Computer controlled polishing requires accurate knowledge of the tool influence function (TIF) for the polishing tool (i.e. lap). While a linear Preston's model for material removal allows the TIF to be determined for most cases, nonlinear removal behavior as the tool runs over the edge of the part introduces a difficulty in modeling the edge TIF. We provide a new parametric model that fits 5 parameters to measured data to accurately predict the edge TIF for cases of a polishing tool that is either spinning or orbiting over the edge of the workpiece.

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Parametric modeling of edge effects for polishing tool influence functions.

In a polishing process the wear is greater at the edge when the tool extends beyond the border of the workpiece. To explain this effect, we propose a new model in which the pressure is higher at the edge. This model is applied to the case of a circular tool that polishes a circular workpiece. Our model correctly predicts that a greater amount of material is removed from the edge of the workpiece.

Edge effects with the Preston equation for a circular tool and workpiece

In the ultra-precision manufacturing of large optical surfaces, industrial robots with small tools have the potential to become an intelligent and economical choice of surface polishing. But one of the most challenging problems is the severe edge roll-off error caused by the small tools. In this paper, an effective method is proposed to reduce the edge error in the polishing of large mirrors. The convergence rate of the form quality can be improved by adjusting the polishing removal amount. A generic space-variant deconvolution algorithm is developed to precisely calculate the dwell time. Experiments are conducted using an industrial robotic polisher and the edge roll-off error is effectively suppressed. As a consequence the polishing accuracy and efficiency of the robotic polishing technology can be improved significantly.

Edge control in precision robotic polishing based on space-variant deconvolution

Edge effect is regarded as one of the most difficult technical issues for fabricating large primary mirrors, especially for large polishing tools. Computer controlled active lap (CCAL) uses a large size pad (e.g., 1/3 to 1/5 workpiece diameters) to grind and polish the primary mirror. Edge effect also exists in the CCAL process in our previous fabrication. In this paper the material removal rules when edge effects happen (i.e. edge tool influence functions (TIFs)) are obtained through experiments, which are carried out on a Φ1090-mm circular flat mirror with a 375-mm-diameter lap. Two methods are proposed to model the edge TIFs for CCAL. One is adopting the pressure distribution which is calculated based on the finite element analysis method. The other is building up a parametric equivalent pressure model to fit the removed material curve directly. Experimental results show that these two methods both effectively model the edge TIF of CCAL.

Edge effect modeling and experiments on active lap processing

Edge effect is regarded as one of the most difficult technical issues in a computer controlled optical surfacing (CCOS) process. Traditional opticians have to even up the consequences of the two following cases. Operating CCOS in a large overhang condition affects the accuracy of material removal, while in a small overhang condition, it achieves a more accurate performance, but leaves a narrow rolled-up edge, which takes time and effort to remove. In order to control the edge residuals in the latter case, we present a new concept of the ‘heterocercal’ tool influence function (TIF). Generated from compound motion equipment, this type of TIF can ‘transfer’ the material removal from the inner place to the edge, meanwhile maintaining the high accuracy and efficiency of CCOS. We call it the ‘heterocercal’ TIF, because of the inspiration from the heterocercal tails of sharks, whose upper lobe provides most of the explosive power. The heterocercal TIF was theoretically analyzed, and physically realized in CCOS facilities. Experimental and simulation results showed good agreement. It enables significant control of the edge effect and convergence of entire surface errors in large tool-to-mirror size-ratio conditions. This improvement will largely help manufacturing efficiency in some extremely large optical system projects, like the tertiary mirror of the Thirty Meter Telescope.

Edge control in a computer controlled optical surfacing process using a heterocercal tool influence function.

In the polishing process, the wear tends to be greater when the tool extends beyond the edge of the workpiece. A linear pressure distribution (between the tool and the workpiece) has been used to explain this effect, however, this model also can predict negative pressures. This could mean that material is deposited instead of being removed. We present a new pressure distribution proposal, which presents like a skin effect. This means that the pressure is significantly higher at the border points than at internal points of the glass. With this model the material removal at the border points is increased considerably since, according to Preston, the wear is proportional to the pressure. This pressure distribution model is applied to calculate the wear produced by a square tool on a glass border moving along straight lines.

Edge effects with Preston equation

An adaptive lens can be made from plastic and elastic material, its focal distance can be changed by appling radial forces at the lens border ring. To make these kind of lenses it is necessary to figure molds. However, these molds can not be figured by using rigid tools for rapid surfaces. Then we are developing a new technique based in a linear array of independent sub-tools. A linear tool consists of subtools, the pressures of each one can be regulated according to the measured surface errors. The pressures are given by weights put over each sub-tool. By using genetic algorithms the pressure values of each subtool have been calculated in order to obtain the optimal wear. They are shown numerical and experimental results for several axisymmetrical surfaces.

Jorge Cuautle-Cortez

Papers

Edge effects with Preston equation

Calculating subtool pressures by using genetic algorithms