A modeling and optimization method for a porous lightweight structure of a space optical mirror

Abstract

The application relates to a modeling and optimization method of a porous lightweight structure of a space optical mirror, which comprises the following steps: calculating a mirror surface deformation sensitivity distribution; obtaining initial Voronoi sites and structures through weighted sampling; performing overall iteration and local optimization; and obtaining a mirror porous lightweight structure model through matching and fusion. Compared with traditional lightweight schemes such as triangular and hexagonal schemes, the method further utilizes the design freedom degree endowed by additive manufacturing, can effectively realize smaller self-weight deformation under the same material consumption, improves the scientificity of the lightweight design, and improves the working efficiency.

Description

Technical Field

[0001] This invention relates to the field of lightweight structure design technology, and in particular to a modeling and optimization method for a porous lightweight structure of a space optical mirror. Background Technology

[0002] With the rapid development of additive manufacturing technology, porous structures, represented by Voronoi structures, have been widely used in fields such as medical and aerospace due to their high degree of optimization freedom, strong boundary adaptability, and excellent comprehensive performance.

[0003] As a key component of optical systems, optical mirrors are increasingly struggling to meet the demands for higher weight reduction rates and surface accuracy through traditional lightweight structural designs that rely on regular weight-reduction holes on the back of the mirror. The application of 3D printing in mirror manufacturing has made it possible to fabricate complex lightweight structures, allowing Voronoi structures to be extended to lightweight mirror design. Numerous researchers have conducted research in this area in recent years.

[0004] In 2018, Atkins et al. implemented a density gradient Voronoi support structure in plane mirror design, obtaining a variable density sandwich structure between the mirror and the base. However, the inventors found that this method only changes the density distribution of the structure in one direction and cannot achieve overall structural adjustment.

[0005] In 2019, HILPERT et al. proposed a two-dimensional Voronoi filling structure, but the inventors found that this modeling method had poor boundary handling capabilities and did not perform well in matching mirrors with irregular shapes such as internal support holes.

[0006] In 2021, von Lukowicz et al. used a two-dimensional random Voronoi foam structure to realize a lightweight reflector, which improved the structural stiffness and fundamental frequency of the reflector. However, the inventors found that this method did not perform iterative optimization of the structure or handle boundary details, nor did it optimize the structure according to the actual load conditions of the reflector.

[0007] In 2022, ZHANG et al. used topology optimization to obtain a hierarchical distribution of sites in the Voronoi structure, achieving targeted optimization of the internal filling structure of the reflector. However, the inventors found that the structure generated by this algorithm contained closed structures, making it difficult to apply to the 3D printing and manufacturing of metal reflectors.

[0008] Because space mirrors operate in the microgravity environment of space, but their manufacturing and polishing processes are completed on Earth, lightweight design primarily considers their own weight rather than external load conditions. The inventors discovered that targeted designs to match the mirror's own weight were rarely considered in previous methods. Furthermore, existing designs mostly focus on lightweighting and optimizing the entire mirror body. They do not consider the performance loss and manufacturing impact of structural features such as support holes and central holes on porous structures, making them unsuitable for mirrors with internal support holes. Summary of the Invention

[0009] The present invention aims to solve the technical problems in the prior art by providing a modeling and optimization method for a porous lightweight structure of a space optical mirror.

[0010] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0011] A method for modeling and optimizing a porous lightweight structure for a space optical mirror includes the following steps:

[0012] Step i: Calculate the distribution of mirror surface deformation sensitivity;

[0013] Step ii: Weighted sampling to obtain the initial Voronoi sites and structure;

[0014] Step iii: Global iteration and local optimization;

[0015] Step iv: Matching and fusing to obtain a porous lightweight structure model of the mirror.

[0016] In the above technical solution, the modeling and optimization method specifically includes the following steps:

[0017] Step 1: Obtain the self-weight deformation data of the mirror in both solid and hollow states;

[0018] Step 2: Generate a large number of random candidate points within the mirror area to match the self-weight deformation data of the mirror in both solid and hollow cases, and calculate the deformation sensitivity factor δ at each point;

[0019] Step 3: After obtaining the sensitivity coefficient density field, select p initial points through weighted sampling;

[0020] Step 4: Based on the selected p points, generate the initial Voronoi structure according to the following formula;

[0021] V i ={x∈Ω|d(x,P i )<d(x,P j )},j={1,2,...,n,j≠i},i=1,...n.

[0022] Step 5: Iteratively optimize the initial Voronoi structure according to the following formula to generate the centroid Voronoi structure;

[0023]

[0024] Step 6: Considering internal cavities such as support holes, make local adjustments to the structure;

[0025] Step 7: Extend the final center of gravity Voronoi structure horizontally along the lines and stretch it vertically to generate a porous support structure.

[0026] Step 8: Combine the obtained porous support structure with the hollow mirror model to obtain a lightweight mirror structure.

[0027] In the above technical solution, in step 1, the solid case represents that the reflector is a solid model without lightweighting, and the degree of lightweighting is 0; the hollow case represents that all lightweightable parts have been removed, and only the necessary thickness of the mirror surface and the outer wall is retained, and the degree of lightweighting is 100%.

[0028] In the above technical solution, in step 1, the self-weight deformation data of the mirror is obtained by performing finite element mesh generation, applying load, applying constraints, calculating the self-weight deformation of the mirror, and extracting the deformation data of the finite element nodes of the mirror surface for two different situations based on the gravity direction and constraint conditions of the mirror.

[0029] In the above technical solution, in step 2, both the solid and hollow cases require the candidate point to obtain the data of its nearest node for subsequent calculations.

[0030] In the above technical solution, in step 2, the deformation sensitivity factor δ satisfies:

[0031] δ0(x,y)=|D f (x,y)-D e (x,y)|

[0032]

[0033] Among them, D f (x,y) represents the mirror deformation data of point (x,y) under solid conditions; D e (x,y) represents the mirror self-weight deformation data of point (x,y) in the hollow case; δ(x,y) represents the deformation sensitivity of point (x,y).

[0034] In the above technical solution, the method for selecting p initial points through weighted sampling in step 3 is as follows:

[0035]

[0036] Where R is a random number uniformly distributed between 0 and 1;

[0037] Each candidate point (xi, yi) is determined according to its K i The values ​​are sorted from largest to smallest, and the top k sample points are selected as the set of points for the design of the reflector structure.

[0038] In the above technical solution, step 6 specifically involves: in the obtained centroid Voronoi structure, the points in each supporting circular hole region are replaced with a set of concentric, uniformly distributed nodes, and a locally optimized centroid Voronoi structure is generated based on the new point set.

[0039] The present invention has the following beneficial effects:

[0040] The present invention provides a modeling and optimization method for the porous lightweight structure of a space optical mirror. With minimizing the surface deformation of the mirror as the design goal, it proposes a surface deformation sensitivity factor and provides a calculation method to scientifically evaluate the degree of demand for the support structure at different positions of the mirror surface, thereby more rationally guiding the distribution of the mirror structure.

[0041] The present invention provides a modeling and optimization method for porous lightweight structures of space optical mirrors. It proposes an overall process for generating porous lightweight structures based on deformation-sensitive factors, which is different from the structure generation method under external load and the layered and partitioned structure design. The method adjusts the density distribution of the Voronoi structure in combination with the actual working conditions of the mirror to achieve distribution optimization of the lightweight structure.

[0042] The present invention provides a modeling and optimization method for porous lightweight structures of space optical mirrors. Addressing the issues of excessively small angles and uneven distribution between the support holes and the resulting lightweight structure, which negatively impact mirror performance and manufacturability, this invention proposes an optimization strategy to adapt to localized holes, thereby improving the structure's adaptability and broadening the applicable scenarios of the design method. Attached Figure Description

[0043] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0044] Figure 1 This is a flowchart of the steps in the modeling and optimization method for the porous lightweight structure of the space optical mirror of the present invention;

[0045] Figure 2A and Figure 2B These are, respectively, the solid model and the hollow model of a planar reflector with three internal support holes calculated according to the present invention;

[0046] Figure 3The initial sample point deformation sensitivity heatmap distribution is obtained according to the method of the present invention;

[0047] Figure 4A and Figure 4B These are the initial Voronoi points and corresponding initial structures obtained according to embodiments of the present invention;

[0048] Figure 5 This is a CVT structure obtained after local optimization according to an embodiment of the present invention;

[0049] Figure 6 This is a schematic diagram of a lightweight reflector structure obtained according to an embodiment of the present invention. Detailed Implementation

[0050] In a specific embodiment of the present invention, CVT stands for centroidal Voronoi tessellation. CVT structure represents a centroidal Voronoi structure.

[0051] The inventive concept of this invention is as follows: This invention provides a lightweight structure design method for additive manufacturing space mirrors based on the Voronoi algorithm. Compared with traditional regular graphic mesh lightweight structures, it achieves better surface deformation under the same or even lower mass, improves surface accuracy, and realizes an intelligent structure generation strategy that matches the self-weight working condition.

[0052] See Figure 2A and Figure 2B As shown, this embodiment of the invention applies to the solid model and hollow model of a planar reflector for a space camera;

[0053] The hollow model retains the necessary mirror surface, peripheral support, and the thickness of the three circular support holes, while the internal design area is completely hollow.

[0054] Finite element meshing was performed on both models. A self-weight load parallel to the optical axis was applied, and constraints were imposed on the inner walls of the three support holes. The deformation of the mirror under its own weight was calculated, and the deformation data (x, y, D) of the finite element nodes on the mirror surface was extracted. (x, y) represents a finite element node on the mirror surface, and D represents the deformation data of that node. f (x,y) represents the deformation data of point (x,y) in the solid model, D e (x,y) represents the deformation data of point (x,y) in the case of a hollow model;

[0055] Since the number of nodes in the finite element method is limited, n random points (x) are generated within the circular region corresponding to the mirror surface. i ,y iThis number is much larger than the number of finite element nodes on the mirror surface. Random points are mapped to finite element nodes in the two cases respectively, and each random point will obtain the deformation data of D of the finite element node that is closest to its set.

[0056] δ0(x i ,y i )=|D f (x i ,y i )-D e (x i ,y i )|

[0057]

[0058] The deformation sensitivity of each random point is calculated using the formula above. Figure 3 This is a deformation sensitivity thermogram of an embodiment of the present invention;

[0059] Based on the distribution of sensitivity, sampling is performed, and p initial sample points are selected. n is much larger than p. Weighted sampling is used as follows, where R is a random number uniformly distributed between 0 and 1. The Ki value of each random point is calculated and arranged from largest to smallest to obtain the first p points as the selected initial points of the structure.

[0060]

[0061] In this embodiment, the reflector model is a circular reflector with rotational symmetry. The sample points used were one-third of the initial point set data, and the remaining point set was obtained through operations such as copying, rotating, and pasting. Figure 4A The image shows the initial point set obtained in this embodiment;

[0062] V i ={x∈Ω|d(x,P i )<d(x,P j )},j={1,2,...,n,j≠i},i=1,...n.

[0063] According to the above formula, the Voronoi generation rules and algorithm obtain the initial Voronoi structure based on the already obtained initial point set. Figure 4B The image shows the initial Voronoi structure obtained in this embodiment;

[0064]

[0065] According to the above formula, the iteration rules and algorithms of the central Voronoi diagram, i.e. the CVT diagram, are to be further iterated and optimized based on the initial structure and cell site obtained, until all grid sites have moved to the centroid of the grid, and the corresponding CVT structure is obtained.

[0066] Considering the reflector with internal support holes, the resulting CVT intersects with the support hole structure. The ribs connecting the support holes are unevenly distributed, which has an adverse effect on local performance. Some of the included angles are small, which poses a potential risk to the machining accuracy and machinability during the manufacturing process.

[0067] By adding several sets of improved points inside the support holes to the sample points, the points in the set are evenly distributed on a circle with the circular support holes as the center. The diameter of this circle is q times the diameter of the circular support hole area. <q<1;

[0068] The point set was improved by deleting and replacing points inside the support holes in the origin set, and the CVT structure was regenerated. Figure 5 The image shows the locally optimized porous CVT structure obtained in this embodiment.

[0069] Based on the optimized porous structure, the structure is extended left and right along the lines and stretched to generate a support structure. This support structure is then matched and fused with the mirror frame to obtain the mirror model. Figure 6 This is a schematic diagram of the porous lightweight structure mirror model obtained in this embodiment.

[0070] The present invention will now be described in detail with reference to the accompanying drawings.

[0071] like Figure 1 As shown, the modeling and optimization method for the porous lightweight structure of the space optical mirror of the present invention includes the following steps:

[0072] Step i: Calculate the distribution of mirror surface deformation sensitivity;

[0073] Step ii: Weighted sampling to obtain the initial Voronoi sites and structure;

[0074] Step iii: Global iteration and local optimization;

[0075] Step iv: Matching and fusing to obtain a porous lightweight structure model of the mirror.

[0076] Specifically, the modeling and optimization method for the porous lightweight structure of the space optical mirror of the present invention includes the following steps:

[0077] Step i: Calculate the distribution of mirror surface distortion sensitivity; specifically including:

[0078] Step 1: Obtain the self-weight deformation data of the mirror in both solid and hollow states;

[0079] Step 2: Generate a large number of random candidate points within the mirror area to match the self-weight deformation data of the mirror in both solid and hollow cases, and calculate the deformation sensitivity factor δ at each point;

[0080] Step ii: Weighted sampling to obtain the initial Voronoi sites and structure; specifically including:

[0081] Step 3: After obtaining the sensitivity coefficient density field, select p initial points through weighted sampling;

[0082] Step 4: Based on the selected p points, generate the initial Voronoi structure according to the following formula;

[0083] V i ={x∈Ω|d(x,P i )<d(x,P j )},j={1,2,...,n,j≠i},i=1,...n.

[0084] Step 5: Iteratively optimize the initial Voronoi structure according to the following formula to generate the centroid Voronoi structure, i.e., the CVT structure;

[0085]

[0086] Step iii: Global iteration and local optimization; specifically including:

[0087] Step 6: Considering internal cavities such as support holes, make local adjustments to the structure;

[0088] In the obtained CVT structure, the points in each support circular hole area are replaced with a set of concentric, uniformly distributed nodes, and a locally optimized CVT structure is generated based on the new point set.

[0089] Step 7: Extend the final CVT structure horizontally along the lines and stretch it vertically to generate a porous support structure;

[0090] Step iv: Matching and fusing to obtain a porous lightweight structure model of the mirror; specifically including:

[0091] Step 8: Combine the obtained porous support structure with the hollow mirror model to obtain a lightweight mirror structure.

[0092] The modeling and optimization method for the porous lightweight structure of the space optical reflector of the present invention, in step 1, the solid case represents that the reflector is a solid model without lightweighting, and the degree of lightweighting is 0; the hollow case represents that all lightweightable parts have been removed, and only the necessary thickness of the mirror surface and the outer wall is retained, and the degree of lightweighting is 100%.

[0093] The self-weight deformation data of the mirror is obtained by performing finite element mesh generation, applying loads, applying constraints, calculating the self-weight deformation of the mirror, and extracting the deformation data of the finite element nodes of the mirror surface for two different cases based on the direction of gravity and constraint conditions of the mirror.

[0094] In the modeling and optimization method of the porous lightweight structure of the space optical mirror of the present invention, in step 2, the candidate points in both the solid and hollow cases obtain the data of the nearest node for subsequent calculations.

[0095] The deformation sensitivity factor δ satisfies:

[0096] δ0(x,y)=|D f (x,y)-D e (x,y)|

[0097]

[0098] Among them, D f (x,y) represents the mirror deformation data of point (x,y) under solid conditions; D e (x,y) represents the mirror self-weight deformation data of point (x,y) in the hollow case; δ(x,y) represents the deformation sensitivity of point (x,y).

[0099] The modeling and optimization method for the porous lightweight structure of the space optical mirror of the present invention, in step 3, the method of selecting p initial points by weighted sampling is specifically as follows:

[0100]

[0101] Where R is a random number uniformly distributed between 0 and 1;

[0102] Each candidate point (xi, yi) is determined according to its K i The values ​​are sorted from largest to smallest, and the top k sample points are selected as the set of points for the design of the reflector structure.

[0103] The present invention provides a modeling and optimization method for the porous lightweight structure of a space optical mirror. With minimizing the surface deformation of the mirror as the design goal, it proposes a surface deformation sensitivity factor and provides a calculation method to scientifically evaluate the degree of demand for the support structure at different positions of the mirror surface, thereby more rationally guiding the distribution of the mirror structure.

[0104] The present invention provides a modeling and optimization method for porous lightweight structures of space optical mirrors. It proposes an overall process for generating porous lightweight structures based on deformation-sensitive factors, which is different from the structure generation method under external load and the layered and partitioned structure design. The method adjusts the density distribution of the Voronoi structure in combination with the actual working conditions of the mirror to achieve distribution optimization of the lightweight structure.

[0105] The present invention provides a modeling and optimization method for porous lightweight structures of space optical mirrors. Addressing the issues of excessively small angles and uneven distribution between the support holes and the resulting lightweight structure, which negatively impact mirror performance and manufacturability, this invention proposes an optimization strategy to adapt to localized holes, thereby improving the structure's adaptability and broadening the applicable scenarios of the design method.

[0106] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for modeling and optimizing a porous lightweight structure for a space optical mirror, characterized in that, Includes the following steps: Step 1: Obtain the self-weight deformation data of the mirror in both solid and hollow states; Step 2: Generate a large number of random candidate points within the mirror area to match the self-weight deformation data of the mirror in both solid and hollow cases, and calculate the deformation sensitivity factor δ at each point; Step 3: After obtaining the sensitivity coefficient density field, select p initial points through weighted sampling; Step 4: Based on the selected p points, generate the initial Voronoi structure according to the following formula; Step 5: Iteratively optimize the initial Voronoi structure according to the following formula to generate the centroid Voronoi structure; Step 6: Consider the internal cavity of the support hole and make local adjustments to the structure; Step 7: Extend the final center of gravity Voronoi structure horizontally along the lines and stretch it vertically to generate a porous support structure. Step 8: Combine the obtained porous support structure with the hollow mirror model to obtain a lightweight mirror structure.

2. The modeling and optimization method for the porous lightweight structure of a space optical mirror according to claim 1, characterized in that, In step 1, the solid case represents a solid model of the reflector that has not been lightweighted, with a lightweighting degree of 0; the hollow case represents the removal of all lightweightable parts, retaining only the necessary thickness of the mirror surface and outer wall, with a lightweighting degree of 100%.

3. The modeling and optimization method for the porous lightweight structure of a space optical mirror according to claim 1, characterized in that, In step 1, the self-weight deformation data of the mirror is obtained by performing finite element mesh generation, applying load, applying constraints, calculating the self-weight deformation of the mirror, and extracting the deformation data of the finite element nodes of the mirror surface for two different cases based on the gravity direction and constraint conditions of the mirror.

4. The modeling and optimization method for the porous lightweight structure of a space optical mirror according to claim 1, characterized in that, In step 2, both the solid and hollow cases require candidate points to obtain data on their nearest node for subsequent calculations.

5. The modeling and optimization method for the porous lightweight structure of a space optical mirror according to claim 1, characterized in that, In step 2, the deformation sensitivity factor δ satisfies: Among them, D f (x,y) represents the mirror deformation data of point (x,y) under solid conditions; D e (x,y) represents the mirror self-weight deformation data of point (x,y) in the hollow case; δ(x,y) represents the deformation sensitivity of point (x,y).

6. The modeling and optimization method for the porous lightweight structure of a space optical mirror according to claim 1, characterized in that, In step 3, the method for selecting p initial points through weighted sampling is as follows: Where R is a random number uniformly distributed between 0 and 1; Each candidate point (xi, yi) is determined according to its K i The values ​​are sorted from largest to smallest, and the top k sample points are selected as the set of points for the design of the reflector structure.

7. The modeling and optimization method for the porous lightweight structure of a space optical mirror according to claim 1, characterized in that, Step 6 specifically involves replacing the points within each supporting circular hole region in the obtained centroid Voronoi structure with a set of concentric, uniformly distributed nodes, and generating a locally optimized centroid Voronoi structure based on the new point set.

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