# Grousers Effect in Tracked Vehicle Multibody Dynamics with Deformable Terrain Contact Model
## 3 Methods: Multibody Modelling  
The MTB model of the tracked vehicle was built into the MSC ADAMS\({}^{\circledR}\) (Newport Beach, CA, USA) software. Modelling of the tracks and the tensioning system was combined with a simplified body representing the main machine geometries. However, the mass and moments of inertia were estimated accordingly to the vehicle characteristics of a real machine for farming applications taken as a reference (see Table 1). Each track was made of 40 rigid bodies (links). The grocket teeth transmit the motion by inserting into the links holes. The lateral movement of the track was bound with respect to the idle wheel by the central rail formed by each track segment (Figure 4).  
Small size tracked machines are usually equipped with rubber tracks. They have a steel core which gives a greater tensile strength. To obtain a track model with behaviour and properties similar to a real rubber track it was necessary to properly model the joints between consecutive links. In this work a bushing element was considered (Figure 4b). Three-dimensional bushing joints allowed to transmit elastic and damping forces and torques between two consecutive links. The required stiffness and damping coefficients were defined applying specific loads and comparing the virtual track behaviour with a reasonable response of a real one. In particular, a static test as the one shown in Figure 5 was simulated to see if the tensioning force and the proposed parameters for the bushing elements were coherent with the deflection of a track with a mass of 20 kg placed in between the idle wheel and the sprocket. Stiffness values are listed in Table 2.  
\begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{2}{c}{**Vehicle Properties**} \\ \hline Mass & 750 kg \\ Length & 1500 mm \\ Width & 700 mm \\ Height & 1130 mm \\ Track width & 180 mm \\ Top speed & 4 km/h \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main characteristics of the tracked vehicle.  
Figure 4: (**a**) Track structure, (**b**) links connected by a bushing element.  
Negligible displacements and angular misalignments in x and y directions between two consecutive links were obtained using high translational and rotational stiffness values along those directions. Comparing the deformed shape of a real rubber track with the deformed shape of its MTB model, rotational stiffness in z direction was set. Track vibrations were limited by setting appropriate rotational damping in z direction, also considering rubber damping effect [43]. Idle wheels, driven wheels and oscillating plates with road-wheels were properly modelled (Figure 6). Contact forces were defined between each track link and each wheel. Low penetration depth and friction coefficient related to rubber-steel contact were defined. A damping value of 5.0 Ns/mm and a stiffness value of 100 N/mm were considered for the contact model of these elements. The driving wheel teeth insertion into links holes allowed torque transmission thanks to the contact force definition. In Figure 6 the position of the machine centre of mass (CM) is highlighted. Its position, as well as the overall moments of inertia of the vehicle are coherent with the vehicle characteristics shown before in Table 1.  
The track tensioning system was modelled so that the simultaneous rotation and translation of the idle wheel could be allowed (Figure 7). A translational joint was applied between a cubic pivot (dummy) body and the main body of the machine. The idle wheel was connected to the pivot body by means of a rotational joint. Considering typical tensioning force values for rubber tracks of small size machines, F force value (Figure 7) was set equal to 5100 N in such a way that the static track deformation would satisfy the test shown in Figure 5.