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Lecture 6:Force, Torque & StrainMeasurement
May 24, 2007
TKM366 Teknik Pengukuran
DR. Joga Dharma Setiawan
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Presentation Overview
Strain gages
Load cell
Wheatstone bridge circuit
Torque cell
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Mechanics of Materials
Axial stress:
Strain:
Poisson ratio:
Modulus elasticity:
L
dLstrainaxial
a
D
dDstraintransverse
t
A
F
a
a
t
E
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Strain Gages Strain gages: for measuring force, pressure, torque, and strain.
How ?
Convert these forms of input into mechanical strain using an elastic member,which is then converted into resistance change.
Resistance change is converted into voltage using a bridge circuit, ie.Wheatstone bridge circuit
Must be properly calibrated first.
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Strain Gages
Electrical resistance:
Resitance relationship to strain:
A
LR
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Strain Gages: Calculation Example
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Strain Gages: Calculation Example
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Strain Gages: Data Example
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Strain Gages Typical Values
Electrical Resistance, R 120 Ohm or 350 Ohm
1000 Ohm with plastic materials
A high Gage Factor is desirable because a large change in R is producedfor a given strain
Metal GF= 1.6 to 4 Resistivity does not change with the strain
Semiconductor GF= 80 to 200 Fragile and sensitive to changes in temperature
Axial strain range = 10-6to 103
dR=0.00024 Ohm to 0.24 Ohm Notice how small this dR
Need to utilize Wheatstone bridge circuit
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Strain Gages: Gage Factor Table
Most GF decreases as temperature increase (NTC)
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Strain Gages Calibration
A measurement instrument
must be calibrated by applyingthe inputs of known values(standards) and measuring itsoutput.
It involves a comparison of theinstrument with a higher
standard and, thus, reducesbias errors.
Once this relationship isestablished or verified, theinput values can be inferredfrom the measured values(often voltage) accurately.
Force (F=mg)
(Standard brass-weight)
Load Cell
(Cantilever Beam)
SGBridge Circuit +
Power Source
Output
Voltage
Force Load Cell Strain Gage(s) Bridge CircuitVoltage
Excitation
Voltage
The voltage vs force relationship
must be determined experimentally.
(Calibration)
Voltage
Force
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Load Cell
Transducers which measure force, torque, orpressure usually contain an elastic member thatconverts the mechanical quantity into a deflection orstrain.
Load cell= elastic members employed in thesetransducers include link, column, rings, beams,cylinders, tubes, washers, diaphragms, etc.
Two main types of load cell
Bending-beam load-cell and
Axial load-cell.
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Load Cell: Bending Beam
The most popular types dueto its simple design and lowcost. To measure an appliedforce F, strain gages aremounted on the beam.
F
H
b
l
L
Support
Beam
FEbh
L
materialofproperty
beamofgeometry
2
locationSGat
16
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Load Cell: Axial
FEbh
materialofproperty
beamofgeometry
11
h
F
b
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Strain Gages Selection
Gage selections based on Alloy selection, number of gages, gage length, gage width, solder
tab type, gage pattern, temperature compensation, grid resistance,accuracy, stability, cyclic endurance, operating environment andinstallation requirements
Transverse sensitivity
Smaller Ktis desirablea
tt
GF
GFK
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Potential Error Sources with Strain Gages
Application errors: Gage may be damaged during installation
Need to verify resistance before stress
Electrical and magnetic field noise
Uneed shielded lead wires and insulated coatings Utilize twisted lead wires
Temperature effects
Thermal expansion of material
Self heating of strain gages
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Wheatstone Bridge Circuit
Balanced condition (EAC=0) when R1R3=R2R4or consider R1=R2 =R3 =R4
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Wheatstone Bridge Circuit: One Active Arm
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Wheatstone Bridge Circuit: Two Active Arms
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Wheatstone Bridge Circuit: Two Active Arms
Temperature compensation:
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Wheatstone Bridge Circuit: Four Active Arms
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Torque Cell
A (static) torque may be measured by observing the angular deflection of a bar or
hollow cylinder.The torque is related to the deflection angle by
where, T: applied torque (Nm)G : Shear Modulus of elasticity(N/m2)
E = YoungsModulus(N/m2)= Poissonsratio
ro= Outside radius (m) L = Length of cylinder (m)
ri = Inside radius (m) = angular deflection (rad)
L
rrG
Tio
2
44
ro
i
No torque applied
Torque T applied
12
EG
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Torque Cell
1
2
3
4
SG3 and SG4 on
opposite side
5
5
T
Gr
propertygeometry
3
11