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

Cordero-Dávila, Alberto; González-García, Jorge; Pedrayes-López, María; Aguilar-Chiu, Luis Alberto; Cuautle-Cortés, Jorge; Robledo-Sánchez, Carlos

doi:10.1364/ao.43.001250

Cited by 51 publications

(15 citation statements)

References 15 publications

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“…The first is linear pressure distribution, the second is the skin model pressure distribution [8] [9]. Shown in Fig.4, at the actual processing, the pressure at the edge of workpiece is more than the other place.…”

Section: The Average Pressure Between the Lap And Workpiecementioning

confidence: 99%

Correction of the removal function of lap in manufacturing large aspherical mirror

Zhang

Zeng

et al. 2014

SPIE Proceedings

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The pendulum type processing technique is a manufacture way that the workpiece is rotating actively and the lap is slave drive from the workpiece under its gravity force and the pressure which comes from the pressure head. The rotational speed of lap is varied. Because the aperture size of the lap can be selected in the processing. So the processing efficiency is high. And this technique is commonly used in the grinding stage to remove a large margin, sub-surface damage layer and to smooth the mirror surface in the stage of polishing. Shown in the Preston equation, the removal function of lap is connected to the relative speed of lap_workpiece. Based on moment-equilibrium principle, a theoretical model is established about the lap which associated with the coherent parameters. Under the condition of the lap and the workpiece at different relative positions, the rotational speed of the lap and correspondence between the parameters is summarized and derived. The speed ratio of lap_workpiece increases with the increment of the eccentricity, and the actual rotational speed is determined by the workpiece's rotational speed, the size of lap and the force acting on the lap.The relationship of speed ratio between the lap and workpiece which impacts on the removal function is given at the last of the paper.

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Section: The Average Pressure Between the Lap And Workpiecementioning

confidence: 99%

Correction of the removal function of lap in manufacturing large aspherical mirror

Zhang

Zeng

et al. 2014

SPIE Proceedings

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“…Figure 2 shows the ring TIFs for the different lap location e; the ω is equal to 1. The edge effect is introduced by using the skin-pressure model when the lap overhangs at the edge of the mirror [21]. The skin-pressure model divided the lap-workpiece contact region into two regions, lower pressure region B and higher pressure region C, when the lap overhangs at the mirror edge.…”

Section: Mathematical Model For Calculating Ring Tifsmentioning

confidence: 99%

Study on active lap tool influence function in grinding 18 m primary mirror

Liu

Zeng

et al. 2013

Appl. Opt.

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We present a theoretical modeling method to predict the ring tool influence function (TIF) based on the computer-controlled active lap process. The gap on the lap-grinding layer is considered, and its influence on the ring TIF is analyzed too. The relationship between the shape of the ring TIF and the lap-workpiece rotation speed ratio is discussed in this paper. The recipe for calculating dwell time for axisymmetric fabrication is discussed. The grinding process of a 1.8 m primary mirror is improved based on these results. The grinding process is accomplished after 30 circles of grinding, and the surface shape error is from PV 82 μm RMS 16.4 μm reduced to PV 13.5 μm RMS 2.5 μm.

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“…R. A. Jones suggested a linear pressure distribution model in 1986 [7]. Luna-Aguilar, et al (2004) developed this approach further using a non-linear high pressure distribution near the edge of the part; however, they did not report the models validity by experimental results [8].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Modelling and measurement of polishing tool influence functions for edge control

Li¹,

Yu²,

Walker³

et al. 2011

JEOS:RP

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We present progress on our development of edge control for fabrication of mirror segments potentially for the European Extremely Large Telescope (E-ELT). Zeekoś Bonnet polishing technology has been adopted to achieve the form correction target. Like other Computer Numerical Controlled (CNC) polishing, accurate and stable tool Influence Functions (IFs) are important. Particular challenges arisen when polishing up to edges where the geometry of the IFs created by a bonnet changes. We described a model based on measured IFs data that allowed us accurately to predict the edge profile. To obtain IFs at the edge, data from interferometers and profilometers have been stitched. Numerical models with empirical Ifs as input data have been used to predict edge profiles with some preliminary success.

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

Cited by 51 publications

References 15 publications

Correction of the removal function of lap in manufacturing large aspherical mirror

Correction of the removal function of lap in manufacturing large aspherical mirror

Study on active lap tool influence function in grinding 18 m primary mirror

Modelling and measurement of polishing tool influence functions for edge control

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