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

Abstract

We present a novel simulation technique that offers efficient mass fabrication strategies for 2m class hexagonal mirror segments of extremely large telescopes. As the first of two studies in series, we establish the theoretical basis of the tool influence function (TIF) for precessing tool polishing simulation for non-rotating workpieces. These theoretical TIFs were then used to confirm the reproducibility of the material removal foot-prints (measured TIFs) of the bulged precessing tooling reported elsewhere. This is followed by the reverse-computation technique that traces, employing the simplex search method, the real polishing pressure from the empirical TIF. The technical details, together with the results and implications described here, provide the theoretical tool for material removal essential to the successful polishing simulation which will be reported in the second study.

Modeling and analysis of the material removal profile for free abrasive polishing with sub-aperture pad

“…In their work, the MRR distribution in the contact region was modeled based on the Preston's equation, and the material removal depth in the contact area was calculated by the integral of local MRR. The MRR distribution was defined as the tool influence function (TIF) by Kim and Kim (2005). Based on the Preston's equation, the TIF was modeled by assuming that the pressure distribution in the contact region is Gaussian.…”

Effect of the inflated-pressure to the tool influence function for polishing using SR bonnet

“…5. Normally, the polishing pressure is rather sensitive to the inflated-pressure, inducing that the inflated-pressure is a major factor to control the material removal rate in bonnet polishing [8]. However, it's abnormal for the SR bonnet according to the analysis above that the inflated-pressure of the SR bonnet has tiny effects on the material removal rate.…”

“…In magnetic abrasive finishing (MAF), Xu et al [5] demonstrated that the finishing pressure is increased obviously and the MAF efficiency of finishing nonferromagnetic materials is improved dramatically by using the "pressure-increasing bag", and Jha et al [6] conducted an experimental setup to study the effect of extrusion pressure and number of finishing cycles on the change in surface roughness of stainless steel grounded work-piece. Walker et al [7] and King et al [8] analyzed several major factors, including the inflated-pressure of the bonnet tool, affecting the tool influence function (TIF) experimentally and theoretically. From the above, we can see that the study on the polishing pressure is necessary for one polishing technology.…”

Deterministic measurement and correction of the pad shape in full-aperture polishing processes

“…Dwell time at local sites of the pad is implemented by controlling the angular speed of the pad as well as the translation (along the pad radius) velocity of the tool. The 'dynamic wear function' during pad shape correction is required to be stable for an efficient correction process [25]. When the angular speed of the pad and translation velocity of the tool are much lower than the angular speeds of the tool, the kinematics is dominated by the angular speeds of the conditioner.…”