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4.1.1. Measuring principle
To measure cables, an ultrasonic sensor
is positioned externally a few centimetres above the surface
of the cable. Water is used as the propagation medium of the
ultrasonic energy. A piezoelectric crystal is excited with
a short electrical pulse. The crystal converts the electrical
energy into sound waves and emits a "Bang", i.e.
a single pulse <1 ms. The system switches to the "waiting,
listening" mode to catch the reflection from all obstacles
in the path of the sound waves. The first echo originates
from the surface of the cable or from the shielding. It is
obvious that the surface only reflects part of the sound energy.
The rest propagates into the insulation until it impinges
on the conductor, triggering a second echo. It is now up to
the electronics to distinguish the first
from the second
echo in a reliable way and to perform an analysis providing
the propagation time of the echoes
multiplied by the velocity of sound in the sheathing material.
Additional echoes, e.g. from the other side of the conductor,
are discarded.
t1 is
the time needed by the ultrasonic signal to cross the distance
from the crystal to the surface of the product (both ways),
while t2 is the time needed
to cross the wall thickness back and forth.
This means that the wall thickness is given by:
The wall thickness is given by:
| W |
= |
v ·
(t2 / 2) |
| W |
= |
Wall thickness |
| V |
= |
Sound velocity |
| t2 |
= |
Time interval between two
echoes |
The distance between the crystal and the
surface is calculated as follows:
| d |
= |
1.5 ·
(t1 / 2) |
| d |
= |
Distance |
| 1.5 |
= |
Sound velocity in water
in mm/µs |
| t1 |
= |
Time elapsed until the
first echo returns. |
The propagation velocity of sound
in some mediums such as PVC is not an absolute constant but
depends on the density of the medium, on the temperature and
on the pressure. The sound velocity can be mathematically
calculated as
where E = K* f(T) also depends on the temperature.
Reflections occur at the boundary between two media with different
characteristic acoustic impedance.
Therefore, the more different the materials,
the more marked the echo.
4.1.2. Ultrasonic Measurement
Methods of Wall Thickness and Eccentricity
The eccentricity is the distance between
the centres of the outer and inner circles.
The formula used is:
| A and B |
AB =  ((A2
+ B2 2*A*B*cos(c)) / (sin(c))
are the largest neighbouring deviations from the inner
circle computed according to the formula.
AB = (IW-W'I) / 2 |
| W + W': |
Two opposite angle wall
thicknesses. |
| c: |
Sector |
| W and W' |
are two opposite values
of the wall thickness (i.e. W1 and W16 with 30 sectors) |
| C |
is the angle between the
axes, of neighbour pairs of measured values
(i.e. c = 360 / 6 = 60 with 6 sectors) |
Important: This relation is only valid with
4, 6 or 8 sensors.
4.1.3. Graphical Example with 6 Sensors
4.1.4. Measuring System Layout
In practical applications, ultrasonic
heads - also known as Transducers - are mounted in so-called
Scanners that can look quite different according to product
dimensions and operating requirements.
New structural shapes allow positioning the device immediately
after the extruder.
4.1.4.1. Types of Transducer
Different types of transducers can
be used to suit the requirements of the application (mixture
of materials, wall thickness, etc.). They differ by their
sonic power, their frequency (2 to 10 MHz) and their focussing
principle.
|
a) cylindrical
|
|
b) flat |
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