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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