Precessions aspheric polishing: new results from the development program

Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes

“…where ∆ z is the integrated material removal from the workpiece surface, κ the removal coefficient of the segment material, P the polishing pressure, V T the magnitude of relative speed between the tool and workpiece surface, and ∆ t the dwell time. Earlier studies [13][14][15][16] showed that the precessing polishing process currently in service uses the measured TIFs of near Gaussian shapes to compute the required dwell time. That method bypasses the need for prior knowledge of the relationship among the material removal (i.e., TIF), polishing pressure, and velocity inside the tool-workpiece contact area (polishing spot).…”

“…These theoretical TIFs were used to re-produce the characteristics of the measured [13,14] TIFs. First, Fig.…”

“…They are: i) low tooling overhead, ii) deterministic material removal and iii) embedded process control intelligence. The bulged precessing polishing process [13,14], recently introduced, may have potentials to bring greater improvement than earlier methods [5][6][7][8][9][10][11] for the three elements defined above. In particular, as it moves across the workpiece, the bulged precessing tool tends to conform its shape to the local surface.…”

Material removal in magnetorheological finishing of optics

“…Full advantage of the deterministic nature of CNC machining can only be taken if a sub-aperture polishing tool instantly adapts (conforms) to the local surface and its removal function is well characterized and stable. Commonly used mechanical tools with air pressure or an elastic cushion behind the polishing pad do not provide the required level of adaptability and stability [1,2].…”

“…is the diameter of particle and  is the shear rate. The dimensionless coefficient K takes into account other flow parameters such as concentration, mechanical properties of particles, carrier fluid damping properties, flow geometry, etc.According to(2), the problem of evaluation of the particle force is mainly reduced to determining of the flow shear rate at the surface of interest. In the following analysis the shear rate is obtained by numerical modeling of the particular shear flow taking into account rheological properties of the media.…”