Laser design method adopting topological optimization technology

Abstract

The invention belongs to the field of laser structure design, and particularly discloses a laser design method adopting a topological optimization technology, which comprises the following steps of: filling traditional weight-reduced holes and grooves of a laser structure needing to be optimized, and carrying out single-target variable-density method topological optimization on sub-targets under multiple targets; meanwhile, all numerical values of the iteration process under the target and under all other dynamic and static optimization target working conditions under the target are required, sub-target weights are determined through a grey correlation method, min-max normalization is carried out firstly, an initial matrix is constructed, the row index of the matrix A is each sub-target such as a target 1 and a target 2, namely, an evaluation object, and the row index of the matrix B is an evaluation object; column indexes are normalized flexibility and normalized modal frequencies of other targets under each sub-target, namely, the normalized flexibility and the normalized modal frequencies are used as indexes, and an optimal value of each column is used as a mother sequence to construct a reference matrix.

Description

Technical Field

[0001] The present invention relates to the field of laser structure design, and particularly to a laser design method using topology optimization technology. Background Art

[0002] The processing of solid laser structures often relies on traditional subtractive manufacturing methods. Using subtractive manufacturing methods will impose some limitations on the mechanism design of lasers, mainly reflected in the following aspects. For some small-volume lasers, the structural components of the laser have the characteristics of small size and thin wall thickness, and the distance between the structural components of the laser is relatively close, which requires high requirements for the cutting tools and equipment for processing lasers. Therefore, the vast majority of subtractive manufacturing solid lasers adopt the traditional method of machining mechanical structures in parts and then assembling them.

[0003] In order to achieve higher automation and avoid mechanical assembly to the greatest extent, a solid laser based on the fused deposition modeling (FDM) additive manufacturing technology is proposed. By using the "print - pause - print" method of the FDM printer, optical components are successfully embedded into the mechanical structure.

[0004] Since the FDM forming uses filamentous plastic as the material, which has the characteristics of low melting temperature and high precision, the optical components can be conveniently placed directly on the formed structure, and printing can continue on the optical components and the plastic, so that the optical components are accurately and firmly embedded in the printed structure.

[0005] The above method has great limitations on the processing materials. Plastic materials often have disadvantages such as easy degradation, poor thermal conductivity, and lower strength than metal materials, which severely limit the application of additive manufacturing lasers.

[0006] To solve this problem, a space-grade laser is first successfully processed using metal materials by selective laser melting (SLM) printing technology. However, during the processing of the laser, there are often trade-offs among the three requirements of structural strength, modal frequency, and lightweight. Therefore, there is an urgent need for a laser design method using topology optimization technology to solve the above problems. Summary of the Invention

[0007] To solve the above technical problems, the present invention provides a laser design method using topology optimization technology.

[0008] To achieve the above object, the present invention is implemented according to the following technical solution: A laser design method using topology optimization technology, which fills the traditional weight-reducing holes and grooves of the laser structure to be optimized.

[0009] (2) Perform single-objective variable density method topology optimization for sub-objectives under multiple objectives, and at the same time obtain all the numerical values in the iterative process under this objective and all other dynamic and static optimization objective conditions. The mathematical expression of the minimum compliance topology optimization under the maximum volume constraint of the single-objective static condition can be expressed as: ; In the formula: is the design variable (element relative density), and its value range is (0, 1); is the minimum relative density (to avoid singularity); is the structural compliance; is the structural volume during the optimization process; is the initial volume of the structure; The expression of the single-objective modal frequency topology optimization is as follows. Similarly, all the numerical values in the iterative process under this objective and all other dynamic and static optimization objective conditions need to be obtained: ; In the formula: is the design variable (element relative density), and its value range is (0, 1); is the minimum relative density (to avoid singularity); is the structural modal compliance; is the structural volume during the optimization process; is the initial volume of the structure; (3) Use the grey relational analysis method to determine the sub-objective weights. First, perform min-max normalization. First, normalize the compliance of the optimization results of each optimization sub-objective and the compliance of all other objective conditions under this optimization objective respectively: ; Normalize the frequency of the optimization results of each optimization sub-objective and the frequency of all other objective conditions under this optimization objective: ; (4) Construct the initial matrix , the row index of matrix A is each sub-objective such as objective 1, objective 2, which is the evaluation object, and the column index is the normalized compliance and normalized modal frequency of other objectives under each sub-objective, which are the indicators; (5) Take the optimal value of each column as the mother sequence , and construct the reference matrix B: ; (6) Find the maximum and minimum values of the reference matrix and , and calculate the grey correlation coefficient of the word target to obtain the correlation coefficient matrix : ; Where: The value range is (0, 1), which 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.

[0010] (7) Use the entropy weight method to determine the weights of the grey correlation coefficients of each index. First, calculate the frequency matrix G: ; (8) Calculate the normalized information entropy of the j-th index , the larger it is, the smaller the variation degree of the index, and the smaller the weight coefficient of this index: ; In the formula, if there is , in order to avoid the situation where is not defined, let this product term be 0, that is ; (9) Calculate the weights of each index: ; (10) According to the weights of each index , the correlation degree of the evaluation object can be calculated: ; (11) From the above process, a functional formula of the correlation degree of the evaluation object with respect to the resolution coefficient is obtained . Divide into appropriate equally spaced partition values, sort the sizes of the correlation degrees of the mother and son tables under each value, define the important sorting as the sorting with the most occurrences, and take the resolution coefficient values of their sorting to form an important sorting resolution coefficient sequence ; (12) Find the one that makes variance the largest The element value in the sequence is the resolution coefficient of the resolution coefficient matrix, denoted as , and calculate the correlation degree of the evaluation object: ; (13) Calculate the topological optimization weight: ; (12) Establish a multi-objective topology optimization mathematical model based on the weights of the obtained sub-goals, and perform topology optimization by the variable density method; ; is the design variable (element relative density), and its value range is (0, 1); is the minimum relative density (to avoid singularity); is the multi-objective optimization function; is the structural volume during the optimization process; is the initial volume of the structure; Reconstruct the structure of the laser according to the density cloud map of the optimization result.

[0011] Perform finite element analysis to verify the structural performance of the laser.

[0012] Compared with the prior art, the present invention first performs grid topology optimization, then uses the relationship between the mechanical properties and density threshold after grid topology optimization to perform topology optimization on the laser workbench, and then fills the grid after topology optimization to realize a variable density structure to give full play to the performance of variable density topology optimization; while reducing the weight of the laser, the present invention ensures the maximum stiffness of the laser, and can ensure that the structure reconstructed after the variable density method topology optimization of the laser workbench is distributed according to the variable density, avoiding the problem of large differences in mechanical properties after optimization and reconstruction, giving full play to the role of variable density topology optimization, and ensuring that the structure reconstructed after topology optimization has equivalent mechanical properties to the topology-optimized structure. Description of the Drawings

[0013] Figure 1 is the flow chart of the present invention; Figure 2 is a schematic diagram of the laser workbench to be optimized in the prior art; Figure 3 is a schematic diagram of the optimized laser workbench; Figure 4 is the acceleration direction diagram of the structural performance test of the present invention; Figure 5 is the upward acceleration stress cloud map of the present invention; Figure 6 is the downward acceleration test acceleration stress cloud map of the present invention; Figure 7 is the forward acceleration test acceleration stress cloud map of the present invention; Figure 8 is the ground backward acceleration test acceleration stress cloud map of the present invention; Figure 9Acceleration stress nephogram of the ground leftward acceleration test for the present invention; Figure 10 7th order vibration mode diagram of the present invention; Figure 11 8th order vibration mode diagram of the present invention; Figure 12 9th order vibration mode diagram of the present invention; Figure 13 Structural diagram of the filled laser for the present invention; Figure 14 3D model diagram of the laser after assembly completion for the present invention. Detailed implementation manners

[0014] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the invention.

[0015] As Figure 1 shown, this embodiment exemplarily shows a laser design method using topology optimization technology, filling the traditional holes and grooves for weight reduction of the laser structure to be optimized.

[0016] (2) Conduct single-objective variable density method topology optimization for sub-objectives under multiple objectives, and at the same time, all numerical values in the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective should be obtained. The mathematical expression for the minimum compliance topology optimization under the maximum volume constraint of the single-objective static condition can be expressed as: ; In the formula: is the design variable (element relative density), and its value range is (0, 1); is the minimum relative density (to avoid singularity); is the structural compliance; is the structural volume during the optimization process; is the initial volume of the structure; The expression for single-objective modal frequency topology optimization is as follows. Similarly, all numerical values in the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective should be obtained: ; In the formula: is the design variable (element relative density), and its value range is (0, 1); is the minimum relative density (to avoid singularity); is the structural modal flexibility; is the structural volume during the optimization process; is the initial volume of the structure; Use the grey relational analysis method to determine the sub - objective weights. First, perform min - max normalization. First, normalize the flexibility of the optimization results of each optimization sub - objective and the flexibility under all other objective conditions of this optimization objective respectively: ; Normalize the frequency of the optimization results of each optimization sub - objective and the frequency under all other objective conditions of this optimization objective: ; (4) Construct the initial matrix , the row index of matrix A is each sub - objective such as objective 1, objective 2, which are the evaluation objects, and the column index is the normalized flexibility and normalized modal frequency of other objectives under each sub - objective, which are the indicators; (5) Take the optimal value of each column as the mother sequence , and construct the reference matrix B; ; (6) Find the maximum value and minimum value of the reference matrix and , calculate the grey relational coefficients of the sub - objectives to obtain the grey relational coefficient matrix ; ; Among them: is the resolution coefficient, and its value range is (0, 1). It is the independent variable of a function. Therefore, this formula is an algebraic calculation formula. A method for finding a suitable resolution coefficient will be given later.

[0017] (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: ; (8) Calculate the normalized information entropy of the j - th index , the larger it is, the smaller the variation degree of the index, and the smaller the weight coefficient of this index: ; In the formula, if there is , to avoid the situation where is not defined, let this product term be 0, that is ; (9) Calculate the weights of each index: ; (10) According to the weights of each index , the correlation degree of the evaluation object can be calculated: ; (11) From the above process, the functional formula of the correlation degree of the evaluation object with respect to the discrimination coefficient is obtained . By making appropriate equally spaced division and taking values of , sorting the correlation degrees of the sub - alphabet table under each value, defining the important sorting as the sorting with the most occurrences, and taking the discrimination coefficient values corresponding to them to form the discrimination coefficient sequence of the important sorting ; (12) Find the element value in the sequence that makes the variance the largest. Denote this value as the discrimination coefficient of the discrimination coefficient matrix, denoted as , and calculate the correlation degree of the evaluation object: ; (13) Calculate the topological optimization weight: ; (13) Establish a multi - objective topological optimization mathematical model based on the weights of the obtained sub - objectives, and perform variable density method topological optimization: ; is the design variable (element relative density), and its value range is (0, 1); is the minimum relative density (to avoid singularity); is the multi - objective optimization function; is the structural volume during the optimization process; is the initial volume of the structure; According to the density cloud map of the optimization result, reconstruct the structure of the laser.

[0018] Conduct finite element analysis to verify the structural performance of the laser.

[0019] The technical solution of the present invention is not limited to the limitations of the above - mentioned specific embodiments. Any technical changes made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims

1. A laser design method using topology optimization technology, characterized in that, It includes the following steps: S100. Fill the holes and grooves of the traditional weight reduction of the laser structure to be optimized. S200. Conduct single-objective variable density method topology optimization for sub-objectives under multiple objectives, and at the same time obtain all the numerical values of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective. S300. Use the grey relational method to determine the sub-objective weights, and first perform min-max normalization. S400. Construct the initial matrix , the row indices of matrix A are each sub-goal such as Goal 1, Goal 2, which are the evaluation objects, and the column indices are the normalized flexibility and normalized modal frequency of other goals under each sub-goal, which are the indicators; S500. Using the optimal value of each column as the mother sequence , construct the reference matrix B; S600. Find the maximum and minimum values of the reference matrix and , calculate the grey correlation coefficient of the word target to obtain the correlation coefficient matrix ; S700. Use the entropy weight method to determine the weights of the grey relational coefficients for evaluating each index. S800, Calculate the normalized information entropy of the j-th indicator ; S900. Calculate the weight values of each index and, based on the weight values of each index , the correlation degree of the evaluation object can be calculated; S1000. The functional formula of the relevance degree of the evaluation object with respect to the discrimination coefficient is obtained from the above process. . Appropriately equally spaced partition and take values for . Sort the relevance degrees of the parent-child tables under each value, define the important sorting as the sorting with the most occurrences, and take the discrimination coefficient values of them to form the important sorting discrimination coefficient sequence ; S1100: Search for the one that makes variance the largest The element value in the sequence is the discrimination coefficient of the discrimination coefficient matrix, denoted as , and calculate the correlation degree of the evaluation object; S1200: Calculate the topology optimization weights, establish a multi-objective topology optimization mathematical model based on the obtained sub-objective weights, and conduct variable density method topology optimization. S1300: According to the density cloud map of the optimization results, reconstruct the laser structure and conduct finite element analysis to verify the structural performance of the laser.

2. The laser design method using topology optimization technology according to claim 1, characterized in that, The minimum compliance topology optimization mathematical expression under the maximum volume constraint of the single-objective static condition in step S200 can be expressed as: ； In the formula: is a design variable, and its value range is 0 - 1; is the minimum relative density; is the structural flexibility; For the structure volume during the optimization process; is the initial volume of the structure.

3. The laser design method using topology optimization technology according to claim 1, characterized in that, The modal frequency topology optimization expression of the single-objective in step S200 is as follows. Similarly, all the numerical values of the iterative process under this objective and all other dynamic and static optimization objective conditions under this objective should be obtained: ; In the formula: is a design variable, and its value range is 0 - 1; is the minimum relative density; is the structural modal flexibility; For the structural volume during the optimization process; is the initial volume of the structure.

4. The laser design method using topology optimization technology according to claim 1, characterized in that, In step S300, first normalize the compliance of the optimization results of each optimization sub-objective and the compliance under all other objective conditions under this optimization objective: ; Normalize the frequency of the optimization results of each optimization sub-objective and the frequency under all other objective conditions under this optimization objective: 。 5. A laser design method using topology optimization technology according to claim 1, characterized in that, Construct the reference matrix B in S500: ； In S600, the grey correlation coefficient of the word target is calculated to obtain the correlation coefficient matrix : ; Where: is the discrimination coefficient, with a value range of 0 - 1 and being the independent variable of a function. Therefore, this formula is an algebraic calculation formula, and a method for finding a suitable discrimination coefficient will be given later.

6. A laser design method using topology optimization technology according to claim 1, characterized in that, First calculate the frequency matrix G in S700: ； In S800, the larger it is, the smaller the degree of variation of the index, and the smaller the weight coefficient of this index. ; In the formula, if there is , in order to avoid the situation of undefined, let this product term be 0, that is .

7. A laser design method using topology optimization technology according to claim 1, characterized in that, Calculate the weights of each index in S900: ； And according to the weight values of each index , the correlation degree of the evaluation object is calculated; ； The correlation degree of the evaluation object in S1100 is: 。 8. A laser design method using topology optimization technology according to claim 1, characterized in that, Calculate the topology optimization weights in S1200: ； Conduct variable density method topology optimization in S1300: ； is the design variable (relative density of the unit), and its value range is 0 - 1; is the minimum relative density; is a multi-objective optimization function; For the structure volume during the optimization process; is the initial volume of the structure.

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