## 4 Modeling and Experimental Validation Dynamics Characteristics of the Truck  
### Truck Modeling  
After modeling the front and rear suspensions and validating the leaf springs as described in the previous section, the next step involved complete truck modeling. This included the integration of the steering system, the front and rear wheels, the chassis, the powertrain, and the driveline. The ADAMS software provides template models in its library, which could be used in the truck model with some modifications according to the truck's requirements. This involved adjusting the hardpoints coordinates and the element properties, such as the wheels, to ensure that the characteristics of the created model are identical to those of the real model.  
The chassis model is represented as a rigid body with some details such as mass and moment of inertia. For the front and rear wheels, the Pacejka 2002 tire model was used, which is based on the Magic Formula, developed by [PERSON] [38], a widely used model in tire dynamics. This model uses semi-empirical formulas to define the wheel-ground contact [39].  
In the property file of the Pacejka 2002 tire model, we modified the characteristics of the tire, including the dimensions and vertical stiffness measured previously. The other parameters were kept unchanged.  
In the ADAMS library, there are models of the powertrain, driveline, and steering system that are similar to those used in the truck. For the powertrain, its mass and transmission ratios were modified. For the driveline, the front and rear transmission ratios were adjusted.  
Some modifications were made to ensure the same steering ratio as the real systems for the steering system. First, we measured the wheel rotation angles (steer angle) when the steering wheel was turned at specific angles and plotted the steering wheel angle versus the steer angle. Then, we assembled the front suspension presented in Figure 5a with the steering subsystems. The assembly is represented in Figure 9a. The measured maximum and minimum steering wheel angles were \(650^{\circ}\) and \(-650^{\circ}\), respectively, and these data were added to the model.  
Figure 9: Steering system: (**a**) multi-body model; (**b**) steering angle vs. steer angle curves.  
We adjusted the gear ratio within the steering model and conducted simulations. We compared the curve of the steering wheel rotation angle as a function of the wheel angles (steer angle) obtained by simulation with the one obtained by measurements. This iterative process was repeated until the acceptable alignment between simulated and measured curves was achieved, as illustrated in Figure 9b.  
The steering ratio has a crucial role in truck validation, especially in scenarios such as open-loop steering events in ADAMS, including single-lane changes or during free-driving scenarios.  
The truck model can be assembled using the ten subsystems of the vehicle mentioned previously (front suspension, front leaf spring, front tire, rear suspension, rear leaf spring, rear tire, steering system, the chassis, powertrain, and driveline) and is presented in Figure 10b.  
Before performing the simulation of the truck, it was essential to analyze its characteristics, such as the mass, center of gravity coordinates, and moment of inertia. For the truck mass and the coordinates of its center mass, we used the values presented in Table 3. However, the moment of inertia for the full truck was difficult to find experimentally, so we created a 3D truck model, as shown in Figure 10a, to determine the approximate values of \(I_{xx}\), \(I_{yy}\), and \(I_{zz}\).  
From there, we proceeded to analyze the dynamics of the truck model and validate it through experimental tests.