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EXM4
Experimental methods E181101
Displacement,
Deformation,
Pressures
Rudolf Žitný, Ústav procesní a
zpracovatelské techniky ČVUT FS 2010
Some pictures and texts were copied
from www.wikipedia.com
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DISTANCEs
or how to measure geometry of samples (thickness…)
Unit of length 1 m (defined in terms of speed of light)
In laboratories/industry are used the following MECHANICAL instruments
Calipers
Gauge blocks (Johansson gauges)
Micrometers
Rudolf Žitný, Ústav procesní a
zpracovatelské techniky ČVUT FS 2010
EXM4
DISTANCEs
or how to measure a motion of samples electronically
In laboratories/industry are used the following ELECTRICAL sensors
Inductive (eddy current sensors, impedance of coil depends upon distance from
metallic sheet)
High frequency
oscillator
Maximum sensing range is roughly coil radius. Linearity
1%, resolution in m. Driving frequencies up to 50 kHz.
Lag and amplitude 1 m
LVDT Linear Variable Differential Transformer. Three solenoidal coils are placed end-toend around a tube. The center coil is the primary, and the two outer coils are the
secondaries. A cylindrical ferromagnetic core slides along the axis of coils. An alternating
current (frequency 1 to 10 kHz) is driven through the primary coil, causing a voltage to be
induced in each secondary proportional to its mutual inductance with the primary.
Mention the fact, that the two transducer
secondaries are connected in opposition.
Therefore at central position of feromagnetic
core the resulting voltage is zero.
Rudolf Žitný, Ústav procesní a
zpracovatelské techniky ČVUT FS 2010
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DISTANCEs
In our laboratories the following ELECTRICAL sensors are used
Potentiometers (linear, string-the spool is coupled to the shaft of a rotational sensor,
you will see this arrangement in our laboratory – piston displacement of extrusional
rheometer measurement).
The same principle is used in the project SYRINGE, see Fig.
x
4x
R
D 2
D
V
Specific electrical conductivity
of liquid in syringe [S/m]
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DISTANCEs
The following OPTICAL instruments will be used in your project
(inflation test)
Laser scanner Epsilon
Confocal probe Chrocodile M4
Cross-correlator Dantec Q 450
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Laser scanner
Wikipedia (Laser
scanner)
A laser rangefinder is a device which uses a laser beam to determine the distance to an object.
The most common form of laser rangefinder operates on the time of flight principle by sending a
laser pulse in a narrow beam towards the object and measuring the time taken by the pulse to be
reflected off the target and returned to the sender. Due to the high speed of light, this technique is
not appropriate for high precision sub-millimeter measurements, where triangulation and other
techniques are often used.
3D laser scanner shines a laser on the subject and exploits a
camera to look for the location of the laser dot. Depending on how
far away the laser strikes a surface, the laser dot appears at
different places in the camera’s field of view. This technique is
called triangulation because the laser dot, the camera and the laser
emitter form a triangle. The length of one side of the triangle, the
distance between the camera and the laser emitter is known. The
angle of the laser emitter corner is also known. The angle of the
camera corner can be determined by looking at the location of the
laser dot in the camera’s field of view. These three pieces of
information fully determine the shape and size of the triangle and
gives the location of the laser dot corner of the triangle. In most
cases a laser stripe, instead of a single laser dot, is swept across
the object to speed up the acquisition process.
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Confocal probe
The chromatic coded principle utilises the chromatic length aberation of specialised lens to measure
distance and transparent layer thickness. Due to the independence of surface properties merely all
materials can be measured by the sensor. The measurement range of the sensor stretches from
some micrometers up to millimeters with corresponding resolution. The passive sensor probe is
connected via an optical fiber to ensure the operation in problematic or hazardous environment like
strong electromagnetic fields, vacuum or explosive areas.
Light is reflected from the point of
changing refractive index
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Cross-correlator
The Digital 3D Correlation System Q-450 is used for non contact measurement
of surface and deformation of any object. A stochastic pattern is applied onto the
surface of the test object. This pattern can be sprayed with a white base colour
and spattering a black colour on top. The surface is observed with two highspeed CCD camertas. In each captured image homologous points of the
stochastic structure are identified using a specific pattern matching algorithm.
The three-dimensional position of each object point is determined by
triangulation performed by the software.
How?
This is in principle matter of a pure geometry:
knowing x1,y1 and x2,y2 position (pixels) of the
same material point in the two 2D images
recorded by two cameras, it is possible to
evaluate its coordinate x,y,z in the 3D space.
(x,y)
It can be illustrated schematically in a 2D
reconstruction of point (x,y) from the two 1D
“images” x1, x2
In 3D there are two cameras giving 4 coordinates (x1,y1, x2,y2)
of point x,y,z. This is overdetermined problem!
(x2)
(x1)
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Cross-correlator
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Cross-correlator DIC
Digital image correlation algorithm is based upon assumed mapping between two images from
camera. The goal is to identify a shift (displacement) and deformation of material points. The whole
image is divided to sub-images, called facets (a set of material points). It is assumed that the material
facet in the second image is shifted (by displacements u,v in the x,y directions) and linearly deformed
(gradient of displacement)
Facet and a point
x,y inside
Coordinates of point x,y with respect to
the facet center
Coordinates in the
second image
Displacements of the
facet center
Gradient of
displacements
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Cross-correlator DIC
6 parameters: u,v (shift) and gradient (du/dx,…) should be identified at each facet. These parameter
(spatial transformation) are selected in such a way that the correlation between corresponding material
points in both images (initial and deformed configuration) is maximized. It is assumed that each
material point has the same intensity of pixel in both images (intensity F in the first and G in the second
image). Then the correlation rij between pixels i,j in both images (facets) can be expressed as
Maximum rij corresponds to optimal
values of displacement and
deformation in a facet.
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Grid-Facet DIC
Problem:
!) averaging DIC params
Grid
2) Interpolation DIC
We do not know how it is
implemented in Q 450
Facet
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Grid-Facet DIC
Grid
Facet
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OCT , ESPI
There are many other different optical methods based upon
interferometry, see e.g. OCT (Optical Coherence Tomography)
ESPI means Electronic Speckle Pattern Interferometry
and it is similar to previously described DIC
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Pressure
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Pressure
Units and terminology:
Gauge pressure – relative to atmospheric (Pa gauge, psig)
Absolute pressure – (psia)
Instruments for pressure measurement
Micromanometers Askania – extremely accurate
(used as a gauge)
U-tube
p2
p1  p2  gh
h
p1
Resolution 0.1 Pa !!
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Pressure
Instruments for pressure measurement (mechanical)
FLEXIBLE elements
Bourdon tube: C/shape-oval
Bellows elements
Diaphragm
Can you explain how the
Bourdon tube will be
deformed by internal
pressure? And why?
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Pressure
Instruments for pressure measurement (electronic)
Piezoresistive Strain Gage (piezoresistive effect of bonded or formed
strain gauges to detect strain due to applied pressure)
Capacitive (a diaphragm create a variable capacitor)
Magnetic (diaphragm displacement measured by inductance, LVDT, Hall
Effect, or by eddy current).
Piezotransducers (piezoelectric effect in certain materials such as quartz
to measure the strain upon the sensing mechanism due to pressure).
Optical (physical change of an optical fiber with strain)
Resonant (changes in resonant frequency of a string, crystal, gas)
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Do you understand principle?
Ultra-precision micro-differential pressure measuring device and ultraprecision differential pressure measuring device
Patent Sekoguchi, Kotohiko (8-10-1304 Sakaemachi, Ikeda-shi, Osaka, JP)
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Strain gauge
SG - Resistor with electrical resistivity dependent on strain
Gauge Factor
R
G
R0
deformation
There are two basic types of SG
Foil SG. Metallic wire (e.g. constantan) included in a thin plastic sheet. The
foil is bonded to surface of measured object e.g. by cyanoacrylate glue. Typical
gauge factor is 2 and resistance 120 (almost the same as resistance of Pt100
thermometers. Therefore the same technique for measurement of electric
resistance Is used (Wheatstone bridge). Problem with temperature dependent
resistance can be compensated using 2 SG bonded to the surface at a place
with the same temperature (half bridge), or even 4 active SG at the same
temperature (full bridge). Selfcompensated SG make use of metallic wire
adjusted to the thermal expansion of basic material.
Semiconductor SG (piezoresistive). Silicon wafer or rod doped by
Germanium or As. Much higher sensitivity
(gauge factor), but also sensitive to temperature.
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Piezoresistive transducers
Exposed silicon
membrane
Separating
membrane +
silicon oil
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Piezoresistive transducers
KULITE XTM – 190 this transducer is used in the project “SYRINGE”.
Please, be careful as concerns the wiring
and polarity of voltage
p
2 mm (!)
Silicon membrane with
integrated strain-gauges
(pressure transducer
Kulite Semiconductors).