Page 390 - Mechatronics with Experiments

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The force corresponding to the V out = 2.0mVDC is F = 80 000 N. It is also interesting to
determine the change in the strain-gauge resistance for this force measurement,
V i
V = ΔR (6.145)
out
4 ⋅ R
o
2 ⋅ 10 −3 = 10 ΔR (6.146)
4 ⋅ 600
ΔR = 0.480 Ω (6.147)
Notice that the percentage change in the resistance of the strain gauge is
ΔR 0.480
⋅ 100 = ⋅ 100 = 0.08% (6.148)
R 600
Since the gauge factor G = 2, the strain (change in the length of the shaft is)
Δl
= (6.149)
l
1 ΔR
= (6.150)
G R
1
= ⋅ 0.08% (6.151)
2
Δl
= 0.04% (6.152)
l
0.04
Δl = ⋅ l (6.153)
100

6.8 PRESSURE SENSORS

Absolute pressure is measured relative to a perfect vacuum where the pressure is zero. The
local atmospheric pressure is the pressure due to the weight of the air of the atmosphere at
that particular location (Figure 6.46). Therefore, the local pressure varies from one location

Gauge pressure Absolute pressure
scale (PSIG) scale (PSIA)
A column of air one square inch +5 +20
cross section and as high as the
atmosphere ...
If we measure the weight of air due
to atmosphere per square inch at sea
level, it would be about 14.7 pounds. 0 PSIG +14.7 PSIA +15
0
Atmospheric pressure is
therefore 14.7 psia. Absolute pressure
o
(59 F @sea Level)
Atmospheric pressure
drops as elevation from -5 +10
sea level increases Absolute pressure
+5
-10
Vacuum
Perfect vacuum ......... -15 0
(Absolute zero pressure) - 14.7 PSIG 0 PSIA
FIGURE 6.46: Absolute pressure, gauge pressure, atmospheric pressure definitions. Adapted
from Bosch-Rexroth.