Fixed metal reflector design method and metal reflector

Abstract

The invention relates to a fixed metal reflector design method and a reflector. The method comprises the following steps: determining a design space, a load, a boundary condition and a material constraint based on a design target; establishing an optical structure model comprising a reflecting surface and a screw hole by designing space, load, boundary conditions and material constraints; performing grid division and finite element simulation on the optical structure model to obtain a first simulation model; performing topological optimization on the first simulation model through multi-physics field coupling and manufacturing constraint to obtain a second simulation model; dividing the second simulation model into an optical mirror surface area, a key structure area and a weight reduction optimization area based on a material retention coefficient; and trimming the weight reduction optimization area through a weight reduction optimization method to obtain a third simulation model. According to the invention, through finite element and topology simulation, the weight of the metal mirror is reduced, the low-order modal frequency of the metal mirror is improved, and shaking of imaging of a reflex optical system is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metal mirrors, and particularly relates to a fixed metal mirror design method and a metal mirror. BACKGROUND

[0002] The first generation of metal mirrors is traditionally made of aluminum alloy through mechanical processing, and the surface shape precision is limited by anisotropy; the second generation (2015-2020): AlSi 10 Mg alloy laser selective melting (SLM) is dominated, lightweight and complex structure integration is realized; the third generation (2020 to now): amorphous metal (such as RSP microcrystalline aluminum) pushes the surface roughness to the sub-nanometer level, which adapts to the EUV lithography demand; additive and subtractive composite manufacturing mainly through SLM forming and single-point diamond ultra-precision cutting solves the bottleneck of additive surface roughness (Ra from 20 μm to 5 nm).

[0003] In the folded optical system, the non-metallic folded mirror has defects such as low vibration mode, low surface shape precision, and general temperature adaptability, while the vibration mode of the metal mirror is slightly improved, but the temperature adaptability is poor. SUMMARY

[0004] To solve the problem of poor adaptability of the metal mirror, in a first aspect of the application, a fixed metal mirror design method is provided, comprising: determining a design space, a load, a boundary condition and a material constraint based on a design target; establishing an optical structure model containing a reflecting surface and a screw hole through the design space, the load, the boundary condition and the material constraint; performing grid division and finite element simulation on the optical structure model to obtain a first simulation model; performing topology optimization on the first simulation model through multi-physical field coupling and manufacturing constraints to obtain a second simulation model; dividing the second simulation model into an optical mirror surface area, a key structure area and a weight reduction optimization area based on a material retention coefficient; and modifying the weight reduction optimization area through a weight reduction optimization method to obtain a third simulation model.

[0005] In some embodiments of the application, the topology optimization of the first simulation model through multi-physical field coupling and manufacturing constraints to obtain the second simulation model comprises: determining a target function and a plurality of first constraint conditions of the first simulation model based on the mirror surface shape error and the optical axis offset; determining a second constraint condition of the thermal boundary and the material model based on thermal coupling simulation; and performing topology optimization on the first simulation model based on the target function, the first constraint condition, the second constraint condition and the manufacturing constraint to obtain the second simulation model.

[0006] Further, the first constraint condition includes an upper limit value of the volume fraction, a lower limit value of the first order modal frequency and an upper limit value of the thermal stress.

[0007] In some embodiments of the present application, the dividing the second simulation model into the optical mirror surface area, the key structure area and the weight reduction optimization area based on the material retention coefficient comprises: dividing the area in the second simulation model with the material retention coefficient greater than or equal to the first threshold value into the optical mirror surface area or the key structure area; dividing the area in the second simulation model with the material retention coefficient greater than or equal to the second threshold value and less than the first threshold value into the weight reduction optimization area; and removing the area in the second simulation model with the material retention coefficient less than the second threshold value.

[0008] Further, the first threshold value is 80%, and the second threshold value is 30%.

[0009] In the above-mentioned embodiments, the establishing the optical structure model containing the reflecting surface and the screw hole based on the design space, the load, the boundary condition and the material constraint comprises: determining the design variable, the objective function and the constraint equation based on the envelope space, the load, the boundary condition and the material constraint; and establishing the optical structure model containing the reflecting surface and the screw hole based on the design variable, the objective function and the constraint equation.

[0010] In a second aspect of the present application, a metal mirror is provided based on the fixed metal mirror design method of the first aspect, comprising: an optical mirror surface area, a key structure area, a weight reduction optimization area and a removed area, a force relief groove is arranged at the connection between the metal mirror and the mirror frame, and the weight reduction optimization area is provided with a honeycomb structure weight reduction groove.

[0011] Further, the honeycomb structure is arrayed in a single direction.

[0012] The present application has the following beneficial effects: The weight reduction groove is arranged to reduce the weight of the metal mirror, improve the low-order modal frequency of the metal mirror, improve the stable shape of the metal mirror under vibration working conditions, and reduce the shaking of the folded optical system imaging. The stress transmission path is prolonged to avoid the transmission of structural stress and thermal stress to the mirror surface. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 FIG. 1 is a basic flowchart of the fixed metal mirror design method in some embodiments of the present application; Figure 2 FIG. 2 is a structural schematic diagram of the fixed metal mirror in some embodiments of the present application; Figure 3 FIG. 3 is another structural schematic diagram of the fixed metal mirror in some embodiments of the present application.

[0014] LIST OF REFERENCE NUMERALS 1. reflecting surface; 2. weight reduction groove; 3. force relief groove; 4. screw hole. DETAILED DESCRIPTION

[0015] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0016] refer to Figure 1 and Figure 2 In a first aspect of the present invention, a design method for a fixed metal mirror is provided, comprising: S100. determining the design space, load, boundary conditions, and material constraints based on design objectives; establishing an optical structure model including a reflecting surface and screw holes through the design space, load, boundary conditions, and material constraints; S200. performing mesh generation and finite element simulation on the optical structure model to obtain a first simulation model; performing topology optimization on the first simulation model through multiphysics coupling and manufacturing constraints to obtain a second simulation model; S300. dividing the second simulation model into an optical mirror region, a key structural region, and a weight reduction optimization region based on a material retention factor; and refining the weight reduction optimization region through a weight reduction optimization method to obtain a third simulation model.

[0017] In step S100 of some embodiments of the present invention, the step of establishing an optical structure model including a reflective surface and a screw hole by designing space, load, boundary conditions and material constraints includes: determining design variables, objective function and constraint equations based on the envelope space, load, boundary conditions and material constraints; and establishing an optical structure model including a reflective surface and a screw hole based on the design variables, objective function and constraint equations.

[0018] Specifically, define the structural envelope space (e.g., the back plate area of ​​the mirror) and exclude non-design domains (screw holes, optical mirrors, mounting interfaces). Non-design domains must be set to a fixed density (ρ=1) in the finite element model. For example, in the design of a metal mirror, the mirror area (requiring high surface accuracy) and the area around the connecting holes (ensuring assembly strength) are set as non-design domains. Static conditions include gravity, assembly preload, and thermal loads; dynamic conditions include vibration frequency constraints (to avoid resonance). Boundary conditions include applying full constraints to fixed support points (e.g., mirror frame connections), and the load application points must consider the actual force-bearing direction. Material properties include elastic modulus, Poisson's ratio, and density. Volume constraints include retaining the material volume fraction and stress constraints.

[0019] For example, the relative density of cells p e (0: empty, 1: solid); The objective function is to minimize flexibility or maximize stiffness. C = F T u ,in F For load vector, u It is the displacement vector; Constraint equations: , V e Represents the unit volume. v frac Retain the volume fraction of the material. v 0 represents the initial volume. s e Represents unit stress, s allow Indicates the allowable stress.

[0020] Understandably, near thermally constrained boundaries or with significant temperature gradients, optimized structures tend to increase material density, forming locally reinforced regions (such as ribs or ring supports) to resist stress concentration caused by thermal expansion. For example, radial or mesh-like stiffeners may form around fixed boundaries to disperse thermal stress. In regions allowing free expansion or with low stress, optimization may result in porous, cavitary, or slender beam structures, reducing overall stress levels by releasing deformation. For instance, porous structures may form around a central high-temperature region to reduce compressive stress caused by constraints. Structures may form directional branches or arcuate channels to guide thermal expansion in specific directions (such as cantilever beams or corrugated geometry), avoiding conflict with fixed boundaries and thus reducing thermal stress.

[0021] In step S200 of some embodiments of the present invention, the step of performing topology optimization on the first simulation model through multiphysics coupling and manufacturing constraints to obtain the second simulation model includes: S201. Determine the objective function and multiple first constraints of the first simulation model based on the mirror surface shape error and optical axis offset; Minimize the mirror surface shape error (RMS) and optical axis offset caused by thermal deformation: , Where ω1 and ω2 are weighting coefficients (usually taken as 0.6 and 0.4); the constraints include: the volume fraction does not exceed 0.4, and the first-order modal frequency does not exceed 500Hz; S201. Based on thermo-mechanical coupling simulation, determine the second constraint conditions of thermal boundary and material model; Simulated temperature gradient: The mirror surface heats up when exposed to light (+10℃), while the support area remains at a low temperature (-5℃); for example, aluminum alloy (AlSi). 10 Mg) Coefficient of thermal expansion, temperature correction for elastic modulus: .

[0022] It is understandable that heat conduction paths can be optimized (e.g., allowing material distribution to influence the temperature field), potentially resulting in optimized heat flux and stress distribution simultaneously. For example, high thermal conductivity materials can be concentrated near heat sources to reduce temperature differences, indirectly reducing thermal stress. Under uniform thermal loads or symmetrical boundary conditions, structures may exhibit symmetrical distributions (e.g., radial or mirror symmetry) to balance the bidirectional stresses caused by thermal expansion.

[0023] S203. Based on the objective function, the first constraint, the second constraint, and the manufacturing constraint, perform topology optimization on the first simulation model to obtain the second simulation model.

[0024] Specifically, the sensitivity of the compliance objective function is expressed as: , Represents the stiffness matrix of a solid element; ue is the unit displacement vector; P represents the penalty factor.

[0025] Specifically, gravitational acceleration g (Direction along the mirror axis), apply volume force density f v = p m g ,in p m The density of the material (e.g., 2700 kg / m³ for aluminum alloy). Initial cylinder (diameter) D ,high H The top circular area is an optical mirror (not part of the design area). p ≡1), The bottom mounting flange serves as a support constraint zone (fixed displacement boundary). u =0).

[0026] The optimization objective of minimizing flexibility (maximizing stiffness) is expressed as: , The constraints include: volume fraction ≤ 0.4, yield strength constraint ≤ 150 MPa.

[0027] In step S300 of some embodiments of the present invention, dividing the second simulation model into an optical mirror region, a key structural region, and a weight reduction optimization region based on the material retention coefficient includes: S301. Divide the regions in the second simulation model where the material retention coefficient is greater than or equal to the first threshold into optical mirror regions or key structural regions; S302. The region in the second simulation model where the material retention coefficient is greater than or equal to the second threshold and less than the first threshold is divided into the weight reduction optimization region; S303. Remove regions in the second simulation model where the material retention coefficient is less than the second threshold.

[0028] Specifically, areas with a material retention factor of 80% or higher are designated as optical mirror areas or critical structural areas, while areas with a retention factor of 30% to 80% are designated as weight reduction optimization areas. Areas with a retention factor below 30% are removed and trimmed from the simplified model. In the weight reduction optimization areas, honeycomb-shaped weight reduction grooves are densely laid in the same direction. Stress-relieving grooves are created at the connection between the metal mirror and the frame. Appropriate mirror substrate materials and reflective coating processes are selected to complete the mirror design.

[0029] It is understandable that topology optimization, with thermal excitation as the boundary and stress minimization as the objective, seeks a balance between resisting thermal deformation and releasing thermal stress through adjustments to material distribution. Its morphology depends on the distribution of thermal load, constraints, and optimization algorithm strategy, and typically manifests as a hybrid structure with localized reinforcement and global flexibility, possessing both mechanical properties and thermal adaptability.

[0030] In this invention, gravity-excited topology optimization is first performed. Using gravity as the excitation and minimizing compliance as the optimization objective, the basic shape of the mirror body is determined to be a frustum of a circle at the top and an ellipse at the bottom. The back of the mirror body is the main weight reduction area. A honeycomb-shaped weight reduction groove is designed to improve the stiffness of the reflector and its ability to resist gravity deformation, while reducing the weight of the reflector. This increases the low-order modal frequency of the structure and improves the stability of the structure, which is beneficial to maintaining the stability of the optical axis under vibration conditions. Then, thermal excitation topology optimization is performed. Using high and low temperatures as boundary conditions and minimizing stress as the optimization objective, the thermal stress transmission path is optimized to reduce the elastic deformation of the mirror surface.

[0031] Example 2 refer to Figure 2 and Figure 3 In a second aspect, the present invention provides a metal reflector based on the fixed metal reflector design method described in the first aspect, comprising: an optical mirror area, a key structural area, a weight reduction optimization area, and a removal area, wherein a stress relief groove 3 is provided at the connection between the metal reflector and the frame, and the weight reduction optimization area is provided with a weight reduction groove 2 with a honeycomb structure.

[0032] Specifically, given a fixed mirror aperture, the overall structural layout is first determined using topology optimization. The structural area is divided into an optical mirror area, a critical structural area, and a weight-reduction optimization area. A honeycomb-shaped weight-reduction groove 2 is created in the weight-reduction optimization area. The metal mirror and frame are fastened together with screws, and a stress-relief groove 3 is added next to the connection area. Figure 2 or Figure 3 In the elliptical mirror shown, there is an unweighted area and an unreflective surface 1. Multiple screw holes 4 are distributed circumferentially at the center of the elliptical mirror.

[0033] Furthermore, the cellular structure is distributed in a single-direction (oriented) array.

[0034] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0035] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a fixed metal reflector, characterized in that, include: The design space, loads, boundary conditions, and material constraints are determined based on the design objectives. An optical structure model including a reflecting surface and screw holes is established by designing space, load, boundary conditions, and material constraints. The optical structure model is meshed and simulated using the finite element method to obtain a first simulation model. Then, through multiphysics coupling and manufacturing constraints, the first simulation model is topologically optimized to obtain a second simulation model. Based on the material retention coefficient, the second simulation model is divided into an optical mirror region, a key structural region, and a weight reduction optimization region. The third simulation model is obtained by modifying the weight reduction optimization region using a weight reduction optimization method.

2. The design method for a fixed metal reflector according to claim 1, characterized in that, The process of performing topology optimization on the first simulation model through multiphysics coupling and manufacturing constraints to obtain the second simulation model includes: The objective function and multiple first constraints of the first simulation model are determined based on the mirror surface shape error and optical axis offset. Based on thermo-mechanical coupling simulation, the second constraint conditions of the thermal boundary and material model are determined; Based on the objective function, the first constraint, the second constraint, and the manufacturing constraint, topology optimization is performed on the first simulation model to obtain the second simulation model.

3. The design method for a fixed metal reflector according to claim 2, characterized in that, The first constraint includes an upper limit for the volume fraction, a lower limit for the first-order modal frequency, and an upper limit for the thermal stress.

4. The design method for a fixed metal reflector according to claim 1, characterized in that, The second simulation model, based on the material retention coefficient, is divided into an optical mirror region, a key structural region, and a weight reduction optimization region, including: In the second simulation model, the regions where the material retention coefficient is greater than or equal to the first threshold are divided into optical mirror regions or key structural regions. The region in the second simulation model where the material retention coefficient is greater than or equal to the second threshold and less than the first threshold is classified as the weight reduction optimization region. Remove regions in the second simulation model where the material retention coefficient is less than the second threshold.

5. The design method for a fixed metal reflector according to claim 4, characterized in that, The first threshold is 80%, and the second threshold is 30%.

6. The design method for a fixed metal reflector according to claim 1, characterized in that, The establishment of the optical structure model, which includes the reflecting surface and the screw hole, through design space, load, boundary conditions, and material constraints includes: Based on the envelope space, loads, boundary conditions, and material constraints, the design variables, objective function, and constraint equations are determined. Based on the aforementioned design variables and objective function, and with a different constraint equation, an optical structure model including the reflecting surface and the screw hole is established.

7. A metal reflector based on the design method of the fixed metal reflector according to claim 1, characterized in that, include: The optical mirror area, the key structural area, the weight reduction optimization area, and the removal area are provided. The metal mirror and the frame are connected by a stress relief groove. The weight reduction optimization area is provided with a weight reduction groove with a honeycomb structure.

8. The metal reflector according to claim 7, characterized in that, The cellular structure is distributed in an array along a single direction.

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