CN112685945B - A magnetic-structural multiphysics topology optimization design method for additive manufacturing - Google Patents

Abstract

The present application discloses a magnetic-structure multi-physics field topology optimization design method for additive manufacturing, comprising: step 10, combining the unit printing density of the object to be printed, based on the structural field and magnetic field material interpolation model and the finite element analysis method, Analyzing and obtaining the structural displacement vector and the magnetic field vector, and establishing the objective function accordingly, and combining the volume constraints to establish a magnetic-structural multi-physics topology optimization model; Step 20, combining the objective function and constraints according to the magnetic-structural multi-physics topology optimization model For the cell design density sensitivity, the cell design density space is iteratively updated by the MMA algorithm. When it is determined that the relative error of the objective function in the magnetic-structural multiphysics topology optimization model is less than the preset threshold, the cell design density space is treated according to the updated cell design density space. Print the object for printing. Through the technical solution in the present application, the self-supporting printing of the structure is realized while taking into account the performance of the magnetic field and the structural field, and the use of supporting materials is avoided.

Description

A magnetic-structural multiphysics topology optimization design method for additive manufacturing

technical field

The present application relates to the technical field of engineering structure and analysis, and in particular, to a magnetic-structural multiphysics topology optimization design method for additive manufacturing.

Background technique

In recent years, with the development of equipment automation, intelligence and light weight, the integrated design requirements for components represented by new energy vehicle motors and electromagnetic actuators have become higher and higher. These components must not only meet the performance requirements of the magnetic field, At the same time, mechanical properties such as stiffness and strength must be met. By carrying out the topology optimization design of the magnetic-structural multi-physics field, the performance of the magnetic field and the structural field can be effectively improved while taking into account the light weight.

The development of additive manufacturing technology provides a manufacturing guarantee for the magnetic-structural multiphysics topology design configuration. Although additive manufacturing greatly increases design and manufacturing freedom relative to subtractive or isomaterial manufacturing.

However, there are still some manufacturing constraints, such as when the topological configuration exceeds the maximum suspension constraint, support materials need to be added to print, resulting in unnecessary material costs and post-processing costs.

The paper "Garibaldi M, Gerada C, Ashcroft I A. Free-Form Design of ElectricalMachine Rotor Cores for Production Using Additive Manufacturing. Journal of Mechanical Design. 2019, 141(7): 1-13" introduces a magneto-mechanical field oriented Coupled topology optimization method, and use this method to design the motor rotor. The objective functions of the topology optimization design in this paper are the minimum mechanical field compliance and the minimum rotor magnetic field energy, and the constraint condition is the volume fraction. The final rotor structure greatly improves the torque performance and reduces the rotor mass. However, the additive manufacturing constraints are not considered when considering multiphysics, and there is a problem that support materials need to be used in the additive manufacturing process, which increases material costs and post-processing costs.

The paper "Langelaar M. An additive manufacturing filter for topologyoptimization of print-ready designs. Structural and MultidisciplinaryOptimization, 2017, 55(3): 871–83." introduces an additive manufacturing filter embedded in the SIMP method, capable of The blueprint density is converted to the print density by the mapping function, and the final configuration does not violate the maximum suspension constraint of 45°, so it can be self-supporting printing. This work mainly considers the topology optimization design of the mechanical field performance for additive manufacturing, but its sensitivity optimization operation is relatively complex and requires high computer hardware performance.

SUMMARY OF THE INVENTION

The purpose of this application is to improve the additive manufacturing capability of the magnetic-structure multiphysics topology optimization configuration of complex equipment, and fully consider the additive manufacturing constraints such as unsupported in the construction of the topology optimization model. Additive manufacturing constraints are embedded in the magneto-structural topology optimization design model to enable self-supporting printing of structures, improve the performance of the structures, reduce the mass of the structures, and reduce the manufacturing costs of the structures. It can effectively improve the magnetic field and mechanical field performance while taking into account the light weight.

The technical solution of the present application is to provide a magnetic-structural multi-physics topology optimization design method for additive manufacturing, the method comprising: step 10, using the unit printing density of the object to be printed as an interpolation, calculating the overall displacement vector and The overall magnetic vector potential vector, and the constraint conditions are generated according to the overall displacement vector and the overall magnetic vector potential vector, and a magneto-structural multiphysics topology optimization model is established, wherein the unit printing density is determined by the unit design density space; Step 20, according to the sensitivity and the magnetic-structural multiphysics topology optimization model to iteratively update the element design density space. When it is determined that the relative error of the objective function in the magnetic-structural multiphysics topology optimization model is less than the preset threshold, the updated element design density Space to print the object to be printed.

In any of the above technical solutions, further, step 10 specifically includes: step 11, performing finite element mesh division on the design domain of the object to be printed, and filtering the element design density space of the finite element mesh to generate a unit The printing density space, the unit printing density space is a vector matrix, and the unit printing density space includes a plurality of unit printing densities; step 12, according to the unit printing density in the unit printing density space, the elastic modulus and magnetic Interpolate the conductivity to obtain the element elastic modulus and element permeability; step 13, according to the element elastic modulus and element permeability, modify the initial element stiffness matrix of the structural field and the initial stiffness matrix of the static magnetic field respectively, and according to the correction After obtaining the structural field element stiffness matrix and the static magnetic field stiffness matrix, calculate the overall displacement vector and the overall magnetic vector potential vector; Step 14, according to the overall displacement vector and the overall magnetic vector potential vector, calculate the multi-physics problem optimization objective function, and combine the volume Constraints, a magnetic-structural multiphysics topology optimization model is established.

In any of the above technical solutions, further, the cell design density space and the cell printing density space are vector matrices.

的计算公式为：In any of the above technical solutions, further, the unit prints the density space

The calculation formula is:

为单元支撑域ρ_s中的第k个单元的单元打印密度，Q为第三参数。In the formula, ρ _s represents the unit support domain, P is the first parameter, ε is the second parameter,

is the cell print density for the kth cell in the cell support domain _ρs , and Q is the third parameter.

和单元磁导率

的计算公式为：In any of the above technical solutions, further, the unit elastic modulus

and cell permeability

The calculation formula is:

为过滤后得到的单元打印密度，E₀为材料的弹性模量，常数E_min为一常数，v_r是材料的相对磁导率，P_s是结构场惩罚参数，P_m是磁场惩罚参数。in,

is the unit printing density obtained after filtering, E ₀ is the elastic modulus of the material, the constant E _min is a constant, v _r is the relative magnetic permeability of the material, P_s is the structural field penalty parameter, and P_m is the magnetic field penalty parameter.

In any of the above technical solutions, further, the magnetic-structure multi-physics topology optimization model includes an objective function and a constraint condition, and the sensitivity is the sensitivity of the objective function to the unit design density space, and the calculation formula of the sensitivity is:

为单元打印密度空间中第j个单元打印密度向量，n_s为支撑域中单元的个数，P为第一参数，ε为第二参数，Q为第三参数。In the formula, ρ _sd,j-1 and ρ _sd,j represent the element design density vector of the j-1th and jth row of the support domain, respectively, c is the objective function, ρ _j is the jth element in the element design density space design density vector,

Print the density vector for the jth unit in the unit print density space, _ns is the number of units in the support domain, P is the first parameter, ε is the second parameter, and Q is the third parameter.

The beneficial effects of this application are:

The technical solution in this application, through the magnetic-structural multi-physics topology optimization technology, can greatly improve the performance of the magnetic field and the mechanical field while achieving light weight, and the multi-physics topology can be successfully transformed by introducing additive manufacturing constraints. The combination of optimization and additive manufacturing enables the structure obtained by using the magnetic-structural multiphysics topology optimization to print the object to be printed without the aid of support materials, reducing material costs and post-processing costs.

The optimization design method proposed in this application has high stability, fast convergence speed, and fewer intermediate density cells in topology optimization, which can be well extended to other multi-physics topology optimization design applications for additive manufacturing.

Description of drawings

The advantages of the above and/or additional aspects of the present application will become apparent and readily understood from the following description of embodiments in conjunction with the accompanying drawings, wherein:

FIG. 1 is a schematic flowchart of a magnetic-structural multiphysics topology optimization design method for additive manufacturing according to an embodiment of the present application;

2 is a schematic diagram of an object to be printed under the action of a structural field-magnetic field according to an embodiment of the present application;

3 is a schematic diagram of a density space according to one embodiment of the present application;

4 is a schematic diagram of a topology optimization result under the action of a single physics field and a multi-physics field according to an embodiment of the present application;

FIG. 5 is a schematic diagram of printing results in different printing directions according to an embodiment of the present application.

Detailed ways

In order to more clearly understand the above objects, features and advantages of the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features of the embodiments may be combined with each other unless there is conflict.

In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can also be implemented in other ways different from those described herein. Therefore, the protection scope of the present application is not subject to the following disclosure. Restrictions to specific embodiments.

As shown in Figures 1 and 2, this embodiment provides a magnetic-structural multiphysics topology optimization design method for additive manufacturing. First, the design domain is divided into finite element meshes, and the initial element design density space is set. Combined with the mapping of the additive manufacturing filter, the unit printing density space is obtained, the elastic modulus and magnetic permeability are interpolated on the basis of the unit printing density space, and the response of the magnetic field machine and the mechanical field is obtained by using the finite element method. On this basis, a multi-physics topology optimization model is constructed, and the weighted method is used to construct the objective function. Finally, the optimization criterion method is used to solve the magnetic-structural multi-physics topology optimization model, and the final material distribution is obtained to realize the magnetic-structural multi-physics topology optimization. design.

The method includes:

Step 10: Use the unit printing density of the object to be printed as an interpolation value, calculate the overall displacement vector and the overall magnetic vector potential vector, and generate constraints according to the overall displacement vector and the overall magnetic vector potential vector, and establish a magnetic-structure multi-component. The physics topology optimization model, wherein the cell printing density is determined by the cell design density space.

In this embodiment, step 10 specifically includes:

其中，单元设计密度空间ρ与单元打印密度空间

为向量矩阵，包括多个元素，即ρ＝[ρ_e],

ρ_e为单元设计密度空间ρ中的任一单元的密度，称为单元设计密度，

为单元打印密度空间

中的任一单元的密度，称为单元打印密度；Step 11: Perform finite element mesh division on the design domain of the object to be printed, and filter the element design density space ρ of the finite element mesh to generate a unit printing density space

Among them, the cell design density space ρ and the cell printing density space

is a vector matrix, including multiple elements, that is, ρ=[ρ _e ],

ρ _e is the density of any unit in the unit design density space ρ, which is called the unit design density,

print density space for cells

The density of any unit in the unit is called the unit printing density;

Specifically, as shown in Figure 3, the armature part of the object to be printed (actuator) is set as a design domain, which is affected by both the magnetic field and the structural field, and the design domain is used to determine the magnetic-structure Boundary conditions for field action. The design domain is divided into finite element mesh from top to bottom, divided into 30×50 meshes, the mesh type is quadrilateral element, and each finite element mesh is regarded as a unit.

It should be noted that the structural field in this embodiment may be a mechanical field.

本实施例中对的过滤方法并不限定，如可以采用增材制造过滤器进行过滤。In this embodiment, the initial value of the element design density ρ _e corresponding to each finite element mesh in the given element design density space ρ is set to 0.6. Set the printing direction as bottom-up, filter the unit design density space ρ, and obtain the unit printing density space

The filtering method in this embodiment is not limited, for example, an additive manufacturing filter can be used for filtering.

中最底层单元的密度即为单元设计密度空间ρ中最底层单元的密度，单元打印密度空间

具体的计算公式如下：It should be noted that the filtering of the unit design density space ρ in this embodiment is based on layers, starting from the bottom layer to the top layer by layer. Therefore, the unit printing density space

The density of the bottom unit is the density of the bottom unit in the unit design density space ρ, and the unit print density space

The specific calculation formula is as follows:

为单元支撑域ρ_s中的第k个单元的单元打印密度，第三参数Q的计算方式如下：In the formula, ρ _s represents the element support domain, that is, the region where the next layer of elements required to support the element (finite element mesh) is located, the first parameter P is the control smoothness parameter, and the second parameter ε is the control approximation parameter, Here we can take 60 and 10 ^-3 respectively, n _s is the number of units in the support domain, here the value is 3,

For the cell print density of the kth cell in the cell support domain _ρs , the third parameter Q is calculated as follows:

ρ_s0＝0.5

ρ _s0 =0.5

和单元磁导率

的可靠性，有助于提高磁-结构多物理场拓扑优化模型的精度，保证了待打印物体单元打印密度空间计算的准确性，最终实现了能够不借助支撑材料打印出待打印物体，减少了材料成本和后处理成本。Through the calculation of the third parameter Q, the accuracy of the calculation of the element support domain can be improved, thereby ensuring the subsequent obtained elastic modulus of the element

and cell permeability

It helps to improve the accuracy of the magnetic-structural multiphysics topology optimization model, ensures the accuracy of the spatial calculation of the printing density of the object to be printed, and finally realizes that the object to be printed can be printed without the aid of supporting materials, reducing the need for Material cost and post-processing cost.

中的单元打印密度

对每一个有限元网格(单元)的弹性模量E和磁导率ν进行插值，获得单元弹性模量

和单元磁导率

Step 12, print the density space according to the unit

Cell Print Density in

Interpolate the elastic modulus E and magnetic permeability ν of each finite element mesh (element) to obtain the element elastic modulus

and cell permeability

的函数，具体插值后的单元弹性模量

和单元磁导率

的计算公式如下：In this embodiment, a topology optimization algorithm is built based on the SIMP framework, and material interpolation is performed on the elastic modulus and magnetic permeability of the material to obtain the elastic modulus and magnetic permeability for the unit printing density space

The function of , the specific interpolated elastic modulus of the element

and cell permeability

The calculation formula is as follows:

为过滤后得到的单元打印密度，E₀为材料的弹性模量，常数E_min为一较小弹性模量值，用于避免结构场整体刚度矩阵奇异，这里取值为10^-3；v_r是材料的相对磁导率，P_s是结构场惩罚参数，P_m是磁场惩罚参数。in,

is the unit printing density obtained after filtering, E ₀ is the elastic modulus of the material, and the constant E _min is a small elastic modulus value, which is used to avoid the singularity of the overall stiffness matrix of the structure field, and the value here is 10 ^-3 ; v _r is the relative permeability of the material, P_s is the structural field penalty parameter, and P_m is the magnetic field penalty parameter.

和所述单元磁导率

分别对结构场初始单元刚度矩阵、静磁场初始刚度矩阵进行修正，并根据修正后的结构场单元刚度矩阵、静磁场刚度矩阵，计算整体位移向量和整体磁矢量势向量。Step 13, according to the element elastic modulus

and the cell permeability

The initial element stiffness matrix of the structural field and the initial stiffness matrix of the static magnetic field are revised respectively, and the overall displacement vector and the overall magnetic vector potential vector are calculated according to the revised structural field element stiffness matrix and the static magnetic field stiffness matrix.

和单元磁导率

修正结构场初始单元刚度矩阵和静磁场初始单元刚度矩阵，对应的计算公式为：According to the interpolated element elastic modulus

and cell permeability

Modify the initial element stiffness matrix of the structural field and the initial element stiffness matrix of the static magnetic field, and the corresponding calculation formula is:

为结构场初始单元刚度矩阵，

为静磁场初始刚度矩阵，两者可以由有限元方法中的能量原理推导而来。in,

is the initial element stiffness matrix of the structural field,

is the initial stiffness matrix of the static magnetic field, both of which can be derived from the energy principle in the finite element method.

It should be noted that, after the finite element mesh division is performed, the nodes of each finite element mesh, that is, the vertices of the finite element mesh, are numbered, and the specific numbering method is not limited in this embodiment.

和静磁场响应—整体磁矢量势向量

对应的计算公式为：According to the node number of the finite element mesh, the modified structural field element stiffness matrix _ke,s and the static magnetic field stiffness matrix _ke,m are assembled respectively to obtain the corresponding overall stiffness matrix. By solving the structural field and static magnetic field control equation to obtain the structural field response-global displacement vector

and the static magnetic field response—the global magnetic vector potential vector

The corresponding calculation formula is:

为组装后的结构场整体刚度矩阵，

是整体位移向量，F是整体力载荷向量，

为组装后的静磁场整体刚度矩阵，

是整体磁矢量势向量，P是整体激励向量；In the formula,

is the overall stiffness matrix of the assembled structural field,

is the global displacement vector, F is the global force load vector,

is the overall stiffness matrix of the static magnetic field after assembly,

is the overall magnetic vector potential vector, and P is the overall excitation vector;

Step 14, according to the overall displacement vector and the overall magnetic vector potential vector, calculate the multi-physics problem optimization objective function, and combine the volume constraints to establish a magnetic-structure multi-physics topology optimization model, the magnetic-structure multi-physics topology optimization model is established. The objective function and the constraints are included in the physics topology optimization model.

In this embodiment, the objective function min c is a normalized function with minimum mechanical compliance and minimum magnetic compliance, and the constraints at least include physical field control equations, component volume constraints and element design density constraints, wherein the physical field control equations include The control equations of the structure field and the static magnetic field are determined by the overall displacement vector and the overall magnetic vector potential vector. The calculation formula of the magneto-structural multiphysics field topology optimization model is:

0<ρ _min ≤ρ _e ≤1

和整体磁矢量势向量

中提取，ρ_e是单元设计密度，k_e,s为结构场单元刚度矩阵，k_e,m静磁场刚度矩阵，In the formula, c _meh is the objective function value of the structure field, c _mag is the objective function value of the magnetic field, _{ue is the element displacement vector, and a e is} the element magnetic vector potential vector, both of which can pass through the nodes of the finite element mesh according to the finite element principle. Id separately from the overall displacement vector

and the overall magnetic vector potential vector

Extracted from , ρ _e is the element design density, _ke,s is the structural field element stiffness matrix, _ke,m static magnetic field stiffness matrix,

C _{ref_mech} and C _{ref_mag} are normalization coefficients, N is the number of units in the design domain, which is 1500 in this embodiment; _ve and V ₀ are the unit volume and allowable volume, respectively; ρ _min is the lower limit of the unit design density, usually A small value to prevent the stiffness matrix from being singular; w ₁ and w ₂ are weight coefficients, which can be adjusted according to actual engineering problems.

In this example, a method for adjusting the weight coefficient is shown, that is, the weight coefficient is calculated according to the structure field objective function value c _mech and the magnetic field objective function value c _mag , and the corresponding calculation formula is:

This embodiment also shows a calculation method of sensitivity.

Specifically, the sensitivity is very important in the topology optimization process. It is the basis for updating the density space of the unit design. Because of the existence of the additive manufacturing filter, the sensitivity of the objective function to the initial density needs to be calculated by the chain rule:

是过滤后的单元密度，ρ_e是设计单元密度。式中，

需要借助伴随方法求得：where c is the objective function,

is the filtered cell density and ρ _e is the design cell density. In the formula,

It needs to be obtained with the help of the accompanying method:

项目计算较为复杂，因为单元打印密度空间中每行元素都是其下层支撑域内单元设计密度空间所有单元的函数，设铺层的顶层为第1层，最底层为第n层，计算单元打印密度空间中第i行对单元设计密度空间中第j行的导数：in the formula

The project calculation is more complicated, because each row of elements in the cell printing density space is a function of all the cells in the cell design density space in its underlying support domain. The top layer of the layup is the first layer, and the bottom layer is the nth layer. Calculate the cell printing density Derivative of the ith row in the space to the jth row in the element design density space:

In the formula, δ _ij is the Kronecker symbol, i=j, δ _ij =1 or i≠j, δ _ij =0. The i-th row of the cell printing density space is a function of the cell design density of all the lower rows in its cell design density space, so the above formula is only true when i≤j, and when i>j,

In this embodiment, the calculation formula of the sensitivity of the objective function to the cell design density space is:

和

的计算公式为：The unknown term in the formula

and

The calculation formula is:

where ρ _sd,j-1 and ρ _sd,j represent the element design density vectors of the j-1th and jth rows of the support domain, respectively.

Step 20, according to the sensitivity and the magnetic-structure multi-physics topology optimization model, through the MMA algorithm, iteratively update the cell design density space, when it is determined that the relative error of the objective function in the magnetic-structure multi-physics topology optimization model is less than a preset threshold value , print the object to be printed according to the updated unit design density space.

Specifically, according to the sensitivity and the magnetic-structure multi-physics topology optimization model, the element design density space ρ is iteratively updated through the optimization criterion method, where the sensitivity is the sensitivity of the objective function to the element design density space, which can be calculated by the above formula. Calculate to determine.

If the relative error δ of the objective function is less than the preset threshold, which can be set to 0.1%, it is considered that the unit design density space ρ is converged, the iteration is stopped, and the object to be printed is printed according to the updated unit design density space ρ; if If the requirement is not met, that is, the relative error δ of the objective function is greater than or equal to 0.1%, then set ρ _k = ρ _k+1 and return to step 11 to solve the next round of element design density space ρ until the convergence condition is reached, and obtain Final cell design density space. Among them, the calculation formula of the relative error δ of the objective function is:

where n is the number of iterations.

Figure 4 shows the topological configuration (w ₁ =1,w ₂ =0) obtained by considering only the structural field (mechanical field), and the topological configuration (w ₁ =0,w ₂ =1) obtained by only considering the action of the magnetic field ), and the topological configuration obtained by the simultaneous action of the two fields (w ₁ ≠0, w ₂ ≠1). From the obtained topological configuration, the final result can satisfy the maximum suspension angle constraint of 45°, thus satisfying the additive manufacturing constraint. Figure 5 shows the magneto-structural multiphysics topology-optimized configurations obtained under different printing directions.

The final output configuration of the present invention is the optimized configuration presented by the unit in the unit printing density space. Due to the embedded additive manufacturing filter, all parts that violate the maximum hanging angle of -45° are filtered out, thereby ensuring the structure. Able to achieve self-supporting printing.

The technical solution of the present application has been described in detail with reference to the accompanying drawings. The present application proposes a magnetic-structural multi-physics topology optimization design method for additive manufacturing, including: step 10, using the unit printing density of the object to be printed as an interpolation , calculate the overall displacement vector and the overall magnetic vector potential vector, and generate constraints according to the overall displacement vector and the overall magnetic vector potential vector, and establish a magnetic-structural multiphysics topology optimization model; Step 20, according to the sensitivity and magnetic-structural multiphysics Field topology optimization model, iteratively updates the cell design density space, when it is determined that the relative error of the objective function in the magnetic-structural multiphysics topology optimization model is less than the preset threshold, print the object to be printed according to the updated cell design density space . Through the technical solution in the present application, the self-supporting printing of the structure is realized, and the use of supporting materials is avoided.

The steps in this application can be adjusted, combined and deleted in sequence according to actual needs.

The units in the device of the present application can be combined, divided and deleted according to actual needs.

Although the present application has been disclosed in detail with reference to the accompanying drawings, it should be understood that these descriptions are merely exemplary and are not intended to limit the application of the present application. The protection scope of the present application is defined by the appended claims, and may include various modifications, alterations and equivalent solutions for the invention without departing from the protection scope and spirit of the present application.

Claims (5)

1. An additive manufacturing-oriented magnetic-structure multi-physical field topological optimization design method is characterized by comprising the following steps:

step 10, taking the unit printing density of the object to be printed as an interpolation, calculating an integral displacement vector and an integral magnetic vector potential vector, generating a constraint condition according to the integral displacement vector and the integral magnetic vector potential vector, and establishing a magnetic-structure multi-physical-field topological optimization model, wherein the unit printing density is determined by a unit design density space, the magnetic-structure multi-physical-field topological optimization model comprises a target function and the constraint condition, the sensitivity is the sensitivity of the target function to the unit design density space, and the calculation formula of the sensitivity is as follows:

in the formula, ρ_sd,j-1And ρ_sd,jCell design density vectors representing the jth-1 and jth rows of the support domain, respectively, c being the objective function, ρ_jDesigning a density vector for a jth cell in the cell design density space,

printing density for the cellThe jth unit in space prints the density vector, n_sThe number of units in the support domain, P is a first parameter, epsilon is a second parameter, and Q is a third parameter;

and 20, iteratively updating the unit design density space according to the sensitivity and the magnetic-structure multi-physical-field topological optimization model, and printing the object to be printed according to the updated unit design density space when the relative error of the objective function in the magnetic-structure multi-physical-field topological optimization model is judged to be smaller than a preset threshold value.

2. The additive manufacturing-oriented magnetic-structure multi-physical-field topological optimization design method according to claim 1, wherein the step 10 specifically comprises:

step 11, performing finite element mesh division on the design domain of the object to be printed, and filtering a unit design density space of the finite element mesh to generate a unit print density space, wherein the unit print density space is a vector matrix and comprises a plurality of unit print densities;

step 12, interpolating the elastic modulus and the magnetic permeability of each finite element grid according to the unit printing density in the unit printing density space to obtain a unit elastic modulus and a unit magnetic permeability;

step 13, respectively correcting the structural field initial unit stiffness matrix and the static magnetic field initial stiffness matrix according to the unit elastic modulus and the unit magnetic permeability, and calculating an integral displacement vector and an integral magnetic vector potential vector according to the corrected structural field unit stiffness matrix and the static magnetic field stiffness matrix;

and 14, calculating a multi-physical-field problem optimization objective function according to the integral displacement vector and the integral magnetic vector potential vector, and establishing the magnetic-structure multi-physical-field topological optimization model by combining with a volume constraint condition.

3. The additive manufacturing oriented magnetic-structure multiphysics field topological optimization design method of claim 2, wherein the cell design density space and the cell print density space are vector matrices.

4. Additive manufacturing oriented magnetic-structure multi-physical field topology optimization design method according to claim 2 or 3, wherein the unit print density space

The calculation formula of (2) is as follows:

in the formula, ρ_sRepresenting the cell support domain, P is a first parameter, ε is a second parameter,

supporting the domain p for the cell_sThe unit print density of the kth cell in (1), Q is a third parameter, ρ is a cell design density space, ρ_eDensity is designed for the cell.

5. The additive manufacturing-oriented magnetic-structure multi-physical-field topological optimization design method of claim 2, wherein the unit elastic modulus

And permeability of the cell

The calculation formula of (2) is as follows:

wherein,

for the unit print density obtained after filtration, E₀Is the modulus of elasticity, constant E, of the material_minIs a constant number of times, and is,_ris the relative permeability of the material, P _ s is the structural field penalty parameter, and P _ m is the magnetic field penalty parameter.

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