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During the last decades in the theory of machining nonmetallic materials some serious advances have been achieved in the field of applying fundamental scientific approaches to the grinding and polishing technologies for
high-quality precision surfaces of electronic components, optical systems, and decorative articles made of natural and synthetic stone [1–9]. These achievements include a cluster model of material removal in polishing dielectric workpieces [1–3, 6–7] and a physical-statistical model of formation of debris (wear) particles and removal thereof
from a workpiece surface [8–10]. The aforesaid models made it possible to calculate, without recourse to
Preston’s linear law, the removal rate in polishing nonmetallic materials and the wear intensity for bound-abrasive
tools. Equally important for the investigation of the workpiece surface generation mechanism and formation of
debris particles are the kinetic functions of surface roughness and reflectance of glass and quartz workpiece
surfaces, which have been established directly in the course of polishing. During the in situ inspection of a
workpiece surface by laser ellipsometry [11] and reflectometry [12] it was found out that the periodic change of
the light reflection coefficient of a workpiece surface being polished is attributed to the formation of fragments of
a deposit consisting of work material particles (debris particles) and tool wear particles [13, 14]. The subsequent studies of the mechanism of interaction between the debris particles and wear particles in the tool–workpiece
contact zone, which were carried out based on classical concepts [15, 16], yielded some unexpected results. It was demonstrated that electrically charged debris and wear particles, which are located in the coolant-filled gap
between a tool and a workpiece, move by closed circular trajectories enclosed in spheres measuring less than one fifth of the gap thickness. This implies that the probability of the debris and wear particles reaching the tool and
workpiece surfaces and, especially, getting localized on the surfaces is extremely low, which contradicts the results of experimental examination of these surfaces. Based on the quantum-mechanical description of the process of scattering of the debris and wear particles that are as small as 3–4 nm in the tool–workpiece contact
zone, the mechanism of formation of a workpiece microrelief and the mechanism of formation of a debris-particle deposit on the tool surface were clarified [17–21]. However, the mechanism of formation of the deposit fragments and their discrete arrangement on the workpiece surface in the process of polishing with a bound-abrasive tool has
not been studied yet.
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