**3.5.1 Principle of the sensor proposed**

The sensor proposed is illustrated in figure 15. In the shape of a thin disc, its structure is made up of a ring with an embedded piezoelectric disc.

A structure like this offers the advantage of being able to work at resonances lower than those of the piezoelectric disc and thus several resonance modes can be used of which the main ones are flexion and radial modes. This type of sensor also offers a large area of contact with the medium studied, which, in the case of soft and aerated materials, can be advantageous.

The resonance modes of a circular structure, notably those of a disc or a thin ring, have been studied for many years by several authors (Aggarwal, 1952a, 1952b; Moseley, 1960; Vogel & Skinner, 1965; Leissa, 1969; Blevins, 1979; Irie & al., 1984; Lee & Singh, 1994) . The main modes of resonance of a disc are radial modes in the disc plane and flexion modes outside the disc plane (Tables 3, 4 & 5). The tables show a good correlation between the theoretical, numerical and experimental analyses.

Low Frequency Acoustic Devices for Viscoelastic Complex Media Characterization 229

1 35.9 2 90 Flexion modes (1.0) 1.6 (2.0) 6.5 Table 5. Resonance frequencies of the first radial and flexion modes for the composite sensor

The objective of this application was to establish the links between the product evolution

From a practical point of view, impulse excitation was used in this system. The excitation was obtained by a controlled mechanical impact (rod of an electromagnet), thus exciting the disc used for the synchronisation. The vibration induced in the dough is received by a

A metrological study of the measuring device carried out using standard samples (for example a pocket of water at 25°C) showed that the standard deviation of the amplitude and

After controlled kneading of the dough, the measurement chamber was placed in an enclosure in order to control the temperature and humidity. The acoustic values studied

the velocity was approximately 2%. Signal acquisition was carried out over 3 hrs.

**3.5.3 Dynamic monitoring of the fermentation process of bread dough** 

were the variation of the time-of-flight and the wave amplitude on reception.

Frequency (kHz)

Radial modes

**3.5.2 Application for monitoring fermenting bread dough** 

receiver disc identical to that of the synchronisation disc (Figure 16).

kinetics and the acoustic characteristics measured.

Fig. 16. Experimental measuring device

Fig. 15. Set-up of the sensor proposed


Table 3. Illustration of the deformations. Amplitude perpendicular to the disc plane Flexion mode (1.0) for a frequency of 1.8 kHz (theoretical and using finite elements)


Table 4. The resonance frequencies of the first two radial modes for a free aluminium disc (R=5cm; h=2mm) obtained analytically and numerically using finite elements

Fig. 15. Set-up of the sensor proposed

Flexion

modes (s, n) Theoretical

Table 3. Illustration of the deformations. Amplitude perpendicular to the disc plane Flexion

Radial modes Analytical calculation (kHz) FEM (kHz)

Table 4. The resonance frequencies of the first two radial modes for a free aluminium disc

(R=5cm; h=2mm) obtained analytically and numerically using finite elements

mode (1.0) for a frequency of 1.8 kHz (theoretical and using finite elements)

(Hz) FEM (Hz)

(1.0) 1798 1794

35.5 35.5

92.6 92.7

Table 5. Resonance frequencies of the first radial and flexion modes for the composite sensor

## **3.5.2 Application for monitoring fermenting bread dough**

The objective of this application was to establish the links between the product evolution kinetics and the acoustic characteristics measured.

From a practical point of view, impulse excitation was used in this system. The excitation was obtained by a controlled mechanical impact (rod of an electromagnet), thus exciting the disc used for the synchronisation. The vibration induced in the dough is received by a receiver disc identical to that of the synchronisation disc (Figure 16).

Fig. 16. Experimental measuring device

A metrological study of the measuring device carried out using standard samples (for example a pocket of water at 25°C) showed that the standard deviation of the amplitude and the velocity was approximately 2%. Signal acquisition was carried out over 3 hrs.

### **3.5.3 Dynamic monitoring of the fermentation process of bread dough**

After controlled kneading of the dough, the measurement chamber was placed in an enclosure in order to control the temperature and humidity. The acoustic values studied were the variation of the time-of-flight and the wave amplitude on reception.

Low Frequency Acoustic Devices for Viscoelastic Complex Media Characterization 231

A repeatability study was carried out to estimate the dispersion of the parameters (delay and amplitude). Several tests were performed under the same operating conditions. The

Table 6 summarises the variations in the characteristic parameters observed on the curves

*τr (min)* 165 105 60 *Tr (min)* 145 70 55 *ΔtM (µs)* 380 385 374 *τa (min)* 160 95 55 *Ta (min)* 130 75 50 *AS (%)* 40 43 44

It can be noted that the maximum relative delay is relatively constant (approximately 380µs) for the three products made under the same operating conditions. This parameter seems to be independent of the temperature, which is in agreement with the hypothesis that it varies according to the gas fraction contained in the matter and the elastic properties of the matrix.

In certain industrial processes it is often difficult to access useful information in real-time due to the conditions imposed on the mechanical and thermal parameters, pressure, hygiene..., conditions which require a specific installation of the sensor with regard to its environment. The difficulty thus arises of an integration taking into account both the process constraints and the acoustic constraints. This is the case of a plate heat exchanger

For the exchanger, the sensor selected is not cumbersome and is sensitive over a temperature range reaching over 100°C (Figure 19). The excitation and synchronisation

**4. Acoustic sensor for in-line monitoring of a manufacturing process** 

which can be considered as a typical example in this category (Figure 18).

Fig. 18. Standard plate heat exchanger

**4.1 Sensor selection criteria** 

**20° 27° 34°** 

standard deviation of the measurements of these parameters was around 3%.

according to the evolution in the temperature

Table 6. Parameters relating to the variation in temperature

Figure 17 shows the variations in these two values. It can be noted that the critical points and phases appear simultaneously on the two curves.

Fig. 17. Evolution of the standardised amplitude and the relative signal delay on reception during the fermentation phase

Where:


Figure 17 shows the variations in these two values. It can be noted that the critical points

Fig. 17. Evolution of the standardised amplitude and the relative signal delay on reception

• **Tr** reflects the period of stability during which the relative delay reaches its maximum

• **ΔtM** is the maximum relative delay. It is linked to the gas fraction contained in the

• **τa** is the period during which the amplitude of the signal decreases before reaching a

• **AS** is defined as being the amplitude of the signal during the period of stability.

during the fermentation phase

and remains relatively constant,

• **τr** is the time necessary to reach a relatively stable zone,

dough and therefore the extensibility of the latter.

• **Ta** is the period of stability of the amplitude,

Where:

plateau,

and phases appear simultaneously on the two curves.

A repeatability study was carried out to estimate the dispersion of the parameters (delay and amplitude). Several tests were performed under the same operating conditions. The standard deviation of the measurements of these parameters was around 3%.

Table 6 summarises the variations in the characteristic parameters observed on the curves according to the evolution in the temperature


Table 6. Parameters relating to the variation in temperature

It can be noted that the maximum relative delay is relatively constant (approximately 380µs) for the three products made under the same operating conditions. This parameter seems to be independent of the temperature, which is in agreement with the hypothesis that it varies according to the gas fraction contained in the matter and the elastic properties of the matrix.
