Page 387 - Mechatronics with Experiments

October 9, 2014 8:1
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JWST499-c06
JWST499-Cetinkunt
SENSORS 373 254mm×178mm
the ratio of change in the length to the total length in that direction,
ΔL
= (6.128)
L
The change in the strain-gauge resistance is converted to a proportional voltage using a
Wheatstone brige,
ΔR
V out = K ⋅ (6.129)
1
R
ΔL
= K ⋅ G ⋅ (6.130)
1
L
ΔL
= K ⋅ (6.131)
2
L
= K ⋅ (6.132)
2
Note that a strain gauge has a finite dimension. It is bounded to the surface of the part over
a finite area. Therefore, the measured strain is the average strain over the area occupied by
the strain gauge. The bonding of the strain gauge to the workpiece is very important for
two reasons: (i) it needs to provide a uniform mechanical linkage between the surface and
sensor in order to make the measurement correctly, (ii) the bonding material electrically
isolates the sensor and the part. The strain gauges themselves have a very high bandwidth.
It is possible to build strain gauge sensors that have almost 1 MHz bandwidth. Using silicon
crystal materials, strain gauge size can be minaturized while having a very large sensor
bandwidth.

6.7.2 Force and Torque Sensors
Force and torque sensors operate on the same principle. There are three main types of force
and torque sensors,
1. spring displacement based force/torque sensors,
2. strain-gauge based force/torque sensors,
3. piezoelectric based force sensors.
Let us consider a weighing station as a force sensor application. If we have a calibrated
spring with a known spring coefficient, K spring , the load force (for torque measurement, we
would use an equivalent torsional spring) can be measured as displacement,

F = K spring ⋅ x (6.133)
Using any of the position sensors, the displacement x can be converted to a proportional
voltage, and hence we obtain the force (or torque) measurement,
V = K ⋅ x (6.134)
out 1
= K ⋅ F (6.135)
2
The strain-gauge based force and torque sensors measure the force (or torque) based
on the measured strain. Again, the sensor relies on an elastic sensing component. Typical
force/torque sensors are called load cells. A load cell has built in elastic mechanical
components on which strain gauges are mounted (Figure 6.44). As the load cell experiences
the force (or torque), it deforms a small amount which induces a strain on the sensing
element. The strain is measured by the strain gauge. As a result, since the force/torque to
strain relationship is linear by the design of the load cell, the measurement is proportional
to the force/torque.