OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 4 2024 cutting parameters on multi-position machines and automated lines equipped with multi-spindle heads. In the work [14], turning was performed on a lathe with two cutting tools mounted on the carriage, one in the front and the other in the back. A number of studies [21–34] have addressed specifi c issues related to the problems of designing multi-tool machining or optimizing the process technology. In the work [30], the opportunity of applying various modeling and optimization methods in metal machining processes, classifi ed by several criteria, was critically evaluated. However, none of these studies have examined the need to organize multiple multi-tool setups, or introduced a system for its analysis. In other words, it has not addressed the classifi cation of multi-tool setups and the creation of a unifi ed algorithmic model for machining errors for the entire set of spatial multi-tool setups, taking into account the compliance of the technological system in all coordinate directions. The machining error component that arises due to the elastic displacements of the elements of the technological system under the infl uence of cutting forces, often referred to as the deformation component, is the most controllable during machining and at the design stage. By varying cutting conditions, cutting tool geometry, initial error (at an intermediate stage of machining), and changing the material of the cutting part, it is possible to signifi cantly infl uence the magnitude of machining error [4, 9, 13, 15, 16, 25, 26, 33]. Therefore, the mathematical model of the deformation component of machining error forms the basis of the computational matrix theory of machining accuracy [13, 14, 15, 25, 26, 33, 35, 37]. Attempts to systematize multi-tool setups can be found in the works of A. A. Koshin [35–36]. He introduced four main and one additional classifi cation levels for setups. The main classifi cation criteria are the type of carriage, the type of cutting tool, its orientation (whether it presses the workpiece toward or away from the carriage), and the method of workpiece mounting. The additional criterion is the type of auxiliary device mounted on the main carriage. However, there is no way to describe a number of features specifi c to multi-tool machining on modern CNC (Computer Numerical Control) machines. The formalized systematization of multi-tool setups forms the basis of the methodological support for the Computer-Aided Design (CAD) system of turning-automatic operations [37]. Modern automatic machines, designed for multi-tool machining and equipped with CNC systems, off er signifi cantly richer technological capabilities for organizing multi-tool operations. Therefore, a new, more multifactorial systematization of multi-tool setups, refl ecting these new capabilities, is required. The purpose of the work is to develop a classifi cation of multi-tool setups on multi-carriage and multispindle CNC lathes, enabling the creation of both amatrixmodel ofmachining accuracy for each classifi cation class and a unifi ed generalized matrix model of machining accuracy for the entire classifi cation class. To achieve the set purpose the following tasks are solved: 1. The principles of classifi cation of multi-tool setups are revealed; 2. The main classes of the proposed systematics of multi-tool setups are defi ned. Research methodology Principles for classifying multi-tool setups The basis of systematics is a set of classifi cation indicators. Taking as a basis the principles of the systematics of multi-tool setups on traditional automatic lathes [37], we will consider the transformation of indicators to the capabilities of modern lathes of the turning group, focused on multi-tool machining. The key issue of systematics is to identify the parameters by which the classifi cation is carried out, and the hierarchy of these parameters, which determines the levels and order of systematics. The proposed systematics of multi-tool setups is focused on the development of models of machining accuracy. The main feature of multi-tool machining is the force interaction between the tools in the setups [31, 32]. Therefore, the classifi cation is aimed at identifying the characteristics of force loading and deformation of the technological system during multi-tool machining. The basis of the scheme of deformation of the technological systemunder force loading duringmachining is the method of fi xing the workpiece. It is a common, single indicator for multi-tool setups. The mounting
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