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INTRODUCTION
Tillage, in agricultural sense, is the physical management of soil to get the conditions required for proper plant growing and crop production (Rao & Chaudhary, 2018). It is one of the most energy consuming processes of agricultural production (Dehghan & Kalantari, 2016), around half of the energy used is consumed in tillage operation due to the magnitude of the draft force generated for breaking the soil (Armin et al., 2015) affected by the agricultural machinery traffic and the compaction (Mileusnić et al., 2022).
Draft force prediction, clod size and distribution and erosion damage by soil tillage are among the major motivations for modelling soil-tillage interaction. Combining field data and laboratory experiments with mathematic models, allow quicker and accurate predictions of the interaction of the new tool design with soil (López, 2012).
In soil tillage modelling, experimental and analytic models arisen in the 40s of last century (Terzaghi, 1943). Later, the tillage forces prediction was investigated by numerical methods, which have acquired importance in the latest years because of the accelerate development of computing techniques (Herrera et al., 2015). Among the numerical methods, the Finite Element Method (FEM) has great acceptation for the computational simulation of soil-tillage tool interaction (González et al., 2013a; 2013b), because of the power for describing it in 3D (Herrera et al., 2013; Naderi et al., 2013; Ibrahmi et al., 2015; Marín & García de la Figal, 2019). Some authors report satisfactory results in modeling tool structural resistance (Biriș et al., 2016; Constantin et al., 2019; Gheorghe et al.,2019), tillage tool efforts prediction over the soil (Arefi et al., 2022) and draft force in static condition (López et al., 2019). It can be used to simulate cohesive soils, getting both the resistance characteristics and data in breaking process and movement of soil mass (Lysych, 2019).
The FEM is appropriated for continuous analyses, although the soil deformations, mainly in tillage process, including separation and mixes of its layers, the appearance of cracks and the flow of particles, cannot be modeled appropriately by this method (Jakasania et al., 2018). However, the results in the direction of forward movement (draft) under tillage depth are more reliable using FEM (Ucgul et al., 2018).
The main objective of this work is to analyze the prediction of cutting forces behavior in the direction of the forward movement of a tillage tool (vibrating bent leg subsoiler) while tilling a clay loam soil (Ferralitic) with forward speed and working depth assigned, as well as physical properties (moisture and density) and certain mechanical properties, by means of the FEM.
METHODS
Soil Model. The linear form of the extended Drucker-Prager model (De la Rosa et al., 2016) was used for modelling the soil (Figure 1). It is classified as an elastoplastic material, as a Rhodic Ferralsol (FAO-UNESCO, 1988); Oxisol according to USDA Soil Survey Staff (2010); typical red Ferralitic, according to the third genetic classification of soils in Cuba (Hernández et al., 1999).
For its texture, it can be considered like a clay loam very plastic, with 17% of sand, 36% of loam, 47 of clay% and 2.58% of organic matter (Herrera et al., 2008b; 2008a). According Naderi et al. (2013); Ibrahmi et al. (2017); Arefi et al., (2022), this model is the most appropriate for modelling the soil material, because it can be gauged obtaining data of triaxle tests.
The yield function of the linear Drucker-Prager model (Drucker and Prager, 1952) can be expressed as:
FIGURE 1 Yield Surface and flow direction in the southern plane of the extended lineal Drucker-Prager model.
Properties and Soil Parameters. The elasticity module (E) was determined as the tangent module to the elastic deformation section of strain stress curve in the right tract, obtained by Herrera et al. (2008b; 2008a) for this kind of soil.
The Poisson coefficient was determined by the following equation:
The shear module G was calculated by:
Table 1 shows the properties or parameters required by the FEM model which were obtained in the laboratory of mechanics of soils from the Company of Investigations Applied to Construction, Villa Clara Province (ENIA.VC).
TABLE 1 Properties or parameters required by the FEM model
| Properties or parameters | Symbol | Dimension | Source |
|---|---|---|---|
| Internal friction angle | φ | 27.19 º | Herrera et al. (2015) |
| Elasticity module | E | 104272 kPa | Herrera et al. (2008) |
| Poisson's ratio | υ | 0,44 | Calculated |
| Flexion stresses | σ f | 693.2 kPa | González et al. (2014) |
| Cohesion | d | 217.2 kPa | González et al. (2014) |
| Dilatancy angle | Ψ | 13º | González, 2011 |
| Resistance to shear effort | τ | 40 kPa | Herrera, 2006 |
| Shear module | G | 1 793 400 Pa | Calculated |
| Kind of soil | Linear elastoplastic | ||
| Traction limit of soil | σ t | 42 000 Pa | Calculated |
| Compression limit of soil | σ c | 48 000 Pa | Calculated |
| Soil-metal friction angle | δ | 23.68º | Herrera et al. (2015) |
| K ratio | K | 1 | |
| Soil humidity | H | 22.4 % | |
| Density | ρ | 1 120 kg.m-3 | (Herrera et al., 2015) |
Finite Element Model. It was formed by the farming tool (curved bent and front shear wedge) which was considered as rigid body and the soil block (deformable in interaction with the bent leg). The bent leg and the soil block were modeled using the design software Solid Works and its complement Simulation. The soil block dimensions were: length (2 m), width (1 m) and height (1 m). The soil block was considered isotropic and homogeneous, it had movement restrictions for the side, bottom and later surfaces (Figure 2a) to which constraints pressures were applied. Over the model act the gravity force and the atmospheric pressure. It is assumed that the increase in the dimensions of the prism of soil cut beyond those assigned, does not affect the draft forces (Bentaher et al., 2013). The interaction soil-farming tool was modeled tangent to the attack surface of the tool, with contact model surface to surface. The general mesh of the model was carried out with an elements size (e) maximum of 0,008 m, minimum size of 0,006 m and the Newton-Raphson iterative method was used. The surfaces in contact, the farming tool and the prism of soil cut, were refined applying mesh control with elements size of 0,004 m (Figure 2b). The bent leg cuts the soil block to a constant forward speed of 0.65 m·s-1 in the direction of the axis X, to a working depth of 0.3 m and cut wide 0.081 m. The soil cut after the flaw slips over the surface of the tool.
RESULTS AND DISCUSSION
Finite Element Simulation. The behavior of the draft force along its travel was analyzed by means of simulations by the FEM. In Figure 3, some steps of the process of soil cut are shown. It can be observed that, as the bent leg is moving through the soil block, big displacements of the soil mass happen, both longitudinally and vertically, overcoming the its internal and external resistance forces and taking place the break of the soil prism. Coinciding with other authors like Bentaher et al. (2013); Ibrahmi et al. (2015); Arefi et al. (2022), it can be observed that the model simulates the cutting process of soil in an appropriate way.
FIGURE 3 Steps of the soil cutting process by the farming tool to different distances of displacement: a) 0.15m, b) 0.6 m, c) 1m, d) 2m.
The draft force reaches a maximum value of 14,1 kN to 0,25 m from the beginning of the contact of the tool with the soil block, diminishing first in parabolic form to 1m, as the tool moves through the soil block (Figure 4 ) and next it is practically constant, while it is almost zero when the wedge of tool comes out of the second one. These results are similar to those estimated by the ASAE D497 Dates (2006) for farming tool of narrow tip.
The finite element model verification is based on the analytic model of Swick & Perumpral (1988), which proposes a soil cut dynamic model that takes into consideration the forward speed. Its area of flaw consists on a central wedge and two growing sides (Figure 5) with a right rupture plane in the bottom.
It is observed (Figure 6) that, in the superior diagram (of soil surface) the soil flaw of the model in finite elements of soil, acquires a similar form to Swick Perumpral's analytical model up to 0,6 m of trajectory through the soil block and is removed by the farming tool.
CONCLUSIONS
The behavior of the bent leg draft efforts along the displacement through the soil block shows coincidence with the works carried out in previous investigations. The force increases abruptly at the beginning of the interaction soil-farming tool, reaching its maximum value (14.1 kN). Then, it is stabilized a little in values smaller than the maximum as the tool moves with tendency to decrease and it diminishes to almost zero at the end of its displacement. The model FEM shows similarity with the analytic model of Swick-Perumpral in the process of formation of the soil flaw area.
