# Numerical Investigation on Handling Stability of a Heavy Tractor Semi-Trailer under Crosswind
## 4 Multi-Body Dynamic Simulation  
Previous research has studied the aerodynamic forces and moments under steady conditions, and just estimated the aerodynamic changes when the vehicles generated a yaw slip [38]. However, these aerodynamic characteristics will have some effects on the vehicle dynamics. Therefore, in this work, a coupling method that combined the changing aerodynamic coefficients with the vehicle dynamics system was used to analyze the effect of crosswind on the handling stability of a tractor semi-trailer. A six-degrees-of-freedom (6-DOF) multi-body dynamic model of a six-axle tractor semi-trailer was constructed in the software TruckSim showed in Figure 14. The model consists of an aerodynamics module, vehicle body, driving system, steering system, braking system, power transmission system and so on. Some specifications of the tractor semi-trailer such as moment of inertia and center of gravity (c.g.) are described in Table 1. The tractor and trailer are treated as a single rigid body. In order to analyze the dynamic characteristics while considering the change of the aerodynamics under crosswind, the aerodynamic module is described by the fitting curves of the aerodynamic coefficients. The proposed tractor semi-trailer is equipped with a 300 kW diesel internal engine model, a torque transfer, a transmission, a transfer case and some differentials. The brake actuator of each wheel has been simply modeled with no braking pressure, and in order to simulate an open-loop steer control, the shifting control of the vehicle was clutch disengaged. The aerodynamic model is \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameters** & **Values** \\ \hline \(m\) & Vehicle total mass (powered unit) & 7600 kg \\ \(m_{s}\) & Vehicle sprung mass (powered unit) & 4455 kg \\ \(l_{f}\) & Distance between c.g. and the 1-axis (powered unit) & 2.0 m \\ \(l_{P}\) & Distance between c.g. and the 3-axis (powered unit) & 2.75 m \\ \(L\) & Vehicle length (powered unit) & 7.25 m \\ \(H\) & Vehicle height (powered unit) & 3.9 m \\ \(l_{ux}\) & Rolling moment of inertia (powered unit) & 22839 kgem\({}^{2}\) \\ \(l_{yy}\) & Pitching moment of inertia (powered unit) & 35,402.8 kgem\({}^{2}\) \\ \(l_{nz}\) & Yawing moment of inertia (powered unit) & 34,802.6 kgem\({}^{2}\) \\ \(m_{t}\) & Vehicle total mass (trailer unit) & 7500 kg \\ \(m_{h}\) & Vehicle spring mass (trailer unit) & 5500 kg \\ \(l_{\mu}\) & Distance between c.g. and the 3-axis (trailer unit) & 3.3 m \\ \(l_{tt}\) & Distance between c.g. and the 6-axis (trailer unit) & 5.01 m \\ \(L_{t}\) & Vehicle length (trailer unit) & 12.2 m \\ \(H_{t}\) & Vehicle height (trailer unit) & 4.2 m \\ \(l_{ant}\) & Rolling moment of inertia (trailer unit) & 8997.1 kgem\({}^{2}\) \\ \(l_{apt}\) & Pitching moment of inertia (trailer unit) & 150,000 kgem\({}^{2}\) \\ \(l_{ext}\) & Yawing moment of inertia (trailer unit) & 150,000 kgem\({}^{2}\) \\ \(K_{sf}\) & Upper vertical spring stiffness & 0.25 N/m \\ \(K_{sf}\) & Lower vertical spring stiffness & 0.7 N/m \\ \(C_{f}\) & Upper vertical damping & 15,000 N/m \\ \(C_{r}\) & Lower vertical damping & 30,000 N/m \\ \(C_{sf}\) & Cornering stiffness of one type (front) & 140,000 N/rad \\ \(C_{ar}\) & Cornering stiffness of one type (rear) & 140,000 N/rad \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters for the tractor semi-trailer. Figure 14: The schematic of multi-body dynamics model. composed of the six aerodynamic coefficients; the force and moment vector acting on the sprung mass represent the aerodynamic effects. The aerodynamic characteristics will be changed when the aerodynamic parameters are different [39]. Finally, a multi-body dynamic model with given aerodynamic properties was established. The aerodynamic coefficients of the vehicle will be changed with the motion dynamically, and the change will have an important influence on the vehicle system dynamics.