Instrumentation & Measurement Magazine 24-5 - 13
If we assume an emitting light with enough of a small spot-size
on the diaphragm center relative to the overall area of it, one
can approximate the diaphragm as a spherical convex mirror
which can reflect this beam to the receiving area of RF.
Fig. 1. Schematic diagram of a double-clad reflective-diaphragm fiber-optic
Pressure Sensor (DFOPS).
Sensor Structures and Modeling
Fig. 1 shows the designed DFOP sensor schematically. It
consists of a double-clad fiber optic probe and a flexible diaphragm
considered in contact with a uniform and smooth
pressure like a stationary fluid in a vessel. The double-clad fiber
has to be set in a way that the diaphragm initial distance
h0
.
Imposing any pressure will lead to a tiny displacement of the
central areas of the diaphragm and the output power increases.
Diaphragm Deflection Model and Analysis
The physical diaphragm deflection model was both experimentally
and theoretically analyzed [24]. The resistance of the
diaphragm against the bending caused by uniform pressure,
for thin plates gives small deflections by:
Yr
Db
,1
64
br
4 2
where shows the applied uniform pressure, and b and r are
the diaphragm radius and the radial coordinate, respectively.
Also, flexural rigidity D is:
D
provides the minimum of receiving power by the receiving
fiber (RF), and therefore the maximum of deflection corresponds
to the maximum received power for a basic distance hb
Et
12 1
2
3
(2)
where t, ν, and E are plate thickness, poisson's ratio, and
Young's modulus of the diaphragm, respectively [27]. Notice
that the pressure here actually means the pressure difference
relative to the other side of the diaphragm which is usually
considered as the atmospheric pressure.
2
(1)
Fig. 2. (a) The radial coordinate of diaphragm deflections versus a maximum pressure of p=1 atm for various diaphragm radiuses b(mm) when its thickness is
t=0.2 mm, and (b) their corresponding central maximum deflections versus pressure. (c) The radial coordinate of diaphragm deflections versus a maximum pressure
of p=1 atm for various diaphragm thicknesses t(mm) when its radius is b=15 mm, and (d) their corresponding central maximum deflections versus pressure. (All for
a Silicon-Nitride diaphragm: E=300 GPa; v = 0.24).
August 2021
IEEE Instrumentation & Measurement Magazine
13
Instrumentation & Measurement Magazine 24-5
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