Modal simulation method for skewed-pole rotor assembly, its storage medium, and computer equipment

By using a modal simulation method that meshes and establishes connections for the skewed-pole rotor assembly, the applicability problem of modal analysis in existing technologies is solved, and high-precision modal simulation results are achieved, which are applicable to skewed-pole rotor assemblies with structural changes.

CN115809551BActive Publication Date: 2026-04-03ZHEJIANG LEAPPOWER TECH CO LTD +1
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-11-25
Publication Date
2026-04-03

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Abstract

This application discloses a modal simulation method for a skewed-pole rotor assembly, along with its storage medium and computer equipment. The modal simulation method includes: meshing the skewed-pole rotor assembly, which comprises a motor shaft, multiple skewed-pole core segments, core end plates, multiple magnets, and axial fixing components. The core end plates are located at both ends of the multiple skewed-pole core segments, the magnets are fixed in the magnet slots of the skewed-pole cores, the motor shaft mates with the shaft holes of the multiple skewed-pole core segments, and the axial fixing components connect the motor shaft and the core end plates; establishing the connection relationships between the components of the skewed-pole rotor assembly along its axial and radial directions, and assigning material parameters to each component; and performing modal simulation calculations on the skewed-pole rotor assembly. Through the above method, the modal simulation method provided in this application is applicable to a wide range of rotor assembly structures, and the simulation results obtained have small errors and high accuracy compared to experimental verification results, demonstrating foresight and guidance.
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Description

Technical Field

[0001] This application relates to the field of motor modal simulation technology, and in particular to a modal simulation method for a skewed rotor assembly, its storage medium, and computer equipment. Background Technology

[0002] The skewed rotor assembly mainly consists of a motor shaft, multiple skewed pole iron cores, rotor end plates, magnets, and axial fixing components. The axial fixing components have various structures, and there are also various ways to fix the magnets to the skewed pole iron cores.

[0003] Current modal analysis methods for this skewed rotor assembly often involve extensive simplification and equivalence, failing to accurately reflect its stiffness characteristics. They rely heavily on calibrating equivalent material parameters assigned to the skewed core to correspond with experimental results, making the model applicable only to the current structure and process. Once the structure of the skewed rotor assembly changes, the same modeling approach and simulation calibration parameters cannot be applied. Previous modal simulations cannot capture accurate rotor modes in advance, resulting in lag and hindering early risk identification and design guidance. Summary of the Invention

[0004] This application mainly provides a modal simulation method for skewed-pole rotor assemblies, as well as its storage medium and computer equipment, to solve the problem that the simulation model of skewed-pole rotor assemblies cannot be applied to a wide range of rotor assembly structures, resulting in modal simulation results that lack foresight and guidance.

[0005] To address the aforementioned technical problems, this application provides a modal simulation method for a skewed rotor assembly. This modal simulation method includes: meshing the skewed rotor assembly, wherein the skewed rotor assembly includes a motor shaft, multiple skewed pole cores, core end plates, multiple magnets, and an axial fixing component. The core end plates are disposed at both ends of the multiple skewed pole cores, the magnets are fixed in the magnet slots of the skewed pole cores, the motor shaft mates with the shaft holes of the multiple skewed pole cores, and the axial fixing component connects the motor shaft and the core end plates; establishing the connection relationships of each component in the skewed rotor assembly along the axial and radial directions, and assigning material parameters to each component in the skewed rotor assembly; and performing modal simulation calculations on the skewed rotor assembly.

[0006] To address the aforementioned technical problems, another technical solution adopted in this application is to provide a storage medium. This storage medium stores program data, which, when executed by a processor, implements the steps of the modal simulation method described above.

[0007] To address the aforementioned technical problems, another technical solution adopted in this application is to provide a computer device. This computer device includes a processor and a memory connected together. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the modal simulation method described above.

[0008] The beneficial effects of this application are as follows: Unlike existing technologies, this application discloses a modal simulation method for a skewed-pole rotor assembly, along with its storage medium and computer equipment. This application fully restores the physical connection characteristics between the various components of the skewed-pole rotor assembly and the actual stiffness transmission path. The established model, calibration parameters, and modeling approach are applicable to a wide range of rotor assembly structures without requiring physical samples. By recalibrating the model using measured parameters, the simulation results have small errors and high accuracy compared to experimental verification results, demonstrating foresight and guidance. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0010] Figure 1 This is a schematic diagram of a structural embodiment of a skewed-pole rotor assembly;

[0011] Figure 2 Is it like this? Figure 1 The diagram shows a cross-sectional view of the skewed pole rotor assembly along the axial direction.

[0012] Figure 3 This is a flowchart illustrating an embodiment of the modal simulation method for the skewed-pole rotor assembly provided in this application;

[0013] Figure 4 Is it like this? Figure 1 A partial structural schematic diagram of the equivalent model of the skewed-pole rotor assembly shown;

[0014] Figure 5 Is it like this? Figure 1 A schematic diagram of the stiffness transmission path of the skewed pole rotor assembly shown.

[0015] Figure 6 Is it like this? Figure 1 A schematic diagram of the cross-sectional structure of the equivalent model of the skewed-pole rotor assembly shown;

[0016] Figure 7 This is a schematic diagram of the structure of an embodiment of the storage medium provided in this application;

[0017] Figure 8 This is a schematic diagram of the structure of an embodiment of the computer device provided in this application. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0019] The terms "first," "second," and "third" used in the embodiments of this application are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first," "second," or "third" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0020] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0021] See Figure 1 and Figure 2 , Figure 1 This is a schematic diagram of one embodiment of the skewed-pole rotor assembly. Figure 2 Is it like this? Figure 1 The diagram shows a cross-sectional view of the skewed pole rotor assembly along the axial direction.

[0022] The skewed-pole rotor assembly 100 includes a motor shaft 10, multiple skewed-pole iron cores 20, iron core end plates 30, multiple magnets 40, and an axial fixing component 50. The multiple skewed-pole iron cores 20 are stacked, and each skewed-pole iron core 20 has multiple magnet slots equipped with magnets 40. The magnets 40 can be fixed to the skewed-pole iron cores 20 by injection molding, adhesive, or riveting. Two iron core end plates 30 are respectively placed at both ends of the multiple skewed-pole iron cores 20. The motor shaft 10 is interference-fitted with the shaft hole of the multiple skewed-pole iron cores 20. The axial fixing component 50 connects the motor shaft 10 and the iron core end plates 30. The axial fixing component 50 can be an iron core pressure ring, a distribution screw, or a bushing nut, etc.

[0023] Current modal analysis methods for the skewed rotor assembly 100 often simplify it into an equivalent form, treating multiple skewed core segments as a single unit along the axial direction. The direct calculation results differ significantly from actual measurements, relying heavily on the calibration of equivalent material parameters based on actual measurements. However, if the structure of the skewed rotor assembly 100 changes, such as a change in the fixing method of the magnet 40, the same modeling approach and simulation calibration parameters cannot be applied. Modal simulation cannot accurately capture rotor modes in advance, resulting in a lag and making it impossible to identify risks and guide the design in advance.

[0024] This application provides a modal simulation method for a skewed-pole rotor assembly 100, see reference. Figure 3 , Figure 3 This is a flowchart illustrating an embodiment of the modal simulation method for the skewed rotor assembly provided in this application. The modal simulation method for the skewed rotor assembly 100 includes:

[0025] Step 10: Perform mesh generation on the skewed pole rotor assembly.

[0026] That is, all the components of the skewed rotor assembly 100 are retained, and each component on the skewed rotor assembly 100 is divided into grids, instead of treating the multiple skewed iron cores 20, iron core end plates 30, multiple magnets 40 and axial fixing parts 50 as a whole. Each component in the skewed rotor assembly 100, as well as each independent component such as each skewed iron core 20 and each magnet 40, is divided into independent grids.

[0027] Step 20: Establish the connection relationship between the components in the skewed rotor assembly along the radial and axial directions, and assign material parameters to each component in the skewed rotor assembly.

[0028] See also Figures 4 to 6 ,in Figure 4 Is it like this? Figure 1 A partial structural schematic diagram of the equivalent model of the skewed-pole rotor assembly is shown. Figure 5 Is it like this? Figure 1 The diagram shows the stiffness transmission path of the skewed pole rotor assembly. Figure 6 Is it like this? Figure 1The diagram shows a cross-sectional structural schematic of the equivalent model of the skewed pole rotor assembly.

[0029] Each component in the skewed rotor assembly 100 is an independent component. In reality, the connection relationship between the components exists. By establishing the connection relationship between the components in the model, more realistic model data can be simulated, thereby improving the accuracy of modal simulation.

[0030] For those requiring instructions, the connection relationships between the components of the skewed rotor assembly 100 are fixed. However, current models commonly used for modal analysis typically treat multiple components as a single unit, such as treating multiple skewed pole cores 20 as a whole. This fails to accurately reflect the stiffness characteristics of the structure and can only correlate experimental results by calibrating equivalent material parameters assigned to the skewed pole cores 20. This is only applicable to the current structure and process. Once any part of the skewed rotor assembly 100 is modified, the model and its calibrated material parameters will not be applicable to the modified model structure. For example, the magnets 40 may be fixed to the skewed pole cores 20 in different ways, or the axial fixing components 50 may have different structures.

[0031] This application will fully consider the actual physical model structure of the skewed rotor assembly 100 in the axial and radial directions and the interaction relationship of each component, and make more realistic and reasonable equivalent simplifications so that the model and the material parameters are applicable to skewed rotor assemblies 100 with different structures and different processes.

[0032] In the axial direction, establish the connection relationships between the axial fixing member 50 and the iron core end plate 30, between the iron core end plate 30 and the adjacent inclined pole iron core 20, between two adjacent inclined pole iron cores 20, and between two adjacent magnets 40.

[0033] In the radial direction, establish the connection relationship between the axial fixing member 50 and the motor shaft 10, the multi-segment slanted pole iron core 20 and the motor shaft 10, and the magnet 40 and the slanted pole iron core 20.

[0034] Furthermore, by setting an equivalent connecting material 22 between two adjacent magnets 40, the axial preload and the repulsive force between adjacent magnets 40 are simulated, wherein the axial preload is generated by the axial fixing member 50.

[0035] Specifically, a rigid contact connection is established between the axial fixing member 50 and the core end plate 30, and between the core end plate 30 and the adjacent end faces of the multi-segment skewed core 20. The two skewed cores 20 that are adjacent in the axial direction are considered to be in no contact. An equivalent connecting material 22 of a preset length is established between the two magnets 40 that are adjacent in the axial direction, and a common node connection is established between the equivalent connecting material 22 and the magnets 40.

[0036] Among them, the axial fixing member 50, the iron core end plate 30 and the magnet 40 are respectively assigned their own material parameters, the inclined pole iron core 20 is assigned anisotropic material parameters, and the equivalent connecting material 22 is assigned special material parameters, so as to comprehensively simulate the axial preload and the repulsive force between adjacent magnets 40 in combination with the preset length.

[0037] The special material parameters of the equivalent connecting material 22 need to be calibrated through test results, which can be obtained through prior testing.

[0038] The preset length can be 1.5mm, 2.0mm or 2.5mm, etc. In this embodiment, the preset length can be 2.0mm.

[0039] Rigid contact connections are established between the multi-segment skewed core 20 and the motor shaft 10, and between the axial fixing member 50 and the motor shaft 10, using adjacent cylindrical surfaces in the radial direction. Equivalent connecting materials 22 adjacent in the radial direction establish common node connections at adjacent locations. The equivalent connecting material 22 and the multi-segment skewed core 20 are considered to be in non-contact. The equivalent connecting material 22 is used to simulate axial preload and repulsive forces between adjacent magnets. The motor shaft 10 is assigned corresponding material parameters.

[0040] In the model of the skewed rotor assembly 100, the connection relationship between the aforementioned components is fixed and unchanging. The position, shape, and size of the connection relationship can be adaptively changed as the shape or size of each component changes. Therefore, the establishment of the connection relationship can adapt to the corresponding structural changes on the model. Even if the corresponding structure on the model is modified, the connection relationship still exists, and the area constituting the connection relationship will change accordingly without the need for the user to establish the connection relationship independently.

[0041] The magnets 40 are fixed in different ways, and their connection relationships on the inclined pole core 20 are different.

[0042] In this embodiment, the magnet 40 is fixed to the skew pole core 20 by injection molding, and the injection molding material 42 is filled between the magnet 40 and the skew pole core 20.

[0043] Establishing the connection relationship of each component in the skewed rotor assembly 100 along the radial direction of the skewed rotor assembly 100 also includes: treating the magnet 40 and the skewed pole core 20 as non-contact; establishing a common node connection between the contact surface of the magnet 40 and the injection molding material 42; and establishing a common node connection between the contact surface of the injection molding material 42 and the skewed pole core 20.

[0044] The above method is based on the actual connection relationship between the injection molding material 42, the magnet 40, and the inclined pole iron core 20, so as to be more in line with reality and make the model more accurate and reliable in modal simulation.

[0045] Furthermore, establishing the connection relationship between the components of the skewed rotor assembly 100 along the axial direction of the skewed rotor assembly 100 also includes: establishing an equivalent connecting material 22 of a preset length between two axially adjacent injection molding materials 42, and establishing a common node connection between the equivalent connecting material 22 and the injection molding materials 42. The equivalent connecting material 22 between the magnets 40 is the same as the equivalent connecting material 22 between the injection molding materials 42, and also has the same length.

[0046] Among them, the radially adjacent equivalent connecting materials 22 establish a common node connection at the adjacent location. The radially adjacent equivalent connecting materials 22 include the equivalent connecting materials 22 located between the magnets 40 and between the injection molding materials 42.

[0047] Based on the established skewed-pole rotor assembly 100 model, the stiffness transmission path between the magnet 40, the skewed-pole core 20, and the injection-molded material 42 is as follows: Figure 5 As shown, the motor shaft 10 transmits to the skewed pole core 20, the skewed pole core 20 transmits to the injection molding material 42, the injection molding material 42 transmits to the magnet 40, and the left and right magnets 40 and the injection molding material 42 transmit through the equivalent connecting material 22. There is no direct stiffness transmission path between the skewed pole cores 20.

[0048] In some embodiments, the magnet 40 and the skewed pole core 20 are fixed using a non-injection molding method, which requires corresponding adjustments to the model of the aforementioned skewed pole rotor assembly 100. Considering that the injection molding material 42 would be incorporated into the skewed pole core 20 to enhance material stiffness, after eliminating injection molding, the material modulus of the multiple skewed pole core 20 sections needs to be reduced to half of the raw material modulus to eliminate the influence of the original injection molding material 42 on the stiffness of the skewed pole core 20.

[0049] Optionally, the magnet 40 and the skew pole core 20 are fixed with adhesive; then the connection relationship of each component in the skew pole rotor assembly 100 is established along the radial direction of the skew pole rotor assembly 100, including: establishing a common node connection at the adjacent position of the magnet 40 and the skew pole core 20.

[0050] Optionally, the magnet 40 and the skew pole core 20 are fixed by riveting; then the connection relationship of each component in the skew pole rotor assembly 100 is established along the radial direction of the skew pole rotor assembly 100, including: determining the contact surface pressure distribution area between the magnet 40 and the skew pole core 20 based on static analysis; and establishing a common node connection between the magnet 40 and the skew pole core 20 in the contact surface pressure distribution area.

[0051] The two methods described above are equivalent to specific non-injection molding methods to establish a more reasonable connection between magnet 40 and skewed pole core 20. After the user modifies the model, such as changing the fixing method of magnet 40, the corresponding connection relationship can be changed after the user selects the changed fixing method. That is, the model can still be used in the modified modal simulation without having to rebuild the model and its calibration parameters from scratch.

[0052] Step 30: Perform modal simulation calculations on the skewed pole rotor assembly.

[0053] Modal simulation calculations were performed on the skewed rotor assembly 100. Taking the skewed rotor assembly 100 of a certain automotive permanent magnet synchronous motor as an example, it has 8 skewed iron cores 20. In the simulation range of 8000Hz, the main modes are: first-order bending mode 3036Hz, first-order torsional mode 3155Hz, and second-order torsional mode 6020Hz. The simulation results are within 5% of the experimental verification results, and the results obtained by modal simulation under this model are highly accurate.

[0054] This application fully restores the physical connection characteristics between the components of the skewed-pole rotor assembly 100 and restores the actual stiffness transmission path. The established model, calibration parameters, and modeling ideas are applicable to a wide range of rotor assembly structures without waiting for physical samples. The model is recalibrated in combination with measured parameters, so that the error between the simulation results and the experimental verification results is small and the accuracy is high. It has foresight and guidance.

[0055] See Figure 7 , Figure 7 This is a schematic diagram of an embodiment of the storage medium provided in this application.

[0056] The storage medium 60 stores program data 61, which, when executed by the processor, implements, as follows: Figure 3 The modal simulation method for the skewed pole rotor assembly is described.

[0057] The program data 61 is stored in a storage medium 60 and includes several instructions for causing a network device (which may be a router, personal computer, server, or other network device) or processor to execute all or part of the steps of the methods described in the various embodiments of this application.

[0058] Optionally, the storage medium 60 can be any medium capable of storing program data 61, such as a USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), disk, or optical disc.

[0059] See Figure 8 , Figure 8 This is a schematic diagram of the structure of an embodiment of the computer device provided in this application.

[0060] The computer device 70 includes a processor 72 and a memory 71 connected together. The memory 71 stores a computer program, and when the processor 72 executes the computer program, it implements, for example, Figure 3 The modal simulation method for the skewed pole rotor assembly is described.

[0061] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the storage medium embodiments and electronic device embodiments are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0062] This application can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc.

[0063] In the several embodiments provided in this application, it should be understood that the disclosed methods and devices can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0064] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0065] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0066] The above description is merely an embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A modal simulation method for a skewed-pole rotor assembly, characterized in that, include: The skewed rotor assembly is divided into grids, wherein the skewed rotor assembly includes a motor shaft, multiple skewed iron cores, iron core end plates, multiple magnets, and axial fixing components. The iron core end plates are disposed at both ends of the multiple skewed iron cores, the magnets are fixed in the magnet slots of the skewed iron cores, the motor shaft mates with the shaft holes of the multiple skewed iron cores, and the axial fixing components connect the motor shaft and the iron core end plates. The connection relationships of each component in the skewed rotor assembly are established along the axial and radial directions of the skewed rotor assembly, and the material parameters of each component in the skewed rotor assembly are assigned. Modal simulation calculations were performed on the skewed-pole rotor assembly; Establishing the connection relationships of the components in the skewed rotor assembly along the axial and radial directions includes: A rigid contact connection is established between the axial fixing member and the core end plate, and between the core end plate and the adjacent end faces of the multi-segment inclined pole core along the axial adjacent end faces; Two adjacent inclined pole cores in the axial direction are considered to be in no contact; An equivalent connecting material of a predetermined length is established between two axially adjacent magnets, and a common node connection is established between the equivalent connecting material and the magnets; A rigid contact connection is established radially between the multiple inclined pole iron cores and the motor shaft, and between the axial fixing member and the motor shaft; The equivalent connecting materials that are radially adjacent establish a common node connection at adjacent locations; The equivalent connecting material and the multi-segment skewed iron core are considered to be in no contact; The equivalent connecting material is used to simulate the axial preload and the repulsive force between adjacent magnets.

2. The modal simulation method according to claim 1, characterized in that, The magnet is fixed to the skew pole core by injection molding, and the injection molding material is filled between the magnet and the skew pole core; Establishing the connection relationship of each component in the skewed rotor assembly along the radial direction of the skewed rotor assembly includes: The magnet and the multi-segment skew-pole iron core are considered to be in no contact; A common node connection is established between the contact surfaces of the magnet and the injection molding material; A common node connection is established between the contact surfaces of the injection molding material and the inclined pole core.

3. The modal simulation method according to claim 2, characterized in that, Establishing the connection relationship between the components in the skewed rotor assembly along the axial direction of the skewed rotor assembly further includes: An equivalent connecting material of a preset length is established between two adjacent injection molding materials in the axial direction, and a common node connection is established between the equivalent connecting material and the injection molding material.

4. The modal simulation method according to claim 1, characterized in that, If the magnet is fixed to the inclined pole core in a non-injection molding manner, the material modulus of the multi-segment inclined pole core is reduced to 1 / 2 of the raw material modulus.

5. The modal simulation method according to claim 4, characterized in that, The magnet is fixed to the inclined pole core with adhesive. Establishing the connection relationship of each component in the skewed rotor assembly along the radial direction of the skewed rotor assembly includes: A common node connection is established at the adjacent point of the magnet and the skew pole core.

6. The modal simulation method according to claim 4, characterized in that, The magnet and the inclined pole core are fixed together by riveting. Establishing the connection relationship of each component in the skewed rotor assembly along the radial direction of the skewed rotor assembly includes: The contact surface pressure distribution area between the magnet and the inclined pole core is determined based on static analysis. A common node connection is established between the magnet and the skew pole core in the pressure distribution area of ​​the contact surface.

7. The modal simulation method according to claim 1, characterized in that, The axial fixing component, the iron core end plate, and the magnet are each assigned their own material parameters, the skew pole iron core is assigned anisotropic material parameters, and the equivalent connecting material is assigned special material parameters, wherein the special material parameters are verified and calibrated by experiments.

8. A storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, it implements the steps of the modal simulation method as described in any one of claims 1-7.

9. A computer device, characterized in that, It includes a connected processor and a memory, the memory storing a computer program, and the processor executing the computer program to implement the steps of the modal simulation method as described in any one of claims 1-7.

Citation Information

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