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Research Papers

Uncertainty in Machining: Workshop Summary and Contributions

[+] Author and Article Information
Tony L. Schmitz

 Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC 28223

Jaydeep Karandikar, Nam Ho Kim

 Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611

Ali Abbas

 Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61820

The uncertainty (of a measurement) is defined in Ref. [1] as a “parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand,” or a particular quantity subject to measurement.

The subscript m denotes measured values from cutting experiments. The measured values were assumed to be statistically independent.

Graduate student supported by National Science Foundation funds.

J. Manuf. Sci. Eng 133(5), 051009 (Oct 17, 2011) (9 pages) doi:10.1115/1.4004923 History: Received August 12, 2010; Revised August 19, 2011; Published October 17, 2011; Online October 17, 2011

A National Science Foundation-sponsored workshop was held from Feb. 24–26, 2010 in Arlington, VA. The purpose of this “Uncertainty in machining” workshop was to address uncertainty and risk in machining and related manufacturing operations. The application of decision theory, which defines how rational decision makers should make decisions in the presence of uncertainty, was discussed. A summary of the meeting outcomes is presented. To aid in the application of decision theory to manufacturing process modeling, an example of Bayesian inference for the well-known mechanistic turning force model is provided. The discrete grid method is presented, and updating is performed using force data from the Assessment of Machining Models study completed by the National Institute of Standards and Technology.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of orthogonal cutting model (a positive side rake angle is shown; the tool’s rake face is inclined above the horizontal for a negative rake angle)

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Figure 2

Prior distribution of φc (top) and bivariate normal distribution of τs and βa (bottom)

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Figure 3

Prior distributions of Kf (top) and Kt (bottom)

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Figure 4

Figure to illustrate calculation of the likelihood function. The distributions (from left to right) have mean values of φc  = {16.75, 17.0, and 17.5} deg. The value of the distributions for the φc value (17.03 deg), which corresponds to the hc measurement (0.501 mm) from Test #1, is the likelihood value.

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Figure 5

Likelihood distribution of φc for hc  = 0.501 mm measurement from Test #1 (top) and posterior distribution of φc after the first update (bottom)

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Figure 6

Likelihood joint distribution of τs and βa for force measurements from Test #1; Ff  = 372 N (top) and Ft  = 565.2 N (bottom)

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Figure 7

Posterior joint distribution of τs and βa after the first update using force measurement data from Test #1; Ff  = 372 N and Ft  = 565.2 N. The posterior was obtained by a point-by-point multiplication of the prior (see Fig. 2) and the likelihood functions for Ff and Ft (see Fig. 6) and a normalization to obtain a unit volume under the surface.

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Figure 8

Posterior distributions of φc for all updates and their comparison with the prior

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Figure 9

Posterior joint distributions of τs and βa after the second update (top left), third update (top right), fourth update (bottom left), and fifth update (bottom right)

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Figure 10

Prior and posterior distributions for Kt

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Figure 11

Prior and posterior distributions for Kf

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Figure 12

Comparison of the measured and predicted forces, Ft and Ff  , using the prior and posterior coefficient distributions (αr  = 5 deg)

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Figure 13

Comparison of the measured and predicted forces, Ft and Ff  , using the prior and posterior coefficient distributions (αr  =−7 deg)

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