Full-factor matrix model of accuracy of dimensions performed on CNC multipurpose machines

OBRABOTKAMETALLOV Том 23 № 4 2021 TECHNOLOGY transformations of multi-product parts in one automatic turning operation before heat treatment, even in most cases it performs all machining, from the workpiece to the fi nished part. The range of lathes working with multi-tool adjustments is quite wide. However, the analysis of the level of use of the capabilities of multi-tool machining on multi-purpose CNC machines, carried out in factories, showed that adjustments with parallel multi-tool machining are little used. [5, 7, 10–12]. For this reason, an increase in the ef fi ciency of using the technological capabilities of multi-tool machining on modern CNC machines is one of the problems in machine building that pushes for the solution. The main prerequisite for solving the problem is the theory of multi-tool machining design, taking into account the capabilities of modern CNC machines. The theory of designing multi-tool machining on modern CNC machines is based on the balance of the mutual in fl uence of the forces of the adjustment tools, taking into account the possibilities of tools movement along curved paths, as well as the arbitrary spatial arrangement of tools in the metalworking machine. For this reason, fi rst of all, it is important to have models of machining errors that take into account the simultaneous in fl uence of all components of the cutting forces of all setting tools in multi-tool adjustments with the spatial arrangement of tools and elastic displacements in all coordinate directions of the technological system. With this in mind, the matrix theory of multi-tool machining accuracy was created [6]. However, the generated machining error models take into account only the plane-parallel displacements of the subsystems of the technological system along the coordinate axes of the Cartesian coordinate system XYZ [5, 6, 12]. This approach to simulating the process of occurrence of machining errors for parts with overall dimensions of the same order in all coordinate directions is permissible. In practice, there are often cases of machining parts with overall dimensions that differ sharply in different directions. For example, long shafts (linear dimensions predominate), discs and fl anges (diametric dimensions predominate). In these cases, the machining error is largely in fl uenced by the rotations of the workpiece being machined, especially in directions with sharply differing overall dimensions, and for this it becomes necessary to create full-factor models of machining accuracy that also take into account angular displacements. Studies of other works [1–4, 13–26] show that in this area works are of a private nature and cover only some parameters. In these works, there are often experimental studies of multi-tool machining. But there is no information in any source about the mathematical simulation of the problem and, at the same time, the speci fi cation of multi-tool processing. The most important thing is that these models do not agree with the general laws of mechanics of elastically deformable systems, therefore it cannot be used to create a uni fi ed theory of machining accuracy that takes into account possible angular displacements of subsystems of a technological system. In the industry, computer-aided design systems are used to design operations on modern multi-purpose CNC machines, but even here there are no possibilities to increase the machining accuracy and productivity of multi-tool machining by the method of numerical determination of feeds based on simulating the elastic displacements of the technological system, taking into account the limitations on dimensional accuracy and mutual in fl uence of simultaneously working tools. Also, onmodernmulti-purposeCNCmachines, solving the problemof imposing technological transitions for double-carriage lathes in the available automated programming systems for operations is carried out in manual mode by trial and error. And this once again con fi rms the absence of a scienti fi cally grounded methodology for the design of multi-tool multi-carriage machining on multi-purpose CNC machines and shows the need for its development. Research methodology The accuracy of the dimensions is the fi rst requirement in the design, adjustment and implementation of the technological process. And therefore, the fi rst task of parametrizing the designed technological process is the calculation of depths of cut and operating dimensions that make up a single section “Dimensional analysis of the technological process”. The second task of the parametrization stage is to calculate cutting conditions [8]. The dimensions carried out in multi-tool adjustments and intermediate depths of cut are