## 2 Material and Methods
### Loads and Forces in the Spading Process  
Soil is a complex, open dynamic system, which is both the result of the interaction of soil-formation factors and the environment in which this process is currently ongoing [11]. Determining the forces and the loads on the implements, which result from tillage of the soil, is a difficult task, as the stresses already laying in the soil can also influence the soil's response to tillage forces, and these should be incorporated into the models, [12].  
Following the movements of a single spade, the spade penetrates the soil, cuts a soil chip, lifts it, and discards it.  
Technologically, soil spading is a process of separating pieces and layers from the soil massif with a wedge-shaped tool. The soil slice geometric dimensions and shape of the loosening zone depends on the physical and mechanical properties of the soil, the number and shape of the tools, and the position of the spade relative to the cutting direction [11].  
The work of soil-cutting tools in various soil works has been verified by several theoretical and experimental studies. The mechanical properties of soils are quite complex, with many factors associated with strength and deformation properties, such as moisture content and soil composition [13; 14].  
Tillage is one of the most power-consuming process in agriculture. In order to study the power demand, the peculiarities of the interaction of the tillage implement must be known. The penetration of the spade in the soil is considered in a plan, and the spade is considered a wedge with a very small thickness [14; 15; 16].  
After penetration, the movement of the spade in the soil is characterized by the \(\alpha\) rake angle, Figure 3. As the spade moves, it causes breakage or shear in the soil, depending on the rake angle \(\alpha\). A large rake angle results in shear, while a smaller angle results in soil break [15; 17].  
In this paper, we consider the work of the spade divided into three elementary processes: the penetration of the soil clumps, the separation process of the soil chip, and the dislocation processes of the soil chip.  
According to these processes, the following forces are considered:  
* the bit force (\(F_{b}\));
* the shear force (\(F_{s}\));
* the inertial force acting on the spade (\(F_{i}\));
* the friction forces (\(T_{1}\) and \(T_{2}\)) on the sides of the spade, according to Figure 3;
* the normal forces (\(N_{1}\) and \(N_{2}\)) acting on the spade sides, according to Figure 3.  
\begin{table}
\begin{tabular}{c c} \hline Machine width & 1.400 [m] \\ \hline Machine height & 1.130 [m] \\ \hline Machine weight & 580 [kg] \\ \hline Number of spades & 6 \\ \hline The dimensions of spades: & \\ Spade height & 0.205 [m] \\ Spade width: bottom, top & 0.100, 0.170 [m] \\ Middle spade width: bottom, top & 0.125, 0.195 [m] \\ Full height, including spade and rod & 0.362 [m] \\ \hline Spading operation sequence & 1, 4, 2, 5, 3, 6 \\ \hline Maximum working depth & 0.30 [m] \\ \hline Slider adjustment options & 0.035; 0.070; 0.105; 0.140 [m] \\ \hline Soil chip thickness on gears I, II, and III, & \\ at 2400 rpm engine revolution & 0.068; 0.124; 0.195 [m] \\ \hline Recommended advancing speed & 0.7–1.5 [km/h] (0.194–0.416 [m/s]) \\ \hline \end{tabular}
\end{table}
Table 1: Technical data of the MS-140-type spading machine.  
As the deflector cover's purpose is to throw back the soil on a narrow area of the machine, in our simulation, it can be omitted also.  
The spade is considered a wedge-type blade having a pentagonal cross-section with parallel sides, Figure 3[14; 15; 16].