JP7826764B2 - Rotor design method and system for rotating machines - Google Patents

Description

The present invention relates to the design of rotors used, for example, in permanent magnet rotating machines.

Permanent magnet rotating machines are highly efficient and have a wide range of adjustable speeds, making them suitable for a variety of applications, including compressors, spindles, and hybrid vehicles. They consist of an outer stator and an inner rotor, with permanent magnets (hereafter referred to as magnets) embedded inside the rotor, improving performance by increasing torque and other aspects.

This rotor is equipped with an iron core, or yoke, that connects the two permanent magnets with magnetic flux. The torque components of this rotor are determined by the relative positions of the iron core/magnets and the stator.

For this reason, rotor design can be considered as the design of a system whose performance is determined by the core shape and magnet arrangement. Core shape design is primarily carried out through topology (shape) optimization. Below, we will provide an overview of conventional topology optimization using Figure 6.

S01: When the rotor design process begins, the dimensions of the magnets to be used in the rotor are determined.

S02: A rotor core "mesh" is generated according to the dimensions of the magnets in S01 (S02).

S03: Perform topology optimization of the rotor core. That is, the topology optimization method first determines the core shape with the magnets initially placed in a "mesh" (S11). Next, a characteristic evaluation of the current core shape is calculated using finite element analysis (S12), and then a sensitivity analysis is performed using the gradient method (S13).

Then, in the gradient method, the design variables (iron core shape) are modified (S14) in accordance with the results of the sensitivity analysis in S13. In the non-gradient method, the design variables (iron core shape) are modified (S14) in accordance with the evaluation values of the characteristic calculation (S12). If the modifications converge, the iron core shape is output (S16). On the other hand, if they do not converge, the process returns to S12 and resumes.

If the optimization process has converged as a result of the output from S16, the design process ends (S05). If it has not converged, return to S01, change the magnet dimensions, and restart the process. Details of this rotor design method (S01-S05) are described in Non-Patent Documents 1-8.

Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "Permanent Magnet Synchronous Motor Rotor Design Method by Coordinating Topology Optimization and System Variable Optimization Using Applied Surface Approximation" [No. 17-32] Proceedings of the 27th Conference of the Japan Society of Mechanical Engineers, Design Engineering and Systems Division [September 13-15, 2017, Shimonoseki, Yamaguchi Prefecture] Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "Permanent Magnet Synchronous Motor Design by Integrated Optimization of Structural Form and Component Layout," Japan Design Association 2017 Spring Research Presentation Lecture (May 20, 2017) Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "Optimal Design Method of Synchronous Motor Considering Permanent Magnet Arrangement and Yoke Structural Form," Jode Design Engineering, ONLINE ISSN: 2188-9023, PRINT ISSN: 0919-2948, Design Engineering, Vol. 53, No. 1 (January 2018) Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "System-level optimization method for permanent magnet synchronous motors considering structural configuration and system variables simultaneously" [No. 17-4] Proceedings of the 30th Japan Society of Mechanical Engineers Conference on Computational Mechanics [September 16-18, 2017, Higashiosaka City] Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "Metamodeling-based Design Parameter Determination Method for Topology Optimization Problems (Application to Permanent Magnet Synchronous Motor Design)," Japan Society of Mechanical Engineers [No. 18-37], Proceedings of the 13th Optimization Symposium 2018 [October 15-16, 2018, Kyoto] Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "Topology Optimization of High-Power Motors for Hybrid Vehicles Considering Nonlinear Magnetic Properties," Japan Society of Mechanical Engineers [No. 16-20], 12th Optimization Symposium 2016 Program [December 6-7, 2016, Sapporo] Katsuya Nomura, Atsuhiro Takahashi, Takashi Kojima, Shintaro Yamazaki, Kentaro Yachi, Daiki Bo, Kikuo Oda, "Dominant Noise Reduction in Noise Filters Using Topology Optimization," Transactions of the Institute of Electrical, Information and Communication Engineers, Vol. J102-B, pp. 669-678, 2019. Daiki Bo, Shintaro Yamazaki, Kentaro Yachi, Katsuya Nomura, Atsuhiro Takahashi, Kikuo Fujita, "Optimization of Conductor Patterns of Filter Circuits for Electromagnetic Compatibility Design" [No. 17-4] Proceedings of the 30th Conference on Computational Mechanics, Japan Society of Mechanical Engineers [September 16-18, 2017, Higashiosaka City] "Ansys TurboGrid: A mesh creation tool for rotating machinery" available online from Ansys Japan Co., Ltd. (Internet URL: https://premium.ipros.jp/ansys/product/detail/2000131706/). CYBERNET Ansys Analysis Course: "First Optimization" Cybernet Systems Co., Ltd. Online <Internet URL: https://www.cybernet.co.jp/ansys/case/lesson/009.html>

Conventionally, as shown in S01 and S02, the "mesh" is created after the magnet dimensions are determined, so topology optimization of the rotor core is performed for each magnet dimension.

In this case, the "mesh" shape differs for each magnet size, so the design variables for the iron core differ. For example, the design variables for topology optimization depend on the "mesh" after magnet placement, and therefore differ for each magnet size A, B...N in Figure 7.

When S04 returns to S01, the magnet dimensions will have changed, creating a different "mesh" and changing the design variables. As a result, topology optimization information cannot be shared, the calculation load increases, optimization takes longer, and there is a risk of design delays.

As described in Non-Patent Documents 2 to 5, methods have been proposed that simultaneously optimize magnet placement and topology, but because magnet placement depends on the magnet dimensions, there is a risk that effective results will not be obtained.

The present invention was made to solve these conventional problems, and its goal is to shorten the time required for rotor topology optimization and avoid delays in rotating machine design.

(1) One aspect of the present invention is
Using a computer,
A method for designing a rotor of a rotating machine having a magnet and an iron core, comprising:
a variable determination step of defining a design domain of the entire rotor and independently determining a first design variable related to the dimensions of the magnets and a second design variable related to the shape of the iron core;
an image generation step of generating a "mesh" of the rotor according to the first design variables and the second variables;
a mapping step of mapping a shape defined in the design domain onto the "Mesh";
and an optimization step of optimizing the shape of the iron core by modifying both design variables in accordance with the evaluation of the mapped shape.

(2) Another aspect of the present invention is a system for designing a rotor of a rotating machine including a magnet and an iron core, comprising:
a variable determination unit that defines a design domain for the entire rotor and determines a first design variable related to the dimensions of the magnets and a second variable related to the shape of the rotor core independently;
an image generation unit that generates a "mesh" of the rotor according to the first design variables and the second variables;
a mapping unit that maps a shape defined in the design domain onto the "Mesh";
and an optimization unit that optimizes the magnet dimensions and the iron core shape by modifying both of the design variables in accordance with an evaluation of the mapped shape.

The present invention reduces the time required for rotor topology optimization and avoids delays in rotating machine design.

1 is a block diagram of a system for executing a rotor design method for a rotating machine according to an embodiment of the present invention; 3 is a flowchart showing the processing steps of the design method. (a) is a variable table of magnet dimensions (design variable 1), (b) is a diagram of magnet dimension and magnet area patterns (5 types), (c) is a schematic diagram showing the maximum and minimum values of magnet [position] patterns (30 types), and (d) is a schematic diagram showing the maximum and minimum values of magnet [rotation angle] patterns (60 types). Transition diagram showing transition patterns (a) to (e) during topology optimization using the density method. Schematic diagram showing an example of magnet dimensions and topology optimization. 1 is a flowchart showing a conventional topology optimization procedure. Diagram of magnet placement on "Mesh".

The following describes a rotor core design method according to an embodiment of the present invention. This method is primarily used in rotor design for interior permanent magnet synchronous motors (IPSMs), and optimizes the rotor core shape (topology).

In this case, the design method defines the core shape by using the entire rotor as the design domain, independent of the magnet dimensions. This makes it possible to optimize the core shape regardless of the magnet dimensions.

An example of the design method will be described with reference to Figures 1 to 5. Here, the design method is executed, for example, by system 1 shown in Figure 1.

This system 1 is composed of a computer and is equipped with the usual hardware resources of a computer (e.g., CPU, RAM, ROM, SSD, HDD, etc.). As a result of cooperation between these hardware resources and software resources (OS, applications, etc.), the system 1 implements a variable determination unit 2, image generation unit 3, mapping unit 4, optimization unit 5, and output unit 6.

<<Processing details>>
The processing steps (S11 to S18) of the design method by the above-mentioned units 2 to 6 will be explained with reference to Figure 2. As mentioned above, rotor design can be considered as designing a system whose performance is determined by the core shape and permanent magnet arrangement. Here, we will mainly explain how to optimize the dimensions of the magnets arranged in the core and the core shape.

S21: When processing begins, the variable determination unit 2 first defines the design domain R. The design domain R defined here covers the entire rotor area of the synchronous motor, with magnets placed in the iron core.

Next, (1) the dimensions (position, shape, and angle) S of the magnet to be embedded in the iron core, and (2) the initial shape C of the iron core are determined. Here, the former will be called design variable 1, and the latter will be called design variable 2.

As shown in Figure 3(a), design variable 1 is the magnet's width W, length L (area is constant), position X, Y, and angle (rotation angle), each of which has a set upper and lower limit. Figure 3(b) shows five examples of width W and length L, with the magnet shape determined by the variables X and Y. Figure 3(c) shows 30 examples of position X and Y, and Figure 3(d) shows 60 examples of angle (rotation angle). Furthermore, the distribution pattern (spacing) of 10 groups of holes (flux barriers, etc.) in the iron core can also be used as design variable 2.

The design variables may be determined based on user input/selection, or predetermined initial design variables may be used, or design variables 1 and 2 from a separate case for which optimization has been completed may be used.

S22: The image generation unit 3 generates a rotor "mesh (G1 in Figure 2)" based on the design variables 1 and 2 (magnet dimensions S and initial core shape C) determined in S21. For example, the initial core shape is confirmed, the vertex coordinates are set in the initial image, and then the order of the vertex coordinates is set in the initial image and drawn to generate it. The "mesh" can be generated using a creation tool such as that described in Non-Patent Document 7.

S23: The mapping unit 4 generates a mapping diagram G2 by mapping the "Mesh" created in S22 onto the design domain defined in S21. At this time, for areas of the iron core that overlap with the magnet area, the magnet is given priority and the magnet is displayed.

S24-S26: The optimization unit 5 performs topology optimization of the rotor core based on the mapping diagram G2 generated in S23. Optimization methods are broadly divided into gradient methods, which use the gradient (sensitivity) of an algorithm, and non-gradient methods, which do not use the gradient.

Gradient methods are generally used in topology optimization, and sensitivity can be determined quickly by using the adjoint variable method as a gradient calculation method (see Non-Patent Document 5). Specifically, known algorithms such as the density method described in Non-Patent Documents 1 to 6 and the level set method described in Non-Patent Documents 7 and 8 are used appropriately. Here, we will explain the use of the density method as an example.

(1) First, an initial structure shown in the mapping diagram G2 is set, and torque performance is evaluated for the set initial structure using finite element analysis (S24). The density method is a technique for solving the structural optimization problem by replacing it with material distribution within the design domain. For the iron core shape expressed by the density (yoke structure) p defined by equation (1), magnetic flux density is determined using nonlinear magnetic field analysis, from which Maxwell's stress tensor T can be obtained. Torque can be determined using the Maxwell's stress method or nodal stress method using this Maxwell's stress tensor T.

Ω _iron = iron core region: region where ρ = 1 Ω _air = air region of the hole 10: region where ρ = 0 (2) Next, in sensitivity analysis (S25), the differential of the design variable (density m) with respect to the objective function is evaluated (S15), and the change in the magnitude of the evaluation function is confirmed. In this case, the evaluation function and the design variable can be directly differentiated in some cases, and the sensitivity is derived by finding the adjoint equation shown in equation (2). Three equations can be considered for sensitivity analysis of rotor torque: Sensitivity equation (1): Adjoint equation of Maxwell stress method; Sensitivity equation (2): Direct equation of nodal stress method; Sensitivity equation (3): Adjoint equation of nodal stress method. In this example, seven sensitivities combining sensitivity equations (1) to (3) were evaluated in advance, and sensitivity equations (2) and (3) were normalized and the sum of these sensitivities was used. However, the combination to be adopted for each target should be considered in advance.

Objective function: J(u(m), m) = torque Design variable: m (m = p: material density of iron core)
Unknown: u (basic equation)
Governing equation: F (m)
(3) Then, design variables 1 and 2 are modified and updated based on the results of the sensitivity analysis in S25 (S26), and an optimal solution for design variables 1 and 2 is searched for. At this time, points where the sensitivity to changes in design variables 1 and 2 is "0" indicate local maxima, and in this embodiment, the search is performed while modifying design variables 1 and 2 from the perspectives of "maximizing average torque" and "minimizing torque ripple." For example, by modifying design variables 1 and 2, the yoke shape is changed as shown in (a) to (e) in Figure 4, and the final search result is obtained.

Figure 5 shows the search results for design variables 1 and 2 using the sensitivity analysis described above. Here, the optimal solution is searched for by focusing on the slope (sensitivity) in the graph; case 1 in Figure 5 has a large average torque, but also a large torque ripple. Therefore, cases 2 to 4 and the optimal solution are searched for within the range of design values.

At the same time, optimization of design variable 1 can be achieved by applying "3.3 Optimization of permanent magnet placement using response surfaces" in Non-Patent Document 3. For example, by replacing "magnet placement" in Non-Patent Document 3 with "magnet dimensions (design variable 1)," it is possible to find the optimal solution for magnet placement using the solution obtained in optimizing the yoke structure configuration (Figure 4).

S27, S28: The convergence of the search in S26 is determined (S17). If the search has not converged, the process returns to S22 and continues. On the other hand, if the search has converged, the optimization is terminated (S28) and the optimization results are output from the output unit 6. The optimization results output here are stored in the computer's storage device.

In this embodiment, the magnet dimensions S and the initial core shape C are determined independently, so the core shape optimized in steps S24 to S26 can be used as the initial shape C during design for a different magnet dimension S. This reduces the number of topology optimization iterations.

Table 1 shows the results of a comparison between topology optimization by the conventional method shown in Figure 1 and the method of the embodiment, in which the iron core shape optimized by steps S24 to S26 is used as the initial shape C at the time of design for another magnet dimension S. This comparison shows the number of iterations, total number of evaluations, and total evaluation time until topology optimization under the following conditions (1) to (3).
(1) Calculation time per case (optimization time per run): 4 minutes (2) Magnets Magnet dimensions: 7 types Magnet arrangement: 25 types Magnet angle: 30 types (3) Topology optimization Core initial shape (distribution pattern of core holes 10): 5 types Optimization method: 3 types Sensitivity analysis formula: 1 type Number of iterations: Conventional method Number of iterations of S01 to S04 (average 340 times)
Method of the Example Number of repetitions of S21 to S27 (average 110 times)
According to the comparison results in Table 1, the conventional method required 26,775,000 iterations of the characteristic evaluation calculation in S12, as shown in the "Total number of evaluations" column. Therefore, as shown in the "Total evaluation time [h]" column, it took 1,785,000 hours.

In contrast, the method of the embodiment only required repeating the S24 characteristic evaluation calculation 8,662,500 times, significantly reducing the total evaluation time to 577,500 hours. As a result, it was confirmed that the method of the embodiment can shorten the time required for rotor topology optimization and avoid delays in rotating machine design.

<Others/Examples>
The present invention is not limited to the above-described embodiment, and can be modified and implemented within the scope of the claims. An example is shown below.

(1) The configuration of the system 1 for implementing the present invention is not limited to that shown in Figure 1, and any configuration is acceptable as long as steps S21 to S28 can be executed on a computer.

(2) The sensitivity analysis in S25 is performed when the gradient method is used, but is not necessary when the gradient method is not used. In this case, an algorithm such as that in Non-Patent Document 10 is used to search for the possibility of a point closer to the optimal solution based on the distribution trends calculated for multiple variables.

REFERENCE SIGNS LIST 1... System 2... Variable determination section 3... Image generation section 4... Mapping section 5... Optimization section 6... Output section 10... Hole section

Claims (4)

Using a computer,
A method for designing a rotor of a rotating machine having a magnet and an iron core, comprising:
a variable determination step of defining a design domain of the entire rotor and independently determining a first design variable related to the dimensions of the magnets and a second design variable related to the shape of the iron core;
an image generation step of generating a "mesh" of the rotor according to the first design variables and the second design variables;
a mapping step of mapping a shape defined in the design domain onto the "Mesh";
an optimization step of optimizing the shape of the iron core by modifying the first design variables and the second design variables in accordance with the evaluation of the mapped shape;
and
In the variable determination step,
The iron core shape optimized in the optimization step is
a rotor design method for a rotating machine, wherein the rotor design method uses the magnet as an initial value of the second design variable when a different magnet is used for the design. 2. The rotor design method for a rotating machine according to claim 1, wherein the dimensions of the magnet include the area, position, and rotation angle of the magnet. In the mapping step,
3. The rotor design method for a rotating machine according to claim 1, wherein when the magnet area and the iron core area overlap, the magnet area is given priority. A system for designing a rotor of a rotating machine having a magnet and an iron core,
a variable determination unit that defines a design domain for the entire rotor and determines a first design variable related to a size of the magnet and a second design variable related to a shape of an iron core of the rotor, independently of each other;
an image generation unit that generates a "mesh" of the rotor according to the first design variables and the second design variables;
a mapping unit that maps a shape defined in the design domain onto the "Mesh";
an optimization unit that optimizes the dimensions of the magnet and the shape of the iron core by modifying the first design variables and the second design variables in accordance with an evaluation of the mapped shape;
Equipped with
The variable determination unit
The iron core shape optimized by the optimization unit is
A rotor design system for a rotating machine, wherein the rotor design system uses the second design variable as an initial value when a different magnet is used in the design.