Investigation of polishing algorithms and removal processes for deterministic subaperture polisher

This thesis provided a basis for deterministic optical polishing of aspheres and ogives with compliant tools. A new deterministic subaperture computer numerically controlled (CNC) polisher called UltraForm Finishing (UFF) is developed by OptiPro Systems (Ontario, NY). The UltraForm Finishing process was designed to remove midspatial frequency surface errors generated by grinding tools, preserve or correct the form of parts and polish the concave surface of tangent ogives made of tough optical materials. The three main goals of this thesis are (1) to develop polishing algorithms that specify collision free tool paths to correct part form, (2) to investigate a local removal model and (3) to investigate sources of any induced surface errors.The form of the part after polishing can be predicted by expressing the removal profile as a convolution integral of the tool removal function and crossfeed velocity. For form correction, the inverse problem is solved to obtain a tool crossfeed velocity profile that can achieve a desired removal profile. Explicit expressions for form correction problem were defined for piano and spherical parts. An approximate formulation was introduced for aspheres and ogives. The form correction problem was solved as a constrained optimization problem using regularization to achieve feasible solutions and overcome ill-conditioning.Algorithms establishing a collision free tool path have been developed. For that purpose, a two-dimensional model was introduced to detect tool-part collisions. Search strategies were defined to adjust the tool position and prevent such collisions.Some properties of the UFF removal function have been characterized. It was shown that a generalized form of Preston's equation combined with Hertz contact mechanics theory predicts fairly accurately the removal function for hard tools and convex surfaces over a range of process parameters.Errors that can produce discrepancies between actual and predicted removal profiles were modeled. Their effects were examined with numerical simulations and shown to depend strongly on the removal function. A diagnostic method was developed to determine the origin of spiral marks induced by UFF. These spirals are formed of discrete marks left on the part by the tool at a constant frequency. The method establishes all the possible frequencies that can create a given pattern and identifies the relevant one. The method was successfully used to identify the frequency that generated spiral marks in a series of experiments and lead to the discovery of a tool defect.