Biomedical Engineering Reference
In-Depth Information
Strain Gauge Transducers
Strain gauges are displacement-type transducers that measure changes in the length of
an object as a result of an applied force. These transducers produce a resistance change that
is proportional to the fractional change in the length of the object, also called strain, S,
which is defined as
¼
D
l
l
S
ð
10
:
6
Þ
where
is the initial length of the object. Examples
include resistive wire elements and certain semiconductor materials.
To understand how a strain gauge works, consider a fine wire conductor of length,
D
l
is the fractional change in length, and
l
l
,
cross-sectional area,
, and resistivity, r. The resistance of the unstretched wire is given
by Eq. (10.5). Now suppose that the wire is stretched within its elastic limit by a small
amount,
A
). Because the volume of the stretched
wire must remain constant, the increase in the wire length results in a smaller cross-sectional
area,
D
l,
such that its new length becomes (
l
þ D
l
A
stretched
.Thus,
lA
¼ð
l
þD
l
Þ
A
ð
10
:
7
Þ
stretched
The resistance of the stretched wire is given by
l
þD
l
A
stretched
R
stretched
¼
r
ð
10
:
8
Þ
The increase in the resistance of the stretched wire
D
Ris
l
A
ð
10
:
9
Þ
D
R
¼
R
r
stretched
Substituting Eq. (10.8) and the value for
A
stretched
from Eq. (10.7) into Eq. (10.9) gives
2
l
A
2
2
2
ð
l
þD
l
Þ
l
r
ð
l
þ
2
l
D
l
þD
l
l
Þ
D
R
¼
r
r
A
¼
ð
10
:
10
Þ
l
A
Assume that for small changes in length,
D
l
<<
l
, this relationship simplifies to
2
D
l
A
2
D
l
l
D
R
¼
r
¼
R
ð
10
:
11
Þ
The fractional change in resistance, (
D
R/R), divided by the fractional change in length,
(
), is called the gauge factor, G. Note that G is a unitless number. Accordingly, the
gauge factor provides sensitivity information on the expected change in resistance for a
given change in the length of a strain gauge. The gauge factor varies with temperature
and the type of material. Therefore, it is important to select a material with a high gauge
factor and small temperature coefficient. For a common metal wire strain gauge made of
constantan, G is approximately equal to 2. Semiconductor strain gauges made of silicon
have a gauge factor about 70 to 100 times higher and are therefore much more sensitive
than metallic wire strain gauges.
D
l
/
l
