Page 389 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

APPLICATIONS 369

to Equation (13.20), the strain sensitivity of the system is estimated to be an impressive
2 x 10 —5 per phase degree.

13.4.1.2 Calibration

The calibration was done on an uniform cantilever beam. The sensor was glued to a
fibreglass cantilever beam of length 172 mm, width 25 mm and thickness 1.5 mm. The
centre of the piezoelectric wafer is 53.3 mm from the root of the beam and the SAW
propagating direction is along the beam length. In order to reduce the effect of the substrate
in the deformation of the structure, a relatively soft plastic epoxy was used to mount the
sensor substrate. The softness of the bonding layer and the wall of the package of the
sensor make the strain on the crystal wafer surface less than the strain on the beam surface.
Therefore, a calibration is required to determine the actual sensitivity of the sensor to the
strain on the beam surface.
If we neglect the effect of the bonded piezoelectric wafer, the strain on the surface of
the beam can be calculated by simple beam theory and written as (Gere and Timoshenko
1990),
., 3r b(/ - *)
= -d s——3 (13.21)
£ x
where / is the length of the beam, jc is the distance of the location of the piezoelectric
wafer from the root, ^ is the thickness of the beam, and d s is the displacement at the tip
of the beam. In this experiment, a force at the tip bends the beam and a dial indicator
measures the tip displacement.
The wireless IDT microsensor system successfully detects the shift of the phase differ-
ence between the two echoes with respect to the variation of the tip displacement.
are calculated, using Equation (13.21), from the tip displacements, and the
The strains s x
results are plotted in Figure 13.10.
The data show that the phase shift varies almost linearly with the strain when the
strain is less than 0.0012. For larger strains, nonlinearity and larger fluctuations appear.
The nonlinearity may be due to the glue used to bond the sensor substrate, the large
deformation of the beam, or some other cause.

13.4.1.3 Dynamic strain measurement test

In a dynamic strain measurement test, the beam was extended to 750 mm in length. A
mass of 200 g was mounted at the tip to reduce the vibration frequency. The beam was
tilted off the vertical axis because of the inclination of the beam support itself, as shown in
Figure 13.11. A static strain was developed on the surface of the beam from gravitational
forces. The end of the original beam was shifted a distance w of 6 mm from the neutral
line. The theoretical strain at this sensor position was calculated from Equation (13.21) to
be about —224 microstrains. The sensor detected an actual strain of —276 microstrains.
The difference between the theoretical and experimental values is less than the resolution
of the sensor system, that is, about 51 microstrains.
Then, a force applied at the tip further deformed the beam, resulting in an additional
deflection of the beam by 15 mm. A free vibration was established by releasing the tip.