0
Research Papers

A Hull Normal Based Approach for Cylindrical Size Assessment

[+] Author and Article Information
Steven Turek

Computer-Aided Manufacturing Laboratory, School of Dynamic Systems, University of Cincinnati, Cincinnati, OH 45221

Sam Anand

Computer-Aided Manufacturing Laboratory, School of Dynamic Systems, University of Cincinnati, Cincinnati, OH 45221sam.anand@uc.edu

J. Manuf. Sci. Eng 133(1), 011011 (Feb 08, 2011) (9 pages) doi:10.1115/1.4003332 History: Received May 30, 2009; Revised December 14, 2010; Published February 08, 2011; Online February 08, 2011

Digital measurement devices, such as coordinate measuring machines, laser scanning devices, and digital imaging, can provide highly accurate and precise coordinate data representing the sampled surface. However, this discrete measurement process can only account for measured data points, not the entire continuous form, and is heavily influenced by the algorithm that interprets the measured data. The definition of cylindrical size for an external feature as specified by ASME Y14.5.1M-1994 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] matches the analytical definition of a minimum circumscribing cylinder (MCC) when rule no. 1 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] is applied to ensure a linear axis. Even though the MCC is a logical choice for size determination, it is highly sensitive to the sampling method and any uncertainties encountered in that process. Determining the least-sum-of-squares solution is an alternative method commonly utilized in size determination. However, the least-squares formulation seeks an optimal solution not based on the cylindrical size definition [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] and thus has been shown to be biased [Hopp, 1993, “Computational Metrology,” Manuf. Rev., 6(4), pp. 295–304; Nassef, and ElMaraghy, 1999, “Determination of Best Objective Function for Evaluating Geometric Deviations,” Int. J. Adv. Manuf. Technol., 15, pp. 90–95]. This work builds upon previous research in which the hull normal method was presented to determine the size of cylindrical bosses when rule no. 1 is applied [Turek, and Anand, 2007, “A Hull Normal Approach for Determining the Size of Cylindrical Features,” ASME, Atlanta, GA]. A thorough analysis of the hull normal method’s performance in various circumstances is presented here to validate it as a superior alternative to the least-squares and MCC solutions for size evaluation. The goal of the hull normal method is to recreate the sampled surface using computational geometry methods and to determine the cylinder’s axis and radius based upon it. Based on repetitive analyses of random samples of data from several measured parts and generated forms, it was concluded that the hull normal method outperformed all traditional solution methods. The hull normal method proved to be robust by having a lower bias and distributions that were skewed toward the true value of the radius, regardless of the amount of form error.

Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Error elements in CMM measurements; adapted from Ref. 13

Grahic Jump Location
Figure 2

Axial view of least-squares solution (5)

Grahic Jump Location
Figure 3

Axial view of MCC solution (5)

Grahic Jump Location
Figure 4

Discretized facet of a perfect cylinder (23)

Grahic Jump Location
Figure 5

Convex hull of 2D data set (23)

Grahic Jump Location
Figure 6

Modified unit dot product, cos(x)−1(23)

Grahic Jump Location
Figure 7

Convex hull of cylindrical data cluster (23)

Grahic Jump Location
Figure 8

Sampled plastic part

Grahic Jump Location
Figure 9

Sampled steel part

Grahic Jump Location
Figure 10

Plastic part (n=32)

Grahic Jump Location
Figure 16

Surface mesh of generated forms with varying axial form error

Grahic Jump Location
Figure 11

Steel part (n=32)

Grahic Jump Location
Figure 15

Steel part (n=128)

Grahic Jump Location
Figure 14

Plastic part (n=128)

Grahic Jump Location
Figure 13

Steel part (n=64)

Grahic Jump Location
Figure 12

Plastic part (n=64)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In