A domain decomposition finite element method for electromagnetic temperature field coupling analysis

Abstract

The present invention discloses a regional decomposition finite element method for electromagnetic temperature field coupling analysis, which is characterized by comprising: regional decomposition of the calculation domain, and ensuring that the calculation scale of each sub-region is equivalent; using the additive Schwarz method to solve the two-dimensional electromagnetic field model and the three-dimensional temperature field model respectively, and performing loss calculation on the two-dimensional electromagnetic field model; through coupling parameter control, the temperature obtained from the three-dimensional temperature field model is further mapped to the two-dimensional electromagnetic field model, and the material properties are updated according to the mapping result. The electromagnetic temperature field coupling analysis is based on the order of "electromagnetic field analysis-loss mapping-temperature field analysis temperature mapping" for cyclic iteration until the parameters such as temperature rise converge. By parallelizing the three key steps of the electromagnetic temperature field analysis and reducing the scale of mapping calculation, the computational efficiency of the motor electromagnetic temperature field coupling analysis can be effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic temperature field coupling analysis, and in particular to a regional decomposition finite element method for electromagnetic temperature field coupling analysis. Background Art

[0002] In recent years, with the increasing demand for power density, the thermal design or thermal management of motors has received more and more attention. Design that fully utilizes materials and approaches the limit of safety margins is essential to achieving these goals, and accurate estimation of motors is the basis of this task. Electromagnetic-temperature field analysis methods based on numerical models, such as finite element models, finite volume models, etc., have been widely used in motor design.

[0003] Electromagnetic-temperature field coupling analysis includes three steps: electromagnetic field analysis, temperature field analysis, and iteration between the two fields. Existing analysis methods require additional algorithms to search for the correspondence between different discrete grids when iterating between physical fields. This nonlinear multi-physics problem usually requires multiple iterations to converge, which makes it more time-consuming than single-field analysis and difficult to meet the needs of fast and efficient motor design. Summary of the invention

[0004] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0005] In view of the above existing problems, the present invention is proposed.

[0006] Therefore, the technical problem solved by the present invention is that the existing analysis method requires additional algorithms to search for the correspondence between different discrete grids when iterating between physical fields. This nonlinear multi-physics problem usually requires multiple iterations to converge, which makes it more time-consuming than single-field analysis and difficult to meet the needs of fast and efficient motor design.

[0007] To solve the above technical problems, the present invention provides the following technical solutions: regional decomposition of the calculation domain is performed, and the calculation scale of each sub-region is guaranteed to be equivalent; the additive Schwartz method is used to solve the two-dimensional electromagnetic field model and the three-dimensional temperature field model respectively, and the loss calculation of the two-dimensional electromagnetic field model is performed; through coupling parameter control, the temperature obtained from the three-dimensional temperature field model is further obtained, and the temperature is mapped to the two-dimensional electromagnetic field model, and the material properties are updated according to the mapping results.

[0008] As a preferred solution of the regional decomposition finite element method for electromagnetic temperature field coupling analysis described in the present invention, the two-dimensional electromagnetic field model and the three-dimensional temperature field model are resolved, and the loss of the two-dimensional electromagnetic field model is calculated. By controlling the coupling parameters, the temperature obtained from the three-dimensional temperature field model is mapped to the two-dimensional electromagnetic field model for updating the material properties until the three-dimensional temperature field model converges with the temperature rise.

[0009] As a preferred scheme of the regional decomposition finite element method for electromagnetic temperature field coupling analysis described in the present invention, the computational domain is regionally decomposed based on a two-dimensional electromagnetic field model and a three-dimensional temperature field model, and is decomposed into sub-computational domains through regional decomposition, and the first type of boundary conditions are applied in the overlapping areas of the computational domains.

[0010] As a preferred solution of the regional decomposition finite element method for electromagnetic temperature field coupling analysis described in the present invention, the two-dimensional electromagnetic field and the three-dimensional temperature field are solved respectively by the additive Schwarz method, and the calculation expression is:

[0011]

[0012]

[0013] Where A is the vector magnetic potential, θ is the magnetic reluctance, J s is the source current density, μ0 is the vacuum magnetic permeability, M x and M y are the two components of the magnetization vector, T is the temperature, k is the thermal conductivity, Q V is the density of the heat source, is the heat flux on the boundary.

[0014] As a preferred solution of the regional decomposition finite element method for electromagnetic temperature field coupling analysis described in the present invention, wherein: a two-dimensional electromagnetic field model sub-computational domain and a corresponding three-dimensional temperature field model sub-computational domain are determined; and bidirectional mapping of the two-dimensional electromagnetic field model and the three-dimensional temperature field model is performed.

[0015] As a preferred solution of the regional decomposition finite element method for electromagnetic temperature field coupling analysis described in the present invention, wherein: the two-dimensional electromagnetic field model performs loss calculation, and the control calculation expression of the coupling parameter is:

[0016]

[0017]

[0018] Among them, P fe is the core loss; P cu / PM is the winding / eddy current loss; k h , k c , k eThey are hysteresis loss coefficient, eddy current loss coefficient and additional loss coefficient; f and B m are the frequency and magnitude of magnetic flux density respectively; J e is the unit current density; V e Unit volume; σ t is the conductivity; μ t is the magnetic permeability; subscript 0 indicates the reference temperature T0; α is the temperature coefficient.

[0019] As a preferred scheme of the regional decomposition finite element method for electromagnetic temperature field coupling analysis described in the present invention, wherein: the loss calculation in the two-dimensional electromagnetic field model includes core loss, winding loss, permanent magnet eddy current loss and heat source transferred to the corresponding unit of the temperature field through a mapping algorithm for use as a temperature field analysis; the temperature distribution obtained by the temperature field analysis is transferred to the corresponding area of ​​the electromagnetic field through a mapping algorithm, the temperature-sensitive material properties are updated according to the temperature distribution, and the two-dimensional electromagnetic field model loss calculation is re-performed based on the updated temperature-sensitive material properties.

[0020] The beneficial effects of the present invention are as follows: by dividing the heat sources into sub-regions of the three-dimensional temperature field model, the temperature distribution obtained by analyzing the three-dimensional temperature field model is transferred to the corresponding sub-regions of the two-dimensional electromagnetic field model through a mapping algorithm to update the temperature-sensitive material properties, and the electromagnetic field analysis is re-performed based on the updated material properties. The electromagnetic temperature field coupling analysis is iterated in a loop based on the sequence of "electromagnetic field analysis-loss mapping-temperature field analysis temperature mapping" until parameters such as temperature rise converge. By parallelizing the three key steps of the electromagnetic temperature field analysis and reducing the scale of mapping calculations, the computational efficiency of the motor electromagnetic temperature field coupling analysis can be effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0022] Figure 1 A schematic diagram of a basic flow chart of a regional decomposition finite element method for electromagnetic temperature field coupling analysis provided by an embodiment of the present invention.

[0023] Figure 2 A schematic diagram of the regional decomposition of a two-dimensional electromagnetic field model and a three-dimensional temperature field model provided by a regional decomposition finite element method for electromagnetic-temperature field coupling analysis according to an embodiment of the present invention.

[0024] Figure 3A data mapping diagram of a regional decomposition finite element method for electromagnetic temperature field coupling analysis provided by an embodiment of the present invention, wherein (a) a three-dimensional model of the rotor yoke regional decomposition, (b) a two-dimensional model of the rotor yoke regional decomposition, and (c) a three-dimensional model of the rotor yoke showing the partition numbers of the two-dimensional model after mapping.

[0025] Figure 4 A temperature distribution diagram of a regional decomposition finite element method for electromagnetic temperature field coupling analysis provided by an embodiment of the present invention.

[0026] Figure 5 A magnetic flux density distribution and equipotential line diagram of a regional decomposition finite element method for electromagnetic temperature field coupling analysis provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0027] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0028] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0029] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0030] The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0031] At the same time, in the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0032] In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0033] Example 1

[0034] Reference Figure 1 , as an embodiment of the present invention, provides a regional decomposition finite element method for electromagnetic temperature field coupling analysis, comprising:

[0035] S1: Perform regional decomposition on the computational domain and ensure that the computational scale of each sub-domain is comparable; perform regional decomposition on the computational domain based on the two-dimensional electromagnetic field model and the three-dimensional temperature field model, decompose it into sub-computational domains through regional decomposition, and apply the first type of boundary conditions in the overlapping areas of the computational domains.

[0036] S2: The additive Schwartz method is used to solve the two-dimensional electromagnetic field model and the three-dimensional temperature field model respectively, and the loss of the two-dimensional electromagnetic field model is calculated.

[0037] The two-dimensional electromagnetic field and three-dimensional temperature field are solved by the additive Schwarz method, and the calculation expressions are:

[0038]

[0039]

[0040] Where A is the vector magnetic potential, θ is the magnetic reluctance, J s is the source current density, μ0 is the vacuum magnetic permeability, M x and M y are the two components of the magnetization vector, T is the temperature, k is the thermal conductivity, Q V is the density of the heat source, is the heat flux on the boundary.

[0041] S3: Through coupling parameter control, according to the coupling between the electromagnetic field and the temperature field, which is reflected in the numerical analysis as the loss and temperature transfer mapping between the solvers, a two-step search strategy is used, that is, first determining the corresponding sub-region and then determining the corresponding unit, narrowing the grid mapping search space, and obtaining the temperature from the three-dimensional temperature field model. The temperature is then mapped to the two-dimensional electromagnetic field model, and the material properties are updated with the mapping results.

[0042] Determine the sub-computational domain of the two-dimensional electromagnetic field model and the corresponding sub-computational domain of the three-dimensional temperature field model; perform bidirectional mapping between the two-dimensional electromagnetic field model and the three-dimensional temperature field model.

[0043] The two-dimensional electromagnetic field model is used for loss calculation, and the control calculation expression of the coupling parameter is:

[0044]

[0045]

[0046] Among them, P fe is the core loss; P cu / PM is the winding / eddy current loss; k h , k c , k e They are hysteresis loss coefficient, eddy current loss coefficient and additional loss coefficient; f and B m are the frequency and magnitude of magnetic flux density respectively; J e is the unit current density; V e Unit volume; σ t is the conductivity; μ t is the magnetic permeability; subscript 0 indicates the reference temperature T0; α is the temperature coefficient.

[0047] The loss calculation in the two-dimensional electromagnetic field model includes core loss, winding loss, permanent magnet eddy current loss and heat source transferred to the corresponding unit of the temperature field through a mapping algorithm for temperature field analysis; the temperature distribution obtained from the temperature field analysis is transferred to the corresponding area of ​​the electromagnetic field through a mapping algorithm, and the temperature-sensitive material properties are updated according to the temperature distribution, and the two-dimensional electromagnetic field model loss calculation is performed again based on the updated temperature-sensitive material properties.

[0048] S4: Resolve the two-dimensional electromagnetic field model and the three-dimensional temperature field model, and perform loss calculation on the two-dimensional electromagnetic field model. By controlling the coupling parameters, the temperature obtained from the three-dimensional temperature field model is mapped to the two-dimensional electromagnetic field model for updating the material properties until the temperature rise of the three-dimensional temperature field model converges. By dividing the heat sources into sub-regions of the three-dimensional temperature field model, the temperature distribution obtained from the three-dimensional temperature field model analysis is transferred to the corresponding sub-regions of the two-dimensional electromagnetic field model through a mapping algorithm to update the temperature-sensitive material properties, and the electromagnetic field analysis is performed again based on the updated material properties. The electromagnetic temperature field coupling analysis is iterated in a loop based on the sequence of "electromagnetic field analysis-loss mapping-temperature field analysis temperature mapping" until parameters such as temperature rise converge. By parallelizing the three key steps of the electromagnetic temperature field analysis and reducing the scale of mapping calculations, the computational efficiency of the motor electromagnetic temperature field coupling analysis can be effectively improved.

[0049] Example 2

[0050] Reference Figure 2-5 , which is another embodiment of the present invention. This embodiment is different from the first embodiment in that it provides a regional decomposition finite element method for electromagnetic temperature field coupling analysis. In order to verify and illustrate the technical effect adopted in this method, this embodiment adopts a traditional technical solution and the method of the present invention for comparative testing, and compares the test results by means of scientific demonstration to verify the real effect of this method.

[0051] Take a surface-mounted permanent magnet synchronous motor with four pole pairs and 24 slots as an example. Its two-dimensional magnetic field model and three-dimensional temperature field model are as follows: Figure 2 As shown in the figure, the winding ends are ignored in the three-dimensional model to simplify the calculation. Based on the model discrete grid, the two-dimensional magnetic field model and the three-dimensional temperature field model are divided into 10 and 6 sub-regions respectively, and the difference in the number of degrees of freedom between the sub-regions of each model is less than 2%. Among them, the regional decomposition electromagnetic field analysis took 1.656s to reach convergence, and the results are shown in Figure 3 As shown in Figure 1, in contrast, the electromagnetic field analysis without regional decomposition took 4.487 seconds to reach convergence. Correspondingly, the efficiency of data mapping transmission and temperature field analysis has been greatly improved by reducing the mapping space or parallel computing (the rotor yoke mapping results and temperature field calculation results are shown in Figure 1). Figure 4 and 5 The efficiency comparison between the method and the traditional method is given in Table 1, which verifies that the method of the present invention can effectively improve the efficiency of electromagnetic-temperature coupling field analysis through parallelization.

[0052] Table 1: Comparison table between the present invention and the traditional method.

[0053]

[0054] It should be appreciated that embodiments of the present invention may be implemented or enforced by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable memory. The method may be implemented in a computer program using standard programming techniques - including a non-transitory computer-readable storage medium configured with a computer program, wherein the storage medium so configured causes the computer to operate in a specific and predefined manner - according to the methods and drawings described in the specific embodiments. Each program may be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system. However, if desired, the program may be implemented in an assembly or machine language. In any case, the language may be a compiled or interpreted language. In addition, the program may be run on a programmed ASIC for this purpose.

[0055] Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that may be executed by one or more processors.

[0056] Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, etc. Aspects of the present invention can be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, an optical read and / or write storage medium, a RAM, a ROM, etc., so that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the process described herein. In addition, the machine-readable code, or part thereof, can be transmitted via a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques described in the present invention, the present invention also includes the computer itself. The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the converted data represents a physical and tangible object, including a specific visual depiction of the physical and tangible object produced on a display.

[0057] As used in this application, the terms "component", "module", "system", etc. are intended to refer to a computer-related entity, which can be hardware, firmware, a combination of hardware and software, software, or software in operation. For example, a component can be, but is not limited to: a process running on a processor, a processor, an object, an executable file, a thread in execution, a program, and / or a computer. As an example, an application running on a computing device and the computing device can both be components. One or more components can exist in a process and / or thread in execution, and a component can be located in a computer and / or distributed between two or more computers. In addition, these components can be executed from various computer-readable media having various data structures thereon. These components can communicate in a local and / or remote process manner, such as according to a signal having one or more data packets (e.g., data from a component that interacts with another component in a local system, a distributed system, and / or interacts with other systems in a signal manner through a network such as the Internet).

[0058] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A regional decomposition finite element method for electromagnetic temperature field coupling analysis, characterized in that: include: Decompose the computational domain into regions and ensure that the computational scale of each sub-region is comparable; The additive Schwarz method is used to solve the two-dimensional electromagnetic field model and the three-dimensional temperature field model respectively, and the loss of the two-dimensional electromagnetic field model is calculated; By controlling the coupling parameters, the temperature is obtained according to the three-dimensional temperature field model, and the temperature is mapped to the two-dimensional electromagnetic field model, and the material properties are updated according to the mapping results; The two-dimensional electromagnetic field and three-dimensional temperature field are solved by the additive Schwarz method, and the calculation expressions are: Where A is the vector magnetic potential, θ is the magnetic reluctance, J s is the source current density, μ0 is the vacuum magnetic permeability, M x and M y are the two components of the magnetization vector, T is the temperature, k is the thermal conductivity, Q V is the density of the heat source, is the heat flux on the boundary; The two-dimensional electromagnetic field model is used for loss calculation, and the control calculation expression of the coupling parameter is: Among them, P fe is the core loss; P cu / PM is the winding / eddy current loss; k h , k c , k e They are hysteresis loss coefficient, eddy current loss coefficient and additional loss coefficient; f and B m are the frequency and magnitude of magnetic flux density respectively; J e is the unit current density; V e Unit volume; σ t is the conductivity; μ t is the magnetic permeability; subscript 0 indicates the reference temperature T0; α is the temperature coefficient.

2. The regional decomposition finite element method for electromagnetic temperature field coupling analysis according to claim 1, characterized in that: The two-dimensional electromagnetic field model and the three-dimensional temperature field model are resolved, and the loss of the two-dimensional electromagnetic field model is calculated. By controlling the coupling parameters, the temperature obtained from the three-dimensional temperature field model is mapped to the two-dimensional electromagnetic field model for updating the material properties until the three-dimensional temperature field model converges.

3. The regional decomposition finite element method for electromagnetic temperature field coupling analysis according to claim 1, characterized in that: Based on the two-dimensional electromagnetic field model and the three-dimensional temperature field model, the computational domain is decomposed into sub-computational domains through regional decomposition, and the first-class boundary conditions are applied in the overlapping areas of the computational domains.

4. The regional decomposition finite element method for electromagnetic temperature field coupling analysis according to claim 1, characterized in that: Determine the two-dimensional electromagnetic field model sub-computational domain and the corresponding three-dimensional temperature field model sub-computational domain; Bidirectional mapping between the two-dimensional electromagnetic field model and the three-dimensional temperature field model.

5. The regional decomposition finite element method for electromagnetic temperature field coupling analysis according to claim 1, characterized in that: The loss calculation in the two-dimensional electromagnetic field model includes core loss, winding loss, permanent magnet eddy current loss and friction loss.

6. The regional decomposition finite element method for electromagnetic temperature field coupling analysis according to claim 1, characterized in that: The temperature is transferred to the corresponding unit of the temperature field through a mapping algorithm and used as a heat source for temperature field analysis. The temperature distribution obtained by the temperature field analysis is transferred to the corresponding area of ​​the electromagnetic field through a mapping algorithm, and the temperature-sensitive material properties are updated according to the temperature distribution. The two-dimensional electromagnetic field model loss calculation is re-performed based on the updated temperature-sensitive material properties.

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