An analytical method based on refined modeling of bidirectional coupling of multiphysics fields

Abstract

This invention discloses an analytical method based on refined modeling using bidirectional coupling of multiple physics fields. The method includes: determining the physical fields involved in the study; establishing models for each physical field; analyzing the coupling mechanism and form of the electro-magnetic-thermal multiphysics fields; establishing a refined transient model of bidirectional coupling of multiple physics fields; solving the multiphysics coupling model; conducting electromagnetic characteristic, energy consumption, and temperature rise tests; determining the transient changes in energy consumption and temperature rise distribution within the research object with time and spatial location, as well as the changes in electromagnetic characteristics under the influence of temperature rise; and obtaining the multiphysics coupling characteristics. This invention, through the coupling of electric, magnetic, and thermal fields, considers the temperature changes caused by accumulated losses, while also incorporating the influence of thermal characteristics on the resistivity of conductors, the permeability of soft magnetic materials, and the operating point of permanent magnets. This reduces the error in describing the internal loss characteristics of the mechanism using the iron loss model, thereby improving the accuracy of the analytical results.

Description

Technical Field

[0001] This invention relates to the field of simulation analysis technology, and specifically to an analysis method based on refined modeling using bidirectional coupling of multiphysics fields. Background Technology

[0002] The operation of an electromagnetic mechanism or motor is a complex process involving the coupling of multiple fields, including electric, magnetic, and thermal fields. These physical fields influence and constrain each other. During normal operation, the relationships between these physical fields need to be coordinated to achieve a relative equilibrium. An unreasonable distribution of these fields can lead to numerous problems and affect the electrical performance of the electromagnetic mechanism or motor. Therefore, clarifying the interrelationships and influencing factors among the characteristics of each physical field and systematically studying the multi-physics coupling characteristics of electromagnetic mechanisms or motors is particularly important.

[0003] There is considerable research on the multi-physics coupling characteristics of electromagnetic mechanisms or motors at present, but the accuracy is not high. This is because the iron loss model used can describe the internal loss characteristics of the mechanism, but the error is large, resulting in low accuracy of energy consumption calculation, which in turn affects the accuracy of temperature rise characteristics calculation. Most studies on the multi-physics coupling characteristics of electromagnetic mechanisms or motors are unidirectional coupling, which only consider the temperature change caused by the accumulation of losses, while ignoring the influence of thermal characteristics on conductor resistivity, permeability of soft magnetic materials and operating point of permanent magnets. Summary of the Invention

[0004] To address the aforementioned shortcomings, this invention provides an analytical method for refined modeling of multi-physics bidirectional coupling with small errors and high precision.

[0005] The objective of this invention is achieved as follows: an analysis method based on refined modeling using bidirectional coupling of multiphysics fields, characterized by the following steps:

[0006] S1: Determination of the physical fields involved in the research;

[0007] S2: Establishment of various physical field models;

[0008] S3: Analyze the coupling mechanism and forms of multiple physical fields including electro-magnetism and heat;

[0009] S4: Establishment of a multi-physics bidirectional coupled transient refined model;

[0010] S5: Solving the multiphysics coupling model;

[0011] S6: Electromagnetic properties, energy consumption and temperature rise test;

[0012] S7: Determine whether the transient changes in energy consumption and temperature rise distribution within the research object in step S5 with time and spatial location, as well as the changes in electromagnetic properties under the influence of temperature rise, match the electromagnetic properties, energy consumption, and electromagnetic properties under the influence of temperature rise in step S6.

[0013] S8: If the match is consistent, the multi-physics coupling characteristics are obtained; if the match is inconsistent, repeat steps S5 to S6.

[0014] Preferably, the establishment and correctness verification of each physical field model in step S2 are carried out using electromagnetic analysis finite element software; the physical field model includes an electric field model, a magnetic field model, and a thermal field model. The electromagnetic analysis finite element software uses the finite element method, the coupling model uses a 3D model, and the iron loss calculation model can be customized to achieve different calculation accuracy requirements. The thermal field is calculated using a non-simplified energy consumption distribution as the heat source, and the analysis results of the thermal field can be back-coupled to adjust the material properties in the electromagnetic field; the electromagnetic analysis finite element software can be version JMAG18.1.

[0015] Preferably, the electric field model includes a power source and an internal coil, and the influence of the frequency and amplitude of the excitation current and the change in coil resistance on the amount of copper loss in the energy consumption.

[0016] The magnetic field model includes the addition of model materials, the application of excitation current and the setting of motion conditions, and the influence of changes in permanent magnet and soft magnetic material properties, magnetic induction intensity, excitation current frequency and motion conditions on the magnitude of iron loss in energy consumption.

[0017] The thermal field model includes the addition of model materials and thermal circuits, the setting of heat exchange boundaries, the determination of heat exchange coefficient, thermal conductivity and heat source, and the influence of energy distribution and accumulation on the magnitude of temperature rise.

[0018] Preferably, in step S3, the coupling mechanism and form of the electro-magnetic-thermal multiphysics fields are analyzed, including the influence of material saturation and excitation conditions on dynamic losses such as eddy currents and stray currents; by establishing an energy consumption theoretical model with iron loss separation and variable coefficients, the heat generation, heat transfer and heat dissipation mechanisms inside the mechanism and the influence of thermal characteristics on resistivity, permeability and permanent magnet operating point are analyzed.

[0019] Preferably, the establishment of the energy consumption theoretical model with iron loss separation and variable coefficient includes:

[0020]

[0021]

[0022] In the formula, σ represents the electrical conductivity of the ferromagnetic material; h represents the thickness of the core laminations; δ represents the density of the ferromagnetic material; T and f represent the period and frequency of the fundamental wave; and B represents the density of the ferromagnetic material. m ΔB i- The maximum magnetic flux density and the local magnetic flux density change within one period; n - The number of local magnetic flux density changes;

[0023] Equation (3) is obtained by modifying the classic Bertotti three-term constant coefficient iron loss model:

[0024]

[0025] According to traditional motor design theory, the value of the Steinmetz coefficient α is generally between 1.6 and 2.2. h k e k a These are the loss coefficients for hysteresis loss, eddy current loss, and stray loss, respectively.

[0026] Using the measured loss data, we can obtain equation (4):

[0027]

[0028] The equation is fitted to a variable B at a certain frequency (first, second, and third order curve fitting can be used), as follows:

[0029] k e =k e0 +k e1 B+k e2 B 2 +k e3 B 3 Equation (5)

[0030] k a =k a0 +k a1 B+k a2 B 2 +k a3 B 3 Equation (6)

[0031] logα = log k h +(α0+α1B+α2B 2 +α3B 3 )log B (7)

[0032] At the same frequency, it is necessary to fit different magnetic flux density points to obtain the coefficient k. e0 k e1 k e2 k e3 k h After determining a0, a1, a2, and a3, the loss coefficients at any frequency and magnetic flux density can be obtained.

[0033] The effects of thermal properties on resistivity, permeability, and the operating point of permanent magnets include:

[0034] The effect of temperature rise on the actuator coil resistance can be expressed by equations (8) and (9):

[0035]

[0036]

[0037] In the formula: R is the coil resistance; ρ is the resistance increase coefficient; t ρ is the resistivity at temperature t0; A0 is the cross-sectional area of ​​the conductor; β is the temperature coefficient of the conductor's resistance; t is the temperature of the conductor.

[0038] The initial permeability of soft magnetic materials can be approximated by equation (10):

[0039]

[0040] In the formula: μ0 is the permeability at room temperature; M S K represents the saturation magnetization. u M is the magnetic anisotropy constant; S and K u The behavior varies with temperature;

[0041] The effect of temperature change on the remanence of permanent magnets can be expressed by equation (11):

[0042]

[0043] In the formula: B rt1 B is the remanence at temperature t1; rt0 t0 represents the remanence at temperature t0; IL represents the irreversible loss rate of the remanence. t1 is the reversible temperature coefficient of remanence; t1 is the operating temperature; t0 is the initial operating temperature.

[0044] Preferably, the establishment of the multi-physics bidirectional coupling transient refined model in step S4 is based on step S3. The loss results of electromagnetic field analysis are used as the heat source for thermal field analysis. The influence of temperature rise on coil resistivity, permeability of soft magnetic material and operating point of permanent magnet is analyzed. Then, the frequency and amplitude of excitation current, coil resistivity and properties of permanent magnet and soft magnetic material are corrected according to the thermal field analysis results. The feedback results are continuously modified to make the simulation results more accurate.

[0045] Preferably, solving the multiphysics coupling model in step S5 can yield the transient variation laws of energy consumption and temperature rise distribution within the research object with time and spatial location, as well as the variation laws of electromagnetic properties under the action of temperature rise.

[0046] The beneficial effects of this invention are as follows: 1. By coupling the physical fields of electric field, magnetic field and thermal field, and taking into account the temperature change caused by the accumulation of loss, the influence of thermal characteristics on the resistivity of conductor, the permeability of soft magnetic material and the operating point of permanent magnet is combined, thereby reducing the error of the iron loss model in describing the internal loss characteristics of the mechanism and improving the accuracy of the analysis results.

[0047] 2. By using a trinomial model with variable coefficients for iron loss separation, the error is reduced to within 5%. An additional magnetic flux density term is introduced into the eddy current loss term and the hysteresis loss term to account for the increase in eddy current loss caused by magnetic circuit saturation and the increase in hysteresis loss caused by harmonic magnetic fields, making the iron loss model more complete and accurate. The frequency and amplitude of the excitation current, the coil resistivity, and the properties of permanent magnets and soft magnetic materials are corrected by the field analysis results, further improving the accuracy of the analysis results. Attached Figure Description

[0048] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0049] The invention will be further summarized below with reference to the accompanying drawings.

[0050] like Figure 1 As shown, an analysis method based on multi-physics bidirectional coupling refined modeling is presented, the method comprising:

[0051] S1: Determination of the physical fields involved in the research; the determination of the physical fields involved in step S1 includes electric field, magnetic field, and thermal field.

[0052] S2: Establishment of each physical field model; The establishment of each physical field model in step S2 is carried out using electromagnetic analysis finite element software. The electric field model includes the power source and internal coils; the magnetic field model includes the addition of model materials, the application of excitation current, and the setting of motion conditions; the thermal field model includes the addition of model materials and thermal circuits, the setting of heat exchange boundaries, and the determination of heat exchange coefficient, thermal conductivity, and heat source. The establishment of each physical field model involves the quantitative analysis of energy consumption and temperature rise within the research object. Among them, the electric field model includes the influence of the frequency and amplitude of the excitation current and the change of coil resistance on the amount of copper loss in energy consumption; the magnetic field model includes the influence of the properties of permanent magnets and soft magnetic materials, magnetic induction intensity, excitation current frequency, and changes in motion conditions on the amount of iron loss in energy consumption; the thermal field model includes the influence of the distribution and accumulation of energy consumption on the amount of temperature rise.

[0053] S3: Analyze the coupling mechanism and form of electro-magnetic-thermal multi-physics fields; Step S3 analyzes the coupling mechanism and form of electro-magnetic-thermal multi-physics fields, including the influence of material saturation and excitation conditions on dynamic losses such as eddy currents and stray currents, establishes an energy consumption theoretical model with iron loss separation and variable coefficients, and analyzes the heat generation, heat transfer and heat dissipation mechanisms inside the research object, as well as the influence of thermal characteristics on resistivity, permeability and permanent magnet operating point.

[0054] The establishment of an energy consumption theoretical model with iron loss separation and variable coefficients includes:

[0055]

[0056]

[0057] In the formula, σ represents the electrical conductivity of the ferromagnetic material; h represents the thickness of the core laminations; δ represents the density of the ferromagnetic material; T and f represent the period and frequency of the fundamental wave; and B represents the density of the ferromagnetic material. m ΔB i - The maximum magnetic flux density and the local magnetic flux density change within one cycle; n - the number of local magnetic flux density changes.

[0058] As shown in Equations (1) and (2) above, the iron loss calculation model is currently the most commonly used model for calculating the iron loss of motors using the finite element method. The calculation error of this model for most silicon steel sheets is within 10%, which is sufficient to describe the internal loss characteristics of the research object. The iron loss separation variable coefficient trinomial model used in this invention can further reduce the error to within 5%.

[0059] Equation (3) is obtained by modifying the classic Bertotti three-term constant coefficient iron loss model:

[0060]

[0061] According to traditional motor design theory, the value of the Steinmetz coefficient α is generally between 1.6 and 2.2. h k e k a These are the loss coefficients for hysteresis loss, eddy current loss, and stray loss, respectively.

[0062] Using the measured loss data, we can obtain equation (4):

[0063]

[0064] To fit this equation at a certain frequency with B as the variable, we can take 1st, 2nd, and 3rd order curve fitting, as follows:

[0065] k e =k e0 +k e1 B+k e2 B2 +k e3 B 3 Equation (5)

[0066] k a =k a0 +k a1 B+k a2 B 2 +k a3 B 3 Equation (6)

[0067] logα = log k h +(α0+α1B+α2B 2 +α3B 3 )log B (7)

[0068] At the same frequency, it is necessary to fit different magnetic flux density points to obtain the coefficient k. e0 k e1 k e2 k e3 k h After determining a0, a1, a2, and a3, the loss coefficients at any frequency and magnetic flux density can be obtained.

[0069] Based on the classic Bertotti three-term constant-coefficient iron loss model, an additional magnetic flux density term is introduced into the eddy current loss term and the hysteresis loss term to account for the increase in eddy current loss due to magnetic circuit saturation and the increase in hysteresis loss due to harmonic magnetic fields. This makes the iron loss model more complete and accurate. In the model, the eddy current loss, hysteresis loss, and stray loss coefficients all vary with the amplitude and frequency of the magnetic flux density, reflecting the influence of nonlinear factors and harmonic magnetic fields on iron loss.

[0070] The effects of thermal properties on resistivity, permeability, and the operating point of permanent magnets include:

[0071] The effect of temperature rise on coil resistivity can be expressed by equations (8) and (9):

[0072]

[0073]

[0074] In the formula: R is the coil resistance; K F To increase the resistance coefficient; ρ t t0 represents the resistivity at temperature t0; A0 represents the cross-sectional area of ​​the conductor; β represents the temperature coefficient of the conductor's resistance; and t represents the temperature of the conductor.

[0075] The initial permeability of soft magnetic materials can be approximated by equation (10):

[0076]

[0077] In the formula: μ0 is the permeability at room temperature; M S K represents the saturation magnetization. u M is the magnetic anisotropy constant. S and K u The situation varies with temperature.

[0078] Temperature has a significant impact on the magnetic properties of permanent magnet materials. The operating point of a permanent magnet differs at different temperatures, affecting the performance of the research object. Therefore, the operating temperature of a permanent magnet directly affects its operating point.

[0079] The effect of temperature change on the remanence of permanent magnets can be expressed by equation (11):

[0080]

[0081] In the formula: B rt1 B is the remanence at temperature t1; rt0 t0 represents the remanence at temperature t0; IL represents the irreversible loss rate of the remanence. t1 is the reversible temperature coefficient of remanence; t1 is the operating temperature; t0 is the initial operating temperature.

[0082] S4: Establishment of a refined transient model of multi-physics bidirectional coupling; 3D transient finite element analysis of the research object is performed using electromagnetic finite element analysis software. The current curve is imported as the excitation source in the magnetic field transient analysis, and motion conditions are set for the research object. The variation laws of copper loss and iron loss (eddy current loss, stray loss, and other dynamic losses) under typical working conditions are simulated and studied. Further analysis is conducted on the variation laws of copper loss and iron loss, including eddy current loss and stray loss, under different working conditions and different motion modes. Based on this, the loss results from electromagnetic field analysis are used as the heat source for thermal field analysis. Relevant property parameters and heat transfer coefficients of each component material are set, and heat exchange boundaries and heat exchange coefficients are set. Temperature rise simulations under different working conditions are conducted to analyze the thermal field distribution and temperature rise of the research object in the thermal field. At the same time, the influence of temperature rise on resistivity, permeability and permanent magnet operating point is revealed. Based on the thermal field analysis results, the frequency and amplitude of the excitation current, coil resistivity and the properties of permanent magnet and soft magnetic materials are corrected. The feedback results are continuously modified, and the interoperability of each physical field is fully utilized to make the simulation results more accurate and more practical.

[0083] S5: Solving the multiphysics coupling model; Solving the multiphysics coupling model in step S5 can yield the transient changes in energy consumption and temperature rise distribution within the research object with time and spatial location, as well as the changes in electromagnetic properties under the influence of temperature rise.

[0084] S6: Electromagnetic characteristics, energy consumption and temperature rise test; The electromagnetic characteristics, energy consumption and temperature rise test in step S6 are all related to the material properties, structural parameters, excitation current and control parameters of the research object.

[0085] S7: Results match? Determine if the transient changes in energy consumption and temperature rise distribution within the research object over time and space, as well as the changes in electromagnetic properties under the influence of temperature rise, in step S5 match the electromagnetic properties, energy consumption, and electromagnetic properties under the influence of temperature rise in step S6.

[0086] S8: If the match is consistent, the multi-physics coupling characteristics are obtained; if the match is inconsistent, repeat steps S5 to S6.

[0087] Working Principle: The analytical method of this invention first identifies the physical fields involved in the study—electric field, magnetic field, and thermal field—and establishes models for each physical field. It then analyzes the coupling mechanism and form of the electro-magnetic-thermal multi-physics fields in a relatively refined and accurate manner, including the influence of material saturation and excitation conditions on dynamic losses such as eddy currents and stray currents. An energy consumption theoretical model with iron loss separation and variable coefficients is established, which can reduce the error to within 5% compared to the classical three-term constant coefficient iron loss model, resulting in higher accuracy in energy consumption calculation. The method analyzes the internal heat generation, heat transfer, and heat dissipation mechanisms of the research object, as well as the influence of thermal characteristics on resistivity, permeability, and the operating point of the permanent magnet. Temperature has a significant impact on the magnetic properties of permanent magnet materials; the operating point of the permanent magnet differs at different temperatures, affecting the performance of the research object. Based on the fact that the operating temperature of the permanent magnet directly affects its operating point, the interrelationships and influencing factors among the characteristics of each physical field are clarified, and the multi-physics coupling characteristics of the research object are systematically studied. By comparing the electromagnetic characteristics, energy consumption, and temperature rise test results of the research object under different operating modes and conditions, the transient variation law of internal energy consumption and temperature rise distribution with time and spatial location and the variation law of electromagnetic characteristics under temperature rise are studied, so as to obtain the high-precision multi-physics coupling characteristics of the research object.

[0088] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. An analysis method based on multi-physical field bidirectional coupling refined modeling, characterized in that: The steps of the analysis method are as follows: S1: determination of physical fields involved in the research; S2: establishment of each physical field model; S3: analysis of the mechanism and form of the electro-magnetic-thermal multi-physical field coupling; The analysis of the mechanism and form of the electro-magnetic-thermal multi-physical field coupling includes the influence of material saturation and excitation conditions on eddy current and stray loss; By establishing an energy consumption theoretical model with separated iron loss and variable coefficients, the mechanism of heat generation, heat transfer and heat dissipation in the mechanism and the influence of thermal characteristics on resistivity, magnetic permeability and permanent magnet operating point are analyzed; The establishment of the energy consumption theoretical model with separated iron loss and variable coefficients includes: Formula (1); Equation (2); wherein - permeability of the ferromagnetic material; h - core lamination thickness; - permeability of the ferromagnetic material; T, - period and frequency of the fundamental wave; 、 - maximum value of the magnetic flux density and the local magnetic flux density variation in one period; n - number of local magnetic flux density transformations; The classical Bertotti three-term constant coefficient iron loss model is modified to obtain formula (3): = j Equation (3); Steinmetz coefficients The value of the Steinmetz coefficients is generally taken as 1.6-2.2 according to the traditional motor design theory, , , Pm, Ph, Ps are the loss coefficients of hysteresis loss, eddy current loss and stray loss, respectively. Using the measured loss data, formula (4) can be obtained: Equation (4); The formula is fitted with B as the variable at a certain frequency, and the 1st, 2nd and 3rd order curve fitting is taken as follows: Formula (5); Equation (6); Equation (7); At the same frequency, the different magnetic density points need to be fitted to obtain the coefficients 、 、 、 、 、 、 、 、 After that, the loss coefficient at any frequency and magnetic density is obtained; The influence of thermal characteristics on resistivity, magnetic permeability and permanent magnet operating point includes: The influence of temperature rise on the coil resistance of the actuator can be represented by formula (8) and formula (9): Equation (8); Equation (9); where: R is the coil resistance; and is resistivity at temperature t; is the cross-sectional area of the wire; is the temperature coefficient of the wire resistance; and t is the wire temperature; The initial magnetic permeability of soft magnetic material can be approximately calculated by formula (10): Equation (10); In the formula: is the magnetic permeability at room temperature; is the saturation magnetization; is the magnetic anisotropy constant; and the case with temperature change; The influence of temperature change on the residual magnetism of the permanent magnet can be represented by formula (11): Equation (11); wherein: is the remanence at temperature T; is the remanence at temperature T; is the remanence at temperature T; IL is the irreversible loss of remanence; is the reversible temperature coefficient of remanence; is the reversible temperature coefficient of remanence; is the working temperature; is the initial working temperature; S4: establishment of a multi-physical field bidirectional coupling transient fine model; S5: solution of the multi-physical field coupling model; S6: electromagnetic property, energy consumption and temperature rise test; S7: whether the transient variation law of the energy consumption and temperature rise distribution in the research object with time and space position and the variation law of electromagnetic property under the action of temperature rise are consistent with the electromagnetic property under the action of electromagnetic property, energy consumption and temperature rise in step S6? S8: if consistent, the multi-physical field coupling characteristics are obtained, if inconsistent, repeat steps S5 to S6.

2. The method of claim 1, wherein: The physical fields in step S1 include electric field, magnetic field and thermal field.

3. The method of claim 1, wherein: The establishment and correctness verification of each physical field model in step S2 are assisted by electromagnetic analysis finite element software; the electromagnetic analysis finite element software defines an iron loss calculation model to meet different calculation precision requirements, and performs thermal field calculation with non-simplified energy consumption distribution as the heat source, and the analysis results of the thermal field can be coupled in reverse to adjust the material properties in the electromagnetic field.

4. The method of claim 2, wherein: The electric field model includes power supply and internal coil, and the influence of the frequency and amplitude of excitation current and the change of coil resistance on the size of copper loss in energy consumption; The magnetic field model includes the addition of model materials, the loading of excitation current and the setting of motion conditions, the influence of the change of permanent magnet and soft magnetic material properties, magnetic induction intensity, excitation current frequency and motion conditions on the size of iron loss in energy consumption; The thermal field model includes the addition of model materials and thermal circuit, the setting of heat exchange boundary, the determination of heat exchange coefficient, thermal conductivity coefficient and heat source, and the influence of energy consumption distribution and accumulation on the size of temperature rise.

5. The method of claim 1, wherein: The step S4 is based on step S3, and the loss result of the electromagnetic field analysis is used as a heat source of the thermal field analysis to analyze the influence of the temperature rise on the coil resistivity, the soft magnetic material permeability and the permanent magnet operating point. Then, the frequency and amplitude of the excitation current, the coil resistivity and the properties of the permanent magnet and the soft magnetic material are corrected according to the thermal field analysis result, and the feedback result is continuously modified.

6. The method of claim 1, wherein: The step S5 is used for solving the multi-physics coupling model to obtain the transient variation law of the internal energy consumption and the temperature rise distribution with time and space position and the electromagnetic characteristic variation law under the temperature rise.

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