# The Subsea Micro-Drilling Vehicle's Dynamic Analysis during Landing
## 2 Landing Process and Establishment of MBD Model
### Establishment of the Multi-Body Dynamic Model  
The SMDV primarily consists of a core extraction mechanism, crawler travel mechanism, power and control device, and other components, as shown in Figure 2; its structural parameters are shown in Table 1. This paper uses the MBD analysis software RecurDyn to model and analyze the SMDV, which adopts the theory of relative coordinate system equations and a fully recursive algorithm, and is suitable for solving large-scale and complex contact dynamics problems. To begin, construct the 3D model of the SMDV in ProE, import it into RecurDyn/TrackLM on an equal scale, and define the constraint relationship between each structure of the SMDV, in which the complex structure of the undercarriage wheel system and the track is constructed through CAD_Link/Sprocket/Flange for the simulation of the interaction between the track and the deep-sea sediment. ### Establishment of the Multi-Body Dynamic Model  
RecurDyn/Track_LM offers mechanical substrate models for sand, heavy clay, and sandy loam soils in the track-ground contact relationship. The implementation principle is based on the empirical indentation-subsidence equation proposed by [PERSON] [22] for the \begin{table}
\begin{tabular}{c c} \hline
**Data Type** & **Values** \\ \hline Weight (in air)/kg & 2000 \\ Weight (in water)/kg & 1500 \\ Size/(m \(\times\) m \(\times\) m) & \(1.6\times 1.2\times 1.2\) \\ Track grounding length/mm & 1220 \\ Track width/mm & 280 \\ Center distance between left and right & 900 \\ tracks/mm & \\ \hline \end{tabular}
\end{table} 
Table 1: Structure parameters of SMDV. Figure 2: Three-dimensional model of SMDV. 1—crawler travel mechanism, 2—core extraction mechanism, 3—power and control device. experimental analysis of many soils (1) and the relationship between shear stress and shear displacement proposed by [PERSON] [23] for brittle soils (2):  
\[p=\left(\frac{k_{c}}{b}+k_{\phi}\right)z^{n} \tag{1}\]  
where \(p\) is the ground pressure between the track and the soil (kPa), \(k_{c}\) is the soil cohesive deformation modulus (kN/mn + 1), \(k_{\phi}\) is the frictional deformation modulus (kN/mn + 2), \(b\) is the length of the short side of the contact plate (mm), \(z\) is the sinkage amount (mm), and \(n\) is the sinkage index. \[\tau=(c+\sigma_{s}\tan\varphi)K_{r}\bigg{\{}1+\bigg{[}\frac{1}{K_{r}(1-e^{-1}) }-1\bigg{]}e^{1-j/K_{\omega}}\bigg{\}}(1-e^{-j/K_{\omega}}) \tag{2}\]  
In Equation (2), \(\tau\) represents shear stress, \(c\) represents cohesion, \(\sigma_{s}\) represents normal stress, \(\psi\) represents the angle of internal friction, \(j\) represents shear displacement, \(K_{\omega}\) represents shear deformation modulus, and \(K_{r}\) represents the ratio of residual shear stress to maximal shear stress. In order to obtain the model parameters, the pressure-sinkage experiment (Figure 3) and triaxial undrained unconsolidated (UU) compression test (Figure 4) were conducted using deep-sea sediment samples at a depth of 2000 m in a sea area. The following experimental analyses were performed on the soil in this area according to the experimental method of measurement of deep-sea sediments by [PERSON] [24] and [PERSON] [25]. Figure 4: The triaxial undrained unconsolidated (UU) compression tests and the Stress Molar Circle. Figure 3: The pressure-sinkage experiment and the double logarithmic curves of compressive stress-sinkage. According to the actual aspect ratio of the SMDV, simulated crawler plates A and B (115 mm \(\times\) 390 mm and 90 mm \(\times\) 400 mm) were selected for data analysis. The compressive stress and sinkage coordinates of simulated crawler plate A and B were simultaneously taken logarithmically to obtain their corresponding double logarithmic curves of compressive stress-sinkage, as shown in Figure 3.  
During test settings with a surrounding pressure of 50 kPa, 100 kPa, and 150 kPa, sediment specimens were subjected to triaxial undrained unconsolidated (UU) compression tests.