Form error estimation techniques based on discrete point measurements can lead to significant errors in form tolerance evaluation. By modeling surface profiles as random variables, we show how sample size and fitting techniques affect form error estimation. Depending on the surface characteristics, typical sampling techniques can result in estimation errors of as much as 50 percent. Another issue raised in the fitting approach is the metric p selection for the fitting objective. We show that for p = 2 and p = ∞, the selection does not appear to significantly affect the estimation of form errors.

1.
ANSI Y14.5M, 1982, Dimensioning and Tolerancing, American National Standard, Engineering Drawings and Related Documentation Practices, The American Society for Mechanical Engineers, New York.
2.
Anderson
and
Osborne
,
1977
, “
Discrete, Nonlinear Approximation Problems in Polyhedral Norms. A Levenberg-like Algorithm
,”
Numer. Math.
,
28
, pp.
157
170
.
3.
Barrodale and Phillips, 1975, “Solution of an Overdetermined System of Linear Equation in the Chebychev Norm,” ACM Trans. on Math. Software, 1, pp. 264–270, 1975.
4.
Caskey, G., et al., 1991, “Sampling Techniques for Coordinate Measuring Machines,” Proc. of the 1991 NSF Design and Mfg. Sys. Conf, January 1991, pp. 779–786.
5.
Caskey, G., et al., 1992, “Sampling Techniques for Coordinate Measuring Machines,” Proc. of the 1992 NSF Design and Mfg. Sys. Conf., January 1992, pp. 983–988.
6.
Dhanish
P. B.
, and
Shunmugam
M. S.
,
1991
, “
An Algorithm for Form Error Evaluation—Using the Theory of Discrete and Linear Chebyshev Approximation
,”
Computer Methods in Applied Mechanics and Engineering
,
92
, pp.
309
324
.
7.
Etesami
F.
, and
Qiao
H.
,
1989
, “
Analysis of Two-dimensional Measurement Data for Automated Inspection
,”
Journal of Manufacturing Systems
, Vol.
9
, No.
1
, pp.
21
34
.
8.
Huang
S. T.
,
Fan
K. C.
, and
Wu
J. H.
, “
New Minimum Zone Method for Evaluating Straightness Errors
,”
Precision Engineering
, Vol.
15
, No.
3
, July
1993
, pp.
158
164
.
9.
Gonin, R., and Money, A. H., 1989, Nonlinear Lp-norm Estimation, Marcel Dekker, New York.
10.
He
J. R.
,
1991
, “
Estimating the Distributions of Manufactured Dimensions With Beta Probability Density Function
,”
Int. J. Mach. Tools Manufact.
, Vol.
31
, No.
3
, pp.
383
396
.
11.
Hocken, R. J., Raja, J., and Babu, U., “Sampling Issues in Coordinate Metrology,” Proceedings of the 1993 International Forum on Dimensional Tolerancing and Metrology, Srinivasan, V. and Voelcker, H. B., eds., CRTD-Vol. 27, pp. 97–111.
12.
Hopp, T. H., 1993, “Computational Metrology,” Proceedings of the 1993 International Forum on Dimensional Tolerancing and Metrology, Srinivasan, V. and Voelcker, H. B., eds, CRTD-Vol. 27, pp. 207–217.
13.
Kanada
T.
, and
Suzuki
S.
, “
Application of Several Computing Techniques for Minimum Zone Straightness
,”
Precision Engineering
, Vol.
15
, No.
4
, Oct.
1993
, pp.
274
280
.
14.
Kendall, M., and Stuart, A., 1977, The Advanced Theory of Statistics, Vol. I, Distribution Theory, Fourth edition, Charles Griffin & Company Limited, London & High Wycombe.
15.
Menq, C. H., Yau, H. T., and Lai, G. Y., 1990, “Statistical Evaluation of Form Tolerances Using Discrete Measurement Data,” Proceedings of the Symposium on Advances in Integrated Product Design and Manufacturing, 1990 ASME Winter Annual Meeting, November 25–30, Dallas, TX, pp. 135–150.
16.
Murthy
T. S. R.
, and
Abdin
S. Z.
,
1980
, “
Minimum Zone Evaluation of Surfaces
,”
Int. J. Mach. Tool Des. Res.
, Vol.
20
, No.
3
, pp.
123
136
.
17.
Roy
U.
, and
Zhang
X.
,
1992
, “
Establishment of a Pair of Concentric Circles With the Minimum Radial Separation for Assessing Roundness Error
,”
Computer Aided Design
, Vol.
24
, No.
3
, pp.
161
168
.
18.
Shunmugam
M. S.
, “
On Assessment of Geometric Errors
,”
1986
,
Int. J. Prod. Res.
, Vol.
24
, No.
2
, pp.
413
425
.
19.
Shunmugam
M. S.
,
1987
a, “
New Approach for Evaluating Form Errors of Engineering Surfaces
,”
Computer-Aided Design
, Vol.
19
, No.
7
, pp.
368
374
.
20.
Shunmugam
M. S.
,
1987
b, “
Comparison of Linear and Normal Deviations of Forms of Engineering Surfaces
,”
Precision Engineering
, Vol.
9
, No.
2
, pp.
96
102
.
21.
Shunmugam
M. S.
,
1990
, “
Establishing Reference Figures for Form Evaluation of Engineering Surfaces
,”
Journal of Manufacturing Systems
, Vol.
10
, No.
4
, pp.
314
321
.
22.
Stout, Davis and Sullivan, 1990, Atlas of Machined Surfaces, Chapman and Hull.
23.
Traband
M. T.
,
Joshi
S.
,
Wysk
R. A.
,
Cavalier
T. M.
,
1989
, “
Evaluation of Straightness and Flatness Tolerances Using the Minimum Zone
,”
Manufacturing Review
, Vol.
2
, No.
3
, pp.
189
195
.
24.
Woo, T., Liang, R., and Pollock, S., 1993, “Hammersley Sampling for Efficient Surface Coordinate Measurements,” Proc. of the 1993 NSF Design and Mfg. Sys. Conf., January 1993, pp. 1489–1495.
25.
Session 10, “The Current State of Affairs,” Proceedings of the 1993 International Forum on Dimensional Tolerancing and Metrology, Srinivasan, V., and Voelcker, H. B., eds., CRTD-Vol. 27, pp. 297–307.
This content is only available via PDF.
You do not currently have access to this content.