Comparison of the pressure distortion coefficients of the LNE and PTB 1 GPa piston-cylinder assemblies

Project Description

Within the scope of EUROMET project 463, the pressure distortion coefficients and the associated uncertainties of LNE 1 GPa piston-cylinder assembly no. 7594 were calculated using the same finite element methods (FEM) on the basis of the materials elastic constants, assemblies dimensions and in particular the dimensional properties of the piston-cylinder gaps.

The actual project should allow to experimentally compare the pressure distortion coefficients of the two assemblies and thus to check the consistency of the FEM results.

For the comparison, a transfer standard will be calibrated with the LNE and PTB standards whose pressure distortion coefficients will be taken as obtained within project 463. The calibrations will be performed two times with the laboratory standards being operated once in the free-deformation and once in the controlled-clearance mode. In this way the FEM results for both operation modes can be verified.

As a transfer standard, a 500 MPa piston-cylinder assembly belonging to PTB will be used, which will be operated at PTB and LNE with their own pressure balances and mass sets. The measurements will be started at PTB in April, performed at LNE in June and repeated at PTB in August 2007. If the results obtained for this pressure range are insufficient for a conclusion, a possibility of repeated measurements at pressures up to 1 GPa will be considered. For the 1 GPa range, a 1 GPa pressure measuring multiplier or an accurate 1 GPa pressure transducer will be applied.

Final Report 2009-03-02

The comparison has been finished and the results are available in the KCDB.

  • Pressure distortion coefficients of the PTB and LNE 1 GPa piston-cylinder units calculated by FEM within EUROMET project 463 for were experimentally verified in the range up to 500 MPa using a 500 MPa pressure balance as transfer standard (TS) calibrated in PTB and LNE
  • Project was registered in KCDB as a supplementary comparison (SC). All details were specified in a Technical Protocol. Coordinator of SC and TS (only p-c unit) provider was PTB.
  • The SC schedule was:May 2007 – PTB (initial investigation)
    • June-July 2007 – LNE (measurements)
    • July-August 2007 – PTB (measurements, final investigation)
    • 07 January 2008 – simultaneous exchange of reports.
  • PTB and LNE 1 GPa standards (lab standards – LS) were operated in free deformation (FD) and controlled clearance (CC) mode. Even if the pressure dependence of the effective area was not perfectly linear, the pressure distortion coefficient (l) of TS was determined from a first order fitting . Analysis of the results was performed with ls of LSs as:
    • attributed by the laboratories
    • FEM-calculated for real gap
    • FEM-calculated for constant gap.


  1. With LSs ls attributed by the laboratories, PTB – by FEM & experimental method, LNE – by experimental method, results are always equivalent within 2u and above 100 MPa within u. The max difference in l of TS is lLNE,FDlLNE,CC = 0.066·10-6 MPa-1.
  2. With LSs l’s calculated by FEM for real gap, the maximum difference in l is  lLNE,CC ‑ lLNE,FD = 0.174·10-6 MPa-1. Without lLNE,CC, the maximum difference is  lPTB,CC ‑ lLNE,FD = 0.043·10-6 MPa-1.
  3. With LSs ls calculated by FEM for constant gap, the max difference in l is only lLNE,FD ‑ lPTB,CC = 0.015·10-6 MPa-1. All these results are by about 0.075·10-6 MPa-1 smaller than the experimental l’s.
  4. Discrepancies of the FEM real gap results are evidently caused by inconsistent dimensional data regarding the clearance value (0.20 µm for LSLNE and 0.32 µm for LSPTB at null pressure approximately) combined with their underestimated uncertainties.
  5. Nevertheless, the results support the CMCs of both labs: for the LSs in normal use, the difference lLNE - lPTB is 0.030·10-6 MPa-1 or -0.017 MPa-1.
Mass and Related Quantities (M)
Coordinating Institute
PTB (Germany)
Participating Partners
LNE (France)