Biomedical Engineering Reference
In-Depth Information
The last term represents the piezoresistive effect of the material, that is, the change in
resistivity of the material with strain.
The relative sensitivity of such a device is given by the gauge factor,
γ
, which is
defined as
γ
=
R
/
R
ε
axial
(2.12)
where
R
is the change is resistance when the structure is stretched by an amount
L
.
This factor is usually specified on the data sheet of the strain gauge, and it can be used to
determine the axial strain directly from the change in resistance.
ε
axial
=
R
/
R
γ
(2.13)
Typical strain gauges have
R
≈
120
and
γ
≈
2.
WORKED EXAMPLE
Strain Gauge
If a 120
10
−
6
(read
as “50 microstrain”), what is the change in resistance from the unloaded to the loaded state?
From equation (2.13)
strain gauge with a gauge factor of 2.0 measures a strain of 50
με(
50
×
)
R
=
R
ε
axial
γ
10
−
6
=
120
×
50
×
×
2
=
0
.
012
2.4.1.2 Measuring with a Wheatstone Bridge
Because the change in resistance is small, measurement can be quite challenging, and
a Wheatstone bridge configuration shown in Figure 2-14 is generally used. It should be
noted that temperature changes can result in resistance changes of the same order as those
caused by strain, so temperature compensation is essential if good accuracy is required.
A typical example of strain gauge based displacement measurement is shown in
Figure 2-15. In this application, the strain gauges are attached to the upper and lower
faces of a cantilever beam. When the beam deflection is downward, the length of the strain
gauges on the upper surface increases, and the length on the lower surface decreases.
It is possible to use a single strain gauge element and three fixed resistors to make up
the bridge, but it is more common to use two or even four elements that provide increased
sensitivity and also compensate for temperature variations (if all the elements on the beam
remain at the same temperature).
Two different measurement modes are possible; they are the static balanced mode and
the dynamic unbalanced mode (Alciatore and Histand, 2003).
In the static balanced mode,
R
1
and
R
2
, are precision resistors, while
R
3
is a precision
potentiometer with an accurate scale displaying its resistance scale.
R
s
is the resistance of
the strain gauge in the circuit as seen in Figure 2-16.
