Modeling and Simulation of Satellite Solar Panel Deployment and Locking

MATERIALS AND METHODS

The satellite is modeled by considering the main body and two yokes, which connect the main body and two adjacent panels as rigid bodies and solar panels, are modeled as flexible bodies. All eight panels have the same geometry. The panels are stowed during launch into a small volume and are then extended on-orbit. At the end of deployment it undergoes locking at the joints. In this study a solar array with two wings has been considered, which is illustrated by Fig. 1a-c. Each wing consists of a yoke and four flexible panels. The solar panels are deployed by the energy provided by preloaded torsion springs mounted at the interpanel hinges. The yoke and the panels are similarly connected with different spring parameters and deployment angles. As the angle between two panels reaches the deployed state the hinge is locked by a locking mechanism.

The finite element modeling of the flexible panel is created using ANSYS and the deployment simulation is made using ADAMS. Thin shell elastic 4 node 181 element type is used for the finite element model of the solar panel in ANSYS. The static and normal mode analysis results of each panel are combined and then it is applied to the flexible body dynamic model of ADAMS and its dynamic and vibration analysis is performed. The deployment simulations were carried out at space without gravity while the satellite is free and can move and rotate. The initial data considered for this simulation are: mass of the center body 680 kg, mass of each solar panel 5 kg, size of each solar panel 1.42x0.76x0.0158 m (LxWxD), material used for the solar panel is aluminum with density of 2.76x103 N m^-3 young’s modulus of 6.8x1010 N m^-2 and poison ratio of 0.33, size of each yoke 1.42x0.36x0.01 m (LxHxD), mass of each yoke 3.3 kg. The simulation is performed with 1.00001 sec end time and 50 steps.

The preload in the deployment springs drives the deployment motion. In this design, the preload decreases linear from 0.39093 N m at the array root hinge line to 0.160 N m at the top hinge line. The torsion stiffness of the root spring is equal to 0.2499 N m rad^-1 and for the other springs is equal to 0.0936 N m rad^-1 giving a constant torque throughout the full deployment. By varying the preload torque in the first hinge and the other springs, the solar array can be used for both 180° panel-hinge deployment and 90° root-hinge deployment.

RESULTS AND DISCUSSION

The result from the simulation is analyzed in various ways. This simulation work helps in predicting the deployment trajectory to investigate any dangerous situations like collision with other parts of the satellite appendages resulting from the deployment of the panels. The deployment must behave in a smooth manner and all panels must deviate as little as possible from their shortest path from stowed to deployed position. The simulation work also helps in predicting the effect of deployment and locking on the attitude of the satellite.

Fig. 1:	Satellite solar panel deployment: (a) stowed position, (b) during deployment and (c) fully deployed state

Fig. 2:	Vibration mode shapes of deployed solar panel: (a) at frequency 1.1042 Hz, (b) at frequency 5.4403 Hz, (c) at frequency 5.6136 Hz and (d) at frequency 14.3396 Hz

Fig. 3:	Angular acceleration of root and external panels

Fig. 4:	Translational deformation acceleration of the outer end of external and root panels

The first four dominant vibration modes that should be thoroughly considered in the design of the vibration control are modes at frequencies of 1.1042, 5.4403, 5.6136 and 14.3396 Hz. These mode shapes of the deployed flexible solar panel after locking are shown in Fig. 2a-d.

From Fig. 3 we can observe that, the rotational acceleration is fastest at the external panel and lowest at root panel. The farther away the panel is from the central hub, the faster its rotational acceleration becomes. Thus, the locking occurs successively during motion, from the last two panels to the first two panels. At the end of deployment, an undesirable high-frequency oscillation of the solar panels occurs.

Figure 4 shows the comparison of the translational deformation acceleration of the outer end of external and root panels. The deformation acceleration is almost the same during the primary stages of deployment, but high amount of variation is observed at the end of deployment during locking.

Fig. 5:	Angular deformation of the outer and inner end of external and root panels

Fig. 6:	Effect of panel deployment on angular velocity of the satellite

The deformation acceleration is higher for the outer point of the inner panel than the outer points on the outer panels. From Fig. 5, we can also observe that, the angular deformation of the inner end of the root panel is dominant than the external one and the same way, the angular deformation of the outer end of the root panel is also more dominant. For all panels the deformation is more dominant on the inner side. This gives us an indication as to where we should place the vibration controlling mechanism. More emphasis should be given to the inner sides and the inner panels. The maximum angular deformation of the solar panel is about 1.2912⁰ which is for the inner side of the root panel.

Satellite needs quiet environment for operation without vibration or oscillation. Vibration degrades the performance of sensitive devices and it also disturbs the satellite attitude from its normal route. Figure 6 shows that, the deployment operation causes disturbance on the angular velocity of the satellite.

Table 1:	Satellite attitude change (maximum) during panel deployment

Fig. 7:	Change in angular displacement of the satellite during deployment

The disturbance is much higher at the end of the deployment process during locking. As shown in Fig. 7, the vibration due to deployment and locking causes a disturbance on the attitude of the satellite. The maximum angular disturbance is about 0.0131⁰. The detailed values of the translational as well as the angular attitude change values for the satellite in the x, y and z axes are shown in Table 1.

CONCLUSIONS

Simulating the non-linear behavior of satellite with flexible appendages is very feasible using a combination of codes such as ANSYS and ADAMS. Virtual prototyping using these softwares helps to identify in advance the critical sensitive parameters to be investigated during physical tests. The result obtained clearly shows that the vibration caused due to the deployment and locking operations impede the attitude of the satellite. The inner side of each solar panels have higher deformation angle than the outer side with the inner solar panel having the maximum contribution, for example, maximum deformation for the inner side of the root panel is about1.2912⁰ but for the inner side of the external panel is about 0.6028⁰, the maximum deformation for the outer side of the root panel is about 0.3286⁰ but the maximum deformation for the outer side of the external panel is about 0.2583⁰. Therefore, placing the vibration controlling mechanism on the inner side of the inner panels will give a good result in the desired vibration attenuation.

ACKNOWLEDGMENT

The author would like to acknowledge National Nature Science Foundation of China, under grant No. 10872054 and 10872055 for funding the project.