The study of vibration disturbance mapping in the geometry of the surface formed by turning

Abstract

Introduction. The development of virtual digital models of the machining process on metal-cutting machines is a dynamically developing direction of increasing the efficiency of machine-building production. Such models include subsystems of parts quality prediction. Accuracy and validity of its work directly depends on the built model of dynamic cutting system, which is perturbed by force noise, the sources of which have different physical origin. In addition, the autonomous dynamic system itself is a generator of various attracting sets of deformations, such as limit cycles or chaotic attractors. Taking into account various nonlinear transformations in the properties of the dynamics of the cutting process allows increasing the adequacy of the model to the real process and is an actual task in the construction of simulation modeling systems of the dynamics of surface machining by cutting. Study object. Our earlier studies allow us to determine the geometry corresponding to the deformation trajectories of the surface formed by cutting. However, the adequacy of the mapping of the calculated trajectories to the geometry estimates remains not quite clear. The proposed paper focuses on achieving an adequate mapping of calculated as well as measured strain trajectories into the geometric topology of the part. The aim of the work is to evaluate the mapping of vibration perturbations of the system into the geometry of the surface formed by cutting. Method and methodology. The research is of experimental-theoretical nature. The content of the research includes the study of the correspondence of frequency characteristics obtained on the model and in real machining. The main attention is paid to the mapping of deformations to the part geometry. For this purpose, the paper considers the coherence functions between the strain functions and the part profile. Results and Discussion. It is shown that the conditioning of these transformations has a limited frequency range in which the explanation of the variable components of the generated relief is statistically significant. Mathematical modeling of the dynamic cutting system based on the mechanics of interaction between tool and workpiece allows adequate prediction of the macro geometry of the part formed by cutting. The obtained mathematical tools can be used to create systems for predicting the geometry of the machined surface.