Determination of the regularities of formation of the profile error at the grinding of products-shells from brittle non-metallic materials

There are certain requirements to the quality of profile-composite thin-walled shells used in aerospace engineering. All the necessary characteristics of the items (such as thickness, profile accuracy and surface quality) can be provided using the method of diamond grinding. Modern equipment makes possible the introduction of high-performance cutting patterns. Besides it gives a possibility of using adaptive control in technological processes. Therefore, the researches, related to establishing an analytical connection between the phenomena arising during tooling of such wares and errors of their form and geometry, are relevant. Most researches are related to reduction of imperfectness of superficial layer of brittle non-metal materials caused by tooling. Several studies are devoted to the problem of increasing the efficiency of treatment of shells due to the decline of vibrations in the technological system of shaping of wares. But complex researches that allow estimating the total error of the diamond grinding of the thin-walled shells depending on treatment conditions are absent. This requires the creation of a mathematical model of the mechanism of formation of pyroceram shells profile error in the process of diamond grinding that takes into account conditions of their treatment and is required for the development of progressive technological processes. The paper provides a generalized mathematical model of formation of total error of the profile of a thinwalled pyroceram shell considering factors influencing the level of vibrations of elements of the grinding technological system and the accuracy of treatment. Mathematical description of formation of the error of thin-wall shell inner con-tour during diamond-abrasive tooling is presented. The model considers the unevenness of the allowance, which occurs at the stage of obtaining the workpiece, as well as the variable stiffness of the workpiece and the machine tool. The model allows to analyze the factors that determine the accuracy of grinding parts and identify ways to reduce their impact on the accuracy of the formed product.