11

Comparison of the pressure distortion coefficients of the LNE and PTB 1 GPa

piston-cylinder assemblies

Objectives:

experimental verification of the pressure distortion coefficients calculated by FEM within EUROMET project 463

check of equivalence of the PTB and LNE pressure standards in the 500 MPa range

Project 931

Participants

PTB (coordinator)LNE

22

Project 931

Results of project 463IMGC-CNR/UNICAS, PTB, NPL, LNE, UME, 1998-2005

Aims:Extension of methods to 1 GPa pressure rangeDevelopment of approach for estimation of λ uncertaintyAdoption of real piston-cylinder gap geometry in calculating methodsCharacterisation of PTB and LNE 1 GPa assemblies

LNE 1 GPa unitA0 = 10 mm2,max. load by 1000 kg

PTB 1 GPa unitA0 = 5 mm2,max. load by 500 kg

33

Project 931

Results of project 463

supportingringsof brass st

eel

WC

+ C

o

p

O-ringsof NBRpj

Common characteristics:Free-deformation / controlled-clearance type

Tungsten carbide, steel

Ball for applying load

Piston

ø 3,5 mm

22 m

mø 18 mm

Cylinder

Jacket pressure

Pressure seal adapter

O-ring

Sleeve

LNE 1 GPa unitPTB 1 GPa unit

44

Project 931

Results of project 463

1248800

1248900

1249000

1249100

1249200

1249300

1249400

1249500

1249600

1249700

1249800

-15 -10 -5 0 5 10 15height / mm

half

diam

eter

/ nm

str. 0°str. 45°str. 90°str. 135°rnd. 0°rnd. 45°rnd. 90°rnd. 135°diam. 0°diam. 90°meanuncert. large

cylinder

piston

PTB 1 GPa unit

h0 = (0.202 ± 0.020) µm

s(r) = s(R) = 55 nm

h0 = (0.32 ± 0.03) µm

Piston: s(r)/nm = 40 + 5⋅|z/mm|Cylinder: s(R)/nm = 60 + 10⋅|z/mm|

1.7664

1.7665

1.7666

1.7667

1.7668

1.7669

1.7670

1.7671

1.7672

-2 0 2 4 6 8 10 12 14 16 18 20 22

height / mm

half

diam

eter

s / m

m

0°90°

cylinder

piston

LNE 1 GPa unit

55

Project 931Results of project 463PTB unit in CC mode

PTB

PTB

IMGC/UNICAS

UME

LNE

experim. method

experim. -u

experim. +u

Lame

Lame -u

Lame +u

IMGC/UNICAS

NPL

LNE

0.30

0.35

0.40

0.45

0.50

0 100 200 300 400 500 600 700 800 900 1000

pressure / MPa

λC

C ×

106 M

Pa

const gap

real gap

Agreement of FEM and experimental methodsreal gap

FD: λFEA - λexp = 0.016·10-6

CC: λFEA - λexp = 0.017·10-6

const gap

-0.073·10-6 MPa-1

-0.42 ·10-6 MPa-1

66

Project 931

PTBIMGC/UNICAS

LNELame

PTB

IMGC/UNICAS

LNE

experimen. method

Lame -u

Lame +u

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 100 200 300 400 500 600 700 800 900 1000

p / MPa

λC

C ×

106 M

PaResults of project 463LNE unit in CC mode

const gap

real gap

Agreement of FEM and experimental methodsreal gap

FD: λFEA - λexp = 0.06·10-6

CC: λFEA - λexp = 0.23·10-6

const gap

-0.008·10-6 MPa-1

-0.014·10-6 MPa-1

77

Project 931

Experimental verification

Using 500 MPa piston-cylinder assembly as a transfer standard (TS)

Calibration of TS using LNE and PTB 1 GPa standards operated in FD and CC mode

Determination of the TS’s λ

Analysis of the results with λ of LNE and PTB 1 GPa standards as:

- usually used by the laboratories

- as FEM-calculated for real gap

- as FEM-calculated for constant gap

88

Project 931

Project organisation

Registration as a supplementary comparison in KCDB

Specification of all procedures in the Technical Protocol

Coordinator and TS (only p-c unit) provider – PTB

Schedule:

- May 2007 – PTB (initial investigation)

- June-July 2007 – LNE (measurements)

- July-August 2007 – PTB (measurements, final investigation)

- 20 December 2007 – simultaneous exchange of reports

99

Project 931

Stability of TS – PTB measurements

1.96094E-06

1.96096E-06

1.96098E-06

1.96100E-06

1.96102E-06

1.96104E-06

1.96106E-06

1.96108E-06

1.96110E-06

1.96112E-06

0 100 200 300 400 500p / MPa

A0 /

m²

CC, lefts, May

CC, rights, May

CC, rights, August

FD, rights, May

FD, rights, August

10 ppm

λ = 0.999 ppm/MPa

λ = 1.005 ppm/MPa

λ = 1.027 ppm/MPa

λ = 1.042 ppm/MPa

λ = 1.046 ppm/MPa

1010

Project 931PTB measurementsInvestigation of nonlinearity

1.96100E-06

1.96102E-06

1.96104E-06

1.96106E-06

1.96108E-06

1.96110E-06

1.96112E-06

0 100 200 300 400 500

p / MPa

A0 /

m²

old Aomean actual Aop-method, no correctionp-method, M-correctionp-method, L-correctionp-method, M&L-correctiondp-method

10 ppm

1111

Project 931Standard deviation (of mean) of PTB and LNE measurements

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500p / MPa

St.D

ev.( A

p,m

ean)

/ A

p x

106

PTB, FDPTB, CCLNE, FDLNE, CC

1212

Project 931

λ of PTB and LNE standards as usually used

-50

-40

-30

-20

-10

0

10

20

30

40

0 100 200 300 400 500

p / MPa

( Ap-A

p,re

f)/A

p,re

f x 1

06

PTB, FD modePTB, CC modeLNE, FD modeLNE, CC mode

10 ppm

1313

Project 931Equivalence checkVertical bars – standard uncertainties

-50

-40

-30

-20

-10

0

10

20

30

40

0 100 200 300 400 500

p / MPa

( Ap-A

p,re

f)/A

p,re

f x 1

06

PTB, FDPTB, CCLNE, FDLNE, CC

10 ppm

1414

Project 931λ of PTB and LNE standards as FEM-calculated for real gap – dashed lines

-60

-40

-20

0

20

40

60

80

100

120

140

0 100 200 300 400 500

p / MPa

( Ap-A

p,re

f)/A

p,re

f x 1

06

PTB, FD mode PTB, CC modeLNE, FD mode LNE, CC modePTB, FD PTB, CCLNE, FD LNE, CC

20 ppm

1515

Project 931λ of PTB and LNE standards as FEM-calculated for constant gap – dashed lines

-60

-50

-40

-30

-20

-10

0

10

20

30

40

0 100 200 300 400 500

p / MPa

( Ap-A

p,re

f)/A

p,re

f x 1

06

PTB, FD mode PTB, CC modeLNE, FD mode LNE, CC modePTB, FD PTB, CCLNE, FD LNE, CC

10 ppm

1616

Project 931Agreement with differently determined λ of PTB and LNE standards

0.95

1.00

1.05

1.10

1.15

1.20

PTB,FD

PTB,CC

LNE,FD

LNE,CC

PTB,FD

PTB,CC

LNE,FD

LNE,CC

PTB,FD

PTB,CC

LNE,FD

LNE,CC

λ x

106 M

Pa-1

λ (p ) calculated by FEM for real gap

λ (p ) calculated by FEM for const. gap

λ normaly used by laboratories

1717

Project 931

Conclusions

With λ normally used by the laboratories, PTB – by FEM & experimental method, LNE - experimental method, results are always equivalent within 2u and above 100 MPa within u. The max difference in λ of TS is λLNE,FD – λLNE,CC = 0.066·10-6 MPa-1.

With λ calculated by FEM for real gap, the max difference in λ is λLNE,CC – λLNE,FD = 0.174·10-6 MPa-1. Without λLNE,CC this difference is λPTB,CC – λLNE,FD = 0.043·10-6 MPa-1.

With λ calculated by FEM for constant gap, the max difference in λ is only λLNE,FD – λPTB,CC = 0.015·10-6 MPa-1. All these results are by about 0.075·10-6 MPa-1 smaller than the experimental λ.

Discrepancies for FEM real gap results are evidently caused by inconsistent dimensional data in combination with their underestimated uncertainty.

The results support the CMCs of both labs