OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 4 4 method largely determines the possible types of tools and its placement in the setup. Therefore, it is logical to put this indicator at the fi rst level of classifi cation of multi-tool setups [31, 32]. Next, it is necessary to describe the types of cutting tools in the setup and its placement relative to the workpiece and each other, i.e. describe the setup structure itself. The basis of the structure of multi-tool setup is a set of carriages on which the tools are placed. Therefore, at the second level of classifi cation, there should be a description of the carriages involved in the setup. The third level is a description of the actual cutting tools that form the setup. The introduced three factors describe the type of cutting tools and its location. However, the force eff ect of the tools on the workpiece is determined by the cutting forces, the values of which and the direction of action are determined by another factor – the feed direction. The feed movement refers to the carriage, so it is advisable to attribute this factor, as an additional one, to the description of the carriage. In multi-tool setups, it is not uncommon for a cutting tool to be rotated relative to the base surfaces of the carriage with the help of special holders. Therefore, an indicator of the orientation of the tool relative to the base of the carriage, or workpiece is introduced. The classifi cation of multi-tool setups on traditional automatic lathes covers setups where the tools are working simultaneously. However, modern CNC machines equipped with a tool magazine allow organizing multi-tool machining with sequential use of tools. Having a single technological base and working from a common control program, these setups are subject to the laws of multi-tool machining, in the traditional sense of the term. Moreover, the machining accuracy models make it possible to take into account technological heredity and reach the design of multi-transition machining. Therefore, it is proposed to expand the concept of multi-tool setup, including setup both with simultaneous operation of tools and with sequential operation. Thus, we get 6 levels of classifi cation of multi-tool adjustments (method of mounting the workpiece, set of carriages, type of cutting tools, types and directions of feed of the carriages, orientation of the cutting tools relative to the workpiece, method of including tools in the work (parallel, sequential)). Summarizing the principles of classifi cation of multi-tool setups taking into account the conditions of modern CNC lathes, it is possible to develop a corresponding classifi cation formula: ( ) ( ) ( ) , y ij c c ij s s ijk u u i j k H Yk C k e S k e u k e ⎧ ⎫ ⎡ ⎤ ⎡ ⎤ ⎪ ⎪ ≡ ⎢ ⎥ ⎢ ⎥ ⎨ ⎬ ⎢ ⎥ ⎢ ⎥ ⎪ ⎪ ⎣ ⎦ ⎣ ⎦ ⎩ ⎭ (1) where Y is the installation method sign; ky is the installation method code; Cij is the carriage sign; kc is the carriage type code; ec is the carriage location; Sij is the carriage feed sign; ks is the carriage feed type code; es is the carriage feed direction; uijk is the cutting tool sign; ku is the cutting tool code; eu is the cutting tool orientation; k is the number of cutting tool on this carriage; j is the carriage number at this working position; i is the working position number; ∩k is the sign of parallel (simultaneous) operation of the tools described in square brackets after this sign; ∩j is the sign of parallel (simultaneous) operation of carriages described in square brackets after this sign; Ui is the sign of consistent development of all working positions. For traditional multi-spindle lathes, the concept of a working position coincides with the generally accepted one. With regard to modern multi-tool CNC machines, it is advisable to expand the concept of a working position. Double-carriage CNC machines equipped with a tool magazine allow to organize a series of successive elementary setups with the simultaneous operation of several tools. Thus, on a modern CNC machine, a sequential execution of a set of multi-tool setups, understood in the traditional sense, can be organized. Since the apparatus of the computational theory of accuracy of multi-tool machining [31, 32] makes it possible to analyze such a sequence of multi-tool setups, it makes sense to introduce into consideration a generalized multi-tool setup, which includes a time-distributed sequence of traditional multi-tool setups with simultaneous operation of several tools. Each stage of the work of such a generalized setup, related to a separate set of simultaneously working tools, is proposed to be called the position of a generalized multi-tool setup. Such a sequential inclusion of traditional multi-tool setups is refl ected in the classifi cation formula (1) by the operator Ui with index i.
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