[Header]
Format=SMU
ver=3
appl=GUMWB32
MR=0
SUR=0
SUP=0
UIP=1
UCR=0
status=2
FUEB=0

[Title]
Title='Calibration of a gauge block of nominal length 50 mm'
Ref=''
Date='03/07/2009'
Version=''
Author=''
Description=21
Description[0]='The calibration of the grade 0'
Description[1]='gauge block (ISO 3650) of 50 mm nominal length is carried out by comparison'
Description[2]='using a'
Description[3]='comparator and a'
Description[4]='calibrated gauge block of the same nominal length and the same material as'
Description[5]='reference standard. The difference in central length is determined in vertical'
Description[6]='position of the two gauge blocks using two length indicators contacting the'
Description[7]='upper and lower measuring faces.'
Description[8]=''
Description[9]='The actual length of the gauge block to be calibrated is related to the actual'
Description[10]='length of the reference standard by the equation'
Description[11]=''
Description[12]='l_X'' ='
Description[13]='l_S'' +'
Description[14]='\delta\l'
Description[15]=''
Description[16]='with \delta\l being the measured length difference. l_X blocks under the'
Description[17]='measurement conditions, in particular at a'
Description[18]='temperature which on account of the uncertainty in the measurement of'
Description[19]='laboratory temperature may not be identical with the reference temperature for'
Description[20]='length measurements.'
PictureCount=1
DCount=1

[Model]
Model=1
Model[0]='l_X = l_S + \delta\l_D + \delta\l + \delta\l_C - L * (\alpha\_av * \delta\t + \delta\\alpha\ * \Delta\t_av + u_at) - \delta\l_V'
CE=1
CTC=1

[Components]
CompOrder=3
Comp=12
Comp[0]=l_X_
Comp[1]=l_S_
Comp[2]=\delta\l_D_
Comp[3]=\delta\l
Comp[4]=\delta\l_C_
Comp[5]=L
Comp[6]=\alpha\_av_
Comp[7]=\delta\t
Comp[8]=\delta\\alpha\
Comp[9]=\Delta\t_av_
Comp[10]=u_at_
Comp[11]=\delta\l_V_

[COMP 0]
Type=Result
Definition='length of the gauge block to be calibrated'
Unit='mm'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=49.999926
Ustd=3.41849578931129E-5
Neff=948
HB=1
HC=0
HR=1
IO=0
PictureCount=1
DCount=1

[COMP 1]
Type=TypBNormal
Definition='length of the reference gauge block at the reference temperature of t_0=20 °C according to its calibration certificate'
Unit='mm'
Description=4
Description[0]='REFERENCE STANDARD: The length of the reference gauge block together with the'
Description[1]='associated expanded uncertainty of measurement is given in the calibration'
Description[2]='certificate of a'
Description[3]='set of gauge blocks as 50,000 02 mm ±30 nm (coverage factor k=2).'
Vnom=50.000020
Uexp=30E-6
Fcov=2.0
PictureCount=1
DCount=1

[COMP 2]
Type=TypBTriangl
Definition='Change of the length of the reference gauge block since its last calibration due to drift'
Unit='mm'
Description=5
Description[0]='DRIFT OF THE STANDARD: The temporal drift of the length of the reference gauge'
Description[1]='block is estimated from previous calibrations to be zero with limits ±30 nm.'
Description[2]='General experience with gauge blocks of this type suggest that the zero drift'
Description[3]='is the most probable value and that a'
Description[4]='triangular probability distribution can be assumed.'
Vnom=0
Hlim=30E-6
PictureCount=1
DCount=1

[COMP 3]
Type=TypAPooled
Definition='observed difference in length between the unknown and the reference gauge block'
Unit='mm'
Description=6
Description[0]='MEASUREMENTS: A'
Description[1]='pooled estimate of standard deviation of 15 nm derived from previous'
Description[2]='measurements is used for the evaluation of the repeatability. The following'
Description[3]='observations are made for the difference between the unknown gauge block and'
Description[4]='the reference standard, the comparator being reset using the reference standard'
Description[5]='before each reading.'
Observations=5
Sp=12E-6
Neff=9
Reading=5
Reading[0]=-100E-6
Reading[1]=-90E-6
Reading[2]=-85E-6
Reading[3]=-95E-6
Reading[4]=-100E-6
Mode=0
MinObs=5
PictureCount=1
DCount=1

[COMP 4]
Type=TypBRectang
Definition='correction for non-linearity and offset of the comparator'
Unit='mm'
Description=10
Description[0]='COMPARATOR: The comparator has been verified to meet the specifications stated'
Description[1]='in EAL-G21. From this it can be ascertained that for length differences D'
Description[2]='up to ±10 µm corrections to the indicated length difference are within the'
Description[3]='limits ±(30 nm +'
Description[4]='0,02 *'
Description[5]='abs(D)). Taking into account the tolerances of the grade 0'
Description[6]='gauge block to be calibrated and the grade K'
Description[7]='reference gauge block the maximum length difference will be within ±1 µm'
Description[8]='leading to the limits of ±32 nm for non-linearity and offset corrections of the'
Description[9]='comparator used.'
Vnom=0
Hlim=32E-6
PictureCount=1
DCount=1

[COMP 5]
Type=Const
Definition='nominal length of the gauge blocks under consideration'
Unit='mm'
Description=1
Description[0]='Nominal length of the gauge block to be calibrated.'
Vnom=50
PictureCount=1
DCount=1

[COMP 6]
Type=TypBRectang
Definition='average of the thermal expansion coefficients of the unknown and the reference gauge block'
Unit='K^-1'
Description=4
Description[0]='TEMPERATURE CORRECTION: Based on the calibration certificate of the reference'
Description[1]='gauge block and the manufacturer’s data for the gauge block to be calibrated'
Description[2]='the linear thermal expansion coefficient of the steel gauge blocks is assumed'
Description[3]='to be within the interval (11,5±1,0)×10^-6 °C^-1^.'
Vnom=11.5E-6
Hlim=1E-6
PictureCount=1
DCount=1

[COMP 7]
Type=TypBRectang
Definition='difference in temperature between the unknown the reference gauge block'
Unit='K'
Description=4
Description[0]='TEMPERATURE CORRECTION: Before calibration care is taken to ensure that the'
Description[1]='gauge blocks assume ambient temperature of the measuring room. The remaining'
Description[2]='difference in temperature between the standard and the gauge block to be'
Description[3]='calibrated is estimated to be within ±0,05 K.'
Vnom=0
Hlim=0.05
PictureCount=1
DCount=1

[COMP 8]
Type=TypBTriangl
Definition='difference in the thermal expansion coefficients between the unknown and the reference gauge block'
Unit='K^-1'
Description=3
Description[0]='TEMPERATURE CORRECTION: Combining the two rectangular distributions the'
Description[1]='difference in linear thermal expansion coefficient is triangularly distributed'
Description[2]='within the limits ±2E-6 °C^-1^.'
Vnom=0.0
Hlim=2E-6
PictureCount=1
DCount=1

[COMP 9]
Type=TypBRectang
Definition='deviation of the average temperature of the unknown and the standard gauge block from the reference temperature'
Unit='K'
Description=3
Description[0]='TEMPERATURE CORRECTION: The deviation of the mean temperature of measurement'
Description[1]='from the reference temperature t_0 ='
Description[2]='20 °C is estimated to be within ±0,5 °C.'
Vnom=0
Hlim=0.5
PictureCount=1
DCount=1

[COMP 10]
Type=TypBNormal
Definition='coorection for second order terms of (\delta\\alpha\ * \Delta\t_av)'
Unit=''
Description=11
Description[0]='TEMPERATURE CORRECTION: The best estimates of the difference in linear'
Description[1]='expansion coefficients (\delta\\alpha\)'
Description[2]='and the deviations of the mean temperature from the reference temperature'
Description[3]='(\Delta\t_av)'
Description[4]='are zero. Therefore second order terms have to be taken into account in the'
Description[5]='evaluation of their uncertainty contribution resulting in the product of'
Description[6]='standard uncertainties associated with the factors of the product term'
Description[7]='(\delta\\alpha\ ×'
Description[8]='\Delta\t_av) in the model equation. The final standard uncertainty is'
Description[9]='u(\delta\\alpha\ × \Delta\t_av) ='
Description[10]='0,236·10^-6^.'
Vnom=0
Uexp=0,236E-6
Fcov=1.0
PictureCount=1
DCount=1

[COMP 11]
Type=TypBRectang
Definition='correction for non-central contacting of the measuring faces of the unknown gauge block'
Unit='mm'
Description=7
Description[0]='VARATION IN LENGTH: For gauge blocks of grade 0'
Description[1]='the variation in length determined from measurements at the centre and the four'
Description[2]='corners has to be within ±0,12 mm (ISO 3650). Assuming that this variation'
Description[3]='occurs on the measuring faces along the short edge of length 9'
Description[4]='mm and that the central length is measured inside a'
Description[5]='circle of radius 0,5 mm the correction due to central misalignment of the'
Description[6]='contacting point is estimated to be within ±6,7 nm.'
Vnom=0
Hlim=6.7E-6
PictureCount=1
DCount=1

[Correlations]
Description=0

[CalCorr]
CNT=7
R[0,4]=0.5404485
R[0,7]=-0.4855592
R[0,1]=0.4387895
R[0,2]=0.3582701
R[0,10]=-0.3451811
R[0,3]=0.1389234
R[0,11]=-0.1131564

[Diagrams]
Count=0