# Simulation of Mouldboard Plough Soil Cutting Based on Smooth Particle Hydrodynamics Method and FEM–SPH Coupling Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Brief Introduction to SPH

#### 2.2. FEM–SPH Coupling Method

#### 2.3. Soil Constitutive Law

## 3. Numerical Simulation

#### 3.1. Establishment of the Finite Element Model of the Plough

#### 3.2. Establishment of SPH Model, FEM–SPH Coupling Model

#### 3.2.1. SPH Model

#### 3.2.2. FEM-SPH Coupling Model

#### 3.2.3. Boundary Conditions Imposed

#### 3.3. Parameter Study

## 4. Results and Discussion

#### 4.1. Cutting Process and Cutting Resistance Analysis

#### 4.2. Stress Variation of Soil

#### 4.3. Model Validation

#### 4.4. Effect of Cutting Speed and Depth on Cutting Resistance

#### 4.5. Effect of Inclination Angle $\alpha $ and Lifting Angle $\beta $ of the Plough on Cutting Resistance

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**FEM–SPH coupling: (

**a**) the attachment and contact algorithm between FEM and SPH; (

**b**) location of the contact point when ${n}_{s}$ lies above master segment.

**Figure 7.**Cutting process and cutting resistance of soil based on SPH model and coupled FEM-SPH model: SPH model: (

**a**) t = 0.74 s, (

**b**) t = 2.02 s, (

**c**) t = 3.78 s; FEM-SPH model: (

**d**) t = 0.74 s, (

**e**) t = 2.02 s, (

**f**) t = 3.78 s.

**Figure 8.**Stress variation in soil cutting process (FEM-SPH model): (

**a**) t = 0 s; (

**b**) t = 0.16 s; (

**c**) t = 0.98 s; (

**d**) t = 1.96 s; (

**e**) t = 3.12 s; (

**f**) t = 4 s.

**Figure 10.**The linear regression plots for the estimated against measured: (

**a**,

**c**) horizontal force; (

**b**,

**d**) vertical force.

**Figure 11.**Relationship between cutting resistance and cutting speed: (

**a**) horizontal; (

**b**) vertical; (

**c**) combined cutting resistance.

**Figure 12.**Relationship between cutting resistance and inclination angle: (

**a**) horizontal; (

**b**) vertical; (

**c**) combined cutting resistance.

**Figure 13.**Relationship between cutting resistance and lifting angle: (

**a**) horizontal; (

**b**) vertical; (

**c**) combined cutting resistance.

Parameters | Value | Parameters | Value |
---|---|---|---|

Density of soil$/\left(\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}\right)$ | 2600 | Static friction coefficient between soil and plough | 0.6 |

Shear modulus of soil$/\mathrm{P}\mathrm{a}$ | $1.2\times {10}^{6}$ | Dynamic friction coefficient between soil and plough | 0.1 |

Poisson’s ratio of soil | 0.38 | Static friction coefficient between two soil particles | 0.422 |

Density of plough$/\left(\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}\right)$ | 7970 | Dynamic friction coefficient between two soil particles | 0.282 |

Young’s modulus of plough$/\mathrm{P}\mathrm{a}$ | $2.10\times {10}^{11}$ | Radius of particle$/\left(\mathrm{m}\mathrm{m}\right)$ | 5 |

Poisson’s ratio of plough | 0.32 | Gravity$/\left(\mathrm{m}/{\mathrm{s}}^{2}\right)$ | 9.806 |

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**MDPI and ACS Style**

Jin, X.; Ma, F.; Wang, D.; Zhu, Z.
Simulation of Mouldboard Plough Soil Cutting Based on Smooth Particle Hydrodynamics Method and FEM–SPH Coupling Method. *Agriculture* **2023**, *13*, 1847.
https://doi.org/10.3390/agriculture13091847

**AMA Style**

Jin X, Ma F, Wang D, Zhu Z.
Simulation of Mouldboard Plough Soil Cutting Based on Smooth Particle Hydrodynamics Method and FEM–SPH Coupling Method. *Agriculture*. 2023; 13(9):1847.
https://doi.org/10.3390/agriculture13091847

**Chicago/Turabian Style**

Jin, Xiaoming, Fangping Ma, Di Wang, and Zhengtao Zhu.
2023. "Simulation of Mouldboard Plough Soil Cutting Based on Smooth Particle Hydrodynamics Method and FEM–SPH Coupling Method" *Agriculture* 13, no. 9: 1847.
https://doi.org/10.3390/agriculture13091847