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This paper investigated the effect of three independent variables including: tillage speed (ranges of below 2.5 m/s and between 2.5 m/s and 5 m/s), tillage depth (range of 10 cm from 0 cm to 30 cm) and frog angle (30° 40°, and 50°) on draught forces. The experimental work was completed with determination of the draught forces using an analytical method (Saunders Equation). Numerical Simulation: Discrete Element Method (DEM) was used to verify the results obtained analytically. The results indicated that tillage depth has a stronger influence on the draught forces as compared to the tillage speed. Minimal draught forces can then be achieved through operating at shallow tillage depth and maintaining a frog angle of 30°. The results showed a variance of ±15.95% to the calculated values supporting DEM as a numerical method capable of predicting draft forces correctly, tillage power optimization and determination of optimal frog angle for the mouldboard plough.

Tillage is a necessary action on soil to prepare favorable conditions for plant growth however, it is costly and time consuming [

Soil-cut interactions have been studied experimentally and analytically [

[

In contrast to the analytical formulas, use of DEM allows for the prediction of draught forces for complex tool geometrics hence optimizing performance for the mouldboard ploughs.

EDEM^{TM} is a modeling platform in-built in DEM. It is based on the Hertz Mindlin contact force model and in particular the parallel particle bond model as shown in

The contact forces, normal force (_{n} and K_{t}), normal and tangential relative displacements. While the damping forces are determined as functions of the damping coefficient and the relative velocity as per [

^{TM}, the units and values of the different parameters. These parameters are found in the main window and are kept constant for all the iterations of simulation performed [

The soil particles were remodeled in EDEM using optimal imaging techniques as shown in the below images.

A virtual soil bin was created using the EDEM as shown in

EDEM^{TM} was calibrated using the angle of repose. Values of surface energy, coefficient of restitution, coefficient of static friction and coefficient of rolling were adjusted iteratively until the value of the angle of repose in simulation was close to the experimental value.

Property | Units | Value |
---|---|---|

Gravity | m/s^{2} | −9.81 |

Poisson’s Ratio of Steel | No units | 0.3 |

Shear Modulus of Steel | Pascal | 7 × 10^{10} |

Density of Steel | Kg/m^{3} | 7850 |

Poisson’s Ratio of Soil | No units | 0.25 |

Shear Modulus of Soil | Pascal | 1 × 10^{10} |

Density of Soil | Kg/m^{3} | 1818 |

Verifications of the simulated results was carried out through experimental work and calculating the total draught force as per the Saunders Equation as explained below.

Saunders Equation[

Equation (3) is quadratic equation that shows the relation between draft, speed, plough design characteristics and the soil conditions according to [

where:

H_{t} is the total draught force in KN.

H_{p} is the draught force due to plough point.

H_{s} is the draught force due to plough share.

H_{mc} is the draught force due to mouldboard soil momentum change and draught force friction along the mouldboard.

H_{e} is the draught force due to the increase in soil potential energy and the mouldboard

H_{cs} and H_{ms} are the draught force arising from friction forces due to lateral forces at the share and at the mouldboard.

H_{fs} is the draught force arising from lateral forces at the mouldboard because of the lateral soil movements.

The above model aims at predicting the total plough draught forces in a semi rigorous manner. The constituents of Equation (3) were further broken down as shown in Equations (4)-(9).

EDEM simulation was performed by conducting iterations for each variable of frog angle, cutting depth and speed on the same type of soil. A VBA was developed and used to perform the rigorous mathematical Saunders equation. All the results were transferred to excel sheets for smoothening.

Sandy Clay soil was used and the soil parameters as determined by the shear test are outlined in

The soil type was not varied. However, the speed, depth and frog angle varied as shown in

The EDEM simulated total draught force results compared ± 15.95% to those determined through Saunders Equation.

The draught force increased as the speed increased. The relationship between draught force and speed was seen as 2^{nd} degree polynomial quadratic equation.

Bulk unit weight (KN/m^{3}) | 18 |
---|---|

Cohesion (KN/m^{2}) | 78 |

Shearing resistance angle | 38˚ |

Soil metal friction angle | 20˚ |

Soil soil friction angle | 0.7813^{*} |

^{*}Soil soil friction angle was determined as Tan of the shearing resistance angle.

Plough angle | 25˚ |
---|---|

Share rake angle | 20˚ |

Mouldboard angle to the direction of motion | 155˚ |

Share edge angle to the direction of motion | 26˚ |

Width of the plough (m) | 0.26 |

Mouldboard length (m) | 0.72 |

Depth of tillage (m) | 0.1 - 0.3^{*} |
---|---|

Speed of tillage (m/s) | 1.0 - 4.0^{**} |

Frog Angle | 30˚ - 50˚^{***} |

^{*}The depth of tillage was varied from 0.1 to 0.3 m with intervals of 0.1 m per range. ^{**}The speed of tillage was broadly divided into low speeds (≤2.5 m/s) and high speeds (2.5 m/s > 5 m/s). ^{***}The frog angles used were 30˚, 40˚ and 50˚.

As the speed increased across the frog angles used, the draught force increased. The optimum speed of operation according to the results was 1.6 m/s which was agreeable with the various literature materials [

As the depth increased the draught force also increased linearly.

The two methods used to determine the draught force showed a linear relationship between the draught force and the depth. The depth of tillage is a determinant of the crop being planted.

A mathematical model (Saunders Equation) of a mouldboard was used to describe the draught force with emphasis on the different forces acting on the mouldboard parts contributing to the total draught force. DEM model was used to simulate the tillage process in a controlled environment. The simulations were iterated to achieve

the optimal operating parameters of the plough. The draught forces determined by the Saunders Equation were verified through DEM simulation showing a variance of ±0.15.

Statistical analyses of the draught forces determined by the two methods showed there was minimal significant difference between the measured and simulated data. It was observed that the mouldboard required more draught force at higher speeds and cutting depth. At higher speeds the Saunders Equation was not able to describe draught force as reliably.

The results determined that DEM is an effective tool of determining draught force as it is fast and reliable. 30˚ frog angle was the optimum angle at a speed of 1.6 m/s. DEM predicted draught forces at this angle was in good agreement with the measured values with an error range of 7.6% to 14.5% for a speed range of 1.5 m/s to 1.8 m/s.

The authors respectfully acknowledge the support from the University of Nairobi support staff for the field work assistance. Sincere gratitude to the professional assistance I received from the Department of Environmental and Biosystems Engineering.

AngelaHiuhu,Ayub NjorogeGitau,Duncan OnyangoMbuge,John NdisyaMulwa, (2015) Optimization of the Angle of Frog in Mouldboard Tillage Operations in Sandy Clay Soil. Open Journal of Optimization,04,131-140. doi: 10.4236/ojop.2015.44013