## 4 Analysis of the Factors Affecting on the Gathering Process and Self-Preservation of the STACER
### Influence of the Top Rod Radius on the Gathering Process of the STACER  
The STACER can be applied as a part of satellite antenna. Due to the installation requirements, the top rod radius can be selected from 8.7, 9.0, and 9.3 mm. The spring reel and storage barrel remains at a certain size. The storage barrel is set with a radius of 25 mm, a height of 130 mm, and a wall thickness of 1 mm. Three kinds of finite element models of STACERs of the mentioned top rod size are built to study the radius's effect on the gathering process of the STACER. The situation results can be seen in Figure 5a-c. The stress type is von Mises and the unit is MPa.  
Figure 5: The stress distribution of spring reels during gathering process with top rod radius of (**a**) 8.7 mm, (**b**) 9.0 mm and (**c**) 9.3 mm.  
In all three cases, the full gathering state can be achieved only when the top rod radius is 8.7 mm. The maximum stress state is 1085 MPa, which is less than the material yield strength of 1291 MPa. It shows that the STACER does not undergo plastic deformation during the process of gathering, which satisfies the working requirements for the spring reel. When the radius of the top rod is changed to 9.0 mm, the maximum stress is more than 1291 MPa, which reaches the yield strength of the spring material. It can be seen from the figure that partial plastic deformation occurs in the surrounding portion of the rivet joint. When the radius of the top rod is 9.3 mm, STACER undergoes even higher stress and extensive plastic deformation. The STACER tends to be damaged.  
In order to study the force evolution tendency of the top rod during gathering process, the relation between the gathering length and the force on the top rod is analyzed, as shown in Figure 6a,b. STACER is a spring which requires constant force when gathering and deploying. Along with the gathering position, the force analysis at the rod top is carried out for the STACER. When the top rod radius is 8.7 mm, the force on the top rod is generally stable, and the force fluctuates between 32.4 and 45.1 N (do not include the initial loading stage). As the top rod moves downwards, the friction is weakened between the layers of the spring reel. The friction force is reduced while the elastic restoring force gently increases. When the top rod radii are 9.0 and 9.3 mm, the force fluctuates frequently and greatly. The force on the top rod can not be kept constant for the STACER. This is the reason that some STACERs are plastically deformed, as shown in Figure 5.  
The mechanical model for analyzing the gathering process of the top rod with a radius of 9.3 mm is shown in Figure 7a-d. When the gathering length is from 0 mm to 770 mm, the STACER is gathered smoothly and the cone angle is small, as shown in Figure 7a. The transition section presents a cylindrical shape. At 770 mm, the transition section produces a large tapered area, and stress concentration occurs at the tapered area without local shell buckling. With the increase of gathering length at 890 mm, local shell buckling occurs, as shown in Figure 7c. It leads to a failure of the material and even destruction in the subsequent gathering process. At the same diameter of storage barrel, the larger the top rod diameter, the larger the conical degree for the spring reel when the gathering distance is the same. This taper greatly increases the friction between the layers of the spring reel so as to block the gathering process. Therefore, the top rod radius is chosen as 8.7 mm in order to avoid possible deformation.  
Figure 6: Force diagram during the gathering process on the top rod with (**a**) a radius of 8.7 mm; (**b**) different radial dimensions.