This study established a feed-rate-based iterative algorithm for the CNC bonnet polishing process. This algorithm calculates the corresponding feed rate distribution which eliminates the surface form error based on the relationship between the feed rate and the material removal depth, furthermore, the predicted surface residual will also be calculated and demonstrated.

    First, the tool influence function (TIF) was extracted from a dynamic polishing experiment, then the relationship between the reciprocal of the feed rate and the material removal depth from the experiment was fitted with an equation by the regression method. Also, the fact that the material removal profile is invariant under the variation of the feed rate was proven. By means of combining the two prerequisites obtained above, the corresponding material removal depth and its profile with different feed rate can be predicted. In this study, a power term initial surface form error with a depth of 120 nm was adopted for algorithm validation, and it was further handled with a suggested pre-processing step to restrict the feed rate distribution at a certain range leading to the optimal surface texture.

    Due to the characteristic of the raster tool path, the significance of superposition effect between polishing tracks cannot be ignored, the iterative approach in calculation was selected in pursuit of algorithm accuracy. After the iterative algorithm was set up, it was further modified with a moving average mask and the conformal mapping method for a higher convergence.

    The simulation results show that the algorithm provides the highest convergence when the surface form data was extended with a width of double spot size on the surface margin. On the cross-section along the X-axis from the experimental surface profile, which was produced by applying this iterative algorithm, the PV value of the experiment converges to 71.66% of the desired form error in the designed-converging area, in addition, the experiment profile along the Y-axis possesses an 70.85% convergence in PV value with respect to the desired form error. When the area with single spot size larger than the designed-converging area was inspected, up to 70% of the convergence was retained on both of the cross-section in X, Y-direction, which sufficiently proved that the feed-rate-based iterative algorithm founded in this research possesses a high predictability of polishing result in bonnet polishing process.

Keyword：Bonnet Polishing, Feed Rate, Tool Influence Function, Iterative Algorithm, Conformal Mapping