Design and Evaluation of Flexible Support Based on Space Mirror

Abstract

The mirror component is one of the most critical components in the space remote sensing payload, and the performance of its support essentially determines the imaging quality of the system. Mirror components need to have high face shape accuracy, high reliability, and high stability. In this paper, taking the square mirror with the size of 550 mm × 450 mm as an example, we chose the Ultra-Low-Expansion Glass (Corning) as the mirror blank material, and through in-depth research on the principle of the three-point backside support and the engineering realization, we designed a three-point backside flexible support structure applied to the space mirror component. The design results were testified by simulation analysis; the results showed that with the mirror’s weight of 13.2 kg, the surface density can reach 48.5 kg/m². For each gravity acceleration of 1 g, within the temperature range from 16 to 24 °C, carrying a forced displacement of 5 μm, the RMS value of the mirror component can reach 1/55λ (λ = 632.8 nm), which meets the requirement of high face shape accuracy of the mirror component in space. Finally, the mechanical test was carried out on the assembled mirror component, and the intrinsic frequencies of three directions of the mirror component were obtained through the test: 173.8 Hz, 176.4 Hz and 271.5 Hz, respectively. The changes of the mirror and its support structure were all less than 5″ after the 8 g sinusoidal vibration test and the 5.66 g random vibration test, which indicates that the flexible support structure meets the requirements of the high reliability of the space remote sensing loads and the high accuracy of the space mirror component. It shows that the flexible support structure meets the high reliability and high stability requirements of space remote sensing loads. The theoretical data and test results in this research can provide theoretical references for mirror components of the same size and type.

1. Introduction

Nowadays, the space remote sensing payload has entered a stage of rapid development, which puts forward higher and higher requirements for its resolution, while increasing the focal length and throughput aperture of the optical system, which are effective ways to improve the resolution of the ground image element. Therefore, in recent years, a long focal length and a large aperture are becoming the development trend of the space remote sensing payload, and consequently, the ratio of the mirror area and the perimeter are becoming larger and larger, thus the design of the mirror component becomes the most essential in restricting the development of the space remote sensing payload, and it is also one of the most urgent problems that needs to be changed [1,2,3].

In the space field, two types of support for mirrors are mostly used: peripheral support and backside multi-point support. The peripheral support presses the mirror into the frame through the pressure plate, and the mirror is fixed with adhesive around the mirror. This form of support is simple and convenient, and is generally applicable to small-diameter mirrors. For medium- and large-diameter mirrors with diameters larger than 350 mm [4], peripheral support will increase the structural size on the one hand, which is not conducive to the lightweight and small-sized design of space remote sensing loads, and on the other hand, it is also difficult to obtain high face shape accuracy. Backside multi-point support connects the back of the mirror with the support structure through appropriate connection methods. Compared with the peripheral support type, the backside multi-point support is easier to obtain higher surface shape accuracy, so the backside multi-point support is often used for medium and large aperture mirrors [5].

With the backside multi-point support mirror component, the mirror and support structure need to have good stiffness to cope with the large number of mechanical vibrations brought about by the transportation during the launch phase. At the same time, the mirror and support structure also need to have a lighter weight and better thermal unloading capability to cope with the complex and variable temperature environment during the on-orbit operation. It is theoretically contradictory to have both strong stiffness, a light weight, and flexible temperature in the unloading structure. Therefore, finding a balance and a compromise among the contradictions, so that the index of the mirror component can reach an optimal solution, becomes the key to the design of the support structure of the mirror component.

The objective of this paper is the secondary mirror component in an optical system, which is located at the farthest end of the optical system, which needs a higher standard to facilitate a more challenging mechanical environment as well as a wider range of thermal environment than other components. The surface shape of the secondary mirror will directly affect the imaging quality of the whole system. As the most remote optical glass component requiring light weight, the optical component needs to have a very high surface stability to accommodate the wide range of temperature variations, as well as a very high structural stability when facing a large order of magnitude of the mechanical environment [6]. However, light weight, high stiffness, and thermal stability will cause mutual repulsion; therefore, a reasonable design is to seek a delicate balance in the contradiction, so that its technical parameters can meet the requirements.

Detailed descriptions incorporated in this paper consist of the selection of mirror materials, the layout of the support points of the mirror, and the design of the flexible support structure, with lighter weight, higher stiffness, and more stable face shape accuracy as the primary objectives. By leveraging the finite element simulation to stimulate the actual engineering boundary conditions to assess the designed mirror component, and to further enhance the design during iteration, an optimal solution is finally obtained. A series of environmental tests, including small-scale sinusoidal scanning, sinusoidal vibration, and random vibration, have been carried out on the mirror assembly. The test results revealed that the design of the mirror component in this paper satisfied the requirements for the remote sensing payload in space.

2. Design of Space Mirror

2.1. Selection of Mirror Material

Currently, the materials that can be used as mirror blanks for space mirrors are Fused Silicon [6], Zerodur, Silicon carbide, Beryllium and Ultra-Low-Expansion Glass (Corning). The material parameters are shown in

Table 1. Comparison of mirror material parameters.

Material	Density g/cm3	Coefficient of Linear Expansion α × 10−6/K	Modulus of Elasticity GPa
Fused silicon	2.2	0.55	67
Zerodur	2.53	0.03	91
Be	1.87	11.3	287
SiC	3.12	2.24	400
ULE	2.21	0.03	68

.

From Table 1, it can be seen that the ultra-low-expansion glass thermal expansion coefficient tends to be close to zero from 5 to 35 °C. From the material science aspect, the ultra-low-expansion glass belongs to the titanium dioxide-silicate glass, which has the property of being easy to be fused, allowing the optical component to have more processing possibilities, as well as to reduce its own weight [7,8,9].

The base structure design of the mirror follows the basis of ensuring rigidity and face shape accuracy, reducing weight, and possessing stress release capability. According to the characteristics of easy fusion bonding of ULE, the mirror is designed as three parts: top mirror, middle mirror and bottom mirror, which are combined together by means of fusion bonding, as shown in Figure 1.

2.2. Design of Mirror Configuration

The force point of a mirror is related to the number of support points. For circular mirrors, Hall et al. [10] proposed an empirical formula for calculating the number of support points of the mirror. However, there is no reasonable and feasible formula for square mirrors. In this research, we take the outer circle of the square mirror as the maximum outer envelope size, bring it into the below Formula (1) proposed by Hall et al. to obtain the approximate number of support points, and then optimize it through the later finite element simulation analysis.

In this research, the size of the mirror is 550 mm × 450 mm, as shown in Figure 2, the diameter of its outer circle is Φ710.6 mm, and the system index requires that the root-mean-square (RMS) of the back shape of the mirror’s gravity change needs to satisfy the requirements of λ/100 (λ = 632.8 nm), which is calculated according to the following equation:

$$N=\frac{1.5r^2}{t}\sqrt{\frac{\rho g}{\delta E}}$$

(1)

In the equation, r represents the radius, t represents the thickness, ρ represents the material density, g represents the gravitational acceleration, E stands for the modulus of elasticity, δ stands for the maximum self-weight deformation. Calculated from Equation (2), the number of support points for a Φ710.6 mm circular mirror is N = 3.8. Regarding a mirror in space, each support point has six degrees of freedom, translational movement along the X, Y, and Z directions, rotation around the X, Y, and Z coordinate axes as shown in Figure 3, then the mirror is unable to produce relative movement after we have completely restricted all six degrees of freedom of all the support points [11]. For the space shape, triangular is the most stable compared with other shapes, so three-point support is chosen for small- and medium-diameter (≤Φ350 mm) optical elements, while three-point or multiples of three are used to complete the support design for large-diameter (≥Φ350 mm) optical elements. In this paper, the number of support points based on the calculation is 3.8, so the three-point support design is chosen.

2.3. Design of Mirror Stiffener

The stiffener structure is the key part of the mirror that releases the stresses, which is also essential to accommodate the large-span temperature-variable environment. The main components of the stiffener configuration consist of the thickness of the outer ring, the width, length, and thickness of the stiffener.

Currently, optical processing can be achieved in the form of lightweight reinforcement: triangular stiffener structure, square stiffener structure, and hexagonal stiffener structure [12] (Figure 4). The stiffener structure form should not only take into consideration the mirror weight but also take into account its own stiffness, and the ability of the production process. The finite element simulation analysis in the modal analysis can characterize the strength of the structural stiffness; the higher the value shown on the calculation results means that the stiffness is stronger.

In this paper, we applied the Finite Element Simulation method to build up the model for three kinds of mirrors with the same thickness of stiffeners (tentatively 4 mm) and carried out a modal analysis. As shown in

Table 2. Comparative analysis of lightweight structure of sandwich.

Shape of Stiffener	Mass	Mirror Frequency
triangular stiffener structure	13.2 kg	1267.5 Hz
square stiffener structure	13.5 kg	1225.6 Hz
hexagonal stiffener structure	13.7 kg	1239.8 Hz

, the modal and weight of different types of stiffener mirrors are obtained. Among them, the triangular stiffener structure has the highest mode and the lightest weight, which indicates that the reflector in this size range is more stable using the triangular stiffener structure. Therefore, in this paper, we chose the triangular stiffener structure.

3. Design of Support Structure for Space Mirror Component

3.1. Design of Support Structure

In this study, the secondary mirror of a system is required to withstand the severe mechanical environment and a wide range of temperature change environments, which requires the mirror component not only to have a high degree of rigidity at the same time, but also needs to have a relatively flexible component support structure to offload the temperature change [13]. First, a back three-point support structure is selected, and a new biaxial circular arc flexible hinge support structure is introduced on the basis of ensuring the stiffness of each component.

The mirror component consists of the mirror blank, nesting, flexible hinges, support seat, and base plate as shown in Figure 5. First, the material of the mirror blank is determined to be ultra-low-expansion glass. Considering the matching of the thermal properties of the material, the inlays connecting the support holes at the back of the mirror and the support structure are selected to be invar steel (4J32) with a lower coefficient of linear expansion, to reduce the effect of the temperature-varying environment on the mirror surface. The nesting, flexible hinges, and support seat are screwed to each other. High specific stiffness, high strength, low density, and mature processing of Titanium alloy (TC4R) is selected for the flexible hinges and supports, while the base plate is made of carbon fiber composite material with high specific stiffness and a low coefficient of linear expansion. The material properties are shown in

Table 3. Mirror material parameters.

Material	Density g/cm3	Coefficient of Linear Expansion α × 10−6/K	Modulus of Elasticity GPa	Poisson Ratio
ULE	2.21	0.03	67.6	0.17
TC4R	4.45	9.1	110	0.34
Invar Steel (4J32)	8.18	0.05	145	0.25
AlSiC	2.9	9.8	145	0.32
Optical Adhesive	1.7	110	600	0.49

[14].

3.2. Design of Flexible Hinges

Flexible hinges play a role in the whole support structure to protect the top and stabilize the bottom. It is necessary to have a certain degree of rigidity to ensure that the components can withstand the harsh mechanical environment, but it also needs to have a certain degree of flexibility to adapt to a wide range of temperature change environments. In order to find a point of agreement in the contradictory conditions, we need to find a compromise value through the formula calculation and simulation analysis.

The new biaxial circular arc flexible hinges support structure designed in this paper is such that each supporting point provides two degrees of freedom in the optical axis direction and tangential direction, and the three supporting points provide exactly six degrees of freedom (three axial supports constrain axial movement, radial rotation, and tangential rotation; three tangential supports constrain tangential movement, radial movement, and axial rotation), which realize decoupling of the degrees of freedom, and this is the typical Boise kinematic localization support. This support structure restricts the rigid motion of the mirror, and it can isolate the mirror from the elastic deformation of the surroundings, thus effectively protecting the mirror.

Analyze and calculate the flexible hinge deflection and corner of the flexible hinge support structure [15]. The empirical equations for the flexible hinge deflection y and corner θ are shown below:

$$y=\int [\int \frac{12Rsin\alpha M\left(X\right)}{{Eb(2R+\tau -2Rsin\alpha )}^3}dx]da$$

(2)

$$\theta =\int \frac{12Rsin\alpha M\left(X\right)}{{Eb(2R+\tau -2Rsin\alpha )}^3}dx$$

(3)

In the equations, R is the cutting radius of the hinge, τ is the thinnest part of the thickness of the hinge, b is the width of the hinge, and M(x) is the torque applied to the end of the hinge, which can be considered as a constant.

The numerical integration method can be used to obtain the value of the corner stiffness of the flexible hinge under different values of R and τ, and then carry out curve fitting; the results find that the corner stiffness increases with the increase in the τ value, and the corner stiffness is not sensitive to the change of R value, so in the process of flexible hinge parameter selecting, the value should be set according to the structural dimensions and technological requirements, then adjust the value of t until the mirror ultimately meets the requirements of stiffness, strength, and thermal dimensional stability requirements. According to the above equations, the R value of the flexible hinge in this paper is 4 mm, and the τ value is 1 mm. The design model of the flexible hinge is shown in Figure 6.

4. Analysis and Evaluation

The surface shape of the mirror component serves as a key factor to affect the imaging quality of the space remote sensing payload, and the surface shape substantially depends on the stiffness of the component with the number of materials as well as the thermal matching ability between various materials. The material data on each part of the mirror component are provided in Table 3. The numerical value will be given to each component to facilitate the simulation model after mechanical and thermal coupling analysis, leveraging the analysis result to assess the rationality of the design.

A finite element simulation analysis discretizes physical problems into mesh elements for the computer to conduct a numerical calculation and simulation. Tetrahedral mesh and hexahedral mesh are two commonly used mesh types when creating finite element simulation models, each targeting different physical shapes. The hexahedral mesh is composed of hexahedral elements, with each hexahedron consisting of six rectangular faces. Hexahedral meshes are more effective in handling models with regular geometric shapes, as they can better approach the shapes of cubes and rectangles. A tetrahedral mesh is composed of tetrahedral elements, with each tetrahedron surrounded by four triangular faces. Tetrahedral meshes have flexibility in handling complex shapes and boundary conditions, making them suitable for modeling complex geometric shapes. They can be well applied to surfaces and irregular shapes in three-dimensional space.

The reflector component model in this article belongs to an irregular and complex model. Based on the advantages and disadvantages of the tetrahedral and hexahedral meshes mentioned above, we chose tetrahedral meshes when building up the finite element simulation model as illustrated in Figure 7, which can greatly save the time required for mesh partitioning.

4.1. Modal Analysis

Modal analysis is also critical to theoretically evaluate the design rationality, and the analysis results can objectively reveal the mechanical characteristics of the structure and assess the vibration response of such structure under mechanical load.

Modal analysis theory is a recognized technique to determine the vibration characteristics of a structure, by which mass frequencies, vibration, and mode-participation coefficients can be determined. Performing a modal analysis at the primary stage of the design allows the structure to avoid resonating or vibrating at a specific frequency, allows the designer to find out how the structure responds to different types of dynamic loads, and helps to estimate the control parameters in other dynamic analyses.

Obtaining the fundamental frequency of the structure before the component is machined, and optimizing the design, ensuring that it avoids forced vibrations during launch and transportation, enables avoidance of structure damage caused by the occurrence of resonance phenomena.

By simulation, the first four order modes of the overall mirror components are shown in

Table 4. Four vibration modes of the mirror component.

First order of vibration modes	Second order of vibration modes
Third order of vibration modes	Fourth order of vibration modes

with analysis results demonstrated in

Table 5. Results of four modes analysis of the mirror component.

Order	Frequency (Hz)	Vibration Modes Description
1	179.6	Secondary mirror rotates around Z-axis
2	188.1	Secondary mirror translational movement towards X-axis
3	215.4	Secondary mirror translational movement towards Y-axis
4	303.7	Secondary mirror rotates around Y-axis

. Based on the stimulation result, the first-order modal of the mirror components reached 179.6 Hz, which has a higher stiffness compared with the mirror components among a similar size.

4.2. Gravity Load Analysis

During the ground mounting process of the mirror component, the mirror will be affected by gravity; the degree of its influence will be analyzed by simulation during the component design process and appropriate countermeasures will be taken [16].

The coordinate values of all points on the mirror surface are obtained by simulation analysis and brought into MATLAB calculation to simulate the mirror surface shape. As shown in the

Table 6. RMS of mirror shape error under Gravity Load of 1G.

Working Condition	X Gravity Load (1G)	Y Gravity Load (1G)
Surface error RMS/λ (λ = 632.8 nm)
	X: RMS = 0.009λ	Y: RMS = 0.009λ

, it is the root-mean-square (RMS) value of the surface shape of the mirror component after loading the gravity in X and Y directions through simulation analysis (since the Z direction is the vertical direction of the optical axis, not the direction of loading and adjusting, the mirror component is not affected by gravity in the stage of on-orbit operation; therefore, it is not included in the scope of this analysis).

4.3. Temperature Load Analysis

The mirror component works in the track process; the mirror component will be affected by the temperature change of the environment, thus in the process of component design, through simulation to analyze the degree of its impact, corresponding countermeasures are made [17]. In this paper, according to the temperature range given by the thermal control analysis, and the loading temperature conditions on the mirror assembly, with the mirror component loading temperature load for 16~24 °C, the mirror component axial and radial affected by the temperature will show different characteristics; therefore, we need to load the mirror component axial, radial 4 °C temperature gradient load. The coordinate values of all the points on the mirror surface are obtained by simulation and analysis software, which are brought into MATLAB 2014 calculation to simulate the mirror surface shape. As shown in

Table 7. RMS of mirror shape error under different Temperature Load.

Working Condition	Temperature Load (20 ± 4 °C)	Axial Temperature Gradient Load (4 °C)	Radial Temperature Gradient Load (4 °C)
Surface error RMS/λ (λ = 632.8 nm)
	RMS = 0.01λ	RMS = 0.008λ	RMS = 0.008λ

, it is the root-mean-square value of the surface shape of the mirror component after loading the temperature load by simulation analysis.

4.4. Forced Displacement Analysis

Regarding the mirror component in the ground mounting process, the parts and parts assembly contact surface can not reach the ideal fitting, and the surface-to-surface fit will cause relative displacement, which can be directly or indirectly transmitted to the mirror to cause changes in the mirror surface shape; we usually refer to this influence factor as the forced displacement. Analyze the degree of impact through simulation in the component design process and make corresponding countermeasures [18]. According to the support structure of the mirror component designed in this paper, there are two contact points that will produce forced displacement, which are the contact surface between the support base and the base plate, and the contact surface between the base plate and the other structures, as shown in Figure 8 below; at this stage, the contact surface error can be considered to be 5 μm.

The variation of coordinates of all points on the mirror surface are obtained by the simulation and analysis software, which are brought into MATLAB 2014 calculations to simulate the values of the face shape. As shown in

Table 8. RMS of mirror shape error under Forced Displacement of 5 μm.

Working Condition	Forced Displacement (5 μm)	Forced Displacement (5 μm)
Surface error RMS/λ (λ = 632.8 nm)
	RMS = 0.001λ	RMS = 0.0005λ

, the following is the root-mean- square value of the face shape of the mirror component after undergoing forced displacement obtained through simulation analysis.

4.5. Error Analysis

The data results for the simulation analysis, with core parameters as the calculation of 1 g gravity load, forced displacement (5 μm) load, 16~24 °C temperature load, axial gradient 2 °C load, and radial gradient 2 °C load, are illustrated in Table 6, Table 7 and Table 8. We substituted the figures into Equation (3) to obtain the average value of RMS for the surface shape of the mirror component [19].

$$\begin{array}{l}\sqrt{X^2+Y^2+t_{(20\pm 4°)}^2+S_{(forced displacement)}^2+t_{(axial or radial 2 °C)}^2}\\ =\sqrt{{0.009}^2+{0.009}^2+{0.01}^2+{0.001}^2+{0.008}^2}\\ =0.018\lambda \end{array}$$

(4)

The average value of the root-mean-square of the mirror shape is calculated to be 0.018λ.

4.6. Mechanical Tests

The space remote sensing payload will experience a short but severe variation during the launch phase [20]; in order to ensure the stability of the mirror component during the on-orbit operation phase, mechanical tests are required for the component during the ground phase, including a small-scale feature-level sinusoidal scanning test, a sinusoidal vibration test, and a random vibration test.

During the mechanical test, it is necessary to paste two test signal points on the mirror component, which are placed at the center of the mirror and at the center of the base. The test signal points can be used to monitor the changes of the participating products during the mechanical test, and at the same time, after the end of the mechanical test, through the computation of all the data, we can locate the component’s weak position and evaluate the level of weakness. Two control signal points are pasted at the edge position of the vibration tooling to control the excitation of the mechanical test. By obtaining the numerical changes of the test points, it can be judged whether the designed component can withstand the influence brought by the mechanics.

The tests procedure in this paper starts with small-scale feature-level sinusoidal scanning tests with a frequency between 10 and 500 Hz and an excitation of 0.2 g, followed by an 8 g sinusoidal vibration test with a frequency between 0 and 100 Hz and an excitation of 8 g, then a feature-level sinusoidal scanning test with a frequency between 10 and 500 Hz and an excitation of 0.2 g, followed by a random vibration test (2 min) with a frequency between 20 and 2000 Hz and an excitation of 5.66 g, and finally carry out the frequency between 10~500 Hz, the excitation is 0.2 g in the feature-level sinusoidal scanning test. During the test preparation stage, firstly, connect the vibration tooling with the shaking table, then connect the mirror component with the vibration tooling; finally, paste the test points and control points. The schematic diagrams for the mechanical tests of the mirror component are shown in Figure 9.

4.7. System Evaluation

4.7.1. Comparison of Small-Scale Feature-Level Sinusoidal Scanning Tests

After collating and comparing the results of three small-scale feature-level scanning tests, it is possible to obtain the resonance frequency of each measurement point of the mirror component, so that the intrinsic frequency of the component can be obtained. The final results show that the intrinsic frequency of the mirror component in the X direction is 173.8 Hz, the intrinsic frequency of the mirror component in the Y direction is 176.4 Hz, and the intrinsic frequency of the mirror component in the Z direction is 271.5 Hz as listed in

Table 9. Comparison of mirror component intrinsic frequencies.

Direction	First Time	Second Time	Third Time	Magnitude of Change
X	178.6 Hz	176.4 Hz	173.8 Hz	4.8 Hz
Y	177.9 Hz	177.3 Hz	176.4 Hz	1.5 Hz
Z	273.1 Hz	272.7 Hz	271.5 Hz	1.6 Hz

. The simulation result is 179.6 Hz, and the error with the real test result is 5.8 Hz, which meets the requirement of analyzing accuracy, and verifies the validity of the finite element model.

After conducting small-scale feature-level scanning tests three times, the intrinsic frequency of the mirror component varies by 4.8 Hz, 1.5 Hz, and 1.6 Hz in X, Y, and Z directions, and the frequency deviation is less than 5%, which shows that the component has good stiffness and little variation before and after the test [21].

4.7.2. Comparison of Sinusoidal Vibration Tests

After the mirror component has been subjected to sinusoidal vibration tests in X, Y, and Z directions, the values of the two test points of the mirror component are not enlarged between the frequencies of 0 and 100 Hz, as shown in the Figure 10, which indicates that the mirror component can withstand sinusoidal vibration of this magnitude.

4.7.3. Comparison of Random Vibration Tests

After the mirror component has been subjected to random vibration tests in the X, Y, and Z directions,

Table 10. Comparison of random vibration data for mirror component.

Direction of Vibration	POV	RMS of Total Response (grms)	Response Amplification
X	Input	5.677
	Mirror center	16.91	2.97
	Base center	20.16	3.55
Y	Input	5.677
	Mirror center	19.86	3.49
	Base center	22.4	3.94
Z	Input	5.677
	Mirror center	18.68	3.29
	Base center	21.15	3.72

shows the comparison of the data of the mirror component in random vibration, through which it can be seen that in the random vibration of the mirror component in the X, Y, and Z directions, the position of the largest response amplification is located in the center of the base, and the magnification of the response is controlled to be less than five times. It shows that the mirror component can withstand sinusoidal vibration of this magnitude; at the same time, it proves that the stiffness of the component can overcome the influence brought by the mechanics of the launching stage.

4.7.4. Comparison of Displacement Change Data

The mirror component is equipped with two optical cubic mirrors of 13 mm × 13 mm × 13 mm, which are used to test the positional change of the structural member relative to the optical member before and after the mechanical test. As shown in the Figure 11, one optical cubic mirror is affixed to the edge of the mirror and another is affixed to the edge of the base, which are used to test the angular change between the two reference mirrors before and after the mechanical test.

After three small-scale feature-level scanning tests, one sinusoidal vibration test, and one random vibration test, the angular changes in the X, Y, and Z directions of the mirror and the base are 5.678872″, −4.180947″, and −5.87815″. As shown in the

Table 11. Variations before and after the mechanical test.

Variations Δ before and after the Mechanical Test (″)
	Mirror (X, Y, Z)
Structure (X, Y, Z)	5.678872	−7.386751	−23.4734
	3.457164	−4.180947	−6.37103
	23.51495	6.529278	−5.87815

, the optical cubic mirror test results show that the changes between the mirror and the support structure before and after the mechanical test are less than 5″, indicating that there is no relative movement between the mirror and the support structure before and after going through the mechanical test, which further proves that the flexible support structure in this paper can withstand the harsh mechanical environment [22].

5. Conclusions

To ensure that the space remote sensing load can work smoothly in the orbit operation stage, the mirror component not only needs to have a high level of face shape precision, but also needs to maintain the stable adaptability of the overall structure to cope with the high mechanical changes as well as the wide temperature span, which are the fundamental factors to design the environmental space remote sensing payload. Based on the research background of the square mirror in the optical system, this paper prioritizes the lightweight design of the mirror, uses Ultra-Low-Expansion Glass (Corning, New York, NY, USA) as the optical raw material of the mirror, fully utilizes the characteristics of the material’s welding, designs the mirror as a three-layer sandwich structure, and selects the triangular stiffener in the middle layer. In this design, the local stiffness of the mirror is enhanced in parallel achieving the lightweight design; a biaxial circular arc flexible hinge support structure is innovatively proposed to strengthen the structural rigidity while offloading the effect of temperature on the mirror component; using the simulation analysis method, a simulation model similar to the actual optical component is established, and its static mechanics, temperature field, and part-to-part forced displacement are analyzed and calculated. The results show that the RMS value of the face shape of the mirror component reaches 0.0009λ (λ = 632.8 nm) under the effect of 1 g gravity, 0.01λ (λ = 632.8 nm) within the temperature-variable environment from 16 to 24 °C, and 0.001λ (λ = 632.8 nm) under the effect of 5 μm forcing displacement. Finally, using the mechanical tests to verify the component, from the test data, the component in the X, Y, and Z three directions of the intrinsic frequency are 173.8 Hz, 176.4 Hz, and 271.5 Hz, close to the results of the simulation calculations of 179.6 Hz; optical tests are added before and after the mechanical tests, and the results show that the variation of the mirror and the support structure in the X, Y, and Z directions is less than 5″, which further proves the reliability of the simulation and analysis results. The flexible support design of the square reflector studied in this paper has the static and dynamic stiffness to withstand the mechanics of the launch section and the stability to adapt to the thermal dimension after orbit. The results revealed that the design is reasonable and reliable for space environment adaptability. Meanwhile, the design and test verification methods of the flexible support of the square mirror can provide certain references for the design and test of similar space mirrors, and can also provide technical guidance for the relevant research of professionals in the industry.