Research Papers

Stochastic Modeling of Microgrinding Wheel Topography

[+] Author and Article Information
Jacob A. Kunz

Graduate Research Assistant
e-mail: jacobakunz@gatech.edu

J. Rhett Mayor

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

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received May 4, 2012; final manuscript received March 3, 2013; published online May 2, 2013. Assoc. Editor: Hitoshi Ohmori.

J. Micro Nano-Manuf 1(2), 021004 (May 02, 2013) (11 pages) Paper No: JMNM-12-1028; doi: 10.1115/1.4024002 History: Received May 04, 2012; Revised March 03, 2013

Superabrasive microgrinding wheels are used for jig grinding of microstructures using various grinding approaches. The desire for increased final geometric accuracy in microgrinding leads to the need for improved process modeling and understanding. An improved understanding of the source of wheel topography characteristics leads to better knowledge of the interaction between the individual grits on the wheel and the grinding workpiece. Analytic stochastic modeling of the abrasives in a general grinding wheel is presented as a method to stochastically predict the wheel topography. The approach predicts the probability of the number of grits within a grind wheel, the individual grit locations within a given wheel structure, and the static grit density within the wheel. The stochastic model is compared to numerical simulations that imitate both the assumptions of the analytic model where grits are allowed to overlap and the more realistic scenario of a grind wheel where grits cannot overlap. A new technique of grit relocation through collective rearrangement is used to limit grit overlap. The results show that the stochastic model can accurately predict the probability of the static grit density while providing results two orders of magnitude faster than the numerical simulation techniques. It is also seen that grit overlap does not significantly impact the static grit density allowing for the simpler, faster analytic model to be utilized without sacrificing accuracy.

Copyright © 2013 by ASME
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Fig. 1

(a) Model of single-layered, spherical grit grinding wheel with a low concentration number, (b) diced grind pin with clean edge, and (c) end view of the diced pin

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Fig. 2

Summary of method for analytical calculation of number of grits in a grinding wheel

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Fig. 3

Grit position coordinate systems

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Fig. 4

Sampling of possible locations of grit i with known diameter Di

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Fig. 5

Bar representation of the intersection of grit i with a radial surface in a multi-layered wheel

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Fig. 6

Bar representation of the intersection of grit i with a radial surface in a single-layered wheel

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Fig. 7

Summary of method for analytical calculation of the probability of grit gi intersection a cylindrical surface with radius Rc

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Fig. 8

Summary of method for analytical stochastic calculation of static grit density for microgrinding wheels

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Fig. 9

Normal probability plot of the simulated number of grits required to fill a #1200 wheel

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Fig. 10

Relocation of a grit i that is overlapped by grit j [12]

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Fig. 11

Visualization of the relocating overlapping particle

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Fig. 12

(a) Static grit density mean and (b) static grit density standard deviation from analytic and simulation models for a #220, 1 mm OD single-layered microgrinding wheel

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Fig. 13

(a) Static grit density mean and (b) static grit density standard deviation from analytic and simulation models for a #1200, 1 mm OD multi-layered grinding wheel

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Fig. 14

Normal probability plot for a #1200 wheel at a radial distance of 439 μm from the wheel core



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