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RESEARCH PAPERS

Search-Guided Sampling to Reduce Uncertainty of Minimum Deviation Zone Estimation

[+] Author and Article Information
Ahmad Barari1

Faculty of Engineering and Applied Science,  University of Ontario Institute of Technology, Oshawa, Ontario, L1H 7K4 Canadaahmad.barari@uoit.ca

Hoda A. ElMaraghy2

Intelligent Manufacturing Systems Centre,  University of Windsor, Windsor, Ontario, N9B 3P4 Canadahae@uwindsor.ca

George K. Knopf3

Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, N6A 5B8 Canadagknopf@engga.uwo.ca

1

URL: http://publish.uwo.ca/∼abararia

2

Corresponding author. URL: www.ims.uwindsor.ca

3

URL: http://www.eng.uwo.ca/people/gknopf

J. Comput. Inf. Sci. Eng 7(4), 360-371 (Aug 17, 2007) (12 pages) doi:10.1115/1.2798114 History: Received February 12, 2007; Revised August 17, 2007

Integrating computational tasks in coordinate metrology and its effect on the inspection’s uncertainty is studied. It is shown that implementation of an integrated inspection system is crucial to reduce the uncertainty in minimum deviation zone (MDZ) estimation. An integrated inspection system based on the iterative search procedure and online MDZ estimation is presented. The search procedure uses the Parzen Windows technique to estimate the probability density function of the geometric deviations between the actual and substitute surfaces. The computed probability density function is used to recognize the critical points in the MDZ estimation and to identify portions of the surface that require further iterative measurements until the desired level of convergence is achieved. Reduction of the uncertainty in the MDZ estimation using the developed search method compared to the MDZ estimations using the traditional sampling methods is demonstrated by presenting experiments including both actual and virtual inspection data. The proposed search method can be used for assessing any geometric deviations when no prior assumptions about the fundamental form and distribution of the underlying manufacturing errors are required. The search method can be used to inspect and evaluate both primitive geometric features and complicated sculptured surfaces. Implementation of this method reduces inspection cost as well as the cost of rejecting good parts or accepting bad parts.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Traditional coordinate metrology system

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Figure 2

Integrated computation model for coordinate metrology

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Figure 5

Errors in 360 measured points

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Figure 8

Error Model 2—one-directional sinusoid wave (magnification: 100× times)

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Figure 9

Error Model 3—two-directional sinusoid waves (magnification: 100× times)

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Figure 10

Error Model 10—local error concentration (magnification: 100× times)

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Figure 11

Average inspection error of 100 times inspection of the second error model (one-directional waviness) for five different data capturing processes

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Figure 12

Stratified low density sampling of error Model 4 and the estimated probability density function

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Figure 13

Random high density sampling of error Model 4 and the estimated probability density

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Figure 14

Stratified high density sampling of error Model 4 and the estimated probability density function

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Figure 15

Stratified extreme density sampling of error Model 4 and the estimated probability density function

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Figure 16

Search method for inspection error Model 4 and the estimated probability density function

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Figure 3

Probability density function with positive maximum absolute Hessian

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Probability density function with negative maximum absolute Hessian

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MDZ of 360 measured points

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Figure 7

Error Model 1—machining errors (magnification: 100× times)

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