# Discrete Element Method Simulation and Field Evaluation of a Vibrating Root-Tuber Shovel in Cohesive and Frictional Soils

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## Abstract

**:**

## 1. Introduction

^{−3}, respectively. However, a 1 Hz increase in vibration frequency increased specific energy consumption by 3.12 kJ m

^{−3}, whereas draught force and total torque decreased by 375.75 N and 28.44 Nm, respectively. Li et al. [21] investigated the mechanism for soil separation and its effectiveness in removing soil by combining DEM with the multi-body dynamics (MBD) method. However, the energy requirements for digging the tuber from the soil were not analysed. The model was validated through field experiments, and the results exhibited a relative error of 3.81%. Wanru et al. [22] utilised the Hertz–Mindlin approach along with a flexible bonding contact model to simulate and establish the process of harvesting tiller taro using DEM.

## 2. Materials and Methods

#### 2.1. Description of the Jerusalem Artichoke Harvester

#### 2.2. Determination of Mechanical and Physical Properties of Jerusalem Artichoke Crop

^{−3}using the water displacement method (Figure 2b). Standard compression test specimens with a diameter of 10 mm and a length of 20 mm were prepared. A single-factor uniaxial compression (Figure 2c) was conducted using a TMS-Pro texture analyser (FTC, Washington, DC, USA). The shear modulus, elastic modulus, and Poisson’s ratio of the Jerusalem artichoke tubers were calculated as 4.23 × 10

^{6}Pa, 1.19 × 10

^{7}Pa, and 0.408, respectively, using Equations (1)–(5). The average diameter of the Jerusalem artichoke roots was determined to be 5.5 mm. The friction coefficients (static and rolling) and the coefficient of restitution of the Jerusalem artichoke tubers and roots were determined using the inclined plane method (Figure 2d). A three-point bending test was carried out on the roots (Figure 2e). From the test, the elastic modulus of the roots was determined to be 1.32 × 10⁷ Pa. The approaches used in determining the mechanical and physical properties of the tubers and roots were utilised for the stem. A summary of the mechanical and physical properties is presented in Supplementary Table S1.

^{2}), p is the load applied (N), σ is the axial stress (N m

^{−2}), ε is the axial strain, ∆L is the change in specimen length (mm), L is the original specimen length (mm), E is the elastic modulus (Pa), v is the Poisson’s ratio, and G is the shear modulus (Pa).

#### 2.3. Determination of Soil Mechanical and Physical Properties

#### 2.4. Discrete Element Method Simulation Setup and Analysis

^{®}Xeon

^{®}CPU 4214R @ 2.4 GHz, 12 cores (24 threads), and 32GB RAM computer running EDEM

^{®}2020 bulk material simulation software was used to perform the DEM simulations. The clay soil was modelled without the Jerusalem artichoke crop. However, the crop was incorporated into the sandy loam model to mimic field conditions. Therefore, the measured mechanical and physical properties determined in Section 2.2 were utilised to set up the DEM soil–crop model described in detail in Section 2.4.1. The two virtual soil bins were both 2500 mm × 2500 mm × 400 mm (width, breadth, and depth) in size. Furthermore, the DEM soil models were fitted with a random particle size distribution (minimum: 0.5, maximum: 1.5 radius scales).

^{2}of 0.82 was in reasonable agreement with the adjusted R

^{2}of 0.93. A mean static angle of repose of 30.06° was obtained with a standard deviation (Std.Dev). of 1.47 and coefficient of variation (CoV) of 4.91%. The regression model was assessed for adequacy by using the diagnostic plots shown in Figure 4. The diagnostic plots did not show any outliers in the data, implying that the data fit the designed model. Numerical optimisation was performed to obtain optimal input parameters by targeting the measured static angle of repose (29.85°). The optimal values are shown in Figure 5, whereas Table 1 lists the input parameters used for the DEM soil–crop mixture model simulation. The procedure used to determine the optimal input parameters for the soil–crop mixture was employed to obtain the optimal input parameters for the clay–soil DEM model (see Supplementary Tables S5 and S6, and Supplementary Figure S4). The DEM input parameters used for the clay soil are shown in Table 2.

#### 2.4.1. Discrete Element Method Soil–Crop Modelling

^{−3}) and depth to prevent the soil bin from becoming excessively loose. The particle size distribution employed created an interlocking effect, which also aided with realistic particle behaviour. The fork-shaped and the S-shaped shovels were then imported to evaluate their ability to dig and translocate the soil–crop mass to the rear of the digging tool, a feature desirable for a tuber-harvesting machine.

#### 2.5. Experimental Design and Analysis

^{−1}forward speeds were employed in the clay soil field at a digging depth of 200 mm (Figure 9a). However, the sandy loam soil field was evaluated using 10 Hz and 12.5 Hz frequencies plus 1 and 2 km h

^{−1}forward speeds at a digging depth of 200 mm. These parameters were selected based on the optimal parameters of previous studies [6] and the available tractor power. The digging depth of 200 mm was used for the Jerusalem artichoke field because the tubers had developed to an average maximum depth of 150 mm (Figure 9b).

## 3. Results and Discussion

^{2}and the predicted R

^{2}(i.e., the difference was less than 0.2) for all the response variables, suggesting that the design model was accurate. Additionally, from Table 5, all the main model treatments and the interaction of the terms were statistically significant at p < 0.05, implying that the treatments affected the measured variables.

#### 3.1. Effect of Speed and Frequency on Draught Force

^{−1}. Soehne [31] found that draught force was a function of soil acceleration and, consequently, proportional to the square of speed. McLaughlin and Campbell [32] also observed a similar outcome. They noted that accelerating the movement of soil particles increased frictional forces on tines.

^{−1}, a 5 mm amplitude, and an 8–10 Hz frequency. Other researchers have reported similar reduction trends [8,37,38].

#### 3.2. Effect of Speed and Frequency on Drawbar Power

^{−1}, respectively.

#### 3.3. Discrete Element Method Model Validation

#### 3.4. Particle Displacement Analysis

^{−1}forward speed, and 200 mm depth in clay soil. In addition, at those same operating parameters, the S-shaped shovel produced a smaller soil bulk density (706.35 kg m

^{−3}) than the fork-shaped shovel (864.53 kg m

^{−3}) after the tool passed (Figure 16).

^{−1}, and 200 mm depth in sandy loam soil. Once again, the results show that the S-shaped shovel was able to translocate the soil–crop mass to the rear better than the fork-shaped shovel. The predicted bulk density for the S-shaped shovel (889.13 kg m

^{−3}) was also smaller than that of the fork-shaped shovel (993.91 kg m

^{−3}).

## 4. Conclusions

^{−1}), draught requirements on the tine increased by 46.38%. It was also found that increasing vibration frequency from 5 to 14.5 Hz decreased both draught force and drawbar power by 42.4%. The S-shaped shovel could crush and translocate soil–crop mass to the rear better than the fork–shaped shovel. This suggests that the S-shaped shovel works well in different soil conditions ranging from frictional to cohesive soils. The findings of this study also show that draught force and drawbar power were generally higher for the clay soil compared to the sandy loam soil evaluated. The methodology used to develop the soil–crop model can be applied to other root and tuber crops, facilitating the virtual evaluation of digging tools or entire harvesters.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Cross-sectional area (mm^{2}) |

ANOVA | Analysis of variance |

ASABE | American Society of Agricultural and Biological Engineers |

CoV | Coefficient of variation |

CFD | Computational fluid dynamics |

DEM | Discrete element method |

E | Elastic modulus (Pa) |

FEM | Finite element method |

G | Shear modulus (Pa) |

HSCM | Hysteretic spring contact model |

JKR | Johnson–Kendall–Roberts |

L | Original specimen length (mm) |

LCM | Linear cohesion model |

P | Load applied (N) |

PB | Parallel bond |

RE | Relative error |

RSM | Response surface methodology |

Std.Dev. | Standard deviation |

2FI | Two-factor interaction |

v | Poisson’s ratio |

∆L | Change in specimen length (mm) |

σ | Axial stress (N m^{−2}) |

ε | Axial strain |

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**Figure 1.**4U-1600A Jerusalem artichoke harvester: (1) diablo rollers (depth adjustment), (2) soil–tuber conveyor, (3) shovel, (4) harvester body, (5) vibration mechanism, (6) hydraulic motor, (7) wheel, (8) hydraulic fluid tank, (9) cleaning cylinder, and (10) tuber conveyor.

**Figure 2.**Mechanical and physical properties experiment for Jerusalem artichoke crop: (

**a**) sampled tubers from artichoke field (different sizes and shapes), (

**b**) tuber density determination, (

**c**) uniaxial compression test, (

**d**) inclined plane method for friction coefficients, and (

**e**) root bending test.

**Figure 3.**Static angle of repose for soil–crop mass calibration: (

**a**) experiment (the red line is a laser pointer which serves as a visual reference for the angle being measured) and (

**b**) DEM simulation.

**Figure 6.**DEM crop–modelling technique: (

**a**) Fresh Jerusalem artichoke tuber, (

**b**) 3D computer-aided design model, (

**c**) DEM tuber particle, and (

**d**) DEM crop model.

**Figure 7.**DEM soil–crop mixture model establishment: (

**a**) factory setup, (

**b**) subsoil creation, (

**c**) crop creation, (

**d**) topsoil creation, and (

**e**) soil–crop model.

**Figure 9.**The depth of operation for the two field experiments: (

**a**) clay soil field and (

**b**) sandy loam field.

**Figure 11.**Effect of forward speed and vibration frequency on draught force: (

**a**,

**b**) clay field experiment 3D and 2D contour plots, and (

**c**,

**d**) DEM simulation 3D and 2D contour plots.

**Figure 12.**Effects of forward speed and vibration frequency on draught force: (

**a**,

**b**) sandy loam field experiment 3D and 2D contour plots, and (

**c**,

**d**) DEM simulation 3D and 2D contour plots.

**Figure 13.**Effect of vibration frequency on draught force for the experiment and DEM simulation: (

**a**) clay soil and (

**b**) sandy loam.

**Figure 14.**Comparison of field data and DEM for drawbar power: (

**a**,

**b**) clay soil field and DEM results, respectively; (

**c**,

**d**) sandy loam soil field and DEM results, respectively.

**Figure 15.**Soil translocation properties of the shovels evaluated in clay soil: (

**a**) field experiment for fork shovel, (

**b**) DEM result for fork-shaped shovel, and (

**c**) DEM result for S-shaped shovel.

**Figure 16.**DEM predicted soil bulk density for clay soil evaluation: (

**a**) fork-shaped shovel and (

**b**) S-shaped shovel.

**Figure 17.**Soil–crop mass translocation properties of the tools evaluated in sandy loam soil: (

**a**) field experiment result, (

**b**,

**c**) DEM result for the fork-shaped shovel, and (

**d**,

**e**) DEM result for the S-shaped shovel.

**Figure 18.**DEM-predicted bulk density for sandy loam soil evaluation: (

**a**) fork-shaped shovel and (

**b**) S-shaped shovel.

Parameter and Unit | Value | Remarks |
---|---|---|

Poison’s ratio: soil | 0.3 | Selected |

Poison’s ratio: steel | 0.3 | [30] |

Poisson’s ratio: root | 0.38 | Measured |

Poison’s ratio: tuber | 0.48 | Measured |

Poison’s ratio: stem | 0.35 | Measured |

Particles’ solid density (kg m^{−3}) | 2600 | [6] |

Density of steel (kg m^{−3}) | 7865 | [30] |

Density of root (kg m^{−3}) | 1132 | Measured |

Density of tuber (kg m^{−3}) | 1184.4 | Measured |

Density of stem (kg m^{−3}) | 250.75 | Measured |

Shear modulus (Pa): soil | $1.7\times {10}^{7}$ | [6] |

Shear modulus (Pa): steel | $7.9\times {10}^{10}$ | [30] |

Shear modulus (Pa): root | $4.78\times {10}^{6}$ | Measured |

Shear modulus (Pa): tuber | $4.23\times {10}^{6}$ | Measured |

Shear modulus (Pa): stem | $2.72\times {10}^{8}$ | Measured |

Coefficient of restitution: soil–soil | 0.6 | [6] |

Coefficient of restitution: soil–steel | 0.6 | [6] |

Coefficient of restitution: soil–root | 0.439 | Calibrated |

Coefficient of restitution: soil–tuber | 0.514 | Calibrated |

Coefficient of restitution: soil–stem | 0.554 | Calibrated |

Coefficient of restitution: root–steel | 0.32 | Measured |

Coefficient of restitution: tuber–steel | 0.62 | Measured |

Coefficient of restitution: stem–steel | 0.53 | Measured |

Coefficient of static friction: soil–soil | 0.45 | [6] |

Coefficient of static friction: root–soil | 0.195 | Calibrated |

Coefficient of static friction: tuber–soil | 0.212 | Calibrated |

Coefficient of static friction: stem–soil | 0.166 | Calibrated |

Coefficient of static friction: soil–steel | 0.45 | [6] |

Coefficient of static friction: root–steel | 0.511 | Measured |

Coefficient of static friction: tuber–steel | 0.446 | Measured |

Coefficient of static friction: stem–steel | 0.5 | Measured |

Coefficient of rolling friction: soil–soil | 0.18 | [6] |

Coefficient of rolling friction: root–soil | 0.015 | Calibrated |

Coefficient of rolling friction: tuber–soil | 0.175 | Calibrated |

Coefficient of rolling friction: stem–soil | 0.069 | Calibrated |

Coefficient of rolling friction: root–steel | 0.21 | Measured |

Coefficient of rolling friction: tuber–steel | 0.32 | Measured |

Coefficient of rolling friction: stem–steel | 0.05 | Measured |

Normal stiffness per unit area (N m^{−3}) | $1\times {10}^{9}$ | Selected |

Shear stiffness per unit area (N m^{−3}) | $2.5\times {10}^{7}$ | Calibrated |

Normal strength (Pa) | $1.3\times {10}^{6}$ | Calibrated |

Shear strength (Pa) | $1.15\times {10}^{6}$ | Calibrated |

Bonded disk scale | 1 | Selected |

JKR surface energy (J m^{−2}) | 10 | Selected |

Parameter and Unit | Value | Remarks |
---|---|---|

Poison’s ratio: soil | 0.3 | Selected |

Poison’s ratio: steel | 0.3 | [30] |

Particles’ solid density (kg m^{−3}) | 2600 | Selected |

Density of steel (kg m^{−3}) | 7865 | [30] |

Shear modulus (Pa): soil | $2\times {10}^{7}$ | Calibrated |

Shear modulus (Pa): steel | $7.9\times {10}^{10}$ | [30] |

Yield strength (Pa): soil (single sphere, dual sphere, and triple sphere) | $2.21\times {10}^{6},2.56\times {10}^{6},\mathrm{a}\mathrm{n}\mathrm{d}2.37\times {10}^{6}$ | Default value in EDEM^{®} 2020 |

Yield strength (Pa): steel | $1\times {10}^{9}$ | Default value in EDEM^{®} 2020 |

Coefficient of restitution: soil–soil | 0.467 | Calibrated |

Coefficient of restitution: soil–steel | 0.05 | Selected |

Coefficient of static friction: soil–soil | 0.388 | Calibrated |

Coefficient of static friction: soil–steel | 0.45 | Selected |

Coefficient of rolling friction: soil–soil | 0.192 | Calibrated |

Coefficient of rolling friction: soil–steel | 0.15 | Selected |

Damping factor | 0.5 | Default value in EDEM^{®} 2020 |

Stiffness factor | 0.85 | Default value in EDEM^{®} 2020 |

Cohesive energy density (J m^{−3}) | 20,965.7 | Calibrated |

Source | Sequential p-Value | Adjusted R^{2} | Predicted R^{2} | Remark |
---|---|---|---|---|

Experiment draught force | ||||

Linear | <0.0001 * | 0.9038 | 0.8475 | |

2FI | 0.0798 ** | 0.9280 | 0.7966 | |

Quadratic | 0.0512 ** | 0.9643 | 0.9324 | Suggested |

Cubic | 0.0340 * | 0.9947 | 0.9664 | Aliased |

DEM draught force | ||||

Linear | <0.0001 * | 0.9017 | 0.8430 | |

2FI | 0.0908 ** | 0.9243 | 0.7748 | |

Quadratic | 0.0394 * | 0.9657 | 0.9120 | Suggested |

Cubic | 0.0240 * | 0.9959 | 0.9538 | Aliased |

Experiment drawbar power | ||||

Linear | <0.0001 * | 0.9473 | 0.9011 | |

2FI | 0.0006 * | 0.9874 | 0.9692 | Suggested |

Quadratic | 0.0963 ** | 0.9923 | 0.9734 | |

Cubic | 0.0085 ** | 0.9995 | 0.9977 | Aliased |

DEM drawbar power | ||||

Linear | <0.0001 * | 0.9450 | 0.8974 | |

2FI | 0.0010 * | 0.9850 | 0.9623 | Suggested |

Quadratic | 0.0777 ** | 0.9915 | 0.9693 | |

Cubic | 0.0073 * | 0.9995 | 0.9968 | Aliased |

Source | Experiment Draught Force | DEM Draught Force |
---|---|---|

Std. Dev. | 368.33 | 362.5 |

Mean | 11,963.1 | 11,411.15 |

CoV% | 3.08 | 3.18 |

R^{2} | 0.9952 | 0.9951 |

Adjusted R^{2} | 0.9857 | 0.9852 |

Predicted R^{2} | 0.9235 | 0.9212 |

Adequacy precision | 22.8498 | 22.4509 |

Experiment Draught Force (Quadratic) | DEM Draught Force (Quadratic) | Experiment Drawbar Power (2FI) | DEM Drawbar Power (2FI) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Source | F-Value | p-Value | Source | F-Value | p-Value | Source | F-Value | p-Value | Source | F-Value | p-Value |

Model | 60.51 | <0.0001 * | Model | 62.89 | <0.0001 * | Model | 288.85 | <0.0001 * | Model | 242.23 | <0.0001 * |

A | 150.65 | <0.0001 * | A | 159.85 | <0.0001 * | A | 66.6 | <0.0001 * | A | 57.39 | 0.0003 * |

B | 157.21 | <0.0001 * | B | 159.02 | <0.0001 * | B | 810.21 | <0.0001 * | B | 678.05 | <0.0001 * |

AB | 8.13 | 0.0291 * | AB | 8.15 | 0.029 * | AB | 29.72 | 0.0006 * | AB | 25.06 | 0.0010 * |

A^{2} | 5.33 | 0.0603 ** | A^{2} | 7.54 | 0.0335 * | ||||||

B^{2} | 4.83 | 0.0.0704 ** | B^{2} | 4.09 | 0.0895 ** | ||||||

Std.Dev. | 876.40 | Std.Dev. | 836.44 | Std.Dev. | 1.01 | Std.Dev. | 1.06 | ||||

Mean | 16,990.08 | Mean | 16,321.74 | Mean | 12.07 | Mean | 11.59 | ||||

CoV% | 5.16 | CoV% | 5.12 | CoV% | 8.37 | CoV% | 9.17 |

**Table 6.**Comparison of clay soil field and DEM simulation result for draught force and drawbar power.

Frequency | Forward Speed | Experiment Draught Force | DEM Draught Force | Experiment Drawbar Power | DEM Drawbar Power | RE |
---|---|---|---|---|---|---|

(Hz) | (km h^{−1}) | (N) | (N) | (kW) | (kW) | (%) |

5 | 1 | 16,542.170 | 15,926.626 | 4.595 | 4.424 | 3.721 |

5 | 2 | 20,951.889 | 20,105.592 | 11.640 | 11.170 | 4.039 |

5 | 4 | 26,036.022 | 25,019.387 | 28.929 | 27.799 | 3.905 |

9.75 | 1 | 13,288.189 | 12,867.725 | 3.691 | 3.574 | 3.164 |

9.75 | 2 | 17,684.548 | 17,270.654 | 9.825 | 9.595 | 2.340 |

9.75 | 4 | 22,677.284 | 21,915.671 | 25.197 | 24.351 | 3.358 |

12.5 | 1 | 12,819.620 | 12,362.924 | 3.561 | 3.434 | 3.562 |

12.5 | 2 | 16,586.874 | 15,699.174 | 9.215 | 8.722 | 5.352 |

12.5 | 4 | 19,479.821 | 18,863.692 | 21.644 | 20.960 | 3.163 |

14.5 | 1 | 10,245.086 | 9795.835 | 2.846 | 2.721 | 4.385 |

14.5 | 2 | 12,573.063 | 11,794.365 | 6.985 | 6.552 | 6.193 |

14.5 | 4 | 14,996.467 | 14,239.182 | 16.663 | 15.821 | 5.050 |

**Table 7.**Comparison of sandy loam soil field and DEM simulation result for draught force and drawbar power.

Frequency | Forward Speed | Experiment Draught Force | DEM Draught Force | Experiment Drawbar Power | DEM Drawbar Power | RE |
---|---|---|---|---|---|---|

(Hz) | (km h^{−1}) | (N) | (N) | (kW) | (kW) | (%) |

10 | 1 | 11,232.587 | 10,669.730 | 3.120 | 2.964 | 5.011 |

10 | 2 | 15,423.266 | 14,753.971 | 8.568 | 8.197 | 4.340 |

12.5 | 1 | 8134.596 | 7705.821 | 2.260 | 2.141 | 5.271 |

12.5 | 2 | 13,061.930 | 12,515.067 | 7.257 | 6.953 | 4.187 |

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## Share and Cite

**MDPI and ACS Style**

Awuah, E.; Aikins, K.A.; Antille, D.L.; Zhou, J.; Gbenontin, B.V.; Mecha, P.; Liang, Z.
Discrete Element Method Simulation and Field Evaluation of a Vibrating Root-Tuber Shovel in Cohesive and Frictional Soils. *Agriculture* **2023**, *13*, 1525.
https://doi.org/10.3390/agriculture13081525

**AMA Style**

Awuah E, Aikins KA, Antille DL, Zhou J, Gbenontin BV, Mecha P, Liang Z.
Discrete Element Method Simulation and Field Evaluation of a Vibrating Root-Tuber Shovel in Cohesive and Frictional Soils. *Agriculture*. 2023; 13(8):1525.
https://doi.org/10.3390/agriculture13081525

**Chicago/Turabian Style**

Awuah, Emmanuel, Kojo Atta Aikins, Diogenes L. Antille, Jun Zhou, Bertrand Vigninou Gbenontin, Peter Mecha, and Zian Liang.
2023. "Discrete Element Method Simulation and Field Evaluation of a Vibrating Root-Tuber Shovel in Cohesive and Frictional Soils" *Agriculture* 13, no. 8: 1525.
https://doi.org/10.3390/agriculture13081525