Modern inspection systems such as coordinate measurement machines generate discrete three dimensional coordinates representing points from the surface of a manufactured part. These coordinates must be compared to a target or nominal geometry to determine if the part conforms to specification. Quite often a least squares fit or a min-max fit are employed to determine the part geometry. However, as described in Part 1 of this paper, acceptable deviations are often specified as tolerance zones about the nominal geometry. Part 1 of this paper presents a zone fitting algorithm having an objective of placing the sampled data points within a specified tolerance zone. If all of the points fit within the zone, the part is passed. This pass/fail result does not provide information as to the quality of the part. The question that is not answered is “Did the points just fit into the tolerance zone, or did the points fit with ample space remaining?” This question is important as it informs production personnel whether their processes are operating well within specifications or just barely within specifications. In this part of the paper, the zone fitting method developed in Part 1 of this paper is extended to a minimum zone evaluation. This can be formulated as a one dimensional search for the critical value of the zone fitting objective function. The minimum zone evaluation algorithm developed in this paper can be applied to an arbitrary geometry profile evaluation. A number of examples are presented to demonstrate its capabilities.

1.
ASME Y14.5M-1994, 1994 National Standard on Dimensioning and Tolerancing, American Society of Mechanical Engineers, New York, NY.
2.
Carr
K.
, and
Ferreira
P.
,
1995
a, “
Verification of Form Tolerances Part I: Basic Issues, Flatness and Straightness
,”
Precision Engineering
, Vol.
17
, pp.
131
143
.
3.
Carr
K.
, and
Ferreira
P.
,
1995
, “
Verification of Form Tolerances Part II: Cylindricity and Straightness of a Median Line
,”
Precision Engineering
, Vol.
17
, pp.
144
156
.
4.
Etesami
F.
, and
Qiao
H.
,
1990
, “
Analysis of Two-dimensional Measurement Data for Automated Inspection
,”
Journal of Manufacturing System
, Vol.
9
, pp.
21
34
.
5.
Huang
S. T.
,
Fan
K. C.
, and
Wu
J. H.
,
1993
a, “
A New Minimum Zone Method for Evaluating Straightness Errors
,”
Precision Engineering
, Vol.
15
, pp.
158
165
.
6.
Huang
S. T.
,
Fan
K. C.
, and
Wu
J. H.
,
1993
b, “
A New Minimum Zone Method for Evaluation Flatness Errors
,”
Precision Engineering
, Vol.
15
, pp.
25
32
.
7.
Kanada
T.
, and
Suzuki
S.
,
1993
a, “
Evaluation of Minimum Zone Flatness by Means of Nonlinear Optimization Techniques and Its Verification
,”
Precision Engineering
, Vol.
15
, pp.
93
98
.
8.
Kanada
T.
, and
Suzuki
S.
,
1993
b, “
Application of Several Computing Techniques for Minimum Zone Straightness
,”
Precision Engineering
, Vol.
15
, pp.
274
280
.
9.
Murthy
T. S. R.
, and
Abdin
S. Z.
,
1980
, “
Minimum Zone Evaluation of Surfaces
,”
International Journal of Machine Tool Design and Research
, Vol.
20
, pp.
123
136
.
10.
Shunmugan
M. S.
,
1987
, “
New Approach for Evaluating Form Errors of Engineering Surfaces
,”
Computer-Aided Design
, Vol.
19
, pp.
368
374
.
11.
Wang
Y.
,
1992
. “
Minimum Zone Evaluation of Form Tolerances
,”
Manufacturing Review
, Vol.
5
, No.
3
, pp.
213
220
.
This content is only available via PDF.
You do not currently have access to this content.