Lecture 2 - Project & Strain Gauges

7/27/2019 Lecture 2 - Project & Strain Gauges

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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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2Process Control & Instrumentation EEE4093FR. Verrinder (2008)

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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27Process Control & Instrumentation EEE4093FR Verrinder (2008)

Workshops & Contacts

Electrical Engineering Workshop (Rm 332) Mr. Wozniak

Mechanical Workshop (Rm 201) Mr. Newins

White Lab Mr. Schrire

Documents

Lecture 2 - Project & Strain Gauges