lecture 2 - project & strain gauges
TRANSCRIPT
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Process Control & Instrumentation EEE4093FR. Verrinder (2008)
EEE4093FDesign Project
2008
Cantilever Force Transducer used as aDigital Scale to Measure Mass
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Deadlines for Project
Design Proposal 10 March (Monday) Mechanical System 20 March (Thursday) Sensor 11 April (Friday)
Digitizer 30 April (Wednesday) Integrated System 12 May (Monday)
Demonstration 16 May (Friday)
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Overview
Description of the design requirements
Overview of general design considerations
A look at how strain gauges work
What is a cantilever?
Resources
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Design Requirements
To construct a working cantilever forcetransducer which can be used as a digital scale,using strain gauges
The scale must be capable of measuring massof up to 1kg and must have a minimumresolution of 10g.
The result must be displayed digitally
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Design Considerations
User requirements
Simplicity
Availability of materials
Reliability
Accuracy
Ease of use
Cost
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What is Mechanical Strain? If a material receives a tensile
force P , a stress s will beproduced relative to that force
The materials cross sectioncontracts and the its lengthelongates by DL from theoriginal length L
This ratio is known as thetensile strain and is expressedas
Kyowa Electronic Instruments Co. Ltd. (2007) D
L
L
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Strain Gauges
Many physical variables can be determined from theamount of strain on a system
A strain gauge, in its simplest form is a piece of wirewhich is attached to the object under strain. If the objectchanges its dimensions so will the piece of wire This willchange the resistance of the wire
Strain gauges are made in three main types foil straingauges, wire strain gauges and semiconductor straingauges
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Strain Gauges
Many physical variables canbe translated into strain
Therefore if we measure thestrain in a system, we canmeasure those variables
For example we can measurethe pressure in a pressure
vessel by attaching straingauges to the vessel walls
KGD Industrial Services (2007)
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What is a Strain Gauge? It is a form of resistive
transducer
The primary measurand in aresistive transducer either directly or indirectly causes achange in ohmic resistance of an electrical element
In its simplest form it is a wire
attached to the object under test
If the object changes itsdimensions, so with the straingauge
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The Resistivity Equation
The resistance of a substance is defined by its length ( l ),cross sectional area ( A ) and resistivity ( r )
Resistivity is a property of a material
A change in any one of these factors will result in achange the resistance of the material
A
l R
r
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The Sensitivity Factor Cont. We can then rewrite the change in resistance as
This means that we can define a gauge factor or sensitivity factor for any type any type of strain gauge where
We can then calculate the strain using the sensitivity factor of thestrain gauge
) r r
r r
d d
l
dl
l
dl
R
dR 1212
11
21
r r
/ d R / dR
S
SR
R D 1
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Types of Strain Gauges: BondedStrain Gauges
These are the most common types of strain gauges
They consist of either of foil or wirewhich has been stuck on to a bonding
material The gauge is stuck onto a material to
which stress is applied. The resultingstrain is communicated to the gaugevia the bonding material
Examples of bonded strain gaugesare: foil gauges, wire gauges andsemiconductor strain gauges
Mansfield, P.H. (1973) Electrical Transducers for IndustrialMeasurement
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Types of Strain Gauges: UnbondedStrain Gauges
This consists of a wirestretched between two pointsin an insulating medium suchas air
This is not a very commonarrangement
It is usually wired in a Full
Wheatstone Bridgearrangement so that two of thegauges will be lengthenedwhile the other two will beshortened by the displacement
of the movable part
Mansfield, P.H. (1973) Electrical Transducers for IndustrialMeasurement
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Typical Gauge Patterns: UniaxialStrain Gauge
The gauge pattern refersto layout and number of the grid
Select a uniaxial straingauge if:
Only one direction of strain needs to bemeasured
Cost is an issue
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Typical Gauge Patterns: Bi-axial andTri-Axial Strain Rosettes
Select a bi-axial strain rosette (0 -90 TeeRosette) if:
The principle stresses need to beinvestigated and the principle axes areknown
Select a tri-axial strain rosette (0 -45- 90or 0-60-120 Delta Rosette) if:
The principle stresses need to beinvestigated and the principle axes areunknown
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Typical Gauge Patterns: Planer Rosette Strain Gauges
There are two main layouts in multi-axial strain rosettes: Planer Stacked
Select a strain rosette with a planer layout if : Heat dissipation is an issue Accuracy and stability are critical
Planer layout allows each gauge to becloser to the measurement surface andthere is no interference between them
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Typical Gauge Patterns: Stacked Rosette Strain Gauges
Select a strain rosette with astacked layout if :
The strain gradient is very
large. Stacked layoutsmeasure at the same point
Space for mounting thegauge is limited
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The Wheatstone Bridge
Contains four resistiveelements
Used widely ininstrumentation tobalance out effects suchas thermal changes inresistivity
Used as a differentialmeasurement system
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Wheatstone Bridge Equations
) ) ) )
) )
) )
4321
1432
4321
24144232
4321
214432
43
4
21
2
21
43
42
21
21
R R R R
R R R R V
R R R R R R R R R R R R V
R R R R
R R R R R R V
R R R V
R R R V
V V V
R R
R V V
R R
R V V
i
i
i
i i
o
i i
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Strain Gauge Arrangements
Kyowa Electronic Instruments Co. Ltd. (2007)
QUARTER BRIDGE
HALF BRIDGE
FULL BRIDGE
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What is a Cantilever?
A cantilever is a beam which is anchored atone end and free to move at the other
Kyowa Electronic Instruments Co. Ltd. (2007)
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Cantilever Dynamics If a force W is exerted on the cantilever beam it will create a bending
moment M at a distance L from the end of the beam
This creates a surface stress s on the strain gauge
The amount of strain on the beam can be calculated using thisequation if it has a rectangular cross section
WLM
Modulus Section
Moment Bending E 0 s
20
6
Ebh
M
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Workshops & Contacts
Electrical Engineering Workshop (Rm 332) Mr. Wozniak
Mechanical Workshop (Rm 201) Mr. Newins
White Lab Mr. Schrire