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Research Papers

Mathematical Foundations for Form Inspection and Adaptive Sampling

[+] Author and Article Information
Robin C. Gilbert

School of Industrial Engineering, University of Oklahoma, Room 124, 202 West Boyd Street, Norman, OK 73019-0631webmaster@robingilbert.com

Shivakumar Raman1

School of Industrial Engineering, University of Oklahoma, Room 124, 202 West Boyd Street, Norman, OK 73019-0631raman@ou.edu

Theodore B. Trafalis

School of Industrial Engineering, University of Oklahoma, Room 124, 202 West Boyd Street, Norman, OK 73019-0631ttrafalis@ou.edu

Suleiman M. Obeidat, Juan A. Aguirre-Cruz

School of Industrial Engineering, University of Oklahoma, Room 124, 202 West Boyd Street, Norman, OK 73019-0631

1

Corresponding author.

J. Manuf. Sci. Eng 131(4), 041001 (Jul 07, 2009) (8 pages) doi:10.1115/1.3160582 History: Received September 07, 2007; Revised November 25, 2008; Published July 07, 2009

Nonlinear forms such as the cone, sphere, cylinder, and torus present significant problems in representation and verification. In this paper we examine linear and nonlinear forms using a heavily modified support vector machine (SVM) technique. The SVM approach applied to regression problems is used to derive quadratic programming problems that allow for generalized symbolic solutions to nonlinear regression. We have tested our approach to several geometries and achieved excellent results even with small data sets, making this method robust and efficient. More importantly, we identify process or inspection tendencies that could help in better designing the processes. Adaptive feature verification can be achieved through effective identification of the manufacturing pattern.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A typical interpolated deformation surface of a face-milled plate. All inspected plates had saddle shaped deformation surfaces. The sides with the highest elevation are the sides of the plates that were clamped during machining

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Figure 2

Interpolated deformation profile of the cylinder (left): the deformation along the x-axis is plotted for y=0.3375 in., y=0.6750 in., and y=1.0125 in. Longitudinal view of the cylinder at y=0.6750 in. with its interpolated deformation surface amplified 50 times (right).

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Figure 3

Contour plot of the interpolated deformation profile of the cone (left). Cross view of the cone at y=0 in. with its interpolated deformation surface amplified ten times (right).

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Figure 4

Interpolated deformation surface of the cone if the desired angle at the top was 60.774 deg

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Figure 5

Interpolated deformation profile of the cylinder (left). Cross view of the sphere at y=0 in. with its interpolated deformation surface amplified ten times (left)

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