Page 389 - Mechatronics with Experiments

Printer: Yet to Come
October 9, 2014 8:1
JWST499-c06
JWST499-Cetinkunt
SENSORS 375 254mm×178mm
2. The strain gauge is subjected to the same strain. The strain–resistance change rela-
tionship is
1 ΔR
= (6.137)
G R
where the change in the resistance is converted to an output voltage by a Wheatstone
bridge circuit,

ΔR 4
= ⋅ V o (6.138)
R V
i
As a result, the relationship between the strain gauge output voltage and force is

( )
4 ⋅ E ⋅ A
F = ⋅ V o (6.139)
V ⋅ G
i
Notice that the stain gauge output voltage to force calibration requires information
about the material (E) on which the strain gauge is bonded, the cross-section area of the
part (A), sensor gauge factor (G), and Wheatstone bridge circuit reference voltage (V ).
i
Finally, force can be measured using piezoelectric sensors, similar to piezoelectric
pressure transducers (Figure 6.41). The piezoelectric sensor creates a charge proportional
to the force acting on it. The advantage of this is that it does not introduce an additional
flexibility into the system as part of the sensor. The only elasticity it introduces is the
elasticity of piezoelectric quartz cystal which has a modulus of elasticity in the range of
2
9
100 GPa = 100 ⋅ 10 N∕m . The typical bandwidth of a piezo based force sensor is about
10 kHz.
Example Consider the force measurement using a strain gauge on a shaft under com-
pression (Figure 6.45b). Let us consider that the shaft material is steel. The elastic Young’s
8
2
2
modulus E = 2 ⋅ 10 kN∕m , and cross-sectional area of the shaft is A = 10.0cm .We
have a strain gauge bonded on the shaft in the direction of the tension. The nominal resis-
tance of the strain gauge is R = 600 Ω, the gauge factor is G = 2.0. The other three legs
0
of the Wheatstone bridge also have constant resistances of R = R = R = 600 Ω.The
4
2
3
reference voltage for the Wheatstone bridge is 10.0 VDC. If the output voltage measured
V out = 2.0 mV, what is the force?
Notice that the stress–strain relationship, assuming the deformation is within the
elastic range,
F
= (6.140)
A
1
= (6.141)
E
ΔR
= G ⋅ (6.142)
R
V i
V out = ΔR (6.143)
4 ⋅ R o
Hence,
V ⋅ G
i
V out = ⋅ F (6.144)
4 ⋅ E ⋅ A