 52, and each setting 53.

After that, the analysis result is stored in the storage device 71, and the analysis result is displayed on the display device 72.

FIG. 3 is an explanatory diagram showing a specific example in the first embodiment, and is an explanatory diagram showing that a partial two-dimensional mesh is extracted from the two-dimensional mesh and a partial three-dimensional mesh is generated based on the partial two-dimensional mesh. ..

In this embodiment, a two-dimensional mesh 300 for two-dimensional transient magnetic field analysis of a motor having a magnet and a magnetic material is prepared, and two-dimensional transient magnetic field analysis is performed. Further, the magnet 303 of interest and the mesh elements in the surrounding area are partially extracted to prepare a partial two-dimensional mesh 305, and the partial two-dimensional mesh 305 is stacked in the direction of the rotation axis of the motor. Prepare. The partial two-dimensional mesh 305 is obtained by extracting a partial region including the magnet 303 and its peripheral region from the region (two-dimensional mesh 300) in which the two-dimensional transient magnetic field analysis is performed.

The motor has a stator 301 and a rotor 302, and a magnet 303 is used for the rotor 302.

First, a two-dimensional transient magnetic field analysis of a motor without eddy currents is performed using a two-dimensional mesh 300. At this time, at each time, the magnetic permeability of each element of the non-linear magnetic material in the partial two-dimensional mesh 305 and the magnetic vector potential value having the rotation axis direction at all the nodes corresponding to the boundary region of the partial two-dimensional mesh 305 are analyzed. Ask for it and store it in the storage device.

The partial two-dimensional mesh 305 targets the elements to be stored as the element number data 31 (see FIG. 1), and here all the elements of the partial two-dimensional mesh. Then, the boundary node to be stored as the node number data 32 is targeted, and here, all the boundary nodes Q of the partial two-dimensional mesh are targeted. In FIG. 3, the node Q is typically indicated by four black circles, but all the nodes on the boundary are targeted.

If the reaction magnetic field due to the magnet eddy current has a large effect, further perform a two-dimensional transient magnetic field analysis of the motor with eddy current. At this time, at each time, the magnetic vector potential value having the rotation axis direction at all the nodes corresponding to the boundary region of the partial two-dimensional mesh 305 is obtained by analysis, and this is also stored in the storage device.

In the following cases, the influence of the reaction magnetic field due to the magnet eddy current can be roughly determined as follows.

Here, d is the thickness of the magnet, a is the shorter length of the width of the magnet and the length in the rotation axis direction, and δ is the skin depth, which can be obtained by the following equation.

Here, f is the frequency of the coil current that excites the magnetic field, μ is the magnetic permeability, and σ is the conductivity.

If g shown in the equation (1) is about 0.01 or less, it can be determined that the reaction magnetic field due to the eddy current is small.

Next, the data of the magnetic permeability stored earlier at each time is set in each element (non-conductive element group) of the non-linear magnetic material of the partial three-dimensional mesh 308, and the boundary region around the partial three-dimensional mesh 308 is set. Each side of the rotation axis direction has the eddy current at each time of the magnetic vector potential value having the rotation axis direction stored earlier. Set the value multiplied by the length of.

Here, γ = 0 means that only the value without eddy current is used, and γ = 1 means that only the value with eddy current is used. If the reaction magnetic field due to the eddy current is small, γ = 0 can be used instead. In this state, a three-dimensional transient analysis is performed.

The compounding ratio γ tends to increase when the reaction magnetic field due to the eddy current is large, and is a monotonic increase function with respect to the ratio of the length and width in the rotation axis direction of the magnet (hereinafter abbreviated as “axis length / width”). Therefore, since it depends on the conductivity of the magnet and the frequency of the coil current, a database is constructed in advance according to the conductivity of the magnet.

FIG. 11 is an explanatory diagram showing the relationship between the magnet shaft length / magnet width and the compounding ratio. As a typical example, FIG. 11 shows the relationship between the compounding ratio γ and the axial length / width of the magnet in the case of a neodymium magnet having a conductivity of 7.1 × 10 ⁵ S / m at a frequency of 1 kHz or less and 2 kHz.

When the influence of the reaction magnetic field due to the eddy current is small at a low frequency of 1 kHz or less, the magnetic vector potential value at the boundary surface of the partial region is almost the same in both cases with and without the eddy current, as described above. As described above, the compounding ratio γ may be set to 0 (zero). In other words, two-dimensional analysis requires only one case without eddy currents.

As described above, FIGS. 1 and 2 show the analysis process, and FIG. 3 shows the setting of the magnetic permeability and the boundary condition information (hereinafter, “boundary”) using a motor in which a magnet is embedded in the rotor as a specific example. The setting of ) described as "condition" is explained. That is, this process is composed of the first half two-dimensional analysis process 101 shown in FIG. 1 and the latter half three-dimensional analysis process 102 shown in FIG.

The partial two-dimensional mesh 305 is a magnet 303 to be analyzed for eddy current loss and a peripheral region in the vicinity surrounding the magnet 303. The three-dimensional analysis process 102 is carried out by using the partial three-dimensional mesh 308 in which the partial two-dimensional mesh 305 is stacked in the rotation axis direction.

As shown in FIG. 3, the partial three-dimensional mesh 308 is configured by stacking a plurality of partial two-dimensional meshes 305 in the rotation axis direction. The stacking height may be half of the length of one divided magnet in the axial direction or the symmetry of the field in the axial direction.

A thin insulating layer (air layer) mesh corresponding to the thickness of the insulating layer on the magnet surface or a gap element (infinitely thin insulating element) representing the thin insulating layer (air layer) is arranged at the uppermost portion of the magnet. In this embodiment, a thin insulating layer mesh having a thickness of about 0.1 mm is arranged at the end in the direction of the rotation axis. When the axial length of the partial 3D mesh 308 to be used is set to the axial length of the magnet, although not explicitly shown in FIG. 3, the magnet surface is insulated not only at the top but also at the bottom. A thin insulating layer mesh corresponding to the thickness of the layer or a gap element representing the thin insulating layer is arranged.

That is, in the partial three-dimensional mesh 308, it is preferable to set an insulating layer (equivalent to an air region in analysis) corresponding to the thickness of the insulating layer on the surface of the magnet 303 at one end in the rotation axis direction. Then, the product of the magnetic vector potential value at each time and the length of the side in the rotation axis direction of each element is set on the side in the rotation axis direction in the boundary region excluding the air region set at one end in the rotation axis direction. It is preferable to set it as a partial three-dimensional mesh 308.

This process will be specifically described with reference to FIG.

The region 81 shown by the broken line of the partial three-dimensional mesh 308 is an element group in which the same two-dimensional elements are stacked in the rotation axis direction.

The magnetic permeability of the element obtained by the two-dimensional analysis corresponding to each time in the three-dimensional transient analysis is set for all the elements of the element group accumulated in the rotation axis direction. This process is performed on all the elements of the partial three-dimensional mesh 308. However, the upper insulating layer (air layer) is excluded. Further, each side of the boundary side 82 (one is shown as a representative in FIG. 3) of the partial three-dimensional mesh 308 whose sides face the rotation axis direction is bounded by the magnetic vector potential value obtained by the two-dimensional analysis. Assign a value multiplied by the length of each side. More specifically, using the boundary side 82 shown in FIG. 3, the length of each side of the boundary side 82 is added to the magnetic vector potential value obtained by the two-dimensional analysis at the node P located at the root of the boundary side 82. The multiplied value is assigned to each side of the boundary side 82.

That is, the magnetic permeability at each time in the transient analysis is assigned to each element of the partial 3D mesh 308, and the magnetic vector potential value and the rotation axis direction at each time are on the side in the rotation axis direction in the boundary region of the partial 3D mesh 308. The product with the length of the side of is set as the boundary condition.

Since the three-dimensional magnetic field analysis described later is premised on the side element finite element method, the directions of the sides are set in the same direction. This process is performed on all the boundary edges facing the rotation axis direction. A zero value is set for other boundary edges. These boundary edge setting values are the boundary conditions in the three-dimensional transient analysis.

Based on the above preparations, a transient three-dimensional magnetic field analysis is performed using the analysis execution module. FIG. 4 is an eddy current density vector distribution diagram in a magnet obtained by three-dimensional analysis. When the stacked height of the partial three-dimensional mesh 308 is half the axial length of the magnet 303, an eddy current field that circulates inside the magnet 303 in the rotation axis direction can be obtained as shown in FIG.

A three-dimensional magnetic field analysis is performed using the partial three-dimensional mesh 308 to calculate the eddy current loss of the magnet 303.

When the stacked height of the partial three-dimensional mesh 308 is the axial length of the magnet, the eddy current field of FIG. 4 rotated 180 degrees so that the upper surface is the lower surface is added to the lower part of FIG. The entire circulating eddy current field can be obtained. From this result, the time average value W of the eddy current loss generated in the target magnet can be obtained by using the equation (3).

Here, J is an eddy current density vector, σ is the conductivity of the magnet, <> is the time average value of the amount in parentheses, and V _mag is the magnet region as the integration region. When the stacked height of the three-dimensional mesh is half the length in the axial direction of the magnet, it is necessary to double the value obtained by the equation (3).

A process 71 (see FIG. 2) for storing these analysis results in the storage device and a process 72 (see FIG. 2) for displaying the analysis results on the display device are performed.

According to this embodiment, the magnet shape is not limited to a rectangular parallelepiped in principle, and there is an effect that a three-dimensional eddy current field and an eddy current loss in which a two-dimensional cross section flows through a magnet having an arbitrary shape can be analyzed.

FIG. 5 is an explanatory diagram showing an analysis process in the first half of Example 2. FIG. 6 is an explanatory diagram showing an analysis process in the latter half of the second embodiment. FIG. 7 is an explanatory diagram showing a specific example in the second embodiment, and is an explanatory diagram showing that a partial two-dimensional mesh is extracted from the two-dimensional mesh and a partial three-dimensional mesh is generated based on the partial two-dimensional mesh.

The same components as those in the first embodiment may be designated by the same reference numerals and the description thereof may be omitted.

Example 2 of the present invention will be described with reference to FIGS. 5, 6 and 7. In the second embodiment, similarly to the first embodiment, the first half two-dimensional analysis process 101'(there is no element number data 31 in FIG. 1, and therefore the input data file 10') shown in FIG. 5 and FIG. It is composed of the latter half of the three-dimensional analysis process 102'(the magnetic permeability is not set in each setting. Therefore, each setting is 53'). As shown in FIG. 7, in the two-dimensional mesh 300, a thin insulating layer is formed around the magnet 303, and the partial three-dimensional mesh 308 is formed of the magnet 303 and the element group of the insulating layer adjacent to the periphery of the magnet 303. Configure.

In this case, when the recoil magnetic permeability of the magnet 303 is constant, the magnetic permeability is constant over time in the partial region, so that it is not necessary to store the magnetic permeability in the two-dimensional analysis. Therefore, as shown in FIGS. 5 and 6, it is not necessary to store the magnetic permeability shown in Example 1 and to assign the magnetic permeability in the three-dimensional analysis, and the others are shown in FIGS. 1 and 2. It is the same as the processing content.

That is, an air region corresponding to the thickness of the insulating layer on the surface of the magnet 303 is set around the magnet 303, and a two-dimensional magnetic field analysis is performed. Then, the time series data of the magnetic vector potential value of the boundary region of the partial two-dimensional mesh 305 obtained from the two-dimensional magnetic field analysis is stored. Then, as the boundary condition of the side parallel to the rotation axis direction at the boundary surface of the partial three-dimensional mesh 308, the product of the magnetic vector potential value of the boundary region of the partial two-dimensional mesh 305 and the length of the side parallel to the rotation axis direction is obtained. assign.

In this embodiment, in the partial three-dimensional mesh 308, the side surface and the upper surface of the magnet 303 are covered with an insulating (air) element group.

According to this embodiment, since the magnetic permeability is invariant, it is not necessary to change the matrix component of the matrix equation to be solved at each time in the magnetic field analysis by the finite element method. Therefore, the partial three-dimensional magnetic field analysis is performed in Example 1. It has the effect of being able to be significantly faster than that.

FIG. 8 is an explanatory diagram showing the first analysis process in the first half of the third embodiment. FIG. 9 is an explanatory diagram showing the second analysis process in the first half of the third embodiment. FIG. 10 is an explanatory diagram showing the analysis process in the latter half of the third embodiment.

The same configurations as those in the first and second embodiments may be designated by the same reference numerals and the description thereof may be omitted.

Example 3 of the present invention will be described with reference to FIGS. 8, 9, and 10. This embodiment is a method in consideration of the reaction magnetic field of the eddy current.

8, 9, and 10 show the process of analysis. This process includes the first half of the two-dimensional analysis processes 101'' and 101'' shown in FIGS. 8 and 9, and the second half of the three-dimensional analysis process 102'' shown in FIG. 10 (three-dimensional mesh in each setting). From the product of the magnetic vector potential value obtained by the predetermined compounding ratio and the length of the side with and without eddy current on the side in the direction of the rotation axis at the boundary surface. Therefore, each setting is 53''). It is composed.

As shown in FIG. 8, in the two-dimensional magnetic field analysis, the two-dimensional magnetic field analysis without eddy current is performed. In this analysis, as a special process, time-series data (permeability time-series data in the nonlinear magnetic element) 43 of the magnetic permeability of all the elements in the obtained nonlinear magnetic material region is stored.

A transient two-dimensional magnetic field analysis (when there is no eddy current) 21'is executed by the analysis execution module based on the two-dimensional mesh data 11 which is the input data and the control data 12 which describes the analysis conditions. Further, time-series data (in the case of no eddy current) 42'of the magnetic vector potential value at the boundary node of each partial two-dimensional mesh with respect to the node number data 32 corresponding to the boundary node of the partial two-dimensional mesh input to the computer. Store in the storage device.

Next, as shown in FIG. 9, a two-dimensional magnetic field analysis with an eddy current is performed.

At this time, using the magnetic permeability time series data 43 of the non-linear magnetic element already obtained in the first two-dimensional analysis, the magnetic permeability of the non-linear magnetic element at each time is set, and a linear magnetic field analysis is performed. ..

That is, transient two-dimensional magnetic field analysis by the analysis execution module (when there is an eddy current) based on the two-dimensional mesh data 11 which is the input data, the control data 12 which describes the analysis conditions, and the magnetic permeability time-series data 43. Execute 21''. In addition, time-series data (when there is an eddy current) of the magnetic vector potential value at the boundary node of each partial two-dimensional mesh with respect to the node number data 32 corresponding to the boundary node of the partial two-dimensional mesh input to the computer 42''. Is stored in the storage device.

It is different from FIG. 5 in that it has magnetic permeability time series data 43, and therefore, it becomes an input data file 10 ″. Then, due to such a difference, the two-dimensional analysis process 101 "" is performed.

Since the eddy current does not significantly affect the magnetic permeability distribution of the non-linear magnetic material, the magnetic permeability distribution when there is no eddy current can be used approximately. As a result, since the second two-dimensional magnetic field analysis is a linear magnetic field analysis, a high-speed analysis of about 3 to 5 times is possible as compared with the first two-dimensional magnetic field analysis which is a nonlinear magnetic field analysis.

Let Aeddy and Anoeddy be the magnetic vector potentials with and without eddy currents obtained by the above-mentioned two two-dimensional analyzes. The magnetic vector potential A used in the three-dimensional analysis is synthesized as follows using the compounding ratio γ (0 ≦ γ ≦ 1).

This compounding ratio γ takes a larger value as the influence of the reaction magnetic field due to the eddy current increases. As the magnet becomes longer in the direction of the rotation axis, the compounding ratio γ becomes monotonously large. The relationship between the axial length-width ratio of the magnet and the compounding ratio γ is shown again in FIG.

The solid line is the compounding ratio when the frequency is 1 kHz or less, and the broken line is the compounding ratio when the frequency is 2 kHz or less. This is a compounding ratio γ adjusted so that the time average values of the eddy current losses in both full 3D analysis and partial 3D analysis are almost the same, and it varies slightly depending on the analysis target, but it depends on the analysis target. Even if the same values as in FIG. 11 are used, approximately good results can be obtained.

FIG. 12 is an explanatory diagram showing the relationship between the time step and the eddy current loss in the magnet (when the reaction magnetic field due to the magnet eddy current is small). Further, FIG. 13 is an explanatory diagram showing the relationship between the time step and the eddy current loss in the magnet (when the reaction magnetic field due to the magnet eddy current is large).

The analysis examples shown in FIGS. 12 and 13 are the results of calculations using the magnet shown in FIG. 7 and a partial three-dimensional mesh composed of a thin air region surrounding the magnet.

FIG. 12 shows the case where the frequency is 100 Hz (the reaction magnetic field due to the eddy current is small), and FIG. 13 shows the case where the frequency is 1000 Hz (the reaction magnetic field due to the eddy current is large).

If the reaction magnetic field due to the eddy current is small, the eddy current loss waveform by the partial three-dimensional analysis agrees very well with that by the full three-dimensional analysis as shown in FIG. Further, if the reaction magnetic field due to the eddy current is large, the eddy current loss waveform by the partial three-dimensional analysis will be slightly different from that by the full three-dimensional analysis as shown in FIG. 13, but the degree of approximation is generally good. Is.

That is, two-dimensional magnetic field analysis is performed for two cases with and without eddy current in the magnet 303, and time-series data of the magnetic vector potential values of the two cases obtained from the two-dimensional magnetic field analysis are stored.

Then, the magnetic vector potential value at each time of the two stored cases is mixed with the magnetic vector potential value at the blending ratio γ (the blending of the magnetic vector potential value with the eddy current with respect to the magnetic vector potential value without the eddy current). The ratio γ increases substantially monotonically with respect to the ratio of the axial length of the magnet to the width of the magnet), and it is preferable to set the product of the length of the side of each element in the rotation axis direction as partial three-dimensional mesh data. ..

FIG. 14 is an explanatory diagram showing the analysis process in the latter half of the fourth embodiment.

In this embodiment, the partial three-dimensional mesh is configured only by the magnet shown in FIG. 7 and the air region adjacent to the magnet.

In the present embodiment, similarly to the second embodiment, the first half of the two-dimensional analysis process 101 ′ and the latter half of the three-dimensional analysis process 102 ″ shown in FIG. 14 are configured.

Since the first half of the two-dimensional analysis process 101 ″ is the same as that of the second embodiment, the latter half of the three-dimensional analysis process 102 ″ will be described here.

The same configurations as those in the first, second, and third embodiments may be designated by the same reference numerals and the description thereof may be omitted.

FIG. 14 shows the latter three-dimensional analysis process 102 ″. The three-dimensional mesh data 51 and the control data 52 describing the analysis conditions for controlling the analysis process are input to the computer. At each time of the 3D transient analysis, using the data obtained by the 2D analysis, the value and side of the harmonic principal component of the magnetic vector potential value at the corresponding time are on the side in the direction of the rotation axis at the boundary surface of the 3D mesh. Set the product of the lengths of. Other processes related to boundary condition setting are the same as those in the second embodiment.

Based on the above preparations, the three-dimensional magnetic field analysis 61'in the frequency domain by the analysis execution module is performed. It is a general solution that replaces the time derivative operator of the time derivative term with fixed magnetic permeability with jω (j: pure imaginary number, ω: angular frequency), and a complex solution related to the magnetic vector potential value can be obtained by one convergence calculation. It is a solution for the main harmonics set by the real part. By executing this analysis only for a plurality of major harmonics that can approximately describe the phenomenon, the entire phenomenon can be analyzed. From the calculated eddy current field for each major harmonic

Therefore, the eddy current loss Wn with respect to the nth harmonic eddy current density component Jn can be obtained.

A process 71 for storing these analysis results in the storage device and a process 72 for displaying the analysis results on the display device are performed.

That is, two cases with and without eddy currents in the magnet 303 were subjected to two-dimensional magnetic field analysis, and the two cases obtained from the two-dimensional magnetic field analysis at each node in the boundary region of the partial two-dimensional mesh 305. Conserve the harmonic component of the magnetic vector potential value.

Then, the magnetic vector potential value in which the harmonic components of the magnetic vector potentials of the two cases are blended at the blending ratio γ (the blending ratio γ of the magnetic vector potential value when there is a vortex current with respect to the magnetic vector potential value when there is no vortex current is , Monotonically increases with respect to the ratio of the axial length of the magnet to the width of the magnet) and the length of the side of each element in the direction of the axis of rotation, the boundary parallel to the axis of rotation at the interface of the partial three-dimensional mesh 308. It is preferable to set the boundary condition on the side and perform the three-dimensional eddy current analysis of the magnet 303 in the frequency region using this boundary condition. It should be noted that the stored magnetic permeability of each element at a certain time or the time-averaged magnetic permeability is set in advance.

In addition, when performing a two-dimensional magnetic field analysis for two cases with and without eddy currents in the magnet, the magnetic permeability of each element of the divided non-linear magnetic material region is preserved, and the preserved magnetic permeability is used. It is preferable to carry out the set linear magnetic field analysis.

According to the present invention, there is an effect that a three-dimensional eddy current field and an eddy current loss related to a plurality of harmonic components flowing through a magnet can be analyzed by a convergence calculation of only the number of harmonic components.

FIG. 15 is a block diagram of hardware for implementing the present invention.

FIG. 15 describes an analysis system that executes the methods shown in these examples, and is a hardware configuration diagram of the analysis system.

This analysis system includes a computer 201, a display device 202, a storage device 203, and an input device 204.

The input device 204 is, for example, a keyboard or a mouse, and is used for inputting data necessary for processing of the computer 201. The required data is, for example, mesh data or control data required for setting analysis conditions.

The storage device 203 stores the processing result data of the computer 201 and the input data input via the input device 204 as a data file. The storage device 203 may be installed outside the computer 201 and connected to the computer 201, or may be installed inside the computer 201.

The display device 202 displays the data file (processing result data, input data, etc.) of the storage device 203.

The computer 201 executes a program for realizing the analysis process shown in FIGS. 1, 2, 5, 6, or 8 to 10 or 14 based on the data file of the storage device 203. ..

This program is, for example, an analysis execution module obtained by compiling a source file in which an algorithm coding the method shown in these examples is coded. The analysis is executed by the CPU (Central Processing Unit) of the computer 201 executing the analysis execution module read into the memory.

FIG. 16 is a functional configuration diagram of an analysis system for embodying the present invention.

FIG. 16 shows the function of the analysis system of FIG. This analysis system includes a discretized data storage unit 111, a control data storage unit 112, an analysis unit 120, an analysis result storage unit 131, and an analysis result display unit 132.

The discretized data storage unit 111 stores mesh data for numerically solving a differential equation as discretized data. This discretized data includes mesh data in the analysis region (position coordinate components of each node constituting the mesh, node numbers of the nodes constituting each element, material numbers of each element, etc.).

The control data storage unit 112 stores control data that summarizes analysis conditions and the like for executing analysis processing by the analysis unit 120. This control data contains information about the magnetic material existing in the magnetic material region. Information about the magnetic material is, for example, the material properties of the magnetic material region and the residual magnetization of the magnet.

Various types of data stored in the discretized data storage unit 111 and the control data storage unit 112 are input via the input device 204 and stored in the storage device 203.

The analysis unit 120 executes an analysis process such as numerically solving a differential equation for the analysis region according to the data contents of the discretized data storage unit 111 and the control data storage unit 112, and the eddy current generated in the magnet. Calculate field and eddy current losses.

The analysis result storage unit 131 stores the analysis result by the analysis unit 120.

The analysis result display unit 132 displays the analysis result by the analysis unit 120 on the screen as a diagram as shown in FIG. 4, for example.

These examples include not only a method for analyzing split magnet eddy current loss, but also a method for displaying the analysis result and a program for executing the analysis method. Further included is a storage medium in which such a program is recorded, that is, a computer-readable storage medium in which the program related to the split magnet eddy current loss analysis method in these examples is stored.

In other words, these examples also include a display method that displays the analysis results analyzed by such a split magnet eddy current loss analysis method, and a computer equipped with an execution module that compiles a program that describes such a split magnet eddy current loss analysis method. There is a feature.

Further, in this embodiment, the split magnet vortex current loss analysis device that executes the split magnet vortex current loss analysis method is the above-mentioned computer (the computer that executes the split magnet vortex current loss analysis method described in the above-mentioned embodiment). , A storage device for storing input data for transient magnetic field analysis of a rotating machine such as a motor, and a storage device for storing the analysis data, and a display device for displaying the analysis result as the analysis data.

The contents described in these examples are not limited to the rectangular parallelepiped shape of the magnet shape. That is, the method described in these examples does not assume that the shape of the magnet is a rectangular parallelepiped, is versatile, and the magnet shape is not only a rectangular parallelepiped but also a more general magnet shape in the axial direction. There is an effect that the eddy current loss of the divided magnet can be calculated.

As described above, according to these examples, it is possible to easily determine the dependence of the vortex current loss of the magnet in the motor using the permanent magnet as the rotor depending on the number of divisions of the magnet in the axial direction. Moreover, it can be obtained at high speed. Calculation of hundreds of steps of tens of thousands of elements can be calculated in about 10 minutes.

The present invention is not limited to the above-described embodiment, and includes various modifications.

201 Computer 202 Display device 203 Storage device 204 Input device 10 Input data file 11 Two-dimensional mesh data 12 Control data 21 Two-dimensional magnetic field analysis 31 Element number data 32 Node number data 41 Time-series data of magnetic permeability 42 When magnetic vector potential value Series data 51 Partial three-dimensional mesh data 61 Three-dimensional magnetic field analysis 71 Process of storing in storage device 72 Process of displaying in display device

Claims (6)

A plane perpendicular to the axis of rotation of a rotating machine with a magnet and a magnetic material is divided into elements, and a two-dimensional magnetic field analysis is performed.
A partial region containing the magnet is extracted from the region of the two-dimensional magnetic field analysis performed as a partial two-dimensional mesh, time-series data of the magnetic permeability of each element of the partial two-dimensional mesh, and the partial two-dimensional mesh. Saves time-series data of magnetic vector potential values in the boundary region,
The extracted partial two-dimensional mesh is stacked in the direction of the rotation axis to half the length in the axial direction of the magnet to form a partial three-dimensional mesh.
The magnetic permeability at each time in the transient analysis is assigned to each element of the partial 3D mesh, and the magnetic vector potential value and the rotation axis direction at each time are on the side of the partial 3D mesh in the rotation axis direction in the boundary region. Set the product with the length of the side as the boundary condition information ,
Using the assigned magnetic permeability and the boundary condition information , a three-dimensional magnetic field analysis is performed to calculate the eddy current loss of the magnet.
A method for analyzing split magnet eddy current loss, which comprises executing the above series of processes by a computer . In the partial three-dimensional mesh, an air region corresponding to the thickness of the insulating layer on the surface of the magnet is set at one end in the rotation axis direction.
The product of the magnetic vector potential value at each time and the length of the side in the rotation axis direction of each element is set on the side in the rotation axis direction in the boundary region excluding the air region set at one end in the rotation axis direction. Set as boundary condition information ,
The split magnet eddy current loss analysis method according to claim 1, wherein the series of processes is executed by a computer . A plane perpendicular to the axis of rotation of a rotating machine having a magnet covered with a thin air layer corresponding to an insulating layer and a magnetic material was divided into elements, and a two-dimensional magnetic field analysis was performed.
The magnet and the thin air layer surrounding it are extracted from the area of the two-dimensional magnetic field analysis performed as a partial two-dimensional mesh, and the time-series data of the magnetic vector potential value in the boundary region of the partial two-dimensional mesh is stored. ,
The extracted partial two-dimensional mesh is stacked in the direction of the rotation axis to half the length in the axial direction of the magnet to form a partial three-dimensional mesh.
The product of the magnetic vector potential value and the length of the side in the rotation axis direction at each time is set as the boundary condition information on the side in the rotation axis direction in the boundary region of the partial three-dimensional mesh.
Using the boundary condition information , a three-dimensional magnetic field analysis is performed to calculate the eddy current loss of the magnet.
A method for analyzing split magnet eddy current loss, which comprises executing the above series of processes by a computer . The two-dimensional magnetic field analysis was performed on the two cases with and without eddy currents in the magnet, and the time-series data of the magnetic vector potential values of the two cases obtained from the two-dimensional magnetic field analysis were saved. ,
The product of the magnetic vector potential value blended at each time of the stored two cases and the magnetic vector potential value blended at the blending ratio γ and the length of the side in the rotation axis direction of each element is set as the boundary condition information .
The split magnet eddy current loss analysis method according to claim 3, wherein the series of processes is executed by a computer . The two-dimensional magnetic field analysis was performed on the two cases with and without eddy currents in the magnet, and the harmonic components of the magnetic vector potential values of the two cases obtained from the two-dimensional magnetic field analysis were preserved. ,
The product of the magnetic vector potential value in which the harmonic components of the magnetic vector potentials of the two cases are blended at the blending ratio γ and the length of the side of each element in the rotation axis direction is set as the boundary condition information , and the boundary condition information is set. Is used to perform a three-dimensional eddy current analysis of the magnet in the frequency region.
The split magnet eddy current loss analysis method according to claim 3, wherein the series of processes is executed by a computer . A computer that executes the split magnet vortex current loss analysis method according to claim 1, a storage device that stores input data for transient magnetic field analysis of a rotating machine and analysis data, and a display device that displays analysis results as analysis data. A split magnet vortex current loss analyzer characterized by having.

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