INTRODUCTION
The acting force in the farming tools affect directly the energy consumption of tillage operations. About half of the energy used for harvest production in agriculture is consumed in tillage operations because of the magnitude of cutting forces generated when fault and breaking up of soil clods happen (^{Davoudi et al., 2008}; ^{Armin et al., 2015}). Some studies have been focused to the measuring of draft force and power requirements of tillage tools under some soil conditions (^{Grisso et al., 1996}). The determination of draft force, necessary for the soil tillage, has gotten the attention of several researchers since 60s of last century ^{Hettiaratchi et al. (1966)}; ^{Gill & VandenBerg (1968)}, to nowadays (^{Abo et al., 2011}; ^{Ibrahmi et al., 2015}) The draft force depends on factors related with tool geometry, soil resistance and operation parameters (^{Armin et al., 2014}; ^{Moeinfar et al., 2014}; ^{Sun et al., 2015}; ^{Ahmadi, 2016}).
Several researchers have used both analytical and numerical methods to investigate the soil fault process and soil-tillage tool interaction (^{Elbashir et al., 2014}). Entre los métodos numéricos, el método de elementos finitos (MEF) ha demostrado ser útil en la comprensió Among numerical methods, the Finite Element Method (FEM) has demonstrated to be useful in the comprehension, research, description and solution of these problems. It has been developed to model soil tillage and fault processes ^{Bentaher et al. (2013)}, to model simple tools of wedge or plow shear ^{Davoudi et al. (2008)}, curved bent leg plows (^{Jafari et al., 2006}), disc plows ^{Abu & Reeder (2003)}, and moldboards plows (^{Plouffe et al., 1999}; ^{Formato et al., 2005}; ^{Jeshvaghani et al., 2013}).
Also, the effects of displacement velocity, working depth and attack angle of tillage tool in draft have been studied by this method (^{Yong y Hanna, 1977}; ^{Chi y Kushwaha, 1990}; ^{Abo et al., 2003}).
Some researchers have attempted improve the tillage tool geometry using physical experiments (^{Soni et al., 2007}), while mathematic simulations were also considered in other investigations (^{Shrestha et al., 2001}). In other research works, the influence of operational conditions in the energy consumption of tillage tool was studied (^{Al-Janobi y Al-Suhaibani, 1998}; ^{Moitzi et al., 2014}; ^{Ehrhardt et al., 2001}).
The main objective of this work was to study the influence of the density of mesh and the angle of attack of the arm of a scarifier in tractional forces, the tensions of contact between the nodes, as well as deformations and fault of the ground for the tool of cultivation, utilizing the Finite Element Method and extended Drucker Prager's Model.
METHODS
Model for Soil. The mechanical behavior of soil under external tillage load is modelled with different yield approaches (^{Ibrahmi et al., 2015}). Several researchers have utilized the Drucker-Prager yield approach and its extended forms (lineal, hyperbolic and exponential) to simulate the interaction between soil and different tools used in civil engineering, excavations and tillage (^{Li et al., 2013}). In the present paper, the soil was modeled as continuous, homogeneous and elastoplastic, using the lineal form of the extended Drucker-Prager Model (Figure 1) employee with success by ^{Herrera (2006)}, given the simplicity of it and the small amount of parameters required for its implementation (^{González, 2008}). The yield function of this model (F) is defined as (^{González, 2008}; ^{De la Rosa, 2014}):
where:
t -deviatory effort; σ_{c} -normal effort actuating over the soil; β - angle that defines the slope lifting of the yield surface, commonly referred to the angle of internal friction of the soil; C is the cohesion; (σ_{1}, σ_{2}, σ_{3} -principal maximum, medium and minimum stresses.
r^{3} third invariant of stresses, calculated as:
The cohesion C, is calculated as:
where τ-tangential stress
Soil Properties and Parameters. The soil taken like object of study was classified as Rhodic Ferralsol Hernández et al. (1975), with density 1 150 kg.m^{-3}, plasticity ratio 36,2% and organic matter content 2,7%. The elastic modulus was determined by the slope of a tangential line of a stress- strain curve in straight section, obtained by ^{Herrera (2006)} for this type of soil. The Poisson rate ν was determined by:
for that:
where:
G -strain modulus and was determined by the slope of a tangential line of straight section of the stress- strain curve obtained of the direct cut tests (^{González, 2008}; ^{De la Rosa, 2014}).
The Table 1 show the values of properties and soil parameters required by the finite element model (^{Herrera, 2006}; ^{García de la Figal, 2013}; ^{De la Rosa, 2014}).
Property or parameter | Symbol | Dimension |
---|---|---|
Friction internal angle | φ | 33º |
Modulus of elasticity | E | 5 M Pa |
Poisson's ratio | υ | 0,4 |
Flexion stress | σ_{f} | 120 kPa |
Dilatancy angle | ψ | 0º |
Cohesion | d | 15 kPa |
Cut resistance | τ | 190 kPa |
Cut modulus | G | 1,793 4 MPa |
Type of soil | Linear elastic | |
Traction limit of soil | σ_{t} | 20 kPa |
Compression limit of soil | σ_{c} | 480 kPa |
K ratio | σ_{e} | 1 |
Elastic limit of soil | δ | 42 kPa |
Soil-metal friction angle | K | 30.5º |
Soil humidity | H | 27% |
Density | ρ | 1 200 kg.m^{-3} |
Finite Element Model. A tridimensional simulation model (3D) of the soil-tillage tool interaction was developed applying the Finite Element Method and modeled, by means the software Solid Works (Figure 2). The vibratory scarifier was compound of: Tool of curved arm with logarithmic profile, the block of soil and the surface of interaction between both.
The arm scarifier was modelled as a rigid discrete body, with reference point located in the tip. The working depth of the arm p is 0,40 m and the attack angles α are 15 and 25^{0}.
The soil block -deformable in interaction with the bent leg scarifier- was modeled as a rectangular prism of length L = 2 m, width B = 1 m and height H = 1 m with contact surface to surface. The work width of the blade coincides with the width of the cut soil prism b = 0,041 m. An increase of the dimensions of the prism of soil, beyond the assigned, as a result of the interaction with the arm of scarifier, can be disregarded (^{Kushwaha y Shen, 1995}; ^{Ibrahmi et al., 2015}).
Loads, Boundary Conditions and Model Mesh. The loads were established as function of acting forces: the gravity g = 9.81 ms^{-1} and environment pressure p_{a} = 101,325 kPa. The block of soil is restricted outwardly surfaces: Two lateral, inferior, posterior and frontal (Figure 3). The arm scarifier has a freedom movement in X and Y axes. It moves in X axis sense at constant velocity of 0,85 m.s^{-1}, oscillating with respect to X axis and with a frequency of 12 Hz and amplitude 0,008 m. The draft force applied to the model was 5 kN. The soil prism deformed and moved displaces tangent to the plowshare's surface of attack in arm scarifier.
According to mismas ^{Abo et al. (2004)}; ^{Bentaher et al. (2013)}. the mesh size has an important effect in the magnitude of tillage force and the calculation time of them. A very fine mesh will allow getting more exact simulation dates, but with a bigger time of calculation (^{Jafari et al., 2006}; ^{Armin et al., 2014}).Therefore, only to the surfaces in contact, both soil block (inferior surface of soil prism that was displaced) and the arm scarifier (attack surface of chisel), mesh control was applied, with element size e = 0,004 m. The rest of model’s surface were meshed with element size 0,006 m and the iterative modified Newton-Raphson Method was used (Figure 3, for a total of 132 891 nodes, 107 262 elements and 364 959 degrees of freedom).
RESULTS AND DISCUSSION
Predicting Tool Forces. The results of the finite element analyses of the implemented simulation model, at work depth of 0,4 m provided information regarding the reaction forces of soil (draft, lateral and vertical forces) and the displacement field of soil particles (^{Li et al., 2015}).Figure 4 shows the distribution of Von Mises stresses when the arm scarifier works on the soil block. In agreement with other authors ^{Bentaher et al. (2013)}; ^{Armin et al. (2014)}; ^{Ibrahmi et al. (2015)}, it can be observed that the model simulates the soil displacement process in appropriate way. The stresses grow progressively as the soil-tool interaction takes place.
Mesh Density Effect in Draft Force. To investigate the mesh density effect in draft force, as result of the soil- tillage tool simulation several runs of the Finite Element Model were realized with different element sizes (0,008 m; 0,014 m; 0,02 m and 0,035 m), at 0,3 m of tool displacement using the same tillage conditions of soil defined in Table 1.
In Figure 5, it is observed that the mesh density, which is proportional to the number of elements (^{Bentaher et al., 2013}; ^{Armin et al., 2014}; ^{Ibrahmi et al., 2015}), has a significant effect in traction forces, both in horizontal direction (draft force) and in vertical direction (vertical force) for the implemented simulation model. That coincides with the obtained results by other researchers in previous papers (^{Abo et al., 2004}). As the density of mesh increases, the draft force Fx decreases, becoming stabilized in an approximate value of 886 N (e = 0.006 m), being this the optimal size of elements for the model under consideration.
Displacement and Formation of Soil Prism. The kind and extent of breaking up of soil clods is the most important factor selecting the tillage tools, but it may be considered together the required draft force for efficient tilling (^{Li et al., 2015}). The distribution of the soil displacement field, both in vertical and forward directions, as well as the prism formation and displacement processes were simulated by the Finite Element Model at 0,3 m of displacement, with the same density mesh: Element size e = 0,006 m and attack anglesm α of 15 and 25^{0}. At the zone above tillage tool (Figure 6), big movements of the prism of soil that moves happened, both, in horizontal direction and in vertical direction and little lateral displacement
As a Figure 6 shows, the attack angle α has a significant effect in the extent of clod breaking up and in the displacement of the deformed soil prism.
For an attack angle α of 15^{0}, the displacement of the soil, both, in horizontal direction and in vertical direction is smaller (Figure 6a) and the required draft forces Fx for the displacement and breaking up of clods is smaller. When the attack angle is 25^{0} (Figure 6b), the necessary draft force Fx increases to get bigger displacements from deformed soil prism in vertical direction.
Effect of the Attack Angle α in the Contact Stresses in the Nodes. Figure 7 shows the magnitude of the maximum contact stresses in nodes obtained by the simulation of Finite Element Model. For an attack angle α of 15^{0} (Figure 7a), the biggest value obtained is 9,93 MPa located in the inferior surface of the deformed soil prism and the high contact stresses zone is smaller. When the attack angle is 25^{0} (Figure 7b), the biggest value of the contact stresses reached is 1 737,2 MPa, located on a chisel tip of the scarifier arm contacting with the inferior surface of the deformed soil prism. The zone of high stresses of contact is wide and is located in the plane that coincides with the work depth of the tillage tool.
CONCLUSIONS
Mesh density Dm has a significant effect in the magnitude of the draft force Fx necessary for deformation and displacement of the soil prism; when Dm increases, the draft force Fx decreases.
The attack angle α has a remarkable influence in the loosening and displacement of the cut soil prism, as well as in the magnitude of the contact stresses in the nodes. When it increases, the grade of displacement of the soil particles increases, both, in the direction of advance of the tool and in vertical direction.
The contact stresses in nodes grow with the increasing of attack angle α, located mainly in the tip of the tilling tool and in the plane of the inferior surface of the formed soil prism.