Curvature correctable sub-mirror topology optimization method

Abstract

The present application belongs to the technical field of space camera mirror analysis, and particularly relates to a curvature correctable sub-mirror topology optimization method; by constructing an equation representing the curvature radius variation of the curvature correctable sub-mirror and the root mean square value of the curvature correction surface shape residual, and taking the ratio of the sub-mirror surface shape residual root mean square value to the curvature radius variation as the core index, the topology optimization is performed with the ratio as the topology optimization target, the sub-mirror volume ratio as the constraint, and the material distribution density as the variable; the optimal distribution of the mirror body material with the optimal curvature is obtained; the present application can guide the design of the back structure of the curvature correctable sub-mirror, and reduce the surface shape residual generated by the curvature correction of the sub-mirror.

Description

Technical Field

[0001] This invention belongs to the field of space camera reflector design technology, and particularly relates to a curvature-correctable sub-mirror topology optimization method. Background Technology

[0002] Space telescopes are evolving towards larger apertures and longer focal lengths to achieve higher light-gathering capabilities and angular resolution. However, the strict limitations imposed by launch vehicle fairings on payload size have become a major bottleneck restricting further increases in the aperture of the telescope's primary mirror. To overcome this physical constraint, modular primary mirror technology has emerged. This technology divides a large primary mirror into multiple foldable or deployable independent sub-mirrors, which are folded up within the launch vehicle fairing envelope during launch and then unfolded and pieced together in orbit to form a complete mirror surface.

[0003] For a modular primary mirror, the core guarantee of its imaging quality lies in maintaining co-phase, meaning all sub-mirrors must work together as a continuous, smooth optical surface. Ensuring a highly consistent mirror curvature (or radius of curvature) among the modular sub-mirrors is fundamental and crucial for achieving and maintaining this co-phase state. Any curvature difference between sub-mirrors will directly introduce wavefront errors that are difficult to correct, leading to severe degradation of the system's image quality. However, in actual engineering manufacturing, due to factors such as material property variations, processing errors, and subsequent coating and environmental stresses, it is almost impossible to directly manufacture independent sub-mirrors with completely consistent curvature. Therefore, correcting the curvature of the sub-mirrors is essential.

[0004] Currently, topology optimization, an advanced design method, is widely used in the initial structural design stage of reflectors. However, existing general-purpose commercial finite element analysis software and its built-in topology optimization modules typically limit their standard optimization objective functions and constraints to global structural mechanical performance (such as minimizing overall compliance and maximizing the first-order natural frequency) or manufacturability requirements. They cannot directly set the core indicator that determines optical performance—namely, the change in the radius of curvature of the sub-mirror or the surface residual after curvature correction—as the optimization objective or key constraint.

[0005] In summary, existing technologies lack a topology optimization design method that starts from optical performance and is directly guided by curvature consistency. This makes it difficult to endow the splicing sub-mirrors with the optimal, intrinsic curvature at the conceptual design stage, thus restricting the development of high-performance spliced ​​space telescopes. Summary of the Invention

[0006] In view of this, the present invention aims to provide a topology optimization method for curvature-correctable sub-mirrors; by constructing an equation characterizing the change in curvature radius of curvature of the curvature-correctable sub-mirror and an equation representing the root mean square value of the curvature correction surface residual, and using the minimum ratio of the root mean square value of the sub-mirror surface residual to the change in curvature radius as the core indicator for topology optimization, with the sub-mirror volume ratio as a constraint and the material distribution density as a variable, topology optimization is performed; thus obtaining the optimal material distribution of the mirror body with the optimal curvature.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] A curvature-correctable sub-mirror topology optimization method includes the following steps:

[0009] Step 1: Create a finite element analysis model of the curvature-correctable sub-mirror, and create the curvature radius change Δ in the finite element analysis model of the curvature-correctable sub-mirror. R and the root mean square value of the curvature correction surface residual e Two variables are used to generate a finite element model calculation file for a curvature-correctable sub-mirror.

[0010] Step 2, extract all the surfaces located on the curvature-correctable sub-mirror. n The number of each node i Extract node number i Corresponding node space coordinates ( x i , y i , z i );

[0011] Step 3, based on the node spatial coordinates ( x i , y i , z i Construct the change in radius of curvature Δ R Solving the equations and the root mean square value of the curvature correction surface residuals e Solve the equations;

[0012] Step 4, construct the topology optimization mathematical model:

[0013] The root mean square value of the curvature correction surface residual e With the change in radius of curvature Δ R The goal is to minimize the ratio of ;

[0014] The volume ratio of the curvature-correctable sub-mirror material is used as an optimization constraint.

[0015] Material distribution density is used as a design variable;

[0016] Step 5: Integrate the solution equations from Step 3 and the topology optimization mathematical model constructed in Step 4 into the curvature-correctable sub-mirror finite element model calculation file.

[0017] Step 6: Submit the integrated curvature-correctable sub-mirror finite element model calculation file to the finite element solver to obtain the optimal distribution topology of the curvature-correctable sub-mirror body material.

[0018] In step 3, construct Δ R The solution equation is:

[0019] ;

[0020] In the formula: R The radius of curvature of the curvature-correctable sub-mirror surface is indicated. Represents a node i The displacement value in the sag direction.

[0021] Build in step 3 e The solution equation is:

[0022] .

[0023] The finite element solver is the Optistruct solver.

[0024] The present invention also provides a curvature-correctable sub-mirror topology optimization device, comprising:

[0025] The analysis model creation module is used to create finite element analysis models of curvature-correctable sub-mirrors;

[0026] The calculation file generation module is used to create the curvature radius change Δ in the finite element analysis model of the curvature-correctable sub-mirror. R and the root mean square value of the curvature correction surface residual e Two variables are used to generate a finite element model calculation file for a curvature-correctable sub-mirror;

[0027] The node extraction module is used to extract all nodes of the curvature-correctable sub-mirrors. n The number of each node i Simultaneously extract node numbers i Corresponding node space coordinates ( x i , y i , z i );

[0028] The equation-solving module is based on the spatial coordinates of the nodes ( x i , y i , zi Construct the change in radius of curvature Δ R The solution equation is based on the spatial coordinates of the nodes ( x i , y i , z i Construct the root mean square value of the curvature correction surface residual. e Solve the equations;

[0029] The topology optimization mathematical model construction module is used to construct topology optimization mathematical models, where the topology optimization mathematical model is:

[0030] The root mean square value of the curvature correction surface residual e With the change in radius of curvature Δ R The goal is to minimize the ratio of ;

[0031] The volume ratio of the curvature-correctable sub-mirror material is used as an optimization constraint.

[0032] Material distribution density is used as a design variable;

[0033] An integration module is used to integrate the solution equations and topology optimization mathematical models into the curvature-correctable sub-mirror finite element model calculation file;

[0034] The calculation module submits the integrated curvature-correctable sub-mirror finite element model calculation file to the finite element solver for calculation, and obtains the optimal distribution topology of the mirror body material of the curvature-correctable sub-mirror.

[0035] The present invention also provides a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the curvature-correctable sub-mirror topology optimization method of the present invention.

[0036] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0037] This invention utilizes a technical approach to construct equations in Hypermesh representing the change in curvature radius of curvature of a curvature-correctable sub-mirror and the root mean square value equation for the curvature correction surface residual. It takes minimizing the ratio of the root mean square value of the sub-mirror surface residual to the change in curvature radius as the topology optimization objective. This achieves topology optimization with the core performance requirements of the curvature-correctable sub-mirror as the optimization target. It also allows for the examination of the sub-mirror topology optimization material distribution, guiding the back structure design of the curvature-correctable sub-mirror and reducing the surface residual generated by curvature correction. This has significant engineering implications for the optimized design of modular, spliced ​​reflectors.

[0038] This invention optimizes the design process and reduces R&D costs and time: the method moves the optical performance verification step to the initial structural concept design stage, thereby compressing the overall R&D cycle and saving huge costs incurred due to major design modifications in the later stages.

[0039] This invention provides key technical support for the development of high-performance modular primary mirrors: the sub-mirror configuration with intrinsically optimal correction characteristics obtained by this invention is a fundamental component for achieving high-precision, high-stability spatial modular mirrors. This method can be extended to modular optical systems of various scales and forms, and has significant engineering application value for promoting the development of large-aperture space telescopes and next-generation ultra-high-resolution Earth observation systems. Attached Figure Description

[0040] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0041] Figure 1 This is a flowchart of the present invention;

[0042] Figure 2 This is a partial schematic diagram illustrating the equation for solving the change in radius of curvature in an embodiment of the present invention;

[0043] Figure 3 This is a partial schematic diagram illustrating the equation for solving the root mean square value of the curvature correction surface residual in an embodiment of the present invention;

[0044] Figure 4 This is a diagram showing the topology optimization results in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to the invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0046] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined to form various implementations. Furthermore, the order of the steps or actions in the method description can be changed or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0047] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0048] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] Please see Figure 1 In one embodiment of the present invention, a curvature-correctable sub-mirror topology optimization method includes the following steps:

[0051] Step 1: Import the 3D model of the curvature-correctable sub-mirror into Hypermesh software. In Hypermesh, create a finite element analysis model of the curvature-correctable sub-mirror based on the 3D model. Then, create a model within the finite element analysis model that represents the change in curvature radius Δ. R and the root mean square value of the curvature correction surface residual eThese two variables are used to generate a finite element model calculation file for a curvature-correctable sub-mirror.

[0052] Step 2: Extract all elements located on the surface of the curvature-correctable sub-mirror in the finite element analysis model of the curvature-correctable sub-mirror. n The number of each node i Extract node numbers i Corresponding node space coordinates ( x i , y i , z i );

[0053] Specifically, in this embodiment, 3182 nodes of the curvature-correctable sub-mirror surface are extracted in this step, with the node numbering range being 1 to 3182.

[0054] Step 3, based on the node spatial coordinates ( x i , y i , z i Construct the change in radius of curvature Δ in Hypermesh software. R Solving the equations and the root mean square value of the curvature correction surface residuals e Solve the equation; where Δ R The solution equation is:

[0055] ;

[0056] In the formula: R The radius of curvature of the curvature-correctable sub-mirror surface is indicated. Represents a node i The displacement value in the sag direction;

[0057] e The solution equation is:

[0058] .

[0059] Specifically, in this embodiment, in this step, Δ is constructed in Hypermesh. R Excerpts from the solution equations are as follows Figure 2 As shown; constructing the root mean square value of the curvature-corrected surface residual in Hypermesh. e The solution equation is as follows Figure 3 As shown, Figure 3 The diagram shown is a partial schematic of the equation for solving the root mean square value of the curvature correction surface residual in this embodiment.

[0060] Step 4, construct the topology optimization mathematical model:

[0061] The root mean square value of the curvature correction surface residual e With the change in radius of curvature Δ R The ratio (i.e.) e / Δ R Minimize as the topology optimization objective;

[0062] The volume ratio of the curvature-correctable sub-mirror material is used as an optimization constraint.

[0063] Material distribution density is used as a design variable;

[0064] Specifically, in this embodiment, in this step, the volume ratio of the curvature-correctable sub-mirror material is constrained to 0.2~0.5; wherein the volume ratio of the curvature-correctable sub-mirror material = design material volume / initial design space total volume, and the final structural material volume is the percentage of the initial design space total volume. The volume ratio in topology optimization directly defines the total amount of material that the optimized structure is allowed to retain.

[0065] Step 5: Integrate the solution equations from Step 3 and the topology optimization mathematical model constructed in Step 4 into the curvature-correctable sub-mirror finite element model calculation file.

[0066] Step 6, calculate the integrated curvature-correctable sub-mirror finite element model file (i.e. The .fem file is submitted to the Optistruct solver for calculation to obtain the optimal distribution topology of the mirror body material for the curvature-correctable sub-mirror.

[0067] The Optistruct solver automatically calculates and waits for the calculation to complete before generating the calculation results, which yields the optimal distribution of the curvature-correctable sub-mirror body material.

[0068] Specifically, in this embodiment, the Optistruct solver is submitted to calculate the optimal distribution map of the curvature-correctable sub-mirror body material after 76 iterations, such as... Figure 4 As shown. Through this Figure 4 By examining the material distribution after sub-mirror topology optimization, we can guide the design of the back structure of the curvature-correctable sub-mirror and reduce the surface residuals caused by sub-mirror curvature correction.

[0069] The present invention also provides a curvature-correctable sub-mirror topology optimization device for implementing the curvature-correctable sub-mirror topology optimization method provided by the present invention. The device includes:

[0070] The analysis model creation module is used to create finite element analysis models of curvature-correctable sub-mirrors;

[0071] The calculation file generation module is used to create the curvature radius change Δ in the finite element analysis model of the curvature-correctable sub-mirror. R and the root mean square value of the curvature correction surface residuale Two variables are used to generate a finite element model calculation file for a curvature-correctable sub-mirror;

[0072] The node extraction module is used to extract all nodes of the curvature-correctable sub-mirrors. n The number of each node i Simultaneously extract node numbers i Corresponding node space coordinates ( x i , y i , z i );

[0073] The equation-solving module is based on the spatial coordinates of the nodes ( x i , y i , z i Construct the change in radius of curvature Δ R The solution equation is based on the spatial coordinates of the nodes ( x i , y i , z i Construct the root mean square value of the curvature correction surface residual. e Solve the equations;

[0074] The topology optimization mathematical model construction module is used to construct topology optimization mathematical models, where the topology optimization mathematical model is:

[0075] The root mean square value of the curvature correction surface residual e With the change in radius of curvature Δ R The goal is to minimize the ratio of ;

[0076] The volume ratio of the curvature-correctable sub-mirror material is used as an optimization constraint.

[0077] Material distribution density is used as a design variable;

[0078] An integration module is used to integrate the solution equations and topology optimization mathematical models into the curvature-correctable sub-mirror finite element model calculation file;

[0079] The calculation module submits the integrated curvature-correctable sub-mirror finite element model calculation file to the finite element solver for calculation, and obtains the optimal distribution topology of the mirror body material of the curvature-correctable sub-mirror.

[0080] The present invention also provides a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the curvature-correctable sub-mirror topology optimization method of the present invention.

[0081] In summary, the above description is merely a preferred embodiment of this specification and is not intended to limit the scope of protection of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

Claims

1. A curvature-correctable sub-mirror topology optimization method, characterized in that, Includes the following steps: Step 1: Create a finite element analysis model of the curvature-correctable sub-mirror, and create a curvature radius change Δ in the finite element analysis model of the curvature-correctable sub-mirror. R and the root mean square value of the curvature correction surface residual e Two variables are used to generate a finite element model calculation file for a curvature-correctable sub-mirror. Step 2, extract all the surfaces located on the curvature-correctable sub-mirror. n The number of each node i Extract the node number i Corresponding node space coordinates ( x i , y i , z i ); Step 3, based on the node spatial coordinates ( x i , y i , z i Construct the change in radius of curvature Δ R Solving the equations and the root mean square value of the curvature correction surface residuals e Solve the equations; Step 4, construct the topology optimization mathematical model: The root mean square value of the curvature correction surface residual e With the change in radius of curvature Δ R The goal is to minimize the ratio of ; The volume ratio of the curvature-correctable sub-mirror material is used as an optimization constraint. Material distribution density is used as a design variable; Step 5: Integrate the solution equations described in Step 3 and the topology optimization mathematical model constructed in Step 4 into the curvature-correctable sub-mirror finite element model calculation file; Step 6: Submit the integrated curvature-correctable sub-mirror finite element model calculation file to the finite element solver to obtain the optimal distribution topology of the curvature-correctable sub-mirror body material.

2. The curvature-correctable sub-mirror topology optimization method according to claim 1, characterized in that, In step 3, Δ is constructed R The solution equation is: ； In the formula: R The radius of curvature of the curvature-correctable sub-mirror surface is indicated. Represents a node i The displacement value in the sag direction.

3. The curvature-correctable sub-mirror topology optimization method according to claim 2, characterized in that, The construction in step 3 e The solution equation is: 。 4. The curvature-correctable sub-mirror topology optimization method according to claim 1, characterized in that, The finite element solver is the Optistruct solver.

5. A curvature-correctable sub-mirror topology optimization device, characterized in that, include: The analysis model creation module is used to create finite element analysis models of curvature-correctable sub-mirrors; The calculation file generation module is used to create the curvature radius change Δ in the finite element analysis model of the curvature-correctable sub-mirror. R and the root mean square value of the curvature correction surface residual e Two variables are used to generate a finite element model calculation file for a curvature-correctable sub-mirror; The node extraction module is used to extract all nodes of the curvature-correctable sub-mirror surface. n The number of each node i Simultaneously extract the node number i Corresponding node space coordinates ( x i , y i , z i ); The equation-solving module is based on the spatial coordinates of the nodes ( x i , y i , z i Construct the change in radius of curvature Δ R The solution equation is based on the spatial coordinates of the nodes ( x i , y i , z i Construct the root mean square value of the curvature correction surface residual. e Solve the equations; The topology optimization mathematical model construction module is used to construct a topology optimization mathematical model, wherein the topology optimization mathematical model is: The root mean square value of the curvature correction surface residual e With the change in radius of curvature Δ R The goal is to minimize the ratio of ; The volume ratio of the curvature-correctable sub-mirror material is used as an optimization constraint. Material distribution density is used as a design variable; An integration module is used to integrate the solution equations constructed by the solution equation construction module and the topology optimization mathematical model constructed by the topology optimization mathematical model construction module into the curvature-correctable sub-mirror finite element model calculation file; The calculation module submits the integrated curvature-correctable sub-mirror finite element model calculation file to the finite element solver for calculation, and obtains the optimal distribution topology map of the curvature-correctable sub-mirror body material.

6. A computer device, characterized in that, include: At least one processor; The at least one processor is also connected in communication with a memory, wherein the memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the curvature-correctable sub-mirror topology optimization method according to any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the curvature-correctable sub-mirror topology optimization method as described in any one of claims 1 to 4.

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