Geometrical Consideration of the Process of Milling a Metal Workpiece

Abstract

Within the framework of the theory of the structure-energy-time fields (the theory of SET-fields) of the properties of physical objects in describing the cutting of metallic materials, it is proposed to use the spatial physical geometric interpretation of the subject of the study, considered using the example of the analysis of the process of cylindrical milling. In one of the variants of the technological process, using the milling parameters t, υ, QUOTE tэ (t is the depth of cutting, m; υ is the speed of the main cutting motion, м× QUOTE мин- 1 ; QUOTE tэ is the test time for one transfer of the workpiece, min), it is possible to represent the cutting operation for one movement of the workpiece in spatial Cartesian rectangular coordinates in the form of a structure-energy-time field П1 (SET-field), the geometrical image of which is displayed as a rectangular parallelepiped. The volume of the parallelepiped is put in correspondence with the physical quantity П1, which is a generalized characteristic of the object of investigation (the process of milling). The equation of the SET-field of the chip cutting process for one displacement of the workpiece relative to the rotating cutter in the octant t-υ-tэ QUOTE is QUOTE П1 = C · Э · B = t · х · tэ.where П, С, Э, В are Russian capital letters.The unit of measurement of value П1 is:[ П1 ] = [С·Э·В] = [t]·[υ]·[ tэ ] = 1 м Д3 × 1 м · мин- 1 Д3 × 1 мин Д3 = 1 м2 (мин/мин) Д9, where (min/min) is the sheath O of a unit of magnitude; Д9 (Д is the Russian capital letter) is the operator of motion. The concepts of the sheath O and the motion operator Д are introduced in the theory of SET-fields for a deeper analysis of the subject of research. Expression 1 m2 QUOTE (min/min) Д9 QUOTE is an example of the designation of the unit of measurement of the SET-field П1, as one of the variants of the technology of the milling process. Here, the shell (min/min) shows that П1 is a function of time. The described technique makes it possible to express each concrete variant of the milling mode with a single numerical index. The scheme of the physical geometric interpretation of the subject of research for this task allows us to designate each milling mode with a certain physical value, because different parameters can be plotted along the axes of the coordinate angle. It increases the geometric visibility of the results obtained by analytical means, contributing to a deeper theoretical understanding of the technological process, as well as the conscious formation of knowledge and the compactness of their representations.