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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.

2

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.


3

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: [email protected]

Guillermo Navarrete CENAM

Km 4,5 Carretera a Los Cués

El Marqués, Querétaro

76246 MEXICO

(52-442) 211-05 00 to 05 est. 3285


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


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,


Coordinator:

Ted Doiron NIST

Building 220, Rm B113

Gaithersburg, MD 20899

USA

Tel. +1-301-975-3472

Fax +1-301-975-8291


Table 1. Participating laboratories

mailto:[email protected]

mailto:[email protected]


4

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.


5

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.


6

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


7

Gage ID Nominal (mm)


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.


8

Gage ID Nominal

(mm) Reference Value


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.


9

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


10

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.


11

APPENDIX A

Laboratory summary graphs are given below. The error bars are k = 2 uncertainties.


12

NOTE: The NIST data of 8-2010 has been offset slightly in nominal diameter so that both data sets and their

uncertainties are visible.


13

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.


14

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)


15

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)


16

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


17

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


18

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


19,5 mm (U-shaped) 23,1 nm 200 1 23


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.


19

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


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.


20

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


21

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


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).

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