Modelling of time-variant material removal functions for abrasive subaperture polishing

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The objective of this project is the development of time-variant material removal functions for abrasive subaperture polishing for the machining of optics and precision parts. This will enable a targeted shape correction with minimal material removal and increase the achievable production accuracy and process reliability. Previous approaches focus on time-consistent material removal functions based on the Preston equation. Although this dwell time controlled removal functions allow a process time saving of up to 35%, they have the disadvantage of an inevitable basic removal, meaning that material has to be removed in any case. In order to remove no material, the polishing tool would theoretically have to be moved infinitely fast over the workpiece. A time-variant removal function allows minimizing or even avoiding this basic removal, which in turn leads to a reduction of process time. For the development of such a removal function, the modeling of a novel polishing algorithm or process control is necessary. Therefore, the material removal must be quantified first, according to significant process parameters such as pressure, nominal removal depth and relative speed. On the basis of these experimental results, specific removal functions will be derived, which are proven by modeling. The underlying model is also based on the Preston approach. However, it is extended by temporally variable terms and thus a time-variant removal function is generated. Main focus is the model description of the variable polishing pressure as well as the variable relative speed. The wear of the polishing tool will also be integrated into the model, since wear also depicts a change in the removal function over time. Part of the modeling will consist in minimizing the deviation between the desired and the actual material removal, i.e. the deviation between the desired and the actual surface. This optimization task will provide the optimal parameter constellation for the individual case. Due to the short computing times, at first a two-dimensional model will be evolved, before a substantially more complex, applicable three-dimensional model is derived.