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ENGR 512Experimental Methods in Engineering

Spring 2011Dr. Mustafa Arafa

Mechanical Engineering Departmentmharafa@aucegypt.edu

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Outline• PART 1: Principles of measurement

– Instrument types & characteristics• PART 2: Sensors and instruments

– Measurement of common engineering parameters, such as temperature, pressure, flow, force, displacement, strain

– Selection of appropriate instruments• PART 3: Lab session & case studies• References:

– Measurement and Instrumentation Principles, Alan S. Morris, Butterworth-Heinemann, 2001.

– The measurement, instrumentation, and sensors handbook, edited by J.G.Webster, CRC Press, 1999.

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Sensors in closed-loop control systems

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Types of measurement• Manufacturing measurements

– Discretely monitor product quality

• Performance measurements – Provide performance evaluation as needed

• Operational measurements– Continuously monitor operation process

• Control measurements– Continuously provide feedback signals

• Others– Research-related

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Examples

Bogie A (#5)

1A3A9A

6A5A

7A

8A12A

11A

2A4A

10A4B

10B

1B3B

9B

2B

11B6B

5B

8B12B

7B

Bogie B (#6)

Accelerometer on traction motor

Accelerometer on axle box

Location of Strain Gauges and Accelerometers for Bogie A (#5) and Bogie B (#6)

NOT TO SCALE

NOT TO SCALE

End beam

Wiring from this side

Wiring from this side

("front" when going towards Marg)("front" when going towards Helwan)

Side beam

Cairo metro, line 1

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Essential elements of measurement

Physical behavior Sensor Transducer Signal

conditioner

Data acquisition system

Sensor: responds to physical quantity to be measured Transducer: converts quantity to be measured to an analog signal Signal conditioner: amplify, filter, integrate, differentiate, etc. Data acquisition: records, displays, processes data (hardware &

software)

Measured variable

Variable conversion element

Output display(measurand)

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Instrument systems

MembranePressure Strain gauge Electrical bridge

Calibration

Output voltage

Environment being sensed for pressure

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Active and passive instruments

Instrument types

Passive: self powered Active: externally powered

potentiometer

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Null-type & deflection-type instruments

Instrument types

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Instrument typesAnalog & digital instruments

Digital: signal can take discrete levelsAnalog: signal is continuous

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Static characteristics of instruments

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Static characteristics of instruments Accuracy: closeness to correct value Precision: indication of spread of readings

• Repeatability/reproducibility: variation of a set of measurements made in a short/long period of time

Measure of Accuracy

Measure of Precision

Accuracy is often quoted as a % of full-scale (f.s.) reading.Example: pressure gauge, range 0-10 bar with accuracy ±1% f.s.This means ± 0.1 bar, or if you are reading 1 bar, the possible error is 10%.

High accuracy, high precision Low accuracy, high precision Low accuracy, low precision

Bias: need to calibrate

Need to average

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Averaging

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

Frequency [Hz]

Acc

eler

atio

n [m

/s2]

One Reading

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

Frequency [Hz]

Acc

eler

atio

n [m

/s2]

5 Averages

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

Frequency [Hz]

Acc

eler

atio

n [m

/s2]

10 Averages

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

Frequency [Hz]

Acc

eler

atio

n [m

/s2]

50 Averages

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

Frequency [Hz]

Acc

eler

atio

n [m

/s2]

100 Averages

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

Frequency [Hz]

Acc

eler

atio

n [m

/s2]

1000 Averages

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Static characteristics of instruments

D i

Resolution

Linearity: is the output reading linearly proportional measured quantity? Sensitivity: change in output per unit change in input (slope) Resolution: smallest increment that can be detected

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Static characteristics of instruments Sensitivity to disturbance: all calibrations/specifications of an instrument are

only valid under controlled conditions of temperature, pressure, etc. Variation to such environmental changes can lead to

Zero drift (bias) Sensitivity drift

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Static characteristics of instruments Example: A spring balance is calibrated in an environment at a temperature of 20°C and has the following deflection-load characteristic.

Load (kg) 0 1 2 3

Deflection (mm) 0 20 40 60

It is then used in an environment at a temperature of 30°C and the following deflection-load characteristic is measured.

Load (kg) 0 1 2 3

Deflection (mm) 5 27 49 71

Determine the zero drift and sensitivity drift per °C change in ambient temperature.

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Static characteristics of instruments Hysteresis effects: output reading

depends on whether input quantity is steadily increased or decreased

Dead space: range of input values over which there is no change in output

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saturation

Static characteristics of instruments Saturation: no further output, even if input is increased

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Dynamic characteristics of instruments

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Instrument dynamics governed by the differential equation:

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1 0 01( ) ( ) ... ( ) ( ) ... ( )

n n m

n n mn n m

d d da y t a y t a y t b x t b x t

dt dt dt

G(s)x(t)X(s)

y(t)Y(s)

Dynamic characteristics of instruments Static characteristics: steady-state readingsDynamic characteristics: behavior of instrument between the time a measured quantity changes and the time when the instrument oupt attains a steady value in response

Measured quantity Output reading

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Zero order instrument: 0 0( ) ( )a y t b x t 0 0( ) ( ) ( )y t b a x t Kx t

Dynamic characteristics of instruments

For a step change in measured quantity, the output moves immediately to a new value. Example: potentiometer

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First order instrument: 1 0 0

dya a y b x

dt

Dynamic characteristics of instruments

Example: liquid-in-glass thermometer

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Second order instrument:2

2 1 0 02

d y dya a a y b x

dt dt

Dynamic characteristics of instruments

Response can be oscillatory, or damped according to damping ratio.

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Errors in measurementErrors in measurement systems:1. Arise during the measurement process

a) Systematic errorsb) Random errors

2. Arise due to later corruption of the signal by induced noiseSystematic error

Random error

Systematic errors: consistently on 1 side of the correct readingSources:1. System disturbance (ex: cold thermometer in hot fluid)2. Environmental changes3. Bent meter needles4. Uncalibrated instruments5. Drift

Random errors: perturbations on either side of true valueSources:1. Human observation of analog meters2. Electrical noise (spurious signals picked up by lead wires)

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Errors in measurementOther sources of error:1. Improper sensing position2. Improper data acquisition3. Improper sampling rate

Usually we record a continuous signal y(t) by a set of samples ys(t) at discrete intervals of time t.

y(t)

t

yS(t)

t

t

The no. of samples recorded each second is defined as the sampling frequency, fS

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• If we sampled too slowly, a recorded data will present a distortion from the original signal.

• Over sampling, on the other hand, raises storage issues.

Original signal Sampled data

Errors in measurementUnder sampling of test data

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High frequency signal when sampled with a low sampling rate may cause the sampled data to appear to have a lower frequency. This behavior is known as aliasing, and the lower frequency (false) signal is often said to be the alias. To avoid aliasing, the sampling rate must be at least twice the highest frequency in the analog signal.

High frequency signal, sampled with low sampling rate

Errors in measurementAliasing

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Errors in measurement

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Frequency [Hz]

Am

plitu

de [

cm]

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Frequency [Hz]

Am

plitu

de [

cm]

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Frequency [Hz]

Am

plitu

de [

cm]

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Strain Measurement

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Strain gauges• Strain gauges are devices that experience a change in resistance when they

are stretched or strained• Typical displacements: 0-50 mm• Can be used as parts in other transducers (ex: pressure sensors)• Accuracies within ±0.15% of full-scale are achievable• Manufactured to nominal resistances (most commonly 120 )W

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Gauge element

Gauge element tab

Solder

Jumper wire

Solder

Lead wiresGauge tab

Sensitive to axial strain

Less sensitive to transverse strain

Strain gauges

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Mechanical strain

F F

Base length

Strain: change in length over some specified base length

Extension

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LR

A

L

Conductor

L

Resistance of a conductor

A

R :Resistance:Resistivity:Length:Area

• Now assume the conductor stretched or compressed.• Resistance will change due to dimensional changes (L,A) AND due

to a fundamental property of materials called piezoeresistance.• Piezoresistance: dependence of on the mechanical strain.

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Change in resistance due to strain

2

L LdR d dL dA

A A A

LR

A

2

A Ld dL LdAdR

A

Gives: Change in resistance

Longitudinal strain:dL

L

L dLTransverse strain:D

dD

D

For linearly elastic behavior: D

D

R R RdR dA dL d

A L

For a small change in R, use Taylor series expansion:

1 2dR d

R

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Change in resistance due to strain

/ /GF 1 2 constant

/ /

dR R d

dL L dL L

• Gauge Factor (GF) is a measure of the sensitivity of the material, i.e. the resistance change per unit applied strain.

• If you know GF, then measurement of allows measurement of the strain .

• This is the principle of the resistance strain gauge

/dR R/dL L

1 2dR d

R

In the absence of a direct resistivity change, 1 2GF For commonly used strain gauges, GF is close to 2.

GF = slope

Change in Resistance with Strain for Various Strain Gage Element Materials

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Example

Measurement of strain in a steel beam.

E

For a stress level of 20 MPa and elastic modulus of 200 GPa:

0.0001 100 micro strain

In engineering materials, typical strain levels range from 2 to 10,000 micro strain.

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Wheatstone bridge

R1

+-

V

R2

R4 R3

Vo

• To convert small changes in resistance to an output voltage, strain gauges are commonly used in bridge circuits.

• Circuit requires DC input or excitation.

V: Bridge excitation

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1 3 2 4

1 2 3 4o

R R R RV V

R R R R

R1

+-

V

R2

R4 R3

Vo

If R1R3=R2R4 Vo=0

Bridge is balanced

• Assume you start with a balanced bridge with R1=R2=R3=R4=R. Then Vo=0.

• Now assume one (or more) of the resistances change by dR1, dR2, dR3 and dR4. The output voltage would then change.

Wheatstone bridge

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Electrical resistance strain gauge

R1

+-

V

R2

R4 R3

Vo

If we replace only one resistance with an active strain gauge, any changes in resistance will unbalance the bridge and produce a non-zero output voltage.

Quarter bridge configuration (one active gauge)

14o

GFV V

Output is proportional to excitation voltage

Quarter bridge

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Other bridge configurations

R1

+-

V

R2

R4 R3

Vo

• Half bridge configuration (two active gauges)

• Useful for measuring bending strain in a thin beam or plate.

1 24o

GFV V

2 1

1

2

12o

GFV V

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Other strain gauge configurations