Authors: A.B. Efremenkov, E.I. Nikitin, D.A. Pashkov, Sh.S. Nozirzoda

Title of the article: Development of a mathematical model for the formation of a semi-convex helicoid shape of the knife of the executive body of the geokhod

Year: 2025, Issue: 2, Pages: 78-88

Branch of knowledge: 2.8.8. Geotechnology, Mining machines (engineering)

Index UDK: 622.271

DOI: 10.26730/1816-4528-2025-2-78-88

Abstract: The article discusses the process of developing a mathematical model for the formation of a semi-convex helicoid shape of the knife of the executive body of the geohod. The relevance of the development is given, which consists in the need to determine the trajectory of the tool in the manufacture of a semi-convex helicoid knife. To develop a mathematical model for the formation of a semi-convex helicoid shape of the knife of the executive body of the geohod, a scheme for the formation of a semi-convex shape of the knife executive body of the geohod is considered. It is noted that it is necessary to take into account geometric parameters such as the radius of the circle, the angle of inclination of the section and the thickness of the knife. A technique for constructing a three-dimensional model of a semi-convex shape of a knife used in the executive bodies of a geohod is considered. Mathematical modeling and 3D modeling methods were used to achieve the goal. Based on the specified parameters of the cross-section of a semi-convex knife, a system of equations has been developed that makes it possible, depending on the rational geometric characteristics of the cutting edge, to determine the trajectory of points on it. To solve this system of equations, a specialized program was created in the MATLAB environment. The results of the program are presented in the form of a graph showing the trajectory of the points of the cutting edges for a knife with a semi-convex helicoid shape. This development is of practical importance, namely, the possibility of using control programs for the manufacture and processing of complex surfaces of the semi-convex shape of the knife of the executive body of the geohod, which ensure high manufacturing accuracy and surface treatment quality. This, in turn, increases the efficiency of the geohod, and can also be used to optimize the design of cutting tools in other areas.

Key words: geokhod bladed executive body cutting edge coordinates geometric parameters

Receiving date: 15.01.2025

Approval date: 01.03.2025

Publication date: 05.06.2025

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