13.9.5 Attenuation of ultrasound
waves
Ultrasound waves suffer attenuation
in the amplitude of the transmitted energy according to the distance travelled.
The amount of attenuation also depends on the nominal frequency of the
ultrasound and the adsorption characteristics of the medium through which it
travels. The amount of adsorption depends not only on the type of transmission
medium but also on the level of humidity and dust in the medium.
The amplitude Xd of the
ultrasound wave at a distance d from the emission point can be expressed as:
Xd/
X0 =
where X0 is the magnitude
of the energy at the point of emission, f is the nominal frequency of the
ultrasound and α is the attenuation constant that depends on the
ultrasound frequency, the medium that
the ultrasound travels through and any pollutants in the medium such as dust or
water particles.
13.9.6 Ultrasound as a range sensor
The basic principles of an ultrasonic
range sensor are to measure the time between transmission of a burst of
ultrasonic energy from an ultrasonic transmitter and receipt of that energy by
an ultrasonic receiver. Then, the distance d can be calculated from:
d =
vt (13.5)
where v is the ultrasound velocity
and t is the measured energy transit time. An obvious difficulty in applying
this equation is the variability of v with temperature according to equation
(13.2). One solution to this problem is to include an extra ultrasonic transmitter/receiver
pair in the measurement system in which the two elements are positioned a known
distance apart. Measurement of the transmission time of energy between this
fixed pair provides the necessary measurement of velocity and hence
compensation for any environmental temperature changes.
The degree of directionality in the
ultrasonic elements used for range measurement is unimportant as long as the
receiver and transmitter are positioned carefully so as to face each other exactly
(i.e. such that the ‘normal’ lines to their faces are coincident). Thus,
directionality imposes no restriction on the type of element suitable for range
measurement. However, element choice is restricted by the attenuation
characteristics of different types of element, and relatively low-frequency
elements have to be used for the measurement of large ranges.
Measurement resolution and accuracy
The best measurement resolution that
can be obtained with an ultrasonic ranging system is equal to the wavelength of
the transmitted wave. As wavelength is inversely proportional to frequency,
high-frequency ultrasonic elements would seem to be prefer[1]able. For
example, whilst the wavelength and hence resolution for a 40 kHz element is 8.6
mm at room temperature (20°C), it is only 0.86 mm for a 400 kHz element.
However, choice of element also depends on the required range of measurement.
The range of higher-frequency elements is much reduced compared with
low-frequency ones due to the greater attenuation of the ultrasound wave as it
travels away from the transmitter. Hence, choice of element frequency has to be
a compromise between measurement resolution and range.
The best measurement accuracy
obtainable is equal to the measurement resolution value, but this is only
achieved if the electronic counter used to measure the transmission time starts
and stops at exactly the same point in the ultrasound cycle (usually the point
in the cycle corresponding to peak amplitude is used). However, the sensitivity
of the ultrasonic receiver also affects measurement accuracy. The amplitude of
the ultrasound wave that is generated in the transmitter ramps up to full
amplitude in the manner shown in Figure 13.12. The receiver has to be sensitive
enough to detect the peak of the first cycle, which can usually be arranged.
However, if the range of measurement is large, attenuation of the ultrasound
wave may cause the amplitude of the first cycle to become less than the
threshold level that the receiver is set to detect.
In this case, only the second cycle
will be detected and there will be an additional measurement error equal to one
wavelength.
13.9.7 Use of ultrasound in tracking
3D object motion
An arrangement of the form shown in
Figure 13.13 can be used to provide measurements of the position of an object
moving in 3D space. In this, an ultrasonic transmitter mounted on the moving
object (T) transmits bursts of energy to three receivers A, B, C located at the
origin (A) and at distances q (to B) and p (to C) along the axes of an xyz
co-ordinate system. If the transit times from T to A, B and C are measured, the
distances a, b and c from T to the receivers can be calculated from equation
(13.5). The position of T in spatial (xyz) co-ordinates can then be calculated
by triangulation by solving the following set of equations:
13.9.8 Effect of noise in ultrasonic
measurement systems
Signal levels at the output of
ultrasonic measurement systems are usually of low ampli[1]tude
and are therefore prone to contamination by electromagnetic noise. Because of
this, it is necessary to use special precautions such as making ground (earth)
lines thick, using shielded cables for transmission of the signal from the
ultrasonic receiver and locating the signal amplifier as close to the receiver
as possible.
Another potentially serious form of
noise is background ultrasound produced by manufacturing operations in the
typical industrial environment that many ultrasonic range measurement systems
operate. Analysis of industrial environments has shown that ultrasound at
frequencies up to 100 kHz is generated by many operations and some operations
generate ultrasound at higher frequencies up to 200 kHz. There is not usually
any problem if ultrasonic measurement systems operate at frequencies above 200
kHz, but these often have insufficient range for the needs of the measurement
situation. In these circumstances, any objects that are likely to generate
energy at ultrasonic frequencies should be covered in sound-absorbing material
such that interference with ultrasonic measurement systems is minimized. The
placement of sound-absorbing mate[1]rial around the
path that the measurement ultrasound wave travels along contributes further
towards reducing the effect of background noise. A natural solution to the problem
is also partially provided by the fact that the same processes of distance travelled
and adsorption that attenuate the amplitude of ultrasound waves travelling
between the transmitter and receiver in the measurement system also attenuate
ultrasound noise that is generated by manufacturing operations.
Because ultrasonic energy is emitted
at angles other than the direction that is normal to the face of the
transmitting element, a problem arises in respect of energy that is reflected
off some object in the environment around the measurement system and back into
the ultrasonic receiver. This has a longer path than the direct one between the
transmitter and receiver and can cause erroneous measurements in some
circumstances. One solution to this is to arrange for the transmission-time
counter to stop as soon as the receiver first detects the ultrasound wave. This
will usually be the wave that has travelled along the direct path, and so no
measurement error is caused as long as the rate at which ultrasound pulses are
emitted is such that the next burst isn’t emitted until all reflections from
the previous pulse have died down. However, in circumstances where the direct
path becomes obstructed by some obstacle, the counter will only be stopped when
the reflected signal is detected by the receiver, giving a potentially large
measurement error.
13.9.9 Exploiting Doppler shift in
ultrasound transmission
The Doppler effect is evident in all
types of wave motion and describes the apparent change in frequency of the wave
when there is relative motion between the transmitter and receiver. If a
continuous ultrasound wave with velocity is v and frequency f takes t seconds
to travel from a source S to a receiver R, then R will receive ft cycles of
sound during time t (see Figure 13.14). Suppose now that R moves towards S at
velocity r (with S stationary). R will receive rt/ʎ extra cycles of sound
during time t, increasing the total number of sound cycles received to (ft +
rt/ʎ). With (ft + rt/ʎ)
cycles received in t seconds, the
apparent frequency f ’ is given by:
If the ultrasound source moves
towards the stationary receiver at velocity s, it will move a distance st in
time t and the ft cycles that are emitted during time t will be compressed into
a distance (vt - st).
Thus, the velocity of an ultrasound
receiver moving with respect to an ultrasound source can be calculated from the
measured ratio between the real and apparent frequencies of the wave. This is
used in devices like the Doppler shift flowmeter.
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