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SIM Regional Comparison on
The Calibration of Internal and External Diameter Standards
SIM.L-K4.2009
FINAL REPORT
July 2012
Theodore Doiron (NIST), J. A. Pires Alves (INMETRO), Bruno R. Gastaldi (INTI), and
Guillermo Navarrete (CENAM)
Contents
1. Introduction ………………………………………………………. 2
2. Organization ……………………………………………………… 3
3. Descriptions of the Artifacts……………………………………….. 4
4. Measurement Instructions and Data Reporting…………………….. 4
5. Measurement Methods and Instruments…………………………… 5
6. Stability of Artifacts……………………………………………….. 5
7. Measurement Results and Uncertainty Components ……………..... 6
8. Reference Value…...…………………………………………………. 7
9. Report of Results…....................................................................... 7
10. Conclusions …………………………………………………………. 9
Appendix A: Summary of Data……………………………………… 10
Appendix B: Uncertainty Budgets…………………………………….. 12
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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1. Introduction
The metrological equivalence of national measurement standards and of calibration certificates
issued by national metrology institutes is established by a set of key comparisons chosen and
organized by the Consultative Committees of the CIPM or by the regional metrology
organizations in collaboration with the Consultative Committees.
This regional comparison was performed with the National Institute of Standards and
Technology (NIST), as the pilot laboratory. The results of this regional comparison will
contribute and be included in the agreement for establishing the metrological equivalence. The
interregional CCL key comparison will be combined, where necessary, with regional
comparisons following the same protocol. Laboratories participating in both, the interregional
and the regional comparisons establish the link between the comparisons and assure their
equivalence.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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2. Organization
2.1 Participants
2.1.1 The general requirement for the participating laboratories is the ability to measure, by any
primary means, provided it is a measurement service to clients, the diameter of external
diameter standards within the range 2 mm to 100 mm and the diameter of internal
diameter standards within the range 5 mm to 100 mm. The uncertainty requirements for
the diameter measurements is set at approximately 200 nm at k = 1.
2.2 Participants details
Contact Person National Metrology Institute
Address
Tel: / Fax:
Email:
Ted Doiron NIST
Building 220, Rm B113
Gaithersburg, MD 20899
USA
Tel. +1-301-975-3472
Fax +1-301-975-8291
e-mail: doiron@nist.gov
Guillermo Navarrete CENAM
Km 4,5 Carretera a Los Cués
El Marqués, Querétaro
76246 MEXICO
(52-442) 211-05 00 to 05 est. 3285
e-mail: gnavarre@cenam.mx
Ing. Bruno R.
Gastaldi
Instituto Nacional De
Tecnologia Industrial Centro
Regional
Cordoba
Metrología Dimensional
Argentina
Teléfono (54 351)
4684835/4698304/4681662/4603974
Fax: (54 351) 4681021/ 4699459
e-mail: gastaldi@inti.gov.ar
J. A. Pires Alves INMETRO
Av. N. Sra. das Graças, 50 ;
Vila Operária; Xerém, Duque
de Caxias, CEP.: 25250-020,
R.J., Brazil
Phone Int 005521-6799036,
Fax Int 005521-6791505,
e-mail: jaalves@inmetro.gov.br
Coordinator:
Ted Doiron NIST
Building 220, Rm B113
Gaithersburg, MD 20899
USA
Tel. +1-301-975-3472
Fax +1-301-975-8291
e-mail: doiron@nist.gov
Table 1. Participating laboratories
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3. Description of the Artifacts
3.1 The package contains 4 ring gages made of steel and 5 cylinders made of steel. The thermal
expansion coefficient of the diameter artifacts has been supplied by the manufacturer and is
assumed to be 11.5 0.5 10-6
K-1
. The artifacts are identified in the following table.
Ring gages:
Identification Nominal diameter (mm) Expansion coeff.
(10-6
K-1
)
Manufacturer
2K97 11.95 11.5 0.5 (k = 1) Glastonbury Gage
NIST-3 25.0 11.5 0.5 (k = 1) Glastonbury Gage
AP-002/02 46.0 11.5 0.5 (k = 1) Glastonbury Gage
NIST-6 75.0 11.5 0.5 (k = 1) Glastonbury Gage
Cylinders:
Identification Nominal diameter (mm) Expansion coeff.
(10-6
K-1
)
Manufacturer
A1 3.0 11.5 0.5 (k = 1) Glastonbury Gage
PI-002 7.0 11.5 0.5 (k = 1) Glastonbury Gage
A4 23.0 11.5 0.5 (k = 1) Glastonbury Gage
L97 49.3 11.5 0.5 (k = 1) SIP
Table 2. Description of Artifacts
4. Measurement Instructions and Data Reporting
4.1 Diameter standards.
4.1.1 Before measurement, the artifacts have to be inspected for damage of the measurement
surfaces, particularly at the gaging points. Any damage must be recorded using the
appropriate forms in appendix B of the protocol.
4.1.2 The measurement item of interest is the diametrical distance between the nominal gauge
points, defined as mid-elevation along the gauge cylinder and in the diameter direction
specified by the engraved marks on the gauge.
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4.1.3 The measurement results must be appropriately corrected to the reference temperature of
20 C using the thermal expansion coefficients given in this document. Additional
corrections have to be applied according to the equipment and procedures used by each
laboratory.
4.1.4 If any artifacts are found to have a magnetic condition, the magnetism must be removed
per individual laboratory practices before the diameter measurements are performed. Note
this condition in the comments on the form in appendix B.
4.1.5 A laboratory may submit measurements from more than one measurement system as long
as the timetable is adhered to and that each measurement system is available to general
clients for measurement services.
5. Measurement Methods and Instruments
CENAM: SIP 305m one axis universal measuring machine calibrated with a laser interferometer.
The gauges were calibrated by comparison to master gauge blocks and ring gauges.
INMETRO: A coordinate measuring machine was used for comparison to master gauge blocks
and rings. The ring gauges were calibrated at PTB. An external laser interferometer was used in
place of the machine scales for the displacement measurements.
INTI: A SIP 420M length measuring machine was used for comparison to master gauge blocks.
An external laser interferometer was used in place of the machine scale for the measurements.
NIST: A coordinate measuring machine which has laser interferometers for scales was used for
all measurements. A precision sphere was used to calibrate the probe.
6. Stability of the Artifacts
The pilot laboratory measured the artifacts twice: at the beginning of the comparison (February
2008) and at the end of the artifact circulation (August 2010). Table 3 shows the results. The
artifacts were measured using both the M48 CMM and the 1D comparator or laser micrometer at
each re-measurement interval. No relevant damage was observed on the artifacts during the
circulation. The observed changes were very small with respect to the uncertainties.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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Gage ID
Nominal
(mm) Opening Closing Change Uncertainty
ring 2K97 11.95 0.284 0.310 0.026 0.110
ring NIST-3 25 -0.250 -0.266 -0.016 0.120
ring AP-002/02 46 16.495 16.528 0.033 0.130
ring NIST-6 75 0.442 0.459 0.017 0.140
plug A1 3 0.346 0.357 0.011 0.120
plug PI-002 7 0.941 0.912 -0.029 0.120
plug A4 23 0.437 0.485 0.048 0.140
plug L97 49.3 1.586 1.648 0.062 0.140
Table 3. Apparent changes in diameter between first and last measurements in micrometers.
7. Measurement Results and Uncertainty Components
Tables 4 and 5 show the results of the comparison participants. The figures are the deviations
from the nominal size of the artifacts in micrometers.
Participants were not given instructions on uncertainty budgets. The number of ways of
measuring diameter is so large that it was up to each lab to assign their uncertainty as they chose.
Table 4. Deviations from the nominal diameter as measured by each laboratory in micrometers.
Gage ID Nominal (mm)
NIST INMETRO INTI CENAM NIST
ring 2K97 11.95 0.284 0.330 0.400 0.276 0.310
ring NIST-3 25 -0.250 -0.490 -0.200 -0.038 -0.266
ring AP-002/02 46 16.495 16.480 16.520 16.543 16.528
ring NIST-6 75 0.442 0.330 0.520 0.443 0.459
plug A1 3 0.346 0.160 0.280 0.404 0.357
plug PI-002 7 0.941 0.750 0.880 1.045 0.912
plug A4 23 0.437 0.520 0.400 0.429 0.485
plug L97 49.3 1.586 1.660 1.790 1.680 1.648
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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Gage ID Nominal (mm)
NIST INMETRO INTI CENAM NIST
ring 2K97 11.95 0.058 0.130 0.150 0.110 0.058
ring NIST-3 25 0.058 0.140 0.150 0.120 0.058
ring AP-002/02 46 0.060 0.140 0.150 0.130 0.060
ring NIST-6 75 0.063 0.140 0.150 0.140 0.063
plug A1 3 0.022 0.100 0.130 0.120 0.022
plug PI-002 7 0.023 0.100 0.130 0.120 0.023
plug A4 23 0.036 0.100 0.130 0.140 0.036
plug L97 49.3 0.060 0.110 0.130 0.140 0.060
Table 5. Reported uncertainty (k = 1) of participants in micrometers.
8. Reference Value
The simple mean was used as the reference value. It was calculated using the average of the
NIST values and then again using both NIST results as separate entries. The changes were found
to be negligible. Further analysis was made using the weighted average for the reference value,
and again the differences were found to be negligible. Because of the small number of
participants and their general agreement, more sophisticated analysis did not seem warranted.
The reference value was taken as the average of all four laboratory results, using the first NIST
measurement only. The standard deviation of the mean was used as the uncertainty of the
reference value.
9. Report of Results
The agreement between the laboratories is presented in Table 6 and Figure 1. Table 7 and
Figure 2 give En values for the measurements. The En value is defined as
22
__
)]([)]([ xuxuk
xxE
i
i
n
where ix is the measurement result for laboratory i, with uncertainty
)( ixu , __
x is the reference value with uncertainty )(xu , and k is the coverage factor which in this
report we take to be 1.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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Gage ID Nominal
(mm) Reference Value
NIST INMETRO INTI CENAM NIST
2K97 11.95 0.323 -0.038 0.007 0.077 -0.047 -0.012
NIST-3 25 -0.245 -0.006 -0.245 0.045 0.207 -0.021
AP-002/02 46 16.509 -0.015 -0.029 0.011 0.034 0.019
NIST-6 75 0.434 0.008 -0.104 0.086 0.009 0.025
A1 3 0.297 0.048 -0.137 -0.017 0.107 0.060
PI-002 7 0.904 0.037 -0.154 -0.024 0.141 0.008
A4 23 0.447 -0.009 0.073 -0.047 -0.018 0.039
L97 49.3 1.679 -0.093 -0.019 0.111 0.001 -0.031
Table 6. Deviations from the Reference Value in micrometers.
Figure 1. The reference value was taken as the average of all four laboratory values. Only the
first value from NIST was used to preserve equal weighting of the results.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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Artifact and
Nominal (mm)
NIST INMETRO INTI CENAM
11.95 ring -0.30 0.03 0.25 -0.20
25 ring -0.03 -0.73 0.13 0.68
46 ring -0.12 -0.11 0.03 0.13
75 ring 0.06 -0.36 0.28 0.03
3 plug 0.43 -0.61 -0.06 0.41
7 plug 0.28 -0.66 -0.08 0.52
23 plug -0.11 0.36 -0.18 -0.06
49.3 plug -0.63 -0.08 0.41 0.00
Table 7. Values for En. All of the values are within the range ± 1.
Figure 2. All of the values of En (at 68% confidence level) are within the range ± 1. There are
no obvious systematic trends in the data.
10. Conclusions
All participant’s results were consistent within the stated uncertainties. This is a gratifying result
that has not been achieved in any previous comparison of diameter measurements. In fact, all
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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values of │En│ values were less than 0.75, nearly a factor of 3 better than required. These
results support the claims of the CMCs of all participants, as will be discussed in more detail in
the Executive Report.
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APPENDIX A
Laboratory summary graphs are given below. The error bars are k = 2 uncertainties.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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NOTE: The NIST data of 8-2010 has been offset slightly in nominal diameter so that both data sets and their
uncertainties are visible.
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Appendix B
Uncertainty Budgets
Each lab provided detailed uncertainty budgets for their measurements. For laboratories that
submitted budgets for each artifact, one budget each for internal and external diameter is
presented for comparison.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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Appendix B1
CENAM Components of uncertainty for: External Diameter
1. External diameters were measured against gage blocks calibrated by interferometry,
U(k=2) : 0.080 µm for lengths of 3 mm, 7 mm, 23 mm and 50 mm.
2. The scale used to transfer the source of traceability, a laser 5519A, our estimated U:
(0.04+0.36*L) µm, L in mm.
3. Elastic deformation (Ed): for each 1 N of force the gage will deform 50 nm, the
measurements were done at 0.5 N, but it is suppose there is a variation of 0.1 N, so the U
for the Ed is taken as 25 nm.
4. Artifacts alignment is considered to be 0.05 x10-6
L which is a reasonable value because
of the resolution of the maximum value indicator device from the comparator (Tesa
modul TTA-80).
5. Uncertainty due to temperature influences is 0.28x10-6
L.
6. The parallelism of the flat feelers, it is estimated to be 70 nm on the whole surface
between them (Ø 8 mm).
7. Uncertainty due to repeatability is: 60 nm
Plug gages nm
xi u(xi), µm (k = 1) u(xi)
i ci = l/xi ui(l) / nm ui(l) L
dependent
nm/mm
1 Li 40 24 1 40 --
2 m (scale laser accuracy) 40 + 0.36 L 78 1 40 0.36L
3 E (contact defoermation) 25 85 1 25 --
4 am (scale alignment) 0.05 L 75 1 -- 0.05L
5 L(ata - mtm) u , utm 80 1 -- 0.28L
6 p (paralelism) 70 95 1 70 --
7 Repeatibility 60 85 1 60 --
uc, nm (111 + 0.46 L) nm, L in mm
Combined standard uncertainty: uc (l) = (111 + 0.46 L) nm, L in mm (1sigma)
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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CENAM Components of uncertainty for: Internal Diameter
1. Internal diameters were measured against gage blocks (GB) calibrated by interferometry,
for lengths of 10 mm. The GB is used as standard in order to get the constant diameter in
case of using an internal diameter feeler (1 axis probe head).
In case of using a “U” feelers iGB (internal fixed GB) are also used to reach the
initialization of the “U” feeler. The GB u = 75 nm, the diameter of sphere has an
uncertainty, ui = 60 nm
2. The scale used to transfer the source of traceablity, a laser 5519A, our estimated u1s:
(40+0.36 L)nm, L in mm.
3. Elastic deformation (Ed): for each 1 N of force the gage will deform 50 nm, the
measurements were done at 0.5 N, but it is has been measured there is a variation of 0.2
N, so the u for the Ed is taken as 25 nm.
4. Artifacts alignment is considered to be 0.05x10-6
L which is a reasonable value because
of the resolution of the maximum value indicator device from the comparator (Tesa
modul TTA-80).
5. Uncertainty due to temperature influences is 0.28x10-6
L.
6. Coaxiality of the “U” feelers, it is estimated to be 24 nm.
Ring gages nm
xi u(xi), µm
(k = 1)
u(xi) i ci = l/xi ui(l) / nm ui(l) L
dependent
nm/mm
1 Li GB standard 75 24 1 75 --
1’ Diameter of probe 1
axis head 60 28 1 60 --
2 m (scale laser
accuracy)
40 + 0.36 L 18 1 40 0.36 L
3 E (contact
defoermation) 25 85 1 25 --
4 am (scale alignment) 0.05L 90 1 -- 0.05 L
5 L(ata - mtm) u , utm 60 1 -- 0.28 L
6 p (coaxiality) 24 85 1 24 --
uc, nm (110 + 0.46 L) nm, L in mm
Combined standard uncertainty: uc (l) = (110 + 0.46 L) nm, L in mm (1sigma)
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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APPENDIX B2
INMETRO Ring Gage Measurement Uncertainty Example
2K97 - 11,95mm
xi u(xi) i ci = l/xi(nm/m) ui(l) / nm
m
Laser resolution 0,0029 Infinite 1000 2,8868
Variation in indication 0,0058 Infinite 1000 5,7735
Laser alignment 0,0090 Infinite 1000 9,0211
Gage alignment 0,0000 Infinite 1000 0,0000
Dead path 0,0000 Infinite 1000 0,0000
Probing 0,1014 Infinite 1000 101,3908
Repeatability 0,0111 4 1000 11,0718
Gage positioning 0,0866 Infinite 1000 86,6025
Air temperature °C nm/ºC
Calibration Certificate 0,0100 Infinite 1,1141E+01 0,1114
Variation in indication 0,0130 Infinite 1,1141E+01 0,1447
Gradient 0,0115 Infinite 1,1141E+01 0,1286
Reading 0,0115 Infinite 1,1141E+01 0,1286
Uncorrected error 0,0035 Infinite 1,1141E+01 0,0386
Air pressure Pa nm/Pa
Calibration Certificate 25,3979 Infinite -0,032031538 0,8135
Variation in indication 2,2484 Infinite -0,032031538 0,0720
Partial vapor pressure Pa nm/Pa
Calibration Certificate 11,8694 Infinite 0,004427659 0,0526
Wavelength m nm/m
0,000000035 Infinite -1,47380E+02 0,0000052
Gage temperature °C nm/ºC
Calibration Certificate 0,0110 Infinite -1,37425E+02 1,5117
Variation in indication 0,0000 Infinite -1,37425E+02 0,0000
Gradient 0,0043 Infinite -1,37425E+02 0,5951
Reading 0,0006 Infinite -1,37425E+02 0,0793
Uncorrected error 0,0023 Infinite -1,37425E+02 0,3174
Thermal expansion coefficient
ºC-1 nm*ºC
0,00000115 Infinite 746875,5798 0,8624
Combined standard uncertainty (uc(l)) nm = 134
k (~95%) = 2
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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INMETRO External Diameter Measurement Example
A1 – 3mm
xi u(xi) (m) i ci = l/xi(nm/m) ui(l) / nm
m
Laser resolution 0,0029 Infinite 1000 2,8868
Variation in indication 0,0058 Infinite 1000 5,7735
Laser alignment 0,0090 Infinite 1000 9,0211
Gage alignment 0,0000 Infinite 1000 0,0000
Dead path 0,0083 Infinite 1000 8,2994
Probing 0,0410 Infinite 1000 40,9648
Repeatability 0,0296 4 1000 29,5904
Gage positioning 0,0866 Infinite 1000 86,6025
Air temperature °C nm/ºC
Calibration Certificate 0,0100 Infinite 2,7909E+00 0,0279
Variation in indication 0,0052 Infinite 2,7909E+00 0,0145
Gradient 0,0115 Infinite 2,7909E+00 0,0322
Reading 0,0115 Infinite 2,7909E+00 0,0322
Uncorrected error 0,0035 Infinite 2,7909E+00 0,0097
Air pressure Pa nm/Pa
Calibration Certificate 25,3979 Infinite -0,008051518 0,2045
Variation in indication -2,2484 Infinite -0,008051518 0,0181
Partial vapor pressure Pa nm/Pa
Calibration Certificate 11,6023 Infinite 0,001111548 0,0129
Wavelength m
0,000000035 Infinite -3,69991E+01 0,0000013
Gage temperature °C nm/ºC
Calibration Certificate 0,0110 Infinite -3,45000E+01 0,3795
Variation in indication 0,0014 Infinite -3,45000E+01 0,0498
Gradient 0,0101 Infinite -3,45000E+01 0,3486
Reading 0,0006 Infinite -3,45000E+01 0,0199
Uncorrected error 0,0023 Infinite -3,45000E+01 0,0797
Thermal expansion coefficient
ºC-1 nm*ºC
0,00000115 Infinite 135000,1731 0,1559
Combined standard uncertainty (uc(l)) nm = 101
k (~95%) = 2
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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APPENDIX B3
INTI Uncertainty for Internal Diameter (Ring)
xi u(xi) i ci = l/xi ui(l) / nm
Laser Wavelength 3,5E-6 nm 200 101923 0
Index of refraction 1,6E-8 50 6,4E7 1
Number wavelengths ring
measured 0,011 13 633 7
Number wavelengths gauge
block measured 0,011 13 - 633 7
Ring expansion coefficient 6,64E-7 1/°C 50 -11999988 8
Ring temperature
measurement 0,02 °C 50 -863 20
Gauge block expansion
coefficient 4,9E-7 1/°C 50 1,9E6 1
Gauge block temperature
measurement 0,03 °C 50 89 2
Searching the point of
maximum diameter 11,55 nm 50 1 12
Ring form deviation 28,87 nm 50 1 29
Length gauge block 10,1 nm 200 1 10
Variation gauge block
10,5 mm (U-shaped) 23,1 nm 200 1 23
Variation gauge block
19,5 mm (U-shaped) 23,1 nm 200 1 23
Variation gauge block
20 mm (U-shaped) 40,4 nm 200 1 40
Dead path 11,5 nm 13 1 12
Optics thermal drift 57,7 nm 13 1 58
Abbe error, XrY
(offset < 4,5 mm) 34,8 nm 13 1 35
Cosine error 1,6 nm 13 1 2
Error U-shaped
arrangement 46,2 nm 13 1 46
Laser resolution 2,9 nm 200 1 3
Probe stability 28,9 nm 50 1 29
Probe calibration 28,9 nm 50 1 29
Back to zero (initial point
measurement) 57,7 nm 50 1 58
Reproducibility 63,5 nm 50 1 64
Standard deviation ring
measurement 17,5 nm 15 1 18
Standard deviation gauge
block measurement 22,5 nm 15 1 23
Others (1)
-------- ------- --------- 25
Combined standard uncertainty ± 147 nm
Expanded uncertainty of measurement (k = 2) ± 296 nm
(1) Others minor components: change temperature ring or gauge block during measurement, stability wavelength,
optics nonlinearity, pressure, temperature and humidity ambient measurement, etc.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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INTI Uncertainty for External Diameter (Cylinder)
xi u(xi) i ci = l/xi ui(l) / nm
Laser Wavelength 3,5E-6 nm 200 61316 0
Index of refraction 1,6E-8 50 3,9E7 1
Number wavelengths plug
measured 0,011 13 633 7
Number wavelengths gauge
block measured 0,011 13 - 633 7
Plug expansion coefficient 6,64E-7 1/°C 50 -24158382 16
Plug temperature
measurement 0,02 °C 50 -567 13
Gauge block expansion
coefficient block 4,9E-7 1/°C 50 6,6E6 3
Gauge block temperature
measurement 0,02 °C 50 89 2
Searching the point of
maximum diameter 11,55 nm 50 1 12
Form deviation of plug 28,87 nm 50 1 29
Length gauge block 10,1 nm 200 1 10
Variation gauge block
10,5 mm 23,1 nm 200 1 23
Dead path 11,5 nm 13 1 12
Optics thermal drift 57,7 nm 13 1 58
Abbe error, ZrY
(offset < 4,5 mm) 28,8 nm 13 1 29
Abbe error, XrZ
(offset < 4,5 mm) 14,8 nm 13 1 15
Cosine error 1,6 nm 13 1 2
Laser resolution 2,9 nm 200 1 3
Probe stability 28,9 nm 50 1 29
Probe calibration 28,9 nm 50 1 29
Back to zero (initial point
measurement) 57,7 nm 50 1 58
Reproducibility 52,0 nm 50 1 52
Standard deviation plug
measurement 20,1 nm 19 1 20
Standard deviation gauge
block measurement 22,4 nm 19 1 22
Others (1)
-------- ------- --------- 17
Combined standard uncertainty ± 125 nm
Expanded uncertainty of measurement (k = 2) ± 252 nm
(1) Others minor components: change temperature plug or gauge block during measurement, stability wavelength,
optics nonlinearity, pressure, temperature and humidity ambient measurement, etc.
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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APPENDIX B4
NIST External Diameter Uncertainty Budget – Laser Micrometer
The NIST wire micrometer was used for small
diameter cylinders. It uses a laser interferometer as
its scale and dead weight to set the force. The
uncertainty budget is primarily from the
micrometer’s long term reproducibility consisting
of check standard measurements with every
cylinder calibrated over the last few years.
Uncertainty Budget – Absolute Measurement of Diameter Standards
Source of Uncertainty
Analysis Method
1 Equivalent Value
(in m)
Length independent terms
Gage repeatability – geometry and
roundness effects
Gage Performance/Control
Charts
0.012
Elastic deformation correction or
extrapolation uncertainty
5% of expected
results/extrapolation data
0.006
Micrometer contact geometry Rectangular dist. of contact
form errors 0.012
Length dependent terms
Control artifact
Performance/Reproducibility
Control Charts
0.50L
Laser wavelength 2 x 10-8
m 0.02L
Velocity of light correction 5 x 10-8
m 0.05L
Air pressure measurement 10 Pa 0.04L
Abbe offset/alignment error 0.5 mm x < 0.1 s. 0.50L
artifact temperature measurement 11.5ppm x 0.02 C error 0.23L
Thermal expansion () uncertainty 0.1ºC x 1ppm 0.10L
Thermometer calibration 0.01ºC @ 11.5ppm 0.12L
Combined uncertainty uc 0.018 + 0.76 x 10-6
L
Expanded uncertainty k = 2 0.036 + 1.52 x 10-6
L
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
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NIST Ring gage and large Cylinder Calibrations on M48
The Moore M48 coordinate measuring machine was used for ring
gages and large cylinders. It has laser interferometers for all three
axes and has been thoroughly monitored since moving to the 0.01 ºC
laboratory.
The primary uncertainty component is the long term reproducibility
of measurements of one dimensional standards (cylinders, ring, end
standards and step gages) over the last 7 years.
Source
Calculation
μm
(parts
in 106)
Residual Positioning Error Multiple rotations of 2D ball
plates, holeplates 0.04
Temperature difference in beam
paths during mapping .02ºC maximum difference 0.01
Mapping Laser Frequency
Difference 2 x 10
-8 0.02
Measurement Reproducibility 7 years, 100’s of data pts on
rings, plugs, step gages 0.04 0.04
Edlén Equation Internationally accepted 0.03
Index of Refraction – Air
Temperature
± 0.006ºC beam path meas.
accuracy
0.01
Index of Refraction - Air Pressure ± 10 Pascal meas. accuracy 0.04
Index of Refraction – Humidity ± 4% meas. accuracy 0.03
Temperature Accuracy 0.003ºC x 12ppm 0.04
Coefficient of Thermal Expansion 0.05ºC x 1ppm 0.05
Contact Deformation Bi-directional, material 0.002
Gage Surface Geometry Csy generation error 0.004
Combined uncertainty uc 0.05 μm + 0.10 x 10-6
L
Expanded uncertainty k = 2 0.11 μm + 0.20 x 10-6
L
SIM Regional Comparison: Calibration of Internal and External Diameter Standards.
22
REFERENCE
[1] Taylor, B.N. and Kuyatt, C.E., “Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results,” National Institute of Standards and Technology
Technical Note 1297, U.S. Government Printing Office, Washington, D.C. (1994).