Method and system for measuring a dimensional variation of a mechanical part

Abstract

A method for measuring a dimensional variation (L) of a mechanical part (V) along a longitudinal direction (x), comprising the steps of: a) providing at least one first (TP1) and a second (TP2) piezoelectric transducer arranged in two different positions (ELV, TV) along said longitudinal direction and acoustically coupled via said mechanical part; b) performing, at different times, a plurality of electrical measurements to determine at least one value of an electrical parameter dependent on an off-diagonal term (Z12) of an impedance matrix of an electrical quadrupole modeling the assembly formed by the first and second acoustically coupled piezoelectric transducers; etc.) deducing from the results of said electrical measurements said dimensional variation of the mechanical part. System for implementing this method. Figure for the abstract: Fig. 4

Description

Title of the invention: Method and system for measuring a variation in the dimension of a mechanical part

[0001] The invention lies in the field of non-destructive testing by ultrasound. It applies in particular, but not exclusively, to measuring the tightness of screw fastening systems during the industrial assembly of parts.

[0002] It is known to use acoustic techniques to accurately and dynamically measure the tightening of screw fastening systems during industrial assembly of parts by an acoustic method.

[0003] As illustrated in [Fig. 1], this can be achieved by attaching a piezoelectric transducer TP to one end ELV of a fastening means (screw) V and exciting it with a sinusoidal voltage. The transducer generates standing acoustic waves OS in the body CV of the fastening means, which are established in the structure according to its length. In turn, these acoustic waves modify the impedance of the piezoelectric transducer TP, which can be measured simultaneously with the excitation of the latter. If the phase and magnitude of the complex impedance of the transducer are plotted as a function of frequency, peaks can be observed corresponding to the acoustic resonance frequencies of the structure.

[0004] As the fastening system is tightened (for example, by screwing in a nut E), its length changes, and with it its resonant frequencies. A frequency shift of the transducer's impedance peaks is then observed. This is illustrated in [Fig. 2], in which four impedance curves—corresponding to voltages of 0, 6 kN, 12 kN, and 18 kN—are superimposed. [Fig. 3] shows that the relationship between the applied voltage and the frequency shift Δf of the impedance peaks is substantially linear, with an error on the order of 1% (the two curves in the lower part correspond to the deviation from a linear relationship during energization and de-energization).

[0005] The tightening of the nut can be controlled and regulated by means of this mechanical tension measurement, so as to control the pre-tension more precisely than by using a simple mechanical measurement of the applied tightening torque.

[0006] This technique, known in English-language literature as "Impedence Frequency Shift" (IFS), is described for example in (Heyman 1977), (Smith 1980), (Joshi 1984), (Shao 2016) and (Dreisbach 2023).

[0007] As can be seen, however, the impedance peaks are quite wide compared to their spacing, which makes it difficult to determine their spacing precisely and, consequently, the variation in length of the element of fixation. In practice, it is necessary to use a frequency analysis which requires acquisition over several periods - therefore with a wide spectral band and a significant acquisition time.

[0008] A competing technique to IFS is based on measuring the time-of-flight (TOF) of an acoustic wave. As in the case of IFS, a piezoelectric transducer is attached to the structure and excited to generate acoustic waves. Unlike IFS, however, the transducer is excited by a voltage pulse that generates a time-limited acoustic wave. The wave propagates through the structure and back, before returning to the transducer. The transducer is then used as a sensor by monitoring its voltage, which varies as the acoustic wave returns. The time between emission and reception depends on the wave speed (obtained by prior calibration) and the length of the structure. TOF is a well-known and widely used technique in the prior art.However, it has a number of drawbacks, including the need to use fast electronics to generate short pulses, and voltage pulses on the order of a few hundred volts (as opposed to volts in the case of IFS).

[0009] The invention aims to overcome, at least in part, the aforementioned drawbacks of the prior art. More particularly, it aims to improve the accuracy and sensitivity of the IFS technique without significantly complicating its implementation.

[0010] According to the invention, this objective is achieved through the combined use of two acoustically coupled piezoelectric transducers across the mechanical part whose length is to be measured. The assembly consisting of the two acoustically coupled transducers can be modeled by an electrical quadrupole, characterized by an impedance matrix Z. Measuring the off-diagonal element Zn of this matrix (or another electrical parameter proportional to this element) as a function of frequency allows for the estimation of a variation in the length of the mechanical part, as in the standard IFS technique. The advantage provided by the invention lies in the fact that, as will be shown later, the impedance peaks are much more pronounced and narrow than in the conventional case where a single transducer is used.

[0011] An object of the invention is therefore a method for measuring a variation in the dimension of a mechanical part along a so-called longitudinal direction, comprising the steps of: a) provide at least one first and one second piezoelectric transducer arranged in two different positions along said longitudinal direction and acoustically coupled via said mechanical part; b) perform, at different times, a plurality of electrical measurements to determine at least one value of an electrical parameter depending on an off-diagonal term of an impedance matrix of an electrical quadrupole modeling the system formed by the first and second acoustically coupled piezoelectric transducers; and c) deduce from the results of said electrical measurements said variation in dimension of the mechanical part.

[0012] According to particular embodiments of such a process:

[0013] - Each said electrical measurement of step b) may comprise the substeps consisting of: bl) apply a first electrical excitation signal to said first piezoelectric transducer to generate acoustic waves propagating in the mechanical part towards the second transducer, while keeping the second piezoelectric transducer in an open circuit, and simultaneously measure the input impedance of said first piezoelectric transducer; b2) apply a second electrical excitation signal to said first piezoelectric transducer to generate acoustic waves propagating in the mechanical part towards the second transducer, while keeping the second piezoelectric transducer short-circuited, and simultaneously measure the input impedance of said first piezoelectric transducer; b3) calculate the value of said electrical parameter from the input impedances thus measured; the order of substeps bl) and b2) can be reversed.

[0014] - Said electrical parameter may be the phase difference of the impedances input measured during substeps bl) and b2).

[0015] - The second piezoelectric transducer may comprise two electrical terminals connected together by a pair of back-to-back diodes in parallel, the first excitation signal being sufficiently weak so that the generated acoustic waves induce across the terminals of said second piezoelectric transducer a voltage lower than a threshold of said diodes, which can then be considered as an open circuit, and the second excitation signal being sufficiently strong so that the generated acoustic waves induce across the terminals of said second piezoelectric transducer a voltage greater than a threshold of said diodes, which can then be considered as a short circuit.

[0016] - Step b) may include determining the value of said parameter in function of frequency.

[0017] - Step c) may include identifying peaks in the value of said parameter electrical as a function of frequency, the variation in the dimension of the mechanical part being deduced from a variation in the position of said peaks.

[0018] - The first and second piezoelectric transducers can be arranged in two opposite ends, along said longitudinal direction, of the mechanical part.

[0019] Another object of the invention is the use of such a method for measuring the tightening of a screw.

[0020] Yet another object of the invention is a system for measuring a variation in the dimensions of a mechanical part along a so-called longitudinal direction, comprising: - a first and a second piezoelectric transducer, adapted to be fixed in two different positions along said longitudinal direction and acoustically coupled via said mechanical part; - an electronic system configured to determine at least one value of an electrical parameter dependent on an off-diagonal term of an impedance matrix of an electrical quadrupole modeling the assembly formed by the first and second acoustically coupled piezoelectric transducers; and to deduce from a variation of said at least one value of said parameter said variation in dimension of the mechanical part.

[0021] According to particular embodiments:

[0022] Said electronic system may include: - a first electronic device configured to apply electrical excitation signals to said first piezoelectric transducer and simultaneously measure its input impedance; - a second electronic device configured to maintain said second piezoelectric transducer successively in open circuit and short circuit; and - a processor configured to drive at least said first electronic device so as to: - apply a first electrical excitation signal to said first piezoelectric transducer to generate acoustic waves propagating in the mechanical part towards the second transducer, while keeping the second piezoelectric transducer in an open circuit, and simultaneously measure the input impedance of said first piezoelectric transducer; - apply a second electrical excitation signal to said first piezoelectric transducer to generate acoustic waves propagating in the mechanical part towards the second transducer, while keeping the second piezoelectric transducer short-circuited, and simultaneously measure the input impedance of said first piezoelectric transducer; - calculate the value of said electrical parameter from the input impedances thus measured.

[0023] - The electronic device can be integrated into a screw clamping system, the the first and second piezoelectric transducers being adapted to be fixed to said screw.

[0024] Other features, details and advantages of the invention will become apparent from the description given with reference to the accompanying drawings provided by way of example, in which:

[0025] [Fig. 1], already described, illustrates a technique for measuring the length of a mechanical part (screw) by impedance phase shift according to the prior art;

[0026] [Fig.2], already described, is a graph illustrating the impedance phase shift at the base of the technique of [Fig.1];

[0027] [Fig.3], already described, is a graph illustrating the quasi-linear relationship between phase shift of impedance and voltage in the technique of [Fig.1];

[0028] [Fig.4] is the functional diagram of a measurement system according to a mode of realization of the invention;

[0029] [Fig.5] illustrates the modeling of a system of two piezoelectric transducers acoustically coupled by an electrical quadrupole;

[0030] [Fig.6], a graph illustrating the variation as a function of the frequency of the element of matrix Zn;

[0031] [Fig.7], [Fig.8], [Fig.9], [Fig.10] and [Fig.11], graphs illustrating the variation in function of the frequency of different parameters function of Z[2 that can be used in the implementation of the invention according to different embodiments;

[0032] [Fig. 12] and [Fig. 13] are detail views of two variants of the system of the [Fig.4]

[0033] In the diagram of [Fig. 4], the reference numeral V designates a screw extending in a longitudinal direction x and having a length L in this direction. The screw V has a head TV at one end that can cooperate with a clamping tool OS2; the opposite end ELV (free end), which is threaded, is inserted into a nut E, which can also cooperate with a clamping tool OS1. Two mechanical components C1 and C2 pass through the screw body CV and are held between the head TV and the nut E. By rotating the nut with the clamping tool OS1 while holding the head TV fixed with the tool OS2, or vice versa, the screw body is put under tension, producing a slight elongation of the latter.

[0034] To measure this elongation, the screw V is equipped with two piezoelectric transducers TPI and TP2, arranged respectively at its free end ELV and its head TV.

[0035] The clamping tools OS1 and OS2, which together form a clamping system, are adapted to interact with a respective transducer via electrical contacts. More specifically, in the embodiment of [Fig. 4], the first clamping tool OS1 comprises a first electronic device AE1 of the vector network analyzer type, enabling the first piezoelectric transducer TPI to be excited with a sinusoidal electrical signal of variable frequency, and simultaneously its complex impedance to be measured. The second clamping tool OS2, in turn, comprises a second electronic device AE1 enabling the first piezoelectric transducer TPI to be excited with a sinusoidal electrical signal of variable frequency and / or simultaneously its complex impedance to be measured, or alternatively, to be subjected to a variable load (for example, alternately a short circuit and an open circuit).A processor P, for example integrated into the first clamping tool, controls the two electronic devices and receives the impedance measurements taken by them.

[0036] As illustrated in [Fig. 5], the assembly consisting of the two transducers acoustically coupled by the body of the screw V can be modeled by an electrical four-terminal network, characterized by an impedance matrix Z, characterized by four complex elements that are functions of frequency: Zn(f), Zi2(f) = Z2i(f), Z22(f). Denoting by Vin the voltage applied across the terminals of transducer TPI, by Iin the current flowing through said transducer, by Vout the voltage appearing across the terminals of transducer TP2, and by Iout the current flowing through the latter, we have:

[0037] ïVin = ZuIin + Zï2lout (1) \Vmit = ZnIin + Z12Iout

[0038] As mentioned above, one idea underlying the invention is to monitor the variation of at least one parameter P as a function of Z[2] and deduce a measurement of the dimensional variation of the mechanical part. This parameter P can be observed at a fixed frequency or over a frequency spectrum. Similarly, the frequency corresponding to a fixed value of this parameter P can be monitored over time.

[0039] Monitoring a parameter P as a function of Z[2], instead of the impedance of a single transducer, offers several advantages. Such a parameter can exhibit greater variations in magnitude and phase (ranging from -180° to +180°) and, in some cases, narrow peaks or abrupt changes that are easily identifiable. Furthermore, Zn is primarily linked to the direct path between the two transducers, thus eliminating standing waves that could be established with other surfaces in the case of a single transducer.

[0040] Fig. 6, given for reference, illustrates the evolution of the modulus (upper panel) and the phase (lower panel) for three values ​​of screw tension: 0 kN (rest), 10 kN and 20 kN.

[0041] Figure 7 illustrates the evolution, under the same conditions, of the parameter Zi2. We note the greater amplitude of relative evolution of the modulus, and the fact that the phase varies between -180° and +180°, compared to a variation of approximately 60° for that of Zn.

[0042] Figure 8 illustrates the evolution, under the same conditions, of the real part of Zi2. We observe the presence of narrow peaks, whose displacement with voltage can be followed by maximum detection algorithms.

[0043] Figure 9 illustrates the evolution, under the same conditions, of the imaginary part of Zi2. This parameter remains close to zero over a large part of the frequency range of interest, but exhibits abrupt variations corresponding to the resonance frequencies. These variations can be detected by signal reversal algorithms.

[0044] Fig. 10 illustrates the evolution, under the same conditions, of the phase z[2. We notice significant variations, which can be followed by zero-crossing algorithms, for example.

[0045] A particularly interesting embodiment is one in which the excitation and impedance measurement are performed on only one side, for example that of TPI. In this case, the second electronic device is limited to maintaining the second transducer TP2 alternately in short circuit and open circuit.

[0046] When AP2 keeps the transducer TP2 short-circuited, Vout = 0. Equation (1) therefore becomes

[0047] [ vin = zniln+zl2i„ul i 7 2\ , (2) z = 4 > v = zn = z. / i - rju n__ yt . 'ir ________________________________» __ i- r (fl \ IL 2^22 / W» ri ■ ' 7 In {U — & 12*in ' ^22^ have .............. *out — ^in

[0048] with _ Ziz. The input impedance measured under short-circuit conditions ~ ^ / 22 7 ce _ I is therefore worth “ ■

[0049] Z,-„“ = Z1I(1-O.(3)

[0050] When AP2 keeps the transducer TP2 in open circuit, Iout = 0. Equation (1) therefore becomes

[0051] lVin = ZnIin (4) = ¾

[0052] The input impedance measured under open-circuit conditions y co _ I is so quite simply

[0053] Zz„c° = Z11(5)

[0054] By calculating the difference between the impedance values, we find

[0055] at y 7 — 7 — 7 : ' (6) ^in-^in ~^in ~ Z22

[0056] We also define

[0057] | A|ZzJ | =

[0058] and

[0059] A arg (Zin) = arg(Zinco) -arg(Zincc) (8)

[0060] Figure 11 shows graphs of |AJZ^j| (upper part) and |A arg(Z / H)| (lower part) as a function of frequency. It can be seen that the peaks—which correspond to the resonance frequencies enabling the establishment of standing acoustic waves in the screw body—are much narrower than in Figures 2 and 6; their position can therefore be determined much more precisely. In particular, in Figure 11, the solid line corresponds to a screw body of length L0 = 1 cm at rest, and the dashed line to the same screw body stretched by 0.25% (L = 1.0036 cm).

[0061] We denote A f the frequency periodicity of these resonance peaks and <5 / the variation of their position following a variation in the length of the screw.

[0062] The wavelength of an acoustic wave of frequency f is given by X = f, with c being the wave speed. The condition for obtaining a standing wave is given by: nX = 2L, where L is the length of the screw (the half-wavelength and the length are multiples). This gives, for the resonance frequencies, f = with n an integer. Figure 11 shows standing waves for n = 18 and n = 21, and identifies the corresponding peaks of impedance Zin. The distance between the peaks is therefore given by

[0063] The positions of the peaks f and their gap Af vary with the elongation AL = g L.

[0064] The speed of sound in a homogeneous medium is given, as a first approximation (neglecting the acousto-elastic effect) by: _ te 1-v where E is the modulus C~\[P (i+vXl-2v) Young's modulus of the screw material, v its Poisson's ratio, and P its density, which also varies with elongation (while Young's modulus and Poisson's ratio are considered constant to a first approximation). The variation of The volume and therefore the density with deformation is given by: AV = V(j_2v) e' where Vo and Pq are, respectively, the volume and density at rest. The resonance frequencies at rest are found to be given by f11 = âis. n / \f, where n is an integer index, c0 is the speed of sound in the screw at rest, and A / is the spacing between the resonance peaks at rest. Under stretching conditions, the resonance frequencies vary such that:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] / \ (7) •^r^E + qE 2 ~l-0.79& for steel with v=0.29. Finally, the variation of the frequency peaks is given by : 2£_J±2v(8) f0 2£ And Af= (9) We do find a linear relationship between the variations in position of the impedance peaks and the variation in length of the screw (the latter being itself directly proportional to the applied tension, as long as the linear elasticity limit is not crossed). Figure 12 illustrates a particular embodiment in which the second electronic device AE2 is simply two diodes DI and D2 connected back-to-back in parallel. When the voltage Vout generated by the transducer TP2 is lower than the diodes' threshold voltage, this configuration behaves as an open circuit, while when Vout is much higher than the threshold, it behaves as a short circuit. It is therefore possible to perform both types of measurements—open circuit and short circuit—simply by varying the amplitude of the excitation signal of the first transducer TPI. The advantage of this embodiment is that the second electronic device AE2 is entirely passive, and only the clamping tool OS1 needs to be equipped with electrical contacts and high-frequency electronics. This device AE2 can even be encapsulated with the transducer TP2 and permanently installed, in which case access to the screw head is not required. Figure 13 illustrates yet another embodiment in which a third piezoelectric transducer TP3 is arranged on a flange of the screw head TV. This makes it possible, for example, to determine a variation in length between TPI and TP2 (mainly related to the deformation of the screw and therefore to the applied force) and a variation in length between TP2 and TP3 (mainly related to a variation in the temperature of the screw).

[0073] The invention has been described with reference to particular embodiments, but variations are possible. For example:

[0074] - Performing measurements by exciting only TPI and changing the state Using TP2 (open circuit / short circuit) is an advantageous choice, but not a straightforward one. It would also be possible, for example, to excite TPI and perform a voltage or current measurement at TP2, or vice versa. The key is to perform measurements that provide access to an electrical parameter dependent on the off-diagonal term Zn of the impedance matrix of the four-terminal network modeling the system formed by the coupled piezoelectric sensors.

[0075] - The parameter of interest is typically complex. We can then take into account counts its phase (preferred choice for robustness reasons), its modulus, its real part, its imaginary part or any combination of these values.

[0076] - Instead of a sinusoidal excitation signal of variable frequency (in a way (continuous or stepped) it is possible to use a signal comprising several frequency components simultaneously, for example, a pulsed signal. This allows for faster measurement of length variation, at the cost of more complex electronics capable of generating and processing intense pulses.

[0077] - Instead of determining the frequency dependence of the parameter, it is possible to measure the value of the parameter of interest at a single frequency, and deduce a variation in the length of the mechanical part from a variation in this value.

[0078] The structure of the clamping system may differ from that of [Fig. 4]. For example, it is not essential that the processor P be integrated into a tool OS1. The processor may, moreover, be implemented using a microprocessor, an ASIC, or even an FPGA. It is possible to have two separate processors to control the electronic device EA (and, if necessary, the electronic device DE) and to calculate the variation in length of the workpiece from the acquired electrical measurements.

[0079] In the example of [Fig. 4] and in that of [Fig. 12], the transducer located on the free end side of the screw is excited, and the one on the head side is "passive". The reverse is also possible. Furthermore, the transducers can be arranged in different locations.

[0080] The part whose length variation is measured does not necessarily have to be a screw, or even a fastener. It can be any mechanical element that allows the establishment of standing acoustic waves and to which piezoelectric transducers can be attached or attached. The length variation (more generally, dimension) to be measured does not necessarily have to be caused by mechanical stress: it can also be, for example, thermal expansion or the effect of corrosion. References

[0081] (Heyman 1977): JS Heyman, “A CW Ultrasonic Bolt-strain Monitor”, Experimental Mechanics (1977)

[0082] (Smith 1980): JFSmith and JD Greiner, “Stress Measurement and Boit Tensioning by Ultrasonic Methods”, Journal of Metals (1980)

[0083] (Joshi 1984): SG Joshi and RG Pathare, “Ultrasonic instrument for measuring water stress”, Ultrasonics (1984)

[0084] (Shao 2016): J. Shao et al., “Boit Looseness Détection Based on Piezoelectric Impédance Frequency Shift”, Applied Sciences, vol. 6 (2016)

[0085] (Dreisbach 2023): A.-L. Dreisbach and C.-P. Fritzen “A Novel Approach for Preload Monitoring in Bolted Connections Using Electro-Mechanical Impedence Spectra” Lecture Notes in Civil Engineering 254, Springer (2023).

Claims

1.

2. Demands A method for measuring a change in dimension (L) of a mechanical part (V) along a longitudinal direction (x), comprising the steps of: a) provide at least one first (TPI) and a second (TP2) piezoelectric transducer arranged in two different positions (ELV, TV) along said longitudinal direction and acoustically coupled through said mechanical part; b) carry out, at different times, a plurality of electrical measurements to determine at least one value of an electrical parameter dependent on an off-diagonal term (Zn) of an impedance matrix of an electrical quadrupole modeling the assembly formed by the first and second acoustically coupled piezoelectric transducers; and c) deduce from the results of said electrical measurements said variation in dimension of the mechanical part. Method according to claim 1 wherein each said electrical measurement of step b) comprises the substeps of: bl) applying said first piezoelectric transducer (TPI) a first electrical excitation signal to generate acoustic waves propagating in the mechanical part towards the second transducer (TP2), while keeping the second piezoelectric transducer in open circuit, and simultaneously measuring the input impedance of said first piezoelectric transducer; b2) apply to said first piezoelectric transducer (TPI) a second electrical excitation signal to generate acoustic waves propagating in the mechanical part towards the second transducer (TP2), while keeping the second piezoelectric transducer short-circuited, and simultaneously measure the input impedance of said first piezoelectric transducer; b3) calculate the value of said electrical parameter from the input impedances thus measured; the order of substeps bl) and b2) can be reversed.

3. Method according to claim 2 wherein said electrical parameter is the phase difference of the input impedances measured during substeps bl) and b2).

4. A method according to any one of claims 2 and 3 wherein the second piezoelectric transducer (TP2) comprises two electrical terminals connected together by a pair of diodes (D1, D2) connected back-to-back in parallel, the first excitation signal being sufficiently weak so that the generated acoustic waves induce across the terminals of said second piezoelectric transducer a voltage lower than a threshold of said diodes, which can then be considered as an open circuit, and the second excitation signal being sufficiently strong so that the generated acoustic waves induce across the terminals of said second piezoelectric transducer a voltage greater than a threshold of said diodes, which can then be considered as a short circuit.

5. A method according to any one of claims 1 to 4 wherein step b) comprises determining the value of said parameter as a function of frequency.

6. A method according to claim 5 wherein step c) comprises identifying peaks of the value of said electrical parameter as a function of frequency, the variation in dimension of the mechanical part being deduced from a variation in position of said peaks.

7. A method according to any one of the preceding claims wherein the first (TPI) and second (TP2) piezoelectric transducer are arranged at two opposite ends (ELV, TV), along said longitudinal direction, of the mechanical part.

8. Use of a method according to one of the preceding claims for measuring the tightening of a screw.

9. A system for measuring a variation in dimension (L) of a mechanical part (V) along a longitudinal direction (x), comprising: - a first (TPI) and a second (TP2) piezoelectric transducer, adapted to be fixed at two different positions (ELV, TV) along said longitudinal direction and acoustically coupled via said mechanical part; - an electronic system (AE1, AE2, P) configured to determine at least one value of an electrical parameter dependent on an off-diagonal term (Zn) of an impedance matrix of a two-port network electrical modeling the assembly formed by the first and second acoustically coupled piezoelectric transducers; and to deduce from a variation of said at least one value of said parameter said variation of dimension of the mechanical part.

10. A measuring system according to claim 9, wherein said electronic system comprises: - a first electronic device (AE1) configured to apply electrical excitation signals to said first piezoelectric transducer and simultaneously measure its input impedance; - a second electronic device (AE2) configured to maintain said second piezoelectric transducer successively in open circuit and short circuit; and - a processor (P) configured to control at least the first electronic device in such a way as to: - apply a first electrical excitation signal to said first piezoelectric transducer (TPI) to generate acoustic waves propagating in the mechanical part towards the second transducer, while keeping the second piezoelectric transducer (TP2) in an open circuit, and simultaneously measure the input impedance of said first piezoelectric transducer; - apply a second electrical excitation signal to said first piezoelectric transducer (TPI) to generate acoustic waves propagating in the mechanical part towards the second transducer, while keeping the second piezoelectric transducer (TP2) in a short circuit, and simultaneously measure the input impedance of said first piezoelectric transducer; - calculate the value of said electrical parameter from the input impedances thus measured.

11. A measuring system according to any one of claims 9 and 10 in which the electronic device is integrated into a screw clamping system (OS1, OS2), the first and second piezoelectric transducers being adapted to be fixed to said screw.

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