A Method for micro-vibration test analysis of small satellites with laser loading

Based on the parameters of the structure configuration and equipment layout of a small laser satellite in the design stage, the in-orbit micro-vibration simulation analysis of the satellite is carried out by finite element method, which mainly includes [1-2]: 1) modal analysis obtaining the main vibration frequency and modal shape of the satellite in orbit; 2) micro-vibration analysis of the satellite in orbit with the micro-vibration disturbance of the moment gyroscope as the excitation condition. Through the in-orbit micro-vibration simulation analysis of the satellite, we can obtain the vibration transmission relationship from the moment gyroscope to the laser communication load and the micro-vibration state of the laser communication load.


Introduction
The entire mass of the satellite is about 35 kg, and the orientation of the star coordinate system (OXYZ) is shown in Table 1.
Table 1.Definition of satellite coordinate system.

Definition of satellite coordinate system Z-axis
Vertical solar panel, the direction in which the camera points Y-axis Parallel to the solar panel

X-axis
Right-handed Y and Z The launch status of the satellite is shown in Figure 1.

Analysis of micro-vibration data of torque gyroscope
The selected torque gyro speed was 0-6, 000 rpm, and different speeds were sampled.Due to the limitations of the test platform and other factors, the cut-off frequency is 400 Hz.Considering the uncertainty, the data is enveloped as conservative analysis input, as shown in Figure 2 to Figure 5.The horizontal axis is frequency (Hz), and the vertical axis is response amplitude (μm).

Finite element model
The model is properly simplified, and the geometric factors that have little influence on the result are ignored, such as chamfer, rounded corners, and small holes.The rest is dealt with as follows: 1) The main load-bearing structure of the satellite is a composite plate and frame structure, and the Shell unit is used to simulate it.The solar wing panel is a carbon fiber aluminum honeycomb panel structure simulated by the Shell unit and set by composite material overlay.The single stand is simulated by the Solid unit.
2) The single machine on the star is simplified into a concentrated mass unit at its center of mass.The quality of solar cells, cables, thermal control materials, etc. is simulated by adjusting the density according to the installation position.
3) The structural plates are connected through common nodes.4) Solar panels are simulated by rotating motion pairs.5) There is no displacement boundary condition in the orbital state, which is a free state.
The three-dimensional model of the satellite is shown in Figure 6.As shown in Figure 7, the satellite finite element model has 132, 762 nodes and 68, 557 units.

Modal analysis
We conduct modal analysis on the whole star and calculate the first 50 modes, as shown in Table 2.
Because the satellite is in a free state, the first six frequencies are 0, which is a rigid body mode.The microvibration analysis is limited to 400 Hz, and the 50th natural frequency is greater than 400 Hz [4][5].

Harmonic response analysis
The influence of disturbance during the operation of torque gyro on laser communication load in orbit is analyzed by the harmonic response.The microvibration response of laser communication load at different frequencies can be obtained by The damping ratio in the analysis is 0.03 [6][7].

Transfer rate analysis
The satellite is equipped with four torque gyroscopes.According to the test results of torque gyroscopes, the load is applied to each torque gyroscope.FX: FY: FZ: MX: MY: MZ = 5:5:1:1:0.05(Units: N and N*m) The influence of different position torque gyro on laser communication load is analyzed and the corresponding transfer relationship is obtained.
Figure 11 to Figure 12 show the transmission curve of the X torque gyro.The same curve can be deduced in other directions.Figure 15 shows the typical installation plate displacement distribution at 200 Hz.At this frequency, the structural vibration angle caused by microvibration is about 1 ".Considering all the comprehensive factors, the micro-vibration of the structure is not more than 5 " [11].

Conclusion
In this paper, the microvibration of a small satellite with laser load in orbit is analyzed, and the vibration transmission relationship and microvibration response relationship between torque gyro and laser communication load is obtained.

Figure 1 .
Figure 1.Definition of the coordinate system of launch state satellite.

Figure 8 to
Figure 8 to Figure 10 show the first modes.

Figure 10 .
Figure 10.The ninth mode of solar wing oscillation.

Figure 11 . 5 Figure 12 .
Figure 11.X torque gyro excitation and displacement transmissibility of laser communication load installation position 1.

Figure 13 .
Figure 13.Installation position of acceleration response of the laser communication load 1.

Figure 14 .
Figure 14.Displacement response of laser communication load installation position 1.Figure15shows the typical installation plate displacement distribution at 200 Hz.At this frequency, the structural vibration angle caused by microvibration is about 1 ".Considering all the comprehensive factors, the micro-vibration of the structure is not more than 5 "[11].

6 Figure 15 .
Figure 15.Displacement distribution of a typical mounting plate at 200 Hz.

Table 2 .
Whole star modal analysis.