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The effect of tine geometry during vertical movement on soil penetration resistance using finite element analysis
Computers and Electronics in Agriculture 130 (2016) 97–108
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Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Original papers
The effect of tine geometry during vertical movement on soil penetration resistance using finite element analysis Changbin He, Yong You ⇑, Decheng Wang ⇑, Guanghui Wang, Donghui Lu, John Morris Togo Kaji College of Engineering, China Agricultural University, P.O. Box 134, No. 17 Qinghua East Road, Haidian District, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 4 April 2016 Received in revised form 17 October 2016 Accepted 21 October 2016
Keywords: Tine Finite element method Soil disturbance Attacked surface area Conservation tillage Soil loosening
a b s t r a c t New tillage and planting tools causing low soil disturbance and minimizing vegetation deterioration are desired in the conservation tillage technology development. This paper attempted to study the effect of tine geometry in its vertical movement on penetration resistance. Four kinds of tines were defined (i.e. rectangle, triangle, crescent and mososeries) based on the geometry of the cutting edge. The effects of tine geometry, thickness, and penetration depth on soil penetration resistance were investigated and side soil disturbance evaluated. Finite element method with a Drucker–Prager elasto-plastic model was introduced to simulate the material behavior of sandy loam soil taken from Hebei province in China. Each tine was considered as a discrete rigid body with a reference point at the top-midpoint of the central plane, at which the vertical force (penetration resistance) was calculated. Results indicated that the rectangle tine obtained the highest penetration resistance as compared to the others. Penetration resistances of all the tines increased with the attack surface area with a power function, nonlinear tendency with thickness and a quadratic function with penetration depth. A crescent soil deformation area existed through the penetration process. It can be concluded that the FEM can maximize the understanding of tine geometry effects on penetration resistance and soil deformation area. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction In conventional agriculture, tillage is a very important operation to improve soil physical characteristics for better aeration, permeability, root development, and as a result plant growth and yield. The type and degree of soil disturbance is the prime factor when selecting tillage implements but this must be considered together with the draught and penetration forces for efficient operation (Godwin, 2007). The tool forces during soil working are extremely important for designers to design cultivation equipment to be effective over a wide range of soil types and conditions as well (Godwin and O’Dogherty, 2007). Most studies have been conducted to research soil-tool interaction including predicting the draught force acting on tool and the soil disturbance ahead of the tool. The two concerned objects of soil-tool interaction are soil and tool, and most of the studies were focused on changes in soil physical conditions. By studying the pattern and mechanism of soil
Abbreviations: FEM, finite element method; DEM, discrete or distinct element method; ANN, artificial neural network. ⇑ Corresponding authors. E-mail addresses: [email protected] (C. He), [email protected] (Y. You), [email protected] (D. Wang). http://dx.doi.org/10.1016/j.compag.2016.10.007 0168-1699/Ó 2016 Elsevier B.V. All rights reserved.
failure, several models were well developed to describe the process of soil-tool interaction. Karmakar and Kushwaha (2006) concluded that there were five major methods that had been used as approaches to solve problems in the area of soil-tool interaction and failure mechanism, namely empirical and semi-empirical, dimensional analysis, finite element method (FEM), discrete or distinct element method (DEM) and artificial neural network (ANN). Liu and Kushwaha (2008) classified modeling of soil-tool interaction into three types: soil movement, static/dynamic forces required to move a tool, and combination of both movement and forces. Many experiments are needed to be carried out for a complete search or investigation of the soil tool interaction with a controlled situation in a range of variations in soil physical conditions (e.g. water content and bulk density). The finite element method (FEM) has been widely used to analyze soil-tool interaction problems in recent years since most interaction problems involve both material and geometric nonlinearities (Bentaher et al., 2013; Li et al., 2013; Naderi-Boldaji et al., 2013; Tagar et al., 2015). The finite element model can be efficiently used to predict the forces on a tool working through the soil, and it is helpful for modeling to estimate tillage forces and energy consumption for different tools geometries (Bentaher et al., 2013; Naderi-Boldaji et al., 2014).
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Table 1 Mechanical component of soil samples used in the simulation model. Grain size (mm)
1–0.5
0.5–0.25
0.25–0.1
0.1–0.05
0.05–0.005
0.005–0.002
<0.002
Mass percent (%)
2.80
9.41
25.79
19.80
32.00
8.20
2.00
As for conventional soil tillage equipments such as ploughs or subsoilers, their working tools were always used to create a totally new soil condition by overturning soil or breaking compacted layers. With development of conservation tillage technology, new tillage and planting tools causing low soil surface residues coverage disturbance are desired, especially for soil aeration implements mentioned by Harrigan et al. (2006), and soil-gashing and rootcutting mechanism reported by You et al. (2010). These mechanisms were designed to remove compacted soil layers or remedy degraded grassland by improving soil drainage and aeration. A rotary soil cutting mechanism with a function of soil-gashing and root-cutting was designed to improve degraded natural Leymus chinensis grassland with negligible soil disturbance by You et al. (2012). Godwin and O’Dogherty (2007) classified simple tines into three types (i.e. wide tines, narrow tines and very narrow tines) based on the depth/width (d/w) ratio. Based on the above classification, the blades reported in You’s (2012) investigation belong to the narrow tines and very narrow tines. In You’s study, the soilgashing and root cutting movements can be divided into many combined processes with penetration and rotation, and different performance and soil disturbance emerged because of different blade types, which indicated that the blade geometry was one of the factors causing the difference between the operational performances. Few literatures on the soil-blade interactions, especially the penetration interaction have been found. The objectives of this study were (a) to simulate the penetration resistance acting on four single tines with different geometries when they were penetrated vertically into a sandy-loam soil bin by FEM, (b) to study the effect of the geometry, thickness and depth on penetration resistance and (c) to study the influence of tine geometry on the soil disturbance.
Table 2 Yield stresses and corresponding plastic strain values used in ABAQUS.
q ¼ ðr1 r3 Þ
ð4Þ
2. Materials and methods
r3 ¼ ðr1 r3 Þ3 ¼ q3
ð5Þ
2.1. Soil model and measurement
where K (flow stress ratio) is the ratio of the tension yield stress to the compression yield stress in triaxial test (0.778 6 K 6 1) (ABAQUS, 2010). If K = 1 then t = q and the yield surface in this case is identical to the Von Mises circle in the deviatoric principal stress plane. r1 ; r2 ¼ r3 are compressive stress in triaxial test; r is the third invariant of deviatoric stress.
2.1.1. Soil material model The soil mechanical behavior under external load of tillage implement was modeled with different yield criteria. The Drucker-Prager model and its extended forms are used to model frictional materials, such as soils and rock, where material yield is associated with hardening (i.e. the material strength increases with stress level). The extended forms include a linear, a hyperbolic and a general exponential form available in ABAQUS; the linear one is the most appropriate for soil materials (ABAQUS, 2010). Several researchers used the Drucker-Prager model and its extended linear form to simulate the interaction between the soil and tillage tools (Naderi-Boldaji et al., 2013; Ibrahmi et al., 2015). In the present work, the soil was modeled as an elastic–plastic with hardening property using the linear form of the extended Druck-Prager model (ABAQUS/Explicit). The model is defined as follows:
F ¼ t ptanb d
ð1Þ
where F is the yield function, t is the deviatoric stress, p is the normal stress, b is the internal friction angle, and d is the cohesion of the material. The normal (p) and deviatoric (t) stresses are given by the equations as follows:
Yield stress (kPa)
Plastic strain (%)
12.5 25 50 100 200
0 0.125 0.267 0.663 1.388
Table 3 Soil parameters used in FEM model. Parameters
Value
Density, (g/cm3) Young’s modulus, E (kPa) Poisson’s ratio, m Internal friction angle, Mohr-Coulomb u (°) Internal friction angle, Drucker-Prager b (°) Flow stress ratio, K Dilatation angle, W (°) Cohension, C (kPa) Soil-metal coefficient of friction, f Precompression stress, rpc (kPa)
1.429 617 0.432 13.77 27.34 0.85 0 44.814 0.5 12.5
p¼
1 ðr1 þ r2 þ r3 Þ 3
" 3 # 1 1 1 r t¼ q 1þ 1 2 K K q
ð2Þ
ð3Þ
2.1.2. Measurement of soil material and soil-metal properties The soil samples were sandy loam soil taken from Guyuan Grassland Ecosystem Observation and Research Station (115°410 E, 41°450 N, Alt. 1400 m) located in Hebei province with dry bulk density of 1429 kg/m3 and moisture content of 27.24% (d.b.). Soil mechanical component analysis was done as shown in Table 1. The soil Young’s modulus was determined by unconfined uniaxial compression test (Eggers et al., 2006), and the Poisson ratio was calculated using Eq. (6) (Yang, 2014).
m¼
1 sin u 1 þ ð1 sin uÞ
ð6Þ
where m is the Poisson ratio, and u is the Mohr-Coulomb internal angle of friction.
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Fig. 1. Tine model. (a) Rectangle, (b) triangle, (c) crescent and (d) mososeries.
Penetration direction
(a)
(b)
Fig. 2. Soil-tine interaction model (rectangle tine), showing the cutting angle (a). (a) Front view and (b) right side view.
K and b were calculated using Eqs. (7) and (8), respectively (ABAQUS, 2010).
K¼
3 sin u 3 þ sin u
ð7Þ
tan b ¼
6 sin u 3 sin u
ð8Þ
The soil-metal coefficient of friction (f) was get and evaluated from the database (Song, 2006), the soil cohesion (C) and the angle of internal friction (u) were measured through laboratory test in a
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Fig. 3. Finite element mesh for soil box and four kinds of tines. (a) Rectangle, (b) triangle, (c) crescent, and (d) mososeries.
Table 4 The maximum penetration resistances of tines. Thickness (mm)
7 10 15 20 25
Penetration resistances (maximum values) (N) Rectangle tine
Triangle tine
Crescent tine
Mososeries tine
476.22 722.33 1107.85 1565.47 1722.16
363.78 489.62 658.28 769.48 873.80
436.20 760.93 1004.99 1365.80 1623.38
340.45 455.88 624.55 728.62 800.47
shear box at four levels of normal stress (100, 200, 300, and 400 kPa). For plastic hardening, confined uniaxial compression test data were used with yield stresses (we used precompression stress (rpc) as the initial yield stress) and corresponding plastic strain values (for the first yield stress and the plastic strain was assumed zero). Several yield stresses and corresponding plastic strain values imported into the toolbox are listed in Table 2. In order to conduct a series of analyses using the model, the input values given in Table 3 were imported into the model.
2.2. Tine model Four tine geometries were used in the simulation, which were defined as rectangle, triangle, crescent and mososeries based on the geometry of the cutting edge, as shown in Fig. 1. The dimensions of the rectangle tine are 207 mm 90 mm (length width)
with a cutting angle of 30°. Each tine has five thickness levels (7, 10, 15, 20, and 25 mm) with the cutting angle fixed. So there were 20 tines used in the simulation. 2.3. Finite element model A 3D soil-tine interaction model was developed using the ABAQUS toolbox (Fig. 2). The model was consisted of two distinct parts: (1) deformable soil and (2) rigid tine. Since the model was symmetric with the central plane and the thickness was very small as compared to the width, only one-half of a total attacked surface was considered and the predicted forces were then duplicated in magnitude in order to obtain the total forces. The tines used in the simulation were modeled as a discrete rigid body. The reference point of each tine was defined at the top-midpoint of the central plane. The dimensions of the used soil material box are 60 cm 30 cm 30 cm (length width height).
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The rigid body of each tine and the soil box were divided into the finite elements using two main element types, namely, R3D4 a quadratic, rigid bilinear element (4-node and 3 degrees of freedom per node element) and C3D8R (8-node linear brick, reduced integration, hourglass control), respectively. The density of a mesh was specified by creating seeds along the edges of the model and a free meshing method available at ABAQUS toolbox was used. Some researchers showed that the mesh size had an important effect on
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the tillage force and calculation time (Bentaher et al., 2013). To reduce the cost of calculation time, in current study a finer mesh was assigned only to the area around the tine penetrated into the soil (Fig. 3). The tine-soil interaction layer was modeled with a contact surface-to-surface tangential layer using a penalty function method. The rigid bodies were selected as master and the deformable part as slave. A series of paired surfaces were selected as the
Fig. 4. Penetration resistances of tines with different types and thicknesses. (a), (b), (c), (d) and (e) represent the thickness of 7, 10, 15, 20, and 25 mm, respectively.
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Fig. 5. The attack surfaces.
Fig. 6. Relationships between attack surface area and penetration depth.
Table 5 The maximum attack surface areas of tines. Thickness (mm)
Attack surface area for one-half tine (cm2) Rectangle tine
Triangle tine
Crescent tine
Mososeries tine
7 10 15 20 25
186.72 186.89 187.19 187.49 187.78
116.98 117.34 117.93 118.47 118.93
173.31 173.51 173.83 174.16 174.47
101.37 101.66 102.13 102.57 103.00
contact surfaces: (1) all the surfaces facing the soil box were master surfaces, (2) the top face of the box (in x-z plane) and the side face near the tine (in x-y plane) were slave surfaces. Boundary conditions applied were: (1) both side walls of the box (in y-z plane) were totally fixed, (2) the bottom face of the box (in x-z plane) was totally fixed whilst the top face of the box was kept free for any constraint, (3) the face far from the tine (in x-y plane) was totally fixed whilst the face near the tine was left free for any constraint, (4) the tine face back to the soil box was constrained in the vertical direction, and (5) the velocity applied on the reference node was fixed in the penetration direction vertically. The outputs of the model were the reaction forces on the reference nodes of the tine. Further outputs of interest were the displacement of the rigid bodies, some energy components of the model including kinetic energy, total internal energy and elastic– plastic strain energies. However, what this study concerned was the reaction force in y-direction on the node. Since the tines are symmetric with the central plane, the forces on the both sides of the tine in the horizontal direction are cancelled by each other out while the vertical force of the tine is doubled, so the penetration resistance of a tine is the total vertical force. The operational conditions were: (1) the velocity of tines penetrated into the soil was 1.3 cm/s throughout all the analyses along the y-axis negative direction, (2) ending time of the simulation was set at 20 s., and (3) all variations in thickness were simulated with a fixed cutting angle (a = 30°) and the same soil condition. 3. Results and discussion 3.1. Penetration resistance prediction Table 4 shows the maximum penetration resistances of the different types and thicknesses of the tines. It was observed that
the penetration resistances increase with the thickness. The rectangle and crescent tines have larger penetration resistances as compared to the triangle and mososeries tines respectively, and the rectangle tine’s penetration resistances were resulted in the largest except the force at the thickness of 10 mm. The results in Table 4 show that the values of rectangle and crescent tines are 1.31 and 1.28 times larger as compared to the triangle and mososeries tines respectively at the thickness of 7 mm, while 1.97 and 2.03 times larger at the thickness of 25 mm. Penetration resistances of the triangle and mososeries tine are less than 1 kN within the variation of thickness. The largest value of these tines’ penetration resistances were found at 1.72 kN. All the tines have small penetration resistances at a lower thickness level. The tine geometry is a main influence factor causing the differences above.
3.2. Effect of the geometry on penetration resistance Fig. 4 shows a typical group of vertical force-depth curves of different types of tines with different thicknesses. The vertical force is the reaction force of the reference node in the penetration direction, i.e. the penetration resistance of the tine. The tendency can be observed that the penetration resistances of rectangle and crescent tines are greater than the ones of triangle and mososeries tines. The curves show nonlinear tendencies in the penetration process. The crescent and rectangle tines have similar curves, as well as the triangle and mososeries tines. In Fig. 1, based on the differences of geometries between the four tines (contact area and the cutting edge), the curves show a parallel tendency to each other after a critical depth in each group, but different in the early penetration stages due to the not quite different cutting edges which is similar in You et al. (2012). The curves can be divided into three phases (i.e. original phases, middle phases and end phases) in Fig. 4. The original phase means the process at the beginning of penetration, the end phase means the process at the end of penetration, and the middle phase means the process between the original phase and the end phase. In the original phase, the penetration force is mainly affected by the cutting edges making the curves different tendency. In the middle phase, the crescent and rectangle tine curves show a parallel tendency to each other because of the similar contact area, as well as the triangle and mososeries tine. In the end phase, the whole tine bodies are penetrated into the soil, and the relationship between the force and depth shows different characteristics even curve intersections showing up in the figures. The soil movements and properties can be concluded as the main reasons but more work needs to be carried out.
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Fig. 7. Relationships between vertical force and attack surface area with different thickness. (a) With the thickness of 7 mm and (b) with the thickness of 25 mm.
Fig. 8. Penetration resistances of tines with different types and thicknesses. (a), (b), (c) and (d) represent the rectangle tine, triangle tine, crescent tine and mososeries tine, respectively.
The attack surface area was used to describe interaction surface and defined as the contact area between both sides of the tine and
soil as shown in Fig. 5. Table 5 shows the maximum attack surface area of each one-half tine (doubled for the whole tine). The
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Fig. 9. Relationships between vertical force and thickness. (a) and (b) represent the penetration depth of 150 mm and 200 mm, respectively.
rectangle tine has the largest attack surface areas, then crescent tine, triangle tine and mososeries tine, and this change is similar with the tendency shown in Fig. 4. It’s easy to be observed that each tine’s maximum attack surface area increases with the thickness, but not significantly. Fig. 6 shows the relationship between attack surface areas of the tines and the penetration depth. It is indicated that the attack surface area shows different characteristics because of the geometry difference. It also can be observed that the tendencies of attack surface area changing with the depth are very similar with the ones in Fig. 4 which proves that the penetration force has a direct relation with the attack surface area which inspired the force variation tendency differences. Pure-shear model was described by Zheng (1995) which means only partial failures including cutting, compression, and plastic flow exist in the blade-soil interaction, and the mean resistances in the blade movements are composed of friction and normal stress from the cutting edge and the side edges. With regard to the soil penetrating based on the pure-shear theory, the resistance coming from the soil reacts on the attack surface area of the tine, the horizontal force components cancel each other out whilst the vertical components comprise the whole penetration resistance together. When the attack surface area changes, so does the penetration resistance. Fig. 7 shows the vertical force-attack surface area curves of the four tines with the thickness of 7 mm and 25 mm. The vertical forces (i.e. penetration resistances) increase with attack surface area nonlinearly. A power function relationship is presented with R2 values exceeding 0.96 within these tines. It can be observed that the power number is less than 1 at the thickness of 7 mm, while more than 1 at the thickness of 25 mm. So there must be a thickness level resulting in a linear relationship between the penetration resistance and attack surface area. The constants also change with the tines’ variation. It was found that the curve tendency remains unchanged with the tine type variation but constants change with the thickness. A function relationship between the penetration resistance and attack surface area can be concluded as follow:
P ¼ ISm
ð9Þ
where P is the penetration resistance (N), S is the attack surface area of tine (cm2), I and m are dimensionless constants which are associated with the soil mechanics and tine geometry parameters.
The tendency is similar with the draught force in the tillage system. Zelenin (1950) found the draught force had a parabolic relation with the working depth through a number of tests using horizontal cutting blade, as shown in Eq. (10):
P ¼ kH
n
ð10Þ
where P is the cutting resistance in horizontal direction, k is the resistance coefficient, H is the working depth and n is the experimental coefficient which approximates 1.35. It has to be pointed out that n changes with the soil condition and working depth variation. For the same tool, it’s easy to conclude that the contact surface area changes with the working depth. There must be a relationship between the depth and the contact surface area for a certain tillage tool, which proves the rationality of Eq. (9) above. The same tendency can also be found from Godwin and Spoor (1977). 3.3. Effect of the thickness and depth on penetration resistances Fig. 8 indicates the different curves of vertical forces through the penetration process with the variation of thickness. It was observed that the large differences between the tines, the rectangle and crescent were resulted at larger magnitude compared with the triangle and mososeries respectively. This tendency can also be analyzed from Fig. 9 which shows the relationship between vertical force and thickness at the penetration depth of 150 mm and 200 mm, respectively. The mososeries tine indicated the smallest penetration resistance in the whole penetration process. The thickness shows a lower influence on triangle and mososeries tine than rectangle and crescent tine, and the penetration resistances of triangle and mososeries tine do not increase as sharply as the rectangle and crescent tine. It is observed that the vertical forces increase with the thickness nonlinearly. The vertical force increases with the thickness, and a power function relationship existing between the vertical force and thickness indicates the power number < 1 and R2 values exceeding 0.97 at the penetration depth of 150 mm and 200 mm respectively. Godwin and Spoor (1977) found the forces increased in proportion to width (very narrow tine range), then at a decreasing rate (narrow tine range) and finally at a linear rate but at a lower rate compared to the initial phase (blade or wide tine range).
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Fig. 10. Penetration resistances of tines with different types and thicknesses. (a), (b), (c), (d) and (e) represent the penetration depth exceeding 10 cm with the thickness level of 7 mm, 10 mm, 15 mm, 20 mm, and 25 mm, respectively.
With the changes of the thickness and depth, the relationship curves show different characteristics. Fig. 10 shows the vertical
force-penetration depth curves. The penetration depths were divided into two parts, within 10 cm and more than 10 cm. Fig-
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Types of tines(thickness of 7mm)
Penetration time(s) and direction
Rectangle tine
Crescent tine
Triangle tine
Mososeries tine
Origin (0.19,0,0)
Origin (0.14,0,0)
Origin (0.15,0,0)
Origin (-0.024,0,0)
Normal axis (1,0,0)
Normal axis (1,0,0)
Normal axis (1,0,0)
Normal axis (-1,0,0)
Axis2 (0,1,0)
Axis2 (0,1,0)
Axis2 (0,1,0)
Axis2 (0,-1,0)
5s
10s
15s
20s
View cut position
Fig. 11. Soil deformation in front of the attack surface area at different time steps.
ure (a) to (e) in Fig. 10 represent the relationship between penetration resistance and the depth for more than 10 cm with the thickness level of 7 mm, 10 mm, 15 mm, 20 mm, and 25 mm, respectively. Furthermore, the penetration resistances of the crescent, triangle and mososeries tine indicated non-linear relationship with depth within the depth of 10 cm were observed in Fig. 8. When the depth exceeds 10 cm, and the tine thickness is over 10 mm, all the curves of vertical force and depth turn into linear ones, and at the end phases, the curve points show a large fluctuation caused by the soil movements and properties but more work
to be done. The tendencies of the curves are nonlinear with the thickness of 7 mm and 10 mm. The curves of vertical force (i.e. penetration resistance) calculated for the soil-tine interaction as a function of depth at different thickness levels were also shown in Fig. 8. The tendencies were described by the quadratic polynomial functions with R2 values exceeding 0.95 throughout the whole penetration process. It was observed that the coefficients change with different geometries. For the rectangle and crescent tines, the quadratic coefficients are negative within a thickness level but turns into positive with
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Time(s)
5s
10s
15s
20s
Rectangle tine
View cut
Origin (0.024,0,0); Normal axis (1,0,0); Axis2 (0,1,0)
Fig. 12. Soil deformation in the front of the attack surface area of rectangle tine with the thickness of 25 mm at different time steps.
Fig. 13. Soil deformation in the vertical direction of rectangle tine at 20 s. (a) and (b) represent the rectangle tine with thickness of 7 mm and 25 mm, respectively.
increasing thickness, while the quadratic coefficient is positive for the triangle and mososeries tine. A function relationship can be concluded as follow: 2
P ¼ aðh þ bÞ þ c
ð11Þ
where P is the penetration resistance, h is the penetration depth, a and b are the constants related to the soil mechanics and tine geometry parameters, c is the calculation constant. You (2011) used the device designed and fabricated to measure the vertical forces acting on three different very narrow blades (thickness of 7 mm) in his doctoral dissertation. When penetrating into a sandy loam soil bin, a tendency was found that the vertical force increases with the depth which is similar to the results obtained in this study, and a semi-empirical and semi-trial model was proposed as Eq. (12):
P ¼ K1h P ¼ K 1 h þ K 2 ðh hc Þ
h 6 hc 2
h > hc
ð12Þ
where P is the penetration force, K1 and K2 are soil resistance coefficients, h is penetration depth, hc is the critical depth, respectively. The critical depth is thought to exist in the penetration process, a linear relationship between penetration resistance and depth within the critical depth, while a quadratic polynomial exist beyond the critical depth. It shows nonlinear throughout the whole penetration process at the thickness of 7 mm in this paper. The differences between the two functions are caused by the errors between the tine geometries or the soil related parameters. It is indicated that the attack surface area shows different characteristics because of the geometry differences from Fig. 6. The penetration resistance has a direct relation with the attack surface area which makes the force variation tendency different. That also causes the different constants variations between a and b as shown in Eq. (11). Furthermore, the soil parameters input in the simula-
tions were obtained from the related soil mechanics experiments. While the soil properties could not show the real soil properties in the field, the simulations represent a perfect working process which has a difference with the field environment, and differences exist between the two soil parameters. A cross term can be concluded in Eq. (11) caused by the interaction of soil property and tine geometry. From another point of view, You’s (2011) trials also show a nonlinear tendency between the penetration resistance and depth. Several soil tillage force prediction models for the tines were proposed by Hettiaratchi et al. (1966), Godwin and spoor (1977) and Meyerhof (1951). The models indicated that the force components have much to do with the soil parameters and tine geometries. The relationship reflected by Eq. (11) is also a semiempirical model based on the curves obtained from the simulation. 3.4. Soil deformation Fig. 11 shows side views of the variation of soil deformation in front of the attack surface areas at the different time steps and for different tines with 7 mm thickness. Considering the different geometries of the cutting edges of those tines, the longest cutting edge was chosen to observe the soil deformation by the view cut toolbox in ABAQUS 6.11. The boundary influence is neglected. The soil deformation forms a soil disturbance area. From the time steps it was found that the soil disturbance area increased when the tine penetrated into the soil bin. The rectangle and crescent tines indicated more soil deformations as compared to the triangle and mososeries tines. When the triangle and mososeries tine penetrate into the soil, the cutting edges and the attack surfaces contact with the soil gradually along with the cutting edges which make the soil deformation lower. In Fig. 11, the different colour represents the different degree of the deformation, it can be observed that the compaction of the soil decreases from the near area to far, and the biggest compaction area moves with the attack
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surface of the tine, especially obvious in Fig. 12, the blue part represents the biggest soil compaction deformation and moves with the tine in different penetration times. When the whole tine body moved into the soil, the top soil layer separated from the attack surface where soil showed resilience, at the time step of 20 s in Figs. 11 and 12. The crescent soil disturbance area exists throughout the penetration process induced by soil compaction. The crescent area could be one reason for causing the soil loosening. Because of the friction between soil and mental tines, compacted soil get loosen when the tines penetrated into and moved out the soil. When the thickness increases to 25 mm, it was observed that the soil has a large deformation caused by the tine in the vertical direction, compared to the thickness of 7 mm. It can also be found in Fig. 13, because of the friction, the vertical deformation caused by the tine with the thickness of 25 mm is higher than the deformation by the tine with the thickness of 7 mm. So, tines with small thickness can be used when low side soil disturbance is requested. 4. Conclusions The finite element method (FEM) was used to model the interaction between the soil and different types of tines penetrating into a sandy loam soil vertically. The simulation was helpful to understand the effect of geometry, thickness and depth on the penetration resistances and side soil disturbance area. Tine geometry affects the penetration force substantially. The rectangle tine resulted in the highest penetration resistances compared to the crescent, triangle and mososeries tine. The changes of different types, geometries and thicknesses of the tines cause the variation of the attack surface area between the tine and soil which directly influence the penetration resistance during the penetration process. The results showed that the penetration resistance increases with a power function with the attack surface area, nonlinear tendency with thickness and a quadratic function with penetration depth. A crescent soil deformation area was found at the sides of the tine during the penetration process due to compaction. It can be concluded that the FEM can improve the understanding of tine geometry effects on penetration resistance and soil deformation area. Acknowledgements The authors would like to acknowledge the funding provided by National Natural Science Foundation of China (NSFC) (51405493), China Agriculture Research System (CARS-35) and Special Fund for Agro-scientific Research in the Public Interest (201203024).
References ABAQUS, 2010. ABAQUS User’s Manuals Version 6.10.1. ABAQUS Inc., Providence, RI. Bentaher, H., Ibrahmi, A., Hamza, E., et al., 2013. Finite element simulation of moldboard–soil interaction. Soil Till. Res. 134, 11–16. Eggers, C.G., Berli, M., Accorsi, M.L., et al., 2006. Deformation and permeability of aggregated soft earth materials. J. Geophys. Res.: Solid Earth 111 (B10). Godwin, R.J., 2007. A review of the effect of implement geometry on soil failure and implement forces. Soil Till. Res. 97, 331–340. Godwin, R.J., O’Dogherty, M.J., 2007. Integrated soil tillage force prediction models. J. Terrramech. 44 (1), 3–14. Godwin, R.J., Spoor, G., 1977. Soil failure with narrow tines. J. Agric. Eng. Res. 22 (3), 213–228. Harrigan, T.M., Bailey, B.B., Northcott, W.J., et al., 2006. Field performance of a lowdisturbance, rolling-tine, dribble-bar manure applicator. Appl. Eng. Agric. 22 (1), 33–38. Hettiaratchi, D.R.P., Witney, B.D., Reece, A.R., 1966. The calculation of passive pressure in two-dimensional soil failure. J. Agric. Eng. Res. 11 (2), 89–107. Ibrahmi, A., Bentaher, H., Hbaieb, M., et al., 2015. Study the effect of tool geometry and operational conditions on mouldboard plough forces and energy requirement: part 1. Finite element simulation. Comput. Electron. Agric. 117, 258–267. Karmakar, Subrata, Kushwaha, R.L., 2006. Dynamic modeling of soil-tool interaction: an overview from a fluid flow perspective. J. Terrramech. 43, 411–425. Li, M., Chen, D., Zhang, S., et al., 2013. Biomimeitc design of a stubble-cutting disc using finite element analysis. J. Bionic Eng. 10 (1), 118–127. Liu, J., Kushwaha, R.L., 2008. Two-decade achievements in modeling of soil-tool interactions. American Society of Agricultural and Biological Engineers. In 2008 Providence, Rhode Island, June 29–July 2, 2008 (p. 1). Meyerhof, G.C., 1951. The ultimate bearing capacity of foundations. Geotechnique 2 (4), 310–332. Naderi-Boldaji, M., Alimardani, R., Hemmat, A., et al., 2013. 3D finite element simulation of a single-tip horizontal penetrometer–soil interaction. Part I: development of the model and evaluation of the model parameters. Soil Till. Res. 134, 153–162. Naderi-Boldaji, M., Alimardani, R., Hemmat, A., et al., 2014. 3D finite element simulation of a single-tip horizontal penetrometer–soil interaction. Part II: soil bin verification of the model in a clay-loam soil. Soil Till. Res. 144, 211–219. Song, J.N., 2006. Nong Ye Ji Xie Yu She Bei (in Chinese). China Agriculture Press. Beijing. Tagar, A.A., Changying, J., Adamowski, J., et al., 2015. Finite element simulation of soil failure patterns under soil bin and field testing conditions. Soil Till. Res. 145, 157–170. Yang, J., 2014. Analysis of soil-tool interaction using extended finite element method and discrete element method. Master Degree Thesis at the Kunming University of Science and Technology. You, Y., Wang, D.C., Liu, J., 2012. A device for mechanical remediation of degraded grasslands. Soil Till. Res. 118, 1–10. You, Y., Wang, D.C., Wang, G.H., and Liu, J., 2010. Effects of a Soil-gashing and Rootcutting Mechanism on Soil Properties and Crop Yield of Grasslands. American Society of Agricultural and Biological Engineers. In 2010 Pittsburgh, Pennsylvania, June 20-June 23, 2010 (p. 1). You, Y., 2011. Mechanical Remediation Technology of Degraded Grassland (Leymuschinensis) by Soil-gashing and Root-cutting. Doctoral dissertation at China Agricultural University. Zelenin, A.N., 1950. Basic Physics of the Theory of Soil Cutting. Akademia Nawk USSR, Moscow-Leningrad (NIAE Translation). Zheng, D.C., 1995. Machinery and Soil Dynamics (in Chinese). Science and Technology Press, Beijing.
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Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Original papers
The effect of tine geometry during vertical movement on soil penetration resistance using finite element analysis Changbin He, Yong You ⇑, Decheng Wang ⇑, Guanghui Wang, Donghui Lu, John Morris Togo Kaji College of Engineering, China Agricultural University, P.O. Box 134, No. 17 Qinghua East Road, Haidian District, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 4 April 2016 Received in revised form 17 October 2016 Accepted 21 October 2016
Keywords: Tine Finite element method Soil disturbance Attacked surface area Conservation tillage Soil loosening
a b s t r a c t New tillage and planting tools causing low soil disturbance and minimizing vegetation deterioration are desired in the conservation tillage technology development. This paper attempted to study the effect of tine geometry in its vertical movement on penetration resistance. Four kinds of tines were defined (i.e. rectangle, triangle, crescent and mososeries) based on the geometry of the cutting edge. The effects of tine geometry, thickness, and penetration depth on soil penetration resistance were investigated and side soil disturbance evaluated. Finite element method with a Drucker–Prager elasto-plastic model was introduced to simulate the material behavior of sandy loam soil taken from Hebei province in China. Each tine was considered as a discrete rigid body with a reference point at the top-midpoint of the central plane, at which the vertical force (penetration resistance) was calculated. Results indicated that the rectangle tine obtained the highest penetration resistance as compared to the others. Penetration resistances of all the tines increased with the attack surface area with a power function, nonlinear tendency with thickness and a quadratic function with penetration depth. A crescent soil deformation area existed through the penetration process. It can be concluded that the FEM can maximize the understanding of tine geometry effects on penetration resistance and soil deformation area. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction In conventional agriculture, tillage is a very important operation to improve soil physical characteristics for better aeration, permeability, root development, and as a result plant growth and yield. The type and degree of soil disturbance is the prime factor when selecting tillage implements but this must be considered together with the draught and penetration forces for efficient operation (Godwin, 2007). The tool forces during soil working are extremely important for designers to design cultivation equipment to be effective over a wide range of soil types and conditions as well (Godwin and O’Dogherty, 2007). Most studies have been conducted to research soil-tool interaction including predicting the draught force acting on tool and the soil disturbance ahead of the tool. The two concerned objects of soil-tool interaction are soil and tool, and most of the studies were focused on changes in soil physical conditions. By studying the pattern and mechanism of soil
Abbreviations: FEM, finite element method; DEM, discrete or distinct element method; ANN, artificial neural network. ⇑ Corresponding authors. E-mail addresses: [email protected] (C. He), [email protected] (Y. You), [email protected] (D. Wang). http://dx.doi.org/10.1016/j.compag.2016.10.007 0168-1699/Ó 2016 Elsevier B.V. All rights reserved.
failure, several models were well developed to describe the process of soil-tool interaction. Karmakar and Kushwaha (2006) concluded that there were five major methods that had been used as approaches to solve problems in the area of soil-tool interaction and failure mechanism, namely empirical and semi-empirical, dimensional analysis, finite element method (FEM), discrete or distinct element method (DEM) and artificial neural network (ANN). Liu and Kushwaha (2008) classified modeling of soil-tool interaction into three types: soil movement, static/dynamic forces required to move a tool, and combination of both movement and forces. Many experiments are needed to be carried out for a complete search or investigation of the soil tool interaction with a controlled situation in a range of variations in soil physical conditions (e.g. water content and bulk density). The finite element method (FEM) has been widely used to analyze soil-tool interaction problems in recent years since most interaction problems involve both material and geometric nonlinearities (Bentaher et al., 2013; Li et al., 2013; Naderi-Boldaji et al., 2013; Tagar et al., 2015). The finite element model can be efficiently used to predict the forces on a tool working through the soil, and it is helpful for modeling to estimate tillage forces and energy consumption for different tools geometries (Bentaher et al., 2013; Naderi-Boldaji et al., 2014).
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Table 1 Mechanical component of soil samples used in the simulation model. Grain size (mm)
1–0.5
0.5–0.25
0.25–0.1
0.1–0.05
0.05–0.005
0.005–0.002
<0.002
Mass percent (%)
2.80
9.41
25.79
19.80
32.00
8.20
2.00
As for conventional soil tillage equipments such as ploughs or subsoilers, their working tools were always used to create a totally new soil condition by overturning soil or breaking compacted layers. With development of conservation tillage technology, new tillage and planting tools causing low soil surface residues coverage disturbance are desired, especially for soil aeration implements mentioned by Harrigan et al. (2006), and soil-gashing and rootcutting mechanism reported by You et al. (2010). These mechanisms were designed to remove compacted soil layers or remedy degraded grassland by improving soil drainage and aeration. A rotary soil cutting mechanism with a function of soil-gashing and root-cutting was designed to improve degraded natural Leymus chinensis grassland with negligible soil disturbance by You et al. (2012). Godwin and O’Dogherty (2007) classified simple tines into three types (i.e. wide tines, narrow tines and very narrow tines) based on the depth/width (d/w) ratio. Based on the above classification, the blades reported in You’s (2012) investigation belong to the narrow tines and very narrow tines. In You’s study, the soilgashing and root cutting movements can be divided into many combined processes with penetration and rotation, and different performance and soil disturbance emerged because of different blade types, which indicated that the blade geometry was one of the factors causing the difference between the operational performances. Few literatures on the soil-blade interactions, especially the penetration interaction have been found. The objectives of this study were (a) to simulate the penetration resistance acting on four single tines with different geometries when they were penetrated vertically into a sandy-loam soil bin by FEM, (b) to study the effect of the geometry, thickness and depth on penetration resistance and (c) to study the influence of tine geometry on the soil disturbance.
Table 2 Yield stresses and corresponding plastic strain values used in ABAQUS.
q ¼ ðr1 r3 Þ
ð4Þ
2. Materials and methods
r3 ¼ ðr1 r3 Þ3 ¼ q3
ð5Þ
2.1. Soil model and measurement
where K (flow stress ratio) is the ratio of the tension yield stress to the compression yield stress in triaxial test (0.778 6 K 6 1) (ABAQUS, 2010). If K = 1 then t = q and the yield surface in this case is identical to the Von Mises circle in the deviatoric principal stress plane. r1 ; r2 ¼ r3 are compressive stress in triaxial test; r is the third invariant of deviatoric stress.
2.1.1. Soil material model The soil mechanical behavior under external load of tillage implement was modeled with different yield criteria. The Drucker-Prager model and its extended forms are used to model frictional materials, such as soils and rock, where material yield is associated with hardening (i.e. the material strength increases with stress level). The extended forms include a linear, a hyperbolic and a general exponential form available in ABAQUS; the linear one is the most appropriate for soil materials (ABAQUS, 2010). Several researchers used the Drucker-Prager model and its extended linear form to simulate the interaction between the soil and tillage tools (Naderi-Boldaji et al., 2013; Ibrahmi et al., 2015). In the present work, the soil was modeled as an elastic–plastic with hardening property using the linear form of the extended Druck-Prager model (ABAQUS/Explicit). The model is defined as follows:
F ¼ t ptanb d
ð1Þ
where F is the yield function, t is the deviatoric stress, p is the normal stress, b is the internal friction angle, and d is the cohesion of the material. The normal (p) and deviatoric (t) stresses are given by the equations as follows:
Yield stress (kPa)
Plastic strain (%)
12.5 25 50 100 200
0 0.125 0.267 0.663 1.388
Table 3 Soil parameters used in FEM model. Parameters
Value
Density, (g/cm3) Young’s modulus, E (kPa) Poisson’s ratio, m Internal friction angle, Mohr-Coulomb u (°) Internal friction angle, Drucker-Prager b (°) Flow stress ratio, K Dilatation angle, W (°) Cohension, C (kPa) Soil-metal coefficient of friction, f Precompression stress, rpc (kPa)
1.429 617 0.432 13.77 27.34 0.85 0 44.814 0.5 12.5
p¼
1 ðr1 þ r2 þ r3 Þ 3
" 3 # 1 1 1 r t¼ q 1þ 1 2 K K q
ð2Þ
ð3Þ
2.1.2. Measurement of soil material and soil-metal properties The soil samples were sandy loam soil taken from Guyuan Grassland Ecosystem Observation and Research Station (115°410 E, 41°450 N, Alt. 1400 m) located in Hebei province with dry bulk density of 1429 kg/m3 and moisture content of 27.24% (d.b.). Soil mechanical component analysis was done as shown in Table 1. The soil Young’s modulus was determined by unconfined uniaxial compression test (Eggers et al., 2006), and the Poisson ratio was calculated using Eq. (6) (Yang, 2014).
m¼
1 sin u 1 þ ð1 sin uÞ
ð6Þ
where m is the Poisson ratio, and u is the Mohr-Coulomb internal angle of friction.
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Fig. 1. Tine model. (a) Rectangle, (b) triangle, (c) crescent and (d) mososeries.
Penetration direction
(a)
(b)
Fig. 2. Soil-tine interaction model (rectangle tine), showing the cutting angle (a). (a) Front view and (b) right side view.
K and b were calculated using Eqs. (7) and (8), respectively (ABAQUS, 2010).
K¼
3 sin u 3 þ sin u
ð7Þ
tan b ¼
6 sin u 3 sin u
ð8Þ
The soil-metal coefficient of friction (f) was get and evaluated from the database (Song, 2006), the soil cohesion (C) and the angle of internal friction (u) were measured through laboratory test in a
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Fig. 3. Finite element mesh for soil box and four kinds of tines. (a) Rectangle, (b) triangle, (c) crescent, and (d) mososeries.
Table 4 The maximum penetration resistances of tines. Thickness (mm)
7 10 15 20 25
Penetration resistances (maximum values) (N) Rectangle tine
Triangle tine
Crescent tine
Mososeries tine
476.22 722.33 1107.85 1565.47 1722.16
363.78 489.62 658.28 769.48 873.80
436.20 760.93 1004.99 1365.80 1623.38
340.45 455.88 624.55 728.62 800.47
shear box at four levels of normal stress (100, 200, 300, and 400 kPa). For plastic hardening, confined uniaxial compression test data were used with yield stresses (we used precompression stress (rpc) as the initial yield stress) and corresponding plastic strain values (for the first yield stress and the plastic strain was assumed zero). Several yield stresses and corresponding plastic strain values imported into the toolbox are listed in Table 2. In order to conduct a series of analyses using the model, the input values given in Table 3 were imported into the model.
2.2. Tine model Four tine geometries were used in the simulation, which were defined as rectangle, triangle, crescent and mososeries based on the geometry of the cutting edge, as shown in Fig. 1. The dimensions of the rectangle tine are 207 mm 90 mm (length width)
with a cutting angle of 30°. Each tine has five thickness levels (7, 10, 15, 20, and 25 mm) with the cutting angle fixed. So there were 20 tines used in the simulation. 2.3. Finite element model A 3D soil-tine interaction model was developed using the ABAQUS toolbox (Fig. 2). The model was consisted of two distinct parts: (1) deformable soil and (2) rigid tine. Since the model was symmetric with the central plane and the thickness was very small as compared to the width, only one-half of a total attacked surface was considered and the predicted forces were then duplicated in magnitude in order to obtain the total forces. The tines used in the simulation were modeled as a discrete rigid body. The reference point of each tine was defined at the top-midpoint of the central plane. The dimensions of the used soil material box are 60 cm 30 cm 30 cm (length width height).
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The rigid body of each tine and the soil box were divided into the finite elements using two main element types, namely, R3D4 a quadratic, rigid bilinear element (4-node and 3 degrees of freedom per node element) and C3D8R (8-node linear brick, reduced integration, hourglass control), respectively. The density of a mesh was specified by creating seeds along the edges of the model and a free meshing method available at ABAQUS toolbox was used. Some researchers showed that the mesh size had an important effect on
101
the tillage force and calculation time (Bentaher et al., 2013). To reduce the cost of calculation time, in current study a finer mesh was assigned only to the area around the tine penetrated into the soil (Fig. 3). The tine-soil interaction layer was modeled with a contact surface-to-surface tangential layer using a penalty function method. The rigid bodies were selected as master and the deformable part as slave. A series of paired surfaces were selected as the
Fig. 4. Penetration resistances of tines with different types and thicknesses. (a), (b), (c), (d) and (e) represent the thickness of 7, 10, 15, 20, and 25 mm, respectively.
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Fig. 5. The attack surfaces.
Fig. 6. Relationships between attack surface area and penetration depth.
Table 5 The maximum attack surface areas of tines. Thickness (mm)
Attack surface area for one-half tine (cm2) Rectangle tine
Triangle tine
Crescent tine
Mososeries tine
7 10 15 20 25
186.72 186.89 187.19 187.49 187.78
116.98 117.34 117.93 118.47 118.93
173.31 173.51 173.83 174.16 174.47
101.37 101.66 102.13 102.57 103.00
contact surfaces: (1) all the surfaces facing the soil box were master surfaces, (2) the top face of the box (in x-z plane) and the side face near the tine (in x-y plane) were slave surfaces. Boundary conditions applied were: (1) both side walls of the box (in y-z plane) were totally fixed, (2) the bottom face of the box (in x-z plane) was totally fixed whilst the top face of the box was kept free for any constraint, (3) the face far from the tine (in x-y plane) was totally fixed whilst the face near the tine was left free for any constraint, (4) the tine face back to the soil box was constrained in the vertical direction, and (5) the velocity applied on the reference node was fixed in the penetration direction vertically. The outputs of the model were the reaction forces on the reference nodes of the tine. Further outputs of interest were the displacement of the rigid bodies, some energy components of the model including kinetic energy, total internal energy and elastic– plastic strain energies. However, what this study concerned was the reaction force in y-direction on the node. Since the tines are symmetric with the central plane, the forces on the both sides of the tine in the horizontal direction are cancelled by each other out while the vertical force of the tine is doubled, so the penetration resistance of a tine is the total vertical force. The operational conditions were: (1) the velocity of tines penetrated into the soil was 1.3 cm/s throughout all the analyses along the y-axis negative direction, (2) ending time of the simulation was set at 20 s., and (3) all variations in thickness were simulated with a fixed cutting angle (a = 30°) and the same soil condition. 3. Results and discussion 3.1. Penetration resistance prediction Table 4 shows the maximum penetration resistances of the different types and thicknesses of the tines. It was observed that
the penetration resistances increase with the thickness. The rectangle and crescent tines have larger penetration resistances as compared to the triangle and mososeries tines respectively, and the rectangle tine’s penetration resistances were resulted in the largest except the force at the thickness of 10 mm. The results in Table 4 show that the values of rectangle and crescent tines are 1.31 and 1.28 times larger as compared to the triangle and mososeries tines respectively at the thickness of 7 mm, while 1.97 and 2.03 times larger at the thickness of 25 mm. Penetration resistances of the triangle and mososeries tine are less than 1 kN within the variation of thickness. The largest value of these tines’ penetration resistances were found at 1.72 kN. All the tines have small penetration resistances at a lower thickness level. The tine geometry is a main influence factor causing the differences above.
3.2. Effect of the geometry on penetration resistance Fig. 4 shows a typical group of vertical force-depth curves of different types of tines with different thicknesses. The vertical force is the reaction force of the reference node in the penetration direction, i.e. the penetration resistance of the tine. The tendency can be observed that the penetration resistances of rectangle and crescent tines are greater than the ones of triangle and mososeries tines. The curves show nonlinear tendencies in the penetration process. The crescent and rectangle tines have similar curves, as well as the triangle and mososeries tines. In Fig. 1, based on the differences of geometries between the four tines (contact area and the cutting edge), the curves show a parallel tendency to each other after a critical depth in each group, but different in the early penetration stages due to the not quite different cutting edges which is similar in You et al. (2012). The curves can be divided into three phases (i.e. original phases, middle phases and end phases) in Fig. 4. The original phase means the process at the beginning of penetration, the end phase means the process at the end of penetration, and the middle phase means the process between the original phase and the end phase. In the original phase, the penetration force is mainly affected by the cutting edges making the curves different tendency. In the middle phase, the crescent and rectangle tine curves show a parallel tendency to each other because of the similar contact area, as well as the triangle and mososeries tine. In the end phase, the whole tine bodies are penetrated into the soil, and the relationship between the force and depth shows different characteristics even curve intersections showing up in the figures. The soil movements and properties can be concluded as the main reasons but more work needs to be carried out.
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Fig. 7. Relationships between vertical force and attack surface area with different thickness. (a) With the thickness of 7 mm and (b) with the thickness of 25 mm.
Fig. 8. Penetration resistances of tines with different types and thicknesses. (a), (b), (c) and (d) represent the rectangle tine, triangle tine, crescent tine and mososeries tine, respectively.
The attack surface area was used to describe interaction surface and defined as the contact area between both sides of the tine and
soil as shown in Fig. 5. Table 5 shows the maximum attack surface area of each one-half tine (doubled for the whole tine). The
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Fig. 9. Relationships between vertical force and thickness. (a) and (b) represent the penetration depth of 150 mm and 200 mm, respectively.
rectangle tine has the largest attack surface areas, then crescent tine, triangle tine and mososeries tine, and this change is similar with the tendency shown in Fig. 4. It’s easy to be observed that each tine’s maximum attack surface area increases with the thickness, but not significantly. Fig. 6 shows the relationship between attack surface areas of the tines and the penetration depth. It is indicated that the attack surface area shows different characteristics because of the geometry difference. It also can be observed that the tendencies of attack surface area changing with the depth are very similar with the ones in Fig. 4 which proves that the penetration force has a direct relation with the attack surface area which inspired the force variation tendency differences. Pure-shear model was described by Zheng (1995) which means only partial failures including cutting, compression, and plastic flow exist in the blade-soil interaction, and the mean resistances in the blade movements are composed of friction and normal stress from the cutting edge and the side edges. With regard to the soil penetrating based on the pure-shear theory, the resistance coming from the soil reacts on the attack surface area of the tine, the horizontal force components cancel each other out whilst the vertical components comprise the whole penetration resistance together. When the attack surface area changes, so does the penetration resistance. Fig. 7 shows the vertical force-attack surface area curves of the four tines with the thickness of 7 mm and 25 mm. The vertical forces (i.e. penetration resistances) increase with attack surface area nonlinearly. A power function relationship is presented with R2 values exceeding 0.96 within these tines. It can be observed that the power number is less than 1 at the thickness of 7 mm, while more than 1 at the thickness of 25 mm. So there must be a thickness level resulting in a linear relationship between the penetration resistance and attack surface area. The constants also change with the tines’ variation. It was found that the curve tendency remains unchanged with the tine type variation but constants change with the thickness. A function relationship between the penetration resistance and attack surface area can be concluded as follow:
P ¼ ISm
ð9Þ
where P is the penetration resistance (N), S is the attack surface area of tine (cm2), I and m are dimensionless constants which are associated with the soil mechanics and tine geometry parameters.
The tendency is similar with the draught force in the tillage system. Zelenin (1950) found the draught force had a parabolic relation with the working depth through a number of tests using horizontal cutting blade, as shown in Eq. (10):
P ¼ kH
n
ð10Þ
where P is the cutting resistance in horizontal direction, k is the resistance coefficient, H is the working depth and n is the experimental coefficient which approximates 1.35. It has to be pointed out that n changes with the soil condition and working depth variation. For the same tool, it’s easy to conclude that the contact surface area changes with the working depth. There must be a relationship between the depth and the contact surface area for a certain tillage tool, which proves the rationality of Eq. (9) above. The same tendency can also be found from Godwin and Spoor (1977). 3.3. Effect of the thickness and depth on penetration resistances Fig. 8 indicates the different curves of vertical forces through the penetration process with the variation of thickness. It was observed that the large differences between the tines, the rectangle and crescent were resulted at larger magnitude compared with the triangle and mososeries respectively. This tendency can also be analyzed from Fig. 9 which shows the relationship between vertical force and thickness at the penetration depth of 150 mm and 200 mm, respectively. The mososeries tine indicated the smallest penetration resistance in the whole penetration process. The thickness shows a lower influence on triangle and mososeries tine than rectangle and crescent tine, and the penetration resistances of triangle and mososeries tine do not increase as sharply as the rectangle and crescent tine. It is observed that the vertical forces increase with the thickness nonlinearly. The vertical force increases with the thickness, and a power function relationship existing between the vertical force and thickness indicates the power number < 1 and R2 values exceeding 0.97 at the penetration depth of 150 mm and 200 mm respectively. Godwin and Spoor (1977) found the forces increased in proportion to width (very narrow tine range), then at a decreasing rate (narrow tine range) and finally at a linear rate but at a lower rate compared to the initial phase (blade or wide tine range).
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Fig. 10. Penetration resistances of tines with different types and thicknesses. (a), (b), (c), (d) and (e) represent the penetration depth exceeding 10 cm with the thickness level of 7 mm, 10 mm, 15 mm, 20 mm, and 25 mm, respectively.
With the changes of the thickness and depth, the relationship curves show different characteristics. Fig. 10 shows the vertical
force-penetration depth curves. The penetration depths were divided into two parts, within 10 cm and more than 10 cm. Fig-
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Types of tines(thickness of 7mm)
Penetration time(s) and direction
Rectangle tine
Crescent tine
Triangle tine
Mososeries tine
Origin (0.19,0,0)
Origin (0.14,0,0)
Origin (0.15,0,0)
Origin (-0.024,0,0)
Normal axis (1,0,0)
Normal axis (1,0,0)
Normal axis (1,0,0)
Normal axis (-1,0,0)
Axis2 (0,1,0)
Axis2 (0,1,0)
Axis2 (0,1,0)
Axis2 (0,-1,0)
5s
10s
15s
20s
View cut position
Fig. 11. Soil deformation in front of the attack surface area at different time steps.
ure (a) to (e) in Fig. 10 represent the relationship between penetration resistance and the depth for more than 10 cm with the thickness level of 7 mm, 10 mm, 15 mm, 20 mm, and 25 mm, respectively. Furthermore, the penetration resistances of the crescent, triangle and mososeries tine indicated non-linear relationship with depth within the depth of 10 cm were observed in Fig. 8. When the depth exceeds 10 cm, and the tine thickness is over 10 mm, all the curves of vertical force and depth turn into linear ones, and at the end phases, the curve points show a large fluctuation caused by the soil movements and properties but more work
to be done. The tendencies of the curves are nonlinear with the thickness of 7 mm and 10 mm. The curves of vertical force (i.e. penetration resistance) calculated for the soil-tine interaction as a function of depth at different thickness levels were also shown in Fig. 8. The tendencies were described by the quadratic polynomial functions with R2 values exceeding 0.95 throughout the whole penetration process. It was observed that the coefficients change with different geometries. For the rectangle and crescent tines, the quadratic coefficients are negative within a thickness level but turns into positive with
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Time(s)
5s
10s
15s
20s
Rectangle tine
View cut
Origin (0.024,0,0); Normal axis (1,0,0); Axis2 (0,1,0)
Fig. 12. Soil deformation in the front of the attack surface area of rectangle tine with the thickness of 25 mm at different time steps.
Fig. 13. Soil deformation in the vertical direction of rectangle tine at 20 s. (a) and (b) represent the rectangle tine with thickness of 7 mm and 25 mm, respectively.
increasing thickness, while the quadratic coefficient is positive for the triangle and mososeries tine. A function relationship can be concluded as follow: 2
P ¼ aðh þ bÞ þ c
ð11Þ
where P is the penetration resistance, h is the penetration depth, a and b are the constants related to the soil mechanics and tine geometry parameters, c is the calculation constant. You (2011) used the device designed and fabricated to measure the vertical forces acting on three different very narrow blades (thickness of 7 mm) in his doctoral dissertation. When penetrating into a sandy loam soil bin, a tendency was found that the vertical force increases with the depth which is similar to the results obtained in this study, and a semi-empirical and semi-trial model was proposed as Eq. (12):
P ¼ K1h P ¼ K 1 h þ K 2 ðh hc Þ
h 6 hc 2
h > hc
ð12Þ
where P is the penetration force, K1 and K2 are soil resistance coefficients, h is penetration depth, hc is the critical depth, respectively. The critical depth is thought to exist in the penetration process, a linear relationship between penetration resistance and depth within the critical depth, while a quadratic polynomial exist beyond the critical depth. It shows nonlinear throughout the whole penetration process at the thickness of 7 mm in this paper. The differences between the two functions are caused by the errors between the tine geometries or the soil related parameters. It is indicated that the attack surface area shows different characteristics because of the geometry differences from Fig. 6. The penetration resistance has a direct relation with the attack surface area which makes the force variation tendency different. That also causes the different constants variations between a and b as shown in Eq. (11). Furthermore, the soil parameters input in the simula-
tions were obtained from the related soil mechanics experiments. While the soil properties could not show the real soil properties in the field, the simulations represent a perfect working process which has a difference with the field environment, and differences exist between the two soil parameters. A cross term can be concluded in Eq. (11) caused by the interaction of soil property and tine geometry. From another point of view, You’s (2011) trials also show a nonlinear tendency between the penetration resistance and depth. Several soil tillage force prediction models for the tines were proposed by Hettiaratchi et al. (1966), Godwin and spoor (1977) and Meyerhof (1951). The models indicated that the force components have much to do with the soil parameters and tine geometries. The relationship reflected by Eq. (11) is also a semiempirical model based on the curves obtained from the simulation. 3.4. Soil deformation Fig. 11 shows side views of the variation of soil deformation in front of the attack surface areas at the different time steps and for different tines with 7 mm thickness. Considering the different geometries of the cutting edges of those tines, the longest cutting edge was chosen to observe the soil deformation by the view cut toolbox in ABAQUS 6.11. The boundary influence is neglected. The soil deformation forms a soil disturbance area. From the time steps it was found that the soil disturbance area increased when the tine penetrated into the soil bin. The rectangle and crescent tines indicated more soil deformations as compared to the triangle and mososeries tines. When the triangle and mososeries tine penetrate into the soil, the cutting edges and the attack surfaces contact with the soil gradually along with the cutting edges which make the soil deformation lower. In Fig. 11, the different colour represents the different degree of the deformation, it can be observed that the compaction of the soil decreases from the near area to far, and the biggest compaction area moves with the attack
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surface of the tine, especially obvious in Fig. 12, the blue part represents the biggest soil compaction deformation and moves with the tine in different penetration times. When the whole tine body moved into the soil, the top soil layer separated from the attack surface where soil showed resilience, at the time step of 20 s in Figs. 11 and 12. The crescent soil disturbance area exists throughout the penetration process induced by soil compaction. The crescent area could be one reason for causing the soil loosening. Because of the friction between soil and mental tines, compacted soil get loosen when the tines penetrated into and moved out the soil. When the thickness increases to 25 mm, it was observed that the soil has a large deformation caused by the tine in the vertical direction, compared to the thickness of 7 mm. It can also be found in Fig. 13, because of the friction, the vertical deformation caused by the tine with the thickness of 25 mm is higher than the deformation by the tine with the thickness of 7 mm. So, tines with small thickness can be used when low side soil disturbance is requested. 4. Conclusions The finite element method (FEM) was used to model the interaction between the soil and different types of tines penetrating into a sandy loam soil vertically. The simulation was helpful to understand the effect of geometry, thickness and depth on the penetration resistances and side soil disturbance area. Tine geometry affects the penetration force substantially. The rectangle tine resulted in the highest penetration resistances compared to the crescent, triangle and mososeries tine. The changes of different types, geometries and thicknesses of the tines cause the variation of the attack surface area between the tine and soil which directly influence the penetration resistance during the penetration process. The results showed that the penetration resistance increases with a power function with the attack surface area, nonlinear tendency with thickness and a quadratic function with penetration depth. A crescent soil deformation area was found at the sides of the tine during the penetration process due to compaction. It can be concluded that the FEM can improve the understanding of tine geometry effects on penetration resistance and soil deformation area. Acknowledgements The authors would like to acknowledge the funding provided by National Natural Science Foundation of China (NSFC) (51405493), China Agriculture Research System (CARS-35) and Special Fund for Agro-scientific Research in the Public Interest (201203024).
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