Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

Displacement, Deformation,Pressures

Experimental methods E181101 EXM4

Some pictures and texts were copied from www.wikipedia.com

Unit of length 1 m (defined in terms of speed of light)

In laboratories/industry are used the following MECHANICAL instrumentsCalipers

Gauge blocks (Johansson gauges)

Micrometers

Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

DISTANCEs or how to measure geometry of samples (thickness…) EXM4

Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

DISTANCEs or how to measure a motion of samples electronically EXM4

In laboratories/industry are used the following ELECTRICAL sensorsInductive (eddy current sensors, impedance of coil depends upon distance from metallic sheet)

LVDT Linear Variable Differential Transformer. Three solenoidal coils are placed end-to-end 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.

High frequency oscillator

Lag and amplitude 1 m

Maximum sensing range is roughly coil radius. Linearity 1%, resolution in m. Driving frequencies up to 50 kHz.

Mention the fact, that the two transducer secondaries are connected in opposition. Therefore at central position of feromagnetic core the resulting voltage is zero.

DISTANCEs EXM4

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.

V

xD

2

4DxR

Specific electrical conductivity of liquid in syringe [S/m]

DISTANCEs EXM4

The following OPTICAL instruments will be used in your project (inflation test)

Laser scanner Epsilon

Confocal probe Chrocodile M4

Cross-correlator Dantec Q 450

Laser scannerEXM4

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.

Confocal probeEXM4

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

Cross-correlatorEXM4

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 high-speed 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.

It can be illustrated schematically in a 2D reconstruction of point (x,y) from the two 1D “images” x1, x2

(x,y)

(x2)

(x1)In 3D there are two cameras giving 4 coordinates (x1,y1, x2,y2) of point x,y,z. This is overdetermined problem!

Cross-correlatorEXM4

Cross-correlator DICEXM4

Facet and a point x,y inside

Coordinates in the second image

Coordinates of point x,y with respect to the facet center

Displacements of the facet center

Gradient of displacements

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)

Cross-correlator DICEXM4

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.

Grid-Facet DICEXM4

Facet

Grid

Problem:

!) averaging DIC params

2) Interpolation DIC

We do not know how it is implemented in Q 450

Grid-Facet DICEXM4

Facet

Grid

OCT , ESPIEXM4

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

PressureEXM4

PressureEXM4

Instruments for pressure measurementU-tube

p1

p2

h

Units and terminology:

Gauge pressure – relative to atmospheric (Pa gauge, psig) Absolute pressure – (psia)

ghpp 21

Micromanometers Askania – extremely accurate (used as a gauge)

Resolution 0.1 Pa !!

PressureEXM4

Instruments for pressure measurement (mechanical)

FLEXIBLE elements

Bourdon tube: C/shape-oval

Bellows elements

DiaphragmCan you explain how the Bourdon tube will be deformed by internal pressure? And why?

PressureEXM4

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)

Do you understand principle?EXM4

Ultra-precision micro-differential pressure measuring device and ultra-precision differential pressure measuring device

Patent Sekoguchi, Kotohiko (8-10-1304 Sakaemachi, Ikeda-shi, Osaka, JP)

Strain gaugeEXM4

0RRG

SG - Resistor with electrical resistivity dependent on strain

Gauge Factor

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.

deformation

Piezoresistive transducersEXM4

Exposed silicon membrane

Separating membrane + silicon oil

Piezoresistive transducersEXM4

KULITE XTM – 190 this transducer is used in the project “SYRINGE”.Please, be careful as concerns the wiring and polarity of voltage

2 mm (!)

Silicon membrane with integrated strain-gauges (pressure transducer Kulite Semiconductors).

p