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

OBRABOTKAMETALLOV Vol. 23 No. 4 2021 TECHNOLOGY directly related to the parameters of the cutting conditions. For this reason, these two tasks of parametrization of the technological process should be solved simultaneously [5, 6]. The basis of the matrix theory of multi-tool machining is formed by mathematical models of the accuracy of the dimensions performed by tools in multi-tool adjustments. Therefore, the modern level of mathematical models for the formation of dimensional errors in multi-tool adjustments is of particular interest. As established in the science of machine building technology, the machining accuracy is determined by a whole complex of a number of random and regular factors, its mutual in fl uence and mutual connection: elastic displacements of the technological system, dimensional wear of the cutting tool, geometric inaccuracy of the links of the technological system, temperature deformations, errors in the location of workpieces on the machine and errors in adjusting it to the size to be performed, scattering of depths of cut of workpieces and its physical and mechanical properties, etc. To a large extent, the machining accuracy is also in fl uenced by the cutting conditions [8, 9]. The quantitative property of machining accuracy is the machining error. This machining error highlights the degree of inconsistency between the shapes and sizes of a real part and a given ideal scheme in the design. All elementary components of the error can be conditionally divided into two groups [8]: 1. The elementary components of the error independent of the cutting conditions or weakly dependent on it (small): the error of the dimensional wear of the cutting tool ( ∆ w), the geometric inaccuracy of the links of the technological system ( ∑∆ f), the error of temperature deformations ( ∑∆ T), the error of placement the workpieces on the machine ( ε ), the error in adjusting the workpiece to the dimension being performed ( ∆ a); 2. An elementary component of the error, completely determined by the cutting conditions: the error of elastic displacements of the technological system ( ∆ y). Errors of the fi rst group are of no interest during the development of simulation models de fi ned for the design of a technological process. These components participate as constants in simulation models. Its meanings are taken from an extensive reference literature. During the simulation of machining accuracy as a result of elastic displacements of the technological system from the in fl uence of cutting forces, a special place is occupied by the elementary error ∆ , which arises in the technological system. Its value is determined by cutting conditions, features of the technological system. For this reason, the elementary error ∆ acts here as the main controlled object and its mathematical expression is required. Due to the distortion of the performed size, in practice, another characteristic of machining accuracy is more in demand – the value of the scattering fi eld of the performed size. Due to the mutual action of the force for multi-tool adjustments, two boundary cases have been established [5, 6]: opposite and non- opposite. In an opposite setup, all components of the cutting force of one carriage are directed against the corresponding components of the other carriage. Such adjustments are common for cam-operated turret lathes and multi-spindle automatic lathes. And in non-opposite adjustments, all the corresponding components of the cutting force of both carriages are directed in the same direction. On the modern group of CNC lathes, both adjustments are used equally. Based on the foregoing, it can be noted that, in order to develop the theory of numerical design of multi- tool adjustments, complex models of distortion of the performed dimensions and its scattering fi elds are required, and these models should consider the structure of multi-tool adjustments – various types of cutters of the longitudinal or transverse carriage, the simultaneous operation of the longitudinal and transverse carriage. The mechanism of the formation of the scattering fi eld in double-carriage opposite adjustments is extremely complicated in comparison with one carriage machining [6]. The scattering of the strength properties of the workpiece material and the rigidity of the technological system determines the scale of the scattering interval of the size distortion 1 w и 2 w . But the effect of changing the depth of cut on the carriages is ambiguous. Due to the fact that the cutting forces on the longitudinal and transverse slide are directed