## 3 Results and Discussion  
In order to determine the kinematic parameters of the machine's mechanism, experimental measurements for the advancing speed \(v\) (m/s) and soil chip thickness \(s\) (m) are considered based on Table 2[20]. Using the relation between those parameters, the crankshaft rotation is calculated and presented in Table 2:  
\[n=\frac{v}{s}[1/s] \tag{11}\]  
Based on the above Equation (11), Table 2 and Figure 5 may be built for the soil chip thickness determination as a function of the advancing speed and crankshaft revolution. Considering the cases presented in Table 2, it is obvious that higher rotation speeds of the spade assembly axes involves higher speeds and accelerations of the mechanism's elements, which clearly implies higher load on the machine axle. In order to expose the effect of different loads during the soil tillage, first the actuation of the machine above the soil surface is considered, involving 0 m working depth. Due to the geometry of the machine's mechanism, the realized spade-tip trace is similar to that in Figure 6, but the curve is shifted above the 0 value. In this case, the load of the rotating axle is produced because of the kinematic parameters of the working mechanism as well the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Crankshaft Revolution \(n\)**}} & \multicolumn{3}{c}{**Soil Chip Thickness \(s\) [m]**} \\ \cline{2-5}  & **[1/min] [1/s]** & **0.068** & **0.124** & **0.195** \\ \hline \hline \multirow{2}{*}{Advancing speed \(v\)} & 0.205 & 180/3 (case I) & 99/1.65 (case II) & 63/1.05 (case III) \\  & 0.350 & 309/5.15 (case IV) & 169/2.82 (case V) & 107/1.79 (case VI) \\  & 0.514 & 453/7.55 (case VII) & 249/4.15 (case VIII) & 158/2.63 (case IX) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Working parameters of the spade machine determining the nine simulation cases. Figure 5: Soil chip thickness determination as a function of the advancing and spade axis rotation speed. mechanical parameters of the mechanism elements. The torque for the awakened inertial forces during cases IV, V, and VI can be seen in Figure 7 for one working cycle in each case. The recommended model (as already presented in Figure 4) calculates the loads acting on the spading mechanism and implements Equations (5), (7) and (10) as further presented. The variables used to determine the implemented equations are chosen according to experimental data for a loam soil with 21% moisture content, with a density value of \(\rho_{soil}=1500\) (kg/m\({}^{3}\)) as considered in [16,17,19]. The values \(\leavevmode\
obreak\ l=0.488\) (m), \(A_{1}=10^{-4}\) (m\({}^{2}\)), and \(A_{2}=27\cdot 10^{-3}\) (m\({}^{2}\)) (Figure 3) were read from the solid modelling system software (Autodesk Inventor) based on the CAD model of the spade. In the case of parameter \(A_{s}=A_{1}+A_{2}\), the \(A_{1}\) component is ignored because \(A_{2}\gg A_{1}\), so the value \(A_{s}=0.027\) (m\({}^{2}\)) is used in our simulations. Further parameters for the soil are based on [16,17,18]: \(k_{1}=12\) (N/m\({}^{2}\)), \(k_{2}=0.5\) (N/m\({}^{2}\)), \(\mu=0.6\), \(\beta=41^{\circ}\), \(c=1000\) (N/m\({}^{2}\)), \(\sigma=20,000\) (N/m\({}^{2}\)), and \(\varphi=32^{\circ}\). Figure 6: Considering cases IV, V, and VI, with a working depth of 0.28 m, the trace of the spade tip (two-cycle representation for each case) reveals the variation of the soil chip thickness by different working parameters. Figure 7: The spade assembly torques considering one cycle of cases IV, V, and VI, with working depth of 0 m.  
In this paper, to present the methodology of the investigation, the working load (with a working depth different from 0 m) is split in three forces acting on the spade. The positions of the acting points are given relative to the spade depicted in Figure 8a. Taking into account one rotation cycle of the spade assembly, the action interval of the loads relative to the tip trace of the moving spade are presented in the Figure 8b.