The aim of the work is to develop the spectral theory of systems with variable parameters in relation to the analysis of the quality of machining. The development of spectral theory is necessary to overcome difficulties in designing a class of non-stationary systems. This solves the problem of identifying patterns of dispersion of quality indicators during machining; On the basis of harmonic analysis, factors that influence the output quality of products are classified; A mathematical model of machining is being considered, considered as a polyharmonic process.
Technological systems of machining relate to non-stationary systems with power and thermal effects. In addition, the division of machining errors into deterministic and random has many uncertainties. For example, tool wear traditionally refers to deterministic processes, and from a mathematical point of view, this process is described by Markov chains (an apparatus used to describe random processes). In many cases, it is difficult to decide whether the phenomenon in question is deterministic or random.
As a result of the work, it was found that all the perturbations that affect the process of processing materials by cutting ultimately lead to relative displacements of the tool and the workpiece, which can be represented by a superposition of the constant component of the displacement and individual harmonics of vibration displacements.