Analysis and mathematical model of the circumferential accuracy of the groove cut on the surface of rotation

Abstract

An analysis is made of the technology of vortex cutting method of groove for sealing rings provided on the lateral surfaces of rotation of a part of the sealing system and the dimensional chains thus formed, as well as accuracy issues by applying probability theories and dimensional chains. Features of the developed technology are presented; the factors influencing the accuracy of the circular diameter of the groove are analyzed, and mathematical dependencies are given for their determination; the mathematical model of the accuracy of the diameter of the groove is derived. The technological dimension chain, which is formed in the vortex cutting method of groove, is given its properties, and the new linear-circular dimensional chain, which is not found in the literature, and its mechanism of formation are presented. The features of the linear-circular dimensional chain and the management of the functional relation between the linear and circular feeds are used to determine the technological capabilities of the vortex method on the lateral surface of the groove. Also, families of possible singleand double-symmetrical forms of the grooves are identified. It is recommended to use the results obtained, when analyzing the technology of cutting of grooving and other similar surfaces with a vortex method, when solving accuracy problems, including the derivation of a mathematical model of accuracy.

Improving the efficiency of grinding teeth by copying with the control of dynamic technological connections

“…Studied and systematized the dynamic connections between the elements of technological systems, taking into account all the indicators of accuracy, surface roughness and quality of the surface layer, which determine the quality of manufacturing parts for various machining methods [5,[15][16][17][18].…”