Lithium extraction rotary kiln light weight cylinder topology optimization design method and system

Abstract

The lithium extraction rotary kiln light-weight cylinder topology optimization design method and system of the application relates to the technical field of structure design, obtains the related parameters of the cylinder, and defines the topology optimization area; taking the related parameters of the cylinder as input characteristics, a machine learning model is constructed, and the output strategy of different topology optimization areas is obtained; the stress information of the topology optimization area is obtained, the stress concentration degree of each point is calculated, and the cylinder is divided into stress concentration areas and non-critical areas based on the stress concentration degree; the corresponding output strategy is executed on the stress concentration areas and the non-critical areas, and the thermal stress response data of the stress concentration areas and the non-critical areas are output; based on the thermal stress response data, local constraints and global constraints are defined, an optimization objective is defined, an optimization model is constructed, and the optimized cylinder topology structure is solved, achieving the balanced consideration of cylinder structure lightweight and thermal stress uniformization.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of structural design, in particular to a topological optimization design method and system for a lightweight cylinder of a rotary kiln for lithium extraction. BACKGROUND

[0002] Ore lithium extraction is an important process link in lithium salt production. Under high temperature conditions, lithium-containing minerals such as spodumene will undergo phase transition to generate crystal phases that are easy to leach lithium. The ore is calcined in a rotary kiln to complete the transformation process. However, the traditional rotary kiln cylinder is a solid cylinder structure, and the cylinder is heavy, and the transmission system is heavily loaded. Therefore, it is of great significance to design the rotary kiln cylinder to be lightweight.

[0003] Traditional lightweight design of structures mainly relies on the experience and intuition of designers, and it is often difficult to obtain the optimal structure. In recent years, topological optimization technology has developed rapidly, especially the design method combining artificial intelligence algorithms with topological optimization, which can automatically search for complex optimal topological structures. Applying this technology to the lightweight design of the rotary kiln cylinder for ore lithium extraction is expected to greatly reduce the weight of the kiln body and improve system efficiency.

[0004] Chinese patent application No. CN117634252A discloses a method for optimizing a ribbed thin-walled cylinder for spinning manufacturing, comprising: step 1, preprocessing the design parameters of the cylinder; step 2, establishing a finite element simulation model of the cylinder; step 3, establishing a topological optimization model of the cylinder and analyzing and solving it; and step 4, post-processing the solution.

[0005] Existing topological optimization methods for cylinders usually use a single-scale modeling strategy, which is difficult to consider the complex thermal stress distribution under high temperature conditions. SUMMARY

[0006] The present application aims to at least partially solve one of the technical problems in the related art. To this end, one object of the present application is to propose a topological optimization design method and system for a lightweight cylinder of a rotary kiln for lithium extraction, which realizes the balanced consideration of cylinder structure lightweight and thermal stress uniformization.

[0007] One aspect of the present application provides a topological optimization design method for a lightweight cylinder of a rotary kiln for lithium extraction, comprising:

[0008] Step S100: Obtain cylinder-related parameters and define a topological optimization region;

[0009] Step S200: Construct a machine learning model with the cylinder-related parameters as input features to obtain output strategies for different topological optimization regions;

[0010] Step S300: Obtain stress information of the topological optimization region, calculate stress concentration degree of each point, and divide the cylinder into a stress concentration region and a non-critical region based on the stress concentration degree;

[0011] Step S400: Perform corresponding output strategies on the stress concentration region and the non-critical region, and output thermal stress response data of the stress concentration region and the non-critical region;

[0012] Step S500: Define local constraints and global constraints based on the thermal stress response data, define an optimization target, construct an optimization model, and solve the optimized cylinder topological structure.

[0013] The specific method for obtaining the cylinder-related parameters and defining the topological optimization region is as follows:

[0014] Step S110: Obtain the geometric parameters of the rotary kiln cylinder; the geometric parameters include the length L, diameter D and wall thickness th of the rotary kiln cylinder;

[0015] Step S120: Obtain the attribute parameters of the lining material of the rotary kiln cylinder; the attribute parameters include the material thermal conductivity , specific heat capacity , density , material elastic modulus E and material thermal expansion coefficient a of the lining material;

[0016] Step S130: Obtain the working condition parameters of the rotary kiln cylinder; the working condition parameters include the inlet flue gas temperature , outlet flue gas temperature and cylinder speed ω of the cylinder;

[0017] Step S140: The geometric parameters, attribute parameters and working condition parameters constitute the cylinder-related parameters;

[0018] Step S150: Define the topological optimization region of the rotary kiln cylinder.

[0019] The specific method for constructing a machine learning model with the cylinder-related parameters as input features and obtaining output strategies of different topological optimization regions is as follows:

[0020] Step S210: Define the input features X of the machine learning model; the input features include the geometric parameters, attribute parameters and working condition parameters of the cylinder;

[0021] Step S220: Define the output strategy Y of the machine learning model; the output strategy Y represents the modeling scale and fidelity adopted in different topological optimization regions;

[0022] The topological optimization region is divided into a stress concentration region and a non-critical region;

[0023] Step S230: Construct a training sample set including N groups of input features and corresponding output strategies, and train the machine learning model based on the training sample set;

[0024] Step S240: Based on the trained machine learning model, input the current input feature X to obtain the recommended output strategy Y, and obtain the modeling scale and fidelity of different topology optimization regions;

[0025] The specific method for obtaining the stress information of the topology optimization region, calculating the stress concentration degree of each point, and dividing the cylinder into a stress concentration region and a non-critical region based on the stress concentration degree is as follows:

[0026] Step S310: Obtain the stress information of each point in the topology optimization region, wherein the stress information includes: von Mises stress , allowable stress , stress gradient, temperature, and material yield strength;

[0027] Step S320: Calculate the stress concentration degree of each point based on the stress information of the point ;

[0028] Step S330: Pre-set a stress concentration threshold, divide the topology optimization region with a stress concentration degree greater than the stress concentration threshold into a stress concentration region , and divide the topology optimization region with a stress concentration degree less than or equal to the stress concentration threshold into a non-critical region .

[0029] The specific method for executing the corresponding output strategy on the stress concentration region and the non-critical region, and outputting the thermal stress response data of the stress concentration region and the non-critical region is as follows:

[0030] Step S410: In the stress concentration region, based on the output strategy obtained by the machine learning model, adaptively divide the hexahedral element grid, and the size of the element grid is equal to the product of the ratio of the reference stress gradient and the stress gradient adopted in the stress concentration region and the modeling scale;

[0031] Step S420: According to the fidelity in the output strategy, adopt a corresponding thermal-structure full coupling method in the stress concentration region to solve the temperature field and the displacement field ; wherein P is a position vector, and t is a time variable;

[0032] Step S430: Update the attribute parameters of each element grid according to the temperature field, and calculate the thermal stress response data of the stress concentration region according to the displacement field;

[0033] Step S440: equivalent the non-critical region of the cylinder to beam elements, determine the beam cross-sectional area and moment of inertia according to the radius and wall thickness of the cylinder, and determine the modeling scale of the non-critical region according to the output strategy determine the element size of the beam element;

[0034] Step S450: select the beam element simplified model according to the fidelity in the output strategy, apply the uniform temperature field and the axial linear temperature field , and solve the displacement field ;

[0035] Step S460: according to the uniform temperature field and the axial linear temperature field , calculate the axial stress and shear stress along the axis of the beam element;

[0036] Step S470: calculate the radial stress and circumferential stress of the non-critical region according to the axial stress and shear stress, and the thermal stress components of the non-critical region are composed of the axial stress, shear stress, radial stress and circumferential stress;

[0037] Step S480: calculate the second von Mises stress according to the thermal stress components of the non-critical region, and for each non-critical region, extract the mean value of the second von Mises stress as the thermal stress response data of the non-critical region.

[0038] The specific method for calculating the thermal stress response data of the stress concentration region according to the displacement field is:

[0039] Step S431: calculate the strain tensor based on the displacement field, and calculate the stress tensor based on the strain tensor and the temperature field;

[0040] Step S432: based on the stress tensor, express it as a 3x3 matrix in the Cartesian coordinate system, obtain each stress component based on each element of the matrix, and calculate the first von Mises stress based on the stress component;

[0041] Step S433: extract the peak value of the first von Mises stress in each stress concentration region as the thermal stress response data of the stress concentration region.

[0042] The specific method for calculating the displacement field u according to the output strategy in the fidelity selection and adopting the beam element simplified model, applying the uniform temperature field and the axial linear temperature field is:

[0043] Step S451: apply the uniform temperature field and the axial linear temperature field on the beam element;

[0044] Step S452: Calculate the displacement field under the action of the uniform temperature field and the axial linear temperature field by using the beam element finite element method .

[0045] The specific method for defining the local constraint and the global constraint based on the thermal stress response data, defining the optimization target, constructing the optimization model, and solving the optimized cylinder topology structure is as follows:

[0046] Step S510: Define the cylinder lightweight target function and the thermal stress response data peak value target function of the stress concentration area to minimize the total mass M of the cylinder and minimize the thermal stress response data peak value of the stress concentration area as the optimization target, and space variable density as the design variable;

[0047] Step S520: Define the local constraint based on the thermal stress response data of the stress concentration area;

[0048] Step S530: Define the global constraint based on the thermal stress response data of the non-critical area;

[0049] Step S540: Introduce the maximum volume fraction constraint to limit the proportion of the solid element volume V to the total volume of the topology optimization area to not more than the maximum volume fraction ;

[0050] Step S550: Based on the optimization target and the local constraint, the global constraint, and the maximum volume fraction constraint, construct the optimization model, and combine the cylinder lightweight target function and the thermal stress response data peak value target function of the stress concentration area into a single target problem;

[0051] Step S560: Optimize the single target problem to obtain the final cylinder topology structure.

[0052] One aspect of the present application provides a rotary kiln lightweight cylinder topology optimization design system for lithium extraction, comprising:

[0053] A data collection and definition module is configured to obtain cylinder-related parameters and define a topology optimization area.

[0054] A modeling strategy output module is configured to use the cylinder-related parameters as input features to construct a machine learning model and obtain output strategies for different topology optimization areas.

[0055] An optimization area division module is configured to obtain stress information of the topology optimization area, calculate the stress concentration degree of each point, and divide the cylinder into a stress concentration area and a non-critical area based on the stress concentration degree.

[0056] The stress data output module is configured to perform corresponding output strategies on the stress concentration region and the non-critical region, and output thermal stress response data of the stress concentration region and the non-critical region.

[0057] The topology optimization solving module is configured to define local constraints and global constraints based on the thermal stress response data, define an optimization target, construct an optimization model, and solve the optimized cylinder topology structure.

[0058] One aspect of the present application provides a readable storage medium storing a computer program adapted to be loaded by a processor to perform the steps in the method for topology optimization design of a lightweight cylinder of a rotary kiln for lithium extraction.

[0059] The method and system for topology optimization design of a lightweight cylinder of a rotary kiln for lithium extraction according to the present application have the following advantages over the prior art:

[0060] The present application introduces a machine learning model to achieve adaptive selection of modeling strategies. The geometric parameters, material properties and working condition parameters of the cylinder are used as input features to train the machine learning model, which adaptively determines the modeling scale and fidelity used in different regions according to the actual working conditions of the cylinder. This adaptive modeling strategy selection method breaks the limitations of single-scale modeling in traditional topology optimization, allowing high-fidelity detailed modeling in stress concentration regions to accurately capture thermal stress distribution details, and low-fidelity simplified modeling in non-critical regions to reduce computational cost. Compared with the single-scale modeling strategy, this method has significant advantages in terms of computational efficiency and optimization accuracy.

[0061] The present application proposes an innovative stress concentration degree criterion to achieve automatic identification of critical regions. The criterion considers the stress level, stress gradient, temperature influence and material yield strength of each point on the cylinder, and quantitatively evaluates the local stress concentration risk through a dimensionless index. Based on this criterion, the cylinder is divided into stress concentration regions and non-critical regions, allowing different modeling strategies and optimization strategies to be adopted accordingly, avoiding the subjectivity and blindness of manual region division in traditional methods.

[0062] The present application constructs a multi-objective topology optimization model that balances the robustness of thermal stress response while improving the lightweight level of the cylinder. The optimization targets are to minimize the total mass of the cylinder and the thermal stress peak in the stress concentration region, and the design variables are spatial variable density, while considering local stress constraints, global stress constraints and maximum volume fraction constraints. Compared with single-objective optimization, the multi-objective topology optimization model of the present application achieves a better balance between cylinder lightweight and thermal stress uniformization, resulting in a more practical and reliable optimization design scheme.

[0063] The design method provided in the application innovates in aspects of adaptive selection of modeling strategies, identification of key areas, multi-objective optimization, etc., and better solves the problem that existing cylinder topological optimization methods are difficult to balance modeling efficiency and optimization accuracy. Through a machine learning model, automatic mapping from working conditions to modeling strategies is realized, through a stress concentration degree criterion, automatic identification of key areas is realized, and through multi-objective optimization, the balance between lightweight design and thermal stress uniformization is realized. Compared with traditional methods, the application has obviously improved and promoted in computing efficiency, optimization accuracy and design reliability, and provides a new efficient, accurate and practical way for lightweight design of rotary kiln cylinder under high temperature working conditions. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 A method flowchart of the lithium extraction rotary kiln lightweight cylinder topological optimization design method provided in the application;

[0065] Figure 2 A method flowchart of the output strategy acquisition method of different topological optimization areas provided in the application;

[0066] Figure 3 A method flowchart of the stress concentration area and non-key area division method provided in the application;

[0067] Figure 4 A schematic diagram of the lithium ore lithium extraction rotary kiln cylinder provided in the application;

[0068] Figure 5 A functional module diagram of the lithium extraction rotary kiln lightweight cylinder topological optimization design system provided in the application. DETAILED DESCRIPTION

[0069] In order to better understand the application, various aspects of the application will be described in more detail with reference to the accompanying drawings. It should be understood that these detailed descriptions are only descriptions of exemplary embodiments of the application, and do not limit the scope of the application in any way. Throughout the specification, like reference numerals refer to like elements. The expression "and / or" includes any and all combinations of one or more of the associated listed items.

[0070] In the drawings, the size, dimensions and shapes of the elements have been slightly adjusted for ease of illustration. The drawings are merely exemplary and are not drawn strictly to scale. As used in this document, the words "approximately," "about," and similar expressions are used as terms of approximation and not as terms of degree, and are intended to account for the inherent deviations in a measuring or computing process that would be recognized by those of ordinary skill in the art. In addition, in the present application, the order of the steps of the process described does not necessarily represent the order in which the processes occur in actual operation, unless otherwise explicitly limited or derivable from the context.

[0071] It should also be understood that any reference to or discussion of a

[0072] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as is commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an overly literal or overly formal sense.

[0073] It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0074] Embodiment 1

[0075] As shown in the topological optimization design method for the rotary kiln light-weight cylinder for lithium extraction provided by the present application, the method comprises the following steps: Figure 1

[0076] Step S100: Obtain cylinder-related parameters and define a topological optimization region.

[0077] The specific method for obtaining the cylinder-related parameters and defining the topological optimization region is as follows:

[0078] Step S110: Obtain the geometric parameters of the rotary kiln cylinder; the geometric parameters include the length L, diameter D and wall thickness th of the rotary kiln cylinder.

[0079] The method for obtaining the geometric parameters of the rotary kiln cylinder is as follows: the geometric parameters of the rotary kiln cylinder are obtained through three-dimensional scanning measurement.

[0080] Step S120: Obtain the attribute parameters of the lining material of the rotary kiln cylinder; the attribute parameters include the material thermal conductivity , specific heat capacity , density , material elastic modulus E and material thermal expansion coefficient a of the lining material.

[0081] ​The method for obtaining the property parameters of the rotary kiln lining material is as follows: by consulting the physical property handbook of the lining material.

[0082] Step S130: Obtain the operating parameters of the rotary kiln shell; the operating parameters include the inlet flue gas temperature of the shell. outlet flue gas temperature and cylinder rotation speed ω;

[0083] The operating parameters of the rotary kiln shell are measured by sensors.

[0084] Step S140: The geometric parameters, property parameters, and working condition parameters constitute the relevant parameters of the cylinder;

[0085] Step S150: Define the topology optimization region of the rotary kiln shell;

[0086] The topology optimization region is: , where x, r, These represent the axial, radial, and circumferential angular coordinates of a point in the cylinder coordinate system within the topology optimization region, while y and z represent the coordinates of the cylinder cross-section along the cosine direction in the rectangular coordinate system. Direction and sin The projection component of the direction, where R is the radius of the cylinder.

[0087] The radial coordinate r represents the radial distance from the cylinder axis to a point, and the circumferential angular coordinate... This represents the angle of rotation about the axis of the cylinder. Given r and... This allows us to uniquely determine a point on the cross-section of the cylinder, and by adding the axial coordinate x, we can determine the spatial position of any point inside the cylinder. If we need to find the point (x, r, ...) in the cylinder's coordinate system... Convert the coordinates of a point (x, y, z) to a Cartesian coordinate system, where r, y, z are the coordinates of the point. The following relationship exists between y and z: y = r × cos z = r × sin ;

[0088] Step S200: Using the relevant parameters of the cylinder as input features, construct a machine learning model to obtain the output strategies for different topology optimization regions;

[0089] like Figure 2 As shown, the specific method for constructing a machine learning model using cylinder-related parameters as input features to obtain output strategies for different topology optimization regions is as follows:

[0090] Step S210: Define the input features X of the machine learning model, wherein the input features include cylinder geometric parameters, attribute parameters and working condition parameters;

[0091] The input features can be represented as: ;

[0092] Step S220: defining an output strategy Y of the machine learning model, the output strategy Y representing modeling scales and fidelities adopted in different topology optimization regions;

[0093] The topology optimization region is divided into a stress concentration region and a non-critical region;

[0094] The output strategy Y can be represented as: , wherein, respectively represent the modeling scale and the fidelity adopted in the stress concentration region, respectively represent the modeling scale and the fidelity adopted in the non-critical region;

[0095] Step S230: constructing a training sample set including N groups of input features and corresponding output strategies, and training the machine learning model based on the training sample set;

[0096] The machine learning model adopts a support vector machine, performs feature selection and extraction on the input features based on a correlation analysis or a principal component analysis method, obtains a preprocessed training sample set, divides the preprocessed training sample set into a training set and a test set, trains the machine learning model on the training set, learns a mapping relationship between the input features and the output strategies by minimizing a training error, the training error adopts a mean square error loss function, and evaluates the performance of the trained model on the test set; the training sample set is obtained based on an engineering design process.

[0097] Step S240: inputting the current input features X based on the trained machine learning model to obtain a recommended output strategy Y, and obtaining modeling scales and fidelities suitable for different topology optimization regions;

[0098] The machine learning model provided by the above steps adaptively selects appropriate modeling scales and fidelities according to input features of different topology optimization structures; for a stress concentration and a critical region with rapid changes, a high-fidelity local fine modeling is adopted to accurately capture thermal stress distribution details; for a stress concentration and a critical region with rapid changes, a low-fidelity macroscopic simplified modeling is adopted to reduce the calculation cost.

[0099] Step S300: obtaining stress information of a topology optimization region, calculating stress concentration degrees of each point, and dividing the cylinder into a stress concentration region and a non-critical region based on the stress concentration degrees;

[0100] As shown in Figure 3 The specific method for obtaining stress information of a topology optimization region, calculating stress concentration degrees of each point, and dividing the cylinder into a stress concentration region and a non-critical region based on the stress concentration degrees is as follows:

[0101] Step S310: Obtain stress information of each point in the topological optimization region, wherein the stress information comprises: von Mises stress , allowable stress , stress gradient, temperature and material yield strength;

[0102] The calculation method of the von Mises stress is:

[0103] A geometric model and a finite element model of the cylinder are established, boundary conditions and load conditions are applied, and finite element solving is performed to obtain stress components of each point of the cylinder , , , , , ; wherein, is the axial normal stress, is the radial normal stress, is the circumferential normal stress, is the shear stress component along the axial and radial directions on the cross section of the cylinder, represents the shear stress component along the radial and circumferential directions on the cross section of the cylinder, represents the shear stress component along the circumferential and axial directions on the cross section of the cylinder.

[0104] According to the definition formula of the von Mises stress, the von Mises stress of each point is calculated;

[0105] The calculation formula of the von Mises stress is:

[0106] ;

[0107] The von Mises stress is an equivalent stress, which is used to evaluate the yield risk of the material under multi-axial stress state, converts a three-dimensional stress tensor into a scalar value, and is convenient for comparison with the material yield strength.

[0108] The calculation method of the allowable stress is:

[0109] Determined according to the material yield strength and the safety factor; the allowable stress calculation formula is: ; the material yield strength is obtained by consulting a material manual, and the safety factor n is selected by engineering experience; preferably, the safety factor is selected from the range of 1.5-2.0;

[0110] The allowable stress refers to the allowable stress of the material under a certain safety factor, which is determined according to the material yield strength and the safety factor.

[0111] The stress gradient reflects the rate of change of stress along the spatial coordinates, and is used to measure the severity of stress concentration, and the mathematical definition of the stress gradient is the partial derivative of the stress component with respect to the spatial coordinates;

[0112] The calculation formula of the stress gradient is: , represents the rate of change of the von Mises stress in the x, y, and z directions;

[0113] The calculation formula of the rate of change of the von Mises stress in the x direction is: ;

[0114] The calculation formula of the rate of change of the von Mises stress in the y direction is: ;

[0115] The calculation formula of the rate of change of the von Mises stress in the z direction is: ;

[0116] , , , are the sizes of the finite element grid along the x, y, and z directions, respectively, represents the von Mises equivalent stress at the spatial point (x, y, z);

[0117] The calculation method of the temperature is to establish a thermodynamic model, give the initial conditions and boundary conditions of the inlet flue gas temperature and outlet flue gas temperature, and solve the temperature distribution inside the cylinder by using the finite element method ;

[0118] The temperature inside the cylinder is a scalar value, which is used to evaluate the influence of thermal load on the degree of stress concentration.

[0119] The calculation method of the material yield strength is:

[0120] The curve between the material yield strength and the temperature can be represented as: , , , are temperature segmentation points, are constant values of the material yield strength of each temperature section, and T is the temperature inside the cylinder;

[0121] The temperature segmentation points and the constant values of the material yield strength are obtained by consulting the material manual;

[0122] The yield strength of a material refers to the critical stress at which a material undergoes plastic deformation, and it is an important indicator for evaluating material strength. For metallic materials such as steel used in rotary kiln shells, the yield strength typically exhibits a significant temperature dependence, decreasing as temperature increases.

[0123] Step S320: Calculate the stress concentration at each point based on the stress information. ;

[0124] The formula for calculating the degree of stress concentration is: ,in, As a reference stress gradient, For reference temperature, , , For the weighting coefficients, satisfying , Represents an exponential function. Indicates reference temperature The material yield strength at that time;

[0125] The stress concentration level, considering the effects of stress level, stress gradient and temperature, incorporates the influence of material yield strength. An exponential function is used to describe the nonlinear effect when the stress approaches the material yield strength, thus accurately assessing the risk of local stress concentration in the cylinder.

[0126] Step S330: Set a preset stress concentration threshold, and divide the topology optimization region with stress concentration degree greater than the stress concentration threshold into stress concentration regions. Topology optimization regions with stress concentration levels less than or equal to the stress concentration threshold are classified as non-critical regions. ;

[0127] The stress concentration region can be represented as: ;

[0128] The non-critical area can be represented as: ;

[0129] in, This is the stress concentration threshold; the value of the stress concentration threshold is determined by those skilled in the art based on the allowable stress of the material and the safety factor; preferably, =0.8;

[0130] like Figure 4 The diagram shown is a schematic of the rotary kiln shell for lithium extraction from lithium ore provided in this application. The red box area is the stress concentration area, and the white box area is the non-critical area.

[0131] It should be noted that the stress concentration area and the non-critical area are not necessarily two completely split areas, they can be composed of multiple discrete sub-areas, because the stress state of the cylinder structure usually has significant spatial variation characteristics, and the stress concentration points can be distributed in different local positions, so the stress concentration area and the non-critical area can present multiple continuous block areas in space.

[0132] The above steps construct a dimensionless stress concentration degree criterion, which quantitatively evaluates the stress concentration risk of each point of the cylinder by comparing the ratio of the von Mises stress to the allowable stress, the ratio of the stress gradient to the reference stress gradient, the ratio of the temperature to the reference temperature, and considering the nonlinear amplification effect when the stress approaches the yield strength.

[0133] Step S400: performing corresponding output strategies on the stress concentration area and the non-critical area to output the thermal stress response data of the stress concentration area and the non-critical area;

[0134] The specific method of performing corresponding output strategies on the stress concentration area and the non-critical area to output the thermal stress response data of the stress concentration area and the non-critical area is:

[0135] Step S410: in the stress concentration area, based on the output strategy obtained by the machine learning model, adaptively dividing the hexahedral element grid, the size of the element grid is equal to the product of the ratio of the reference stress gradient to the stress gradient adopted in the stress concentration area and the modeling scale;

[0136] The size s of the element grid can be represented as: ;

[0137] Wherein, is the modeling scale;

[0138] The modeling scale used to calculate the size of the element grid is the modeling scale corresponding to the stress concentration area in the output strategy, which serves as the initial element size for adaptively adjusting the size of the element grid when adaptively dividing the hexahedral element grid.

[0139] Figure 4 The stress concentration area in the middle is composed of multiple adaptively divided hexahedral element grids, wherein the size of the element grid is s, high-fidelity refined modeling is performed in the stress concentration area, and the size of the element grid decreases with the increase of the stress gradient , and the grid is encrypted at the stress concentration.

[0140] Adopting adaptive grid division to adjust the element size according to the size of the stress gradient, and encrypting the grid at the stress concentration, not only improves the calculation accuracy, but also avoids excessive calculation amount.

[0141] Step S420: according to the fidelity in the output strategy, a corresponding thermal-structure full coupling method is adopted in the stress concentration area to solve the temperature field and displacement field ; wherein P is a position vector, and t is a time variable;

[0142] The thermal-structure full coupling method includes a heat conduction equation, a momentum balance equation and a constitutive equation;

[0143] The expression of the heat conduction equation is: , wherein Ts is temperature, t is a time variable, is a material thermal conductivity, is a gradient operator, and Q is an internal heat source, is a material elastic modulus, is a material thermal expansion coefficient, is a first reference temperature, and u is displacement;

[0144] The temperature field is a function of the position vector P and the time variable t, and the displacement field is a function of the position vector and the time variable; the position vector P represents a point in space, which is represented in three-dimensional space by ;

[0145] The material thermal conductivity is a function of temperature, and the curve of the material thermal conductivity with temperature is obtained by consulting a material property manual.

[0146] The gradient operator is represented in three-dimensional space as ;

[0147] The internal heat source represents the heat generation inside the material, and its value is set by a person skilled in the art according to actual requirements and experience. Specifically, for a cement rotary kiln, the value range of the internal heat source can be ; for a metallurgical rotary kiln, the value range of the internal heat source can be ; and for a gas medium in the kiln, the value range of the internal heat source can be ;

[0148] The material elastic modulus and the material thermal expansion coefficient represent the mechanical and thermal properties of the material, and are functions related to temperature, and the curves of the material elastic modulus and the material thermal expansion coefficient with temperature are obtained by consulting a material mechanics and thermal properties manual;

[0149] Preferably, the value of the first reference temperature is set to room temperature, i.e. 25 degrees Celsius.

[0150] The expression of the momentum balance equation is: , wherein is a stress tensor, and f is a body force;

[0151] The volume force refers to the distributed load acting inside the material, such as gravity or electromagnetic force;

[0152] Preferably, the volume force can be expressed as Where g is the acceleration due to gravity;

[0153] The expression for the constitutive equation is: ,in, For strain tensor, The material damping coefficient, It is a double dot product;

[0154] The double dot product represents the tensor shrinkage operation;

[0155] The material damping coefficient characterizes the energy dissipation characteristics of the material, and the damping coefficient value of the material is obtained by consulting the material damping characteristic handbook.

[0156] The stress tensor is a function of displacement u and temperature Ts, representing the stress state inside the material.

[0157] The strain tensor represents the deformation state of the material and is a function of the displacement field;

[0158] The formula for calculating the strain tensor is: ,in, Let be the displacement gradient tensor. It is the transpose of the displacement gradient tensor.

[0159] In stress concentration regions, a high-fidelity refined modeling strategy is employed. This strategy determines the element mesh scale based on the modeling scale in the output strategy and selects the appropriate thermal-structural fully coupled method based on the required fidelity. The fidelity determines the complexity of the physical effects considered in the thermal-structural fully coupled method, i.e., the thermal-stress coupling term. and damping term The introduction of;

[0160] Furthermore, the constant values ​​of the material's thermal conductivity, specific heat capacity, density, elastic modulus, and coefficient of thermal expansion in different temperature ranges are represented by piecewise functions.

[0161] The piecewise function can be expressed as: ;in, For the first A temperature range, Let be the constant values ​​of the material's thermal conductivity, specific heat capacity, density, elastic modulus, and coefficient of thermal expansion for the i-th temperature range, and let Ni be the number of temperature ranges.

[0162] The division of the temperature range and the selection of constant values ​​are determined according to the material handbook.

[0163] Step S430: updating the attribute parameters of each unit grid according to the temperature field, and calculating the thermal stress response data of the stress concentration area according to the displacement field;

[0164] The specific method of calculating the thermal stress response data of the stress concentration area according to the displacement field is:

[0165] Step S431: calculating the strain tensor based on the displacement field, and calculating the stress tensor based on the strain tensor and the temperature field;

[0166] The calculation formula of the strain tensor is:

[0167] The calculation formula of the stress tensor is: ; wherein, is the strain tensor, is the symmetric gradient operator, is the stress tensor, is the material attribute matrix;

[0168] The material attribute matrix is updated according to the temperature field and the material attribute temperature dependence.

[0169] Step S432: based on the stress tensor, expressing it as a 3x3 matrix in the Cartesian coordinate system, obtaining each stress component based on each element of the matrix, and calculating the first von Mises stress based on the stress component;

[0170] The stress components of the first von Mises stress include , , , , , ; , , respectively are the axial normal stress, the radial normal stress and the circumferential normal stress of the first von Mises stress, , , respectively are the shear stress components of the first von Mises stress along the axial and radial directions on the cylinder cross section, the shear stress components along the radial and circumferential directions on the cylinder cross section, and the shear stress components along the circumferential and axial directions on the cylinder cross section.

[0171] The stress tensor can be expressed as a 3x3 matrix in the Cartesian coordinate system, and each stress component can be obtained according to the symmetry of the stress tensor, and the first von Mises stress is calculated based on the stress component;

[0172] The calculation formula of the first von Mises stress is:​ ;

[0173] Step S433: extracting the peak value of the first von Mises stress in each stress concentration region as the thermal stress response data of the stress concentration region;

[0174] In the modeling process, the high-fidelity thermal-structure full coupling method is adopted for the stress concentration region, the bidirectional coupling effect between the temperature field and the displacement field is considered, and the thermal stress distribution can be more accurately predicted. At the same time, an adaptive strategy is adopted in meshing, the unit size is adjusted according to the stress gradient, the mesh is encrypted at the stress concentration, and a relatively coarse mesh is used at the stress flat. This adaptive meshing method improves the calculation accuracy while avoiding excessive calculation, and improves the problem of low calculation efficiency of the traditional topology optimization method.

[0175] Step S440: equivalent the non-critical region of the cylinder to a beam element, determining the beam cross-sectional area and the moment of inertia according to the radius and the wall thickness of the cylinder determining the unit size of the beam element;

[0176] The calculation formula of the unit size of the non-critical region is as follows: ;

[0177] The calculation formula of the beam cross-sectional area is as follows: , wherein, is the radius of the rotary kiln cylinder, A is the beam cross-sectional area, and I is the moment of inertia;

[0178] Figure 4 The non-critical region in the beam element simplified model is simplified by low-fidelity simplified modeling. The non-critical region of the cylinder is equivalent to a beam element, and the center line of the beam is the axis of the cylinder.

[0179] The calculation formula of the beam cross-sectional area is as follows: determining the unit size of the beam element refers to dividing the beam element along the axial direction of the cylinder, and the unit length is ;

[0180] Step S450: according to the fidelity selection in the output strategy, adopting the beam element simplified model, applying a uniform temperature field and an axial linear temperature field , and solving the displacement field ;

[0181] The calculation formula of the beam cross-sectional area is as follows: and an axial linear temperature field The specific method for solving the displacement field u is as follows:

[0182] Step S451: applying a uniform temperature field and an axial linear temperature field on the beam element;

[0183] The calculation formula of the uniform temperature field is as follows: ;

[0184] The calculation formula of the axial linear temperature field is as follows: , wherein x represents the coordinate along the x-axis of the cylinder;

[0185] Step S452: calculating the displacement field under the action of the uniform temperature field and the axial linear temperature field by using the beam element finite element method ;

[0186] Specifically, the method for calculating the displacement field under the action of the uniform temperature field and the axial linear temperature field by using the beam element finite element method includes the following steps: obtaining a stiffness matrix of a beam element based on the material elastic modulus, the beam cross-sectional area and the length of the beam element; obtaining equivalent node forces generated by the uniform temperature field and the axial linear temperature field on the beam element respectively; combining the stiffness matrices of the beam elements into a global stiffness matrix and combining the equivalent node forces generated by the uniform temperature field and the axial linear temperature field on the beam elements into a global load vector according to the connection relationship between the beam elements; modifying the global stiffness matrix and the global load vector according to the boundary conditions of the cylinder to obtain a balance equation considering the boundary conditions; solving the balance equation to obtain a node displacement solution vector; and obtaining the displacement field of any point in the beam element by using a shape function difference according to the node displacement solution vector.

[0187] The calculation formula of the stiffness matrix of the beam element is as follows: ; wherein E is the material elastic modulus, A is the beam cross-sectional area, and L is the length of the beam element. The calculation formula of the equivalent node force generated by the uniform temperature field on the beam element is as follows:

[0188] , wherein is the material thermal expansion coefficient. The calculation formula of the equivalent node force generated by the axial linear temperature field on the beam element is as follows:

[0189] ; wherein and are temperature rise values at two ends of the beam element. The balance equation considering the boundary conditions is as follows:

[0190] , wherein is the global stiffness matrix considering the boundary conditions, is the global load vector considering the boundary conditions, and The overall load vector considering the boundary condition is The unknown node displacement vector is

[0191] The node displacement solution vector is ;

[0192] The displacement field of any point in the beam element is , wherein is the beam element shape function matrix, is the beam element node displacement vector.

[0193] The fidelity in the output strategy determines the complexity of the physical effects considered in the simplified modeling of the beam element in the non-critical area, i.e., the simplification of the thermal load distribution form.

[0194] Step S460: According to the uniform temperature field and the axial linear temperature field , the axial stress and the shear stress along the axis of the beam element are calculated;

[0195] The calculation formula of the axial stress is ;

[0196] The calculation formula of the shear stress is ;

[0197] Step S470: According to the axial stress and the shear stress, the radial stress and the circumferential stress of the non-critical area are calculated, and the thermal stress components of the non-critical area are composed of the axial stress, the shear stress, the radial stress and the circumferential stress;

[0198] Further, it is assumed that the normal stress of the cylinder structure in the thickness direction is zero, i.e. For the cylinder structure, the radial stress corresponds to the thickness direction stress under the plane stress state, so it can be assumed that the radial stress is zero, i.e. ; According to the plane stress assumption, the circumferential stress can be calculated by the axial stress and the Poisson's ratio ;

[0199] The calculation formula of the radial stress is ;

[0200] The calculation formula of the circumferential stress is ;

[0201] Step S480: According to the thermal stress components of the non-critical area, the second von Mises stress is calculated, and for each non-critical area, the mean value of the second von Mises stress is extracted as the thermal stress response data of the non-critical area;

[0202] The formula for calculating the second von Mises stress is: ; wherein, is the shear stress component perpendicular to the x-axis plane along the y-axis direction, is the shear stress component perpendicular to the y-axis plane along the z-axis direction, is the shear stress component perpendicular to the z-axis plane along the x-axis direction;

[0203] When the beam element simplified model is used to analyze the thermal stress response of the non-critical area, the beam element simplified model assumes that the beam is stressed and deformed along the x-axis direction, and the deformation and stress in the y-axis direction and the z-axis direction can be ignored, so only the axial stress and shear stress, radial stress and circumferential stress are considered in the beam element simplified model.

[0204] In the non-critical area, the beam element simplified model is used, and the simplified thermal load is applied according to the fidelity in the output strategy. This simplified modeling strategy takes full advantage of the uniform stress distribution in the non-critical area, and can still reasonably evaluate the thermal stress level in the non-critical area on the premise of ensuring the calculation efficiency. Compared with the traditional simplified modeling method, the concept of fidelity is introduced in the present application, making the simplified modeling process more flexible and controllable.

[0205] The above steps specify how to use high-fidelity refined modeling in the stress concentration area and low-fidelity simplified modeling in the non-critical area according to the modeling strategy output by the machine learning model and the division of different areas. The four components in the modeling strategy vector correspond to the modeling scale and fidelity of the two areas respectively, guiding the strategy selection in grid division, thermal-structure coupling equation, material property description and simplified modeling, etc. This adaptive multi-scale and multi-fidelity modeling method can improve the overall calculation efficiency while ensuring the calculation accuracy of the critical area, and provides high-quality thermal stress response information for subsequent topology optimization.

[0206] Step S500: defining local constraints and global constraints based on thermal stress response data, defining optimization objectives, constructing an optimization model, and solving the optimized cylinder topology structure;

[0207] The specific method for defining local constraints and global constraints based on thermal stress response data, defining optimization objectives, constructing an optimization model, and solving the optimized cylinder topology structure is:

[0208] Step S510: defining a cylinder lightweight objective function and a thermal stress response data peak value objective function of the stress concentration area to minimize the total mass M of the cylinder and minimize the thermal stress response data peak value of the stress concentration area The spatial variable density is used as the design variable for the optimization objective.

[0209] The expression of the cylinder lightweight target function is: ; wherein, is the spatial variable density, is the mass property per unit volume;

[0210] The expression of the thermal stress response data peak value target function of the stress concentration area is: ;

[0211] The spatial variable density is a design variable;

[0212] The spatial variable density is an artificial variable introduced in topology optimization, which is used to represent the relative density of the material at each position in the topology optimization area and can continuously change between 0 and 1. The distribution of the spatial variable density field determines the optimized material topology configuration.

[0213] Step S520: defining a local constraint based on the thermal stress response data of the stress concentration area;

[0214] The local constraint is that the peak value of the thermal stress response data of the stress concentration area is less than or equal to the amplification value of the allowable stress;

[0215] The expression of the local constraint is: ; wherein, is the amplification coefficient of the allowable stress, is the peak value of the first von Mises stress of the stress concentration area;

[0216] Preferably, the amplification coefficient value is 1.2;

[0217] Step S530: defining a global constraint based on the thermal stress response data of the non-critical area;

[0218] The global constraint is that the thermal stress response data of the non-critical area is less than or equal to the allowable stress;

[0219] The expression of the global constraint is: ; wherein, is the mean value of the second von Mises stress of the non-critical area;

[0220] Step S540: introducing a maximum volume fraction constraint to limit the proportion of the solid element volume V to the total volume of the topology optimization area to be not more than the maximum volume fraction ;

[0221] The expression of the maximum volume fraction constraint is: ;

[0222] The maximum volume fraction The value is set by a person skilled in the art according to experience.

[0223] Step S550: based on the optimization target and the local constraint, the global constraint and the maximum volume fraction constraint, an optimization model is constructed, and the cylinder lightweight target function and the stress concentration area thermal stress response data peak value target function are combined as a single target problem;

[0224] The function expression of the single target problem is: ; wherein, , are weight coefficients of the cylinder lightweight target function and the stress concentration area thermal stress response data peak value target function, respectively;

[0225] By adjusting the weight coefficients, the optimization preference of quality and stress is dynamically controlled, ;

[0226] Step S560: the single target problem is optimized, and a final cylinder topology structure is obtained.

[0227] The application provides a lithium ore lithium extraction rotary kiln cylinder lightweight design method based on artificial intelligence and multi-scale modeling, introduces a machine learning model to realize adaptive selection of a modeling strategy, proposes a stress concentration degree to realize identification of a key area, constructs a multi-objective topology optimization model to simultaneously improve the lightweight level of the cylinder and the robustness of the thermal stress response, improves the modeling efficiency in the structure design of the rotary kiln cylinder, and provides a new idea and scheme for the structure optimization design of a large rotary equipment.

[0228] Embodiment 2

[0229] As shown in Figure 5 , a rotary kiln lightweight cylinder topology optimization design system for lithium extraction provided by the application includes:

[0230] A data collection definition module is configured to obtain cylinder related parameters and define a topology optimization area.

[0231] A modeling strategy output module is configured to take the cylinder related parameters as input features, construct a machine learning model, and obtain output strategies for different topology optimization areas.

[0232] An optimization area division module is configured to obtain stress information of the topology optimization area, calculate stress concentration degrees of points, and divide the cylinder into a stress concentration area and a non-key area based on the stress concentration degrees.

[0233] A stress data output module is configured to execute corresponding output strategies on the stress concentration area and the non-key area, and output thermal stress response data of the stress concentration area and the non-key area.

[0234] The topological optimization solving module is configured to define local constraints and global constraints based on the thermal stress response data, define an optimization target, construct an optimization model, and solve the optimized topological structure of the cylinder.

[0235] In addition, the parts of the above technical solutions provided in the embodiments of the present application that are consistent with the implementation principles of the corresponding technical solutions in the prior art are not described in detail to avoid excessive repetition.

[0236] The specific embodiments described above further illustrate the objects, technical solutions, and advantages of the present application. It should be understood that the above description is merely a specific embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements, improvements, and the like made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for topological optimization design of a rotary kiln light-weight cylinder for lithium extraction, characterized in that, The method comprises the following steps: obtaining cylinder related parameters and defining a topology optimization region; using the cylinder related parameters as input features to construct a machine learning model and obtain output strategies for different topology optimization regions; the output strategies represent the modeling scale and fidelity adopted in different topology optimization regions; obtaining stress information of the topology optimization region, calculating the stress concentration degree of each point, and dividing the cylinder into a stress concentration region and a non-critical region based on the stress concentration degree; The stress information includes: von Mises stress , allowable stress , stress gradient, temperature and material yield strength; based on the stress information of each point, the stress concentration degree of the point is calculated ; executing corresponding output strategies on the stress concentration region and the non-critical region, and outputting thermal stress response data of the stress concentration region and the non-critical region; defining local constraints and global constraints based on the thermal stress response data, defining an optimization objective, constructing an optimization model, and solving the optimized cylinder topology structure; the specific method for obtaining cylinder related parameters and defining a topology optimization region comprises the following steps: obtaining geometric parameters of the rotary kiln cylinder; the geometric parameters include the length L, diameter D and wall thickness th of the rotary kiln cylinder; Obtaining property parameters of a lining material in a rotary kiln shell, the property parameters including a material thermal conductivity of the lining material , a specific heat capacity , a density , a material elastic modulus E and a material thermal expansion coefficient α Obtain the working condition parameters of the rotary kiln shell; the working condition parameters include shell inlet flue gas temperature , outlet flue gas temperature and shell rotating speed ω; the geometric parameters, attribute parameters and working condition parameters constitute the cylinder related parameters; defining the topology optimization region of the rotary kiln cylinder; the specific method for executing corresponding output strategies on the stress concentration region and the non-critical region and outputting thermal stress response data of the stress concentration region and the non-critical region comprises the following steps: in the stress concentration region, based on the output strategy obtained by the machine learning model, adaptively divide the hexahedral element grid, and the size of the element grid is equal to the product of the ratio of the reference stress gradient and the stress gradient adopted in the stress concentration region and the modeling scale; According to the fidelity in the output strategy, a corresponding thermal-structural full coupling method is adopted in the stress concentration area to solve the temperature field and displacement field ; wherein P is a position vector, and t is a time variable update the attribute parameters of each element grid according to the temperature field, and calculate the thermal stress response data of the stress concentration region according to the displacement field; the specific method for defining local constraints and global constraints based on the thermal stress response data, defining an optimization objective, constructing an optimization model, and solving the optimized cylinder topology structure comprises the following steps: Defining a cylinder lightweighting objective function and a thermal stress response data peak value objective function for the stress concentration area to minimize the cylinder total mass M and minimize the thermal stress response data peak value for the stress concentration area Optimization objectives are defined with spatially varying density as design variables; define local constraints based on the thermal stress response data of the stress concentration region; define global constraints based on the thermal stress response data of the non-critical region; A maximum volume fraction constraint is introduced to limit the ratio of the volume of the solid elements V to the total volume of the topology optimization region to a maximum volume fraction . ; based on the optimization objective and the local constraints, the global constraints and the maximum volume fraction constraint, construct an optimization model, combine the cylinder lightweight objective function and the thermal stress response data peak value objective function of the stress concentration region into a single objective problem; optimize the single objective problem to obtain the final cylinder topology structure.

2. The method for topology optimization design of the rotary kiln light-weight cylinder for lithium extraction according to claim 1, characterized in that, the specific method for using the cylinder related parameters as input features to construct a machine learning model and obtain output strategies for different topology optimization regions comprises the following steps: define the input features X of the machine learning model, which include the geometric parameters, attribute parameters and working condition parameters of the cylinder; define the output strategy Y of the machine learning model; the topology optimization region is divided into a stress concentration region and a non-critical region; construct a training sample set, which includes N groups of input features and corresponding output strategies, and train the machine learning model based on the training sample set; based on the trained machine learning model, input the current input features X to obtain the recommended output strategy Y, and obtain the modeling scale and fidelity of different topology optimization regions.

3. The method for topology optimization design of the rotary kiln light-weight cylinder for lithium extraction according to claim 2, characterized in that, The specific method for obtaining stress information of each point in the topologically optimized region, calculating stress concentration degrees of the points, and dividing the cylinder into stress concentration regions and non-critical regions based on the stress concentration degrees comprises: Obtaining stress information of each point in the topologically optimized region; The preset stress concentration threshold divides the topology optimization region with a stress concentration degree greater than the stress concentration threshold into a stress concentration region divides the topology optimization region with a stress concentration degree less than or equal to the stress concentration threshold into a non-critical region .

4. The method for topology optimization design of the rotary kiln light-weight cylinder for lithium extraction according to claim 3, characterized in that, The specific method for calculating thermal stress response data of the stress concentration regions according to the displacement field comprises: Calculating a strain tensor based on the displacement field, and calculating a stress tensor based on the strain tensor and the temperature field; Based on the stress tensor, expressing it as a 3x3 matrix in a Cartesian coordinate system, obtaining each stress component based on each element of the matrix, and calculating a first von Mises stress based on the stress component; Extracting a peak value of the first von Mises stress in each stress concentration region as thermal stress response data of the stress concentration region.

5. The method for topology optimization design of rotary kiln light-weight cylinder for lithium extraction according to claim 4, characterized in that, The specific method for executing corresponding output strategies on the stress concentration regions and the non-critical regions, and outputting thermal stress response data of the stress concentration regions and the non-critical regions further comprises: equivalent the non-critical region of the cylinder to beam element, determine the beam section area and the moment of inertia according to the radius and the wall thickness of the cylinder, determine the element size of the beam element according to the modeling scale adopted by the non-critical region in the output strategy determine the element size of the beam element; According to the fidelity selection in the output strategy, a beam element simplified model is adopted, and a uniform temperature field is applied and an axial linear temperature field , and the displacement field is solved ; According to the uniform temperature field and the axial linear temperature field , the axial stress and the shear stress along the beam element axis are calculated; Calculating radial stress and circumferential stress of the non-critical regions according to axial stress and shear stress, and constructing thermal stress components of the non-critical regions from the axial stress and the shear stress, the radial stress, and the circumferential stress; Calculating a second von Mises stress according to the thermal stress components of the non-critical regions, and extracting a mean value of the second von Mises stress of each non-critical region as thermal stress response data of the non-critical region.

6. A system for topological optimization design of a rotary kiln lightweight cylinder for lithium extraction, which is used to implement the method for topological optimization design of a rotary kiln lightweight cylinder for lithium extraction according to any one of claims 1-5, characterized in that, Comprise: A data collection definition module for obtaining cylinder-related parameters and defining topologically optimized regions; A modeling strategy output module for constructing a machine learning model with the cylinder-related parameters as input features, and obtaining output strategies for different topologically optimized regions; An optimized region division module for obtaining stress information of the topologically optimized regions, calculating stress concentration degrees of the points, and dividing the cylinder into stress concentration regions and non-critical regions based on the stress concentration degrees; A stress data output module for executing corresponding output strategies on the stress concentration regions and the non-critical regions, and outputting thermal stress response data of the stress concentration regions and the non-critical regions; A topological optimization solving module for defining local constraints and global constraints based on the thermal stress response data, defining an optimization objective, constructing an optimization model, and solving an optimized cylinder topology.

7. A readable storage medium characterized by, The readable storage medium stores a computer program, and the computer program is adapted to be loaded by the processor to execute the steps in the lithium extraction rotary kiln lightweight cylinder topological optimization design method according to any one of claims 1-5.

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