Dynamical analysis of free tool rotation on a glass rotating at a constant angular velocity

This work presents a dynamical analysis of a tool rotating freely due to the action of glass rotating at a constant angular velocity is presented. Preston [J. Soc. Glass Tech.XI, 214 (1927) JSGLAI0368-4105] analyzed tool movement neglecting the tool thickness, and only one torque component was obtained along the tool's normal direction. From this analysis, Preston concluded that angular velocities for tool and glass must be equal, even when this is not true experimentally. In this paper, a tool thickness different from zero was assumed. Then, two new torque components along the interface plane were found, which produced a non-homogenous pressure between the surfaces, and then an erratic tool angular velocity, meaning that the tool's known random rotation could be understood. If the tool's center is fixed on glass, a point with coordinates (x _G,0) and a torque along the X _G direction can be obtained. This new torque component predicts a non-synchronic and random rotation, while slowing down the tool angular velocity, which was confirmed experimentally.