1 ENGR 512 Experimental Methods in Engineering Spring 2011 Dr. Mustafa Arafa Mechanical Engineering...
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Transcript of 1 ENGR 512 Experimental Methods in Engineering Spring 2011 Dr. Mustafa Arafa Mechanical Engineering...
1
ENGR 512Experimental Methods in Engineering
Spring 2011Dr. Mustafa Arafa
Mechanical Engineering [email protected]
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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.
4
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
5
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
10
Instrument typesAnalog & digital instruments
Digital: signal can take discrete levelsAnalog: signal is continuous
12
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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Instrument dynamics governed by the differential equation:
1
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
22
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.
24
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 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