Model of the ripper tooth deepening based on the example of the motion of a straight stamp



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Abstract

BACKGROUND: The purpose of industrial loosening is to destroy a single ground layer and it is used on hard (frozen or rocky) grounds. The fundamental difference between industrial loosening and agricultural loosening is the presence of forced deepening. The process of deepening the ripper into the ground is very important, and largely determines the efficiency of operation of the entire unit. During the process of forced deepening, the ripper performs a combined motion in the horizontal and vertical directions. Currently, there is a lot of experimental data on the process of deepening the working tool, but there is no adequate mathematical model.

AIM: Development of a mathematical model for deepening a ripper into the ground using the example of the motion of a straight stamp.

METHODS: At the initial stage of deepening the stamp into the ground, a linear dependence between vertical deformation and force is assumed. The inverse problem of dynamics was solved in the paper. The equation for the motion path of a working tool in the ground was found based on the known vertical force and horizontal motion of the tractor.

RESULTS: A mathematical model of the motion of a straight stamp under the vertical force during horizontal motion of the tractor has been developed. The two models describe the process of deepening a stamp in the ground. For the horizontal motion within the width of the stamp, the motion is described by a linear equation with separable variables. In case of the horizontal motion greater than the width of the stamp, the motion is described by a differential equation with a retarded argument.

CONCLUSION: Dimensionless variables made it possible to reduce the equation of the working tool path to a single form, regardless of the size of the stamp and the type of ground. The developed mathematical model can be used as a basis for describing the process of deepening any working tool into the ground.

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About the authors

Irina P. Troyanovskaya

South Ural State Agrarian University

Author for correspondence.
Email: tripav63@mail.ru
ORCID iD: 0000-0003-2763-0515
SPIN-code: 8733-7935

Honorary Mechanical Engineer of the Russian Federation, Dr. Sci. (Engineering), Professor

Russian Federation, Troitsk

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Supplementary files

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2. Fig. 1. Diagram of vertical deepening of a straight stamp into the ground.

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3. Fig. 2. Diagram of horizontal motion of a straight stamp in the ground under the vertical force (within the width of the stamp).

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4. Fig. 3. Diagram of horizontal motion of a straight stamp in the ground under the vertical force (beyond the width of the stamp).

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5. Fig. 4. The motion path y(x) of the stamp for different а: widths b and b: initial depths у0.

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6. Fig. 5. Motion path of the stamp y(x) for various soils and stamp sizes.

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