ST3_Strain_meas za šant

7/29/2019 ST3_Strain_meas za šant

http://slidepdf.com/reader/full/st3strainmeas-za-sant 1/40

http://www.doitpoms.ac.uk/tlplib/mechanical-testing/images/

Lecture OutlineStrain Measurement Introduction:

¾ Definitions: Stress, Strain, Elastic Modulus and Poisson’s Ratio

Methods for Strain Measurements:

¾ Grid method, brittle coating

¾ Electrical-resistance strain gauges:

o working principle

o gauge factor

o resistivity

o characteristics of strain gauge materials

o bonding of strain gauges

o factors influencing strain gauge installation: temperature, moisture, wiring¾ Calibration of strain gauges

¾ Bridge circuit for strain gauges

Introduction of commercially available strain gauges

Appl ication cases



Stress : A quick re-cap

- Stress (sigma)F - force

A - area

Engineering Stress is defined as the “force per unit area”.

Stress strains / deforms

The original cross-sectional area is used

Stress : A quick re-capy Review engineering stress

y True Stress???

The true stress is defined as the ratio of the applied Force to the

instantaneous cross-sectional area.

A is instantaneous area.



Strain : A quick re-cap

Engineering strain is defined as the amount of deformation an object

experiences compared to its original shape and size.

Engineering strain is

vaild iff < 5%


The true strain is defined as the

sum of all the instantaneous

engineering strains.

http://www.shodor.org/~jingersoll/weave/tutorial/node3.html




Difference between true stress and

engineering stress in elastic region explain

later.

Stress and Strain : A quick re-cap

Behavior of a subject under stress

depends on the:

• material

• nature of the forces

• shape

• orientation of the subject



Young’s ModulusYoung’s modulus E, is a measure of the stiffness of a material.

E can be determined experimentally

by calculating the gradient of the

linear region of the graph, as shown

in red in the stress strain curve.

It is defined as the ratio of in the region which Hooke’s Law is obeyed.

Poisson’s RatioPoisson's ratio is the ratio of transverse contraction strain to

longitudinal extension strain in the direction of stretching force.

Where v = Poisson’s ratio,

v = transverse / longitudinal



Poisson’s Ratioy Steel = 0.29

y Aluminium = 0.35

y Lead = 0.44

y Rubber = 0.48 - 0.50

y Poisson's ratio in bending.

Poisson's ratio governs the curvature in a direction perpendicular to the

direction of bending. This "anticlastic curvature" is easily seen in the

bending of a rubber eraser.

Revision is over…

Strain Measurement:

y Grid Method

y Brittle Method



Methods for Strain Measurements

y Grid Method

y Simplest

y Oldest

To measure the strain:

•Scribed

•Drawn with fine ink

•Photo etched

-Mark the surface with lines,

dots or a grid (the grid is most

common as it is easy to

analyse).

Subject under

zero load

conditions.


y Grid Method

• Simplest

• Oldest

To measure the strain:

•Analyse Deformation- micrometer microscope

Subject under

load.




y Grid Method:

Advantages Disadvantages

-Simple and easy to

implement

-Cost effective

-Can only be used on

materials with appreciable

deformation under load.

-Extremely inaccurate

- Needs 100% accessibility

to take readings

-Can not take digitalreadings.


Brittle Method:

Coat part of the subject with substance

having very brittle properties.

As the nature of the coating isknown, we can estimate strain

values on the subject.


Stress Applied Cracks appear





y Brittle Method:

Advantages Disadvantages

-overall picture of the stress

distribution.

-stress concentration points

-Can only be used on

materials with appreciable

deformation under load.

- Needs 100% accessibility

to take readings

-Can not take digital

readings.

-Does not give actual

measurements

Electrical Resistance Strain Gauges

•Most widely used device for strain measurement

•Operates on principle that the electrical resistance of a

conductor changes with mechanical deformation

•Attached to specimen using suitable adhesive

• As the specimen deforms, the strain gauge deforms,

causing electrical resistance to change

•This resistance change (small) measured using a

Wheatstone bridge, related to strain by gauge factor .

•Ideal strain gage is small in size and mass, low in cost,easily attached, and highly sensitive to strain but

insensitive to ambient or process temperature

variations.

Video from www.sensorwiki.org/index.php/strain_gauge

Introduction



Types of Electrical Resistance Strain Gauges

•3 main types:

-Wire gauge

-Foil gauge

-Semiconductor gauge

•Wire gauges use wire between 12 – 25 μm. Developed in 1938, not widely used as

they are larger and more expensive than foil gauges.

•Foil gauge uses foil less than 25 μm. Many different configurations which lend to a

wide variety of applications. Most commonly used gauge.

Semiconductor Strain Gauges

•Semiconductor gauge is a wafer (about 0.25mm) with theresistance element diffused into a substrate of silicon.

Advantages:

- high unit resistance and sensitivity- lower size and cost

Disadvantages:

- greater sensitivity to temperature variations

- tendency to drift- nonlinear resistance-to-strain relationship

•Thin-film strain gauges are produced by depositingelectrical insulation (typically a ceramic) onto stressed

metal surface then strain gauge on top.

Advantages:

- molecularly bonded to the specimen therefore no need for adhesive bonding- installation is much more stable and resistance values experience less drift.

• Diffused semiconductor strain gauges uses photolithography masking techniques and solid-state

diffusion of boron to molecularly bond the resistance elements.

Advantages:

- By eliminating bonding agents, errors due to creep and hysteresis also are eliminated.Disadvantages:

- Limited to moderate-temperature applications and requires temperature compensation.



The resistance of the conductor is

where L = length

A = cross-sectional area

ρ= resistivity of the material

Taking the natural logarithm of this equation

Now taking the differential of this, using

In general we may write where D is a cross section dimension and C is a

constant (eg. C = π and D =R for a circle). Using the same method as above,

substituting in

Theoretical Background

A

LR ρ =

A

dA

L

dLd

R

dR−+=

ρ

ρ

D

dD

L

dLd

R

dR 2−+=

ρ

ρ

D

dD

A

dA2=

)()()()( ALnLnLLnRLn −+= ρ

x

dxxLnd

xxLn

dx

d=⇒= ))((

1))((

2CDA=

Substituting in the equations for axial strain and Poisson’s ratio we have

The Gauge Factor (sometimes called “sensitivity factor”) F is the ratio of fractional change inelectrical resistance to the fractional change in length (strain) and is defined by

and therefore

We can now express local strain in terms of the gauge factor, the resistance of the gauge, and thechange in resistance with the strain:

If the resistivity of the material does not vary with the strain,

( )μ ε ρ

ρ 21++= a

d

R

dR

a

RdRF

ε

/=

ρ

ρ

ε μ

dF

a

121 ++=

R

R

F

Δ=

1ε

⎟ ⎠

⎞⎜⎝

⎛ −+=

LdL

DdD

L

dLd

R

dR

/

/21

ρ

ρ rearranging

21+=F



Example: Calculating Strain

Example: Calculating Gauge Factor

Q. Calculate the strain in a specimen if the attached strain gauge has a gaugefactor of 2, a resistance of 120Ω and the change in resistance measured is 0.1 Ω

A.R

R

F

Δ=

1ε

120

1.0

2

1×=ε

410*1667.4

−=ε

Q. What is the gauge factor of a strain gauge made from a material that acts like

a perfectly incompressible material deforming elastically at small strain

(assuming the resistivity doesn’t change with strain)?

A. μ +=1F

For a perfectly incompressible material deforming elastically at small strain,

5.0=

5.0*21+=F

2=F

Gauge Factor

•Gauge factor and resistance normally specified therefore only ∆R need be measured.

•High gauge factor is desirable because larger ∆R is produced for a given strain input

•Can vary from -140 to 175

•Usually the same for both compressive and tensile strains

•Constant over a wide range of strains for most gauges

•Various physical properties of the resistance material can have an influence on F

•The manufacturer should always supply data on the temperature sensitivity of the gage

factor.



Ideal Electr ical-Resistance Strain

Gauge Material

• The ideal gauge material will be:• Highly sensitive to strain.

• Suitable for a large range of temperatures

• Insensitive to Δ temperature

• Must be weaker than the specimen

• Low in cost

• Easily attached



Common Electrical Resistance

Strain Gauge Materials

• Constantan (55% Cu, 45% Ni)• Nichrome V (80% Ni, 20% Cu) • Manganin (84% Cu, 12% Mn, 4% Ni) • Isoelastic (55.5% Fe, 36% Ni, 8% Cr, 0.5% Mo) • Monel (67% Ni, 33% Cu) • Karma (74% Ni, 20%Cr, 3% Al, 3% Fe) • Platinum alloys (usually tungsten)

• Silicon semiconductors

Constantan.

• Useful over a largerangeof strain.

• Is useful for changingtemperatures below360 ºc.

• It is very common andit is cheap.

• Use it whenever outsideof extremeconditions.

• Stats:• GF = 2.0

• Resistivity = 49• Temp. Coef = 11

* Temperature Coef of

Resistance (ºc-1 * 106)

ΔS = ΔT*Temp Coef

* Resistivity @ 20 ºc

(µΩ.cm)



Nichrome V

• Suitable for hightemperature use up to800ºc.

• A cheaper material for high temperature use.

• Stats:• GF = 2.0

• Resistivity = 108

• Temp. Coef = 400

Isoelastic.

• Only useful intemperatures below300ºc.

• Great for lowunchangingtemperatures.

• Ideal if a high signal-noise ratio is needed.

• Performs well for testing fatigue.

• Stats:• GF = 3.5




Karma

• Useful to 750ºc.• Great for varying

temperatures

• Stats:• GF = 2.4

• Resistivity = 125

• Temp. Coef = 20

Platinum Alloys

• Great for use in hightemperatureenvironments, beinguseful up to 1000ºc.

• Needs an environmentwith a stabletemperature.

• Stats:• GF = 5.0




Silicon Semi Conductors

• Great for almost anytemperature as long asit is stable.

• Very sensitive.• Unsuitable for large

strain measurements.

• Stats• GF = -100 to +150• Resistivity = 1.0*109

• Temp. Coef = 90 000

Bonding Strain Gauges

• Bonding is very difficult due to the:• sizeand fragility of the gauges.

• high degree of accuracy that they must be fitted to.

• large number of different problems that can occur.

• Most strain gauges require a cement or some typeof adhesive to attach itself to, and insulateitfrom, the specimen material.

• When attaching the strain gauge ENSURE thesurface of the specimen is absolutely clean.

• Instructions for bonding• http://www.efunda.com/DesignStandards/sensors/strai

n_gages/strain_gage_install_prepare.cfm



Ideal Adhesive

• The ideal adhesive will be:

• an insulator

• quick to dry

• Suitable over a large range of temperatures.

• low in cost

• Applied thinly• Ensure to match the appropriate adhesive to the

gauge material you use.

Common Adhesives

• Cyanoacrylate cement (the “general” option) •Only short tests required (less than months) •Dries quickly

• Epoxy•Good to measure high strains•Has a very strong bond•Requires extended time and special pressure/temperatureconditions to set.

• Ceramic cement•Good for high temperature environments – 980 ºc.

• Cellulose nitrate cement•Good if using paper backing

•Conditions must be dry.



Common Backings

• An appropriate backing must be selected also to fitwith the gauge material and the adhesive.

• Polyimide (the “general” option) • Not in extreme conditions•Mostly static strain

• Paper •As Above

• Epoxy•Low error required – very difficult to install.

• Glass fiber reinforced epoxy

•Moderate temperature•Good for fatigue

• Strippable Backing•High temperatures•Adhesive must be used as an insulator.

Extreme Temperatures

• Testing strain in certain temperatures, high or low, causes a problem with certain gauge

materials.

• This is simply solved by selecting an appropriatematerial, adhesive and backing, however often

the material is more expensive or trades off other benefits.



Unstable Temperatures

• Δ Temperature causes an issue with thermalexpansion. Why?− Can use gauge material selection to combat this.

• It can also, depending on the temperaturecoefficient of resistance, change the resistanceof the gauge material.

Temperature Compensation

Arrangement

• R1 = R3• R

s= R + ΔR

Temp+ ΔR

strain

• R u= R + ΔR

Temp

• Must be careful to ensure

both gauges are inidentical environmentsand fitted correctly.



Wiring

• Common wiring issues are:− Poor soldering connections

− Tight wires which can pull the gauge loose or out of

position, or damage the gauge.

• Simple fixes:• Be careful.

• Ensure soldering connections are done correctly.

• Have short, secured but not inflexible wires.

• Wireless.

Moisture

• Moisture is an issue because it can alter theelectrical resistance of the strain gauge or theexternal circuit.

• Main causes for moisture are from:• Environment• The adhesive attaching the gauge to the specimen is

not allowed to dry (ideally 24 hours should be

allowed – reduced for hotter environments) • To Combat

• Let it dry!

• Unstrained specimen, in identical environment.



Measuring the Strain Gauge

Wheatstone Bridge

4231 RRRR ×=×For a balanced bridge, e = 0when:

Quarter-Bridge Circuit

• R 1 = R 3

• R 2 = R sg (unstressed)

• Δ V = ¼ ( ΔR sg/R sg )* Vsrce



• Lead wire resistance desensitises strain gauge

bridge. In effect, reduces gauge factor

• Rwire3 carries minimal current

• Rwire1 is negated

• Considerable improvement over two wire

quarter bridge

Three-wire, quarter-bridge strain gauge

circuit

Temperature Compensation

• One active gauge

• One ‘Dummy’ gauge to provide temperature compensation

• Three wire configuration preferential to two wire configuration



Half Bridge strain gauge circuit

• Gauges placed in tension and compression

• Voltage sensitivity to strain is twice that of quarter bridge

• Can be used to selectively measure different properties,

i.e.. Bending, axial loading, torsion.

Full Bridge strain gauge circuit

• Strain gauge placed in compression and

tension

• Four times the sensitivity of quarter

bridge

• Can be hard to install strain gauges in

this configuration, best for thin plate

• Compensates for temperature if gauges

in same environment



Bridge Configurations for

Uniaxial Members


Flexural Members




Torsional Members

Bridge Balancing

For the Wheatstone Bridge to function as expected, the

bridge needs to be balanced, with all resistances being equal.

The bridge balancing equation is:

Due to inherent irregularities between strain gauges and resistors, this will not be

the case in reality.

As a result of the bridge being unbalanced, the differential output voltage may

differ up to 0.1% of the source voltage, which may be larger than the strain gaugeoutput.

There is a need to have a way of balancing the Wheatstone bridge, to calibrate it

for use.

4231 RRRR ×=×



Bridge Balancing

Circuits• Series

• Requires precision small resistancepotentiometer

• Shunt• Can use easy to find, large resistancepotentiometers• Need to know which side will beunbalanced

• Potentiometric• Can balance both sides of bridge• Suffers limitations of series circuit

• General• Can balance both sides of bridge• Resistance is in parallel configuration

Calibrating Strain Gauges

Calibration circuits for Strain Gauge Bridges are used

to:

• Test that the bridge is working

• Simulate strain gauge measurements

Useful when designing and testing amplifier for strain

gauge bridge circuits.




Series or Shunt?


Simulating Strains

The parallel resistor Rccan be used

to simulate strain



Introduction of Commercially Available Strain Gauges

• What strain measurement devices

are available for you to use as a

engineer?

• Practical Metal-Foil characteristics

• Gauge selection, given a sample

under known conditions

Mechanical Strain Gauges

• Designs vary a lot, and thus quality is

dependant on the quality of design

• Immune to electrical noise at point of

acquisition, although subject to vibration

• To acquire very accurate strain data

the sensor cost increases dramatically

• Not as common as conventional

electrical strain gauges

• Primarily used in civil applications

•Companies that produce mechanical

strain gauges – HBM, Mastrad

DD1 - DD1 - Strain transducer - Made by HBM

Mechanical strain gauge installed on the Hudson-Athens

Lighthouse to measure the growth of foundation cracks.



Optical Strain Gauges

• Several types of gauges

- Photoelastic

- Moire Interferometry

- Holographic Interferometry

- Fibre Bragg grating

• Relatively new technology

• Requires expensive interface

equipment to obtain data

• Electrical noise is not a variable in the

measurement

• Used in applications where the environment

may not permit electricity, or very high precision

is required

Fibre Bragg grating strain gauge courtesy of “http://www.aos-fiber.com”

And many more...

• Pneumatic Strain Gauge

•Semiconductor Strain Gauge

•Mercury-in-rubber (Whitney) Strain Gauge

•MEMS (Micro-Electromechanical Systems) Strain Gauge



Metal-Foil Strain Gauges

• Most commonly used strain gauges in

industry

• Relatively Cheap

• Readily Available

• Extensive variations in design to suite

various applications

• Australian company Davidson stocks

a large range Micro Strain® strain gauges

Characteristics of Practical Metal-Foil Strain Gauges

• Gauge dimensions

• Gauge pattern

• Grid resistance

• Operational temperature range

• Gauge factor

• Cyclic endurance

• Thermal coefficient of – resistivity

– gauge factor

• Foil Material

- most popular alloys used are

- Copper-Nickel (Cu-Ni)- Nickel-Chromium (Ni-Cr)

• Backing Material (Carrier)

- Polyimide

- Epoxy-Phenolic

• S-T-C (Self Temperature Correction) number

• Microstrain (µ) Range / % elongation range



Choosing a Suitable Metal-Foil Strain Gauge

Gauge Length

• 0.2mm – 100mm

• Must suit application

- Holes, fillets, notches GL = 0.1 x radius

• Lengths between 3mm – 6mm are typically

used as more design options are available

• Short gauge length embody restricted performance

- low maximum allowable elongation

- instability

- relatively poor cyclic endurance

- difficult installation

• Long gauge lengths

- easier to handle

- improved heat dissipation (applications of plastics, wood)

- stress values along the length are averaged….


Strain Averaging

For a sample with points of highly

concentrated stress the gauge length

is important in obtaining accurate

results




S-T-C (Self Temperature Correcting) Number

•The strain gauge’s thermal expansion behaviour must match the

sample being measured

• Suppliers provided S-T-C values for all strain gauges catalogued

- S-T-C 30, 40 or 50 (unreinforced plastics)

- S-T-C 05 (6Al-4V Titanium alloy)

- DY (Dynamic systems where Temperature compensation is

negligible)

Leadwire Configurations

• Provides flexibility of installation

• Solder dots available at pads

Case study “ Spur Gear Stress Measurement – Practical Gauge Selection”

Specifications

•Measurements at root of gear teeth

• Fillet radius at root is 3mm

• Expected temperature -20 to 80 degrees Celsius




Gauge Selection

• Gauge length = 0.1 x 3mm

= 0.3mm

• Gauge pattern

-principal axis known therefore only single grid

gauges are required

• Low strain levels = small µ range

•Signal must be transmitted using slip rings or telemetry

- highest available Ω value

- high gauge factor in order to reduce signal to noise ratio

• S-T-C number will be DY as it is a dynamic system

Case study

Courtesy of “www.vishay.com”



Case study


Case study





Gauge Designation

Part No. ED-DY-031CF-350/Option E

Extracted from the Davidson catalogue

Gauge Factor 3.2

Gauge length 0.8mm

Temperature Range 195 deg to +205 deg C

Strain Range +2%

Fatigue Life

106 cycles at +2500 microstrain

107 cycles at +2200 microstrain

Grid Resistance 350ΩFoil Material Isoelastic Alloy (D Alloy)

Carrier Material Epoxy-Phenolic

Strain Gauge Applications - requirements

• Different applications require the strain gauge to be manufactured to better suit

certain environments.

Example:

Measuring the propagation of a crack in a building over time

vs.

Measuring the strain in a F1 car carbon fibre monocoque chassis during testing

Building measurements:

• Crack may propagate a few mm over a period of months• Gauge may be exposed to elements, wind, rain etc.

F1 chassis measurements:

• High levels of strain (very high inertial forces, in excess of 4G lateral)

• Gauge may be exposed to very high temps, harsh, dirty environment

D i f f e

r e n t G a

u g e s ?



Case #1 – Automated Deformation Monitoring http://www.iti.northwestern.edu/about/reports/year5semisum.html

Strain gauges installed at the quarter points of a diagonal bracing element and the

communications links

Case #1 – Automated Deformation Monitoring http://www.iti.northwestern.edu/about/reports/year5semisum.html

¾ Excavation site for a research centre on a university campus in USA

¾ Strain gauges were utilised to monitor the deformation of bracing which

provided lateral support of a temporary support structure.

¾Purpose of the project was to help improve the practice of predicting and

controlling ground movements associated with supported excavations andtunnelling operations.

¾36 vibrating wire strain gauges were installed on diagonal and cross-lot bracing

of the temporary structure (bracing and SGs shown in picture on previous slide)

Case Background



Case #1 – Automated Deformation Monitor ing

http://www.iti.northwestern.edu/about/reports/year5semisum.html

Typical processed strain gauge data.

Total force and extreme fibre stresses over a 6 week period.

Case #2 – Motorsport, Ignition Cut Signal

Strain gauges are widely used in the motorsport industry, but not only for data

acquisition purposes. An interesting application is the utilization of a strain gauge

on a gear lever to aid in the shifting process.

Case Background

Clutch-less shifting, commonly referred to as “flat shifting” is the process of

changing gears without engaging the clutch or lifting off the throttle. This greatly

reduces gear change times (a reliable shift time of 50ms was achieved using a

pneumatic shifter on the UQ FSAE car).

To successfully “flat shift”, the engine must be temporarily ‘unloaded’ duringshifting, which is usually achieved by cutting the engine ignition via the ECU

(engine control unit).

Various methods for creating this “cut-signal” to the ECU are used, one of which is

the implementation of a strain gauge on the gear lever.




So what is the main benefit of using a strain gauge as opposed to a micro-switch?

¾ A strain gauge produces a force sensitive signal, i.e. the harder the driver throws

the gear lever, the larger the signal. A micro-switch is simply on or off.

¾ Allows the ECU to discern between a slow shift (where the driver does not wish

for ignition cut to occur and clutches normally, ie in pit lane) and a quick shift (driver

does want ignition cut, ie race situation). This is setup using the ECU or controller.

¾ Most high-end aftermarket motorsport ECU’s now provide a special function

specifically for strain gauge ignition cut systems, allowing for easy installation and

setup.

www.motec.com.au http://www.dataspares.com/acatalog/

0-5V output 2.5V normal (centred)

+1000N = 0.5V

-1000N = 4.5V


Motec ECU manager, ignition cut setup (example using a strain gauge)



ST3: Strain Measurements(Chapter 10)

Documents

ST3_Strain_meas za šant