Generic model of time-variant tool influence function and dwell-time algorithm for deterministic polishing

Abstract

In computer-controlled optical surfacing (CCOS) techniques, the tool influence function (TIF) is generally assumed to be time-invariant; thus, two-dimensional convolution can be employed to compute the dwell time. However, the material removal rate is time-variant in some CCOS processes. This time-variant material removal rate makes it difficult to accurately model the TIF and leads to impracticality of the two-dimensional convolution algorithm. We herein establish a novel modelling framework of the TIF considering the time-variant material removal rate in CCOS based on a partial differential equation. An updated dwell-time algorithm is also proposed to address the inverse problem of freeform surface generation by using the established TIF. The proposed modelling technique is well demonstrated in magnetically driven internal finishing and abrasive jet machining. The results demonstrate that the model can precisely predict the polished profile against the polishing time, and the novel dwell-time algorithm outperforms the conventional convolution algorithm in terms of efficiency and accuracy. The modelling framework enables localised freeform surface generation and corrective polishing on internal surfaces. The proposed TIF model and dwell-time algorithm may be extended to other CCOS techniques to achieve better figuring accuracy, such as bonnet polishing, ion beam figuring, and plasma jet machining.