Tutorial AB: Measurement capability

Books	Drake, Dimensioning and Tolerancing Handbook, ch. 20 (measurement systems analysis) and ch. 25 (gauge repeatability and reproducibility)
Standards	ISO 14253-1 (decision rules), ANSI/NCSL Z540.3 (test uncertainty ratio), AIAG MSA
You learn	Measurement uncertainty U on PMI, TUR, guard-banded acceptance limits, Analysis › Gauge Study
Sizes	A plate 60 × 40 × 12 with a bore Ø20 H7

A tolerance is only as good as the measurement that checks it. A caliper reading of 12.04 on a 12 ±0.05 thickness does not prove that the part is good. The inspection method’s uncertainty belongs with the characteristic.

The inspection methods' uncertainties are ours. The first gauge study uses the ranges of Drake’s worked example.

Step by step

1. The plate

The plate is made by script. Its datums are A, B and C, the bore is positioned Ø0.2 to A|B|C (RFS, as in Drake’s gauge study), and the general tolerances are ISO 2768-mK.

2. The characteristics and their methods

In each PMI dialog, Measurement uncertainty U is the expanded uncertainty of the method:

Characteristic	U	Method
Bore Ø20 H7	0.002	bore gauge
Thickness 12 ±0.05	0.01	micrometer
Flatness 0.01 of the top	0.004	surface plate and indicator

Characteristic

Method

Bore Ø20 H7

0.002

bore gauge

Thickness 12 ±0.05

0.01

micrometer

Flatness 0.01 of the top

0.004

surface plate and indicator

3. The inspection plan

PMI › Inspection Plan adds a TUR and the acceptance limits to each characteristic:

U 0.002: TUR 5.2:1 (meets 4:1); accept 20.002 to 20.019 (ISO 14253-1)
U 0.010: TUR 5.0:1 (meets 4:1); accept 11.960 to 12.040 (ISO 14253-1)
U 0.004: TUR 1.2:1 (below 4:1: guard band or a better method); accept 0.006 max (ISO 14253-1)

A bore reading of 20.020 is inside the tolerance but within U of its limit, so it proves nothing. The flatness check uses 80 % of its tolerance on uncertainty: accept up to 0.006, or measure it better.

TUR and acceptance limits in the inspection plan

4. Drake’s gauge study

Select the position frame, then Analysis › Gauge Study: gauge CMM, ten parts with two readings each, and spread 3 sigma (Drake ch. 25). The average range is 0.032, so σ = 0.032 / 1.128 = 0.0284 and 3σ = 0.085: 42.6 % of the 0.2 tolerance. That is over 30 %, so the measurement system is not acceptable, as in the book. With AIAG’s 6σ the share would be twice that.

5. An air gauge on the bore

The same study on the bore H7 with an air gauge, at 6σ, uses under 7 % of the 0.021 tolerance: acceptable. The study stays in the Part Navigator beside the PMI it qualifies, and recomputes if the tolerance changes.

The replay

#	In the book (NX)	In FreeCAD NX-Style	Result	Notes
AB1	The bearing plate: a bore Ø20 positioned Ø0.2 to A\|B\|C (RFS, as in Drake’s gauge study)	modelled by script, datums and frame made as in tutorial T	differs	datum feature A; datum feature B; datum feature C; position \| Ø0.200 \| A \| B \| C
AB2	Rapid Dimension: the bore Ø20 H7, checked with a bore gauge, U = 0.002	1 face(s) selected + ribbon 'PMI › Dimension > Rapid Dimension'; 'H7' typed, measurement uncertainty 0.002 typed; MB2 = OK	differs	Ø20.000 H7 (+0.021/0)
AB3	Rapid Dimension: the thickness 12 ±0.05, measured with a micrometer, U = 0.01	2 face(s) selected + ribbon 'PMI › Dimension > Rapid Dimension'; ±0.05 and the uncertainty typed; MB2 = OK	differs	12.000 ±0.050
AB4	Feature Control Frame: the top face flat to 0.01, on a surface plate with an indicator, U = 0.004	1 face(s) selected + ribbon 'PMI › Annotation > Feature Control Frame'; Flatness, 0.01, the uncertainty typed; MB2 = OK	differs	flatness \| 0.010
AB5	Inspection Plan: each method’s TUR and the ISO 14253-1 acceptance limits	ribbon 'PMI › Inspection > Inspection Plan'	differs	the bore is accepted only from 20.002 to 20.019, the thickness from 11.960 to 12.040: the specification less U at each limit, so no part is accepted on a doubtful reading. The flatness check uses 80 % of its tolerance (TUR 1.25): accept up to 0.006, or find a better method. NX has no measurement capability in its PMI
AB6	Gauge Study on the position Ø0.2: Drake’s worked example (ten parts, two readings each)	the frame selected + ribbon 'Analysis › Tolerance > Gauge Study'; gauge, 20 readings and the spread typed; MB2 = OK	differs	average range 0.032, σ = 0.0284, 3σ = 0.085 mm: 42.6 % of the tolerance, unacceptable (Drake: 42.6 %, over 30 %). With AIAG’s 6σ it would be twice that
AB7	Gauge Study on the bore Ø20 H7 with an air gauge	the bore’s PMI selected + ribbon 'Analysis › Tolerance > Gauge Study'; readings typed; 6σ; MB2 = OK	differs	σ = 0.23 µm, 6σ uses 6.6 % of the 0.021 tolerance: acceptable. The study is kept in the part, beside the PMI it qualifies
AB8	The bearing plate with its PMI	render of the graphics window	same	6.5% of the view shows the part

In the book (NX)

In FreeCAD NX-Style

Result

Notes

AB1

The bearing plate: a bore Ø20 positioned Ø0.2 to A|B|C (RFS, as in Drake’s gauge study)

modelled by script, datums and frame made as in tutorial T

differs

datum feature A; datum feature B; datum feature C; position | Ø0.200 | A | B | C

AB2

Rapid Dimension: the bore Ø20 H7, checked with a bore gauge, U = 0.002

1 face(s) selected + ribbon 'PMI › Dimension > Rapid Dimension'; 'H7' typed, measurement uncertainty 0.002 typed; MB2 = OK

differs

Ø20.000 H7 (+0.021/0)

AB3

Rapid Dimension: the thickness 12 ±0.05, measured with a micrometer, U = 0.01

2 face(s) selected + ribbon 'PMI › Dimension > Rapid Dimension'; ±0.05 and the uncertainty typed; MB2 = OK

differs

12.000 ±0.050

AB4

Feature Control Frame: the top face flat to 0.01, on a surface plate with an indicator, U = 0.004

1 face(s) selected + ribbon 'PMI › Annotation > Feature Control Frame'; Flatness, 0.01, the uncertainty typed; MB2 = OK

differs

flatness | 0.010

AB5

Inspection Plan: each method’s TUR and the ISO 14253-1 acceptance limits

ribbon 'PMI › Inspection > Inspection Plan'

differs

the bore is accepted only from 20.002 to 20.019, the thickness from 11.960 to 12.040: the specification less U at each limit, so no part is accepted on a doubtful reading. The flatness check uses 80 % of its tolerance (TUR 1.25): accept up to 0.006, or find a better method. NX has no measurement capability in its PMI

AB6

Gauge Study on the position Ø0.2: Drake’s worked example (ten parts, two readings each)

the frame selected + ribbon 'Analysis › Tolerance > Gauge Study'; gauge, 20 readings and the spread typed; MB2 = OK

differs

average range 0.032, σ = 0.0284, 3σ = 0.085 mm: 42.6 % of the tolerance, unacceptable (Drake: 42.6 %, over 30 %). With AIAG’s 6σ it would be twice that

AB7

Gauge Study on the bore Ø20 H7 with an air gauge

the bore’s PMI selected + ribbon 'Analysis › Tolerance > Gauge Study'; readings typed; 6σ; MB2 = OK

differs

σ = 0.23 µm, 6σ uses 6.6 % of the 0.021 tolerance: acceptable. The study is kept in the part, beside the PMI it qualifies

AB8

The bearing plate with its PMI

render of the graphics window

same

6.5% of the view shows the part

Result	Means
same	The book’s NX steps work as written.
differs	It works, but the FreeCAD way is different; the notes say how.
limit	The book’s way fails in FreeCAD itself; a workaround follows in the next steps.
missing	FreeCAD has no such function; a stand-in follows.
skipped	Not replayed; the notes give the reason.
FAILED	Did not work.

Result

Means

same

The book’s NX steps work as written.

differs

It works, but the FreeCAD way is different; the notes say how.

limit

The book’s way fails in FreeCAD itself; a workaround follows in the next steps.

missing

FreeCAD has no such function; a stand-in follows.

skipped

Not replayed; the notes give the reason.

FAILED

Did not work.

What differs from NX

NX’s PMI has no measurement uncertainty, TUR or gauge study; quality systems hold them. These tools are NX-Style’s (Inspection). The range method of one operator gives repeatability only; studies with several operators (reproducibility) are not implemented.