Permanent magnet motor rotor structure topological optimization method considering nonlinear saturation characteristic of ferromagnetic material

Abstract

The invention relates to the technical field of permanent magnet motor rotor structure optimization, and particularly discloses a permanent magnet motor rotor structure topological optimization method considering the nonlinear saturation characteristic of a ferromagnetic material, and the method comprises the steps: S101, carrying out the initial parameterization and meshing optimization of a design region variable; s102, determining the performance of the actual operation condition point of the permanent magnet motor load; s103, carrying out finite element analysis on an electromagnetic field and a mechanical field of the permanent magnet motor; and S104, carrying out iterative analysis on the magnetic conductivity of the nonlinear saturated ferromagnetic material, judging whether a result is converged or not, if the result is converged, entering the step S105, otherwise, returning to the step S103, and the like. The weight of the rotor of the permanent magnet motor is effectively reduced through a lightweight design result, the lightweight design of the rotor of the permanent magnet motor is realized while the mechanical and electromagnetic properties are ensured, and a design reference for actual production and manufacturing is provided for the weight reduction design of a rotor region of a permanent magnet region.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of permanent magnet motor rotor structure optimization, and particularly relates to a permanent magnet motor rotor structure topology optimization method considering nonlinear saturation characteristics of ferromagnetic materials. BACKGROUND

[0002] At present, permanent magnet synchronous motors have become core components in modern electrical drive and electromagnetic energy conversion systems due to their high efficiency, high power density, high power factor, excellent dynamic response performance and good control characteristics, and have shown great commercial application value in many fields.

[0003] A permanent magnet synchronous motor mainly comprises a stator core, a rotor core, windings and permanent magnets. During high-speed rotation, the rotor core and the permanent magnet sheath will inevitably produce spatial displacement under the action of their own load and centripetal force, which may lead to stress concentration or local damage in the structure of the rotor and the permanent magnet. Therefore, the rotor core support structure with good structural strength performance is an important condition to ensure the efficient operation of the permanent magnet motor system. At the same time, with the gradual increase of the current motor magnetic load, the saturation degree of the motor core also needs to be considered in the prediction of the electromagnetic output characteristics of the permanent magnet synchronous motor. Therefore, the optimization design of the rotor structure of the permanent magnet synchronous motor not only affects the electromagnetic performance of the system, but also affects the economic performance of the system.

[0004] At present, mechanical and electromagnetic performance needs to be considered in the process of topology optimization of the rotor structure of the permanent magnet synchronous motor. However, the existing topology optimization methods still face great challenges in dealing with such strong coupling and nonlinear interaction. The topology optimization tends to produce complex, irregular or even porous material distribution structures (such as "checkerboard" phenomenon and microstructure). These results often exceed the capability range of traditional manufacturing processes (such as lamination stamping, casting and machining), or have extremely high manufacturing cost and low yield. At the same time, the B-H curve of the ferromagnetic material in the motor has a high degree of nonlinearity and saturation characteristics, and the performance of the permanent magnet also changes with temperature and demagnetization field. In order to simplify the calculation, many current topology optimization methods use linear or approximate material models, which may lead to distortion of the topology optimization results of the permanent magnet motor in the high saturation area or complex working conditions, and there is a certain deviation from the actual operation output performance.

[0005] In view of the above, there is an urgent need for a new topology optimization method for the rotor structure of a permanent magnet motor. SUMMARY

[0006] Therefore, the present application provides a topology optimization method for the rotor structure of a permanent magnet motor considering nonlinear saturation characteristics of ferromagnetic materials, which realizes lightweight design of the rotor of the permanent magnet motor while ensuring mechanical and electromagnetic performance, and provides a design reference for weight reduction design of the permanent magnet region of the rotor in actual production and manufacturing.

[0007] In order to achieve the above-mentioned purpose, the basic scheme of the present application provides a permanent magnet motor rotor structure topology optimization method considering the nonlinear saturation characteristics of ferromagnetic materials, comprising:

[0008] Step S101, initial parameterization and meshing optimization design region variable;

[0009] Step S102, permanent magnet motor load actual operating condition point performance determination;

[0010] Step S103, permanent magnet motor electromagnetic field and mechanical field finite element analysis;

[0011] Step S104, nonlinear saturation ferromagnetic material permeability iterative analysis, and judge whether the result converges, if the result converges, enter step S105, otherwise return to step S103;

[0012] Step S105, permanent magnet motor mechanical and electromagnetic performance sensitivity analysis;

[0013] Step S106, update the rotor optimization region silicon steel sheet material density, and judge whether it meets the requirements, if it meets the requirements, output the final rotor lightweight topology optimization result, otherwise return to step S103.

[0014] In one possible design, in step S101, the basic design parameters and requirements of the motor are determined, a unit motor of the permanent magnet motor is set as an optimization analysis model to simplify the number of mesh analysis of the model, a rectangular mesh is used to construct the rotor region of the permanent magnet motor, the rotor region is divided, the lightweight region of the core that needs to be lightened is set as a topology optimization region, and other regions such as the permanent magnet region are set as normal finite element analysis regions, different region material unit properties are assigned according to the material, the rotor region can be divided into air domain, permanent magnet region and core support region, the elastic modulus and permeability are respectively assigned to the corresponding units, in order to produce a hollow structure in the optimized structure to reduce the weight of the rotor, the density of the air region is set to 1, and the unit density of the permanent magnet and the core support material is set to 0.

[0015] In one possible design, in step S102, according to the rated load operating condition of the motor, i.e. motor parameters, speed, voltage and output power, the three-phase current output parameters of the permanent magnet synchronous motor during operation are determined, which are used for permanent magnet motor operating characteristic analysis under load state.

[0016] In one possible design, in step S103, the magnetic saturation performance of the motor core under load is first analyzed. Regarding the magnetic field distribution of the permanent magnet synchronous motor, the magnetic field parameters are analogized to circuit parameters, and circuit laws are used to analyze the problems in the magnetic circuit. The permanent magnet is equivalent to a magnetic flux source or a magnetomotive force source, and the demagnetization curve of the permanent magnet is approximated as a straight line. When the magnetic field strength is taken as an absolute value, the magnetic induction intensity B of the permanent magnet at the operating point is expressed as:

[0017] B = B r -μ r μ0H (1)

[0018] Where μ0 is the free permeability, μ r Where B is the relative permeability, H is the magnetic field strength, and B is the magnetic field strength. r Remanence density,

[0019] The internal permeability Λ0 of the permanent magnet can then be expressed as:

[0020]

[0021] Among them, A m h is the area of ​​magnetic flux per pole of the permanent magnet. m The thickness of the permanent magnet.

[0022] If the permanent magnet in a permanent magnet motor is equivalent to a constant magnetic flux source connected in parallel with the internal magnetic permeability, or a constant magnetomotive force connected in series with the internal magnetic permeability, and a current flows through the stator winding under the rated load of the motor, and the stator winding is equivalent to a magnetomotive force source connected in series with the magnetic permeability of the stator yoke, then the magnetomotive force Fs generated by a single slot winding is:

[0023]

[0024] Where, N s i represents the number of single-layer conductors in a single slot. s1 i is the armature winding current in the upper coil. s2 To determine the armature winding current in the lower coil, rectangular magnetic permeability units are used to divide the stator, rotor, and air gap regions of the permanent magnet motor, establishing an equivalent magnetic network analysis model of the motor. The magnetic permeability G of a single rectangular unit region is... e for:

[0025]

[0026] Among them, S e Let l be the cross-sectional area in the direction of conduction. e The length in the direction of conduction.

[0027] Under rated load conditions, the magnetomotive force of each node in the equivalent magnetic network model of the permanent magnet motor is solved based on the nodal voltage method, and is expressed as:

[0028] Φ=GF (5)

[0029] Φ = [Φ(1), Φ(2), ..., Φ(n)] T (6)

[0030]

[0031] F = [F(1),F(2),...,F(n)] T (8)

[0032] Where Φ is the magnetic flux matrix, F is the magnetomotive force matrix, G is the magnetic permeability matrix, Φ(i) is the magnetic flux flowing into node i, when i < j, G(i,j) is the magnetic permeability between node i and node j, G(i,i) is the sum of all magnetic permeabilities connected to node i, when i > j, G(i,j) = -G(j,i), and F(i) is the magnetomotive force of node i.

[0033] Based on the magnetic network model, calculate the average magnetic flux density B on each reluctance path. ij for:

[0034]

[0035] In the formula, i and j are the starting and ending points of the corresponding magnetoresistive paths.

[0036] In one possible design, in step S103, based on the specific silicon steel sheet material, its BH curve is obtained, and the magnetic flux density B and magnetic induction intensity H are correlated in different magnetic flux density ranges based on the least squares method, where the unit of B is T and the unit of H is A / cm.

[0037] In one possible design, in step S104, to accelerate the iteration of the core saturation unit, the relative permeability update iteration factor of the magnetic permeability unit is introduced as follows:

[0038] u (k+1) =(u (k+1) ) 0.95 +(u k ) 0.05 (11)

[0039] Step S104 includes the following steps performed sequentially:

[0040] Step S1041: Set the rotor position and establish the equivalent magnetic network model of the permanent magnet motor.

[0041] Step S1042: Set the relative permeability of the magnetic permeability unit in the initial iteration calculation.

[0042] Step S1043, solve the nodal magnetopotential equation F = G-1 Φ and magnetic induction intensity B g ,

[0043] Step S1044, determine If the condition is met, the iterative calculation ends, and the magnetic field density distribution in all regions of the motor, as well as the saturation degree of the iron core in the stator and rotor regions, is obtained. Then, proceed to step S105. If the condition is not met, proceed according to the updated relative permeability u. (k+1) Update the magnetic permeability matrix G and return to step S1043.

[0044] In one possible design, step S105 involves analyzing the mechanical properties of the permanent magnet motor at its rated speed. Considering the centripetal force during high-speed rotation and the preload force when the permanent magnet is fixed, based on the physical equations of plane problems in elasticity, the relationship between stress and strain in the rotor can be obtained as follows:

[0045]

[0046] In the formula, σ is the normal stress, τ is the shear stress, ε is the strain, E is the elastic modulus, and v is the Poisson's ratio. The displacement matrix of a single rectangular element e can be solved according to the following formula, expressed as:

[0047] K e =U e FF e (13)

[0048] In the formula, K e Let U be the stiffness matrix of element e. e Let FF be the nodal displacement matrix of element e. e Let be the nodal load matrix of element e.

[0049] For a rectangular element with 4 nodes, its unit stiffness matrix is:

[0050]

[0051] Where l is the length of the rectangular element and w is the width of the rectangular element.

[0052] The coefficients of each parameter in the unit stiffness matrix are:

[0053]

[0054]

[0055] After assembling the element stiffness matrices, the total stiffness matrix of the rotor structure can be obtained, which satisfies F = KU;

[0056] In the formula, F is the external load matrix, K is the stiffness matrix, and U is the displacement matrix.

[0057] In one possible design, in step S105, under the action of centripetal force and permanent magnet assembly preload, the sensitivity of the rotor structure compliance c to element e is:

[0058]

[0059] In the formula, x is the element density;

[0060] The complex magnetoresistive network in the stator yoke region can be simplified to an equivalent magnetoresistive network between two nodes i and j. When the reference magnetomotive force of the selected reference node j is 0, based on the two-port resistance equivalent theory and the magnetic permeability matrix control equation, the magnetic permeability matrix of n purely reluctant connections in the stator yoke region can be simplified to an (n-1)th order equivalent magnetic network matrix, expressed as:

[0061]

[0062] In the formula, G ii G represents the self-permeability of element node i; ij Φ represents the mutual magnetic permeability of element nodes i and j; i Let be the magnetomotive force at node i;

[0063] Based on the (n-1)th order magnetic permeability matrix, the magnetopotential at node i can be obtained as follows:

[0064]

[0065] The equivalent magnetic reluctance between node i and node j is:

[0066]

[0067] In the formula, R i,j Ii represents the equivalent magnetic reluctance between node i and node j; I0 represents the magnetic flux source flowing into node i.

[0068] Ignoring the influence of the change in permeability of element e on the external magnetic flux source and the permeability of other elements, the sensitivity of the permeability of the permanent magnet rotor core to a single core element e is:

[0069]

[0070] In the formula, The meaning of G n-1i,i The adjoint matrix of a matrix, u e Let be the permeability of element node e.

[0071] In one possible design, after solving for the rotor's stiffness and permeability sensitivity, a mesh filtering algorithm is added, in which a convolution operator is incorporated:

[0072]

[0073] Where r is the set mesh filtering radius, and dist(e,i) is the center distance between element e and element i within a circle with element e as the center and a filtering radius of r.

[0074] After adjusting the sensitivity, the filtered unit sensitivity can be obtained as follows:

[0075]

[0076] In the formula, ρ is the element density, and H i It is a convolution operator;

[0077]

[0078] In the formula, R is the magnetoresistance, N is the number of elements in the optimization region, and ρ is the element density.

[0079] In one possible design, step S106 involves progressively "removing" elements with lower sensitivity during the optimization process. This minimizes the impact of each iteration on the optimization objective, ultimately leading to the optimal topology optimization design result.

[0080] To simultaneously characterize the electromagnetic and mechanical properties of the design unit, a normalization strategy was employed during the optimization process to transform the multi-objective optimization model into a single-objective optimization problem for solution. The unified electromagnetic-mechanical sensitivity deviation value of the unit is shown in the formula. The smaller the deviation value, the better the unit simultaneously possesses electromagnetic and mechanical properties.

[0081]

[0082] In the formula, O i R is the normalized electromagnetic-mechanical sensitivity deviation value for element i; max To determine the maximum non-positive electromagnetic sensitivity within the design region element; C min To define the minimum non-positive mechanical sensitivity in the design region element, Re represents the element electromagnetic sensitivity, and Ce represents the element compliance sensitivity.

[0083] To ensure that the optimized rotor topology of a permanent magnet synchronous motor (PMSM) possesses both good electromagnetic and mechanical properties, the optimization model established with the electromagnetic and mechanical properties of the PMSM as optimization objectives can be expressed mathematically as follows:

[0084]

[0085] Where Ω represents the rotor core optimization design region, x iFor element density, there are only two states, 0 or 1, during the optimization process. 0 represents air elements, which are also the weight-reducing areas that are deleted, and 1 represents rotor core elements. R is the equivalent magnetic reluctance of the rotor core, and U is the displacement of the rotor structure under centripetal force and permanent magnet assembly preload. limit For rotor displacement constraints, V0 is the rotor core volume constraint, and B is the rotor displacement constraint. air For air gap magnetic flux density, B limit For minimum air gap magnetic flux density constraint,

[0086] Based on each electromagnetic and mechanical performance analysis, the element with the lowest normalized electromagnetic-mechanical sensitivity deviation value is removed, thereby gradually bringing the structure closer to the optimal topological configuration, i.e., removing elements that satisfy a deletion rate less than RR. i All units:

[0087]

[0088] Simultaneously, the evolution rate ER is introduced, and the deletion rate of the next stable state is modified according to equation (38). This deletion rate is then used for iteration until the specified deletion rate is reached.

[0089] RR i+1 =RR i +ER (38)

[0090] In the formula, RR i ER represents the deletion rate in each iteration, and ER represents the evolution rate.

[0091] Finally, the topology optimization results for lightweight permanent magnet synchronous motor rotor can be obtained.

[0092] The principle of this invention is as follows:

[0093] (1) The technology of this patent takes into account the unsaturated characteristics of the motor core under load during the rotor topology optimization process of permanent magnet motor, establishes the overall magnetic reluctance analysis model of the motor, and realizes the iterative correction of the magnetic reluctance of the saturated part of the core through the iterative calculation of the magnetic permeability of the stator core, thereby reducing the electromagnetic performance calculation error caused by the magnetic saturation of the core area of ​​the high-saturation motor.

[0094] (2) Since the rotor reluctance and structural strength of the permanent magnet motor are simultaneously analyzed during the calculation process, a better electromagnetic-mechanical structure topology can be generated in each optimization iteration. The multi-objective optimization problem is transformed into a single-objective optimization problem by using the normalization method. The electromagnetic performance optimization target involved in the present invention can be replaced by other features such as electromagnetic torque, torque pulsation or air gap flux density, without affecting the applicability of the electromagnetic-mechanical field coupling optimization process involved in the present invention.

[0095] (3) A grid filtering technique was added during the topology optimization process to avoid the "chessboard" result generated during the topology optimization process, making the topology optimization structure more suitable for actual production and manufacturing.

[0096] (4) By using rectangular units to divide the rotor region of the permanent magnet motor at the same time, the electromagnetic and strength characteristics of the rotor can be calculated simultaneously in the same permanent magnet synchronous motor optimization analysis model.

[0097] Compared with the prior art, the advantages of the present invention are as follows:

[0098] (1) The topology optimization algorithm proposed in this invention can obtain the optimal rotor topology optimization configuration, effectively reduce the weight of the permanent magnet motor rotor through lightweight design results, achieve lightweight design of permanent magnet motor rotor while ensuring mechanical and electromagnetic performance, or provide a design reference for actual production and manufacturing of the weight reduction design of the permanent magnet region rotor region.

[0099] (2) The grid filtering method can ensure that the optimized permanent magnet synchronous motor generates a better manufacturing structure. By adjusting the filtering radius, the hole structure that is not conducive to production and manufacturing caused by the grid size being too small is avoided. The topology optimization result can be controlled by adjusting the filtering radius parameter during the optimization process.

[0100] (3) The nonlinear reluctance curve of the core material was fitted based on the interpolation method. Iterative calculation of the nonlinear saturation degree of the core in different regions under no-load and load conditions of the motor can be performed to avoid the generation of oversaturated regions in the optimized structure, which would affect the electromagnetic performance of the motor and reduce the errors generated in the electromagnetic performance design and analysis of the motor.

[0101] (4) It can generate the optimal topology optimization configuration of permanent magnet motor rotor under different volume constraints and mechanical-electromagnetic target performance. It can be applied to different types of permanent magnet motor rotor topology structures such as built-in or surface-mounted, and realize the multi-objective optimization design of permanent magnet motor rotor structure under electromagnetic-mechanical multi-physics field coupling. Attached Figure Description

[0102] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0103] Figure 1 A flowchart illustrating a method for optimizing the rotor structure topology of a permanent magnet motor considering the nonlinear saturation characteristics of ferromagnetic materials, as proposed in an embodiment of this application, is shown.

[0104] Figure 2 A schematic diagram of the nonlinear saturation analysis model of the ferromagnetic material of the permanent magnet motor unit rotor in an embodiment of this application is shown.

[0105] Figure 3 A schematic diagram of the magnetization curve of the ferromagnetic material of the permanent magnet motor in an embodiment of this application is shown;

[0106] Figure 4 This paper illustrates a schematic diagram of the iterative analysis solution process for the nonlinear permeability of the core of a high-saturation permanent magnet synchronous motor in an embodiment of this application.

[0107] Figure 5 A schematic diagram of unit sensitivity filtering in an embodiment of this application is shown;

[0108] Figure 6 A schematic diagram of the initial rotor design model in an embodiment of this application is shown;

[0109] Figure 7 This paper shows a schematic diagram of the initial optimization model mesh generation for a 350kW permanent magnet motor rotor in an embodiment of this application.

[0110] Figure 8 A schematic diagram of the topology optimization results for the lightweight design of the 350kW permanent magnet motor rotor in an embodiment of this application is shown. Detailed Implementation

[0111] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention. The components in the drawings are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0112] This invention patent proposes a topology optimization method for permanent magnet motor rotor structures using nonlinear saturated ferromagnetic materials. The method mainly includes rotor core optimization region construction, finite element analysis of mechanical and electromagnetic properties, core saturation iteration, mesh filtering, and region element density updating. The overall process is as follows: Figure 1 As shown, it includes the following steps:

[0113] S1: Define the basic design parameters and requirements of the motor, set the permanent magnet motor unit motor as the optimization analysis model to simplify the number of meshes in the model, and use a rectangular mesh to construct the rotor region of the permanent magnet motor. Generally, a size of 1mm×1mm can be used (the actual size accuracy can be adjusted). Divide the rotor region, set the iron core lightweighting region that needs to be reduced in weight as the topology optimization region, and set other regions such as the permanent magnet region as the normal finite element analysis region.

[0114] S2: Based on the material unit properties assigned to different regions, the rotor region can be divided into the air region, the permanent magnet region, and the iron core support (magnetic permeability) region. The elastic modulus and magnetic permeability are assigned to the corresponding units respectively. In order to generate a void structure in the optimized structure to reduce the rotor weight, the density of the air region is set to 1 and the unit density of the permanent magnet and iron core support materials is set to 0 during the optimization process.

[0115] S3: Based on the rated load operating conditions of the motor, namely the motor parameters, speed, voltage and output power, determine the three-phase current output parameters of the permanent magnet synchronous motor during operation, which are used for the analysis of the operating characteristics of the permanent magnet motor under load conditions.

[0116] S4: First, the magnetic saturation performance of the motor core under load is analyzed. Regarding the magnetic field distribution problem of the permanent magnet synchronous motor, the magnetic field parameters are analogized to circuit parameters, and circuit laws are used to analyze the problems in the magnetic circuit. The permanent magnet is equivalent to a magnetic flux source or a magnetomotive force source. The demagnetization curve of the permanent magnet is approximated as a straight line. When the magnetic field strength is taken as an absolute value, the magnetic induction intensity B of the permanent magnet at the operating point is expressed as:

[0117] B = B r -μ r μ0H (1)

[0118] Where μ0 is the free permeability, μ r Where B is the relative permeability, H is the magnetic field strength, and B is the magnetic field strength. r Remanence density.

[0119] The internal permeability Λ0 of the permanent magnet can then be expressed as:

[0120]

[0121] Among them, A m h is the area of ​​magnetic flux per pole of the permanent magnet. m The thickness is the permanent magnet thickness.

[0122] The permanent magnet in a permanent magnet motor is equivalent to a constant magnetic flux source connected in parallel with the internal magnetic permeability or a constant magnetomotive force connected in series with the internal magnetic permeability.

[0123] S5: Under rated load, current will flow through the stator winding of the motor. If the stator winding is considered as a magnetomotive force source connected in series with the magnetic permeability of the stator yoke, then the magnetomotive force Fs generated by a single slot winding is:

[0124]

[0125] Where, N s i represents the number of single-layer conductors in a single slot. s1 i is the armature winding current in the upper coil. s2 This represents the armature winding current in the lower coil.

[0126] S6: Rectangular magnetic permeability units are used to divide the various regions (stator, rotor, air gap) of the permanent magnet motor, and an equivalent magnetic network analysis model of the motor is established, such as... Figure 2 As shown, the magnetic permeability G of a single rectangular unit region is... e for:

[0127]

[0128] Among them, S e Let l be the cross-sectional area in the direction of conduction. e is the length in the direction of conduction.

[0129] S7: Under the rated load condition of the permanent magnet motor, the magnetomotive force of each node in the equivalent magnetic network model of the permanent magnet motor is solved based on the nodal voltage method, and is expressed as:

[0130] Φ=GF (5)

[0131] Φ = [Φ(1), Φ(2), ..., Φ(n)] T (6)

[0132]

[0133] F = [F(1),F(2),...,F(n)] T (8)

[0134] Where Φ is the magnetic flux matrix, F is the magnetomotive force matrix, G is the magnetic permeability matrix, Φ(i) is the magnetic flux flowing into node i, when i < j, G(i,j) is the magnetic permeability between node i and node j, G(i,i) is the sum of all magnetic permeabilities connected to node i, when i > j, G(i,j) = -G(j,i), and F(i) is the magnetomotive force of node i.

[0135] Based on the magnetic network model, calculate the average magnetic flux density B on each reluctance path. ij for:

[0136]

[0137] In the formula, i and j are the starting and ending points of the corresponding magnetoresistive paths.

[0138] S8: Based on the specific silicon steel sheet material, obtain its BH curve. Taking 0.5mm thick non-oriented cold-rolled silicon steel sheet DW470-50 as an example, its BH performance curve is as follows: Figure 3 As shown,

[0139] Based on the least squares method, the magnetic flux density B(T) and magnetic induction H(A / cm) are correlated in different magnetic flux density ranges. The interpolation correlation is expressed as:

[0140]

[0141] S9: During the optimization process, in order to accelerate the iteration of the core saturation unit, the relative permeability update iteration factor of the magnetic permeability unit is introduced as follows:

[0142] u (k+1) =(u (k+1) ) 0.95 +(u k ) 0.05 (11)

[0143] S10: The iterative solution process for establishing the unit magnetic field density of the entire motor region and the nonlinear saturation region of the iron core is as follows: Figure 4 As shown.

[0144] The magnetic field density distribution in all regions of the motor, as well as the saturation degree of the iron core in the stator and rotor regions, can then be obtained through the process.

[0145] S11: Next, the mechanical properties of the permanent magnet motor at its rated speed are analyzed. Considering the centripetal force during high-speed rotation and the preload force when the permanent magnet is fixed, based on the physical equations of plane problems in elasticity, the relationship between stress and strain in the rotor can be obtained as follows:

[0146]

[0147] In the formula, σ is the normal stress, τ is the shear stress, ε is the strain, E is the elastic modulus, and v is Poisson's ratio.

[0148] The displacement matrix of a single rectangular element e can be solved using the following formula, expressed as:

[0149] K e =U e FF e (13)

[0150] In the formula, K e Let U be the stiffness matrix of element e. e Let FF be the nodal displacement matrix of element e. e Let be the nodal load matrix of element e.

[0151] For a rectangular element with 4 nodes, its unit stiffness matrix is:

[0152]

[0153] Where l is the length of the rectangular unit and w is the width of the rectangular unit.

[0154] The coefficients of each parameter in the unit stiffness matrix are:

[0155]

[0156]

[0157] After assembling the element stiffness matrices, the total stiffness matrix of the rotor structure can be obtained, satisfying F = KU; where F is the external load matrix, K is the stiffness matrix, and U is the displacement matrix.

[0158] S12: A mechanical and electromagnetic sensitivity analysis is performed on the element matrix in the rotor of a permanent magnet synchronous motor. To ensure good structural strength of the supporting structure during the lightweight design of the rotor, the sensitivity of the rotor structural flexibility c to element e under the action of centripetal force and permanent magnet assembly preload is:

[0159]

[0160] In the formula, x is the element density;

[0161] S13: To ensure good magnetic reluctance of the core during the lightweight design of the rotor, the complex magnetic reluctance network in the stator yoke region is simplified to an equivalent magnetic reluctance between two nodes i and j. When the reference magnetomotive force of the selected reference node j is 0, based on the two-port resistance equivalent theory and the magnetic permeability matrix control equation, the magnetic permeability matrix of n purely reluctance-connected nodes in the stator yoke region can be simplified to an (n-1)th order equivalent magnetic network matrix, expressed as:

[0162]

[0163] In the formula, G ii G represents the self-permeability of element node i; ij Φ represents the mutual magnetic permeability of element nodes i and j; i Let I be the magnetomotive force of node i; and let I0 be the magnetic flux source flowing into node i.

[0164] Based on the (n-1)th order magnetic permeability matrix, the magnetopotential at node i can be obtained as follows:

[0165]

[0166] The equivalent magnetic reluctance between node i and node j is:

[0167]

[0168] In the formula, R i,j Let be the equivalent magnetic reluctance between node i and node j;

[0169] Ignoring the influence of the change in permeability of element e on the external magnetic flux source and the permeability of other elements, the sensitivity of the permeability of the permanent magnet rotor core to a single core element e is:

[0170]

[0171] In the formula, The meaning of G n-1i,i The adjoint matrix of a matrix, u e Let be the permeability of element node e.

[0172] S14: To avoid a checkerboard-like structure in the final structure, a grid filtering algorithm is added after solving for the rotor's stiffness and permeability sensitivity, such as... Figure 5 As shown, the sensitivity within the radius r is calculated using weighted averages.

[0173] Introducing a convolution operator into the grid filtering algorithm:

[0174]

[0175] Where r is the set mesh filtering radius, and dist(e,i) is the center distance between cell e and cell i within a circle with cell e as the center and a filtering radius of r.

[0176] After adjusting the sensitivity, the filtered unit sensitivity can be obtained as follows:

[0177]

[0178] In the formula, ρ is the element density, and H i It is a convolution operator.

[0179]

[0180] In the formula, N is the number of elements in the optimization region, and ρ is the element density.

[0181] S15: In order to carry out appropriate lightweight design of the structure during the design of permanent magnet motor, the less sensitive units are gradually "removed" during the optimization process. This can minimize the impact of each iteration on the optimization objective and finally obtain the optimal topology optimization design result.

[0182] To simultaneously characterize the electromagnetic and mechanical properties of the design unit, a normalization strategy is adopted during the optimization process to transform the multi-objective optimization model into a single-objective optimization problem for solution. The unified unit electromagnetic-mechanical sensitivity deviation value is shown in the formula. The smaller the deviation value, the better the unit has both electromagnetic and mechanical properties.

[0183]

[0184] In the formula, O i R is the normalized electromagnetic-mechanical sensitivity deviation value for element i; maxTo determine the maximum non-positive electromagnetic sensitivity within the design region element; C min Re represents the minimum non-positive mechanical sensitivity in the design region element, Re represents the element electromagnetic sensitivity, and Ce represents the element compliance sensitivity.

[0185] To ensure that the optimized rotor topology of the permanent magnet synchronous motor possesses both good electromagnetic and mechanical properties, the optimization model established in the following optimization process, with the electromagnetic and mechanical properties of the permanent magnet synchronous motor as the optimization objectives, can be expressed mathematically as follows:

[0186]

[0187] Where Ω represents the rotor core optimization design region, x i For element density, there are only two states, 0 or 1, during the optimization process. 0 represents air elements, which are also the weight-reducing areas that are deleted, and 1 represents rotor core elements. R is the equivalent magnetic reluctance of the rotor core, and U is the displacement of the rotor structure under centripetal force and permanent magnet assembly preload. limit For rotor displacement constraints, V0 is the rotor core volume constraint, and B is the rotor displacement constraint. air For air gap magnetic flux density, B limit It is the minimum air gap magnetic flux density constraint.

[0188] Based on each electromagnetic and mechanical performance analysis, the element with the lowest normalized electromagnetic-mechanical sensitivity deviation value is removed, thereby gradually bringing the structure closer to the optimal topological configuration. That is, elements satisfying a deletion rate less than RR are removed. i All units:

[0189]

[0190] At the same time, the evolution rate ER is introduced, and the deletion rate of the next stable state is modified according to Equation (38), and this deletion rate is used for iteration until the specified deletion rate is reached.

[0191] RR i+1 =RR i +ER (38)

[0192] In the formula, RR i ER represents the deletion rate in each iteration.

[0193] Finally, the topology optimization results for lightweight permanent magnet synchronous motor rotor can be obtained.

[0194] verify:

[0195] Taking the lightweight optimization design process of a 350kW permanent magnet synchronous motor rotor as an example, its main initial design parameters are shown in Table 1.

[0196] Table 1 Main Dimensions of 350kW Permanent Magnet Synchronous Motor

[0197] Parameter Value Output power 350 kW Rated rotational speed 3,000 rpm Rated voltage 690V Stator inner diameter 335 mm Stator outer diameter 445 mm Rotor inner diameter 60 mm Rotor outer diameter 330 mm Axial length 150 mm Permanent magnet type Interior

[0198] The 350kW permanent magnet synchronous motor adopts a 12-pole, 76-slot configuration. The initial optimized rotor physical model for one pair of poles is as follows: Figure 6 As shown.

[0199] A 1 / 6 scale model of the permanent magnet motor rotor was used as a simplified analysis region. A 1mm × 1mm rectangular mesh was used to divide the 350kW permanent magnet motor rotor region, resulting in the initial optimized model mesh division as follows: Figure 7 As shown.

[0200] To ensure good manufacturability, the rotor permanent magnet section and the iron core in the air gap were designated as non-optimized regions, while the rotor iron core was designated as the optimized region. The rotor inner diameter was used as the displacement constraint. With a volume constraint set to 70% and a mesh filter radius of 2mm, the initial iterative permeability of the silicon steel sheet was set to 7000. Under applied centripetal force and permanent magnet assembly preload, the lightweight topology optimization results for the permanent magnet rotor are as follows: Figure 8 As shown, the optimized model meets the requirements for yield strength and electromagnetic torque output performance, as verified by the commercial finite element software Workbench.

[0201] Although the methods described above are illustrated and depicted as a series of actions for the sake of simplicity, it should be understood and appreciated that these methods are not limited by the order of the actions, as some actions may occur in a different order and / or concurrently with other actions from the illustrations and descriptions herein or not illustrated and described herein but which may be understood by those skilled in the art, according to one or more embodiments.

[0202] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any indirect modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials, characterized in that, include: Step S101: Initial parameterization and meshing optimization of design region variables; Step S102: Determine the performance of the permanent magnet motor under actual operating conditions. Step S103, Finite element analysis of electromagnetic and mechanical fields of permanent magnet motor; Step S104: Iterative analysis of the magnetic permeability of nonlinear saturated ferromagnetic materials, and determine whether the results converge. If the results converge, proceed to step S105; otherwise, return to step S103. Step S105, Sensitivity analysis of the mechanical and electromagnetic performance of the permanent magnet motor; Step S106: Update the silicon steel sheet material density in the rotor optimization region and determine whether it meets the requirements. If it does, output the final rotor lightweight topology optimization result; otherwise, return to step S103.

2. The method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 1, characterized in that, In step S101, the basic design parameters and requirements of the motor are clarified, and the unit motor of the permanent magnet motor is set as the optimization analysis model to simplify the number of meshes in the model. A rectangular mesh is used to construct the rotor region of the permanent magnet motor. The rotor region is divided, and the iron core lightweighting region that needs to be weight-reduced is set as the topology optimization region. Other regions, such as the permanent magnet region, are set as normal finite element analysis regions. According to the material, different material element properties are assigned to different regions. The rotor region can be divided into air region, permanent magnet region and iron core support region. The elastic modulus and permeability are assigned to the corresponding elements respectively. In order to generate a void structure in the optimized structure to reduce the rotor weight, the density of the air region is set to 1 and the element density of the permanent magnet and iron core support materials is set to 0 during the optimization process.

3. A method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 1 or 2, characterized in that, In step S102, based on the rated load operating conditions of the motor, namely the motor parameters, speed, voltage and output power, the three-phase current output parameters of the permanent magnet synchronous motor during operation are determined for analysis of the operating characteristics of the permanent magnet motor under load conditions.

4. The method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 3, characterized in that, In step S103, the core magnetic saturation performance of the motor under load is first analyzed. Regarding the magnetic field distribution of the permanent magnet synchronous motor, the magnetic field parameters are analogized to circuit parameters, and circuit laws are used to analyze the problems in the magnetic circuit. The permanent magnet is equivalent to a magnetic flux source or a magnetomotive force source, and the demagnetization curve of the permanent magnet is approximated as a straight line. When the magnetic field strength is taken as an absolute value, the magnetic induction intensity B of the permanent magnet at the operating point is expressed as: B=B r -m r μ0H (1) Where μ0 is the free permeability, μ r Where B is the relative permeability, H is the magnetic field strength, and B is the magnetic field strength. r Remanence density, The internal permeability Λ0 of the permanent magnet can then be expressed as: Among them, A m h is the area of ​​magnetic flux per pole of the permanent magnet. m The thickness of the permanent magnet. If the permanent magnet in a permanent magnet motor is equivalent to a constant magnetic flux source connected in parallel with the internal magnetic permeability, or a constant magnetomotive force connected in series with the internal magnetic permeability, and a current flows through the stator winding under the rated load of the motor, and the stator winding is equivalent to a magnetomotive force source connected in series with the magnetic permeability of the stator yoke, then the magnetomotive force Fs generated by a single slot winding is: Where, N s i represents the number of single-layer conductors in a single slot. s1 i is the armature winding current in the upper coil. s2 To determine the armature winding current in the lower coil, rectangular magnetic permeability units are used to divide the stator, rotor, and air gap regions of the permanent magnet motor, establishing an equivalent magnetic network analysis model of the motor. The magnetic permeability G of a single rectangular unit region is... e for: Among them, S e Let l be the cross-sectional area in the direction of conduction. e The length in the direction of conduction. Under rated load conditions, the magnetomotive force of each node in the equivalent magnetic network model of the permanent magnet motor is solved based on the nodal voltage method, and is expressed as: Φ=GF (5) Φ=[Φ(1),Φ(2),...,Φ(n)] T (6) F=[F(1),F(2),...,F(n)] T (8) Where Φ is the magnetic flux matrix, F is the magnetomotive force matrix, G is the magnetic permeability matrix, Φ(i) is the magnetic flux flowing into node i, when i < j, G(i,j) is the magnetic permeability between node i and node j, G(i,i) is the sum of all magnetic permeabilities connected to node i, when i > j, G(i,j) = -G(j,i), and F(i) is the magnetomotive force of node i. Based on the magnetic network model, calculate the average magnetic flux density B on each reluctance path. ij for: In the formula, i and j are the starting and ending points of the corresponding magnetoresistive paths.

5. The method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 4, characterized in that, In step S103, based on the specific silicon steel sheet material, its BH curve is obtained, and the magnetic flux density B and magnetic induction intensity H are correlated in different magnetic flux density ranges based on the least squares method, where the unit of B is T and the unit of H is A / cm.

6. A method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 4 or 5, characterized in that, In step S104, to accelerate the iteration of the core saturation unit, the relative permeability update iteration factor of the magnetic permeability unit is introduced as follows: in (k+1) =(in (k+1) ) 0.95 +(in k ) 0.05 (11) Step S104 includes the following steps performed sequentially: Step S1041: Set the rotor position and establish the equivalent magnetic network model of the permanent magnet motor. Step S1042: Set the relative permeability of the magnetic permeability unit in the initial iteration calculation. Step S1043, solve the nodal magnetopotential equation F = G -1 Φ and magnetic induction intensity B g , Step S1044, determine If the condition is met, the iterative calculation ends, and the magnetic field density distribution in all regions of the motor, as well as the saturation degree of the iron core in the stator and rotor regions, is obtained. Then, proceed to step S105. If the condition is not met, proceed according to the updated relative permeability u. (k+1) Update the magnetic permeability matrix G and return to step S1043.

7. The method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 6, characterized in that, In step S105, the mechanical properties of the permanent magnet motor at its rated speed are analyzed. Considering the centripetal force during high-speed rotation and the preload force when the permanent magnet is fixed, based on the physical equations of plane problems in elasticity, the relationship between stress and strain in the rotor can be obtained as follows: In the formula, σ is the normal stress, τ is the shear stress, ε is the strain, E is the elastic modulus, and v is Poisson's ratio. The displacement matrix of a single rectangular element e can be solved using the following formula, expressed as: K e =U e FF e (13) In the formula, K e Let U be the stiffness matrix of element e. e Let FF be the nodal displacement matrix of element e. e Let be the nodal load matrix of element e. For a rectangular element with 4 nodes, its unit stiffness matrix is: Where l is the length of the rectangular element, w is the width of the rectangular element, and the coefficients of each parameter in the unit stiffness matrix are: After assembling the element stiffness matrices, the total stiffness matrix of the rotor structure can be obtained, which satisfies F = KU; In the formula, F is the external load matrix, K is the stiffness matrix, and U is the displacement matrix.

8. The method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 7, characterized in that, In step S105, under the action of centripetal force and permanent magnet assembly preload, the sensitivity of rotor structure flexibility c to element e is: In the formula, x is the element density; The complex magnetoresistive network in the stator yoke region can be simplified to an equivalent magnetoresistive network between two nodes i and j. When the reference magnetomotive force of the selected reference node j is 0, based on the two-port resistance equivalent theory and the magnetic permeability matrix control equation, the magnetic permeability matrix of n purely reluctant connections in the stator yoke region can be simplified to an (n-1)th order equivalent magnetic network matrix, expressed as: In the formula, G ii G represents the self-permeability of element node i; ij Φ represents the mutual magnetic permeability of element nodes i and j; i Let be the magnetomotive force at node i; Based on the (n-1)th order magnetic permeability matrix, the magnetopotential at node i can be obtained as follows: The equivalent magnetic reluctance between node i and node j is: In the formula, R i,j Ii represents the equivalent magnetic reluctance between node i and node j; I0 represents the magnetic flux source flowing into node i. Ignoring the influence of the change in permeability of element e on the external magnetic flux source and the permeability of other elements, the sensitivity of the permeability of the permanent magnet rotor core to a single core element e is: In the formula, The meaning of G n-1i,i The adjoint matrix of a matrix, u e Let be the permeability of element node e.

9. A method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 8, characterized in that, After solving for the rotor's stiffness and permeability sensitivity, a mesh filtering algorithm is added, in which a convolution operator is introduced: Where r is the set mesh filtering radius, and dist(e,i) is the center distance between element e and element i within a circle with element e as the center and a filtering radius of r. After adjusting the sensitivity, the filtered unit sensitivity can be obtained as follows: In the formula, ρ is the element density, and H i For convolution operators, In the formula, R is the magnetoresistance, N is the number of elements in the optimization region, and ρ is the element density.

10. A method for topology optimization of permanent magnet motor rotor structure considering the nonlinear saturation characteristics of ferromagnetic materials according to claim 8 or 9, characterized in that, In step S106, gradually "removing" units with low sensitivity during the optimization process can minimize the impact of each iteration on the optimization objective, ultimately yielding the optimal topology optimization design result. To simultaneously characterize the electromagnetic and mechanical properties of the design unit, a normalization strategy was employed during the optimization process to transform the multi-objective optimization model into a single-objective optimization problem for solution. The unified electromagnetic-mechanical sensitivity deviation value of the unit is shown in the formula. The smaller the deviation value, the better the unit simultaneously possesses electromagnetic and mechanical properties. In the formula, O i R is the normalized electromagnetic-mechanical sensitivity deviation value for element i; max To determine the maximum non-positive electromagnetic sensitivity within the design region element; C min To define the minimum non-positive mechanical sensitivity in the design region element, Re represents the element electromagnetic sensitivity, and Ce represents the element compliance sensitivity. To ensure that the optimized rotor topology of the permanent magnet synchronous motor possesses both good electromagnetic and mechanical properties, the optimization model established in the following optimization process, with the electromagnetic and mechanical properties of the permanent magnet synchronous motor as the optimization objectives, can be expressed mathematically as follows: Where Ω represents the rotor core optimization design region, x i For element density, there are only two states, 0 or 1, during the optimization process. 0 represents air elements, which are also the weight-reducing areas that are deleted, and 1 represents rotor core elements. R is the equivalent magnetic reluctance of the rotor core, and U is the displacement of the rotor structure under centripetal force and permanent magnet assembly preload. limit For rotor displacement constraints, V0 is the rotor core volume constraint, and B is the rotor displacement constraint. air For air gap magnetic flux density, B limit To minimize the air gap magnetic flux density constraint, after each electromagnetic and mechanical performance analysis, the element with the lowest normalized electromagnetic-mechanical sensitivity deviation value is removed, thereby gradually bringing the structure closer to the optimal topological configuration, i.e., removing elements that satisfy a deletion rate less than RR. i All units: Simultaneously, the evolution rate ER is introduced, and the deletion rate of the next stable state is modified according to equation (38). This deletion rate is then used for iteration until the specified deletion rate is reached. RR i+1 =RR i +IS (38) In the formula, RR i ER represents the deletion rate in each iteration, and ER represents the evolution rate. Finally, the topology optimization results for lightweight permanent magnet synchronous motor rotor can be obtained.

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