Development of axi-symmetric acoustical and structural Finite Elements for the analyse of the deformation of the piston-cylinder unit of a metrological pressure balance.
Pierre Lamary1; Luiz Soares Junior1; Francisco Ilson da Silva Junior1
1 Federal University of Ceara, Department of Mechanical Engineering
doi:10.20906/CPS/CON-2016-1135
Resumo
Metrological pressure balances are used to calibrate industrial equipments such as manometers. The main part of the system is the piston-cylinder unit. When the instrument to be calibrated is plugged to the pressure balance, the measured pressure is not directly given by the pressure balance. It is deduced from an equilibrium position obtained by putting masses at the top of the piston which enters into the chamber of the cylinder and from an analytical normative phenomenological formula. Several authors have suspected that this formula does not account for the true deformation of the piston-cylinder unit and have proposed to address this question using numerical methods such as the Finite Element Method. The modelling is somehow difficult owing to the micro-metric gap between the piston and the cylinder and owing to fluid behaviour. Any new approach or model is therefore welcome to consolidate the first results obtained. This paper will focus on the development we have carried out in order to model the piston-cylinder unit of a pressure balance used at our department. The model takes benefit of the axi-symmetry of the problem and reduces to a two-dimensional finite element model as if the piston-cylinder unit were cut by an half radian plane. Axi-symmetric structural and acoustical fluid finite elements were developed for this purpose and implemented in our finite element code. The paper will enter in some theoretical and implementation details which are generally not presented in the literature. Finally, a model is constructed with millimetric and micrometric elements. For the pressure balance studied, results indicate that the effective area of the piston is a function of the engagement length of the piston in the cylinder and a function of the applied pressure.
Palavras-chave: Metrology; Pressure balance; Axi-symmetry; Finite Element