SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 1 / 29
2014-10-29

Centro Nacional de Metrología
SIM Regional Supplementary Comparison
SIM.L-S6
Calibration of Gauge Blocks by Mechanical
Comparison
Final Report
October 2014
M. Viliesid
CENAM, Centro Nacional de Metrología
C. Colín
CENAM, Centro Nacional de Metrología
T. Chávez
CENAM, Centro Nacional de Metrología
K.P. Chaudhary
NPLI, National Physical Laboratory INDIA

CMI, Czech Metrology Institute
J. Stoup
NIST, National Institute of Standards and
Technology
W. Santos
INMETRO, Instituto Nacional de Metrologia
L. Vaudagna
INTI, Instituto Nacional de Tecnología Industrial
R. Morales
DICTUC, Laboratorio Nacional de Longitud
A. Acquarone
LATU, Laboratorio Tecnológico del Uruguay
J. Carrasco
INDECOPI, Servicio Nacional de Metrología
M. Vega
IBMETRO, Instituto Boliviano de Metrología
M. Salazar
INEN, Instituto Ecuatoriano de Normalización
V. Gil
SIC, Superintendencia de Industria y Comercio
J. Dimas
CENAMEP, Centro Nacional de Metrología de
Panamá AIP
E. Reyes
LACOMET, Laboratorio Costarricense de
Metrología
F. Hamilton
TTBS, Trinidad and Tobago Bureau of
Standards
T. Reddock
TTBS, Trinidad and Tobago Bureau of
Standards
S. Durga
BSJ, Bureau of Standards Jamaica
T. Burton
BSJ, Bureau of Standards Jamaica

Centro Nacional de Metrología (CENAM)
km 4.5 Carretera a Los Cués,
El Marqués, Querétaro
76246, MEXICO

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1. Introduction
The Mutual Recognition Arrangement (MRA) of the Conférence Internationale des Poids et
Mesures (CIPM) signed by the National Metrology Institutes (NMI) of different nations
provides mutual recognition among the NMI of their national standards and their calibration
services. A database has been set up by the Bureau Interantional des Poids et Mesures
(BIPM) at its website where the Calibration and Measurement Capabilities (CMC) of each
NMI are posted. To support the CMC claims of the NMI, the MRA requires, among other
things, that they participate on a regular basis in Key Comparisons (KC) that test key
measuring techniques. This would prove their technical competence, that they can provide
this calibration service with the claimed uncertainty of the corresponding CMC and that they
have metrological equivalence with the other signatory NMI that provide the same service.
The CIPM has therefore instructed the different CC (Comité Consultatif) to identify key
techniques in order to define KC, as it is, for example, the calibration of Gauge Blocks (GB)
by optical interferometry, identified as a key measuring technique by CCL ( CC de
Longueurs). Additionally, the CC as well as the regions may also identify other important
comparisons called supplementary and identified with an S. The SIM region has identified
the Calibration of GB by Mechanical Comparison as one if this comparisons. The Centro
Nacional de Metrología (CENAM) was designated by SIM as pilot laboratory and CENAM
has carried out this exercise under the name of SIM.L-S6:2007.
The calibration of GB by Mechanical Comparison is indeed a technique of paramount
importance as it is at the highest level in the traceability chain of length for most countries of
the American Continent. This comparison is meant to support the submitted CMC of these
countries.
The measurand is the central length of the GB as defined in [1] and the circulated GB were
used for two comparisons carried out in two stages:
First stage, SIM.L- K1:2007, Calibration of GB by Optical Interferometry. Circulation from
2007-11-01 to 2010-04-25. The GB were also measured by Mechanical Comparison for
those NMI also participating in SIM.L-S6:2007.
Second stage, SIM.L-S6:2007, Calibration of GB by Mechanical Comparison. Circulation
from 2010-03-02 to 2011-05-06 for the participants that measured only by Mechanical
Comparison, this dates included two control measurements by interferometry.
In this second comparison there were 16 participants, 14 from the Americas, and 2 invited
NMI from other regions. The circulation in the second stage had 10 participants. It should be
noted that the circulation took relatively short time for the large number of participants thanks
to the hand delivery from one NMI to the following one in nine out of the 10 steps so that
customs clearance was simplified or avoided.
2. Participants
This comparison had 16 participants. Table 1 shows the participating NMI and their
corresponding contact person and information.

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Contact NMI Information
Carlos Colín
Castellanos

CENAM, Centro Nacional de Metrología
km 4.5 Carretera a los Cués, El Marqués
CP 76241, Querétaro, MÉXICO.
Tel. +52 442 211 0500
Fax +52 442 211 0577
e-mail: ccolin@cenam.mx
K. P. Chaudhary NPLI, National Physical Laboratory INDIA
Dr. K,S. Krishnan Road, New Delhi
110012, INDIA.
Tel. +91 11 25732865
Fax +91 11 25726938
e-mail: kpc@mail.nplindia.ernet.in
Ing. Vladimir
Stezka
Ing. Frantisek


CMI, Czech Metrology Institute
Slunecna 23
460 01 Liberec
CZECH REPUBLIC.
Tel. +42 485 107 532
Fax +42 485 104 466
e-mail: vstezka@cmi.cz
fdvoracek@cmi.cz
Leandro Vaudagna INTI, Instituto Nacional de Tecnología Industrial
División de Metroplogía Dimensional-Rafaela
km 227,6 Ruta Nac. No 34
CP 2300, Rafaela, Santa Fé, ARGENTINA
Tel. +54 34 92440471
Fax +54 34 92422804
e-mail: vaudagna@inti.gov.ar
Wellington Santos
Barros
INMETRO, Instituto Nacional de Metrologia,
Normalização e Qualidade Industrial.
Av. N.Sra. das Graças, 50 Villa Operária
Xerém Duque de Caixas RJ. CEP 25250-
020, BRASIL.
Tel. +55 21 2679-9271
Fax +55 21 2679-9207
e-mail: wsbarros@inmetro.go.br

John Stoup NIST, National Institute of Standards and
Technology
Room B113, Metrology Building
Gaithersburg, MD 20899-0001 USA
Tel. +1 301 975 3476
Fax + 1 301 869 0822
e-mail: John.Stoup@nist.gov
Roberto Morales

DICTUC, Laboratorio Nacional de Longitud
Avenida Vicuña Mackenna 4860 Macul
Santiago (edificio nº 9 metrología), CHILE.
Tel. 56 2 3544624
Fax 56 2 3544624
e-mail: metrologia@dictuc.cl
Alejandro
Acquarone
Luis Mussio
LATU, Laboratorio Tecnológico del Uruguay
Avenida Italia 6201, Montevideo, URUGUAY.
CP 11500
Tel. 598 2 601 3724 ext 298
Fax 598 2 601 8554
e-mail: lmussio@latu.org.uy
aacqua@latu.org.uy
Janet Carrasco
Tuesta
INDECOPI, Servicio Nacional de Metrología
Calle de la Prosa 138, San Borja
Lima 4,1 PERÚ.
Tel. 51 1 224 7800 1618
Fax 51 1 224 7800 1264
e-mail: jcarrasco@indecopi.gob.pe
María del Carmen
Vega Amonzabel
IBMETRO, Instituto Boliviano de Metrología
Av. Camacho No. 1488
La Paz, BOLIVIA.
Tel. 591 2 2372046
Fax 591 2 2310037
e-mail: mvega@ibmetro.gob.bo
Manuel Salazar INEN, Instituto Ecuatoriano de Normalización
Casilla: 17-01-3999
Quito ECUADOR.
Tel. 593 2 2343716
Fax 593 2 2344394
e-mail: msalazar@inen.gov.ec
Victor Hugo Gil SIC, Superintendencia de Industria y Comercio
División de Metrología
COLOMBIA.
Tel. 571 3153265 - 69
Fax 571 3153292
e-mail: vgil@correo.sic.co
Julio Dimas CENAMEP, Centro Nacional de Metrología de
Panamá AIP, Edificio 215, Ciudad del Saber,
PANAMÁ.
Tel. 507 517-0081
Fax 507 517-0019
e-mail: jdimas@cenamep.org.pa
Eduardo Reyes LACOMET, Laboratorio Costarricense de
Metrología.
Apartado Postal 1736 2050, San Pedro de
Montes de Oca, San Jose. COSTA RICA.
Tel. 506 - 2283 - 6580
Fax 506 - 2283 - 5133
e-mail: ereyes@lacomet.go.cr
Theodore Reddock
Francis Hamilton
TTBS, Trinidad and Tobago Bureau of
Standards
Century Drive Trincity Industrial Estate Macoya,
Tunapuna, TRINIDAD AND TOBAGO.
Tel. 868-662-8827
Fax 868-663-4335
e-mail: Theodore.Reddock@ttbs.org.tt
e-mail:Francis.Hamilton@ttbs.org.tt
Tomokie Burton
Carlton Thomas
Siew Durga
BSJ, Bureau of Standards, Jamaica
6 Winchester Rd.,
Kingston 10. JAMAICA.

Tel.: 926-3140-5 ext. 1102
Fax: 929-4736
e-mail: cthomas@bsj.org.jm
e-mail: TBurton@bsj.org.jm
Tabla 1. List of participants in comparison SIM.L-S6:2007.

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3. Circulation Schedule
As we mentioned, nine out of the ten participants in the second circulation stage delivered
the artifacts by hand to the following participant which made the circulation time relatively
short. Table 2 shows the circulation schedule for the two circulation stages. LACOMET
retained 13 weeks the GB because of end-of-the-year holidays and internal administrative
problems, they mentioned.
NMI Dates Reception of results Reception Shipment
Stage One Circulation
NPLI 2008-03-02 2008-06-09 2009-08-07
CMI 2008-06-16 2008-08-05 2008-10-17
NIST 2009-04-20 2009-07-15 2010-03-02
INMETRO 2009-08-11 2009-09-08 2009-09-21
INTI 2009-11-13 2010-01-11 2010-01-11
Stage Two Circulation
DICTUC 2010-04-29 2010-05-18 2010-06-15
LATU 2010-06-11 2010-07-06 2010-07-21
INDECOPI 2010-07-06 2010-07-30 2010-08-12
IBMETRO 2010-08-02 2010-08-18 2010-09-24
INEN 2010-08-18 2010-09-13 2011-05-16
SIC 2010-09-13 2010-10-13 2010-11-10
CENAMEP 2010-10-13 2010-11-09 2011-01-28
LACOMET 2010-11-09 2011-02-09 2011-04-01
TTBS 2011-02-14 2011-03-16 2011-04-13
BSJ 2011-03-16 2011-04-27 2011-06-09
CENAM (Pilot) 2011-04-28 2011-05-25
Tabla 2. SIM.L-S6:2007 dates of reception and shipment of artifacts and reception of
results by the pilot laboratory.
4. Comparison Artifacts
A total of 14 grade K (according to [1]) rectangular GB were selected for the exercise. Seven
steel GB and seven ceramics GB covering the range of short GB (from 0.5 mm to 100 mm).
The specifications on the GB are shown in tables 3 and 4. The associated Coefficients of
Thermal Expansion (CET) shown in the tables are those quoted by the manufacturer.
Nominal Length
(mm)
Serial Number Coefficient of Thermal
Expansion ( 10-6 K-1 )
Manufacturer
1.000 5 010223 10.9 1 Mitutoyo
5 000482 10.9 ± 1 Mitutoyo
7 010764 10.9 1 Mitutoyo
10 001329 10.9 ± 1 Mitutoyo
50 012254 10.9 1 Mitutoyo
75 010630 10.9 1 Mitutoyo
100 010850 10.9 1 Mitutoyo
Table 3. Steel Gauge Blocks.

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Nominal Length
(mm)
Serial Number Coefficient of Thermal
Expansion ( 10-6 K-1 )
Manufacturer
1.000 5 000288 9.3 1 Mitutoyo
5 051836 9.3 1 Mitutoyo
7 010323 9.3 1 Mitutoyo
10 052351 9.3 1 Mitutoyo
50 011002 9.3 1 Mitutoyo
75 010370 9.3 1 Mitutoyo
100 010773 9.3 1 Mitutoyo
Table 4. Ceramics Gauge Blocks.
5. Measurement Protocol
Detailed instructions were included in the technical protocol. Participants were invited to
perform the measurements according to their own calibration procedures, used to calibrate
the GB of their customers.
The measurement was performed in all cases with a double probe GB comparator and in the
vertical position as indicated in [1]. The method determines the difference in central length,
lc, of two GB of same nominal length set beside in the comparator platen as illustrated in
Figure 1. The first GB calibrated by optical interferometry;
and the test GB which is under circulation.

Figure 1. Illustration of the calibration method of GB by mechanical comparison showing the different
variables of influence (taken from [9]).

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6. Measuring Instruments
All participants measured with double probe electromechanical GB comparators with a
resolution of 10 nm. Table 5 shows the makes, models and characteristics of the different
instruments.
NMI Manufacturer Model
Measuring
range
mm
Traceability
Temperature
variation range
during
measurements
(°C)
CENAM TESA TESA-UPC 0 - 102
To SI standards of CENAM via
GB calibrated by interferometry 19.32 19.60
NPLI Mahr Not indicated 0 175 Not indicated 19.5 20.5
CMI TESA TESA-UPC 0 100
To the Czech National
Standard of Length (He-Ne/I2
633nm,
He-Ne/I2 543.5nm, fs comb)
Not indicated
NIST Mahr/Federal 130B-24 0 -102 NIST maintained Iodine- Stabilized Laser 20.08 20.17
INMETRO TESA TESA-UPC 0 - 102
To SI standards of INMETRO
via GB calibrated by
interferometry
20.0 20.5
INTI Mahr 826E 0 - 175 To SI standards of INTI via GB calibrated by interferometry 20 ± 0.5
DICTUC TESA TESA-UPC 0 - 100
To SI standards of PTB via GB
calibrated by interferometry
Steel 19.91
20.05
Ceramics 19.85
20.16
LATU Mahr 826 0 - 100
Comparator to SI standards of
PTB via GB calibrated by
interferometry and to SI
standards of CENAM via GB
calibrated by interferometry
19.68 20.50
INDECOPI Mahr 826 PC 0 175 To SI standards of CENAM via GB calibrated by interferometry 20.0 ± 0.5
IBMETRO Steinmayer EMP II 0 100 To SI standards of PTB via GB grade 0 19.95 20.15
INEN Mahr 826 0 - 170
Not indicated, only mentioned
that their GB are calibrated by
interferometry
19 21
SIC TESA UPD 0 - 500 To SI standards of METAS via GB calibrated by interferometry 20 20.3
CENAMEP Mitutoyo GBCD-250 0 - 250
To SI standards of CENAM via
GB calibrated by interferometry 20.3 20.6
LACOMET TESA TESA-UPC 0.5 - 100
To SI standards of PTB and
CENAM via GB calibrated by
interferometry
0.34
TTBS TESA TESA-UPC 0.5 - 100
To SI standards of METAS and
NPL via GB calibrated by
interferometry
0.018
JBS Mahr-Federal 2247386 1 - 100 To SI standards of NIST

19.60 20.20

Table 5. GB comparators, measurement range, traceability and temperature
variation of the participant laboratories.

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7. State and Behavior of Artifacts
7. 1 State of the Artifacts upon Reception
The participants were to inspect the state of the artifacts upon reception and inform the pilot
according to the protocol. Although the selected GB were not brand new, they were in good
conditions. They suffered some damage after the circulation, but the stability and the results
obtained in the comparison prove the damages did not hamper or alter the measurements
and the pilot laboratory was able to wring them all to a measurement platen without problems
after circulation. Figures 1 through 11 show the physical conditions of some of the steel GB
upon reception at the pilot laboratory at the end of the exercise. The steel GB ended-up with
quite a few scratches and specifically, the 5 mm GB, also presented rust spots.

Figures 1, 2 and 3. Aspect of the measuring faces of the 1.000 5, 5 and 7 mm Steel GB at the end of
circulation.

Figures 4, 5 and 6. Aspect of the measuring faces of the 10, 50 and 75 mm Steel GB at the end of
circulation.

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Figure 7. Aspect of the measuring faces of the 100 mm Steel GB at the end of circulation.
Four out of the seven ceramic GB suffered some damage on one of their measuring faces as
shown in Figures 8 to 11, which consisted of burs or chipped edges. However, this condition
did not hamper the wringing or caused any variation in length as it was proved by the control
measurements performed at the end by the pilot laboratory by interferometry as well as by
mechanical comparison.

Figures 8, 9, 10 and 11. Aspect of the measuring faces of the 10, 50, 75 and 100 mm Ceramic GB at
the end of circulation.
7. 2 Stability of the Standards
The GB were measured by interferometry several times by the pilot laboratory to verify their
stability: when they were purchased (2002), two years before starting the comparison (Nov.
2005), before circulating them (Nov. 2007), after the round by interferometry (April 2010) and
at the end of the circulation (May 2011). Table 6 shows the deviations from nominal length
determined at these different occasions for the steel GB, including the stated values on the
certificates of the manufacturer. Graphs 1 through 7 show these values for each GB.

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Serial
Number
Nominal
length
(mm)
Deviation from nominal value (nm)
Manufacturer
certificate
2001
2002 2005 2007 2010 2011
010223 1.000 5 0 5 3 -4 -9 -2
000482 5 40 14 11 35 20 27
010764 7 30 19 13 -5 1 -10
001329 10 50 31 22 37 21 31
012254 50 60 46 3 7 -3 8
010630 75 -50 -54 -104 -100 -107 -106
010850 100 20 18 -50 -51 -64 -50
Table 6. Pilot Laboratory measured values of the steel GB at different occasions.

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Table 7 shows the deviations from nominal length determined at these different occasions
for the ceramics GB, including the stated values on the certificates of the manufacturer.
Graphs 8 through 14 show these values for each GB.
Serial
Number
Nominal
length
(mm)
Deviation from nominal value (nm)
Manufacturer
certificate
2001
2002
Manufacturer
certificate
2005
2007 2010 2011
000288 1.0005 0 -6 ---- -14 7 -17
051836 5 ---- ---- 13 12 8 14
010323 7 50 46 ---- 57 48 35
052351 10 ---- ---- 3 -13 -19 -29
011002 50 90 95 ---- 139 117 97
010370 75 100 110 ---- 118 124 123
010773 100 -60 -42 ---- -34 -36 -41
Table 7. Pilot Laboratory measured values of the ceramics GB in different occasions.

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8. Measurement Results of Participants
All laboratories sent their results by e-mail. All information was received on the specified
formats from appendices A, B, C, D and E of the Technical Protocol.
8.1 Measurement of the Central Length
Tables 8 and 9 and graphs 16 through 22, show the deviations of the central length with
respect to nominal values and the claimed standard measurement uncertainties of each
participant for the seven steel GB. Additionally, graph 15 shows the claimed standard
uncertainties of all participants.
Nominal
Value
mm
Deviation (eij) from nominal length for Steel GB
nm
NPLI CMI NIST INMETRO INTI LATU DICTUC INDECOPI
1.000 5 -20 20 -27 20 -12 -35 -15 20
5 10 60 27 62 -4 4 5 20
7 -40 20 2 21 -38 -12 -35 10
10 10 70 39 24 12 39 20 40
50 -30 80 15 11 -11 13 -10 0
75 60 -50 -107 -93 -127 -126 -110 -80
100 10 40 -67 -60 -66 -68 -60 10
Table 8A. Measurement results of the participants for the Steel GB.

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Nominal
Value
mm
Deviation (eij) from nominal length for Steel GB
nm
IBMETRO INEN SIC CENAMEP LACOMET TTBS BSJ CENAM
1.000 5 -40 -10 -27 -13 22 30
Not
reported -2
5 0 10 -6 -3 46 70 11 23
7 -40 -30 -38 -13 27 20 -37 6
10 20 20 -7 31 66 20 15 24
50 -10 10 0 -10 36 200 -26 14
75 -130 -140 -127 -143 -83 -40 -295 -109
100 -70 40 -23 -112 -68 290 -47 -33
Table 8B. Measurement results of the participants for the Steel GB.

Nominal
Value
mm
Claimed standard uncertainties, u(eij), Steel GB
nm
NPLI CMI NIST INMETRO INTI LATU DICTUC INDECOPI
1.000 5 26 23 13 29.5 23.0 26.0 27 27
5 28 23.1 13 29.8 23.0 26.0 27 27
7 29 23.1 13 29.8 23.0 26.0 27 27
10 30 23.3 13 29.8 23.0 26.0 27 27
50 53 29.2 15 35.2 35.0 38.0 29 36
75 67 35.5 20 41.4 46.0 40.0 34 45
100 81 42.7 30 49.1 58.0 47.0 36 55
Table 9A. Claimed standard uncertainties of the participants for the Steel GB.

Nominal
Value
mm
Claimed standard uncertainties, u(eij), Steel GB
nm
IBMETRO INEN SIC CENAMEP LACOMET TTBS BSJ CENAM
1.000 5 34 55.4 23 12 25.3 52
Not
reported 14.5
5 35 57.2 23 12 25.4 53 28 14.7
7 35 58 23 12 36.7 53 29 14.9
10 36 59.3 24 13 36.9 77 31 15.2
50 44 76.5 34 35 43.7 160 71 27.6
75 50 87.3 44 51 43.8 170 100 38.1
100 55 98 55 66 54.4 170 130 49.2
Table 9B. Claimed standard uncertainties of the participants for the Steel GB.

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Tables 10 and 11 and graphs 24 through 30, show the deviations of the central length with
respect to nominal values and their claimed standard measurement uncertainties of each
participant for the seven ceramic GB. Graph 23 shows the claimed standard uncertainties of
the participants.

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Nominal
Value
mm
Deviation (eij) from nominal length for Ceramics GB
nm
NPLI CMI NIST INMETRO INTI LATU DICTUC INDECOPI
1.000 5 -40 0 -27 -32 -9 -37 -17 -15
5 0 30 14 -14 10 -29 -17 -15
7 10 50 58 34 35 13 13 25
10 -80 0 -9 -24 -15 -18 -32 -25
50 20 140 116 97 89 103 65 55
75 40 150 148 89 122 111 101 135
100 -80 10 -5 -55 16 -53 -65 -15
Table 10A. Measurement results of the participants for Ceramics GB.
Nominal
Value
mm
Deviation (eij) from nominal length for Ceramics GB
nm
IBMETRO INEN SIC CENAMEP LACOMET TTBS BSJ CENAM
1.000 5 310 -10 -5 -12 -9 60 Not reported -10
5 340 -20 -10 -1 -16 80 -36 -6
7 370 20 32 38 44 90 -18 65
10 320 -10 -40 -18 -15 Not reported -68 -20
50 460 140 138 103 84 480 -16 100
75 480 170 155 164 102 480 -140 127
100 360 40 40 2 8 660 -195 -12
Table 10B. Measurement results of the participants for Ceramics GB.
Nominal
Value
mm
Claimed standard uncertainties, u(eij), Ceramics GB
nm
NPLI CMI NIST INMETRO INTI LATU DICTUC INDECOPI
1.000 5 26 23 13 32.5 23 26 27 27
5 28 23.1 13 33.2 23 26 27 27
7 29 23.1 13 32.7 23 26 27 27
10 30 23.3 13 32.7 23 26 27 27
50 53 29.2 15 38.1 33 36 28 38
75 67 35.5 20 44 42 45 35 48
100 81 42.7 30 50.6 52 47 34 59
Table 11A. Claimed standard uncertainties of the participants for Ceramics GB.
Nominal
Value
mm
Claimed standard uncertainties, u(eij), Ceramics GB
nm
IBMETRO INEN SIC CENAMEP LACOMET TTBS BSJ CENAM
1.000 5 34 55.4 23 12 25.3 58 Not reported 19.0
5 35 57.2 23 12 25.4 58 39 19.2
7 35 58 23 12 25.5 58 40 19.4
10 36 59.3 24 13 25.7 Not reported 43 19.9
50 44 76.5 34 34 43.5 160 99 34.5
75 50 87.3 44 50 43 170 140 47.1
100 56 98 55 66 55.3 180 182 60.6
Table 11B. Claimed standard uncertainties of the participants for Ceramics GB.

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9. Reference Value (RV) and equations to determine
the performance of participants
All usual parameters of the central tendency were calculated: the median, the simple mean
and the inverse-variance weighted mean. All of these values appear in Annex A. However,
the Supplementary Comparison Reference Values were obtained from the Regional Key
Comparison SIM.L-K1:2007, as the artifacts were the same. These RV were calculated as
the simple mean for all consistent results of the interferometric comparison [2].
The Reference Values, and their Expanded Uncertainties, for the different GB j of
both materials are shown in Table 13.
Supplementary Comparison Reference Values (RV)
Nominal
Length
mm
Steel Ceramics
Ref.
Value,
Ref.
Value,
1.005 -9.3 8.2 -3.9 7.8
5 26.4 8.3 10.6 7.9
7 -2.6 8.3 51.7 7.9
10 36.2 7.8 -14.3 8.1
50 4.9 12.5 105.9 11.3
75 -105.6 17.0 136.2 13.9
100 -42.0 17.1 -23.1 15.6
Table 13. Reference values (simple mean of largest sub-set of consistent results of SIM.L-K1:2007
comparison) as deviations from Nominal Value and corresponding Expanded Uncertainty for both
steel and ceramic GB. All values in nanometers.

For each laboratory, i, which measures each gauge block, j, let the measured deviation from
nominal length be denoted by dij and calculated as,
(1)
Statistical consistency of the results with their associated uncertainties can be verified by
calculating the normalized error En.
(2)
If En is greater than 1 it is considered that the result is inconsistent.

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10. Participants Results of the Comparison
The reported measurement results were analyzed by simple statistical means to allow
identification of any significant bias. Tables 14 and 15 show the differences of the results of
the participants with respect to the RV of each GB j, dij, and the corresponding Normalized
Error, En calculated from equation (2). Note that the uncertainties in this equation are
expanded uncertainties.
NMI
NPLI CMI NIST INMETRO INTI LATU
Nominal
dij En dij En dij En dij En dij En dij En
1.000 5 -10.7 0.20 29.3 0.63 -17.7 0.65 29.3 0.49 -2.7 0.06 -25.7 0.49
5 -16.4 0.29 33.6 0.72 0.6 0.02 35.6 0.59 -30.4 0.65 -22.4 0.43
7 -37.4 0.64 22.6 0.48 4.6 0.17 23.6 0.39 -35.4 0.76 -9.4 0.18
10 -26.2 0.43 33.8 0.72 2.8 0.10 -12.2 0.20 -24.2 0.52 2.8 0.05
50 -34.9 0.33 75.1 1.26 10.1 0.31 6.1 0.09 -15.9 0.22 8.1 0.11
75 165.6 1.23 55.6 0.76 -1.4 0.03 12.6 0.15 -21.4 0.23 -20.4 0.25
100 52 0.32 82 0.94 -25 0.40 -18 0.18 -24 0.20 -26 0.27
Table 14A. Deviation from reference value for each GB, dij (nanometers) and Normalized Error, En, of
the Steel GB for the first six participants.
NMI
DICTUC INDECOPI IBMETRO INEN SIC CENAMEP
Nominal
Length dij En dij En dij En dij En dij En dij En
1.000 5 -5.7 0.10 29.3 0.54 -30.7 0.45 -0.7 0.01 -17.7 0.38 -3.7 0.15
5 -21.4 0.39 -6.4 0.12 -26.4 0.37 -16.4 0.14 -32.4 0.69 -29.4 1.16
7 -32.4 0.59 12.6 0.23 -37.4 0.53 -27.4 0.24 -35.4 0.76 -10.4 0.41
10 -16.2 0.30 3.8 0.07 -16.2 0.22 -16.2 0.14 -43.2 0.89 -5.2 0.19
50 -14.9 0.25 -4.9 0.07 -14.9 0.17 5.1 0.03 -4.9 0.07 -14.9 0.21
75 -4.4 0.06 25.6 0.28 -24.4 0.24 -34.4 0.20 -21.4 0.24 -37.4 0.36
100 -18 0.24 52 0.47 -28 0.25 82 0.42 19 0.17 -70 0.53
Table 14B. Deviation from reference value for each GB, dij (nanometers) and Normalized Error, En, of
the Steel GB for the next six participants.
NMI
LACOMET TTBS BSJ CENAM
Nominal
dij En dij En dij En dij En
1.000 5 31.3 0.61 39.3 0.38 Not reported
Not
reported 7.3 0.24
5 19.6 0.38 43.6 0.41 -15.4 0.27 -3.4 0.11
7 29.6 0.40 22.6 0.21 -34.4 0.59 8.6 0.28
10 29.8 0.40 -16.2 0.11 -21.2 0.34 -12.2 0.39
50 31.1 0.35 195.1 0.61 -30.9 0.22 9.1 0.16
75 22.6 0.25 65.6 0.19 -189.4 0.94 -3.4 0.04
100 -26 0.24 332 0.98 -5 0.02 9 0.09
Table 14C. Deviation from reference value for each GB, dij (nanometers) and Normalized Error, En, of
the Steel GB for the last four participants.

SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 24 / 29
2014-10-29
NMI
NPLI CMI NIST INMETRO INTI LATU
Nominal
dij En dij En dij
En
En
dij En dij En dij En
1.000 5 -36.1 0.69 3.9 0.08 -23.1 0.85 -28.1 0.43 -5.1 0.11 -33.1 0.63
5 -10.6 0.19 19.4 0.41 3.4 0.13 -24.6 0.37 -0.6 0.01 -39.6 0.75
7 -41.7 0.71 -1.7 0.04 6.3 0.23 -17.7 0.27 -16.7 0.36 -38.7 0.74
10 -65.7 1.09 14.3 0.30 5.3 0.19 -9.7 0.15 -0.7 0.01 -3.7 0.07
50 -85.9 0.81 34.1 0.57 10.1 0.32 -8.9 0.12 -16.9 0.25 -2.9 0.04
75 -96.2 0.71 13.8 0.19 11.8 0.28 -47.2 0.53 -14.2 0.17 -25.2 0.28
100 -56.9 0.35 33.1 0.38 18.1 0.29 -31.9 0.31 39.1 0.37 -29.9 0.31
Table 15A. Deviation from reference value for each GB, dij (nanometers) and Normalized Error, En, of
the Ceramics GB for the first six participants.

NMI
DICTUC INDECOPI IBMETRO INEN SIC CENAMEP
Nominal
dij En dij En dij En dij En dij En dij En
1.000 5 -13.1 0.24 -11.1 0.20 313.9 4.59 -6.1 0.05 -1.1 0.02 -8.1 0.32
5 -27.6 0.51 -25.6 0.47 329.4 4.68 -30.6 0.27 -20.6 0.44 -11.6 0.46
7 -38.7 0.71 -26.7 0.49 318.3 4.52 -31.7 0.27 -19.7 0.42 -13.7 0.54
10 -17.7 0.32 -10.7 0.20 334.3 4.61 4.3 0.04 -25.7 0.53 -3.7 0.14
50 -40.9 0.72 -50.9 0.66 354.1 3.99 34.1 0.22 32.1 0.47 -2.9 0.04
75 -35.2 0.49 -1.2 0.01 343.8 3.41 33.8 0.19 18.8 0.21 27.8 0.28
100 -41.9 0.60 8.1 0.07 383.1 3.39 63.1 0.32 63.1 0.57 25.1 0.19
Table 15B. Deviation from reference value for each GB, dij (nanometers) and Normalized Error, En, of
the Ceramics GB for the next six participants.

NMI
LACOMET TTBS BSJ CENAM
Nominal
dij En dij En dij En dij En
1.000 5 -5.1 0.10 63.9 0.55 Not reported
Not
reported -6.1 0.16
5 -26.6 0.52 69.4 0.60 -46.6 0.59 -16.6 0.42
7 -7.7 0.15 38.3 0.33 -69.7 0.87 13.3 0.34
10 -0.7 0.01 Not reported
Not
reported -53.7 0.62 -5.7 0.14
50 -21.9 0.25 374.1 1.17 -121.9 0.61 -5.9 0.08
75 -34.2 0.39 343.8 1.01 -276.2 0.99 -9.2 0.10
100 31.1 0.28 683.1 1.90 -171.9 0.47 11.1 0.09
Table 15C. Deviation from reference value for each GB, dij (nanometers) and Normalized Error, En, of
the Ceramics GB for the last four participants.
Table 16 shows the Root Mean Square (RMS) values of the deviations of the participants,
RMS, with respect to the RV. It gives a general idea of the deviations of each participant with
respect to RV. It is determined as:

n
)ee(
n
1i
2
jij
RMS
(3)

SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 25 / 29
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Where:
eij Deviation from nominal of laboratory i on GB j,
RV of GB j,
n Number of GB
NMI RMS (nm)
Steel GB Ceramics GB
NPLI 69.5 62.5
CMI 52.2 20.9
NIST 12.4 13.0
INMETRO 21.9 27.1
INTI 24.1 18.2
LATU 18.6 28.6
DICTUC 18.4 32.5
INDECOPI 25.2 24.7
IBMETRO 26.5 340.3
INEN 36.3 34.4
SIC 27.6 31.3
CENAMEP 32.8 16.1
LACOMET 27.5 22.1
TTBS 149.7 350.0
BSJ 80.8 147.5
CENAM 8.1 10.5
Table 16. RMS Values of the deviations with respect to the RV, RMS, of the participants.
In this case, as the RV is determined external to the comparison, it is not possible calculate Birge ratio.
11. Discussion and Conclusions
11.1 Discussion
The comparison was linked to a previous interferometric comparison that measured
the same artifacts. This was an advantage as the RV were obtained from the
interferometric stage providing low uncertainty RV for the Mechanical Compariosn
exercise. Not only were the RV obtained by a metrological superior technique, but it
was the result of the measurement of several participants that measured by this
technique.
In the second stage of circulation which included only those NMI that measured
exclusively by mechanical comparison (10 laboratories), the timing of circulation (from
2010-04-15 to 2011-04-28) was short thanks to the hand-delivery of the artifacts to
the following participant. We would like to thank the participants for having taken this
trouble and we suggest adopting this transport option whenever possible as it
reduces the time of circulation and the risk of damage to the artifacts during transport.

SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 26 / 29
2014-10-29
There was also some time saving during circulation in the first stage, as the NMI that
participated in both exercises received the artifacts only once and measured by both
techniques during the same period.
Declared standard uncertainties among participants spread over a 6 fold range, going
from 10 nm to 60 nm for the shortest GB and from 25 nm to 180 nm for the 100 mm
GB.
A few participants had the same traceability source because their master GB were
calibrated at a same laboratory. However, we consider the influence of these
correlations minimal and they were not taken in account in the present analysis.
11.2 Conclusions
From Section 7 we observe that there were no appreciable changes on the
measurements performed by the pilot laboratory of the ensemble of the GB of both
materials over the last five years. Even though some drift may be appreciated on the
steel GB during their first years of their history, the values shown prove they reached
stability since 2005 approximately. Therefore, it can be assumed that the artifacts
behaved adequately during the comparison exercise and that the exercise was valid.
It may not be asserted that there was more consistency in one material or another
and results were similar for both materials.
From the comparison of the simple mean and weighted mean presented in Appendix
A with the RV for all GB, we observe that both means are always pretty close to the
RV. We do not identify either any systematic effect between the Interferometric mean
or RV and the mechanical comparison mean.
Once Expanded Uncertainties are considered, the performance of most of the
participants for the steel GB was good, even though three results had normalized
errors greater than one: NPLI on the 75 mm, CMI on the 50 mm and CENAMEP on
the 5 mm; and BSJ did not present results for the 1.000 5 mm GB.
IBMETRO presented inconsistent results for the ceramic GB. As they obtained
consistent results for the steel GB, we presumed their raw measurements of the
Ceramic GB were probably good, but that they applied a wrong correction for
comparing GB of two different materials. In effect, they informed us after circulation of
DRAFT A, they made such a mistake and they are already amending the
miscalculation in the procedures of their Quality Management System.
Also for the ceramic GB TTBS obtained inconsistent results for the three longer ones;
and TTBS and BSJ did not present results for two nominal values.
For the rest of the participants their results are judged satisfactory which proves their
technical competence.
12. Acknowledgements
We would like to acknowledge:
SIM WG.4 Length and SIM Technical Committee for having funded the
purchase of the fourteen GB to carry this comparison.

SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 27 / 29
2014-10-29
In an anonymous way, the technicians and colleagues from our different
institutions that contributed directly or indirectly to the measurements of the
artifacts in this comparison.

13. References
1. ISO 3650:1998(E), Geometrical Product Specification (GPS) Length Standards
Gauge Blocks, International Organization for Standardization, Geneva, Switzerland.
2. C. Colín, M. Viliesid, et.al. SIM Regional Key Comparison SIM.L-K1:2007.
Calibration of Gauge Blocks by Optical Interferometry. June 2012.
3. Thalmann R., CCL-K1 Final report, Calibration of gauge blocks by interferometry,
Wabern, Switzerland, November 2000. At BIPM website, http://www.bipm.fr.
4. Viliesid M., Comparison CCL-
Two-dimensional (2-D) Artifacts (Ball plates , 2008- 10-27
At BIPM website, http://www.bipm.fr.
5. Cox, M.G., 2002, The evaluation of key comparison data, Metrologia, 2003, 39, pp
589-595.
6. Beissner, K., 2002, On a measure of consistency in comparison measurements,
Metrologia, 2003, 39, pp 59-63.
7. Kacker, R., Datla, R., Parr, A., 2002, Combined result and associated uncertainty
from interlaboratory evaluations based on the ISO Guide, Metrologia, 2003, 39, pp
279-293.
8. Decker J., Ulrich A., Lapointe A., Viliesid M., Pekelsky J. R., Two-part Study towards
Lowest Uncertainty Calibration O Ceramic Gauge Blocks: Interferometry And
Mechanical Comparison Techniques, in Recent Developments in Traceable
Dimensional Measurements, Proceedings of SPIE The International Society for
Optical Engineering, Vol. 4401 presented at Munich, Germany, June 2001.
9. Decker J., Pekelsky J. R., Uncertainty of Gauge Block Calibration by Mechanical
Comparison: A Worked Example Case 1: Gauges of Like Materials, NRC Doc 39998,
presented at National Conference of Standards Laboratories, Ottawa, Ontario, 1996.

SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 28 / 29
2014-10-29
Annex A Calculation of Alternate Statistical Parameters.
Steel gauge blocks / Nominal length, mm
Statistical estimator 1.000 51 5 7 10 502 753 1004
Reference Value, RV -9.3 26.4 -12.5 36.2 4.9 -105.6 -42.0
Standard uncertainty 4.1 4.2 4.2 3.9 6.3 8.5 8.6
Simple arithmetic mean -5.9 20.9 -11.1 27.7 0.1 -104.6 -50.3
Standard uncertainty 7.7 7.6 7.8 8.7 11.7 17.1 17.6
Birge Ratio 0.77 0.83 0.83 0.57 0.40 0.50 0.54
Weighted mean -10.2 16.9 -8.8 29.7 5.4 -104.9 -54.9
Standard uncertainty 5.5 5.4 5.5 5.7 8.6 10.5 13.8
Birge Ratio 0.87 0.97 0.94 0.76 0.44 0.62 0.56
Median -11.0 10.5 -12.5 22.0 0.0 -109.5 -60.0
Observed chi-squared 10.7 17.3 14.6 10.1 2.6 5.0 4.6
Degrees of freedom 14 15 15 15 13 13 12
0.71 0.30 0.94 0.82 1.00 0.976 0.97
Reduced chi-squared 0.76 1.16 0.97 0.67 0.20 0.38 0.39



1 BSJ not considered in the statistical parameter calculations as they did not measure.
2. CMI and TTBS were eliminated from the statistical parameter calculations.
3. NPLI and BSJ were eliminated from the statistical parameter calculations.
4 CMI, INEN and TTBS were eliminated from the statistical parameter calculations.

SIM.L-S6 Calibration of Gauge Blocks by Mechanical Comparison 29 / 29
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Ceramics gauge blocks / Nominal length, mm
Statistical estimator 1.000 55 56 76 107 508 759 1008
Reference Value, RV -3.9 10.6 51.7 -14.3 105.9 136.2 -23.1
Standard uncertainty 3.9 4.0 4.0 4.1 5.7 7.0 7.8
Simple arithmetic mean -11.6 -2.0 33.9 -26.7 96.2 131.2 -13.0
Standard uncertainty 8.2 8.2 8.2 8.0 11.2 13.7 16.3
Birge Ratio 0.78 0.89 0.82 0.75 0.87 0.56 0.66
Weighted mean -16.1 -0.5 39.8 -20.6 102.8 132.4 -17.5
Standard uncertainty 5.8 5.7 5.7 5.9 8.6 11.1 13.6
Birge Ratio 0.64 0.79 0.86 0.77 0.91 0.62 0.73
Median -11.0 -10.0 34.0 -19.0 100.0 131.0 -5.0
Observed chi-squared 9.8 12.5 14.7 8.9 10.1 4.4 6.6
Degrees of freedom 13 14 14 13 12 11 12
0.71 0.57 0.40 0.78 0.61 0.96 0.88
Reduced chi-squared 0.75 0.89 1.05 0.69 0.84 0.40 0.55


5 IBMETRO and BSJ were not considered for the statistical parameter calculations.
6 IBMETRO was not considered for the statistical parameter calculations.
7 IBMETRO and TTBS not considered for the statistical parameter calculations.
8 IBMETRO, TTBS and BSJ not considered for the statistical parameter calculations.
9 NPLI, IBMETRO, TTBS and BSJ were eliminated from the statistical parameter calculations.