## 3 Optimization and Matching Design of Rubber-Based SMA Suspension Systems
### Modeling and Analysis of Rubber-Based SMA Suspension System
#### 3.1.2 Multi-Body Dynamics Modeling and Reliability Verification of the Cab  
Suspension System  
This study employs Adams/View2016 version software to develop a multi-body dynamic model of the cab suspension system. The modeling process primarily utilizes the following parameters: the mass inertia characteristics of the cab, the stiffness and damping parameters of the suspension system, and the installation and fixation parameters of the suspension components. The necessary parameters are detailed in Table 5[38]. The 3D model of the cab was imported into Adams, and the cab's mass and moment of inertia were set according to the values provided in Table 5. The connections at the installation positions of the four suspension systems were modeled using bushing connections to represent the rubber-based SMA suspension. Three-dimensional stiffness and damping values were assigned to the bushing module. Notably, although the bushing module differs in form from the rubber-based SMA composite damper, its three-dimensional stiffness and damping characteristics are identical to those of the SMA suspension. The resulting multi-body dynamic model of the rubber-based SMA suspension system within the cab is depicted in Figure 9. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter Classification** & **Parameter Name** & **Numerical Value** \\ \hline \multirow{6}{*}{Quality parameters} & Cabin quality (kg) & 560 \\  & X-axis moment of inertia lxx (kg-m\({}^{2}\)) & 520.8 \\  & Y-axis moment of inertia lyy (kg-m\({}^{2}\)) & 690.83 \\  & Z-axis moment of inertia lzz (kg-m\({}^{2}\)) & 602.74 \\  & Inertia product lyy (kg-m\({}^{2}\)) & 21.1 \\  & Inertia product lxz (kg-m\({}^{2}\)) & 3.16 \\  & Inertia product lyz (kg-m\({}^{2}\)) & 77.37 \\ \hline \multirow{6}{*}{Positioning parameters} & Centroid coordinates (X/Y/Z m) & (0,0,0) \\  & Seat coordinates (X/Y/Z m) & (0.261, 0.124, \(-0.206\)) \\  & Left front suspension point coordinates (X/Y/Z m) & (\(-0.5015,\)\(-0.271,\)\(-0.7635\)) \\  & Right front suspension point coordinates (X/Y/Z m) & (\(0.5015,\)\(-0.771,\)\(-0.7635\)) \\  & Left rear suspension point coordinates (X/Y/Z m) & (\(-0.5405,\)\(1.217,\)\(-0.641\)) \\  & Right rear suspension point coordinates (X/Y/Z m) & (\(0.5405,\)\(1.217,\)\(-0.641\)) \\ \hline \multirow{2}{*}{Mechanical characteristic parameters} & Suspension three-dimensional stiffness (Ks/Y/Kz N\(\cdot\)mm\({}^{-1}\)) & (176.33, 603.35, 176.33) \\  & Suspension three-way damping (Cx/Cy/Cz N\(\cdot\)s\(\cdot\)mm\({}^{-1}\)) & (1.4408, 3.7864, 1.4408) \\ \hline \end{tabular}
\end{table} 
Table 5: Parameters of the cab suspension system [38]. Figure 9: [PERSON] multi-body dynamics model of cab suspension system. The calculation of modal frequency holds profound significance in the modeling and analysis of rubber-based SMA suspension systems. Modal frequency serves as a crucial parameter of the inherent vibration characteristics of a system, capable of reflecting the stiffness and mass distribution within the system. Through calculating the modal frequency, one can understand the response characteristics of the suspension system under different vibration modes. In the absence of external force excitation, the vibration module was employed to analyze the first six modes of the system. The results of this analysis were then compared with theoretical results obtained using the Newmark-Beta algorithm, as presented in Table 6. It is evident that the discrepancy in the first six modal frequencies calculated by both methods is less than 2%. Comparing the modal frequencies calculated via the [PERSON] multi-body dynamics model with the theoretical analysis results obtained by employing the Newmark-Beta algorithm can verify the accuracy and reliability of the multi-body dynamics model. A harmonic excitation force with an amplitude of 2000 N and a frequency of 20 Hz was applied to the four suspension points. A vibration analysis was conducted, and the z-direction displacement time-frequency response data at the seat position were measured.