2 May 2007 Contact mechanics models and algorithms for dome polishing with UltraForm Finishing (UFF)
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Abstract
UltraForm Finishing (UFF) is a new deterministic subaperture computer numerically controlled (CNC) polisher. Because UFF uses compliant tools with large contact patches, the depth of removal is prescribed by adjusting the tool crossfeed velocity. The equations for the depth of removal as the tool traverses an axisymmetric part are derived. The form correction problem consists in solving these equations by adjusting the tool crossfeed velocity to achieve a desired removal profile. The solution must satisfy constraints on the tool velocity and acceleration. Solutions for flats, spheres and aspheres are achieved by treating the problem as a constrained optimization after writing the depth of removal equations in matrix form. The solutions were validated experimentally. The removal function is evaluated by making a removal spot for one set of process parameters. Its variations, as a function of the process parameters, are predicted by using Hertz contact theory and the Preston equation. To prevent tool-part collisions and to analyze part and spot measurements, algorithms were developed for the tool path and evaluation of metrology inputs.
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Christophe Bouvier, Christophe Bouvier, Sheryl M. Gracewski, Sheryl M. Gracewski, Stephen J. Burns, Stephen J. Burns, } "Contact mechanics models and algorithms for dome polishing with UltraForm Finishing (UFF)", Proc. SPIE 6545, Window and Dome Technologies and Materials X, 65450R (2 May 2007); doi: 10.1117/12.719041; https://doi.org/10.1117/12.719041
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