Mathematical modelling of instruments for pressure metrology

The development and application of mathematical models for instruments used in pressure metrology are presented. Applications to industrial instrument design are followed by the use of finite element analysis applied to the modelling of an optically driven vibratory sensor. Results for the latter compare favourably with measurements on an experimental prototype. For pressure standards metrology, an interactive program, PVE (Pressure Viscosity Elasticity), has been developed to simulate oil and gas operated pressure balances, inclusive of both pressure-elasticity and pressure-viscosity effects. The program uses "unit" load data generated by a purpose-built FEA (Finite Element Analysis) program to characterise a given pressure balance. Then by iteration, the pressure and the piston-cylinder gap profiles along the engagement length are computed and displayed graphically. The distortion coefficient, A, defined by the effective area equation A = A0(1 + λ P), is then calculated from the piston and cylinder elastic distortions and the pressure profile. The PVE program has been applied to the NPL range of (simple geometry) pressure balances (series 100,200, 300 and 400). Results show that A is essentially constant for each of the balances. For the series 100 and 200 balances, A is approximately 3.3 ppm/MPa whereas for the series 300 and 400 balances its value is 3.0 ppm/MPa. The oil viscosity variations along the engagement length are large for the series 400 balance operating at its full pressure (320 MPa) but even in this case, A remains constant. Applications were also made to two other designs, a RUSKA 2481 re-entrant oil operated balance and a RUSKA 2470 re-entrant gas operated balance. For the oil operated one, A was found not to be constant and the effective area, A needed to be approximated with a cubic polynomial. Consequently, for this balance, A varied between -0.7 and -1.94 ppm/MPa in the range 28 to 280 MPa. For the gas operated balance, A was found to be constant at 0.14 ppm/MPa in its operating range up to 17 MPa. The PVE and FEA programs are both implemented on a graphics workstation. The theoretical approach adopted and the programs developed are discussed and presented