Mathematical model of the Lame' Problem for Simplified Elastic Theory applied to Controlled-Clearance Pressure Balances

Abstract

In order to obtain more accurate measurements, the use of pressure balances with the controlled-clearance system is well known in the history of high pressures metrology. Furthermore, the introduction of assemblies with cylinders made up of two materials to the construction of controlled-clearance pressure balances, is one of the most important developments in the field of high pressure measurements. The use of some analytical procedures for the characterization of the pressure balances (also known as piston gauges) becomes more difficult especially for the case of geometries with composite cylinders. Those geometries were also studied with the analytical method developed by the author[1] (based on a simplified model) and described in this paper. This method was also reported in some not original publications from 2003 to 2007. The analysis begins with the mathematical model of thick-walled cylinder applied to the Mechanical theory of elastic equilibrium for the formulation of the so called Simplified Elastic Theory which represents an analytical approach for the study of pressure balances. This analysis is known as the Lame' problem. The solution of the Lame' Problem is used to determine the pressure distortion coefficient for the controlled-clearance pressure balances including the case of pressure balances with the cylinder made up of two materials.