**5. Revised results**

**Figure 5.** Constraints on image data processing

336 Advances in Vibration Engineering and Structural Dynamics

The initial results of these measurements were reported in another paper in this series (Oda et al., 2011). Fig. 6 shows typical results. It shows an offset of a few millimeters appeared when solar array paddle illuminated by the Sun and when in an eclipse. However, these re‐ sults pose certain difficulties in explaining the phenomena, as the tendency of the solar array paddle to bend does not agree with the observation results and conventional research.

Sun illuminated Eclipse

**Figure 6.** Motion of the solar array paddle's tip position as estimated from onboard camera images

**4. Previous results**

Fig. 6 shows a sudden offset in the motion of the solar array paddle. When the solar array paddle is straight, the value of displacement may indicate -12 or -11 [mm] in Fig.6. Although we attempted to identify cause of this offset, we could not imagine a proper mechanism that would produce such a direction. We therefore assumed that the previous image data proc‐ essing contained unidentified data processing errors, and consequently modified the algo‐ rithm that identifies the target markers. The earlier version of the algorithm used to identify locations of the target markers assumed such highly illuminated areas as those of the target markers. This algorithm works well when the markers are brightly illuminated. When the target markers are weakly illuminated, however, we found that this algorithm produces some data processing errors.

Fig. 7 and Fig. 8 illustrate the difference described above. Fig. 7 is based on the previous al‐ gorithm. The areas enclosed by a yellow line are pixels that are brighter than the threshold level and thus can be assumed to be the target markers as based on sub-pixel level image data processing. The red cross indicates the center position of the marker.

**Figure 7.** Target markers estimated by the previous algorithm under weak illumination. The areas of target markers assumed by the previous algorithm are smaller than the actual target marker size.

Fig. 7 shows that the sizes of the estimated target markers are smaller than the actual target markers. We therefore modified the algorithm used to estimate the area of a target marker so that the size of the predicted target marker is similar to that calculated from the actual target marker. This modification worked well to identify the target marker and its displace‐ ment. Fig. 8 is a result based on the revised algorithm. In this revised algorithm, the areas to be considered target makers are decided based on the brightness level of each pixel and also on the size of the areas considered to be target markers. When an assumed target marker is too small, then the threshold level of brightness is automatically adjusted to meet the possi‐ ble size of the target markers.

From these data, we can conclude that the temperature of the solar array paddle changes steadily but not drastically, depending on its thermal capacity. And we also assume like as

Vibration of Satellite Solar Array Paddle Caused by Thermal Shock When a Satellite Goes Through the Eclipse

http://dx.doi.org/10.5772/52626

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**1.** When the solar array paddle is illuminated by the Sun, its temperature is governed by

**2.** When in an eclipse, the solar array paddle shows lower temperature depending on its thermal capacity. When the satellite's LST (Local Sun Time) is around noon, the solar cell side of the panels faces the Earth and receives solar radiation from Earth. In the eve‐ ning and the early morning of satellite LST, however, both sides of the solar panels face

In order to verify whether the observation results described above are correct, and to under‐ stand the features of thermal snap on the solar array paddle, we conducted numerical simu‐ lation of the solar array paddle. There are many studies analyzing the thermal snap (Thornton, 1996; Boley, 1972; Johnston, 1998; Lin, 2004; Xue2007), we develop the method using a thermal model and a structural model and revising these models by applying the observed data. This section presents the analytical system that we constructed, the result of a thermal-structural analysis and its problems. To solve the problems, we have developed a new model in considering the effects of hinge/latch mechanisms and friction. The result of

This section describes the thermal snap analysis procedure. Fig. 12 shows a flowchart of thermal snap analysis. The analysis can be broken down into to three parts: construction of the structural model, calculation of temperature distribution, and thermal snap analysis for

In the first part, a structural model of the solar array paddle is constructed for thermal snap analysis. To verify the structural model, we conducted modal analysis to obtain the natural frequency and vibrational mode of the solar array paddle model. These results will be com‐ pared with an on-orbit preliminary experiment, and if necessary, we will then revise the model (see Section 6.2 for details). In the second part, a thermal model is developed for the solar array paddle. Thermal analysis for the whole orbit is then conducted to verify the ther‐ mal model. The thermal analysis results will be applied to GOSAT's trajectory information, and also compared with data obtained by GOSAT, in order to verify accuracy. After accura‐ cy is verified, thermal analysis will focus on GOSAT during its integration and testing. In order to improve the accuracy of thermal analysis, a profile of thermal input was deter‐

mined based on the brightness of the solar paddles (see Section 6.3 for details).

solar energy from the Sun (as well as that reflected from Earth).

toward space, resulting in a rapid drop in temperature.

following.

**6. Numerical simulation**

using new model is also introduced.

**6.1. Thermal snap analysis procedure**

the penumbra.

Finally, Fig. 9 shows the motion of a target marker as based on the revised algorithm. We can see that the estimated motion of the solar array paddle has less dispersion.

**Figure 8.** Target markers estimated by the revised algorithm

**Figure 9.** Displacement of GOSAT's solar array paddle when going into eclipse

From these data, we can conclude that the temperature of the solar array paddle changes steadily but not drastically, depending on its thermal capacity. And we also assume like as following.

