# Fatigue Assessment of Explosive Bolts Considering Vibration of Fixtures
## 3 Dynamics Analysis of the Missile Vehicle Based on ADAMS  
The missile vehicle is simplified as shown in Figure 2. The DOFs of \(Y\) translational degree of freedom--the rotation degree of freedoms about axis \(X\) and \(Z\), ROT \(X\) and ROT \(Z\)--are set to zero. The chassis is simplified as a rigid body, the suspension systems are described as Spring-Damping systems, and the Pacejka 89 tire model is picked to simulate the tire. The suspension systems are constrained to the chassis with fixed joints, and all DOFs of these joints are constrained to zero. The tire and the suspension system are constrained with revolute joints at the center of the tire, where only the DOF of ROT \(Y\) exists. Suppose that the rear wheels be driven at a constant speed of 12 m/s along axis \(X\) and that the river torque has not been taken into consideration, by supposing the vehicle drives at a constant speed. Because the vehicle drives at a relatively low speed, we suppose the tires and the road surface be kept in contact during the whole transportation process. Figure 1: Road roughness curves of Class A, C, and E.  
Figure 2: Simplified vehicle model for the dynamics analysis. The road surfaces obtained in Section 2 are used as the excitation in the vehicle dynamic simulation to produce longitudinal displacement \(X\), vertical displacement \(Z\), and pitch angle \(\phi\). The suspension is modeled by a damping-spring system. Magic tire Pacejka89 in ADAMS is picked as the tire model. The related parameters of the missile and its vehicle are listed in Table 1.  
The virtual prototype of the missile and the carrying vehicle are assembly-built by the dynamics analysis software ADAMS, as shown in Figure 3. Here, we suppose the total mass (including missile body, warhead, filler, and structures inside) of the missile is about 8300 kg; 1000 kg for the warhead and filler inside, and 7300 kg for the missile body and structures inside. The filler inside mainly affects the performances of the vehicle more, such as rollover. Our research focuses on the safety of the explosive bolt, so we neglect the effect of the filler and other structures inside, and construct a model according to mass equality. This simplification makes it more convenient to analyze the structures we are interested in, namely the explosive bolts. Since we are interested only in the effect of road roughness on the carrying structure's loading, instead of the dynamic process and performance of the vehicle, for the convenience of analysis we suppose the missile vehicle drives at a speed of 12 m/s on Class A, C, and E roads, and the wheelbase and the road surface are constrained coplanar in \(X\)-\(Z\) plane so as to remain in a linear motion. Performing dynamical analysis, we obtain the longitudinal, vertical, and pitch angle accelerations of point A on the missile vehicle when driven on Class A, C, and E roads, as shown in Figure 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Components** & **Conditions** & **Parameters** \\ \hline \multirow{4}{*}{Assembly} & Drive mode & 8 \(\times\) 2 \\  & Wheelbase & (1600 + 3500 + 1600) mm \\  & Body mass & 18,300 kg \\  & Center-of-mass coordinate & (3294.2, 305.1, 0) mm \\  & The moment of inertia to centroid & 56,178,826,615 kg\(\cdot\)mm\({}^{2}\) \\ \hline \multirow{4}{*}{Suspension} & Suspension type & Rigid axle suspension \\  & Mass & 200 kg \\  & Stiffness coefficient & 300 N/mm \\  & Damping coefficient & 5 N\(\cdot\)s/mm \\ \hline \multirow{4}{*}{Tire} & Mass & 25 kg \\  & Free radius & 67.15 mm \\ \cline{1-1}  & Aspect ratio & 0.35 \\ \cline{1-1}  & Longitudinal stiffness coefficient & 300 N/mm \\ \cline{1-1}  & Longitudinal damping coefficient & 1.6 N\(\cdot\)s/mm \\ \hline \multirow{4}{*}{Warhead and missile body} & Connection mode & Explosive bolts connection \\ \cline{1-1}  & Number of connections & 4 \\ \cline{1-1}  & Position of connections & Quadrantal points of a \(\phi\)840 mm circle \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the missile and the carrying vehicle.