Research Papers

Stochastic Characteristics in Microgrinding Wheel Static Topography

[+] Author and Article Information
Jacob A. Kunz

George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: jacobakunz@gatech.edu

J. Rhett Mayor

Associate Professor
George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: rhett.mayor@me.gatech.edu

Contributed by the Manufacturing Engineering of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received June 18, 2013; final manuscript received January 17, 2014; published online February 21, 2014. Assoc. Editor: Stefan Dimov.

J. Micro Nano-Manuf 2(2), 021001 (Feb 21, 2014) (9 pages) Paper No: JMNM-13-1052; doi: 10.1115/1.4026545 History: Received June 18, 2013; Accepted January 17, 2014; Revised January 17, 2014

Superabrasive grind wheels are used for the machining of brittle materials such as tungsten carbide. Stochastic modeling of the wheel topography can allow for statistical bounding of the grind force characteristics allowing improved surface quality without sacrificing productivity. This study utilizes a machine vision method to measure the wheel topography of diamond microgrinding wheels. The results showed that there are large variances in wheel specifications from the manufacturer and that microgrinding wheels suffer from statistical scaling effects that increase wheel-to-wheel variability in the topography. Analysis of the static grit density values measured on the microgrinding wheels showed that the distributions provided by both analytic stochastic and numerical simulation models accurately predicted the static grit density within a significance level of 5%. Utilizing only manufacturer-supplied specifications caused the models to predict the static grit density with errors as large as 25.3% of the predicted value leading to a need for improved wheel tolerancing and in situ wheel measurement. The spacings between the grits on the wheel surface were shown to be independent of direction and can best be described by a loglogistic distribution.

Copyright © 2014 by ASME
Topics: Wheels , Density
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Otsu, N., 1975, “A Threshold Selection Method from Gray-Level Histograms,” Automatica, 11(285-296), pp. 23–27.
Yin, L., Spowage, A., Ramesh, K., Huang, H., Pickering, J., and Vancoille, E., 2004, “Influence of Microstructure on Ultraprecision Grinding of Cemented Carbides,” Int. J. Mach. Tools Manuf., 44(5), pp. 533–543. [CrossRef]
Verkerk, J., 1977, “Final Report Concerning Cirp Cooperative Work on the Characterization of Grinding Wheel Topography,” Ann. CIRP, 26(2), pp. 385–395.
Brecker, J., and Shaw, M., 1974, Measurement of the Effective Number of Cutting Points in the Surface of a Grinding Wheel, Proceedings of the International Conference on Production Engineering, Japan Society of Precision Engineers, Tokyo, Japan, pp. 740–745.
Shaw, M., 1972, Fundamentals of Grinding, Proceedings of the International Grinding Conference, McGraw-Hill Co., pp. 221–258.
Malkin, S., and Guo, C., 2008, Grinding Technology: Theory and Applications of Machining With Abrasives, Industrial Pr, New York.
Park, H., 2008, “Development of Micro-Grinding Mechanics and Machine Tools,” Ph.D. thesis, Georgia Institute of Technology, Atalnta, GA.
Klocke, F., and Kuchle, A., 2009, Manufacturing Processes 2: Grinding, Honing, Lapping, Springer–Verlag, Berlin, Germany.
Marinescu, I., Hitchiner, M., Uhlmann, E., and Inasaki, I., 2007, Handbook of Machining With Grinding Wheels, CRC, Boca Raton, FL.
Standard for Superabrasive Grain Sizes, Federation of European Producers of Abrasives, Standard 61-2009.
Basuray, P., Sahay, B., and Lal, G., 1981, “Surface Generated in Fine Grinding. Part 1 Probabilistic Model,” Int. J. Prod. Res., 19(6), pp. 677–688. [CrossRef]
Agarwal, S., and Rao, P. V., 2005, “A New Surface Roughness Prediction Model for Ceramic Grinding,” Proc. Inst. Mech. Eng., Part B, 219(11), pp. 811–819. [CrossRef]
Law, S., Wu, S., and Joglekar, A., 1973, “On Building Models for the Grinding Process,” ASME J. Eng. Ind., 95(4), pp. 983–991. [CrossRef]
Orioka, T., 1961, “Probabilistic Treatment on the Grinding Geometry,” Bull. Jpn. Soc. Grinding Eng., 1(1), pp. 27–29.
Mcadams, H., 1964, “Markov Chain Models of Grinding Profiles,” ASME J. Eng. Ind., 86(4), pp. 383–387. [CrossRef]
Law, S., and Wu, S., 1973, “Simulation Study of the Grinding Process,” ASME J. Eng. Ind., 95(4), pp. 972–978. [CrossRef]
Koshy, P., Jain, V., and Lal, G., 1997, “Stochastic Simulation Approach to Modelling Diamond Wheel Topography,” Int. J. Mach. Tools Manuf., 37(6), pp. 751–761. [CrossRef]
Hasegawa, M., 1974, “Statistical Analysis for the Generating Mechanism of Ground Surface Roughness,” Wear, 29(Compendex), pp. 31–39. [CrossRef]
Younis, M., and Alawi, H., 1984, “Probabilistic Analysis of the Surface Grinding Process,” Trans. Can. Soc. Mech. Eng., 8(4), pp. 208–213.
Koshy, P., Jain, V., and Lal, G., 1993, “A Model for the Topography of Diamond Grinding Wheels,” Wear, 169(2), pp. 237–242. [CrossRef]
Hwang, T., and Evans, C., 2000, “High Speed Grinding of Silicon Nitride With Electroplated Diamond Wheels, Part 2: Wheel Topography and Grinding Mechanisms,” ASME J. Manuf. Sci. Eng., 122(1), pp. 42–50. [CrossRef]
Kunz, J., and Mayor, J. R., 2012, “Stochastic Modeling of Microgrinding Wheel Topography,” ASME J. Micro Nano-Manuf., 1(2), p. 021004. [CrossRef]
Kunz, J., and Mayor, J. R., 2011, Static Grit Density Measurement Methods for Medium-Grit Diamond Microgrinding Wheels, 6th International Conference on MicroManufacturing, March 7–10, 2011, Tokyo, Japan.
Lowry, R., 1998, Concepts and Applications of Inferential Statistics, R.Lowry, ed., Vassar Stats: Website for Statistical Computation. http://vassarstats.net [Accessed Jan 3 2013].
Corder, G. W., and Foreman, D. I., 2009, Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach, John Wiley & Sons, NJ.
Anderson, T. W., and Darling, D. A., 1952, “Asymptotic Theory of Certain" Goodness of Fit" Criteria Based on Stochastic Processes,” Ann. Math. Stat., 23(2), pp. 193–212. [CrossRef]


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Fig. 3

Stitched imaged surface of 0.5 mm OD, #200 grit diamond grind wheel composed from 61 individual images

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Fig. 2

Microscope image of 1 mm OD, #220 grit diamond grind wheel in a microscope at 10× magnification

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Fig. 1

SEM image of 1 mm OD, metal bonded, #220 grit diamond grind wheel

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Fig. 4

Machine vision algorithm for locating individual grits

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Fig. 5

Effects of machine vision algorithm steps on select region of a #200 microgrinding wheel

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Fig. 16

Frequency PDF of measured circumferential grit spacings in wheel 6.2 with fitted distribution comparison between the currently used rayleigh distribution and proposed (a) lognormal distribution, and (b) loglogistic distribution

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Fig. 6

Bond thickness measurements showing no definite variation across different wheel diameters

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Fig. 7

Bond thickness measurements showed no definite variation across different wheel widths

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Fig. 8

Bond thickness measurements showed no definite variation across different grit sizes

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Fig. 11

Normal probability plot for the shank diameter error across all wheels

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Fig. 12

Normal probability plot for the wheel width error across all wheels

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Fig. 13

Histogram of static grit density residual error between experimental measurement and (a) numerical simulation model, and (b) analytic stochastic model

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Fig. 14

Potential scale effect of higher static grit density relative standard deviation in microgrinding wheels due to the few number of grits in the wheel

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Fig. 15

Histogram of the circumferential grit spacings in wheel 6.2

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Fig. 9

Normal probability plot for the measured wheel concentration number across all wheels

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Fig. 10

Normal probability plot for the measured bond thickness across all wheels




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