Mathematical modelling of influence functions in computer-controlled polishing: Part I

Schinhaerl, Markus; Smith, Gordon; Stamp, Richard; Rascher, Rolf; Smith, Lyndon; Pitschke, Elmar; Sperber, Peter; Geiss, Andreas

doi:10.1016/j.apm.2007.10.013

Cited by 42 publications

(19 citation statements)

References 24 publications

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“…Note that Eq. [8] Downloaded by [New York University] at 23:52 15 July 2015 has the same form as Eq. [1] proposed in Shorey, et al (5).…”

Section: Materials Removal Ratementioning

confidence: 87%

“…[6] and [7], obtained from the modeling and experimental efforts, into Eq. [8] gives the MRR in the MR finishing in the form…”

Section: Materials Removal Ratementioning

confidence: 99%

“…DeGroote, et al (7) further developed this model through the inclusion of the near surface mechanical properties, abrasive size and concentration, glass chemical durability, and glass average single bond strength and quantified the effect of each term on the MRR by performing various experiments. Schinhaerl, et al (8), (9) performed a mathematical modeling study that takes into account process parameters, such as the wheel speed, the magnetic field strength, and the fluid flow rate, to predict the shape and size of the influence function that contains the information about the material removal characteristic of the polishing tool on high-quality optical lenses, and they experimentally verified the effectiveness of their model. In the wheel-type MR finishing process, the MR fluid is attached to a rotating wheel-shaped permanent magnet and directly imposes the shear stress at the workpiece surface, thus removing the materials (Seok, et al (11)).…”

Section: Introductionmentioning

confidence: 98%

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Tribological Properties of a Magnetorheological (MR) Fluid in a Finishing Process

Seok

Lee

Jang

et al. 2009

Tribology Transactions

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This article examines the tribological properties of a magnetorheological (MR) fluid in a finishing process. The MR fluid under investigation contains about 85 wt% of micro-sized carbonyl iron (CI) particles and about 15 wt% of water and surfactant(s) compound. A semi-empirical material removal model is proposed for the description of the tribological behavior of the MR fluid in the finishing process by considering both the solid-and fluid-like characteristics of the fluid in a magnetic field. Additionally, Archard's theory and Amonton's law of friction are applied to the model, which is completed by experimental efforts to identify the relationship between the effective friction coefficient and the ratio of the interfacial particle velocity to the imposed pressure on the workpiece surface.It turns out that the effective friction coefficient has a linear relationship with this ratio. The validity of the proposed model is supported through material removal rate measurements. It is also shown that the proposed model is substantially different from the conventional Preston equation in that the material removal rate is not only a function of the product of the applied normal pressure and relative velocity, but it also strongly depends on the square of the relative velocity.

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“…Note that Eq. [8] Downloaded by [New York University] at 23:52 15 July 2015 has the same form as Eq. [1] proposed in Shorey, et al (5).…”

Section: Materials Removal Ratementioning

confidence: 87%

“…[6] and [7], obtained from the modeling and experimental efforts, into Eq. [8] gives the MRR in the MR finishing in the form…”

Section: Materials Removal Ratementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Tribological Properties of a Magnetorheological (MR) Fluid in a Finishing Process

Seok

Lee

Jang

et al. 2009

Tribology Transactions

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“…Due to the magnetic field, the fluid adheres the periphery of the wheel. The shape of the fluid is determined by wheel speed, the magnetic field strength, gap between the workpice and wheel, and fluid flow rate (Schinhaerl, Smith et al 2008). Researchers have tried different variants in wheel type MRF both include using permanent magnets and electromagnets.…”

Section: Magnetorheological Finishing(mrf)mentioning

confidence: 99%

Magnetorheological Finishing: A Review

Saraswathamma¹

2010

Int.J.of Curr. Engg. and Technol

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“…Computer-controlled polishing machines and mathematical models to analyze material removal characteristics have been developed for polishing spherical, aspheric and free form surfaces, where small-size tools are employed [3][4][5][6] . We presented our efforts in developing a polishing process using a large size polishing lap, where a mathematical model was developed to estimate the residual surface errors under a given set of operating parameter and lap configurations 7,8 .…”

Section: Introductionmentioning

confidence: 99%

Computer-controlled cylindrical polishing process for development of grazing incidence optics for the hard x-ray region

et al. 2010

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The focusing performance of shell optics for the hard X-ray region strongly depends on their axial mid-spatialfrequency-range figure errors. This paper presents the development of a deterministic computer-controlled polishing process to minimize these axial figure errors on cylindrical shaped mandrels from which the mirror shells are replicated. A mathematical model has been developed to simulate the residual surface figure errors due to the polishing process parameters and the polishing tools used, along with their non-conformance to the mandrel. We present design considerations of a large-size polishing lap where the experimentally determined process variables have been used for optimizing the lap configuration and the machine operational parameters. Furthermore, the developed model is capable of generating a corrective polishing sequence for a known surface error profile. Practical polishing experiments have been performed to verify the model and to determine its ability to correct known axial figure errors through polishing machine control.

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Mathematical modelling of influence functions in computer-controlled polishing: Part I

Cited by 42 publications

References 24 publications

Tribological Properties of a Magnetorheological (MR) Fluid in a Finishing Process

Tribological Properties of a Magnetorheological (MR) Fluid in a Finishing Process

Magnetorheological Finishing: A Review

Computer-controlled cylindrical polishing process for development of grazing incidence optics for the hard x-ray region

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