RU2159427C2 - Sensitive element for ultrasonic piezoelectric receiving converter - Google Patents

Abstract

FIELD: nondestructive inspection of industrial objects, inspection of extended objects and objects with high attenuation of sound. SUBSTANCE: expansion of bandwidth and reduced irregularity of amplitude-frequency characteristic are achieved thanks to insertion of cylindrical piezoelement carrying frequency- lowering cylinder into sensitive element for ultrasonic piezoelectric receiving converter. Their dimensions and resonance frequencies are chosen from conditions: D^pe> H^pe, f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{R}}$ = K₁f₂, f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{p}}$ = K₂f₂, f₁< f $\genfrac{}{}{0ex}{}{\text{cyl}}{\text{p1}}$ < f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{R}}$ , D^cyl< H^cyl, where f₁ is lower boundary of bandwidth; f₂ is upper boundary of bandwidth; D^pe is diameter of piezoelement; H^pe is height of piezoelement; f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{R}}$ is own frequency of radial vibrations of piezoelement; 0.70,7 ≤ K₁< 1 is first empirical coefficient; f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{p}}$ is own frequency of longitudinal vibrations of piezoelement; 1.51,5 ≤ K₂≤ 2,5 is second empirical coefficient; f $\genfrac{}{}{0ex}{}{\text{cyl}}{\text{p1}}$ is first own frequency of longitudinal vibrations of frequency-lowering cylinder; D^cyl is diameter of frequency- lowering cylinder; H^cyl is height of frequency-lowering cylinder. Second own frequency f $\genfrac{}{}{0ex}{}{\text{cyl}}{\text{p2}}$ of longitudinal vibrations of frequency-lowering cylinder is chosen from condition f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{R}}$ < f $\genfrac{}{}{0ex}{}{\text{cyl}}{\text{p2}}$ < f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{p}}$ . Own frequency f $\genfrac{}{}{0ex}{}{\text{cyl}}{\text{R}}$ of radial vibrations of frequency-lowering cylinder is selected from condition f $\genfrac{}{}{0ex}{}{\text{cyl}}{\text{R}}$ = (0,9-1,1)f $\genfrac{}{}{0ex}{}{\text{pe}}{\text{R}}$ . EFFECT: expanded bandwidth and reduced irregularity of amplitude-frequency characteristic. 4 cl, 2 dwg

Description

 The invention relates to non-destructive testing of industrial facilities, based on the registration of acoustic waves using contact receiving transducers, and in particular to sensitive elements for ultrasonic piezoelectric receiving transducers, and can be used, in particular, for monitoring extended objects and objects with high sound attenuation, during which acoustic waves are recorded in the frequency range from 20 to 200 kHz.

Sensitive elements of any primary converters are subject to very high requirements for technical characteristics that determine the resolution (electro-acoustic conversion coefficient, width of the working frequency range, frequency response unevenness, etc.). Ensuring high sensitivity and an operating frequency range from 20 to 200 kHz requires the use of sensitive elements operating in a resonant mode, the length of which is comparable with the wavelength in a piezoceramic material. However, the design of such sensitive elements is associated with a number of features:
1) the size of the sensitive element in the longitudinal direction (when using the longitudinal vibration mode) can exceed 100 mm (the use of radial vibrations of the sensitive elements in the form of piezoceramic disks with a diameter of up to 100 mm is impractical due to the deterioration of the acoustic contact of the transducer with the curved surface of the controlled object);
2) when monitoring long objects (for example, oil and gas pipelines), long cable lines (meters - tens of meters) are used. To ensure the required signal level at the input of the amplification-conversion equipment, it is necessary that the intrinsic electrical capacitance of the sensing element is as large as possible than the load capacitance of the connecting cables or, at least, be commensurate with it;
3) piezoelectric elements of a simple structural form (in the form of a disk or cylinder) have a rugged amplitude-frequency characteristic (AFC), the unevenness (indentation) of which in the region of radial resonance, depending on the material, can reach 10-25 dB.

 The solution of the tasks is complicated by the technological problems of polarization of piezoelectric elements tens of mm long. To polarize, for example, elongated piezoceramic cylinders, a very high polarizing voltage is required (tens of kilovolts - based on a calculation of 2 - 2.5 kV / mm). The polarization technology of elongated piezoelectric elements at voltages above 20 kV is very complex, which leads to a rise in the cost of piezoelectric elements and, accordingly, transducers.

 Known ultrasonic transducer / 1 / containing the housing and located in it axially polarized disk piezoelectric plate and protector. The choice of the relationship between the sizes of the piezoelectric plate and the tread within certain limits provides an increase in the sensitivity and accuracy of measurements. However, the use of this converter is limited due to the very narrow bandwidth. Given the ratios of the thickness of the piezoelectric plate to its diameter, a relatively close arrangement of the two main resonances of the oscillations of the piezoelectric element (the resonance of radial vibrations and the resonance of vibrations through the thickness) is realized, in which the areas of dynamic rise in the amplitude-frequency characteristic almost completely overlap and merge into one resonance in the form narrow band bells. In addition, the implementation of the required frequency range requires the use of piezoelectric elements in the form of a cylinder with a height of over 20 mm, which leads to a complication of manufacturing technology.

 Also known is a wideband piezoelectric receiver for studying acoustic emission signals / 2 / containing a piezoelectric plate glued between the tread and the rod delay line, which is actually a frequency-lowering element. However, such a converter is used to study high-frequency acoustic signals, the duration of which is less than the double run time of a longitudinal wave along the delay rod line. At low frequencies, he has resonance, narrowing the passband and worsening the frequency response unevenness.

 The problem solved by the invention is aimed at creating a sensitive element for ultrasonic piezoelectric receiving transducers (hereinafter referred to as a sensitive element), designed to control extended objects and objects with high sound attenuation.

 The technical result of the present invention is to expand the bandwidth and reduce the unevenness of the amplitude-frequency characteristics.

The technical result is achieved by the fact that in the known sensitive element for an ultrasonic piezoelectric receiving transducer containing a cylindrical piezoelectric element and a frequency-decreasing cylinder mounted on it, it is new that the dimensions and resonant frequencies of the piezoelectric element and the frequency-decreasing cylinder are selected from the conditions:
D ^pe > H ^pe
f _R ^pe = K ₁ • f ₂ ,
f _P ^pe = K ₂ • f ₂ ,
f ₁ <f _P1 ^c <f _R ^pe ,
D ⁱ <H ^q,
where f ₁ is the lower limit of the passband;
f ₂ - the upper limit of the passband;
D ^pe - the diameter of the piezoelectric element;
H ^pe - the height of the piezoelectric element;
f _R ^pe - the natural frequency of the radial oscillations of the piezoelectric element;
0.7 ≤ K ₁ <1 - the first empirical coefficient;
f _P ^pe - natural frequency of the longitudinal oscillations of the piezoelectric element;
1,5 ≤ K ₂ ≤ 2,5 - the second empirical coefficient;
f _P1 ^c - the first natural frequency of longitudinal vibrations of the frequency-lowering cylinder;
D ^c - the diameter of the frequency-lowering cylinder;
H ^c - the height of the frequency-lowering cylinder.

In order to reduce the frequency response unevenness, the second natural frequency of longitudinal vibrations of the frequency-lowering cylinder f _P2 ^c is selected from the condition:
f _R ^pe <f _P2 ^c <f _P ^pe .

In order to reduce the frequency response unevenness, the natural frequency of radial vibrations of the frequency-lowering cylinder f _R ^c is selected from the condition:
f _R ^c = (0.9-1.1) • f _R ^pe .

 In order to increase the coefficient of electroacoustic conversion, the mechanical quality factor of the material of the frequency-lowering cylinder is selected above the mechanical quality factor of the material of the piezoelectric element.

 In order to reduce the frequency response unevenness in the body of the frequency-lowering cylinder, a recess or a flat cut, not parallel to the base, are made that do not intersect the base.

 The broadening of the passband and reducing the unevenness of the amplitude-frequency characteristic are achieved by choosing the ratio of the sizes of the piezoelectric element and the frequency-decreasing cylinder, as well as by choosing the ratios of their resonant frequencies and the boundaries of the passband, which determines the shape and properties of the amplitude-frequency characteristic (electro-acoustic conversion coefficient, unevenness or irregularity Frequency response, slope of the frequency response near the borders of the passband, etc.). The amplitude-frequency characteristic is synthesized from partially overlapping vibration modes in the longitudinal and radial directions. The regions of dynamic rise of adjacent resonances partially overlap each other and form an AFC that is similar in shape to a trapezoid with a wide passband.

The condition D ^pe > H ^pe determines the strip properties of the piezoelectric element. With this ratio of the sizes of the piezoelectric element, the natural frequency of radial vibrations will be lower than the natural frequency of longitudinal vibrations. Under this condition, in most practical cases, the inequality (1.5-2.4) holds: • f _R ^pe <f _P ^pe (the factor in front of f _R ^pe depends on the ratio of sound velocities in the longitudinal and transverse directions, as well as on the ratio of geometric dimensions piezoelectric element). The oscillation modes of the piezoelectric element in the longitudinal and radial directions partially intersect and are synthesized in the frequency response, in shape close to the trapezoid.

The conditions f _R ^pe = K ₁ • f ₂ and f _P ^pe = K ₂ • f ₂ determine the dimensions of the piezoelectric element and set the boundaries of the passband of the piezoelectric element. In this case, the passband of the piezoelectric element is realized slightly higher than required (≈ from 0.7 • f ₂ to 2.5 • f ₂ ). After installing the frequency-lowering cylinder on the piezoelectric element, the bandwidth is shifted to the desired region of low frequencies (f ₁ - f ₂ ). This connection should provide acoustic contact between the piezoelectric element and the frequency-lowering cylinder and can be carried out by gluing, soldering, welding, etc.

The limits of the empirical coefficient K _{1 are} determined by the ratio of the width and shape of the spectra of natural vibrations of the sensitive element in the longitudinal (F _P ) and radial direction (F _R ), as well as the feasibility of reducing the diameter of the piezoelectric element D ^pe and, accordingly, the area of the flat acoustic contact of the receiving transducer with a curved surface controlled object. These oscillation modes should be within the passband (f ₁ - f ₂ ), partially intersect and synthesized into a band-frequency response. In the practical majority of cases, the longitudinal vibrational mode of sensitive elements based on piezoelectric elements in the form of a disk or cylinder is characterized by a wider spectrum compared to the radial mode limited by a more pronounced resonance curve. This ratio of the width and shape of the spectra of the natural vibrations of the sensing element in the longitudinal and radial direction determines the position of the frequency F _R in the area of sharp decline of the resonance curve F _P. The limitation of the area of the acoustic contact determines the location of the frequency F _R near the upper boundary of the passband f ₂ . Thus, the lower limit of the empirical coefficient (K ₁ = 0.7) shows the permissible deviation of the frequency F _R from f ₂ at which the synthesis of a band-frequency response with acceptable unevenness (indentation) in the region of intersection of the spectra of natural vibrations of the sensitive element, as well as the permissible diameter a piezoelectric element providing reliable acoustic contact of the transducer with the controlled object. The upper limit of the empirical coefficient (K ₁ <1) determines the position of the frequency f _R ^pe and, accordingly, F _R (the radial frequency of the sensitive element F _R remains equal to the natural frequency of the radial oscillations of the piezoelectric element f _R ^pe ) necessary for the synthesis of the strip frequency response, within the band transmission (f ₁ - f ₂ ).

The limits of the empirical coefficient K _{2 are} determined by the optimal ratios of the coefficient of electroacoustic conversion and electric capacitance, as well as technological considerations of the permissible polarization voltage of the piezoelectric element and, accordingly, its height. On the one hand, elongated piezoelectric elements in the form of cylinders, ceteris paribus, are characterized by higher sensitivity compared to piezoelectric elements in the form of thin disks, since the electroacoustic conversion coefficient is generally proportional to the volume of the piezoelectric element, and on the other hand, with an increase in the height of the piezoelectric element, the sensitivity of the receiving converter loaded on a long cable line. Thus, the lower limit of the empirical coefficient (K ₂ = 1.5) shows the maximum height of the piezoelectric element, providing an acceptable decrease in the amplitude of the received signal at the input of the amplification-conversion equipment with a load of a long cable line when monitoring extended objects, as well as the manufacturability of the structure of the piezoelectric element. The upper limit (K ₂ = 2.5) determines the minimum allowable coefficient of electro-acoustic transformation. In addition, the condition f _P ^pe = K ₂ • f ₂ helps to achieve a uniform frequency response due to a significant shift of this eigenfrequency beyond the bandwidth.

Соотношение размеров частотно-понижающего цилиндра D^ц < H^ц предопределяет, что основной низкочастотной модой колебаний чувствительного элемента будет продольная мода. При этом радиальная мода колебаний частотно-понижающего цилиндра будет смещена к верхней границе полосы пропускания либо за ее пределы, что позволяет достичь требуемой равномерности АЧХ.The condition f ₁ <f _P1 ^c <f _R ^pe provides the maximum coefficient of electro-acoustic conversion and minimal non-uniformity of frequency response. This condition determines the position of the natural frequencies of the vibrations of the sensing element in the longitudinal F _P and radial directions F _R in the following order: f ₁ <F _P <F _R <f ₂ (the frequency F _P , due to the size ratios of the piezoelectric element and the frequency-lowering cylinder, is somewhat shifted to lower frequencies compared with the frequency f _P1 ^c , and the frequency F _R remains equal to f _R ^pe ). These oscillation modes partially intersect with each other and are synthesized into a band-frequency response. When the resonance f _P1 ^c coincides with the resonance f _R ^pe there is a decrease in the electroacoustic conversion coefficient and an increase in the frequency response indentation near the upper boundary of the frequency range f ₂ as a result of substantial suppression of the radial mode of the piezoelectric vibrations. Under the condition f _P1 ^q <f _{1, the} natural frequency of the sensitive element is shifted beyond the boundaries of the operating range (f ₁ ), which, of course, violates the necessary conditions for the synthesis of a band-frequency response (frequency F _P within the passband from f ₁ to f ₂ ) . For f _P1 ^c > f _R ^{pe, the} frequency-lowering cylinder is inefficient and the amplitude-frequency characteristic of the sensitive element approaches the spectrum of the piezoelectric element. Moreover, at f _P1 ^c ≈ (0.8 - 1.2) • f _P ^pe there is a significant suppression of the longitudinal mode of oscillations of the piezoelectric element, a decrease in the coefficient of electroacoustic conversion, and an increase in the frequency response unevenness (roughness) in the entire operating frequency range. The preferred option is the equidistant position of the natural frequency of oscillation of the frequency-lowering cylinder f _P1 ^c between the lower boundary of the passband and the natural frequency of the radial oscillations of the piezoelectric element

The ratio of the dimensions of the frequency-lowering cylinder D ^c <H ^c determines that the main low-frequency mode of oscillations of the sensitive element will be the longitudinal mode. In this case, the radial oscillation mode of the frequency-lowering cylinder will be shifted to the upper boundary of the passband or beyond, which allows you to achieve the required uniformity of frequency response.

The combination of distinctive features allows you to implement the required spectrum of the sensing element in the frequency domain (f ₁ - f ₂ ), similar in shape to a trapezoid, with a high coefficient of electro-acoustic conversion and acceptable frequency response unevenness. Its average frequency (natural frequency) is determined by the travel time of the longitudinal acoustic wave along the sensitive element. At higher frequencies, harmonics (eigenfrequencies of higher order vibrations) are observed. Due to the narrow bandwidths and significantly lower sensitivity, harmonics are not used for registration and analysis of acoustic signals propagating in a controlled object.

При задании собственной частоты радиальных колебаний частотно-понижающего цилиндра f_R ^ц в окрестности собственной частоты радиальных колебаний пьезоэлемента (0,9-1,1)•f_R ^пэ частично подавляется радиальная мода пьезоэлемента, в результате чего возможно выравнивание амплитудно-частотной характеристики вблизи верхней границы полосы пропускания, что является важным при использовании пьезокерамического материала с высокой механической добротностью.The choice of the second eigenfrequency of the longitudinal oscillations of the frequency-lowering cylinder from the condition f _R ^pe <f _P2 ^c <f _P ^pe allows to reduce the frequency response unevenness. If this condition is not met, it is possible to partially suppress a particular mode of oscillations of the piezoelectric element and, accordingly, worsen the coefficient of electroacoustic conversion and uniformity of frequency response. The preferred option is the equidistant position of the second natural frequency of the longitudinal vibrations of the frequency-lowering cylinder f _P2 ^c between the natural frequencies of the radial and longitudinal vibrations of the piezoelectric element:

When setting the natural frequency of the radial vibrations of the frequency-lowering cylinder f _R ^c in the vicinity of the natural frequency of the radial vibrations of the piezoelectric element (0.9-1.1) • f _R ^{pe the} radial mode of the piezoelectric element is partially suppressed, as a result of which the amplitude-frequency characteristic can be aligned near the upper border bandwidth, which is important when using a piezoceramic material with high mechanical quality factor.

 The choice of the material of the frequency-lowering cylinder with a mechanical quality factor higher than the quality factor of the piezoceramic material allows one to realize more pronounced resonances of the oscillations of the frequency-lowering cylinder and, accordingly, of the sensitive element and, thereby, increase the coefficient of electroacoustic conversion of the sensitive element.

 The completion in the body of a frequency-lowering cylinder of a recess or a flat oblique cut that does not intersect the base contributes to a decrease in the dynamic rise of the frequency response at the corresponding resonant frequency and to an increase in the passband due to the different dimension (different height) of the sensing element. The recess can be formed by the cross section of the body of the frequency-lowering cylinder by any curved surface that provides a given correction of the frequency response, for example, in the form of a cylindrical groove intersecting the generatrix and the upper surface of the cylinder.

 In FIG. 1 shows an embodiment of a sensing element for ultrasonic piezoelectric receiving transducers. In FIG. Figure 2 shows typical frequency response of a sensitive element and a piezoelectric element when receiving longitudinal waves normally incident on the base.

 The sensitive element consists of a cylindrical piezoelectric element 1 and a frequency-lowering cylinder 2 mounted on it with a curved recess that does not cross the base.

 In FIG. 2 are shown: 1 - amplitude-frequency characteristic of a sensitive element consisting of a piezoelectric element in the form of a disk ⌀ 12.5 × 5 mm made of piezoceramic material TsTS-19 and a frequency-lowering cylinder ⌀ 12.5 × 15 mm made of 30KhGSA steel; 2 - amplitude-frequency characteristic of a piezoelectric element.

где n = 1 при расчете первой собственной частоты частотно-понижающего цилиндра f_P1 ^ц; n = 2 при расчете второй собственной частоты частотно-понижающего цилиндра f_P2 ^ц; E^ц - модуль упругости материала частотно-понижающего цилиндра; ρ^ц- плотность материала частотно-понижающего цилиндра.In the above example, the bandwidth of the sensing element is 150 kHz (f ₁ = 30 kHz, f ₂ = 180 kHz), the electro-acoustic conversion coefficient at a frequency of 100 kHz is ≈60 dB rel. 1 V / m / s, and the unevenness of the amplitude-frequency characteristic does not exceed ± 6 dB relative to the value of the conversion coefficient at a frequency of 100 kHz. The natural frequency of the radial vibrations of the piezoelectric element is f _R ^pe ≈185 kHz, and the natural frequency of its longitudinal vibrations is f _P ^pe ≈ 450 kHz. The conversion coefficient of the piezoelectric element at a frequency of 100 kHz is ≈53 dB rel. 1 V / m / s, and the frequency response uneven exceeds ± 10 dB. The electric capacitance of the piezoelectric element is ≈400 pF and allows the use of a cable line several meters long without significant loss of resolution. The first natural frequency of the longitudinal oscillations of the frequency-lowering cylinder is f _P1 ^c ≈80 kHz, and the second frequency is f _P2 ^c ≈240 kHz. The amplitude-frequency characteristics of the sensitive element and the piezoelectric element were determined experimentally on metrological equipment for calibrating ultrasonic receiving transducers under the influence of normally incident longitudinal waves, the frequencies f _P1 ^c and f _P2 ^{c were} determined theoretically by the well-known formula for a rod fixed at one end:

where n = 1 when calculating the first natural frequency of the frequency-lowering cylinder f _P1 ^c ; n = 2 when calculating the second natural frequency of the frequency-lowering cylinder f _P2 ^c ; E ^c - the modulus of elasticity of the material of the frequency-lowering cylinder; ρ ^c - the density of the material of the frequency-lowering cylinder.

 The choice of the material of the frequency-lowering cylinder — steel 30KhGSA with a mechanical Q factor (≈4500) higher than the Q factor of the PZT-19 piezoceramic material (≈50 - 85) allows to increase the electro-acoustic conversion coefficient by 6-10 dB.

 The sensitive element operates as follows.

When receiving an acoustic wave, the piezoelectric element is in a volumetric stress-strain state and experiences deformations in the circumferential, radial and axial directions, leading to the appearance of an electric charge on the surfaces of the piezoelectric element. An electric charge proportional to the deformations of the piezoelectric element is removed from the electrodes. The frequency-lowering cylinder allows you to shift the passband to the low frequency region, which allows you to control extended objects and objects with high sound attenuation. Adjacent resonances of oscillations of the sensing element in the longitudinal and radial directions partially overlap and are synthesized into an amplitude-frequency characteristic with a given passband (f ₁ - f ₂ ). The specified ratios of the sizes and frequencies of the piezoelectric element and the frequency-lowering cylinder determine the relative position of the natural frequencies (vibrational resonances in the longitudinal and radial directions) and provide a high coefficient of electro-acoustic conversion and minimal frequency response unevenness. The choice of the material of the frequency-lowering cylinder with a mechanical quality factor higher than the quality factor of piezoceramics makes it possible to increase the coefficient of electroacoustic conversion. The choice of the natural frequency of the radial oscillations of the frequency-lowering cylinder from the condition f _R ^c = (0.9 -1.1) • f _R ^pe , as well as making a notch or a flat oblique cut, can reduce the frequency response unevenness.

 The design and manufacturing technology of such a sensitive element is simple and does not require specialized equipment. To polarize a piezoelectric element, a polarizing voltage of 10-12 kV is required, which is allowed by traditional technological equipment. The electric capacitance of piezoelectric elements that satisfy the given ratios is hundreds to thousands of pF and allows the use of long cable lines without significant deterioration in resolution.

Sources of information
1. Copyright certificate of the USSR N 1128159, M.cl. G 01 N 29/04, publ. in BI N45, 1984

 2. E.V. Nesmashny, B.V. Skiba, V.N. Neighbors. Broadband piezoelectric receiver for studying acoustic emission signals // Defectoscopy, N 5, 1975, pp. 111-112.

Claims (5)

1. A sensitive element for an ultrasonic piezoelectric receiving transducer containing a cylindrical piezoelectric element and a frequency-lowering cylinder mounted on it, characterized in that their sizes and resonant frequencies are selected from the conditions:
D ^pe > H ^pe
f _R ^pe = K ₁ f ₂ ,
f _p ^pe = K ₂ f ₂ ,
f ₁ <f _p1 ^q <f _R ^pe
D ⁱ <H ^q,
where f ₁ is the lower limit of the passband;
f ₂ - the upper limit of the passband;
D ^pe - the diameter of the piezoelectric element;
H ^pe - the height of the piezoelectric element;
f _R ^pe - the natural frequency of the radial oscillations of the piezoelectric element;
0.7 ≤ K ₁ <1 - the first empirical coefficient;
f _p ^pe - natural frequency of the longitudinal oscillations of the piezoelectric element;
1,5 ≤ K ₂ ≤ 2,5 - the second empirical coefficient;
f _p1 ^c - the first natural frequency of longitudinal vibrations of the frequency-lowering cylinder;
D ^c - the diameter of the frequency-lowering cylinder;
H ^c - the height of the frequency-lowering cylinder. 2. The sensitive element according to claim 1, characterized in that the second natural frequency of longitudinal vibrations of the frequency-lowering cylinder f _p2 ^c selected from the condition
f _R ^pe <f _p2 ^c <f _p ^pe . 3. The sensitive element according to claim 1 or 2, characterized in that the natural frequency of radial oscillations of the frequency-lowering cylinder f _R ^C selected from the conditions:
f _R ^c = (0.9 - 1.1) f _R ^pe  4. The sensitive element according to any one of claims 1 to 3, characterized in that the mechanical quality factor of the material of the frequency-lowering cylinder is higher than the mechanical quality factor of the material of the piezoelectric element.  5. A sensitive element according to any one of claims 1 to 4, characterized in that in the body of the frequency-lowering cylinder there is a recess or a flat cut not crossing the base that is not parallel to the base.

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