Development of a mathematical model of the spatial motionof the tool of the generalized schemeof a drillingexecutive unitofcomplete destruction

Abstract

Purpose. The purpose of the work is to develop a mathematical model of the kinematics of the spatial motion of a single cutting tool of the generalized scheme of the executive unit of complete destruction. Methodology. The basis for the development of the basic generalized scheme of the kinematics of the cutting tool movement is the analytical synthesis of all existing constructive schemes of the drilling executive unit, the work of which is based on the transmission of one or more rotational movements to the tool simultaneously with the forward movement. Individual cases of structural schemes have been discovered by analyzing the possible positions of the working disk, as well as the number of movements transmitted to the cutting tool during its operation. Results. As a result of a comprehensive analysis of the kinematics of the spatial motion of a single cutting tool, the feasibility of creating a generalized scheme of its movement for a drilling executive unit of complete destruction has been substantiated. This scheme is valid for all constructive implementations of planetary and rotary executive units of mining machines. Made on its basis the analytical dependencies between constructive and kinematic parameters represent a mathematical model of a spatial motion of a cutting tool of a general scheme of a drilling executive unit of complete destruction. Received as special cases, some analytical dependencies describe the movement of the cutting tool in constructive schemes as already implemented in the existing mining machines, and also as theoretically possible. Scientific novelty. The developed mathematical model of the kinematics of the spatial motion of a cutting tool accurately describes its trajectory with any values of constructive and kinematic parameters of a drilling executive unit of complete destruction. The analysis of factors that affect the nature of the movement of the working tool allows identifying a set of generalizing parameters of the executive unit and setting the limits of their values, which define individual constructive schemes. The proposed scheme and the mathematical model of a tool motion allow carrying out theoretical studies, criterial analysis and optimization of the parameters of the executive unit in a general case. Practical significance. The model of a spatial motion of a working tool is the basis for deep and detailed applied studies of the process of its interaction with a massif that is being destroyed, on the basis of generally accepted criteria of efficiency. The results of such research allow establishing rational constructive schemes of the executive unit for the specified operating conditions and creating a scientifically grounded method of assignment of their constructive and kinematic parameters. The research of trajectory of movement and geometry of cutting allow selecting, installing and setting the tools on the working disks of the executive unit more rationally.