# Numerical Performance Investigation of a Hybrid eCVT Specialized Agricultural Tractor
## 2 Case Study  
In this work, analysis focused on an a specialized orchard tractor, a category where compactness is crucial. These vehicles must be able to work nimbly among narrow rows and to have good curving capabilities to increase productivity. Table 1 shows the relevant characteristics of the conventional diesel-powered orchard tractor considered for this analysis. Traditionally, these working vehicles adopt high-power diesel units to cover the widest possible range of applied loads. However, considering the most common working scenarios for these tractors, their powertrains usually work at medium-low loads far from the optimal efficiency condition, leading to unnecessary fuel consumption. In order to simulate the behavior of the conventional tractor, its main subsystems were numerically modelled with MATLAB/Simulink using a modular and multiphysics power-based approach described in previous works [22]. The main subsystems covered in this work were:  
* vehicle and trailer dynamics;
* engine;
* gearbox and clutches;* PTO loads. The longitudinal dynamic behaviour of the tractor was modelled using a 1D model as shown in Figure 1.  
\[m\dot{V}_{x}=2\left(F_{xf}+F_{xx}\right)-F_{d}-mg\cdot sin\beta \tag{1}\]  
\[F_{zf}=\frac{-h(F_{d}+mg\cdot sin\beta)+b\cdot mg\cdot cos\beta}{2(a+b)} \tag{2}\]  
\[F_{zr}=\frac{+h(F_{d}+mg\cdot sin\beta)+a\cdot mg\cdot cos\beta}{2(a+b)} \tag{3}\]  
where:  
* \(a\), \(b\), and \(h\) represent the relative position of the centre of gravity of the vehicle with respect to the front and rear axles;
* \(m\) is the tractor mass; g the acceleration of gravity;
* \(\beta\) is the road slope angle;
* \(V_{x}\) is the vehicle longitudinal speed;
* \(F_{d}\) is the aerodynamic drag force as \(F_{d}=0.5\rho\zeta_{d}AV_{x}{}^{2}\cdot sign(V_{x})\), \(\rho\), air density; and \(C_{d}\), drag coefficient, a frontal cross-sectional area of the vehicle. However, this contribution is almost negligible for this specific application. * \(F_{xf}\) and \(F_{zr}\) are contact forces between wheels and ground on the longitudinal direction (front and rear axle). * \(F_{zf}\) and \(F_{zr}\) are normal contact forces between wheels and ground (front and rear axle). When modelling the presence of a trailer attached to the tractor, the connection between them was considered to be rigid. As a consequence, they shared the same longitudinal speed. During simulations, different payloads were considered for the trailer by changing its body mass. The engine's power output, as a combination of torque and speed, was numerically modelled using a tabulated torque data approach. Figure 2 shows the torque and power curves of the thermal unit considered in this work for the conventional \begin{table}
\begin{tabular}{l l} \hline Mass & 2570 kg \\ Vehicle wheelbase & 1900 mm \\ Track width & 1850 mm \\ Rolling radius & 680 mm \\ Nominal power & 73 kW @ 2400 rpm \\ Max engine rotational speed & 2400 rpm \\ Max vehicle speed & 40 km/h \\ Minimal speed & 0.4 km/h \\ \hline \end{tabular}
\end{table} 
Table 1: Main orchard-tractor characteristics. Figure 1: 1D longitudinal tractor model. powertrain. The proposed torque and power curves were derived from data available online for commercial diesel-engine units having nominal characteristics as close as possible to the ones of the reference conventional tractor studied in this and previous works by the authors. In order to compare the traditional powertrain and the proposed hybrid architecture, the engine subsystem included a multiparameter fuel consumption model that could consider both the ICE operating point characteristics and its nominal power rating. This model was developed by the Nebraska Tractor Test Laboratory and proposed by [PERSON] et al. [32]. This model was derived from fuel consumption measurements by the previously mentioned laboratory on more than 500 diesel engines designed for tractors.