## 3 Results and Discussion
### Model Validation  
The final goal of our investigation is to compare the energy needs for the soil tillage obtained with the simulation and the energy needs determined with experiments, presented in [8], for a 15 m soil tillage length. In each of the above presented three cases, the torque variation is calculated during one revolution of the crankshaft, defining the mechanical work for one cycle of soil tillage. Based on the soil chip thickness, the number of the cycles may be determined, which are needed for the 15 m tillage completion. These two computed parameters specified, through their product, the total required mechanical work needed to complete our virtual experiment.  
Figure 17 presents the torque values needed for the effective soil tillage process: it is calculated from the torque values obtained by the simulation of cases I, V, and IX (as in Figure 15 for other cases) and decreased by the torques needed to move the mechanism itself (as in Figure 7 for other cases) in the three cases. This figure also shows the presence of the three types of loads, as described in the above part of the paper.  
Figure 16: Comparison of the acceleration modulus and the variation of the spade-tip vertical displacement for the working cases I, V, and IX (first cycle presented).  
Because one cycle represents a rotation of 360\({}^{\circ}\) of the crankshaft, the area beneath the curves relative to one rotation, between the [0,2\(\pi\)] interval, determines the mechanical work corresponding to one cycle done by one spade. Taking into account the soil chip thicknesses, the cycle numbers are determined along the 15 m, so the total mechanical work can be calculated. The investigated spading machine is equipped with six spading mechanisms, so the required total amount of mechanical work for the whole tillage is calculated by multiplying the results for a single spade by six. The obtained values are presented in Table 3.  
At this point, the simulation result may be compared with the real experiment result (Table 4). Based on [8], the energetic needs were determined taking into account the measured diesel fuel consumption for the tillage processes (\(C_{cl}\) (m\({}^{3}\))), having as parameters the calorific power (\(H\) = 41 (MJ/kg)) and the fuel density (\(\rho_{fuel}\) = 820 (kg/m\({}^{3}\))) using the following equation:  
\[Q=C_{cl}\;\rho_{fuel}\;H\;[J]. \tag{12}\]  
The result from the last columns of Tables 3 and 4 are presented together in Figure 18 and provide acknowledgment of the correctness of our Matlab(r) Simulink model. The numerical comparison is shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Working Cases**} & **Average** & **Fuel Consumption of the** & **Energy Calculated** & **Available Mechanical Work** \\  & **Advancing Speed** & **Tillage Process** & **Based on Consumption** & **Due to 40\% Engine Efficiency** \\  & **[m/s]** & **[cm\({}^{3}\)]** & **Q [J]** & **Q \(\times\) 0.40 [J]** \\ \hline case I & 0.205 & 67.66 & 2,274,729.0 & 909,891.6 \\ case V & 0.350 & 39.14 & 1,315,887.0 & 526,354.8 \\ case IX & 0.514 & 28.84 & 969,600.8 & 38,784.32 \\ \hline \end{tabular}
\end{table}
Table 4: Measured and derived working parameters for 15 m soil tillage (extract from [8]).  
Figure 18: Graphical comparison between experimental and simulated data for the mechanical work.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Working Cases**} & **Soil Chip** & **Mechanical Work** & **No. of Cycles** & **Total Mechanical Work Done by** \\  & **Thickness** & **Done by One Cycle** & **Completing** & **6 Spades Completing 15 m Tillage** \\  & **[m]** & **[J]** & **15 m Tillage** & **[J]** \\ \hline case I & 0.065 & 567.4508 & 220.588 & 771,517.72 \\ case V & 0.124 & 653.9611 & 120.967 & 493,321.43 \\ case IX & 0.195 & 762.6923 & 76.923 & 369,069.05 \\ \hline \end{tabular}
\end{table}
Table 3: Mechanical work done by the spade machine in the three simulated cases.