Force, Torque & Strain Measurement

Teknik Pengukuran

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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:

LdLstrainaxial a

DdDstraintransverse t

AF

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:

ALR

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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 produced for 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 = 10-6 to 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 applying the inputs of known values (standards) and measuring its output.

It involves a comparison of the instrument with a higher standard and, thus, reduces bias errors.

Once this relationship is established or verified, the input values can be inferred from the measured values (often voltage) accurately.

Force (F=mg)(Standard brass-weight)

Load Cell(Cantilever Beam)

SGBridge Circuit +Power Source

OutputVoltage

Force Load Cell Strain Gage(s) Bridge Circuit

Voltage

ExcitationVoltage

The voltage vs force relationshipmust be determined experimentally.(Calibration)

Voltage

Force

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Load Cell

Transducers which measure force, torque, or pressure usually contain an elastic member that converts the mechanical quantity into a deflection or strain.

Load cell= elastic members employed in these transducers 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

due to its simple design and low cost. To measure an applied force F, strain gages are mounted on the beam.

F H b l L

Support

Beam

F

EbhL

material ofproperty

beamofgeometry

2

locationSGat

16

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Load Cell: Axial

F

Ebh

material ofproperty

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 and installation requirements

Transverse sensitivity Smaller Kt is desirable

a

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 CellA (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 = Young’s Modulus(N/m2) = Poisson’s ratioro = Outside radius (m) L = Length of cylinder (m)ri = Inside radius (m) φ = angular deflection (rad)

L

rrGT io

2

44

T

ro

ri

L

No torque applied

Torque T applied

12EG

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Torque Cell

T

r

1

2

3

4

SG3 and SG4 onopposite side

45

45

T

Gr

propertygeometry

3

11