A laser design method using topology optimization technology

Abstract

The application belongs to the field of laser structure design, and specifically discloses a laser design method using a topology optimization technique, wherein traditional weight-reducing holes and grooves of a laser structure to be optimized are filled, multi-target sub-target single-target variable-density method topology optimization is performed, all numbers of an iteration process under the target and under all dynamic and static optimization target working conditions of the target are required, sub-target weights are determined by using a grey correlation method, min-max normalization is first performed, an initial matrix is constructed, row indexes of the matrix A are various sub-targets such as target 1 and target 2, i.e., evaluation objects, column indexes are normalized flexibility and normalized modal frequency of other targets under various sub-targets, i.e., indexes, and a reference matrix is constructed by taking optimal values of each column as a mother sequence.

Description

Technical Field

[0001] This invention relates to the field of laser structure design, and in particular to a laser design method employing topology optimization technology. Background Technology

[0002] The fabrication of solid-state laser structures often relies on traditional subtractive manufacturing methods. However, subtractive manufacturing methods impose some limitations on the mechanical design of lasers, mainly in the following aspects: For some small-volume lasers, the structural components of the laser are characterized by small size and thin wall thickness, and the distance between the structural components of the laser is relatively close, which places high demands on the cutting tools and equipment used to process the laser. Therefore, most subtractive manufacturing solid-state lasers adopt the traditional method of processing the mechanical structure in parts and then assembling them.

[0003] To achieve greater automation and minimize mechanical assembly, a solid-state laser based on deposition fusion (FDM) additive manufacturing technology is proposed. The optical element is successfully embedded into the mechanical structure using the "print-pause-print" method of an FDM printer.

[0004] Because FDM molding uses filament plastic as the material, it has the characteristics of lower melting temperature and higher precision. Optical components can be easily placed directly on the formed structure, and printing can continue on the optical components and plastic, so that the optical components are accurately and firmly embedded in the printed structure.

[0005] The above methods have significant limitations on the materials to be processed. Plastic materials often have disadvantages such as easy degradation, poor thermal conductivity, and lower strength than metal materials, which seriously limit the application of additive manufacturing lasers.

[0006] To address this issue, a space-grade laser was successfully fabricated using selective laser melting (SLM) printing technology on metallic materials. However, the laser fabrication process often faces a trade-off between structural strength, modal frequency, and lightweight requirements. Therefore, there is an urgent need for a laser design method employing topology optimization techniques to solve these problems. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a laser design method employing topology optimization technology.

[0008] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0009] A laser design method employing topology optimization technology fills in the holes and slots that are traditionally used for weight reduction in laser structures requiring optimization.

[0010] (2) Perform single-objective variable density topology optimization for sub-objectives under multi-objective conditions, and simultaneously obtain all numerical values ​​of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective. The mathematical expression for the minimum compliance topology optimization under the maximum volume constraint of the single-objective static condition can be expressed as:

[0011] ;

[0012] In the formula: The design variable (relative density of the element) has a value range of (0,1);

[0013] To achieve the minimum relative density (to avoid singularities);

[0014] For structural flexibility;

[0015] To optimize the structural volume during the process;

[0016] This represents the initial volume of the structure.

[0017] The modal frequency topology optimization expression for a single objective is as follows. Similarly, we need to find all the values ​​of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective:

[0018] ;

[0019] In the formula: The design variable (relative density of the element) has a value range of (0,1);

[0020] To achieve the minimum relative density (to avoid singularities);

[0021] For structural modal compliance;

[0022] To optimize the structural volume during the process;

[0023] This represents the initial volume of the structure.

[0024] (3) Determine the weights of sub-objectives using the grey relational analysis method, first by performing min-max normalization.

[0025] First, the compliance of the optimization result for each optimization sub-objective and the compliance of all other objective conditions under that optimization objective are normalized:

[0026] ;

[0027] Normalize the frequency of the optimization results for each optimization sub-objective and the frequencies for all other objective conditions under that optimization objective:

[0028] ;

[0029] (4) Construct the initial matrix The row index of matrix A is the sub-objective, such as object 1, object 2, which are the evaluation objects. The column index is the normalized compliance and normalized modal frequency of other objects under each sub-objective, which are the indicators.

[0030] (5) Use the optimal value of each column as the parent sequence. Construct reference matrix B:

[0031] ;

[0032] (6) Find the maximum and minimum values ​​of the reference matrix. and The grey relational coefficient of the word targets is calculated to obtain the relational coefficient matrix. :

[0033] ;

[0034] in: The value range is (0, 1), and it is the independent variable of a function. Therefore, this expression is an algebraic expression, and a suitable method for finding the resolution coefficient will be given later.

[0035] (7) Use the entropy weight method to determine the weights of the grey relational coefficients of each evaluation index. First, calculate the frequency matrix G:

[0036] ;

[0037] (8) Calculate the normalized information entropy of the j-th index. The larger the value, the smaller the degree of variation of the indicator, and the smaller the weight coefficient of the indicator.

[0038] ;

[0039] In the formula, if there is In order to avoid If the term is not defined, then set the product term to 0, i.e. ;

[0040] (9) Calculate the weights of each indicator:

[0041] ;

[0042] (10) Based on the weights of each indicator The correlation degree of the evaluated objects can be calculated:

[0043] ;

[0044] (11) The above process yielded the correlation coefficient between the evaluation object and the resolution coefficient. Function ,Will Perform appropriate equidistant partitioning, sort the parent and child tables by their correlation under each value, define the most important ranking as the ranking that appears most frequently, and take their resolution coefficient values ​​to form an important ranking resolution coefficient sequence. ;

[0045] (12) Search for variance The largest The element values ​​in the sequence are the resolution coefficients of the resolution coefficient matrix, denoted as . And calculate the correlation degree of the evaluation objects:

[0046] ;

[0047] (13) Calculate the topology optimization weights:

[0048] ;

[0049] (12) Establish a multi-objective topology optimization mathematical model based on the obtained sub-objective weights, and perform topology optimization using the variable density method;

[0050] ;

[0051] The design variable (relative density of the element) has a value range of (0,1);

[0052] To achieve the minimum relative density (to avoid singularities);

[0053] It is a multi-objective optimization function;

[0054] To optimize the structural volume during the process;

[0055] This represents the initial volume of the structure.

[0056] Based on the density cloud map of the optimization results, the laser structure is reconstructed.

[0057] Finite element analysis was performed to verify the structural performance of the laser.

[0058] Compared with existing technologies, this invention first optimizes the mesh topology, then uses the relationship between the mechanical properties of the optimized mesh and the density threshold to optimize the laser stage topology, and then fills the stage with the topology-optimized mesh to achieve a variable density structure and fully utilize the performance of variable density topology optimization. This invention reduces the weight of the laser while ensuring maximum stiffness of the laser. It ensures that the structure reconstructed after the variable density topology optimization of the laser stage follows a variable density distribution, avoiding the problem of large differences in mechanical properties between the optimized and reconstructed structures. This fully utilizes the role of variable density topology optimization and ensures that the reconstructed structure has comparable mechanical properties to the optimized structure. Attached Figure Description

[0059] Figure 1 This is a flowchart of the present invention;

[0060] Figure 2 This is a schematic diagram of a laser stage in the prior art that needs to be optimized.

[0061] Figure 3 This is a schematic diagram of the optimized laser stage;

[0062] Figure 4 This is the acceleration pattern for structural performance testing of the present invention;

[0063] Figure 5 This is the upward acceleration stress cloud diagram of the present invention;

[0064] Figure 6 This is an acceleration stress cloud diagram for the downward acceleration test of the present invention;

[0065] Figure 7 This is an acceleration stress cloud diagram for the forward acceleration test of the present invention;

[0066] Figure 8 This is a back-to-back acceleration test acceleration stress cloud diagram of the present invention;

[0067] Figure 9 This is a leftward acceleration stress cloud diagram for the ground acceleration test of the present invention;

[0068] Figure 10 This is the 7th order mode shape diagram of the present invention;

[0069] Figure 11 This is the 8th order mode shape diagram of the present invention;

[0070] Figure 12 This is the 9th order mode shape diagram of the present invention;

[0071] Figure 13 This is a structural diagram of the laser after filling according to the present invention;

[0072] Figure 14This is a three-dimensional model of the laser after assembly according to the present invention. Detailed Implementation

[0073] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0074] like Figure 1 As shown in the figure, this embodiment exemplarily demonstrates a laser design method using topology optimization technology, which fills the holes and slots in the traditional weight-reduction laser structure that need to be optimized.

[0075] (2) Perform single-objective variable density topology optimization for sub-objectives under multi-objective conditions. At the same time, it is necessary to find all the numerical values ​​of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective. The mathematical expression of the minimum compliance topology optimization under the maximum volume constraint of the single-objective static condition can be expressed as:

[0076] ;

[0077] In the formula: The design variable (relative density of the element) has a value range of (0,1);

[0078] To achieve the minimum relative density (to avoid singularities);

[0079] For structural flexibility;

[0080] To optimize the structural volume during the process;

[0081] This represents the initial volume of the structure.

[0082] The modal frequency topology optimization expression for a single objective is as follows. Similarly, we need to find all the values ​​of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective:

[0083] ;

[0084] In the formula: The design variable (relative density of the element) has a value range of (0,1);

[0085] To achieve the minimum relative density (to avoid singularities);

[0086] For structural modal compliance;

[0087] To optimize the structural volume during the process;

[0088] This represents the initial volume of the structure.

[0089] The weights of sub-objectives are determined using the grey relational analysis method, first by performing min-max normalization.

[0090] First, the compliance of the optimization result for each optimization sub-objective and the compliance of all other objective conditions under that optimization objective are normalized:

[0091] ;

[0092] Normalize the frequency of the optimization results for each optimization sub-objective and the frequencies for all other objective conditions under that optimization objective:

[0093] ;

[0094] (4) Construct the initial matrix The row index of matrix A is the sub-objective, such as object 1, object 2, which are the evaluation objects. The column index is the normalized compliance and normalized modal frequency of other objects under each sub-objective, which are the indicators.

[0095] (5) Use the optimal value of each column as the parent sequence. Construct reference matrix B;

[0096] ;

[0097] (6) Find the maximum and minimum values ​​of the reference matrix. and The grey relational coefficient of the word targets is calculated to obtain the relational coefficient matrix. ;

[0098] ;

[0099] in: The resolution coefficient, with a range of (0, 1), is the independent variable of a function. Therefore, this formula is an algebraic calculation formula, and a suitable method for finding the resolution coefficient will be given later.

[0100] (7) Use the entropy weight method to determine the weights of the grey relational coefficients of each evaluation index. First, calculate the frequency matrix G:

[0101] ;

[0102] (8) Calculate the normalized information entropy of the j-th index. The larger the value, the smaller the degree of variation of the indicator, and the smaller the weight coefficient of the indicator.

[0103] ;

[0104] In the formula, if there is In order to avoid If the term is not defined, then set the product term to 0, i.e. ;

[0105] (9) Calculate the weights of each indicator:

[0106] ;

[0107] (10) Based on the weights of each indicator The correlation degree of the evaluated objects can be calculated:

[0108] ;

[0109] (11) The above process yielded the correlation coefficient between the evaluation object and the resolution coefficient. Function ,Will Perform appropriate equidistant partitioning, sort the parent and child tables by their correlation under each value, define the most important ranking as the ranking that appears most frequently, and take their resolution coefficient values ​​to form an important ranking resolution coefficient sequence. ;

[0110] (12) Search for variance The largest The element values ​​in the sequence are the resolution coefficients of the resolution coefficient matrix, denoted as . And calculate the correlation degree of the evaluation objects:

[0111] ;

[0112] (13) Calculate the topology optimization weights:

[0113] ;

[0114] (13) Establish a multi-objective topology optimization mathematical model based on the obtained sub-objective weights, and perform variable density topology optimization:

[0115] ;

[0116] The design variable (relative density of the element) has a value range of (0,1);

[0117] To achieve the minimum relative density (to avoid singularities);

[0118] It is a multi-objective optimization function;

[0119] To optimize the structural volume during the process;

[0120] This represents the initial volume of the structure.

[0121] Based on the density cloud map of the optimization results, the laser structure is reconstructed.

[0122] Finite element analysis was performed to verify the structural performance of the laser.

[0123] The technical solutions of the present invention are not limited to the specific embodiments described above. Any technical changes made in accordance with the technical solutions of the present invention shall fall within the protection scope of the present invention.

Claims

1. A laser design method employing topology optimization technology, characterized in that, Includes the following steps: S100. Fill the holes and slots in the laser structure that need to be optimized to reduce weight. S200. Perform single-target variable density topology optimization of sub-targets under multiple targets for holes and slots in the filled laser structure. At the same time, find all the values ​​of the iterative process under the target and all other dynamic and static optimization target conditions under the target. S300. Use the grey relational analysis method to determine the weights of sub-targets, and first perform min-max normalization. S400, Construct the initial matrix The row indices of matrix A represent the sub-objectives, which are the evaluation objects, and the column indices represent the normalized compliance and normalized modal frequencies of other objectives under each sub-objective, which are the indicators. S500, using the optimal value of each column as the parent sequence. Construct reference matrix B; S600, Find the maximum and minimum values ​​of the reference matrix. and The grey relational coefficients of the sub-targets are calculated to obtain the relational coefficient matrix. ; S700. Use the entropy weight method to determine the weights of the grey relational coefficients of each evaluation indicator; S800, Calculate the normalized information entropy of the j-th index. ; S900, Calculate the weight of each indicator and based on the weight of each indicator... This allows us to calculate the correlation degree of the evaluation objects; S1000, The above process yielded the correlation coefficient between the evaluation object and the resolution coefficient. Function ,Will Perform appropriate equidistant partitioning, sort the parent and child tables by their correlation under each value, define the most important ranking as the ranking that appears most frequently, and take their resolution coefficient values ​​to form an important ranking resolution coefficient sequence. ; S1100: Searching for... variance The largest The element values ​​in the sequence are the resolution coefficients of the resolution coefficient matrix, denoted as . And calculate the correlation degree of the evaluation objects; S1200: Calculate the topology optimization weights, establish a multi-objective topology optimization mathematical model based on the obtained sub-objective weights, and perform variable density topology optimization. S1300: Based on the density cloud map of the optimization results, the laser structure is reconstructed, and finite element analysis is performed to verify the structural performance of the laser. In step S200, the mathematical expression for the minimum compliance topology optimization under the maximum volume constraint of the single-objective static working condition can be expressed as: ； In the formula: This is a design variable, and its value range is 0-1; The minimum relative density; C represents structural flexibility; To optimize the structural volume during the process; This represents the initial volume of the structure. The modal frequency topology optimization expression for a single objective in step S200 is as follows. Similarly, all values ​​of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective are required: ; In the formula: This is a design variable, and its value range is 0-1; The minimum relative density; f represents the structural modal compliance; To optimize the structural volume during the process; This represents the initial volume of the structure. To represent the n-dimensional real space, that is, the value space of the design variables; ,..., These are the relative densities of the 1st to the nth units, respectively.

2. The laser design method using topology optimization technology according to claim 1, characterized in that, In step S300, the compliance of the optimization result for each optimization sub-objective and the compliance of all other objective conditions under that optimization objective are first normalized: ; Normalize the frequency of the optimization results for each optimization sub-objective and the frequencies for all other objective conditions under that optimization objective: ； —Scheme numbers for single-objective optimization with different sub-objectives, used to distinguish different single-objective optimizations; — Sub-target subscript number, used to distinguish different sub-targets; —with the first The result of single-objective optimization of each sub-objective is the compliance optimization result under the i-th sub-objective. —with the first The normalized value of the frequency optimization result under the i-th sub-objective for single-objective optimization of each sub-objective.

3. The laser design method using topology optimization technology according to claim 1, characterized in that, Construct reference matrix B in S500: ； In S600, the grey relational coefficient of the word targets is calculated to obtain the relational coefficient matrix. ; ; in: The resolving factor, which takes values ​​from 0 to 1, is the independent variable of a function.

4. The laser design method using topology optimization technology according to claim 1, characterized in that, In S700, the frequency matrix G is calculated first: ； In S800, the larger the value, the smaller the degree of variability of the indicator, and the smaller the weight coefficient of the indicator. ; In the formula, if there is In order to avoid If the term is not defined, then set the product term to 0, i.e. =0.

5. A laser design method employing topology optimization technology according to claim 1, characterized in that, Calculate the weights of each indicator in S900: ； And based on the weights of each indicator Calculate the correlation degree of the evaluation object; ； The correlation of the objects evaluated in S1100 is as follows: ； Calculate the topology optimization weights in S1200: ； In S1300, topology optimization using the variable density method is performed: ； x is a design variable, and its value ranges from 0 to 1; The minimum relative density; f(x) is a multi-objective optimization function; To optimize the structural volume during the process; This represents the initial volume of the structure. —A space described by n real numbers; —Relative density of the unit cell, with a value range of (0, 1); —The weights ultimately used in topology optimization; —A function of the i-th compliance sub-objective with respect to the design variable vector of the structural design domain; —A function of the i-th frequency sub-objective with respect to the design variable vector of the structural design domain; —The maximum frequency among different single-objective optimization schemes under the i-th sub-objective; —The minimum frequency among different single-objective optimization schemes under the i-th sub-objective.

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