ORIGINAL ARTICLE

Influence of the Forward Speed in the Cutting Forces of a Vibrating Subsoiler

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

In the present work, it is analyzed the behavior of the cutting forces (draft force and vertical force)of a vibrating subsoiler tilling a silt loam soil (ferralitic), by a soil-tillage interaction simulation model, developed applying the Finite Element Model and using the elastoplastic Drucker-Prager constitutive model and Solid Works design software. The soil parameters and properties required for simulation, the boundary conditions and acting loads were assigned to model and the meshing of the model was realized. Several running of the model were also realized for four forward speeds (0 ms^-1; 0, 4 ms^-1; 0, 8 ms^-1 and 1, 2 ms^-1). The results showed the quadratic behavior of both forces with the increasing of forward speed.

Key words: FEM; Draft Force; Simulation Model; Forward Speed

INTRODUCTION

Soil tillage has always been a major research area in agriculture. As a tillage operation is a procedure for breaking up soil, soil failure depends mainly upon the soil properties, tool geometry and cutting speed (^{Abu & Reeder, 2003}). The speed effects of the farming tool on the soil, both static and dynamic, and their influence in the cutting forces has been analyzed by several investigators (^{Ibrahmi et al., 2015}; ^{Lamia et al., 2020}). The MEF has shown to be able to simulate different forms of farming tools and the dynamic effects of the forward speed (^{Abu & Reeder, 2003}; ^{Marín et al., 2011}).

The Finite Element Method (FEM) is a numerical technique for analyzing the complex engineering problems, especially for dynamic systems with large deformation and failure (^{Rosa & Wulfsohn, 2002}). This method has been used by numerous researchers to analyze problems related to soil mechanics and the interaction between soil and tillage tools (^{Abo et al., 2003}; ²⁰⁰⁴; ^{Gebregziabher et al., 2007}; ^{Topakci et al., 2010}). However, for an accurate modeling of soil working implement, important physical and mechanical properties of soil should also be taken into account (^{Hesar & Kalantari, 2016}).

The objective of this study is to analyze the prediction of the cutting forces behavior in the direction of forward movement of the farming tool (vibratory subsoiler), tilling a silt loam soil (ferralitic) with forward speed and work depth assigned, as well as physical and mechanical properties of soil (humidity, density) determined.

MATERIAL AND METHODS

Model of Soil

The lineal form of the extended Drucker-Prager model, according to ^{De la Rosa et al.( 2016)} was used to model (Fig.1). It was classified as an elastoplastic material, as a Rhodic Ferralsol according to ^{Soil Survey Staff (2014)}; Oxisol according to ^{Soil Survey Staff (2010)} and Typical Red Ferralitic according to the third Genetic Classification of Soils in Cuba (^{Hernández et al., 1999}). According to their texture, it can be considered a clay very plastic loam, with 17% of sand, 36% silt, 47 clay% and organic matter content 2,58% (^{Herrera et al., 2008b}; ^2008a). According to ^{Naderi et al. (2013)}; ^{Ibrahmi et al. (2017)}; ^{Arefi et al. (2022)}, this model is the most appropriate for the soil material simulation, because it can be gauged by obtaining data from triaxial tests. The yield function of the ^{Drucker & Prager (1952)} model lineal is expressed as:

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

FIGURE 1 Yield surface and flow direction in meridional plane of extended linear Drucker-Prager model. 

Properties and Soil Parameters

The elastic module (E) was determined as the tangent module to the effort-deformation curve of the soil in its right tract, obtained by ^{Herrera et al. (2008b}; ^2008a) for this type of soil. The Poisson coefficient was determined by means of the equation:

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

The shear modulus G is determined by:

$G=\frac{E}{2\times (1+)}$ (3)

The properties or parameters required by the MEF model (Table 1) were obtained in the Laboratory of Soil Mechanics of the Company of Applied Investigations to Construction in Villa Clara (CAIC.VC).

TABLE 1 Properties or parameters required by FEM model 

Property or parameter	Symbol	Dimension	Source
Internal friction angle	φ	27,19 º	Herrera et al. (2015)
Elasticity module	E	104 272 kPa	Herrera et al. (2008)
Poisson coefficient	υ	0,44	Calculated
Bending stress	σ f	693,2 kPa	González et al. (2014)
Cohesion	d	217,2 kPa	González et al. (2014)
Dilatancy angle	Ψ	13º	González (2011)
Shear Resistance	τ	40 kPa	Herrera (2006)
Shear module	G	1 793, 4 kPa	Calculated
Soil type	Lineal elástoplástico
Soil-metal friction angle	δ	23,68º	Herrera et al. (2015)
Humidity	H	23,9 %	Herrera et al. (2008)
Density	ρ	1 200 kg.m^-3	Calculated

Finite Element Model

It is formed by the farming tool (arm scarifier) which is treated as rigid body and the soil block (deformable in interaction with the arm scarifier). Both, the arm and the soil block were modeled using the design software Solid Works and its complement Simulation. The soil block dimensions were longitude (2 m), wide (1 m) and height (1 m). The soil block was considered isotropic and homogeneous, with movement restrictions for side, bottom and upper surfaces (Fig. 2a), to which confining pressures were applied. On the soil model, the gravity force and the atmospheric pressure act. It is accepted that the increase of the dimensions of the prism of cut soil beyond those assigned does not affect the cutting forces (^{Bentaher et al., 2013}; ^{Marín & García de la Figal, 2019}). The interaction soil-tool was modeled tangent to the attack surface of the tool, with contact model surface to surface. The general meshing of the model was carried out with a size of elements (e) maximum of 0,008 m, minimum size of 0,006 m and the Newton-Raphson iterative method was used. The surfaces in contact, both, of the tool and of the soil prism cut were modeled applying meshing control with size of elements of 0,004 m (Fig. 2b). The arm cuts the soil block to constant speed of 0, 65 ms^-1 in the direction of the X axis, to a working depth of 0, 3 m and cutting wide 0,081 m. The soil cut slips above the surface of the tool after the fault.

FIGURE 2 Finite element model: a) Boundary conditions b) Mesh of model. 

RESULTS AND DISCUSSION

3D models have been developed using the MEF for the realization of both, dynamic analysis (^{Abo et al., 2003}; ^{Mollazade et al., 2010}) and narrow farming tool behavior (^{Payne, 1956}). Most of them have been used for slow tools and have not had into account the speed effects. For the analysis of the influence of the tool forward speed (Vm) on the soil cutting forces, the results were evaluated for four different speeds: 0 ms^-1; 0,4 ms^-1; 0,8 ms^-1 and 1,2 ms^-1 (Fig 3). Several runs of the simulation model were carried out, with the parameters in Table 1 and those that appear related in Table 2.

FIGURE 3 Soil cutting forces at different forward speed: a) Vm = 0 ms^-1; b) Vm = 0,4 ms^-1; c) Vm = 0,8 ms^-1; d) Vm = 1,2 ms^-1. 

TABLE 2 Arm scarifier parameters of simulation model 

Name	Category	Value	Unit	Comment
Density	Simulation ▼	1.2 ∑	g/cm^3 ▼
Humidity	Simulation ▼	23.9 ∑	N/A ▼
Frequency	Simulation ▼	14 ∑	rad/d ▼
Width,	Simulation ▼	11 ∑	N/A ▼
Speed	Simulation ▼	∑	N/A ▼
	Bench mark of the model▼	0	N/A ▼

The analysis carried out showed the increase in a quadratic way, of both, the draft force (Fx) and the vertical force (Fy) with the increase of the forward speed (Fig. 4), which coincides with several authors as ^{Onwualu & Watts (1998)} and ^{Wang et al. (2019)}

FIGURE 4 Cutting forces behavior to different forward speeds. 

CONCLUSSIONS

The cutting forces of soil, both, vertical and draft forces increase in a quadratic way with the increase of the forward speed, being the last one, the force with more magnitude.

The FEM has been able to simulate, in an appropriate way, the effects of the forward speed of the farming tool on the soil cutting forces.

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Received: June 12, 2022; Accepted: December 09, 2022

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

Luis Orlando Marín Cabrera. MSc., Especialista, 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]

Armando Eloy García de la Figal Costales. Dr.C., 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. Dr.Cs., 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].

The authors of this work declare no conflict of interests.

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 Figa,l A. Martínez. Writing, review & editing: A. García de la Figal, A. Martínez.