ORIGINAL ARTICLE

Draft Force Prediction of Narrow Tillage Tool Using the Finite Element Method

0000-0002-2545-8865Luis Orlando Marín Cabrera^{*  1}  , 0000-0001-7658-563XArmando Eloy García de la Figal Costales¹  , 0000-0002-0539-1114Arturo Martínez Rodríguez¹ 

¹Universidad Agraria de La Habana (UNAH), Centro de Mecanización Agropecuaria (CEMA); Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba.

ABSTRACT

The Finite Element Model (FEM) has been used to predict the soil behavior disturbed by tillage tool, as well as the necessary draft force to break it. The aim of the present work is to analyze, by a simulation model of soil-tillage tool interaction in finite element, the draft force behavior of the vibratory subsoiler bent leg (narrow farming tillage tool), tilling a Ferralitic soil block, using the linear form to the extended Drucker-Prager elastoplastic constitutive relation model. The software used was Solid Works and its complement Simulation to model the vibratory bent leg and the soil block. The mechanical properties of soil were determined in the soil box CS-CEMA-25 and assigned to simulation model which was analyzed in function of moisture, bulk density, working depth and forward speed. The results showed the FEM reliability to predict the draft forces behavior of narrow tillage tool.

Key words: FEM; Simulation Model; Soil Mechanical Properties

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:

$f\left({\sigma }_1,{\sigma }_2,{\sigma }_3\right)=t-p\times tan\beta d$ (1)

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:

$\nu =\frac{E}{2\times G}-1$

The shear module G was calculated by:

$G=\frac{E}{2\times (1+)}$

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.

FIGURE 2 Finite Element Model: a) Boundary conditions b) Model mesh. 

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.

FIGURE 4 Draft force behavior along the farming tool displacement. 

$m=\frac{14.1-12.5}{2-0.4 }=\frac{1.6}{1.6}=1\frac{kN}{m}$ (4)

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.

FIGURE 5 Analytic model of Swick-Perumpral (^{Isavi, 2015}). 

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.

FIGURE 6 Finite element model verification: a) Beginning of formation of the soil flaw area, b) c) and d) Soil removed of the flaw area. 

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.

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Received: December 16, 2021; Accepted: June 24, 2022

^*Author for correspondence: Luis Orlando Marín Cabrera, e-mail: [e-mail]

Luis Orlando Marín Cabrera, Especialista, Universidad Agraria de La Habana (UNAH), Facultad de Ciencias Técnicas, Centro de Mecanización Agropecuaria (CEMA), San José de las Lajas, Mayabeque, Cuba, mail: [e-mail]

Armando Eloy García de la Figal Costales, Prof. Titular. Universidad Agraria de La Habana (UNAH). Facultad de Ciencias Técnicas, San José de las Lajas, Mayabeque, Cuba, e-mail: [e-mail]

Arturo Martínez Rodríguez, Prof. Titular e Inv. Titular, Prof. de Mérito. Universidad Agraria de La Habana (UNAH). Facultad de Ciencias Técnicas, Centro de Mecanización Agropecuaria (CEMA), San José de las Lajas, Mayabeque, Cuba, e-mail:[e-mail]

AUTHOR CONTRIBUTIONS: Conceptualization: L. O. Marín. Data curation: L. O. Marín, A. García de la Figal A. Martínez. Formal analysis: L. O. Marín, A. García de la Figal A. Martínez. Investigation: L. O. Marín, A. García de la Figal A. Martínez. Methodology: L. O. Marín, A. García de la Figal A. Martínez. Supervision: A. García de la Figal A. Martínez. Roles/Writing, original draft: L. O. Marín, A. García de la Figal A. Martínez. Writing, review & editing: A. García de la Figal, A. Martínez.

The authors of this work declare no conflict of interests.