Comparison of methods for calculating distortion in pressure balances up to 400 MPa - EUROMET Project 256

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.

A comparative approach for the characterization of a pneumatic piston gauge up to 8 MPa using finite element calculations

“…Prior to computation, a model of the piston-cylinder assembly was designed. The piston-cylinder assembly is taken as a 2D model [2,3,13] assuming axial symmetry as shown in figure 2. Assuming point no 8 in figure 2 as the origin, the coordinates of the other key points were calculated.…”

“…For simple piston-cylinder geometry the effective area under pressure is given by equation (3). As already mentioned, the NPLI-8A, with pressure range 8 MPa pneumatic pressure unit with a nominal effective area of 4.902 445 586 × 10 −5 m 2 and piston-cylinder made of tungsten carbide operating in free deformation mode (FDM) was selected as the object for our calculations.…”

“…All the components are interdependent and complex in nature, and very few available methods provide solution. It is for this reason a number of quite different techniques have been reported to be used, and among them application of the finite element method (FEM) has been quite significant and important [2,3]. The complexity of the geometry and the boundary conditions makes the FEM more reasonable in solving mechanical problems.…”

Experimental and dimensional characterization of a prototype piston-cylinder unit and validation using finite element analysis (FEA)

“…According to these assumptions, the derived Navier-Stokes equations was used for calculation pressure distributions along the clearance and obtained as the following [5][6][7]:…”

“…Iterative method is used to determine the exact pressure distributions in the clearance. The method was explained in [5][6][7]. Firstly, a linear pressure distribution was applied in the clearance and obtained elastic deformations in the radial directions for both piston and cylinder and derived the new gap profile from these deformations and constant gap width.…”