The application of freeform surface in the off-axis three-mirror imaging system can greatly improve its optical performance. However, it is difficult for fabrication of freeform optical surface to high precision by traditional machining technology. This paper focuses on the corrective polishing of the primary mirror and tertiary mirror, which are fabricated on one monolithic substrate and described by NURBS-based freeform surfaces, in an off-axis three-mirror imaging system. The integrated polishing process system is proposed for polishing the two mirrors on the 4-axis CNC polishing machine by use of spherical polishing tool. The tool influence function (TIF) module, polishing path generation and dwell time calculation module included in the integrated polishing process system are described respectively. The material removal on the measurement line of part surface is predicted to validate the dwell time calculation algorithm. The polishing experiments of the primary mirror and tertiary mirror are performed to verify the proposed integrated polishing process system.

This paper presents a new polishing path planning method for physically uniform overlap of polishing ribbons instead of traditional geometrically uniform coverage of polishing path on freeform surfaces, which attempts to achieve the even material removal on the polished surface in consideration of contact mechanics in polishing process. The polishing ribbon is defined as the ribbon with varying width generated by continuous contact areas along the polishing path. The boundary extraction algorithm (BEA) is proposed to determine the specific polishing ribbon boundary which is next to the to-be-planned path. The path extraction algorithm (PEA) is given to predict the location of the adjacent polishing path. Those BEA and PEA make the overlap of polishing ribbons along two adjacent polishing paths physically uniform. Proposed polishing path planning is implemented for a typical freeform surface and the polishing paths with physically uniform overlap of polishing ribbons between two adjacent paths are obtained, while the under-polishing and over-polishing phenomena occur when the traditional scanning path is applied. In addition, the comparative experiments and analysis are also conducted and the experimental results further verify the feasibility of the proposed polishing path to promote even material removal.

•We present a statistical model about the polished profile for free-abrasive polishing.•The effect of slurry properties on the material removal depth is formulated.•The topographical parameters of sub-aperture pad on polished depth are considered.•Polished depth is proportional to (normal force)0.65 and (volume concentration)2/3.•The polished profile is affected by the polishing path.This paper addresses the problem of material removal in free abrasive polishing (FAP) with the sub-aperture pad both theoretically and experimentally. The effects of some polishing conditions upon the material removal are analyzed, including not only the process parameters, which refer to the normal force, angular spindle velocity and angular feed rate, but also the abrasive grain size, polishing slurry properties, topographical parameters of the sub-aperture pad, as well as tool path curvature. Based on the analysis, a model of material removal profile is proposed to facilitate more accurate polishing. First, by analyzing the contact among polishing pad, abrasive grain and workpiece surface in the micro level, the removal depth per unit length of the polishing path is derived, which is defined as the material removal index. Then, the distribution of this removal index can be obtained via modeling the pressure and relative sliding velocity in the contact region of polishing pad and workpiece. After that, the material removal profile can be calculated by integrating the material removal index along the tool path in the tool-workpiece contact region. To verify the effectiveness of the proposed model, a series of polishing experiments have been conducted. Experimental results well demonstrate that our model can accurately predict the material removal depth during the FAP.