JP7348525B2 - Core design device, core design method, and program - Google Patents

Description

The present invention relates to a core design device, a core design method, and a program, and is particularly suitable for use in designing a core.

In electrical equipment having a core, the design of the core has a significant impact on the performance of the electrical equipment. For example, the shape of the rotor of an IPMSM (Interior Permanent Magnet Synchronous Motor) is becoming more complex. In such rotors, it is possible to improve torque characteristics, reduce iron loss, and alleviate stress by controlling the magnetic flux by appropriately placing a flux barrier around the permanent magnets embedded in the iron core. . The design of such cores is often performed using empirical guidelines or parameter studies.
However, such a method relies heavily on the knowledge and experience of the designer. Therefore, optimization techniques using numerical analysis have been developed.

Non-Patent Document 1 describes designing a flux barrier for an IPM motor by topology optimization. Topology optimization is a general term for a method of searching for an optimal shape by changing the shape with a high degree of freedom within a design area. One of the topology optimization methods is the On-Off method. The On-Off method is a method that divides the design area into multiple finite elements and switches the physical properties of each finite element. For example, the on and off states correspond to magnetic material and air, respectively. An optimization method is used to search for the on and off states of each finite element such that the objective function is minimized (or maximized) within the range where the constraint conditions are satisfied. In Non-Patent Document 1, instead of giving on and off states to each finite element independently, a normalized Gaussian function (NGnet (Normalized Gaussian Network)) whose value changes spatially smoothly is given, and the normalized Gaussian Gives on and off states depending on the output of the function.

Patent No. 3643334

Takahiro Sato and 5 others, "Rotor shape optimization of embedded magnet synchronous motors by topology optimization", IEEJ Transactions on Industry Applications, Vol. 135, No. 3, IEEJ Transactions on Industry Applications, Vol. 135, No. 3, pp.291-298, 2015 Takayoshi Nakata and Norio Takahashi, "Finite Element Method for Electrical Engineering", 2nd edition, Morikita Publishing Co., Ltd., April 1986. Masashi Fujita and 9 others, "Electromagnetic field analysis of benchmark motors of the Institute of Electrical Engineers of Japan -Characteristics evaluation of IPM motors-", Institute of Electrical Engineers of Japan Joint Study Group on Stationary and Rotating Machines, SA11-27/RM-11-27, pp.73-78 , January 2011 Edited by Japan Society for Plastic Processing, "Nonlinear Finite Element Method - From Linear Elastic Analysis to Plastic Processing Analysis", Coronasha Co., Ltd., December 1994.

However, in the technique described in Non-Patent Document 1, the result of the optimization calculation depends on the pitch at which the normalized Gaussian function is arranged. Advanced know-how is required to determine the pitch at which the normalized Gaussian function is arranged. Therefore, it is not easy to appropriately set the pitch at which the normalized Gaussian function is arranged. Furthermore, since the number of normalized Gaussian functions is the number of weighting coefficients that are decision variables, increasing the shape resolution widens the solution space. Therefore, the technique described in Non-Patent Document 1 has a problem in that the core cannot be designed easily and accurately.

The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to enable easy and accurate core design.

The core design device of the present invention is a core design device that performs calculations related to the design of a core shape using an optimization problem algorithm, and in which elements of the core are Among them, a setting means for setting the basic shape of at least one design target element as a design target element, which is a design target element, and for deforming and moving the basic shape of the design target element set by the setting means optimization calculation means for calculating an optimal solution of a mapping applied to the basic shape of the element to be designed using an algorithm for the optimization problem; The design calculates the mapping when the value indicating the characteristics of the electrical equipment when the electrical equipment having the core including the design target element is operated is maximized or minimized in the algorithm of the optimization problem. It is characterized in that it is calculated as the optimal solution of mapping applied to the basic shape of the target element.

The core design method of the present invention is a core design method that performs calculations related to the design of a core shape using an optimization problem algorithm, and in which elements of the core are Among them, a setting step of setting the basic shape of at least one design target element as a design target element, which is a design target element, and a step of deforming and moving the basic shape of the design target element set by the setting process. an optimization calculation step of calculating an optimal solution of a mapping to be applied to the basic shape of the element to be designed using an algorithm for the optimization problem; The design calculates the mapping when the value indicating the characteristics of the electrical equipment when the electrical equipment having the core including the design target element is operated is maximized or minimized in the algorithm of the optimization problem. It is characterized in that it is calculated as the optimal solution of mapping applied to the basic shape of the target element.

The program of the present invention is characterized in that it causes a computer to function as each means of the core design device.

According to the present invention, the core can be designed easily and accurately.

FIG. 1 is a diagram showing an example of the functional configuration of a core design device. FIG. 2 is a flowchart illustrating an example of a core design method. FIG. 3 is a diagram conceptually showing an example of the core design process. FIG. 4 is a diagram illustrating an example of overlap. FIG. 5 is a diagram illustrating an example of protrusion. FIG. 6 is a diagram showing a core before design and a core after design.

Hereinafter, one embodiment of the present invention will be described with reference to the drawings.
Note that the comparison objects are the same in terms of length, position, size, spacing, etc., as well as cases in which they are strictly the same, and items that are different within the scope of the invention (for example, due to tolerances determined at the time of design). This shall also include items that are different within the scope.
FIG. 1 is a diagram showing an example of the functional configuration of the core design device 100. FIG. 2 is a flowchart illustrating an example of a core design method performed by the core design device 100. The hardware of the core design device 100 is realized, for example, by using an information processing device including a CPU, ROM, RAM, HDD, and various interfaces, or by using dedicated hardware.

The core design device 100 performs calculations related to the design of the core shape using an optimization problem algorithm. Here, the core elements include the core, tangible objects (parts and materials) placed inside the core, spaces formed inside the core, and spaces in recesses on the outer and inner peripheries of the core. It will be done. Parts of the tangible objects (components and materials) placed inside the core may be exposed. If at least one of the tangible objects (parts and materials) placed inside the core, the space formed inside the core, and the recessed spaces on the outer and inner peripheries of the core is an element of the core, then Not everything has to be a core element.

In FIG. 1, the core design device 100 includes a setting section 110, an optimization calculation section 120, and an output section 130.
In step S201 in FIG. 2, the setting unit 110 sets information on a design area that is a design target area of the core, information on at least one design target element, and information on core elements other than the design target element. The design target element is an element to be designed among the core elements.

FIG. 3 is a diagram conceptually showing an example of the core design process. The region shown in FIG. 3 is one of four regions obtained by dividing a cross section of the IPMSM rotor perpendicular to the center line of the IPMSM into four equal parts. It is assumed that these four regions have a 4-fold symmetrical relationship. Therefore, by designing one of these four regions, it is possible to design the entire cross section of the IPMSM rotor cut perpendicular to the centerline of the IPMSM.

Here, it is assumed that the rotor of the IPMSM has an iron core, a permanent magnet disposed within the iron core, and a flux barrier formed within the iron core. Therefore, by rotating the iron core, permanent magnet, and flux barrier designed in one of these four regions by 90°, 180°, and 270° around the centerline of the IPMSM, The entire cross-section of the rotor taken perpendicular to the centerline of the IPMSM can be designed. It is assumed that the flux barrier is space (air). However, instead of space, the flux barrier may be made of, for example, a non-magnetic material.

In this embodiment, a case where a flux barrier formed in the core of a rotor of an IPMSM is an element to be designed will be described as an example. However, an explanation that takes into consideration the fact that permanent magnets are included in the design in addition to flux barriers is also included. In this way, when designing a rotor for an IPMSM, for example, at least one of a flux barrier and a permanent magnet can be used as a design target element.
Further, in this embodiment, a case will be described using as an example a case where a two-dimensional shape of a cross section cut perpendicularly to the center line of an IPMSM is designed. In FIG. 3, the cross section taken perpendicular to the centerline of the IPMSM is the xy plane.

FIG. 3A is a diagram showing an example of a core element before the basic shape of the design target element is set.
In the example shown in FIG. 3A, it is assumed that the design area is an area surrounded by the outer edge of the core area 310. As shown in FIG. 3A, the outer edge of the core region 310 has an annular sector shape with a central angle of 90°. The setting unit 110 sets the coordinates of an area surrounded by the outer edge of the core area 310 as information indicating the position of the design area. Further, the setting unit 110 sets identification information ID1 for each coordinate of the design area as information for identifying the design area.

In the example shown in FIG. 3(a), it is assumed that the core elements other than the design target elements are permanent magnets. Therefore, the area of the core element other than the design target element is an area surrounded by the outer edge of the permanent magnet area 320. As shown in FIG. 3, the outer edge of the permanent magnet region 320 has a rectangular shape. The setting unit 110 sets the coordinates of the area surrounded by the outer edge of the permanent magnet area 320 as information indicating the position of the core element other than the design target element. Further, the setting unit 110 sets identification information ID2 for each coordinate of the region of the core element other than the design target element as information for identifying the core element other than the design target element. Note that when there are multiple types of core elements other than the design target element, the setting unit 110 sets different identification information ID2 for each type of design target element.

Further, the setting unit 110 sets identification information ID3 as information for identifying the design target element. Note that when there are multiple types of design target elements, the setting unit 110 sets different identification information ID3 for each type of design target element.

The above-mentioned information indicating the position of the design area and information indicating the positions of core elements other than the design target element are input to the core design apparatus 100 via the interface of the core design apparatus 100, for example. By operating the user interface of the core design device 100, the designer inputs into the core design device 100 information indicating the position of the design area and information indicating the positions of core elements other than the design target element. can be done. Further, the external device transmits information indicating the position of the design area and information indicating the positions of core elements other than the design target element to the core design device 100, and the external device receives these information through the communication interface. Accordingly, information indicating the position of the design area and information indicating the positions of core elements other than the design target element can be input to the core design apparatus 100.

Further, the identification information ID1 that identifies the design area, the identification information ID2 that identifies the core elements other than the design target element, and the identification information ID3 that identifies the design target element are transmitted to the core through the interface of the core design device 100, for example. It is input to the design device 100. The designer can input these identification information ID1 to ID3 into the core design device 100 by operating the user interface of the core design device 100. In addition, the external device sends these identification information ID1 to ID3 to the core design device 100, and the external device receives these identification information ID1 to ID3 through the communication interface, so that these identification information ID1 to ID3 are sent to the core design device 100. It can be input into the design device 100.

In addition, the identification information ID1 that identifies the design area and the identification information ID2 that identifies the core elements other than the design target elements are information indicating the position of the design area and information indicating the position of the core elements other than the design target elements. Based on this, the setting unit 110 may automatically set the setting.

Next, in step S202, the setting unit 110 sets information on the basic shape of the design target element set in step S201. The basic shape can be, for example, a shape that is assumed to be the shape of the element to be designed. The basic shape is preferably a simple shape such as a circle or a rectangle in order to prevent the final calculated shape from becoming excessively complex. The number of basic shapes is arbitrary and may be one, two, three or more. When a plurality of basic shapes are set, each basic shape may be the same shape or different shapes. The position and size of the basic shape are not particularly limited as long as the basic shape is located within the design area.

The present embodiment will be described using an example in which the element to be designed is a flux barrier. In the IPMSM rotor, the region of the iron core is not surrounded by a flux barrier (the iron core floats within the flux barrier). Therefore, it is preferable that the basic shape of the element to be designed is set such that an element of a different type than the element to be designed is not included inside the element to be designed.

FIG. 3(b) is a diagram showing an example of a core element in which the basic shape of the design target element is set.
In the example shown in FIG. 3(b), two basic shapes are set as the basic shapes of the design target element. The setting unit 110 sets the coordinates of regions 330a and 330b of the basic shape of the element to be designed as information indicating the initial position of the element to be designed. Information indicating the initial position of the design target element is set individually for each of the two basic shapes. The setting unit 110 changes the identification information ID1 set for each coordinate of the regions 330a and 330b of the basic shape of the element to be designed to identification information ID3 that identifies the region of the element to be designed.

Information indicating the initial position of the basic shape of the element to be designed as described above is input to the core design device 100 via the interface of the core design device 100, for example. For example, the design unit 110 displays a GUI (Graphical User Interface) including an image of the core elements shown in FIG. 3A on the computer display. In this GUI, it is assumed that in the image of the core element, a region other than the permanent magnet region 320 in the core region 310 can be specified by operating the user interface of the core design device 100. By making such a designation, the designer can cause the core design apparatus 100 to input information indicating the initial position of the basic shape of the element to be designed.

Further, the external device transmits information indicating the position of the element to be designed to the core design apparatus 100, and the external device receives information indicating the position of the element to be designed via the communication interface, thereby indicating the position of the element to be designed. Information can be input into core design device 100.

Next, in steps S203 to S213, the optimization calculation unit 120 calculates the optimal solution of the mapping to be applied to the basic shape of the design target element in order to deform and move the basic shape of the design target element using the optimization problem algorithm. Calculate using. In this embodiment, an example will be described in which a genetic algorithm, which is one of the metaheuristic methods, is used as an algorithm for an optimization problem.

First, in step S203, the optimization calculation unit 120 derives a plurality of candidates as mapping candidates to be applied to each coordinate of the outer edge of the regions 330a, 330b of the basic shape of the design target element. In the following description, the mapping applied to each coordinate of the outer edge of the regions 330a and 330b of the basic shape of the element to be designed will be abbreviated as mapping as necessary. If the xy coordinates of the outer edges of the areas 330a and 330b of the basic shape of the design target element before mapping are (x, y), then the xy coordinates of the outer edge of the area of the design target element after mapping are (x', y') is expressed by the following equation (1).

In this embodiment, a case where the mapping is a linear mapping will be described as an example. Therefore, the components a, b, c, d, e, and f of the matrix in equation (1) are real numbers (numeric values). In the case of a linear mapping, the mapping is obtained by obtaining these components a to f. Therefore, each of the plurality of mapping candidates includes the values of components a to f. That is, one of the combinations of values of components a to f is one of the mapping candidates. Components a, b, c, and d of the matrix in equation (1) are examples of coefficients that determine mapping. The components e and f of the matrix in equation (1) are examples of constants that determine mapping.
In the first step S203, the optimization calculation unit 120 derives a plurality of mapping candidates using random numbers. In the second and subsequent steps S203, the optimization calculation unit 120 updates the already derived mapping candidates according to the genetic algorithm.

Next, in step S204, the optimization calculation unit 120 selects mapping candidates that have not been selected in step S204 from among the plurality of mappings derived in step S203. If the number of elements to be designed is one, in step S204 one mapping candidate is selected from among the plurality of mapping candidates derived in step S203. If the number of elements to be designed is plural, in step S204, one combination of mapping candidates for the number of elements to be designed is selected from among the plurality of mapping candidates derived in step S203.

Next, in step S205, the optimization calculation unit 120 gives the values of components a to f included in the mapping candidate selected in step S204 to equation (1).
If the number of elements to be designed is one, one mapping candidate is selected in step S204. Therefore, in step S205, the optimization calculation unit 120 gives the values of components a to f included in the one mapping to equation (1). Therefore, only one equation (1) is set.

Then, the optimization calculation unit 120 gives the coordinates (x, y) of the outer edge of the area of the basic shape of the element to be designed to equation (1), and calculates the outer edge of the area of the element to be designed after mapping. The coordinates (x', y') are derived for all the coordinates (x, y) of the outer edge of the area of the basic shape of the element to be designed.

On the other hand, if the number of design target elements is plural, a combination of mapping candidates for the number of design target elements is selected in step S204. In step S205, the optimization calculation unit 120 allocates mapping candidates of the number of design target elements one by one to a plurality of design target regions. Then, the optimization calculation unit 120 provides equation (1) with the values of components a to f included in the mapping candidates for each of the mapping candidates for the number of design target elements. Therefore, Equation (1) is set as many times as there are elements to be designed.

Then, the optimization calculation unit 120 calculates the coordinates (x, y) of the outer edge of the area of the basic shape of the element to be designed by using the components a to f included in the mapping candidates assigned to the element to be designed. (1) to derive the coordinates (x', y') of the outer edge of the area of the element to be designed after the mapping is performed. This is performed for all coordinates (x, y) of the outer edge. The optimization calculation unit 120 performs such derivation for each element to be designed.

In the example shown in FIG. 3(b), the optimization calculation unit 120 calculates the coordinates (x, y) of the outer edge of the area 330a of the basic shape of the element to be designed, using the components a to y assigned to the element to be designed. The coordinates (x', y') of the outer edge of the area of the design target element after mapping are derived by applying f to equation (1), which is the area of the basic shape of the design target element. This is performed for all coordinates (x, y) of the outer edge of 330a.

Similarly, the optimization calculation unit 120 calculates the coordinates (x, y) of the outer edge of the area 330b of the basic shape of the element to be designed, given the components a to f assigned to the element to be designed (1 ) to derive the coordinates (x', y') of the outer edge of the area of the design target element after mapping, all the coordinates of the outer edge of the area 330b of the basic shape of the design target element. Do this for (x, y).

FIG. 3(c) is a diagram showing an example of the core element after mapping has been performed on the basic shape of the design target element.
In the example shown in FIG. 3(c), the region of the design target element is obtained by performing linear mapping on the regions 330a and 330b of the basic shape of the design target element shown in FIG. 3(b). The regions 330a and 330b of the basic shape are respectively changed to regions 340a and 340b of the design target element after mapping.

Then, when the identification information set for each coordinate of the areas 340a and 340b of the design target element after mapping is ID1, the optimization calculation unit 120 uses the identification information ID1 to define the area of the design target element. Change the identifying information to ID3. Before mapping, regions 340a and 340b of the design target element after mapping shown in FIG. 3(c) are regions 310 of the iron core, as shown in FIG. 3(b). Therefore, the identification information set in the areas 340a and 340b before mapping is ID1. Therefore, the identification information set for each coordinate of the regions 340a and 340b of the design target element after mapping is changed from ID1 to ID3.

Furthermore, the optimization calculation unit 120 uses identification information set for the coordinates of the regions 330a and 330b of the basic shape of the design target element that do not overlap with the regions 340a and 340b of the design target element after mapping. Change from ID3 to ID1. In the examples shown in FIGS. 3(b) and 3(c), regions 330a and 330b of the basic shape of the design target element do not overlap with regions 340a and 340b of the design target element after mapping. Therefore, the identification information set for each coordinate of the regions 330a and 330b of the basic shape of the element to be designed is changed from ID3 to ID1. Thereby, the regions 330a and 330b of the basic shape of the design target element become the region of the iron core 310.

Next, in step S206, the optimization calculation unit 120 determines whether there is any element to be designed that overlaps or protrudes. As a result of this determination, if there is no element to be designed that overlaps or protrudes, the process of step S207 is omitted, and the process of step S208, which will be described later, is executed. On the other hand, if there is at least one design target element that overlaps or protrudes, the process of step S207 is executed. Note that overlapping/protruding refers to at least one of overlapping and protruding.

In step S207, the optimization calculation unit 120 changes the design target element again so that the overlap/protrusion in the design target element in which the overlap/protrusion occurs is eliminated.
FIG. 4 is a diagram illustrating an example of overlap.
FIG. 4A is a diagram conceptually illustrating an example of overlap between design target elements of the same type.
As shown in the left diagram of FIG. 4A, when regions 410a and 410b of a plurality of design target elements of the same type after mapping overlap with each other, in step S207, the optimization calculation unit 120 , as shown in the right diagram of FIG. 4(a), one area 410c surrounded by the outer edges of the areas 410a and 410b of the multiple design target elements after mapping includes the area 410a of the multiple design target elements after mapping, 410b.

FIG. 4(b) is a diagram conceptually showing an example of the overlap between different types of design target elements.
As shown in the left diagram of FIG. 4B, when the regions 420a and 420b of the plurality of design target elements of different types after mapping overlap with each other, in step S207, the optimization calculation unit 120 As shown in the right figure in (b), the mutually overlapping region is defined as the region 420a of the design target element with the highest priority, and the region obtained by excluding the mutually overlapping region from the region 420b of the design target element with the lowest priority. 420c is the region 420b of the design target element having a low priority. The optimization calculation unit 120 sets only the identification information ID3 that identifies the design target element with the highest priority for each coordinate of the mutually overlapping area, and deletes the other identification information ID3. For example, when a permanent magnet is also a design target element in addition to a flux barrier, the priority of the permanent magnet can be set higher than the priority of the flux barrier. In this case, in the example shown in FIG. 4(b), the flux barrier area is the area 420c, and the permanent magnet area is the area 420a. The priority order is set in advance based on core design guidelines, attributes of design target elements, and the like.

FIG. 4C is a diagram conceptually showing a first example of the overlap between the mapped design target element and a predetermined core element other than the design target element. The predetermined core elements other than the design target elements are elements whose shape does not change, and are set in advance. Here, although the shape of the iron core can be changed, the shape of the permanent magnet is not changed.
As shown in FIG. 4(c), a partial area of the design target element 430a after mapping is a partial area of a predetermined core element (permanent magnet area 320) other than the design target element, and a design target element 430a. If the elements of the predetermined core other than the elements are overlapped without straddling them, in step S207, the optimization calculation unit 120 calculates the area 430a of the design target element after mapping, as shown in the right diagram of FIG. A region 430b obtained by removing a region overlapping with a predetermined core element other than the design target element from the region is set as the region of the design target element. Furthermore, the optimization calculation unit 120 deletes the identification information ID3 that identifies the design target element set for each coordinate of the mutually overlapping portion.

FIG. 4D is a diagram conceptually showing a second example of the overlap between the mapped design target element and a predetermined core element other than the design target element.
As shown in FIG. 4(d), a partial area of the design target element 440a after mapping is a partial area of a predetermined core element (permanent magnet area 320) other than the design target element, and a design target element 440a. If the element overlaps across a predetermined core element other than the element, in step S207, the optimization calculation unit 120 calculates the area 440a of the design target element after mapping, as shown in the right diagram of FIG. A plurality of regions 440b and 440c obtained by excluding a region overlapping with a predetermined core element other than the design target element are defined as the region of the design target element. Furthermore, the optimization calculation unit 120 deletes the identification information ID3 that identifies the design target element set for each coordinate of the mutually overlapping portion.
In order to suppress an increase in the number of design target elements, the optimization calculation unit 120 may select only one of the plurality of regions 440b and 440c in step S207. For example, the optimization calculation unit 120 may select the largest region among the plurality of regions 440b and 440c and erase the other regions.

FIG. 5 is a diagram illustrating an example of protrusion.
As shown in the left diagram of FIG. 5, if a part of the area 510a of the design target element after mapping protrudes from the design area (iron core area 310), in step S207, the optimization calculation unit 120 performs the mapping. An area 510b obtained by removing the area protruding from the design area from the area 510a of the subsequent design target element is set as the area of the design target element.

When an overlap as shown in FIG. 4 and a protrusion as shown in FIG. 5 occur at the same time for one design target element after mapping, the optimization calculation unit 120 performs the calculation as described with reference to FIG. The design target element is changed, and the area of the changed design aspect element that protrudes from the design area is removed as described with reference to FIG. 5.

Next, in step S207, the optimization calculation unit 120 performs numerical analysis on values indicating the characteristics of the electrical equipment when operating the electrical equipment having the core whose design target area has been changed in steps S205 and S207. It is derived by In the following description, the characteristics of the electric device when the electric device is operated will be referred to as the characteristics of the electric device as necessary.
Examples of the characteristics of the electrical equipment include the average torque of the rotor, the iron loss of the core, and the efficiency of the IPMSM. In this way, the characteristics of an electrical device are a concept that includes the characteristics of the parts that constitute the electrical device. In this embodiment, the optimization calculation unit 120 calculates the magnetic flux density vector B generated in the core when the core whose design target area has been changed is excited by performing numerical analysis using the finite element method, and calculates the calculated result. Based on this, the average torque of the rotor is derived as a characteristic of the electrical equipment.

The optimization calculation unit 120 calculates the magnetic flux density vector B and eddy current vector J _e in each minute region (mesh) using the finite element method based on Maxwell's equations according to electromagnetic field analysis conditions including excitation conditions. . Note that as long as the magnetic flux density vector B and the eddy current vector J _e in each minute region can be calculated, the electromagnetic field analysis may be performed using a method other than the finite element method (such as the finite difference method).

The basic equations for calculating the magnetic flux density vector B and the eddy current vector Je are generally given by the following equations (2) to (5).

In equations (2) to (5), μ is magnetic permeability [H/m], A is vector potential [T・m], and σ is electrical conductivity [S/m], J ₀ is the excitation current density [A/m ² ], and φ is the scalar potential [V].
After solving equations (2) and (3) simultaneously to obtain vector potential A and scalar potential φ, from equations (4) and (5), magnetic flux density vector B and eddy current vector J _e can be calculated. Calculated.

The method of analyzing an electromagnetic field using the finite element method is a general method, as described in detail in Non-Patent Document 2, and so a detailed explanation thereof will be omitted here.
The optimization calculation unit 120 calculates the torque in each minute area based on the magnetic flux density vector B in each minute area, and derives the average torque based on the calculated torque. Here, the torque F can be calculated as a Maxwell stress using the following equation (6), for example.

In equation (6), n _x and n _y are unit vectors in the x-axis and y-axis directions, respectively, and μ ₀ is the magnetic permeability of vacuum. ∫dΓ indicates that it is a line integral along a closed curve surrounding the object for which the electromagnetic force is sought. Further, B is the magnitude of the magnetic flux density vector, and B _x and B _y are the x-axis component and y-axis component of the magnetic flux density vector, respectively.

Next, in step S209, the optimization calculation unit 120 determines whether all of the plurality of mapping candidates derived in step S203 have been selected. When the number of elements to be designed is one, in step S209, the optimization calculation unit 120 determines whether all of the plurality of mapping candidates derived in step S203 have been selected. If the number of design target elements is plural, in step S209, the optimization calculation unit 120 calculates a mapping of the number of design target elements selected from among the plurality of mapping candidates derived in step S203. It is determined whether all possible combinations of candidates have been selected.

As a result of this determination, if all of the plurality of mapping candidates derived in step S203 have not been selected, the process in step S204 is executed again. Then, in step S204, unselected mapping candidates are selected. Then, in steps S205 to S207, the design target area is changed by the unselected mapping candidates, and in step S208, values indicating the characteristics of the electrical device having the core whose design target area has been changed are calculated.

As described above, when it is determined in step S209 that all of the plurality of mapping candidates derived in step S203 have been selected, the process of step S210 is executed. In step S210, the optimization calculation unit 120 determines whether there is a value satisfying a predetermined condition among the values indicating the characteristics of the electrical device calculated in step S208. When the characteristic of the electrical device is the average torque of the rotor, the predetermined condition is that the value of the average torque of the rotor is greater than or equal to the predetermined value. The predetermined value is determined, for example, based on the value required by the IPMSM to be designed.

As a result of this determination, if there is a value that satisfies a predetermined condition among the values indicating the characteristics of the electrical equipment calculated in step S208, the process of step S211 is executed. In step S211, the optimization calculation unit 120 applies a mapping that yields a value indicating that the characteristic is the best among the values indicating the characteristic of the electrical device satisfying the predetermined conditions to the basic shape of the element to be designed. Determine the mapping to be applied. When the characteristic of the electrical device is the average torque of the rotor, the optimization calculation unit 120 determines the mapping that gives the largest value of the average torque of the rotor as the mapping to be applied to the basic shape of the element to be designed. Then, the process of step S214, which will be described later, is executed.

As a result of the determination in step S210, if there is no value that satisfies the predetermined condition among the values indicating the characteristics of the electrical equipment calculated in step S208, the process of step S212 is executed. In step S212, the optimization calculation unit 120 determines whether the number of repetitions of the processes in steps S203 to S210 exceeds a predetermined value. The predetermined value is a value commonly used in genetic algorithms. As a result of this determination, if the number of repetitions does not exceed the predetermined value, the process of step S203 is executed again. The process of step S203 performed in this manner becomes the process of step S203 from the second time onwards. As described above, in the second and subsequent steps S203, the optimization calculation unit 120 updates the already derived mapping candidates according to the genetic algorithm. The processes of steps S204 to S210 described above are executed using the mapping candidates updated in this manner.

As a result of the determination in step S212, if the number of repetitions of the processes in steps S203 to S210 exceeds a predetermined value, the process in step S213 is executed. In step S213, the optimization calculation unit 120 uses the mapping candidates derived in the immediately preceding step S203 to determine whether the characteristic is the best among the values of the characteristics of the electrical equipment derived through the repeated calculations in steps S204 to S209. A mapping that yields a value indicating this is determined as a mapping to be applied to the basic shape of the element to be designed. Then, the process of step S214 is executed.

In step S214, the output unit 130 outputs information regarding the mapping determined in step S211 or S213. The output unit 130 outputs, for example, information specifying the position, shape, and size of the region of the design target element subjected to the mapping determined in step S211 or S213. The form of output can be at least one of display on a computer display, storage on a storage medium internal or external to core design device 100, and transmission to an external device.

For example, regions 340a and 340b of the design target element after mapping shown in FIG. 3(c) are obtained by applying the mapping determined in step S211 or S213 to the basic shape of the design target element. Suppose there is. In this case, the output unit 130 may display an image showing the core region 310, the permanent magnet 320 region, and the regions 340a and 340b of the design target element after mapping, as shown in FIG. 3(c).
The above is the process according to the flowchart of FIG.

Next, a calculation example will be explained. FIG. 6 is a diagram showing a core before design and a core after design.
In this calculation example, a flux barrier was added to the core shown in FIG. 6(a) using the method described in this embodiment. FIG. 6A shows a D1 motor, which is a benchmark model of the Institute of Electrical Engineers of Japan, and is described in Non-Patent Document 3.

As described above, the calculation target element in this calculation example is the flux barrier. In FIG. 6, the flux barrier area is a white area. The iron core area is the dark gray area. Permanent magnets are the light gray area.
The design area was defined as the area surrounded by the outer edge of the iron core area.
In FIG. 6(a), eight circular regions were set as the basic shape of the flux barrier, which is an element to be designed, in the region within the design region of the core and on the outer peripheral side of the permanent magnet.

Further, in this calculation example, the average torque when the core is excited with an excitation current having a peak value of 5.5 A and a lead angle of 20° is used as the characteristic of the electric device. A genetic algorithm was used to search for a linear mapping that maximized the average torque. FIG. 6 shows the result of applying the linear mapping searched in this way to a basic-shaped flux barrier.
In the core shown in FIG. 6(a), the average torque when excited with an exciting current having a peak value of 5.5 A and an advance angle of 20° was 0.79 Nm. On the other hand, in the core shown in FIG. 6(b), the average torque when excited with the excitation current was 1.22 Nm. In this way, the average torque of the core shown in FIG. 6(b) was improved by about 54% over the average torque of the core shown in FIG. 6(a). Moreover, as shown in FIG. 6(b), the flux barrier was distributed in a somewhat solidified manner, and it was possible to avoid the flux barrier from having an extremely complicated shape.

As described above, in the present embodiment, the core design device 100 sets the areas 330a and 330b of the basic shape of the element to be designed, and sets the regions 330a and 330b of the basic shape of the element to be designed as an optimal solution for mapping to be applied to the areas 330a and 330b of the basic shape of the element to be designed. , a mapping is calculated when the value representing the characteristics of the electrical equipment when the electrical equipment having the core is operated is maximized or minimized in the algorithm of the optimization problem. The number and shape of basic shapes can be set without advanced know-how. Furthermore, since the mapping is a variable, it is possible to prevent the solution space from becoming wide. Therefore, the core can be designed easily and accurately.

Further, in the present embodiment, the core design device 100 sets a shape that does not include any element other than the design target element within the regions 330a and 330b of the basic shape of the design target element as the basic shape of the design target element. Set. Therefore, it is possible to prevent the shape of the design target element from becoming an unexpected shape. Moreover, it is possible to suppress the shape of the design target element from becoming complicated.

In addition, in the present embodiment, the core design device 100 performs mapping on the area of the basic shape of the element to be designed, and as a result, some of the areas 420a, 430a, and 440a of the element to be designed are part of the element to be designed. If the regions 420b, 430b, 440b of other predetermined elements of different types overlap, the regions 420a, 430a of the design target element are mapped so that the design target element does not overlap with the other predetermined elements. , 440a are changed to regions 420c, 430b, and 440b to 440c (see FIGS. 4(b) to 4(d)). Therefore, it is possible to prevent the core elements from being designed to overlap with each other, and it is possible to prevent the elements from being arranged in a way that cannot actually occur.

In addition, in the present embodiment, the core design device 100 performs mapping on the area of the basic shape of the element to be designed, and as a result, a part of the area 410a of the element to be designed is other than the same type as the element to be designed. If the area 410b of the design target element overlaps with the area 410b of the design target element, the overlapping areas 410a and 410b of the design target element are treated as one design target element 410c (see FIG. 4A). Therefore, it is possible to prevent the number of basic shapes of the design target element from increasing beyond the initially set basic shape regions 330a and 330b of the design target element. Moreover, it is possible to suppress the shape of the design target element from becoming complicated.

Furthermore, in this embodiment, the core design device 100 performs linear mapping on the region of the basic shape of the element to be designed. Therefore, the number of variables is six times the basic shape (in equation (1), the matrix has six elements a to f). Therefore, it is possible to further prevent the solution space from becoming wide. For example, the shape of a permanent magnet in the xy plane is a quadrilateral, so when a permanent magnet is used as an element to be designed, the basic shape of the element to be designed is a quadrilateral, and a linear mapping is applied to the area of the basic shape of the element to be designed. By applying this, it becomes possible to optimize the shape while maintaining the rectangular shape.

<Modified example>
<<First modification example>>
In this embodiment, the case where the design area is an area surrounded by the outer edge of the core area 310 has been described as an example. If this is done, there is a risk that the flux barrier may reach the outer periphery of the core, as shown in FIG. 6(b). If the flux barrier reaches the outer periphery of the iron core in the rotor, there is a risk that the rotor will break due to the centrifugal force exerted on the rotor due to rotation of the rotor. Therefore, a region of the core excluding the end portion of the core and a region in the vicinity thereof may be used as the design region. In this way, it is possible to prevent a core that does not meet the specifications of the electrical device from being designed without performing complicated calculations.

Further, instead of or in addition to setting the design area in this way, the following may be used. That is, the optimization calculation unit 120 calculates the magnetic flux density vector and stress vector in each minute region by solving a forward problem that couples electromagnetic field analysis and stress analysis, and thereby calculates the amount of stress that the rotor receives as it rotates. Analyze the stress generated in the core due to centrifugal force. Then, the optimization calculation unit 120 searches for an optimal solution of the mapping based on both the characteristics of the electrical device based on the magnetic flux density vector and the characteristics of the electrical device based on the stress vector.

For example, the optimization calculation unit 120 uses the finite element method to calculate a stress vector to be applied to each microregion (mesh) of the core according to the stress conditions. The method of analyzing stress using the finite element method is a common method, as described in Non-Patent Document 4 and the like. Note that as long as the stress vector in each minute region (mesh) can be calculated by numerical analysis, methods other than the finite element method (such as the finite difference method) may be used.

If the micro region used in the electromagnetic field analysis (calculation of the magnetic flux density vector B and eddy current vector J _e in each micro region) described in this embodiment is different from the micro region used in the stress analysis, the optimization calculation unit 120 For example, by performing interpolation processing on the stress vector of each minute area used in the stress analysis, the stress vector in the minute area used in the electromagnetic field analysis is calculated.

In electromagnetic field analysis (calculation of magnetic flux density vector B and eddy current vector J _e in each minute region), a BH curve according to stress is used as the BH curve. Electromagnetic field analysis is performed using a BH curve corresponding to a stress vector in a minute region used in electromagnetic field analysis. Note that the forward problem in which electromagnetic field analysis and stress analysis are coupled can be realized by a known method described in Patent Document 1, for example, so detailed explanation thereof will be omitted here.

For example, the optimization calculation unit 120 sets the value of the characteristic of the electric device determined based on the result of the electromagnetic field analysis to V1, and sets the weighting coefficient for the characteristic of the electric device determined based on the result of the electromagnetic field analysis to W1 (>0), Let V2 be the value of the characteristics of the electrical equipment determined based on the results of stress analysis, and let W2 (>0) be the weighting factor for the characteristics of the electrical equipment determined based on the results of stress analysis, and the value of W1×V1+W2×V2 is the maximum or Search for a minimal mapping. In addition, when indicating that the larger the value of the characteristic of the electrical device determined from the result of electromagnetic field analysis is, the better the characteristic is, and the smaller the value of the weighting coefficient for the characteristic of the electrical device determined from the result of stress analysis is, the better the characteristic is, For example, the optimization calculation unit 120 may search for a mapping that minimizes -W1×V1+W2×V2.
Furthermore, depending on the characteristics of the electrical equipment that are taken into consideration when designing the core, only stress analysis may be performed without performing electromagnetic field analysis.

<<Second variant>>
This embodiment has been described using an example in which linear mapping is performed. However, the mapping may also be a nonlinear mapping. By applying nonlinear mapping to the basic shape of the element to be designed, the expressiveness of the shape can be enhanced. In this case, the mapping is preferably a topological mapping. This is because it is possible to prevent the number of basic shapes of the design target element from increasing beyond the initially set area of the basic shapes of the design target element.

<<Third modification example>>
In this embodiment, the case where a genetic algorithm is used as an algorithm for an optimization problem has been described as an example. However, algorithms for optimization problems are not limited to genetic algorithms. Metaheuristic methods other than genetic algorithms may also be used. It is preferable to use a metaheuristics method because it can prevent the optimal solution from being calculated as a local solution and also makes it easier to obtain a novel shape. However, algorithms for optimization problems other than metaheuristic methods such as the gradient method may be used.

<<Fourth variation>>
This embodiment has been described using an example in which a rotor for an IPMSM is designed. However, the core to be designed is not limited to the core of the IPMSM rotor. For example, the core of the rotor of a squirrel-cage induction motor may be the object of design. In this case, a conductor bar embedded in an iron core constituting the core can be a design target element. Alternatively, the core of the stator may be the object of design. In this case, for example, the space in the recess at the tip of the teeth of the iron core that constitutes the core of the stator can be a design target element. In addition, the core of the rotor/stator of a generator, which is a rotating electric machine other than a motor, may be the element to be designed, or the core of a transformer may be the element to be designed.

<<Other variations>>
Note that the embodiments of the present invention described above can be realized by a computer executing a program. Furthermore, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, hard disk, optical disk, magneto-optical disk, CD-ROM, magnetic tape, nonvolatile memory card, ROM, etc. can be used.
Furthermore, the embodiments of the present invention described above are merely examples of implementation of the present invention, and the technical scope of the present invention should not be construed as limited by these. It is something. That is, the present invention can be implemented in various forms without departing from its technical idea or its main features.

100: Core design device, 110: Setting section, 120: Optimization calculation section, 130: Output section, 310: Iron core region, 320: Permanent magnet region, 330a to 330b: Basic shape region of design target element, 340a ~340b: Area of design target element after mapping

Claims (14)

A core design device that performs calculations related to the design of a core shape using an optimization problem algorithm,
Setting means for setting a basic shape of at least one design target element as a design target element among the elements of the core in a design region that is a design target region of the core;
Optimization for calculating, using the algorithm for the optimization problem, an optimal solution for mapping applied to the basic shape of the design target element in order to deform and move the basic shape of the design target element set by the setting means. calculation means;
The optimization calculation means is configured such that a value indicating a characteristic of the electrical equipment when operating the electrical equipment having the core including the element to be designed which has been subjected to the mapping is a maximum value in the algorithm of the optimization problem, or A core design device characterized in that the mapping when the mapping is minimized is calculated as an optimal solution of mapping applied to the basic shape of the element to be designed. The core according to claim 1, wherein the setting means sets a shape that does not include any elements other than the design target element inside the design target element as the basic shape of the design target element. Design equipment. When the optimization calculation means performs the mapping on the basic shape of the design target element, a part of the design target element overlaps with another predetermined element of a different type from the design target element, Changing the designed element to which the mapping has been performed so that the designed element does not overlap with the other predetermined element, and operating the electrical device having the core including the changed designed element. The core design device according to claim 1 or 2, wherein the core design device calculates a value indicating a characteristic of the electric device when the electric device is operated. When the optimization calculation means performs the mapping on the basic shape of the design target element, a part of the design target element overlaps with another design target element of the same type as the design target element. , consider the plurality of overlapping design target elements as one design target element, and calculate a value indicating the characteristics of the electrical equipment when the electrical equipment having the core including the one design target element is operated. The core design device according to any one of claims 1 to 3, characterized in that: 5. The core design apparatus according to claim 1, wherein the setting means sets a plurality of basic shapes as the basic shapes of the design target element of the same type. 6. The core design apparatus according to claim 1, wherein the setting means sets a plurality of types of basic shapes of the element to be designed. The core design device according to claim 1, wherein the mapping is a linear mapping. The core design device according to claim 1, wherein the mapping is a topological mapping. 9. The optimization calculation means calculates an optimal solution for mapping applied to the basic shape of the design target element using a metaheuristic method. core design equipment. The optimization calculation means calculates, by performing numerical analysis, a magnetic flux density vector generated in the core when the core including the design target element subjected to the mapping is excited, and based on the calculated result. The core design device according to any one of claims 1 to 9, characterized in that the core design device calculates a value indicating a characteristic of the electrical device. The optimization calculation means calculates, by performing numerical analysis, a stress vector generated in the core when an external force acts on the core including the design target element subjected to the mapping, and based on the calculated result. , the core design device according to any one of claims 1 to 10, characterized in that the core design device calculates a value indicating a characteristic of the electrical device. 12. The core design device according to claim 1, wherein the design target element includes at least one of a flux barrier and a permanent magnet in a rotor of a rotating electric machine. A core design method that uses an optimization problem algorithm to perform calculations related to the design of a core shape, the method comprising:
a setting step of setting a basic shape of at least one design target element as a design target element among the elements of the core for a design region that is a design target region of the core;
Optimization that calculates an optimal solution of mapping to be applied to the basic shape of the design target element in order to deform and move the basic shape of the design target element set in the setting step using the optimization problem algorithm. a calculation step;
The optimization calculation step is performed such that a value indicating a characteristic of the electrical equipment when operating the electrical equipment having the core including the design target element to which the mapping has been performed is the maximum or maximum in the algorithm of the optimization problem. A core design method characterized in that the mapping when minimized is calculated as an optimal solution of mapping applied to the basic shape of the element to be designed. A program that causes a computer to function as each means of the core design device according to any one of claims 1 to 12.

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