# Simulation Analysis and Experimental Verification of the
## 4 Analysis  
### Frequency Response Analysis  
In order to evaluate the proper locking force of the MP under vibration environment, the frequency response analysis of the MSHML was carried out. Dynamic analysis was carried out in the Hypermesh/Patran/Nastran environment: Preprocessing was established in the Hypermesh. The whole model is composed of tetrahedron, hexahedron, shell element, and plate element, with a total of 1,882,080 units and 1,148,797 nodes. 7075 aluminum alloy was mainly used for the main body, and carbon fiber material T300 was used for the skin of the MSHML. The mm-t system of units was used in the analysis and the material parameters are shown in Table 1. The boundary condition was that six degrees of freedom of top and bottom connection points of the MSHML are constrained. The premise of vibration analysis in this analysis is that the MP and the locking screws are not separated, that is, they are locked and reliable, and they are connected by RBE2 as a complete whole to simulate the locking state in the finite element.  
Next, the finite element model of the configured MSHML was submitted to Nastran for solution and calculation. The input positions were top and bottom connection points of the MSHML, and the input condition of frequency response analysis is shown in Table 2. Finally, Patran was used for post-processing to extract the MPCFORCES of all nodes on RBE2 connecting to the lead screw at the resonant frequency, and the location of locking force was extracted as shown in Figure 4.  
The MPCFORCE of nodes at resonance frequency was extracted, the real and imaginary parts of the proposed node force were summed, respectively, to obtain \(F_{\rm r}\) and \(F_{\rm l}\), and according to the Pythagorean theorem to obtain the amplitude of locking force, which is the locking force under resonance condition. During the vibration experiment, in order to prevent separating, the preload force of the L/R mechanism must be greater than this value. For safety reasons, it was multiplied by 1.2 that is the safety factor, and the obtained value \(F_{\rm s}\) is the preload force during the vibration experiment.  
\[F_{\rm S}=1.2\sqrt{F_{r}^{2}+F_{l}^{2}} \tag{12}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Material** & **E1 (MPa)** & **E2 (MPa)** & **NU12** & **G12 (MPa)** & **RHO (t/mm\({}^{3}\))** \\ \hline
7075 & 72,000 & - & 0.33 & - & \(2.81\times 10^{-9}\) \\ T300 & 13,500 & 8500 & 0.35 & 4800 & \(1.6\times 10^{-9}\) \\ \hline \end{tabular}
\end{table}
Table 1: Material parameters.  
Through modal analysis, the x-direction resonance frequency is 55.8 Hz. The cloud diagram of the MSHML in X-direction is shown in Figure 5, and the locking force of eight locking positions at this frequency was extracted as shown in Table 3, and the positions of eight locking force are shown in Figure 6. In the process of locking, the front beam of the MSHML will produce slight predeformation under the action of locking force and absorb part of the energy. The closer it is to the central front beam, the greater the deformation will be. The rear beam is connected to the back structure, with relatively higher structural stiffness and almost no deformation. It can be found from the data in Table 3 that the locking force of the back measuring points is larger than the measuring points in the front. The locking force of the lower measured points is larger than the measured upper points, and the result of the locking force is consistent with the analysis. The maximum locking force is 1606 N at position 8. In order to make the MP lock reliably during vibration, according to Equation (12), the \(F_{s}\) (\(s=1,\,2,\ldots,\,8\)) can be estimated at no more than 2000 N.  
Figure 4: The position of nodal forces.  
Figure 5: X-direction modal nephogram.