Main Title Slide
Sensing Systems and Signal Processing
Dr Richard
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Measuring Force
We are going to look at:
Acceleration
Piezoelectricity
How they are typically measured and some example application areas.
Strain Gauges
Strain Gauges
Where might strain gauges be used?
Applications of Strain Gauges
Structural monitoring – monitoring the performance of big structures for example bridges.
Tacoma narrows 1940 – https://www.youtube.com/watch?v=j-zczJXSxnw
Millennium bridge wobble – https://www.youtube.com/watch?v=eAXVa__XWZ8
https://www.microstrain.com/content/wireless-bridge-structural-health-monitoring
Strain Gauges
Used to detect very small displacements – 50 microns
Vast range of applications
Strains in bridges and other civil structures
Power generation
Railway infrastructure
With a knowledge of elastic properties, we can measure stress indirectly
Stress / Strain
The relative change in the size or shape of an object due to an externally applied force
Dimensionless, but often written as mm/mm, % or microstrains (i.e. strain x 106)
The internal force per unit area associated with a strain
Units of Pascals, where 1 Pa = 1 Nm-2
Same units as pressure
Practical units are MPa (i.e. N/mm2) or GPa (kN/mm2)
Relation to Hooke law
Hookes Law
Stress is directly proportional to strain
Hookes law is only valid for a limited range of stress, up to the elastic limit
Young’s modulus
Ratio of (uniaxial) stress over (uniaxial) strain below the elastic limit
Hence, same units as stress (N/m2)
Also known as tensile modulus
Also widely known as elastic modulus (modulus of elasticity)
Young’s modulus is the most widely used modulus of elasticity, but there are others (e.g. bulk, shear)
Elastic Region
Extension (m)
Compressive / Tensile stress and strain
Compressive/tensile stress
displacement δx
Compressive/tensile strain
Transverse Stress and Strain
Transverse stress
Transverse (shear) strain
Strain Gauges
There are many types of strain gauges electrical, acoustic, capacitive inductive, mechanical, optical piezo-resistive semi-conductive etc.
Let’s consider an electric resistive strain gauge:
This is formed from a resistive elastic material whose change in resistance is a function of applied strain.
The change in resistance depends on the change in length l, area A and resistivity .
Strain Gauges
This is formed from a resistive elastic material whose change in resistance is a function of applied strain.
We’re interested in the relative change in resistance with an applied strain
The change in resistance depends on the change in length l, area A and resistivity .
Resistivity and Strain
Assume square faced wire with length S, Area is therefore S2
Work out change in R due to change in S
Also have change in R due to change in
Resistivity and Strain
If the strain gauge is bonded to the test piece, then changes in the dimensions of the piece due to strain will affect the strain gauge in the same way.
Recall the longitudinal strain is
However the cross-sectional area will also change due to the Poisson’s ratio () of the material. So we can work out how the change in length effects the area.
Taking length to be x direction on slide 10
Resistivity and Strain
Finally we get:
Sensitivity or Gauge factor is the relative change in resistance per unit strain
Sensitivity or Gauge factor
Material Sensitivity S or G
Platinum (Pt 100%) 6.1
Platinum-Iridium (Pt 95%, Ir 5%) 5.1
Platinum-Tungsten (Pt 92%, W 8%) 4.0
Isoelastic (Fe 55.5%, Ni 36% Cr 8%, Mn 0.5%) * 3.6
Constantan / Advance / Copel (Ni 45%, Cu 55%) * 2.1
Nichrome V (Ni 80%, Cr 20%) * 2.1
Karma (Ni 74%, Cr 20%, Al 3%, Fe 3%) * 2.0
(Fe 70%, Cr 20%, Al 10%) * 2.0
Monel (Ni 67%, Cu 33%) * 1.9
Manganin (Cu 84%, Mn 12%, Ni 4%) * 0.47
Nickel (Ni 100%) -12.1
Most metals have a Poisson’s ratio of between 0.25-0.35
So the first term is 1.5-1.7
Depending on the material often most of the sensitivity comes from the term and is usually given in the data sheet.
Strains are usually small (10-3 10-6) so dR/R is small
dR/R = G*strain = 6.1*10-3 (This is a big strain)
dR = 120 Ohms * 6.1*10-3=0.732 Ohms
Bridge Circuit
Strain gauges are usually used in a bridge circuit because the change in R is small, so it is hard to measure directly.
Bridge Circuit
This is ‘Balanced’ if = 0.
For this we have two conditions
Use Potentiometer at R2 to allow the circuit to be balanced for initial conditions.
Sensitivity
Make R3 a strain gauge and we have a circuit that gives an output voltage depending on the strain gauge resistance.
Strain Gauge
Assume balanced initial conditions, so:
And Strain is applied
Sensitivity
This is known as a Quarter Bridge Circuit
A change in strain produces a linear change in the output voltage.
Requires measuring circuit to have high input impedance so that it doesn’t effect circuit operation
This circuit can be sensitive to changes in temperature as this changes the resistances and so produces an output voltage.
Strain Gauge
for small strains
Sensitivity Example
Strain Gauge
Assuming initial balanced operation, what will V0 become if a strain of 0.001 is applied to the bridge containing a strain gauge with a sensitivity of 2?
Sensitivity – another way
Strain Gauge
Assuming initial balanced operation, what will V0 become if a strain of 0.001 is applied to the bridge containing a strain gauge with a sensitivity of 2?
Half Bridge Circuit
In a similar way the response for the other positions can be calculated and the response is the same for each position, except for R2 and R4 where the response is of the opposite sign.
Strain Gauge
Using two strain gauges (a half bridge) can increase the response but only if
The strain they see is the same and that they have the same sign of response
Or the strain is opposite sign (e.g. bending of a beam)
Strain opposite sign
Applications of Strain Gauges
Structural monitoring – monitoring the performance of big structures for example bridges.
Tacoma narrows 1940 – https://www.youtube.com/watch?v=j-zczJXSxnw
Millennium bridge wobble – https://www.youtube.com/watch?v=eAXVa__XWZ8
https://www.microstrain.com/content/wireless-bridge-structural-health-monitoring
Applications of Strain Gauges
Stone crushers – strain through the machine, hardness of rocks etc are variable so track the performance of the machine
http://www.weighing-engineering.com/dosing-mixing-systems/silo-weighing/
https://www.hbm.com/en/7689/terex-jaw-crusher-in-road-test-with-somatxr/
Silo weighing – how much material is in a silo / hopper. Tracked with strain gauges in the base
Applications of Strain Gauges
Testing of loading on aircraft components, especially the wings
Torque and power measurement on shafts
e.g. driven by motor, turbine or fan, by measuring the strain in the shaft and using the material properties, diameter of shaft and strain.
Applications of Strain Gauges
Medical Applications:
Monitoring the flow of liquids to ensure uniform flow, blockages / kinks etc, reduce fluid flow and increase the pressure in the system, this can be sensed with strain gauges, attached close to the delivery point.
For example in:
Insulin Pumps
Medical Infusion Pumps/Syringe Pumps.
Kidney Dialysis Machines
https://sensing.honeywell.com
Infusion Pumps
Strain Gauges
Applications of Strain Gauges
Monitoring applied force, for example in mammography. The physical forced used on the breast tissue during imaging needs to be monitored to ensure it is sufficient to allow imaging while not being excessive and causing undue pain to the patient.
Weight distribution for scanning machines such as CT or MRI scanners, knowing the weight distribution allows feedback to the stage controllers to ensure smooth, accurate movement of the patient.
Mammogram. Credit: Blausen.com staff. “Blausen gallery 2014”. Wikiversity Journal of Medicine. DOI:10.15347/wjm/2014.010. ISSN 20018762. CC BY 3.0
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