ENGR 512 Experimental Methods in Engineering

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1

ENGR 512

Experimental Methods in Engineering

Spring 2011

Dr. Mustafa
Arafa

Mechanical Engineering Department

mharafa@aucegypt.edu



2

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.

3

Sensors in closed
-
loop control systems

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)
1A
3A
9A
6A
5A
7A
8A
12A
11A
2A
4A
10A
4B
10B
1B
3B
9B
2B
11B
6B
5B
8B
12B
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

6

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)

7

Instrument systems

Membrane

Pressure

Strain gauge

Electrical
bridge

Calibration

Output
voltage

Environment being
sensed for pressure

8

Active and passive instruments

Instrument types

Passive: self powered

Active: externally powered

potentiometer

9

Null
-
type & deflection
-
type instruments

Instrument types

10

Instrument types

Analog & digital instruments

Digital: signal can take discrete levels

Analog: signal is continuous

11

Static characteristics

of instruments

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

13

Averaging

0
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
1.2
Frequency [Hz]
Acceleration [m/s
2
]
One Reading
0
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
1.2
Frequency [Hz]
Acceleration [m/s
2
]
5 Averages
0
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
1.2
Frequency [Hz]
Acceleration [m/s
2
]
10 Averages
0
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
1.2
Frequency [Hz]
Acceleration [m/s
2
]
50 Averages
0
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
1.2
Frequency [Hz]
Acceleration [m/s
2
]
100 Averages
0
1
2
3
4
5
6
7
8
9
10
0
0.2
0.4
0.6
0.8
1
1.2
Frequency [Hz]
Acceleration [m/s
2
]
1000 Averages
14

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

15

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

16

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.

17

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

18

saturation

Static characteristics of instruments


Saturation
: no further output, even if input is increased

19

Dynamic characteristics

of instruments

20

Instrument dynamics governed by the differential equation:



1
1 0 0
1
( ) ( )...( ) ( )...( )
n n m
n n m
n n m
d d d
a 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 readings

Dynamic

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

21

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
dy
a a y b x
dt
 
Dynamic characteristics of instruments

Example: liquid
-
in
-
glass thermometer

23

Second order instrument:

2
2 1 0 0
2
d y dy
a a a y b x
dt dt
  
Dynamic characteristics of instruments

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

24

Errors in measurement

Errors in measurement systems:

1.
Arise during the measurement process

a)
Systematic errors

b)
Random errors

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

Systematic error

Random error

Systematic errors: consistently on 1 side of the correct reading

Sources
:

1.
System disturbance (ex: cold thermometer in hot fluid)

2.
Environmental changes

3.
Bent meter needles

4.
Uncalibrated instruments

5.
Drift

Random errors: perturbations on either side of true value

Sources
:

1.
Human observation of analog meters

2.
Electrical noise (spurious signals picked up by lead wires)

25

Errors in measurement

Other sources of error:

1.
Improper sensing position

2.
Improper data acquisition

3.
Improper sampling rate

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

y(t)

t

y
S
(t)

t

D
t

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

26


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 measurement

Under sampling of test data

27

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 measurement

Aliasing

28

Errors in measurement

0
1
2
3
4
5
6
7
8
9
10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Frequency [Hz]
Amplitude [cm]
0
1
2
3
4
5
6
7
8
9
10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Frequency [Hz]
Amplitude [cm]
0
1
2
3
4
5
6
7
8
9
10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Frequency [Hz]
Amplitude [cm]
29

Strain Measurement

30

Strain gauges


Strain gauges are devices that experience a change in resistance when they
are stretched or strained


Typical displacements: 0
-
50
m
m


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)


31

Gauge element

Gauge element tab

Solder

Jumper wire

Solder

Lead wires

Gauge tab

Sensitive to axial strain

Less sensitive
to transverse
strain

Strain gauges

32

Mechanical strain

F

F

Base length

Strain: change in length over some specified base length

Extension

33

L
R
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.


34

Change in resistance due to strain

2
L L
dR d dL dA
A A A
 

  
L
R
A



)
2
A Ld dL LdA
dR
A
  
 

Gives:

Change in resistance

Longitudinal strain:

dL
L


L

dL

Transverse strain:

D
dD
D


For linearly elastic behavior:

D
 
 
D

R R R
dR dA dL d
A L


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


)
1 2
dR d
R

 

  
35

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 2
dR d
R

 

  
In the absence of a direct resistivity change,

1 2
GF
 
For commonly used strain gauges, GF is close to 2.

GF

=

slope

Change in Resistance with Strain for
Various Strain Gage Element Materials

36

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.

37

Wheatstone bridge

R
1

+

-

V

R
2

R
4

R
3

V
o


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

38


)

)
1 3 2 4
1 2 3 4
o
R R R R
V V
R R R R


 
R
1

+

-

V

R
2

R
4

R
3

V
o

If
R
1
R
3
=R
2
R
4

V
o
=0

Bridge is
balanced



Assume you start with a balanced bridge with

R
1
=R
2
=R
3
=R
4
=R
. Then
V
o
=0.



Now assume one (or more) of the resistances
change

by

dR
1
,
dR
2
, dR
3

and

dR
4
.
The output voltage would then change
.

Wheatstone bridge

39

Electrical resistance strain gauge

R
1

+

-

V

R
2

R
4

R
3

V
o


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)





)
1
4
o
GF
V V


Output is proportional to
excitation voltage

Quarter bridge

40

Other bridge configurations

R
1

+

-

V

R
2

R
4

R
3

V
o


Half bridge configuration (two
active gauges)






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


)
1 2
4
o
GF
V V
 
 
2 1
 
 
1

2


)
1
2
o
GF
V V


41

Other strain gauge configurations