Rotor design method and system for rotating machines

Abstract

To provide a rotor design method and a design system that reduces the time required for rotor topology optimization and avoids delays in rotating machine design.SOLUTION: A method defines a design area for the entire rotor and independently determines a first design variable regarding the dimensions of a magnet and a second design variable regarding the shape of an iron core S21, generates a "Mesh" of the rotor according to the first design variable and the second variable S22, maps the shape defined in a design domain to the "Mesh" S23, calculates a characteristic evaluation of the mapped shape S24, executes the sensitivity analysis of the gradient method S25, corrects the magnet dimensions and the core shape according to the results of the sensitivity analysis S26, determines whether the optimization of the core shape (topology) has converged or not S27, and if converged, finishes optimization S28.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to the design of rotors used in, for example, permanent magnet rotating machines. [Background technology]

[0002] Permanent magnet rotating machines are highly efficient and have a wide range of variable speeds, and are used in a variety of applications such as compressors, spindles, and hybrid vehicles. They have an outer stator and an inner rotor, and are designed with permanent magnets (hereafter referred to as magnets) embedded inside the rotor to improve performance, such as increasing torque.

[0003] This rotor is equipped with an iron core, or yoke, to connect the magnetic flux between the two permanent magnets. The torque components of this rotor are determined by the relative positions of the iron core, magnets, and stator.

[0004] Therefore, rotor design can be considered as the design of a system whose performance is determined by the core shape and magnet arrangement. In this case, the core shape design is mainly carried out by optimizing the topology (shape). Below, we will explain an overview of conventional topology optimization using Figure 6.

[0005] S01: When the rotor design process begins, the dimensions of the magnets to be used in the rotor are determined.

[0006] S02: A rotor core "mesh" is generated according to the dimensions of the magnets in S01 (S02).

[0007] S03: Optimize the rotor core topology. The topology optimization method involves first determining 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).

[0008] Then, in the gradient method, the design variables (iron core shape) are modified (S14) according to the results of the sensitivity analysis in S13. In the non-gradient method, the design variables (iron core shape) are modified (S14) according to the evaluation value 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.

[0009] If the optimization process has converged as a result of the output of S16, the design process ends (S05), but if it has not converged, the process returns to S01, the magnet dimensions are changed, and the process is restarted. Details of such a rotor design method (S01 to S05) are described in Non-Patent Documents 1 to 8. [Prior art documents] [Non-patent literature]

[0010] [Non-Patent Document 1] Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "Permanent Magnet Synchronous Motor Rotor Design Method by Collaboration of 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] [Non-patent document 2] 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) [Non-patent document 3] 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.No1 (January 2018) [Non-patent document 4] Shun Maruyama, Shintaro Yamazaki, Kentaro Yachi, Kikuo Fujita, "System-level optimization method for permanent magnet synchronous motors considering both structural configuration and system variables" [No.17-4] Proceedings of the 30th Japan Society of Mechanical Engineers Conference on Computational Mechanics [September 16-18, 2017, Higashiosaka City] [Non-patent document 5] 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)", JSME [No. 18-37], Proceedings of the 13th Optimization Symposium 2018 [October 15-16, 2018, Kyoto] [Non-patent document 6] 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 [2016.12.6-7, Sapporo] [Non-Patent Document 7] 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 [Non-patent document 8] 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] [Non-Patent Document 9] "Ansys TurboGrid: A mesh creation tool for rotating machinery" ANSYS Japan Co., Ltd. Online <Internet URL: https: / / premium.ipros.jp / ansys / product / detail / 2000131706 / > [Non-Patent Document 10] "CYBERNET Ansys Analysis Course: First Optimization" Cybernet Systems Co., Ltd. Online <Internet URL: https: / / www.cybernet.co.jp / ansys / case / lesson / 009.html> Summary of the Invention [Problem to be solved by the invention]

[0011] Conventionally, as shown in S01 and S02, a "mesh" is created after determining the magnet dimensions, and therefore topology optimization of the rotor core is performed for each magnet dimension.

[0012] 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, so they differ for each magnet size A, B...N in Figure 7.

[0013] When S04 returns to S01, the magnet dimensions 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.

[0014] Therefore, as shown in Non-Patent Documents 2 to 5, methods have been proposed for simultaneously updating magnet arrangement optimization and topology optimization, but since magnet arrangement depends on the dimensions of the magnets, there is a risk that effective effects will not be obtained.

[0015] The present invention has been made to solve such conventional problems, and aims to shorten the time required for rotor topology optimization and avoid delays in the design of a rotating machine. [Means for solving the problem]

[0016] (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 for 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 variable and the second variable; 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.

[0017] (2) Another aspect of the present invention is a system for designing a rotor of a rotating machine having a magnet and an iron core, comprising: a variable determination unit that defines a design domain of 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 design variables in accordance with an evaluation of the mapped shape. [Effects of the Invention]

[0018] According to the present invention, it is possible to reduce the time required for rotor topology optimization and avoid delays in the design of a rotating machine. [Brief explanation of the drawings]

[0019] [Figure 1] 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; [Figure 2] 3 is a flowchart showing the processing steps of the design method. [Figure 3](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). [Figure 4] Transition diagram showing transition patterns (a) to (e) during topology optimization using the density method. [Figure 5] Schematic diagram showing an example of magnet dimensions and topology optimization. [Figure 6] 1 is a flowchart showing a conventional topology optimization procedure. [Figure 7] Diagram of magnet placement on "Mesh". DETAILED DESCRIPTION OF THE INVENTION

[0020] A rotor core design method according to an embodiment of the present invention will be described below. This method is primarily used for rotor design of interior permanent magnet synchronous motors (IPSMs), and involves optimizing the rotor core shape (topology).

[0021] In this case, the design method defines the core shape by using the entire rotor as the design domain, independently of the magnet dimensions, which makes it possible to optimize the core shape independently of the magnet dimensions. [Example]

[0022] An embodiment of the design method will be described with reference to Figures 1 to 5. Here, the design method is executed by, for example, a system 1 shown in Figure 1.

[0023] This system 1 is configured by 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, an image generation unit 3, a mapping unit 4, an optimization unit 5, and an output unit 6.

[0024] <<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.

[0025] S21: When the process starts, first, the variable determination unit 2 defines a design domain R. The design domain R defined here is the entire rotor domain of the synchronous motor, with magnets arranged in the iron core.

[0026] 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 is called design variable 1, and the latter is called design variable 2.

[0027] As shown in Figure 3(a), design variable 1 is the magnet's width W and 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 positions X and Y, and Figure 3(d) shows 60 examples of angles (rotation angles). Furthermore, the distribution pattern (spacing) of 10 groups of holes (flux barriers, etc.) in the core can also be used as design variable 2.

[0028] The design variables may be determined according to input / selection by the user, or may be initial design variables determined in advance, or design variables 1 and 2 of another case for which optimization has been completed may be used.

[0029] S22: The image generation unit 3 generates a rotor "Mesh (G1 in FIG. 2)" according to the design variables (magnet dimensions S, initial core shape C) 1 and 2 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.

[0030] 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.

[0031] S24 to 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 classified into gradient methods that use the gradient (sensitivity) of an algorithm, etc., and non-gradient methods that do not use the gradient.

[0032] In topology optimization, the gradient method is generally used, and sensitivity can be found 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, the case where the density method is used will be explained as an example.

[0033] (1) First, the initial structure shown in the mapping diagram G2 is set, and then torque performance is evaluated for the set initial structure using finite element analysis (S24). The density method is a technique for solving the structural shape 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), nonlinear magnetic field analysis is used to determine the magnetic flux density, from which Maxwell's stress tensor T can be obtained. Torque can be obtained using the Maxwell's stress method or nodal stress method using this Maxwell's stress tensor T.

[0034]

number

[0035] Ω iron = Iron core region: region where ρ=1 Ω air = Air region of 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. At this time, there are cases where the evaluation function and the design variable can be directly differentiated, and cases where this cannot be done, and the sensitivity is derived by finding the adjoint equation shown in equation (2). For sensitivity analysis related to rotor torque, three equations can be considered: Sensitivity formula (1): Adjoint formula for Maxwell stress method Sensitivity formula (2): Direct formula of nodal stress method Sensitivity formula (3): Adjoint formula for nodal stress method In this example, seven different sensitivities obtained by combining sensitivity formulas (1) to (3) were evaluated in advance, and sensitivity formulas (2) and (3) were normalized and the sum of the sensitivities was adopted. However, the combination to be adopted for each subject will be considered in advance.

[0036]

number

[0037] 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 the 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.

[0038] Figure 5 shows the search results for design variables 1 and 2 using the sensitivity analysis. Here, the optimum solution is searched for by focusing on the slope (sensitivity) in the graph, and case 1 in Figure 5 has a large average torque, but also a large torque ripple. Therefore, cases 2 to 4 and the optimum solution are searched for within the range of design values.

[0039] At the same time, we will optimize design variable 1 by applying "3.3 Optimization of permanent magnet placement using response surfaces" in Non-Patent Document 3. For example, we can replace "magnet placement" in Non-Patent Document 3 with "magnet dimensions (design variable 1)" and use the solution obtained in optimizing the yoke structure configuration (Fig. 4) to find the optimal solution for magnet placement.

[0040] 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 result is output from the output unit 6. The optimization result output here is stored in the computer's storage device.

[0041] In this case, in this embodiment, the magnet dimension S and the initial shape C of the core are determined independently, so the core shape optimized in steps S24 to S26 can be used as the initial shape C at the time of design for another magnet dimension S. This reduces the number of iterations of topology optimization.

[0042] [Table 1]

[0043] Table 1 shows the results of a comparison between topology optimization using the conventional method shown in Figure 1 and the method of the embodiment, in which the iron core shape optimized using 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 for one case (one optimization): 4 minutes (2) Magnet Magnet size: 7 types Magnet arrangement: 25 types Magnet angle: 30 types (3) Topology optimization Initial core shape (distribution pattern of core holes 10): 5 types Optimization methods: 3 types Sensitivity analysis formula: Type 1 Number of iterations: Conventional method, number of iterations of S01 to S04 (average 340 times) Number of repetitions of steps S21 to S27 in the example (average 110 times) According to the comparison results in Table 1, the conventional method required 26,775,000 iterations of the S12 characteristic evaluation calculation, 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.

[0044] In contrast, the method of the embodiment only required repeating the S24 characteristic evaluation calculation 8,662,500 times, significantly shortening 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.

[0045] Other 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.

[0046] (1) The configuration of the system 1 for carrying out the present invention is not limited to that shown in FIG. 1, and any configuration may be used as long as it is possible to execute steps S21 to S28 on a computer.

[0047] (2) The sensitivity analysis of S25 is performed when the gradient method is used, but it is not necessary when the gradient method is not used. In this case, the possibility of a point closer to the optimal solution is searched for from the distribution trend calculated using multiple variables using the algorithm of Non-Patent Document 10 or the like. [Explanation of symbols]

[0048] 1. System 2...Variable determination section 3...Image generation unit 4...Mapping section 5...Optimization section 6. Output section 10・Hole

Claims

1. 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 dimensions of the magnet include the area of ​​the magnet, the position of the magnet, and the rotation angle of the magnet.

2. The rotor design method for a rotating machine according to claim 1.

3. In the mapping step, If the magnet area and the iron core area overlap, the magnet area takes priority.

3. The rotor design method for a rotating machine according to claim 1 or 2.

4. 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.

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