Optimization and verification of mechanical design for small total reflection optics

Mechanical performance assurance is one of the key concerns in the design of small total reflection optics. This article addresses the issue of insufficient strength margin in the design of a total reflection optics for a space photoelectric sensor. Firstly, structural design optimization research was conducted on the optics, and the effectiveness of structural improvement was verified through finite element analysis; Secondly, a concave analysis was conducted under mechanical test conditions to further reduce the risk; Afterwards, the accuracy of the simulation results was verified by comparing the simulation with the experiment through small-scale random vibration tests; Finally, sine vibration tests, random vibration tests, shock tests, acceleration tests were conducted on the entire machine, and optical tests were conducted before and after the tests. The experimental and testing results indicate that the entire machine has passed the mechanical test assessment at the appraisal level and maintained good optical performance. The total reflection optics optimized by mechanical design meets the requirements of engineering applications.


Introduction
Optical payloads are widely used in satellites such as surveying, reconnaissance, and environmental monitoring [1,2], often with significant weight and volume [3].With the demand for lightweight satellites and the development of commercial small satellites, there is a trend towards miniaturization of payloads [4].The commonly used total reflection optical system for optical loads has gradually been applied to space photoelectric sensors represented by search cameras and star trackers after miniaturization design [5].The total reflection optical system has the advantages of compact structure, wide spectral band, and no color difference compared to the commonly used transmission optics in the past, which is conducive for improving the imaging quality of single unit products and has broad application prospects [6].The mechanical design of a total reflection optics has a significant impact on the structural stability of a single unit.Shanliang Ke designed an ultra light stable main support structure for ultra light space cameras and optimized it.The results showed that this structure can ensure the overall stability of the entire machine [7].Wei Li optimized the support structure of the primary and secondary lens of the space camera and verified its structural stability through dynamic environment experiments [8].Quanfeng Guo optimized the structural design of the support for the main lens and focusing lens of the coaxial three optics camera, and the experimental results showed that the structural stability of this space camera was good, meeting the indicator requirements [9].After the miniaturization design of the optics, changes in support form, component configuration, and other factors may pose risks to the mechanical properties.This article focuses on the problem of insufficient strength margin in the design of a total reflection optics structure for a space photoelectric sensor, and optimizes the structural design.The concave conditions of the mechanical test were determined through exploratory testing, and the simulation results showed that the strength margin of the optics was high.The effectiveness of the structural improvement was verified through comparative analysis between the experiment and simulation.

Optics overview
The total reflection optics used in a space photoelectric sensor adopts one-axis four-optics structure as shown in Figure 1 (a), and its envelope size is Φ 142mm × 70mm, with a weight of 1.155kg.It has the characteristics of compact structure, light weight, and easy installation and adjustment.The reflector is supported by flexible joints, as shown in Figure 1 (b).Its main function is to eliminate the influence of internal stress caused by structural processing and installation factors, bu t at the same time, there is also a risk of reducing support stiffness, excessive response during vibration, and significant increase in stress at flexible joints.Therefore, comprehensive consideration is needed for design.

Simulation analysis
To ensure a good mechanical interface for the installation of spatial photoelectric sensors, it is generally required that the first resonance frequency of the entire machine shall be higher than 100Hz.Conduct modal analysis of the entire machine using finite element analysis software.After analysis, the firstresonance frequency is 206.02Hz, with high stiffness.The random vibration frequency range is generally required to be within 2000Hz, and the resonance frequency of the optics part within this range is shown in Table 1.There are multiple resonance points within this range, so it is necessary to analyze the maximum stress of the optics in random vibration.The random vibration test conditions for the entire machine appraisal level are shown in Table 2. Random vibration simulation analysis was conducted on the entire machine, and the stress cloud diagram of the component where the maximum stress of the optics in different directions is located is shown in Figure 2. In addition, the stress at the connection between the upper bearing cylinder and the main bearing cylinder, as well as the truss, is also large, as shown in Figures 3 and 4.   According to the analysis results, the maximum stress in the X and Y directions of the random vibration reached 326.48MPa and 302.93MPa, which occurred at the secondary mirror frame, while the maximum stress in the Z direction was 266.11MPa, which occurred at the primary lens frame.Both the primary and secondary frame materials are made of invar steel.The yield stress of invar steel is 279MPa, and the allowable stress is 186MPa (with a safety factor of 1.5).The maximum stress obtained from simulation analysis has far exceeded the allowable stress, so the mechanical properties do not meet the requirements.

Structural improvement
Based on the aforementioned simulation analysis, it is known that: (1) The maximum stress of random vibration occurs at the secondary mirror component, and the stress at the primary mirror component is also relatively high; (2) The stress at the connection between the upper and the main bearing cylinder is relatively high.
(3) The stress at the root of the truss is relatively high .Therefore, the following design improvements are conducted as Figure 5~Figure 8.

Design verification
Qualification simulation analysis of the entire machine is conducted, and the optics simulation analysis results are shown in Figure 9.The comparison of the maximum stress of random vibration of the optics before and after structural improvement is shown in Table 3.The calculation formula for safety margin is as follows: . ./ 1 ae M S S S =− In the formula, M.S. is the safety margin, and the general metal requirement is greater than 0.15; Sa is the allowable stress, and Se is the stress generated by the qualification load.According to equation ( 1), the safety margin of random vibration of the optics is above 0.22.The safety margin of strength in the X, Y and Z directions meets the requirements.According to the table 3, the maximum stress decreased by 42.7%~62.1%,indicating that the structural improvement is effective.Due to possible deviations between simulation and testing, in order to further reduce risks, it is necessary to concave the mechanical test conditions to reduce the maximum stress at the optics component.

Concave analysis under mechanical test conditions 3.3.1. Determination of concave test conditions
In order to determine the concave frequency point, sine vibration simulation was conducted on the optics component, and the peak response points are shown in Table 4. Conduct concave processing near the response peak frequency point, and determine the concave test conditions as shown in Table 5, Table 6, and Table 7.

Analysis of Random Vibration after Concave
Perform random vibration simulation based on the previously determined concave test conditions, and the analysis results are shown in Figure 10.The maximum stress comparison of random vibration of the front and rear concave lenses is shown in the table.According to equation (1), the safety margin is above 0.522, and the strength safety margin in the X, Y, and Z directions is relatively high.From the results in Table 6, it can be seen that the maximum stress after indentation has decreased by more than 19.9%, indicating that the indentation test conditions are effective.

Figure 1 .
Figure 1.Schematic diagram of optics model

Figure 2 .Figure 3 .
Figure 2. Random vibration analysis of the optics

Figure 4 .
Figure 4. Local stress of the truss

Figure 9 .
Figure 9. Stress cloud in random vibration of the optics

Figure 10 .
Figure 10.Random vibration of the optics after concave

Table 1 .
Modal analysis results of optics

Table 2 .
The level of the random vibration

Table 3 .
Comparison of maximum stress before and after optics design optimization

Table 5 .
Random vibration conditions after concavity

Table 6 .
Comparison of maximum stress of the optics before and after concave