No abstract

EUROMET project #256 was established to compare agreement between laboratory calculations of the elastic distortion that piston-cylinder assemblies of pressure balances, the primary standard for pressure measurements, undergo when subjected to pressure applied via liquid media. The following piston-cylinder assemblies were selected for comparison of the calculations: (i) PTB, 400 MPa, free-deformation type; and (ii) BNM-LNE, 200 MPa, free-deformation and controlled-clearance types. Calculations made at the IMGC using an analytical method were compared with those made at the NPL and the PTB, each using a different finite element technique.All three methods couple calculation of the elastic deformation of the piston-cylinder with calculation of the pressure distribution in the piston-cylinder clearance from a flow model. After reviewing the calculation methods, the paper presents results for each of the comparison systems. The calculated piston and cylinder distortion, annular gap profile, annular pressure distribution, piston fall rates, and pressure distortion coefficients are presented and compared with experimental measurements.A discussion is presented of the extent of the agreement between the calculation methods and what this implies for the reliability of calculated distortion coefficients. The comparison also resulted in other useful knowledge being obtained, for example on the influence of the cylinder boundary conditions and the influence of simplifications adopted in the geometrical model. This information will be of use in the application of such calculations to the design of piston-cylinder assemblies or prediction of the effect of experimentally measurable parameters.

The national metrology institutes and their partners participating in EUROMET Project 463 developed finite element methods (FEM) for calculation of the pressure distortion coefficients, including their uncertainties, of pressure balances operated at pressures up to 1 GPa and applied them to a PTB 1 GPa piston–cylinder assembly. The methods use axisymmetric models developed and analysed on the basis of the experimental data including the elastic properties of the piston–cylinder materials, pressure-dependent density and viscosity of the pressure-transmitting fluid, dimensions of the piston and cylinder and the piston–cylinder clearance as well as the conditions at the piston–cylinder boundaries. Results such as pressure distributions and radial distortions along the piston–cylinder engagement length, pressure distortion coefficients and their uncertainties as well as piston fall rates dependent on pressure are presented for the free deformation (FD) and the controlled-clearance operating modes of the assembly. The theoretical results are verified by comparing them with the distortion coefficients determined by an experimental method and with the jacket pressure distortion coefficients. The participants' results demonstrate good agreement of the distortion coefficients up to 1 GPa but rather large differences in the uncertainties of the distortion coefficients as well as in the pressure distributions, gap profiles and piston fall rate at maximum pressure. The FEM distortion coefficients obtained for the real piston–cylinder gap profile are in good agreement with the coefficients determined by the experimental method; the FEM values obtained for the ideal gap agree well with the distortion coefficients furnished by the simplified theory. For the real gap model, the uncertainty of the gap geometry is the main uncertainty source. The total standard uncertainties of the controlled-clearance distortion coefficient obtained by different methods lie between (0.078 and 0.17) × 10−6 MPa−1 at 400 MPa and between (0.04 and 0.098) × 10−6 MPa−1 at 1 GPa.

Elastic distortions in piston-cylinder units, used in primary standard piston gauges, are responsible for large uncertainties in pressure measurement values typically higher than 50 MPa. The present study considers the results obtained in the calculation of the pressure distortion coefficients of two 100 MPa piston-cylinder units and one 500 MPa unit. The calculation of distortions in the above piston-cylinder units follows the application of an analytical technique taking account iteratively of mechanical distortions and pressure distribution in the piston-cylinder clearance. The distortion values experimentally determined on the outer surface of the cylinders are compared with the calculated results. Pressure distributions in the piston-cylinder clearances, and piston and cylinder radial displacements, are calculated for various conditions of use and the results allow the pressure distortion coefficient of each unit to be obtained. Different effects on piston-cylinder units are evaluated to acquire useful information on piston gauges and to improve their accuracy.