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Academic literature on the topic 'Magnetorheological finishing process'

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Published: 6 September 2023

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Journal articles on the topic "Magnetorheological finishing process"

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KORDONSKI, W. I., and S. D. JACOBS. "MAGNETORHEOLOGICAL FINISHING." International Journal of Modern Physics B 10, no. 23n24 (October 30, 1996): 2837–48. http://dx.doi.org/10.1142/s0217979296001288.

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The technology of finishing for optics, ceramics, and semiconductors is one of the most promising uses of the magnetorheological effect. It perfectly coupled with computer control, allowing in quantity production the unique accuracy and quality of a polished surface to be achieved. The polishing process may appear as follows. A part rotating on the spindle is brought into contact with an magnetorheological polishing (MRP) fluid which is set in motion by the moving wall. In the region where the part and the MRP fluid are brought into contact, the applied magnetic field creates the conditions necessary for the material removal from the part surface. The material removal takes place in a certain region contacting the surface of the part which can be called the polishing spot or zone. The polishing process comes to the program-simulated movement of the polishing spot over the part surface. The mechanism of the material removal in the contact zone is considered as a process governed by the particularities of the Bingham flow in the contact zone. The problem like the hydrodynamic theory of lubrication is treated for plastic film. As this takes place the shear stresses distribution in the film is obtained from the experimental measurements of the pressure distribution in the contact spot. Reasonable correlation between calculated and experimental magnitudes of the material removal rate for glass polishing lends support to the validity of the approach.
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Singh, Anant Kumar, Sunil Jha, and Pulak M. Pandey. "Magnetorheological Ball End Finishing Process." Materials and Manufacturing Processes 27, no. 4 (April 2012): 389–94. http://dx.doi.org/10.1080/10426914.2011.551911.

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Grover, Vishwas, and Anant Kumar Singh. "Modeling of surface roughness in the magnetorheological cylindrical finishing process." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 1 (December 13, 2017): 104–17. http://dx.doi.org/10.1177/0954408917746354.

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The magnetorheological cylindrical finishing process is developed for fine finishing of the internal surface of cylindrical objects. The process uses smart fluid known as magnetorheological polishing fluid. This fluid consists of carbonyl iron (CI) and silicon carbide (SiC) abrasive particles mixed in the base fluid. The magnetorheological cylindrical finishing process consists of an internal finishing tool, which induces magnetic field over its outer surface due to which CI particles experience magnetic force and form chains between the magnetized tool outer surface and inner surface of the cylindrical workpiece. The CI particles push SiC abrasive particles towards the inner surface of the cylindrical workpiece and with the movement of finishing tool inside the cylindrical workpiece, finishing is performed in the process. In the present work, a mathematical model is developed for calculating the change in surface roughness values in the magnetorheological cylindrical finishing process after consideration of forces as acting on SiC particles. To validate the proposed mathematical model, the experimentation is performed by the magnetorheological cylindrical finishing process for finishing the internal surface of cylindrical hardened ferromagnetic steel workpiece. Results of both i.e. mathematical modeling and experimentation are found to be in close agreement with least percentage error of 1.28%. The developed mathematical model is helpful in predicting the process performance, which proves to be useful for industries dealing with internal finishing like injection molding, gas, and liquid pipes, etc.
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Kang, Gui Wen, and Fei Hu Zhang. "Optics Manufacturing Using Magnetorheological Finishing." Key Engineering Materials 375-376 (March 2008): 274–77. http://dx.doi.org/10.4028/www.scientific.net/kem.375-376.274.

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Magnetorheological finishing (MRF) is a novel precision optical machining technology. Owing to its flexible finishing process, MRF can eliminate subsurface damage, smooth rms micro roughness and correct surface figure errors. The finishing process can be easily controlled by a computer. Through proper designing of numerical control, sphere and asphere optics can be machined by magnetorheological finishing with high quality. Optical sphere is machined using dwell time algorithm and surface shape 2 pt. PV has been improved from 0.17um to 0.07um.
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Mangal, S., and M. Kataria. "Characterization of Magnetorheological Finishing Fluid for Continuous Flow Finishing Process." Journal of Applied Fluid Mechanics 11, no. 6 (November 1, 2018): 1751–63. http://dx.doi.org/10.29252/jafm.11.06.28928.

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Iqbal, Faiz, Zafar Alam, Dilshad Ahmad Khan, and Sunil Jha. "Automated insular surface finishing by ball end magnetorheological finishing process." Materials and Manufacturing Processes 37, no. 4 (November 8, 2021): 437–47. http://dx.doi.org/10.1080/10426914.2021.2001502.

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Sharma, Anand, and M. S. Niranjan. "Magnetorheological Fluid Finishing of Soft Materials: A Critical Review." INTERNATIONAL JOURNAL OF ADVANCED PRODUCTION AND INDUSTRIAL ENGINEERING 4, no. 1 (January 5, 2019): 48–55. http://dx.doi.org/10.35121/ijapie201901138.

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Magnetorheological Finishing (MRF) is one of the precision finishing processes and recently commercialized method for finishing of various materials like optical glasses, metals, non-metals etc. This method utilizes a suspension consisting of a fluid carrier which can be water or oil, both magnetic and non-magnetic particles and stabilizing agents. Rheological behavior of this mixture of magnetorheological (MR) fluid with abrasives changes under the influence of magnetic field which in turn regulates the finishing forces during finishing processes. Present study critically reviews the MRF process used for achieving nano-level finishing of soft materials and the advancements made in this process
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Hashmi, Abdul Wahab, Harlal Singh Mali, Anoj Meena, Irshad Ahamad Khilji, Chaitanya Reddy Chilakamarry, and Siti Nadiah binti Mohd Saffe. "Experimental investigation on magnetorheological finishing process parameters." Materials Today: Proceedings 48 (2022): 1892–98. http://dx.doi.org/10.1016/j.matpr.2021.09.355.

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Hashmi, Abdul Wahab, Harlal Singh Mali, Anoj Meena, Irshad Ahamad Khilji, Chaitanya Reddy Chilakamarry, and Siti Nadiah binti Mohd Saffe. "Experimental investigation on magnetorheological finishing process parameters." Materials Today: Proceedings 48 (2022): 1892–98. http://dx.doi.org/10.1016/j.matpr.2021.09.355.

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Khatri, Neha, Suman Tewary, Xavier J. Manoj, Harry Garg, and Vinod Karar. "Magnetorheological finishing of silicon for nanometric surface generation: An experimental and simulation study." Journal of Intelligent Material Systems and Structures 29, no. 11 (April 24, 2018): 2456–64. http://dx.doi.org/10.1177/1045389x18770869.

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Silicon mirrors are essential for guiding the X-ray beam and focusing it to a specific location. These mirrors using total internal reflection require super smooth surface finish due to small wavelength of X-ray. Magnetorheological finishing is a computer-controlled technique used in the production of high-quality optical lenses. This process utilizes polishing slurries based on magnetorheological fluids, whose viscosity changes with the change in magnetic field. In this work, polishing potential of silicon mirrors by magnetorheological finishing process is examined to achieve nanometric surface finish for X-ray applications. The individual effect of parameters such as magnetizing current, working gap, rotational speed on surface roughness is investigated, and optimized parameters are identified. To investigate the physical essence underlying magnetorheological finishing process, the molecular dynamics simulations are used. Molecular dynamics simulation is used to study the atomic-scale removal mechanism of single-crystalline silicon in magnetorheological finishing process and attention is paid to study the effect of gap between the tool and the workpiece on surface quality. The outcome is promising and the final surface roughness achieved is as low as 6.4 nm. The surface quality is analyzed in terms of arithmetic roughness, power spectral density, and image analysis of scanning electron microscopy for uniform evaluation.
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Dissertations / Theses on the topic "Magnetorheological finishing process"

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Li, Ying-Song, and 李英松. "Numerical Analysis on the Finishing Performance of Magnetorheological Abrasive Flow Finishing(MRAFF) Process." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/50882107466231420449.

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碩士
國立屏東科技大學
車輛工程系所
98
Magnetorheological Abrasive Flow Finishing (MRAFF) is a novel precision finishing process using smart magnetorheological polishing fluid. The said fluid can lead to a solid-liquid phase change under external magnetic field, and thus change Newtonian fluid to non-Newtonian Bingham plastic fluid. This smart behavior of MR-polishing fluid is utilized to precisely control the high normal and shear force, hence final cutting and polishing in work piece surface. However, because the MRAFF process coupled with magnetic field, thermal flow field, and multi-phase flow. The mechanism is so complicated that difficult to obtain operate parameters. Therefore, this research develops the numerical tools to analyze the characteristics of magnetorheological fluids and the finishing efficiency of abrasives, and meanwhile, investigates the cutting efficiency on curved-surface parts and the variations in magnetorheological fluids using the characteristic equations of magnetorheological fluid under different work piece materials and working parameters. The research result shows: when Reynolds number and Hartmann number are enhancement, will be helpful to the work piece cut depth increase, but surface roughness quality will drop, and mesh size increase can improve the surface roughness quality . In addition, in the research case analysis, the magnetic conductive material can obtain the greatly prediction of cutting depth, but fluid flow shear force is smaller than the material yield force . The cutting mechanism of the overall role is bad, can not achieve the desired effect of cutting. On the other hand, cutting depth is low in the polishing non-magnetic conductive material, because surface shear force rise since the velocity field distribution, by the Lorentz force action influence, cause better cutting effect of prediction. Finally, we can derive cutting depth equations and surface roughness quality equations from all of the parameter analysis in this research. The research results will be helpful that someone could blend magnetorheological fluid in further, prediction cutting depth and roughness quality of work piece surface in research matrix range.
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Book chapters on the topic "Magnetorheological finishing process"

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Iqbal, F., Z. Alam, D. A. Khan, and S. Jha. "Part Program-Based Process Control of Ball-End Magnetorheological Finishing." In Lecture Notes on Multidisciplinary Industrial Engineering, 503–14. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9471-4_41.

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Kumar, Manjesh, Abhinav Kumar, Hari Narayan Singh Yadav, and Manas Das. "Gear Profile Polishing Using Rotational Magnetorheological Abrasive Flow Finishing Process." In Lecture Notes in Mechanical Engineering, 565–76. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3266-3_44.

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Rajput, Atul Singh, Sajan Kapil, and Manas Das. "Computational Techniques for Predicting Process Parameters in the Magnetorheological Fluid-Assisted Finishing Process." In Advanced Computational Methods in Mechanical and Materials Engineering, 125–46. New York: CRC Press, 2021. http://dx.doi.org/10.1201/9781003202233-10.

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Aggarwal, Ankit, and Anant Kumar Singh. "A Novel Magnetorheological Grinding Process for Finishing the Internal Cylindrical Surfaces." In Lecture Notes on Multidisciplinary Industrial Engineering, 179–89. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9471-4_15.

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Alam, Z., D. A. Khan, F. Iqbal, and S. Jha. "Theoretical and Experimental Study on Forces in Ball End Magnetorheological Finishing Process." In Advances in Forming, Machining and Automation, 391–401. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3866-5_33.

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Kanthale, V. S., and D. W. Pande. "Experimental Study of Process Parameters on Finishing of AISI D3 Steel Using Magnetorheological Fluid." In Advanced Engineering Optimization Through Intelligent Techniques, 739–48. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8196-6_65.

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Rajput, Atul Singh, Deokant Prasad, Arpan Kumar Mondal, and Dipankar Bose. "2D Computational Fluid Dynamics Analysis into Rotational Magnetorheological Abrasive Flow Finishing (R-MRAFF) Process." In Lecture Notes in Mechanical Engineering, 67–73. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1307-7_7.

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Paswan, S. K., and A. K. Singh. "Nano-finishing of Internal Surface of Power Steering Housing Cylinder Using Rotational Magnetorheological Honing Process." In Lecture Notes on Multidisciplinary Industrial Engineering, 299–307. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9425-7_26.

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Singh, Manpreet, Ashpreet Singh, and Anant Kumar Singh. "Nanofinishing of External Cylindrical Surface of C60 Steel Using Rotating Core-Based Magnetorheological Finishing Process." In Lecture Notes on Multidisciplinary Industrial Engineering, 53–66. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9471-4_5.

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Alam, Z., D. A. Khan, F. Iqbal, A. Kumar, and S. Jha. "Design and Development of Cartridge-Based Automated Fluid Delivery System for Ball End Magnetorheological Finishing Process." In Advances in Simulation, Product Design and Development, 805–13. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9487-5_67.

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Conference papers on the topic "Magnetorheological finishing process"

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Singh, Anant Kumar, Sunil Jha, and Pulak M. Pandey. "A Novel Ball End Magnetorheological Finishing Process." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36284.

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A novel ball end magnetorheological finishing process was developed for performing stable and controllable finishing operation on flat as well as 3D free form features of magnetic or non-magnetic materials. The main innovation in this process was generating a magnetic flux density at the end of a cylindrical tool that facilitates the shaping of the magnetorheological polishing fluid in a fashion to resemble like a ball nose cutter. A 4-axis motion controller program directs the resembled polishing fluid to follow the surface to be finished. This paper focuses on the various stages of the development of a novel finishing process. This leads to significant improvement in process performance in terms of smooth controllable functionality, percentage reduction in surface roughness, surface textures at microscopic level of the workpiece surfaces. In the initial stage of development, the magnetorheological cylindrical finishing tool was made to rotate as a whole during the finishing operation with all its constituent components like inner core, magnetic coil and outer core. In this stage, there was no provision of cooling magnetic coil because magnetic coil was rotated with the rotation of the finishing tool during finishing operation. Therefore, it was difficult to incorporate any cooling arrangement over the outer surface of magnetic coil to cool it continuously. Hence, the tool was limited to shorter time of finishing operation due to continuous heating of magnetic coil. Also, some other additional limitations were noticed such as constraint on magnetic coil to produce higher magnetic field, noise and vibration during the finishing operation. These limitations resulted in low effectiveness of finishing operation. To overcome these specific limitations which were observed after initial development of finishing setup, the limitations were overcome by redesigning of cylindrical finishing tool with stationary magnetic coil (integrated with cooling coils) and only central core was allowed to rotate during operation without the outer core. This resulted in smooth rotational motion of the tool without much noise and vibration during finishing operation. The experiments were performed on flat magnetic material workpiece using the modified magnetorheological cylindrical finishing tool. The surface finish obtained was 23.7 nm from the initial surface roughness of 126.1 nm in 30 min with continuous cooling of magnetic coil.
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Jacobs, Stephen D., Donald Golini, Yuling Hsu, Birgit E. Puchebner, D. Strafford, Igor V. Prokhorov, Edward M. Fess, D. Pietrowski, and William I. Kordonski. "Magnetorheological finishing: a deterministic process for optics manufacturing." In International Conferences on Optical Fabrication and Testing and Applications of Optical Holography, edited by Toshio Kasai. SPIE, 1995. http://dx.doi.org/10.1117/12.215617.

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Ghosh, Gourhari, Ajay Sidpara, and P. P. Bandyopadhyay. "Preliminary Results on Finishing of WC-Co Coating by Magnetorheological Finishing Process." In ASME 2019 14th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/msec2019-2914.

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Abstract Thermal spray coating has the ability to enhance the lifetime of engineering components by reinforcing the surface properties. The surface roughness of the as-sprayed coatings needs to be suitably finished for its end use. The nanofinished WC-Co coatings are widely used in aerospace and automobile industries. In this present investigation, surface grinding followed by the magnetorheological finishing (MRF) processes is employed for finishing of WC-Co coating. Boron carbide (B4C) powder is used as the abrasive particles in the MRF process. MRF spot finishing technique is performed on the ground coating. The plastically deformed layer from the ground surface is removed completely by the gentle mechanical abrasion of MR fluid ribbon. The surface roughness and volume of material removed are measured over the finishing time. It is perceived that the surface roughness of the finishing spot is increased after a threshold machining time. This is attributed to the aging of MR fluid and the mechanical abrasion of wear debris. The experiment is also performed with the assistance of Murakami’s reagent to perform etching and finishing, simultaneously. A comparatively higher finishing rate is observed in this case.
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Khan, Dilshad Ahmad, Zafar Alam, and Sunil Jha. "Nanofinishing of Copper Using Ball End Magnetorheological Finishing (BEMRF) Process." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65974.

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The ball end magnetorheological finishing (BEMRF) is an advanced nanofinishing process for flat, curved and freeform surfaces of ferromagnetic as well as diamagnetic materials. While finishing copper (diamagnetic material) by this process, a low finishing effect is obtained as its surface repels the externally applied magnetic field. In this work a magnetic simulation is carried out over both copper and ferromagnetic material. For the ferromagnetic material the simulation result shows a high flux density region below the tool tip. However in case of copper the magnetic flux density is too low for finishing. It is also observed through simulations that when copper workpiece is placed on a mild steel base the flux density improves marginally. This led to the idea of using a permanent magnet (in place of mild steel) as a base for finishing of copper using the BEMRF process. Using this technique copper was finished and the experimental results indicate that this method can realize ultra-precision finishing of copper.
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Kordonski, William I., Aric B. Shorey, and Marc Tricard. "Magnetorheological (MR) Jet Finishing Technology." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61214.

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Conformal (or freeform) and steep concave optics are important classes of optics that are difficult to finish using conventional techniques due to mechanical interferences and steep local slopes. One suitable way to polish these classes of optics is by using a jet of abrasive/fluid mixture. In doing so, the energy required for polishing may be supplied by the radial spread of a liquid jet, which impinges a surface to be polished. Such fluid flow may generate sufficient surface shear stress to provide material removal in the regime of chemical mechanical polishing. Once translated into a polishing technique, this unique tool may resolve a challenging problem of finishing steep concave surfaces and cavities. A fundamental property of a fluid jet is that it begins to lose its coherence as the jet exits a nozzle. This is due to a combination of abruptly imposed longitudinal and lateral pressure gradients, surface tension forces, and aerodynamic disturbance. This results in instability of the flow over the impact zone and consequently polishing spot instability. To be utilized in deterministic high precision finishing of remote objects, a stable, relatively high-speed, low viscosity fluid jet, which remains collimated and coherent before it impinges the surface to be polished, is required. A method of jet stabilization has been proposed, developed and demonstrated whereby the round jet of magnetorheological fluid is magnetized by an axial magnetic field when it flows out of the nozzle. It has been experimentally shown that a magnetically stabilized round jet of MR polishing fluid generates a reproducible material removal function (polishing spot) at a distance of several tens of centimeters from the nozzle. In doing so, the interferometrically derived distribution of material removal for an axisymmetric MR Jet, which impinges normal to a plane glass surface, coincides well with the radial distribution of rate of work calculated using computational fluid dynamics (CFD) modeling. Polishing results support the assertion that the MR Jet finishing process may produce high precision surfaces on glasses and single crystals. The technology is most attractive for the finishing of complex shapes like freeform optics, steep concaves and cavities.
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Golini, Don, Paul Dumas, William Kordonski, Stephen Hogan, and Stephen Jacobs. "Precision optics fabrication using magnetorheological finishing." In Optical Fabrication and Testing. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/oft.1998.omd.1.

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In general terms, the magnetorheological finishing (MRF)1 process occurs as follows (refer to Fig.1). A workpiece is installed at some fixed distance from a moving wall, so that the workpiece surface and the wall form a converging gap. An electromagnet, placed below the moving wall, generates a non-uniform magnetic field in the vicinity of the gap. The magnetic field gradient is normal to the wall. The MR polishing fluid is delivered to the wall just above the electromagnet pole pieces. The MR polishing fluid is pressed against the wall by the magnetic field gradient, acquires the wall velocity, and becomes a plastic Bingham medium before it enters the gap. Thereafter, a shear flow of plastic MR suspension occurs through the gap, resulting in the development of high stresses in the interface zone and thus, material removal over a portion of the workpiece surface. This area is designated as the “polishing spot” or removal function.
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Geiss, Andreas, Markus Schinhaerl, Elmar Pitschke, Rolf Rascher, and Peter Sperber. "Analysis of thermal sources in a magnetorheological finishing (MRF) process." In Optics & Photonics 2005, edited by H. Philip Stahl. SPIE, 2005. http://dx.doi.org/10.1117/12.616751.

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Golini, Don, Yiyang Zhou, Steve Jacobs, Fuqian Yang, Dave Quesnel, Cheryl Gracewski, Mark Atwood, and Ed Fess. "Aspheric Surface Generation Requirements in Magnetorheological Finishing." In Optical Fabrication and Testing. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/oft.1996.jtha.2.

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A manufacturing system for grinding and polishing aspheres is under development. Polishing is accomplished using the magnetorheological finishing (MRF) technique. MRF utilizes the unique properties of MR fluids to achieve high polishing removal rates. The fluid is carried through a magnetic field, in which its viscosity is increased by several orders of magnitude. The lens is polished in this viscous zone to optical quality. MRF is very effective at polishing high spatial frequency errors (microroughness) and at figuring global form errors (e.g. power), but has limitations for smoothing of mid-frequency errors. The work presented here is intended to define the problematic mid-spatial frequency regime, and to use this a criteria for the aspheric grinding process.
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Golini, Don, Steve Jacobs, Yiyang Zhou, Ed Fess, and Mark Atwood. "Aspheric Surface Generation Requirements for Magnetorheological Finishing." In Extreme Ultraviolet Lithography. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/eul.1996.of98.

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A manufacturing system for grinding and polishing aspheres is under development at the Center for Optics Manufacturing (COM). Polishing is accomplished using the magnetorheological finishing (MRF) technique. MRF utilizes the unique properties of MR fluids to achieve high polishing removal rates. The fluid is carried through a magnetic field, in which its viscosity is increased by several orders of magnitude. The lens is polished in this viscous zone to optical quality. MRF is very effective at polishing high spatial frequency errors (microroughness) and at figuring global form errors (e.g. power), but has limitations for smoothing of mid-frequency errors. The work presented here will describe the problematic mid-spatial frequency regime, and use this a criteria for the aspheric grinding process.
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Jain, V. K., Pankaj Singh, Puneet Kumar, Ajay Sidpara, Manas Das, V. K. Suri, and R. Balasubramaniam. "Some Investigations Into Magnetorheological Finishing (MRF) of Hard Materials." In ASME 2009 International Manufacturing Science and Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/msec2009-84335.

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Magnetorheological finishing (MRF) process is one of the fine abrasive finishing processes used to get better surface finish on a semi finished part. The present work is aimed at investigating the effectiveness and validity of magnetorheological finishing process and finding out the process parameters (such as finishing time, rotational speed of carrier wheel, abrasive concentration, and working gap) and their effectiveness on surface finish characteristics. MRF process is applied on brass and nonmagnetic stainless steel workpieces which were initially finished by the grinding process. The results of experiments were statistically analyzed by response surface methodology (RSM) to form an empirical model for the responses generated during the process. Also, an attempt has been made to model and simulate the finishing operation in MRF process. Apart from this, the micro structure of the mixture of magnetic and abrasive particles in magnetorheological polishing fluid (MR Fluid) has been proposed. Thereafter the normal force on the abrasive particles is calculated from the applied magnetic field and a model for the prediction of surface roughness has also been presented. Finally, theoretical results calculated using the proposed model, have been compared with the experimental results to validate the model developed.
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