Complex forms such as conicity have been largely ignored in the coordinate form literature, in spite of the sufficient need to inspect them in parts such as tapered rollers in bearings. This paper attempts to develop guidelines for inspection of cones and conical frustums using probe-type coordinate measuring machines. The sampling problem, the path determination, and fitting of form zones are each addressed in detail. Moreover, an integrative approach is taken for form verification and detailed experimental analysis is conducted as a pilot study for demonstrating the need for the same. Three separate sampling methods are applied: Hammersley, Halton-Zaremba, and Aligned Systematic; at various sample sizes using sampling theory and prior work in two-dimensional sampling. Linear and nonlinear deviations are formulated using optimization and least-squared methods and solved to yield competitive solutions. Comprehensive experimental analysis investigated issues of model adequacy, nesting, interactions, and individual effects, while studying conicity as a response variable in the light of sampling strategies, sizes, cone surface areas, and fitting methods. In summary, an orderly framework for sampling and fitting cones is developed which can lead to the development of comprehensive standards and solutions for industry.
Issue Section:
Technical Papers
1.
Liang
, R.
, Woo
, T. C.
, and Hsieh
, C. C.
, 1998
, “Accuracy and Time in Surface Measurement, Part 2: Optimal Sampling Sequence
,” ASME J. Manuf. Sci. Eng.
, 120
(1
), pp. 150
–155
.2.
Woo
, T. C.
, and Liang
, R.
, 1993
, “Dimensional Measurement of Surfaces and Their Sampling
,” Comput.-Aided Des.
, 25
(4
), pp. 233
–239
.3.
Woo
, T. C.
, Liang
, R.
, Hsieh
, C. C.
, and Lee
, N. K.
, 1995
, “Efficient Sampling for Surface Measurements
,” J. Manuf. Syst.
, 14
(5
), pp. 345
–354
.4.
Lee
, G.
, Mou
, J.
, and Shen
, Y.
, 1997
, “Sampling Strategy Design for Dimensional Measurement of Geometric Features Using Coordinate Measuring Machine
,” Int. J. Mach. Tools Manuf.
, 37
(7
), pp. 917
–934
.5.
ASME Y14.5M-1994., 1995, Dimensioning and Tolerancing, The American Society of Mechanical Engineers, New York, NY.
6.
Traband
, M. T.
, Joshi
, S.
, Wysk
, R. A.
, and Cavalier
, T. M.
, 1989
, “Evaluation of Straightness and Flatness Tolerances Using the Minimum Zone
,” Manufacturing Review
, 2
(3
), pp. 189
–195
.7.
Hong
, J. T.
, Liao
, Y. S.
, and Fan
, K. C.
, 1991
, “A Computational Geometry Approach to Minimum Zone Evaluation of Straightness
,” J. Chin. Inst. Eng.
, 14
(5
), pp. 463
–470
.8.
Roy
, U.
, and Zhang
, X.
, 1992
, “Establishment of a Pair of Concentric Circles with the Minimum Radial Separation for Assessing Roundness Error
,” Comput.-Aided Des.
, 24
(3
), pp. 161
–168
.9.
Huang
, S. T.
, Fan
, K. C.
, and Wu
, J. H.
, 1993
, “A New Minimum Zone Method for Evaluating Straightness Errors
,” Precis. Eng.
, 15
(3
), pp. 158
–165
.10.
Huang
, S. T.
, Fan
, K. C.
, and Wu
, J. H.
, 1993
, “A New Minimum Zone Method for Evaluating Flatness Errors
,” Precis. Eng.
, 15
(1
), pp. 25
–32
.11.
Shunmugam
, M. S.
, 1986
, “On Assessment of Geometric Errors
,” Int. J. Prod. Res.
, 24
(2
), pp. 413
–425
.12.
Shunmugam
, M. S.
, 1987
, “Comparison of Linear and Normal Deviations of Forms of Engineering Surfaces
,” Precis. Eng.
, 9
(2
), pp. 96
–102
.13.
Shunmugam
, M. S.
, 1987
, “New Approach for Evaluating Form Errors of Engineering Surfaces
,” Comput.-Aided Des.
, 19
(7
), pp. 368
–374
.14.
Tsukada
, T.
, Kanada
, T.
, and Liu
, S.
, 1988
, “Method for the Evaluation of Form Errors of Conical Tapered Parts
,” Precis. Eng.
, 10
(1
), pp. 8
–12
.15.
Kim, H. M., and Lee, B. C., 1997, “Geometric Form Evaluation of Cone Based on the Minimum Zone Criteria,” Proceedings of the Twelfth Annual Meeting of the American Society of Precision Engineering, ASPE, Norfolk, Virginia, pp. 86–89.
16.
Chatterjee
, G.
, and Roth
, B.
, 1998
, “Chebychev Approximation Methods for Evaluating Conicity
,” Journal of the International Measurement Confederation
, 23
(2
), pp. 63
–76
.17.
Menq, C. H., Yau, H. T., Lai, G. Y., and Miller, R. A., 1990, “Statistical Evaluation of Form Tolerances Using Discrete Measurement Data,” American Society of Mechanical Engineers, Production Engineering Division (Publication) PED, Vol. 47, pp. 135–149.
18.
Liang
, R.
, Woo
, T. C.
, and Hsieh
, C. C.
, 1998
, “Accuracy and Time in Surface Measurement, Part 1: Mathematical Foundations,”
ASME J. Manuf. Sci. Eng.
, 120
(1
), pp. 141
–149
.19.
Kim
, W. S.
, and Raman
, S.
, 2000
, “On the Selection of Flatness Measurement Points in Coordinate Measuring Machine Inspection
,” Int. J. Mach. Tools Manuf.
, 40
(3
), pp. 427
–443
.20.
Dowling
, M. M.
, Griffin
, P. M.
, Tsui
, K. L.
, and Zhou
, C.
, 1997
, “Statistical Issues in Geometric Feature Inspection Using Coordinate Measuring Machines
,” Technometrics
, 39
(1
), pp. 3
–17
.21.
Murthy
, T. S. R.
, and Abdin
, S. Z.
, 1980
, “Minimum Zone Evaluation of Surfaces
,” Int. J. Mach. Tools Des. Res.
, 20
, pp. 123
–136
.22.
Roy
, U.
, 1995
, “Computational Methodologies for Evaluating Form and Positional Tolerances in a Computer Integrated Manufacturing System
,” Int.J. Adv. Manuf. Tech.
, 10
(2
), pp. 110
–117
.23.
Chetwynd
, D. G.
, 1979
, “Roundness Measurement Using Limacons
,” Precis. Eng.
, 1
(3
), pp. 137
–141
.24.
Chetwynd
, D. G.
, 1985
, “Applications of Linear Programming to Engineering Metrology
,” Proceedings of the Institute of Mechanical Engineers
, 199
(B2
), pp. 93
–100
.25.
Carr
, K.
, and Ferreira
, P.
, 1995
, “Verification of Form Tolerances Part I: Basic Issues, Flatness, and Straightness
,” Precis. Eng.
, 17
(2
), pp. 131
–143
.26.
Carr
, K.
, and Ferreira
, P.
, 1995
, “Verification of Form Tolerances Part II: Cylindricity and Straightness of a Median Line
,” Precis. Eng.
, 17
(2
), pp. 144
–156
.27.
Wang
, Y.
, 1992
, “Minimum Zone Evaluation of Form Tolerances
,” Manufacturing Review
, 5
(3
), pp. 213
–220
.28.
Suen
, D. S.
, and Chang
, C. N.
, 1997
, “Application of Neural Network Interval Regression Method for Minimum Zone Circle Roundness
,” Meas. Sci. Technol.
, 8
(3
), pp. 245
–252
.29.
Sharma
, R.
, Rajagopal
, K.
, and Anand
, S.
, 2000
, “A Genetic Algorithm Based Approach for Robust Evaluation of Form Tolerances
,” J. Manuf. Syst.
, 19
(1
), pp. 46
–57
.30.
Cochran, W. G., 1977, Sampling Techniques, 3rd Ed., John Wiley & Sons, Inc., New York.
31.
Sukhatme, P. V., and Sukhatme, B. V., 1970, Sampling Theory of Surveys, With Applications, 2nd Ed., Iowa State University Press, Ames, Iowa.
32.
Montgomery, D. C., 1997, Design and Analysis of Experiments, 4th Ed., John Wiley & Sons, Inc, New York.
33.
Prakasavudhisarn, C., 2002, “Dimensional Measurement of Conical Features Using Coordinate Metrology,” Ph.D. Dissertation, University of Oklahoma, Norman, OK.
34.
Badar
, A.
, Raman
, S.
, and Pulat
, S.
, 2002
, “Intelligent Search-based Selection of Sample Points for Form Error Estimation
,” ASME J. Manuf. Sci. Eng.
, in press.35.
Malyscheff
, A.
, Trafalis
, T. B.
, and Raman
, S.
, 2002
, “From Support Vector Machine Learning to the Determination of the Minimum Enclosing Zone
,” Computers and Industrial Engineering
, 42
(1
), pp. 59
–74
.36.
Prakasvudhisarn, C., Trafalis, T. B., and Raman, S., 2002, “Determination of the Minimum Enclosing Zone for Straightness and Flatness Using Support Vector Regression,” Proceedings of ANNIE.
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