On the Matrix Generalization of the Theory of Machining Accuracy

Abstract

The article provides a matrix generalization of distortion models and scattering fields of dimensions performed during turning with a spatial arrangement of the tool, taking into account the simultaneous action of all components of the cutting forces of the setting tool and elastic deformations of the technological system in all coordinate directions. A full-factor model of dimension distortion for single-carriage adjustment has been developed, which allows taking into account not only planeparallel movements of technological subsystems, but also their angular movements around base points. Thus, the Eq. developed for the total displacement vectors 𝑢𝑖 is proposed to be taken as the basis for a full-factor model of the machining error. The presented analytical models describe only plane-parallel displacements of contacting bodies. It is shown that in order to take into account the whole complex of displacements in them, i.e. and angular displacements, it is sufficient to replace the plane-parallel displacement vectors of each contacting body 𝑟𝑖.