# Research on Design, Simulation, and Experiment of Separation Mechanism for Micro-Nano Satellites
## 3 Design of the Separation Mechanism
### Mechanism Design  
Solar panels are mounted on the MF satellite's \(\pm\)Y sides, and the optical camera hood protrudes from the satellite's surface. Interference collisions between the satellite and the separation mechanism must be avoided during the separation process to avoid damage to the solar panel or the camera. Therefore, a detailed analysis and calculation of the separation mechanism's motion system are required. The motion system is primarily composed of two components. The ejection system of the satellite comes first, followed by the OMLDC. The following is a detailed design for the two mechanisms mentioned previously.  
**Ejection system**  
The deployment spring is the most critical component of the ejection system (a cylindrical compression spring). The deployment spring's primary function is to release the energy storage once the satellite is on-orbit, allowing the satellite to separate from the launch vehicle. Without considering the elastic damping of the spring and the friction between the MF satellite and the separation mechanism, the relationship is as follows:  
\[\frac{1}{2}kx_{\text{max}}^{2}=\frac{1}{2}Mv^{2} \tag{1}\]  
where  
\(k\)--stiffness coefficient of the deployment spring;  
\(x_{\text{max}}\)--maximum displacement of the deployment spring;  
\(M\)--mass of the MF satellite;  
Figure 4: Mechanical interface diagram for the separation mechanism and the MF satellite.  
\(v\)--initial ejecting velocity of the MF satellite.  
The deployment spring's maximum displacement is determined by the length of the separation mechanism's guide rail, the mass of the MF satellite is constant, and the MF satellite's initial ejecting velocity is determined by the overall index. To ensure satellite separation reliability in this paper, the spring's maximum displacement is 420 mm, the MF satellite's initial ejecting velocity is 0.5 m/s-2 m/s, and the satellite weighs 20 kg. According to Formula (1), the range of the deployment spring's stiffness coefficient \(k\) is 28.3 N/m-453.5 N/m.  
The deployment spring's mean diameter and slenderness ratio should not be too small to maintain the push board's stability; otherwise, the deployment spring's axial load will cause lateral bending, resulting in the push board losing stability. The deployment spring's slenderness ratio must satisfy Formula (2) for the spring to be stable.  
\[b=\frac{H_{0}}{D}\leq 5.3 \tag{2}\]  
where  
\(H_{0}\)--free height of the deployment spring;  
\(D\)--mean diameter of the deployment spring.  
Given the spring's maximum displacement of 420 mm and its free height \(H_{0}\) of approximately 470 mm, the spring's mean diameter can be calculated to be greater than 88.7 mm using Formula (2). We initially chose a mean diameter of 100 mm for the deployment spring in this paper. At the moment, the deployment spring's stiffness coefficient, mean diameter, and maximum displacement are known, and the remaining parameters can be calculated using Formula (3). The spring is made of 1 Cr18 Ni9, which has a shear modulus of 71 GPa. Based on the calculation, a variety of spring parameter groups can be chosen.  
\[k=\frac{Gd^{4}}{8 nD^{3}} \tag{3}\]  
where  
\(G\)--shear modulus of the deployment spring material;  
\(D\)--mean diameter of the deployment spring;  
\(n\)--active coil number of the deployment spring;  
\(d\)--wire diameter of the deployment spring.