The finite element method (FEM) was used in this study for the
analysis of the strain distribution of a strain gauge pressure transducer for
hydrostatic pressure measurements up to 150 MPa. The pressure transducer, which
we investigated, on the basis of `thick-walled cylindrical vessel' theory has
a free steel active element. Pressure is applied to the inside and both open
ends of this active element. The symmetrical shape of the transducer and all
the design parameters of the active element were selected in such a way as to
ensure that a symmetrical stress and strain distribution was obtained even at
the maximum working pressure of the transducer. The FEM analysis was conducted
by investigating one half of the element in three dimensions. This paper
presents the FEM output strain values for the area where the strain gauges
were bonded. The validity of those values was established by comparing them
with the results obtained from the strain gauge measurements. The relative
difference between the two sets of values determined to be lower than 13% of
the full scale. The two kinds of measuring elements were made of two different
materials; AISI 4340 steel and Invar steel, which work in the hydraulic gauge
pressure ranges of up to 150 and 100 MPa respectively. The transducers were
calibrated using piston pressure balance. The metrological specifications of a
total of eight specimens were evaluated. Although the scope of the study is
only an application of the FEM, this evaluation also suggests that this type
of transducer can be used with an estimated uncertainty of up to 0.1% of the
full scale. However, this uncertainty can be improved by a small modification
in design, to reduce the reproducibility and hysteresis errors of the device,
which are the main parameters in the evaluation of the uncertainty. The
results presented in this paper will be helpful for practical static pressure
measurements as well as for the appropriate design of this kind of pressure
transducer using the FEM.
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