Introduction
⌅Tillage is one of the important field operations for the production of agricultural crops (Zhu et al., 2020)ZHU, L.; ZHANG, J.W.; CHEN, P.; WU, Q.M.; WEI, M.; YIN, C.L.; LI, G.L.: “Flowing interaction between cutting edge of ploughbreast with soil in shifting tillage operations”, Engineering Applications of Computational Fluid Mechanics, 14(1): 1404-1415, 2020, ISSN: 1994-2060., is the practice of modifier the soil state to achieve suitable conditions for growing of crops (Meselhy, 2020MESELHY, A.: “Effect of Tillage Depth Division and Vibration on Subsoiler Performance”, Plant Archives, 20(2): 3548-3567, 2020, ISSN: 2581-6063 (online), ISSN: 0972-5210.). The draft force is affected by three parameters, namely: soil conditions, tool shape and operational parameters (Li et al., 2014LI, X.Y.; ELBASHIR, M.H.; ZHAO, Z.; HEBEIL, E.A.: “Comparative finite element analysis of the effects of tillage tool geometry on soil disturbance and reaction forces”, Research Journal of Applied Sciences, Engineering and Technology, 7(15): 3145-3149, 2014, ISSN: 2040-7467.; Armin et al., 2015ARMIN, A.; FOTOUHI, R.; SZYSZKOWSKI, W.: “3D Finite Element Analysis for Mechanics of Soil-Tool Interaction”, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 9(5): 843-848, 2015.; Ibrahmi et al., 2015IBRAHMI, A.; BENTAHER, H.; HBAIEB, M.; MAALEJ, A.; MOUAZEN, A.M.: “Study the effect of tool geometry and operational conditions on mouldboard plough forces and energy requirement: Part 1. Finite element simulation”, Computers and Electronics in Agriculture, 117: 258-267, 2015, ISSN: 0168-1699.; Tagar et al., 2015TAGAR, A.; CHANGYING, J.; ADAMOWSKI, J.; MALARD, J.; QI, C.S.; QISHUO, D.; ABBASI, N.: “Finite element simulation of soil failure patterns under soil bin and field testing conditions”, Soil and Tillage Research, 145: 157-170, 2015, ISSN: 0167-1987.; He et al., 2016HE, C.; YOU, Y.; WANG, D.; WANG, G.; LU, D.; KAJI, J.M.T.: “The effect of tine geometry during vertical movement on soil penetration resistance using finite element analysis”, Computers and Electronics in Agriculture, 130: 97-108, 2016, ISSN: 0168-1699.).
The effects of rake angle over the soil and it influence in cutting forces has been analyzed by some researchers (Li et al., 2014LI, X.Y.; ELBASHIR, M.H.; ZHAO, Z.; HEBEIL, E.A.: “Comparative finite element analysis of the effects of tillage tool geometry on soil disturbance and reaction forces”, Research Journal of Applied Sciences, Engineering and Technology, 7(15): 3145-3149, 2014, ISSN: 2040-7467.; Armin et al., 2015ARMIN, A.; FOTOUHI, R.; SZYSZKOWSKI, W.: “3D Finite Element Analysis for Mechanics of Soil-Tool Interaction”, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 9(5): 843-848, 2015.; Ibrahmi et al., 2015IBRAHMI, A.; BENTAHER, H.; HBAIEB, M.; MAALEJ, A.; MOUAZEN, A.M.: “Study the effect of tool geometry and operational conditions on mouldboard plough forces and energy requirement: Part 1. Finite element simulation”, Computers and Electronics in Agriculture, 117: 258-267, 2015, ISSN: 0168-1699.; Tagar et al., 2015TAGAR, A.; CHANGYING, J.; ADAMOWSKI, J.; MALARD, J.; QI, C.S.; QISHUO, D.; ABBASI, N.: “Finite element simulation of soil failure patterns under soil bin and field testing conditions”, Soil and Tillage Research, 145: 157-170, 2015, ISSN: 0167-1987.; He et al., 2016HE, C.; YOU, Y.; WANG, D.; WANG, G.; LU, D.; KAJI, J.M.T.: “The effect of tine geometry during vertical movement on soil penetration resistance using finite element analysis”, Computers and Electronics in Agriculture, 130: 97-108, 2016, ISSN: 0168-1699.).
The Finite Element Method (FEM) is a numerical technique for the analysis of complex problems of engineering, specially for dynamic systems with big deformations and failures (Rosa y Wulfsohn, 2002ROSA, U.; WULFSOHN, D.: “Application of the finite element method in agricultural soil mechanics”, En: Advances in Soil Dynamics Volume 2, Ed. American Society of Agricultural and Biological Engineers, vol. 2, p. 117, publisher: American Society of Agricultural and Biological Engineers, 2002, ISBN: 1-892769-82-4.). Este método ha sido utilizado por numerosos investigadores
This method has been used by several researchers to analyze problems related with the soil mechanic and the interaction soil- farming tool (Abo et al., 2003ABO, E.M.; HAMILTON, R.; BOYLE, J.T.: “3D Dynamic analysis of soil-tool interaction using the finite element method”, Journal of Terramechanics, 40(1): 51-62, 2003, ISSN: 0022-4898.; 2004ABO, E.M.; HAMILTON, R.; BOYLE, J.: “Simulation of soil-blade interaction for sandy soil using advanced 3D finite element analysis”, Soil and Tillage Research, 75(1): 61-73, 2004, ISSN: 0167-1987.; Topakci et al., 2010TOPAKCI, M.; CELIK, H.K.; CANAKCI, M.; RENNIE, A.E.; AKINCI, I.; KARAYEL, D.: “Deep tillage tool optimization by means of finite element method: Case study for a subsoiler tine”, Journal of Food, Agriculture & Environment, 8(2): 531-536, 2010.); and it has shown to be able to simulate different forms of farming tools and the effect of the geometry in the cutting forces (Abu & Reeder, 2003ABU, H.N.H.; REEDER, R.C.: “A nonlinear 3D finite element analysis of the soil forces acting on a disc plow”, Soil & Tillage Research, (74): 115-124, 2003, ISSN: 0167-1987.). However, for a precise tool modeling, important physical and mechanical properties should be kept in mind (Dehghan & Kalantari, 2016DEHGHAN, H.H.; KALANTARI, D.: “Design a biomimetic disc using geometric features of the claws”, Agricultural Engineering International: CIGR Journal, 18(1): 103-109, 2016, ISSN: 1682-1130.).
The aim of this study is to analyze, using the Finite Element Method, the rake angle influence of a farming tool (vibrating subsoiler) in cutting forces (draft force and vertical force), as well as the soil failure behavior to different rake angles, tilling a clay loam soil (ferralitic), with forward speed and working depth assigned, as well as soil physical properties (humidity, density) and soil mechanical properties determinates.
Methods
⌅Soil model
⌅The soil was classified as elastoplastic material, as Rhodic Ferralsol according to FAO- UNESCO (1988)FAO- UNESCO: Soil map of the world, reviewed legend, Ed. FAO, Report 80, Roma. Italia, Roma. Italia, 1988.; Oxisol según Soil Survey Staff (2014)SOIL SURVEY STAFF: Keys to soil taxonomy, Ed. Government Printing Office, USDA Natural Resources Conservation Service, Washington, DC, USA, 12 th Edition. Natural Resources Conservation Service, United States Department of Agriculture, Washington, DC ed., Washington, DC., USA, 346 p., 2014, ISBN: 0-16-085427-X.; Oxisol according Soil Survey Staff (2014)SOIL SURVEY STAFF: Keys to soil taxonomy, Ed. Government Printing Office, USDA Natural Resources Conservation Service, Washington, DC, USA, 12 th Edition. Natural Resources Conservation Service, United States Department of Agriculture, Washington, DC ed., Washington, DC., USA, 346 p., 2014, ISBN: 0-16-085427-X. and typical red ferralitic soil according to the Third Genetic Classification of Soil in Cuba (Hernández et al., 1999HERNÁNDEZ, J.A.; PÉREZ, J.J.M.; MESA, N.Á.; BOSCH, I.D.; RIVERO, L.; CAMACHO, E.: Nueva versión de la clasificación genética de los suelos de Cuba., Ed. AGRINFOR, Barcaz L L ed., vol. I, La Habana, Cuba, 64 p., 1999, ISBN: 959-246-022-1.). It was considered as a loam clay very plastic, with 15% of sand, 38 of lime %, 47 of clay% and organic matter content of 2,59% (Herrera et al., 2008bHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008b, ISSN: 1010-2760.; 2008aHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008a, ISSN: 1010-2760.).
The lineal form of the extended Drucker-Prager model according to De la Rosa et al. (2016)DE LA ROSA, A.A.A.; QUINTEROS, P.R.; GONZÁLEZ, C.O.; RODRÍGUEZ, A.M.; SUÁREZ, H.M.: “Adjustment of the plastic parameters of the Extended Drucker Prager model for the simulation of the mechanical response of a clayey soil (Vertisol)”, Revista Ciencias Técnicas Agropecuarias, 25(3): 4-12, 2016, ISSN: 1010-2760. it was used to model the same one (Fig. 1). According to Arefi et al., (2022)AREFI, M.; KARPARVARFARD, S.H.; AZIMI, N.H.; NADERI, B.M.: “Draught force prediction from soil relative density and relative water content for a non-winged chisel blade using finite element modelling”, Journal of Terramechanics, 100: 73-80, 2022, ISSN: 0022-4898, DOI: https://doi.org/10.1016/j.jterra.2022.01.001. this model is the most appropriate for modeling the soil material, because it can be gauged obtaining data of triaxial tests. The yield function of the Drucker y Prager (1952)DRUCKER, D.C.; PRAGER, W.: “Soil mechanics and plastic analysis or limit design”, Quarterly of applied mathematics, 10(2): 157-165, 1952, ISSN: 0033-569X. is expressed as:
Properties and soil parameters
⌅The elastic modulus (E) was determined by the slope of a tangential line of a stress- strain curve in straight section, obtained by Herrera et al. (2008bHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008b, ISSN: 1010-2760.; 2008aHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008a, ISSN: 1010-2760.) for this soil type. The Poisson rate was determined by the following equation:
The shear modulus (G) is determined by:
The properties and soil parameters required by the FEM model (Table 1) has been obtained in the soil mechanic laboratory of Applied Investigations National Enterprise to construction (ENIA. VC).
| Propertie or parameter | Symbol | Dimension | Font |
|---|---|---|---|
| Internal friction angle | υ | 33º | (Herrera et al., 2008aHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008a, ISSN: 1010-2760.; 2008bHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008b, ISSN: 1010-2760.). |
| Elasticity modulus | E | 44 000 kPa | (Herrera et al., 2008aHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008a, ISSN: 1010-2760.; 2008bHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008b, ISSN: 1010-2760.). |
| Shear modulus | G | 15 909 kPa | (Herrera et al., 2008aHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008a, ISSN: 1010-2760.; 2008bHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008b, ISSN: 1010-2760.). |
| Poisson's ratio | ν | 0,32 | Calculated |
| Cohesion | c | 50 kPa | (Herrera et al., 2008aHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008a, ISSN: 1010-2760.; 2008bHERRERA, S.M.; IGLESIAS, C.C.E.; GONZÁLEZ, C.O.; LÓPEZ, B.E.; SÁNCHEZ, I.A.: “Propiedades mecánicas de un Rhodic Ferralsol requeridas para la simulación de la interacción suelo implemento de labranza mediante el Método de Elementos Finitos: Parte I”, Revista Ciencias Técnicas Agropecuarias, 17(3): 31-38, 2008b, ISSN: 1010-2760.). |
| Shear efforts resistance | τ | 295 kPa | Herrera, 2006HERRERA, S.M.: Simulación del comportamiento mecánico de los suelos ferralíticos rojos mediante el método de elementos finitos, Universidad Agraria de La Habana, Centro de Mecanización Agropecuaria, Tesis (en opción al grado científico de Doctor en Técnicas Agropecuarias), San José de las Lajas, La Habana, Cuba, 109 p., 2006. |
| Traction limit of soil | σt | 20 kPa | García de la Figal, 2022GARCÍA DE LA FIGAL, C.A.E.: Maquinaria Agrícola II. Apuntes de clases. Tema I. Teoría y cálculo de órganos de preparación de suelos. 1.1. Principales propiedades físico-mecánicas (tecnológicas) de suelos, Ed. UNAH, Universidad Agraria de La Habana, Centro de Mecanización Agropecuaria, 2022. |
| Compression limit of soil | σc | 750 kPa | García de la Figal, 2022GARCÍA DE LA FIGAL, C.A.E.: Maquinaria Agrícola II. Apuntes de clases. Tema I. Teoría y cálculo de órganos de preparación de suelos. 1.1. Principales propiedades físico-mecánicas (tecnológicas) de suelos, Ed. UNAH, Universidad Agraria de La Habana, Centro de Mecanización Agropecuaria, 2022. |
| Soil-metal friction angle | ϕ | 25º | Herrera, 2006HERRERA, S.M.: Simulación del comportamiento mecánico de los suelos ferralíticos rojos mediante el método de elementos finitos, Universidad Agraria de La Habana, Centro de Mecanización Agropecuaria, Tesis (en opción al grado científico de Doctor en Técnicas Agropecuarias), San José de las Lajas, La Habana, Cuba, 109 p., 2006. |
Finite element model
⌅Is formed by scarifier arm (threated as rigid body) and the soil block (deformable in interaction with the arm). Both were modeled using the design software Soil Works and its complement Simulation. The soil block dimensions are: length (L= 2 m), width (B = 1 m) and height (H = 0,9 m), was considered as isotropic and homogeneous, have movement restrictions by lateral, bottom and back surfaces (Fig. 2a), to which constraints pressures were applied.
Over the model acting the gravidity force and atmospheric pressure. Is assumed that the growing of the dimensions of sheared soil prism beyond those assigned, does not affect the draft forces (Bentaher et al., 2013BENTAHER, H.; IBRAHMI, A.; HAMZA, E.; HBAIEB, M.; KANTCHEV, G.; MAALEJ, A.; ARNOLD, W.: “Finite element simulation of moldboard-soil interaction”, Soil and Tillage Research, 134: 11-16, 2013b, ISSN: 0167-1987.; Marín et al., 2019).
The soil-tool interaction was modeled tangent to the tool attack surface, with contact model surface to surface. The model was discretized with element size (e) maxim of 0,006 m and the Newton-Raphson iterative method was used.
The contact surfaces, both tool and cut soil prism were discretized applying mesh control, with element size of 0.004 m (Fig. 2b). The arm cut the block soil a constant forward speed (Vm) in axis X direction, working depth of 0,3 m and cutting wide 0,081m. The soil cut after the flaw slips over the surface of the tool.
Results and discussion
⌅Attack angle influence α in the cutting forces
⌅Several running of the simulation model was realized (Figs. 3, 4 y 5) with different attack angle (15; 25 y 35°), f= 14 Hz, peak amplitude YPeak =11mm, Vm = 0,8 m·s-1, using the same properties and parameters of the Table 1.
The results showing the growing of Fx in polynomic form of second order with the growing of the attack angle α (Fig. 6a), showing coincidence with other authors Abbaspour et al. (2014)ABBASPOUR, F.M.; HOSEINI, S.A.; AGHKHANI, M.; SHARIFI, A.: “The behavior of tillage tools with acute and obtuse lift angles”, Spanish journal of agricultural research, 12(1): 44-51, 2014, ISSN: 2171-9292. & Lamia (2020)LAMIA, D.A.: “Modeling the effect of soil-tool interaction on draft force using visual basic”, Annals of Agricultural Science, Moshtohor, 58(2): 223-232, 2020, ISSN: 1110-0419..
Growing in 5 grades of attack angle α, increasing the draft force in approximately 4 kN (25 % of growing).
The vertical force of the soil-tool interaction Fy, the best adjusts (R2= 0,957) of your varying concerning the attack angle α was obtained with a polynomic function of second order (Fig. 6b), showing coincidence with other authors (Bentaher et al., 2013bBENTAHER, H.; IBRAHMI, A.; HAMZA, E.; HBAIEB, M.; KANTCHEV, G.; MAALEJ, A.; ARNOLD, W.: “Finite element simulation of moldboard-soil interaction”, Soil and Tillage Research, 134: 11-16, 2013b, ISSN: 0167-1987.; Odey et al., 2018ODEY, S.O.; OVAT, F.A.; OKON, O.O.: “Draughts, Power Requirements and Soil Disruption of Subsoilers”, World Journal of Engineering Research and Technology, 6(9): 17-39, 2018, ISSN: 2349-4395 (Print) & ISSN 2349-4409 (Online).).
Soil failure
⌅The soil failure process, both in vertical address and forward address, was simulated by several running of the finite element model, along the travel, with mesh density (e=6 mm), f = 14 Hz, YPeak =11mm to different cutting angles α: 15 y 250. The properties and parameters of the Table 1 were used.
In the zone over the farming tool (Fig. 7), take place great movements of the cut soil prism, both vertical and horizontal address, as well as displacements in lateral direction.
For α = 15° and the farming tool working with forced vibrations, the disruption of the soil, both horizontal and vertical address is less than α = 25° (Fig. 7a), as well as the draft force required for his breaking.
When α = 25° (Fig. 7b), great disrupting of the cut soil prism is obtained, as well as great displacement of the soil in vertical sense (Abu y Reeder, 2003ABU, H.N.H.; REEDER, R.C.: “A nonlinear 3D finite element analysis of the soil forces acting on a disc plow”, Soil & Tillage Research, (74): 115-124, 2003, ISSN: 0167-1987.; Odey y Okon, 2019ODEY, S.; OKON, O.: “Measurement of tillage forces and soil disturbance of subsoilers”, World Journal of Engineering Research and Technology, 5(2): 131-147, 2019, ISSN: 2454-695X.). It can be observed, as well, the failure plane formation of the removed soil.
Conclusions
⌅The cutting forces of soil, both draft and vertical, increasing in quadratic form with the growing of the attack angle, being the draft force the greatest.
The attack angle has a great influence in the disruption level, loosing, displacement and turning of cut soil prism.
Increasing the attack angle, increase the turning grade of cut soil, as well as the particles displacement, both in forward direction and vertical.
The FEM has been able to simulate, in adequate form, the effect of the farming tool attack angle in cutting forces of soil.