Yoke structure design method based on variable density method, yoke structure, device, equipment, medium and program product

Abstract

The invention provides an iron yoke structure design method based on a variable density method, and is applied to the field of superconducting electrical iron yoke design. The method comprises the following steps: establishing a target equipment two-dimensional model comprising a superconducting coil, a workpiece and an iron yoke, and setting coil excitation, material attributes and electromagnetic boundary conditions; defining an iron yoke design space and dividing finite elements, and taking the relative density of the finite elements as a design variable; establishing a topological optimization model by taking the magnetic pole gap magnetic flux density as a target function and the yoke volume as a constraint; carrying out magnetic field finite element analysis by utilizing a material attribute interpolation model to obtain magnetic field distribution, and then calculating a magnetic pole gap magnetic flux density module value integral to obtain a target function value; solving the sensitivity of the target and the constraint function to the design variable, modifying the sensitivity, inputting a gradient optimization algorithm, and updating the design variable under the condition that the constraint is satisfied; and if the target function change is smaller than the convergence tolerance, outputting the yoke structure. The invention further provides an iron yoke structure, a device, equipment, a medium and a program product.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of superconducting electrical iron yoke design, in particular to the design of iron yokes for high-temperature superconducting direct current induction heating systems, and more particularly to an iron yoke structure design method based on a variable density method, an iron yoke structure, a device, an apparatus, a medium, and a program product. BACKGROUND

[0002] High-temperature superconducting direct current induction heating technology has a wide application prospect in the industrial heating field due to its high efficiency, low energy consumption, and environmental protection characteristics. Iron yokes, as key components, are used to guide and concentrate magnetic fields, improving heating efficiency and uniformity. However, traditional iron yokes often use regular structures, and their design relies on experience or parameter optimization, resulting in low magnetic field utilization and high material costs, and the global optimization of the structure topology cannot be achieved. SUMMARY

[0003] In view of the above problems, the present application provides an iron yoke structure design method based on a variable density method to improve electromagnetic utilization, an iron yoke structure, a device, an apparatus, a medium, and a program product.

[0004] According to a first aspect of the present application, an iron yoke structure design method based on a variable density method is provided, comprising: establishing a two-dimensional model of a target device containing a superconducting coil, a workpiece, and an iron yoke, taking the superconducting coil as an excitation source, setting its material properties and corresponding electromagnetic boundary conditions; taking the area where the iron yoke is located as the iron yoke design space and defining the corresponding electromagnetic boundary conditions; dividing the iron yoke design space into n finite elements, and taking the relative density of each finite element as a design variable according to the variable density method; setting the filter radius of the design variable and the volume constraint value; taking the magnetic flux density of the pole gap as the objective function, and taking the volume of the iron yoke as the constraint function, establishing a topology optimization model, the pole gap containing the area where the workpiece is located, wherein n is a positive integer; performing magnetic field finite element analysis on the target device using a material property interpolation model to obtain the magnetic field distribution of the target device; calculating the integral of the magnetic flux density modulus of the pole gap area to obtain the function value of the objective function; solving the sensitivity of the design variable to the objective function and the constraint function; modifying the sensitivity of the objective function and the constraint function according to the filter radius, taking the obtained function value of the objective function and the constraint function and their sensitivity information to the design variable as the input conditions of the gradient-type optimization algorithm, solving and updating the design variable under the premise of meeting the constraint function and the volume constraint value; if the change of the function value of the objective function is less than the preset convergence tolerance, obtaining the structure of the iron yoke according to the topology optimization model of the iron yoke.

[0005] According to the embodiment of the present application, the material attribute interpolation model is used to perform the magnetic field finite element analysis on the target device, including: using the solid isotropic material with penalization model, obtaining the magnetic permeability of each finite element by interpolating the relative magnetic permeability and calculating the magnetic resistance; and performing the magnetic field finite element analysis on the target device under the action of the electromagnetic boundary condition.

[0006] According to the embodiment of the present application, the relative magnetic permeability is interpolated and the magnetic resistance is calculated, including: obtaining the nonlinear magnetic characteristic curve of the yoke material, the design variable and the penalty factor; obtaining the relative magnetic permeability of the finite element based on the nonlinear permeability model interpolation; and calculating the magnetic resistance in combination with the size of the finite element.

[0007] According to the embodiment of the present application, the sensitivity of the objective function to the design variable is solved, including: in the area of the magnetic pole gap, the sensitivity of the objective function is obtained according to the 2 times integral of the product of the magnetic flux density and the change rate of the design variable.

[0008] According to the embodiment of the present application, the sensitivity of the constraint function to the design variable is solved, including: in the yoke design space, the sensitivity of the constraint function to the design variable is obtained according to the integral of the partial derivative of the angle variable to its component.

[0009] According to the embodiment of the present application, the structure of the yoke is obtained according to the topology optimization model of the yoke, including: converting the topology optimization model of the yoke into solid and hollow distribution according to the preset threshold value, obtaining the yoke structure after threshold processing; and performing smoothing processing on the yoke structure after threshold processing, obtaining the structure of the yoke.

[0010] The second aspect of the present application provides a yoke structure obtained by any of the above methods.

[0011] The third aspect of the present application provides a variable density method-based iron yoke structure design device, comprising: a modeling and initialization module, configured to establish a two-dimensional model of a target device comprising a superconducting coil, a workpiece and an iron yoke, set material properties and corresponding electromagnetic boundary conditions of the superconducting coil as an excitation source; an optimization model construction module, configured to define corresponding electromagnetic boundary conditions in an iron yoke design space of an area where the iron yoke is located; divide the iron yoke design space into n finite elements, and set the relative density of each finite element as a design variable according to the variable density method; set a filtering radius of the design variable and a volume constraint value; set the magnetic flux density of the pole gap as an objective function, and set the volume of the iron yoke as a constraint function, and establish a topology optimization model, wherein the pole gap comprises an area where the workpiece is located, and n is a positive integer; a magnetic field finite element analysis module, configured to perform magnetic field finite element analysis on the target device by using a material property interpolation model to obtain a magnetic field distribution of the target device; an objective function calculation module, configured to calculate the integral of the modulus of the magnetic flux density of the pole gap area to obtain a function value of the objective function; a sensitivity analysis module, configured to solve the sensitivity of the objective function and the constraint function to the design variable; a solution and variable updating module, configured to modify the sensitivity of the objective function and the constraint function according to the filtering radius, take the function value of the objective function and the constraint function and the sensitivity information of the design variable as input conditions of a gradient-type optimization algorithm, and solve and update the design variable under the premise of meeting the constraint function and the volume constraint value; and a structure acquisition module, configured to obtain the structure of the iron yoke according to the topology optimization model of the iron yoke if the change of the function value of the objective function is less than a preset convergence tolerance.

[0012] The fourth aspect of the present application provides an electronic device, comprising: one or more processors; a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method.

[0013] The fifth aspect of the present application further provides a computer-readable storage medium having a computer program or instructions stored thereon, wherein the computer program or instructions are executed by a processor to implement the steps of the method.

[0014] The sixth aspect of the present application further provides a computer program product comprising a computer program or instructions, wherein the computer program or instructions are executed by a processor to implement the steps of the method. BRIEF DESCRIPTION OF DRAWINGS

[0015] The above and other objects, features and advantages of the present application will become more apparent from the following description of embodiments of the present application, taken in conjunction with the accompanying drawings, in which:

[0016] Figure 1 An iron yoke structure diagram of a double-C type is schematically shown;

[0017] Figure 2 An E-type adjustable air-gap iron yoke structure is schematically shown;

[0018] Figure 3 A flow chart of a variable density method based iron yoke structure design method according to an embodiment of the present application is schematically shown;

[0019] Figure 4 A flow chart of another variable density method based iron yoke structure design method according to an embodiment of the present application is schematically shown;

[0020] Figure 5 An iron yoke structure before optimization according to an embodiment of the present application is schematically shown;

[0021] Figure 6 An iron yoke structure after optimization according to an embodiment of the present application is schematically shown;

[0022] Figure 7 A magnetic pole air-gap magnetic field distribution before optimization according to an embodiment of the present application is schematically shown;

[0023] Figure 8 A magnetic pole air-gap magnetic field distribution after optimization according to an embodiment of the present application is schematically shown;

[0024] Figure 9 A structure block diagram of a variable density method based iron yoke structure design apparatus according to an embodiment of the present application is schematically shown; and

[0025] Figure 10 A block diagram of an electronic device suitable for implementing a variable density method based iron yoke structure design method according to an embodiment of the present application is schematically shown. DETAILED DESCRIPTION

[0026] Hereinafter, embodiments of the present application will be described with reference to the accompanying drawings. It is to be understood, however, that the description is merely exemplary of the present application, and is not intended to limit the scope of the present application. In the following detailed description of the embodiments of the present application, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one skilled in the art that the present application can be practiced without these specific details. In other instances, well-known structures and functions have not been described in detail in order to avoid obscuring aspects of the present application.

[0027] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used herein, the term "includes" and tautological expressions thereof, such as "including," "includes," "include," "contains," "containing," and so forth, shall be read expansively and without limitation. The terms "comprising," "comprise" and / or "comprises" and tautological expressions thereof (for example, "comprising a," "comprises an," etc.) shall be interpreted open as taking their broadest possible interpretation given the context.

[0028] All terms used herein, including technical and scientific terms, have the meanings commonly understood by one of ordinary skill in the art unless otherwise defined. It should be noted that the use of any terms herein should not be interpreted as excluding the use of other terms that have the same or similar meanings unless otherwise defined.

[0029] In the case of using expressions similar to "at least one of A, B, and C, etc.", it should be generally interpreted as the meaning of the expression as understood by one of ordinary skill in the art (for example, "a system having at least one of A, B, and C" should include but not be limited to a system having A alone, a system having B alone, a system having C alone, a system having both A and B, a system having both A and C, a system having both B and C, and / or a system having A, B, and C, etc.).

[0030] Figure 1 A double-C type iron yoke structure is schematically shown; Figure 2 An E type adjustable air gap iron yoke structure is schematically shown.

[0031] In the prior art, the common practice for optimizing the iron yoke in high temperature superconducting direct current induction heating equipment is to make a large degree of structural changes to the overall shape of the iron yoke, such as adopting a double-C type iron yoke, an E type iron yoke with adjustable air gap, or a structure of a split type iron yoke. As shown in Figure 1 , Figure 2 The double-C type iron yoke and the E type iron yoke with adjustable air gap include superconducting coils, iron yokes, and aluminum ingots. These structures improve the magnetic circuit closing characteristics to some extent, but their specific size and structural parameters are mostly determined by the engineering experience of the designer, lacking systematic theoretical optimization guidance. This experience-dependent design process is prone to result in low electromagnetic utilization rate of the iron yoke in the process, and in order to meet the performance indicators, a larger structure size is often required, causing material waste and volume increase.

[0032] Embodiments of the present application provide an iron yoke structure design method based on the variable density method. The method first gives an initial design domain, which can adopt a relatively arbitrary initial shape. By establishing an optimization model with the maximum magnetic flux density of the magnetic pole gap as the objective function, the material distribution is continuously iteratively optimized using the variable density method, and finally a better iron yoke topology structure is obtained in terms of better magnetic conductivity performance, higher material utilization rate, and higher heating uniformity. This method breaks through the limitations of traditional experience-based design and can automatically find a better iron yoke configuration, providing a new technical approach for the design of the core components of the high temperature superconducting direct current induction heating system.

[0033] Figure 3 A flowchart of an iron yoke structure design method based on the variable density method according to an embodiment of the present application is schematically shown.

[0034] As shown in Figure 3As shown, in some embodiments of the present application, the variable density method-based iron yoke structure design method includes operations S310-S370.

[0035] In operation S310, a two-dimensional model of a target device including a superconducting coil, a workpiece, and an iron yoke is established, the superconducting coil is set as an excitation source, and material properties and corresponding electromagnetic boundary conditions are set.

[0036] In this embodiment, a two-dimensional model of a high-temperature superconducting direct current induction heating system can be established in a physical simulation software, including a superconducting coil, a workpiece, and an iron yoke. Material properties, boundary conditions, and excitation sources are set. Since most electromagnetic devices have axial symmetry or planar characteristics, a two-dimensional model can greatly reduce the computational load while ensuring analysis accuracy.

[0037] The superconducting coil is the excitation source of the magnetic field and generates a strong magnetic field by passing a current. The workpiece is the object of the magnetic field and is the conductor to be heated, and its electromagnetic response can be one of the analysis targets. The iron yoke belongs to a magnetic conductive structure and is used to guide and concentrate the magnetic field to reduce magnetic leakage.

[0038] In operation S320, the area where the iron yoke is located is defined as the iron yoke design space and the corresponding electromagnetic boundary conditions are defined; the iron yoke design space is divided into n finite elements, and the relative density of each finite element is used as a design variable according to the variable density method; the filter radius of the design variable and the volume constraint value are set; the magnetic flux density between the magnetic poles is used as the objective function, and the volume of the iron yoke is used as the constraint function to establish a topology optimization model, and the magnetic pole gap includes the area where the workpiece is located, where n is a positive integer.

[0039] In this embodiment, the relative density of each element is used as a design variable based on the variable density method. When the relative density of each element is used as a design variable, the relative density of each element is used as a design variable. The area where the iron yoke is located is defined as the iron yoke design space, and the material distribution of the iron yoke area is optimized. The electromagnetic boundary conditions define the physical behavior of the magnetic field at the boundary of the design space. For example, it includes the interface between the iron yoke and the air, the interface between the iron yoke and the workpiece, and the outer boundary, etc. The continuous iron yoke design space is divided into N small elements (such as quadrilaterals, triangles) to facilitate numerical solution.

[0040] The filter radius solves the numerical instability problem of topology optimization. By setting the filter radius, the density change of each element is affected by the weighted influence of the surrounding elements, making the optimization result smoother.

[0041] The magnetic flux density of the magnetic pole gap directly determines the performance of the target device, so it is used as the objective function. The constraint function specifies the maximum allowed volume of the iron yoke (such as 70% of the original volume), which is the constraint condition for optimization. The iron yoke volume is used as the constraint function to avoid unlimited increase of material to improve the magnetic flux density. ​

[0042] The model finally formed in this embodiment is as follows: under the volume constraint, the relative density of the iron yoke unit is found to maximize the magnetic flux density of the pole gap, thereby providing a calculation framework for subsequent optimization iterations.

[0043] The topology optimization model of the embodiment of the present application can be expressed as follows.

[0044]

[0045] wherein, is a vector composed of n design variables , and n is the number of finite elements in the iron yoke design space; is an objective function, representing the integral of the square of the modulus of the magnetic flux density in the pole gap region; is the volume of the iron yoke, is the initial volume of the iron yoke design domain, is a volume constraint coefficient, representing that the volume constraint is not more than times the initial volume; is the magnetic vector potential, is the current density, is the magnetic permeability.

[0046] In operation S330, the material property interpolation model is used to perform magnetic field finite element analysis on the target device to obtain the magnetic field distribution of the target device.

[0047] The material property interpolation model can be one of the following models: SIMP interpolation model (Solid Isotropic Material with Penalization), RAMP model (Rational Approximation of Material Properties), and step function.

[0048] The RAMP model penalizes the intermediate density by using a rational function. Without intermediate density values (only 0 or 1), numerical stability techniques (such as filtering, regularization) are required to avoid singularity of the stiffness matrix. The embodiment of the present application preferably uses the SIMP interpolation model.

[0049] In particular, the material property interpolation model is used to obtain the magnetic permeability of each finite element, and the device is subjected to magnetic field finite element analysis under the action of given electromagnetic boundary conditions to obtain the magnetic field distribution of the structure.

[0050] In operation S340, the integral of the modulus of the magnetic flux density in the pole gap region is calculated to obtain the function value of the objective function.

[0051] The magnetic pole gap region, i.e., the gap between the magnetic pole and the workpiece, is a key region for energy transmission of the magnetic flux, and the magnetic flux density thereof directly determines the performance of the target device. The magnetic flux density B is a vector, and the magnitude |B| thereof reflects the strength of the magnetic field. By integrating the surface of the magnetic pole gap region, the total amount of the magnetic flux density is obtained by accumulating the size of the magnetic flux density on all microelement areas in the region. The larger the value is, the stronger the overall magnetic flux density of the magnetic pole gap is, and the better the performance of the target device is.

[0052] In an embodiment, the integral of the magnetic flux density modulus value can be calculated using a domain probe in physical simulation software or other numerical integral algorithms.

[0053] In operation S350, the sensitivity of the objective function and the constraint function to the design variable is solved.

[0054] The sensitivity of the objective function and the constraint function to the design variable indicates the rate of change of the objective function and the constraint function when the design variable changes slightly. The sensitivity of the objective function to the design variable reflects the degree of influence of the change of the unit density on the integral of the magnetic flux density of the magnetic pole gap. The sensitivity of the constraint function to the design variable reflects the degree of influence of the change of the unit density on the volume of the iron yoke.

[0055] In topology optimization, the core methods for obtaining the sensitivity of the objective function and the constraint function to the design variable can be divided into two categories: analytical method and approximate method. The analytical method includes direct differentiation method, adjoint method, etc.; the approximate method includes finite difference method, automatic differentiation method, etc. The direct differentiation method establishes an analytical relationship of the sensitivity by respectively deriving the control method, the objective function and the constraint function with respect to the design variable. The adjoint method introduces an adjoint variable and an adjoint equation, converts the sensitivity calculation into solving an adjoint equation independent of the number of design variables, and substitutes the sensitivity expression to obtain the sensitivity. The sensitivity is obtained by numerical approximation rather than strict analytical derivation.

[0056] In operation S360, the sensitivity of the objective function and the constraint function is modified according to the filtering radius, the function values of the obtained objective function and constraint function and the sensitivity information thereof to the design variable are taken as the input conditions of the gradient type optimization algorithm, and the design variable is solved and updated under the premise of meeting the constraint function and the volume constraint value.

[0057] In this embodiment, one of the sensitivity filtering technique, the density filtering technique or the projection filtering technique can be used to modify the sensitivity of the objective function and the constraint function. The sensitivity filtering technique performs local smoothing on the original sensitivity of the objective function and the constraint function through spatial weighted averaging, eliminates the sensitivity mutation caused by grid or numerical fluctuation, makes the adjustment of the design variables in the optimization iteration more stable, and avoids the appearance of small redundant structures. The density filtering technique directly performs local weighted averaging on the design variables, smoothes the distribution of the cell density, prevents the appearance of chessboard and other non-physical forms, and ensures the continuity of the structure after optimization. The projection filtering technique: by means of a mathematical projection function, the design variables with intermediate density are mapped to a discrete state closer to 0 or 1, the all-or-nothing material distribution characteristics are strengthened, and the transition area is reduced.

[0058] In this embodiment, the gradient-based optimization algorithm can include the method of moving asymptotes (MMA), sequential quadratic programming (SQP) or convex linearization algorithm (CONLIN) and the like.

[0059] The method of moving asymptotes constructs a local approximation model of the objective function and the constraint function by moving asymptotes, and updates the asymptotes at each iteration to gradually approach the optimal solution. It can efficiently converge under volume constraints and performance constraints, and is highly efficient in using sensitivity information. It is the preferred choice for iron yoke electromagnetic topology optimization, structure lightweight design and the like. The sequential quadratic programming algorithm approximates the optimal solution of the nonlinear constraint optimization by iteratively solving quadratic programming subproblems. At each step, a quadratic approximation model is constructed using the gradient and Hessian matrix of the objective function and the constraint. It has high precision and fast convergence, and is suitable for smooth nonlinear optimization problems. The calculation cost of large-scale variables is relatively high, and it is more suitable for small-scale and fine optimization scenarios. The sequential convex programming algorithm approximates the original nonlinear optimization problem to a convex function problem in the iteration process, and realizes the approximation of global optimization by repeatedly solving convex subproblems.

[0060] Preferably, in this embodiment, the sensitivity filtering technique is used to modify the sensitivity of the objective function and the constraint function. The function values of the obtained objective function and constraint function and the sensitivity information thereof with respect to the design variables are used as the input conditions of the method of moving asymptotes, and the optimization problem is solved and calculated to update the design variables.

[0061] In operation S370, if the change of the function value of the objective function is less than the preset convergence tolerance, the structure of the iron yoke is obtained according to the topology optimization model of the iron yoke.

[0062] In this embodiment, it is determined whether the optimization convergence condition is met. If not, the process proceeds to step S320 and continues the calculation. If the condition is met, the topology optimization process is terminated, and a topology optimization model of the iron yoke that meets the magnetic performance requirements is obtained. Based on this iron yoke topology optimization model, post-processing is performed to generate the final iron yoke solid structure.

[0063] This embodiment employs a variable-density topology optimization method, discretizing the design space of the iron yoke into finite elements and using the relative density of these elements as the design variable. Combined with a material property interpolation model, finite element analysis of the magnetic field is conducted, achieving intelligent distribution of the iron yoke material and resulting in a more rational magnetic circuit structure. By focusing on the core performance characteristic of the magnetic flux density between magnetic poles as the objective function, and using volume as a constraint, the electromagnetic utilization rate during magnetic conduction is effectively improved. The optimized iron yoke structure can better guide and concentrate magnetic lines of force, reduce magnetic leakage, and significantly improve magnetic energy transfer efficiency.

[0064] In some embodiments of this application, a magnetic field finite element analysis of the target device is performed using a material property interpolation model, including: using a solid isotropic material penalty model (SIMP interpolation model), interpolating the relative permeability and calculating the magnetic reluctance to obtain the permeability of each finite element; and performing a magnetic field finite element analysis of the target device under electromagnetic boundary conditions.

[0065] The SIMP interpolation model can be expressed as follows.

[0066]

[0067] in, For unit The relative permeability, For unit relative density, The relative permeability of the solid iron yoke material. The permeability of free space, It is a penalty factor, which can be set here. .

[0068] Figure 4 The flowchart illustrates another iron yoke structure design method based on the variable density method according to an embodiment of this application.

[0069] like Figure 4As shown, the flow of the iron yoke structure design method based on the variable density method in this embodiment includes the following operations: in the starting stage, defining the iron yoke design space, setting the electromagnetic boundary conditions, and initializing the design variables; calculating the unit permeability by using the variable density method and the SIMP interpolation model; performing finite element analysis of the electromagnetic field to calculate the magnetic field distribution and the magnetic flux density; iteratively updating the design variables by using the moving asymptote method (MMA); determining whether the convergence condition is met, and if not, returning to the step of calculating the unit permeability by using the variable density method and the SIMP interpolation model; if yes, performing post-processing to generate the iron yoke solid structure; obtaining the optimal iron yoke topology structure, and the flow ends.

[0070] The optimization convergence condition in this embodiment can be expressed as follows.

[0071]

[0072] wherein, is the objective function value after the n-th iteration, is the objective function value after the (n-1)-th iteration, is the convergence tolerance, and is 0.001.

[0073] Based on the solid isotropic material penalty model, the design variables are pushed to full or no convergence by the penalty factor in this embodiment, the relative permeability interpolation and the reluctance calculation are combined to realize the reasonable assignment of the magnetic permeability of each finite element, and then the finite element analysis of the magnetic field is carried out under the constraint of the electromagnetic boundary conditions. The matching of numerical stability, magnetic characteristics, material distribution and magnetic field solving precision are derived, which can effectively support the iterative calculation of the iron yoke topology optimization.

[0074] In some embodiments of the present application, the relative permeability is interpolated, and the reluctance is calculated, including: obtaining the nonlinear magnetic characteristic curve of the iron yoke material, the design variable and the penalty factor; obtaining the relative permeability of the finite element based on the nonlinear permeability model interpolation; and calculating the reluctance in combination with the size of the finite element.

[0075] The material interpolation is obtained based on the nonlinear permeability model of the B-H curve, and is expressed as follows.

[0076]

[0077] wherein, is the magnetic field strength, which can be obtained by the B-H curve of the material.

[0078] The above formula quantifies the relative permeability through the relationship between B and H, and is used to describe the nonlinear magnetic characteristics of the magnetic material. The position variable x i and the power p are introduced to describe the non-uniform distribution of the relative permeability.

[0079] The embodiment is based on nonlinear permeability model interpolation to obtain the relative permeability of the finite element, and combines the element size to calculate the magnetic resistance to obtain the element permeability. The continuous correlation between the design variable and the magnetic property is realized by means of the solid isotropic material penalty model, and the material nonlinear magnetic property is integrated, so that the influence of the iron yoke material distribution on the magnetic resistance and the magnetic field is accurately quantified. The magnetic property input conforming to the actual situation is provided for the finite element analysis of the magnetic field, which is suitable for nonlinear simulation, topology optimization and other scenes of the electromagnetic field, and the accuracy of the magnetic field performance evaluation in the topology optimization is ensured.

[0080] In some embodiments of the application, the sensitivity of the objective function to the design variable is solved, comprising: on the region of the magnetic pole gap, the sensitivity of the objective function is obtained according to the double integral of the product of the magnetic flux density and its change rate with respect to the design variable.

[0081] The magnetic flux density of the embodiment is calculated as follows.

[0082]

[0083] Wherein, B is the magnetic flux density, A is the magnetic vector potential, is a vector differential operator.

[0084] The sensitivity of the objective function is expressed as follows.

[0085]

[0086] Wherein, Ω gap represents the region of the magnetic pole gap. The influence of the iron yoke structure change (design variable) on the magnetic flux density of the magnetic pole gap (objective function) is quantified by the above formula.

[0087] The embodiment obtains the magnetic flux density distribution through the curl of the magnetic vector potential, and then calculates the sensitivity of the objective function to the design variable through the integral of the region of the gap, which provides a basis for the iterative update of the electromagnetic topology optimization of the iron yoke.

[0088] The embodiment performs double integration of the product of the magnetic flux density and its change rate with respect to the design variable in the magnetic pole gap region to solve the sensitivity of the objective function, which can accurately and physically self-consistently quantify the influence of the design variable on the magnetic flux density of the magnetic pole gap, provide reliable gradient guidance for electromagnetic topology optimization, and ensure that the iteration process efficiently and accurately improves the magnetic flux density target.

[0089] In some embodiments of the application, the sensitivity of the constraint function to the design variable is solved, comprising: on the iron yoke design space, the sensitivity of the constraint function to the design variable is obtained according to the integral of the partial derivative of the angle variable to its component.

[0090] The sensitivity of the constraint function to the design variable of the embodiment can be expressed as follows.

[0091]

[0092] where, is the sensitivity of the volume V of the iron yoke to the design variable x i is the design space of the iron yoke. design is the design space of the iron yoke. is the relevant angle variable, is the angle component associated with the design variable x i is the angle component associated with the design variable x; dA represents an area infinitesimal.

[0093] The embodiment can accurately derive and quantify the sensitivity of the volume constraint to the design variable by integrating the partial derivative of the angle variable component on the design space of the iron yoke, provide continuous and accurate gradient information for topology optimization, and guarantee strict satisfaction of the volume constraint and stability of the optimization iteration.

[0094] Figure 5 An iron yoke structure diagram before optimization is schematically shown according to an embodiment of the present application. Figure 6 An iron yoke structure diagram after optimization is schematically shown according to an embodiment of the present application.

[0095] In some embodiments of the present application, the structure of the iron yoke is obtained according to a topology optimization model of the iron yoke, including: converting the topology optimization model of the iron yoke into a solid and hollow distribution according to a preset threshold value, to obtain an iron yoke structure after threshold value processing; and performing smoothing processing on the iron yoke structure after threshold value processing, to obtain the structure of the iron yoke.

[0096] The embodiment performs post-processing on the relative density distribution obtained by optimization, to generate a final iron yoke solid structure. The post-processing method is to convert the continuous density distribution into a clear solid-hollow distribution by using a threshold value, and is expressed as the following formula.

[0097]

[0098] where, is the final determined unit state (1 represents reserved material, and 0 represents removed material), is a threshold value, and is usually taken as 0.3-0.7.

[0099] The smoothing processing is performed on the iron yoke structure after threshold value processing, to eliminate the jagged boundary, and to generate an iron yoke shape result diagram that can be used for manufacturing.

[0100] The embodiment converts the continuous density distribution of the iron yoke topology optimization model into a discrete solid and hollow distribution by using a preset threshold value, solves the problem that the topology optimization result is difficult to be directly processed, and further performs smoothing processing to eliminate the sharp boundary and irregular defects of the structure after threshold value processing, to avoid stress concentration in use, and finally obtain an iron yoke structure with continuous boundary, regular shape and engineering manufacturing.

[0101] Based on the above iron yoke structure design method based on the variable density method, the application also provides an iron yoke structure obtained according to any of the above methods.

[0102] The two-dimensional model of the iron yoke before optimization in this embodiment is shown in Figure 5 The manufacturable iron yoke structure after optimization is shown in Figure 6 .

[0103] Figure 7 The magnetic pole air gap magnetic field distribution diagram before optimization according to the embodiment of the application is schematically shown. Figure 8 The magnetic pole air gap magnetic field distribution diagram after optimization according to the embodiment of the application is schematically shown.

[0104] By using the above method to simulate and verify the high-temperature superconducting DC induction heating iron yoke, the simulation results show that the topology optimization based on the variable density method effectively improves the magnetic circuit performance of the high-temperature superconducting DC induction heating device. Under the condition of reducing the volume by 40%, the magnetic pole air gap magnetic flux density (surface magnetic flux density module) is significantly improved from 0.285-0.405 Tesla (min: 0.285, max: 0.405) before optimization to 0.750-1.164 Tesla (min: 0.7503, max: 1.164), with an average increase of about 177%. This new structure with intelligent material distribution not only greatly improves the magnetic field strength and uniformity, reduces the magnetic leakage loss, but also improves the electromagnetic energy efficiency by optimizing the magnetic circuit path, realizing the synergistic optimization of lightweight design and performance improvement, and providing an effective solution for efficient design of high-temperature superconducting DC induction heating devices.

[0105] Based on the above iron yoke structure design method based on the variable density method, the application also provides an iron yoke structure design device based on the variable density method. The device will be described in detail below. Figure 9 .

[0106] Figure 9 The structure block diagram of the iron yoke structure design device based on the variable density method according to the embodiment of the application is schematically shown.

[0107] As shown in Figure 9 , the iron yoke structure design device based on the variable density method of this embodiment 900 includes a modeling and initialization module 910, an optimization model construction module 920, a magnetic field finite element analysis module 930, a target function calculation module 940, a sensitivity analysis module 950, a solution and variable update module 960, and a structure acquisition module 970.

[0108] The modeling and initialization module 910 is used to establish a two-dimensional model of a target device containing a superconducting coil, a workpiece and an iron yoke, with the superconducting coil as the excitation source, and the material properties and corresponding electromagnetic boundary conditions are set.

[0109] The optimization model construction module 920 is configured to define a yoke design space as an area where the yoke is located and define corresponding electromagnetic boundary conditions; divide the yoke design space into n finite elements, and take the relative density of each finite element as a design variable according to a variable density method; set a filter radius of the design variable and a volume constraint value; take the magnetic flux density of the pole gap as an objective function, and take the volume of the yoke as a constraint function, to establish a topology optimization model, the pole gap including an area where the workpiece is located, where n is a positive integer.

[0110] The magnetic field finite element analysis module 930 is configured to perform magnetic field finite element analysis on the target device by using a material property interpolation model, to obtain a magnetic field distribution of the target device.

[0111] The objective function calculation module 940 is configured to calculate an integral of the modulus of the magnetic flux density in the pole gap area, to obtain a function value of the objective function.

[0112] The sensitivity analysis module 950 is configured to solve the sensitivity of the objective function and the constraint function to the design variable.

[0113] The solution and variable updating module 960 is configured to modify the sensitivity of the objective function and the constraint function according to the filter radius, take the function value of the objective function and the constraint function and the sensitivity information of the design variable as input conditions of a gradient-type optimization algorithm, and solve and update the design variable under the premise of meeting the constraint function and the volume constraint value.

[0114] The structure acquisition module 970 is configured to obtain the structure of the yoke according to the topology optimization model of the yoke, if the change of the function value of the objective function is less than a preset convergence tolerance.

[0115] According to an embodiment of the present application, the magnetic field finite element analysis module 930 is further configured to obtain the magnetic permeability of each finite element by interpolating the relative permeability and calculating the magnetic resistance by using a solid isotropic material penalty model.

[0116] According to an embodiment of the present application, the magnetic field finite element analysis module 930 is further configured to obtain a nonlinear magnetic characteristic curve of the yoke material, the design variable and a penalty factor, interpolate the relative permeability of the finite element based on a nonlinear permeability model, and calculate the magnetic resistance in combination with the size of the finite element.

[0117] According to an embodiment of the present application, the sensitivity analysis module 950 is further configured to obtain the sensitivity of the objective function according to a double integral of the product of the magnetic flux density and the change rate of the design variable in the area of the pole gap.

[0118] According to an embodiment of the present application, the sensitivity analysis module 950 is further configured to obtain the sensitivity of the constraint function to the design variable according to the integral of the partial derivative of the component of the angle variable on the iron yoke design space.

[0119] According to an embodiment of the present application, the structure obtaining module 970 is further configured to convert the topology optimization model of the iron yoke into a solid and void distribution according to a preset threshold value, to obtain a threshold-processed iron yoke structure; and perform smoothing processing on the threshold-processed iron yoke structure, to obtain the structure of the iron yoke.

[0120] The iron yoke structure design method, the iron yoke structure and the device based on the variable density method have the following beneficial effects: (1) The intelligent distribution of the iron yoke material is realized by the variable density topology optimization method, the magnetic circuit structure is more reasonable, and the electromagnetic utilization rate in the magnetic conduction process is effectively improved. The optimized iron yoke structure can better guide and concentrate the magnetic force lines, reduce the magnetic leakage phenomenon, and significantly improve the magnetic energy transmission efficiency. (2) The optimized iron yoke structure produces a more uniformly distributed magnetic field, greatly improving the efficiency and uniformity of induction heating. This improved magnetic field distribution ensures that the workpiece is heated more uniformly during the heating process, effectively avoiding the problems of local overheating or insufficient heating, and improving the heating quality. (3) On the premise of ensuring the performance of the magnetic circuit, the optimized distribution of the material is realized by strict volume constraint, effectively reducing the amount of material used, reducing the manufacturing cost of the equipment, and reducing the weight of the equipment, so that the equipment has stronger engineering applicability while maintaining high performance.

[0121] According to embodiments of the present application, any multiple of the modeling and initialization module 910, the optimization model construction module 920, the magnetic field finite element analysis module 930, the objective function calculation module 940, the sensitivity analysis module 950, the solving and variable updating module 960 and the structure acquisition module 970 can be combined in one module, or any one of them can be split into multiple modules. Alternatively, at least part of the function of one or more of these modules can be combined with at least part of the function of other modules and implemented in one module. According to embodiments of the present application, at least one of the modeling and initialization module 910, the optimization model construction module 920, the magnetic field finite element analysis module 930, the objective function calculation module 940, the sensitivity analysis module 950, the solving and variable updating module 960 and the structure acquisition module 970 can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on chip, a system on board, a system on package, an application specific integrated circuit (ASIC), or any other reasonable way of integrating or packaging a circuit, etc. hardware or firmware, or in any one of the three implementation ways of software, hardware and firmware or in a proper combination of any of them. Alternatively, at least one of the modeling and initialization module 910, the optimization model construction module 920, the magnetic field finite element analysis module 930, the objective function calculation module 940, the sensitivity analysis module 950, the solving and variable updating module 960 and the structure acquisition module 970 can be at least partially implemented as a computer program module which, when executed, can perform the corresponding functions.

[0122] Figure 10 A block diagram of an electronic device suitable for implementing the variable density method based iron yoke structure design method according to embodiments of the present application is schematically shown.

[0123] As shown in Figure 10 The electronic device 1000 according to embodiments of the present application includes a processor 1001 which can perform various appropriate actions and processes according to programs stored in a read only memory (ROM) 1002 or loaded from a storage portion 1008 into a random access memory (RAM) 1003. The processor 1001 can include, for example, a general purpose microprocessor (e.g. a CPU), an instruction set processor and / or a related chipset and / or a special purpose microprocessor (e.g. an application specific integrated circuit (ASIC)), etc. The processor 1001 can also include an on-board memory for cache use. The processor 1001 can include a single processing unit or multiple processing units for performing different actions of the method processes according to embodiments of the present application.

[0124] In the RAM 1003, various programs and data required for the operation of the electronic device 1000 are stored. The processor 1001, the ROM 1002, and the RAM 1003 are connected to each other via the bus 1004. The processor 1001 performs various operations of the method flow according to the embodiments of the present application by executing the programs in the ROM 1002 and / or the RAM 1003. It should be noted that the programs can also be stored in one or more memories other than the ROM 1002 and the RAM 1003. The processor 1001 can also perform various operations of the method flow according to the embodiments of the present application by executing the programs stored in the one or more memories.

[0125] According to the embodiments of the present application, the electronic device 1000 can further include an input / output (I / O) interface 1005, which is also connected to the bus 1004. The electronic device 1000 can further include one or more of the following components connected to the input / output (I / O) interface 1005: an input part 1006 including a keyboard, a mouse, and the like; an output part 1007 including a cathode ray tube (CRT), a liquid crystal display (LCD), and the like, and a speaker, and the like; a storage part 1008 including a hard disk, and the like; and a communication part 1009 including a network interface card such as a LAN card, a modem, and the like. The communication part 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the input / output (I / O) interface 1005 as necessary. A removable medium 1011 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, and the like is mounted on the drive 1010 as necessary, so that a computer program read therefrom is installed in the storage part 1008 as necessary.

[0126] The present application also provides a computer readable storage medium, which can be included in the device / apparatus / system described in the above embodiments; or can exist separately without being assembled into the device / apparatus / system. The above computer readable storage medium carries one or more programs, when the one or more programs are executed, the method according to the embodiments of the present application is implemented.

[0127] According to an embodiment of the present application, the computer readable storage medium can be a non-transitory computer readable storage medium, for example, can include but is not limited to: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In this application, a computer readable storage medium can be any tangible medium that contains or stores a program for use by or in connection with an instruction execution system, apparatus, or device. For example, according to an embodiment of the present application, the computer readable storage medium can include one or more of the above-described ROM 1002 and / or RAM 1003 and / or a memory other than the ROM 1002 and the RAM 1003.

[0128] Embodiments of the present application also include a computer program product, which includes a computer program containing program codes for executing the method shown in the flow chart. When the computer program product is run in a computer system, the program codes are used to make the computer system implement the variable density method-based iron yoke structure design method provided by the embodiments of the present application.

[0129] The above-described functions defined in the system / device of the embodiments of the present application are performed when the computer program is executed by the processor 1001. According to an embodiment of the present application, the above-described system, device, module, unit, etc. can be implemented by computer program modules.

[0130] In one embodiment, the computer program can rely on a tangible storage medium such as an optical storage device, a magnetic storage device, etc. In another embodiment, the computer program can also be transmitted, distributed, and downloaded in the form of a signal on a network medium, and be downloaded and installed through the communication part 1009, and / or installed from the detachable medium 1011. The program codes contained in the computer program can be transmitted by any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination of the foregoing.

[0131] In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1009, and / or installed from the detachable medium 1011. When the computer program is executed by the processor 1001, the above-described functions defined in the system of the embodiments of the present application are performed. According to an embodiment of the present application, the above-described system, device, apparatus, module, unit, etc. can be implemented by computer program modules.

[0132] According to embodiments of the present application, program code for implementing the computer programs provided by embodiments of the present application can be written in any combination of one or more programming languages, and can be implemented in a high-level procedural and / or object-oriented programming language, and / or in assembly / machine language. Programming languages include, but are not limited to, Java, C++, python, "C", or the like. Program code can execute entirely on a user's computing device, partly on the user's device, as a stand-alone software package, partly on a remote computing device, or entirely on the remote computing device or server. In the latter scenario, the remote computing device can be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computing device, such as through the Internet using an Internet Service Provider.

[0133] The computer program instructions can also be loaded onto a computer or other programmable information processing apparatus to cause a series of operations to be performed on the computer or other programmable information processing apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable information processing apparatus implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0134] Those skilled in the art will appreciate that features recited in the various embodiments of the present application can be combined and / or integrated in various combinations, even if such combinations have not been explicitly recited in the present application. In particular, the features recited in the various embodiments of the present application can be combined and / or integrated in various combinations, without departing from the spirit and teachings of the present application. All such combinations are within the scope of the present application.

Claims

1. A design method for iron yoke structures based on the variable density method, characterized in that, include: A two-dimensional model of the target device, including the superconducting coil, the workpiece, and the iron yoke, is established. The superconducting coil is used as the excitation source, and its material properties and corresponding electromagnetic boundary conditions are set. The region where the yoke is located is taken as the yoke design space and the corresponding electromagnetic boundary conditions are defined; the yoke design space is divided into n finite elements, and the relative density of each finite element is taken as the design variable according to the variable density method; the filter radius and volume constraint value of the design variable are set; the magnetic flux density of the magnetic pole gap is taken as the objective function and the volume of the yoke is taken as the constraint function to establish a topology optimization model, wherein the magnetic pole gap includes the region where the workpiece is located, and n is a positive integer; The magnetic field distribution of the target device is obtained by performing finite element analysis on the target device using a material property interpolation model. The integral of the magnetic flux density modulus in the magnetic pole gap region is calculated to obtain the function value of the objective function; Solve for the sensitivity of the objective function and constraint function to the design variables; The sensitivity of the objective function and the constraint function is modified according to the filtering radius. The obtained function values ​​of the objective function and the constraint function and their sensitivity information to the design variables are used as input conditions for the gradient optimization algorithm. Under the premise of satisfying the constraint function and the volume constraint value, the design variables are solved and updated. If the change in the value of the objective function is less than the preset convergence tolerance, the structure of the yoke is obtained according to the topology optimization model of the yoke.

2. The method according to claim 1, characterized in that, The magnetic field finite element analysis of the target device using a material property interpolation model includes: Using a solid isotropic material penalty model, the permeability of each finite element is obtained by interpolating the relative permeability and calculating the magnetoresistance. The target device was subjected to magnetic field finite element analysis under the electromagnetic boundary conditions.

3. The method according to claim 2, characterized in that, The process of interpolating relative permeability and calculating magnetic reluctance includes: Obtain the nonlinear magnetic property curve of the iron yoke material, the design variables, and the penalty factor; The relative permeability of the finite element is obtained by interpolation based on a nonlinear permeability model. The magnetic reluctance is calculated based on the dimensions of the finite element.

4. The method according to claim 1, characterized in that, Solving for the sensitivity of the objective function to the design variables includes: In the region of the magnetic pole gap, the sensitivity of the objective function is obtained by integrating twice the product of the magnetic flux density and the rate of change of the design variable.

5. The method according to claim 1, characterized in that, Solving for the sensitivity of the constraint function to the design variables includes: In the yoke design space, the sensitivity of the constraint function to the design variable is obtained by integrating the partial derivatives of the angle variable with respect to its components.

6. The method according to claim 1, characterized in that, Obtaining the structure of the iron yoke based on its topology optimization model includes: Based on a preset threshold, the topology optimization model of the iron yoke is converted into a solid and void distribution to obtain the iron yoke structure after threshold processing. The iron yoke structure after the threshold processing is smoothed to obtain the iron yoke structure.

7. A yoke structure, characterized in that, Obtained by the method described in any one of claims 1 to 6.

8. A design device for an iron yoke structure based on the variable density method, characterized in that, include: The modeling and initialization module is used to establish a two-dimensional model of the target device, which includes a superconducting coil, a workpiece, and a yoke. The superconducting coil is used as the excitation source to set its material properties and corresponding electromagnetic boundary conditions. The optimization model construction module is used to define the corresponding electromagnetic boundary conditions with the region where the yoke is located as the yoke design space; divide the yoke design space into n finite elements, and use the relative density of each finite element as the design variable according to the variable density method; set the filter radius and volume constraint value of the design variable; and establish a topology optimization model with the magnetic flux density of the magnetic pole gap as the objective function and the volume of the yoke as the constraint function, wherein the magnetic pole gap includes the region where the workpiece is located, and n is a positive integer. The magnetic field finite element analysis module is used to perform magnetic field finite element analysis on the target device using a material property interpolation model to obtain the magnetic field distribution of the target device. The objective function calculation module is used to calculate the integral of the magnetic flux density modulus in the magnetic pole gap region to obtain the function value of the objective function; The sensitivity analysis module is used to solve the sensitivity of the objective function and constraint function to the design variables; The solution and variable update module is used to modify the sensitivity of the objective function and the constraint function according to the filtering radius, and to use the obtained function values ​​of the objective function and the constraint function and their sensitivity information to the design variables as input conditions for the gradient-type optimization algorithm. Under the premise of satisfying the constraint function and volume constraint values, it solves and updates the design variables; and The structure acquisition module is used to obtain the structure of the yoke based on the topology optimization model of the yoke if the change in the function value of the objective function is less than a preset convergence tolerance.

9. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs. The characteristic feature is that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 6.

11. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 6.

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