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 |
|
