RU2584719C1 - Digital method of measuring parameters of piezoelectric elements - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measurement equipment. Peculiarity of claimed digital method of measuring parameters of piezoelectric elements is that drive signal has a pulse duration T₁ = T₀-τ, where τ is duration of pause between end of signal with linear frequency modulation and end of detection of digital signals, while reception of digital signals is T₀, determining resonance frequency ƒ_r, antiresonance frequency ƒ_a and Q of piezoelectric element, and value of parallel capacitance C₀ from received plurality of complex conductivity values by its fractional rational approximation frequency dependence of complex conductivity canonical equivalent circuit in resonant frequency interval.

EFFECT: high accuracy of measuring complex conductivity piezoelectric element.

2 cl, 10 dwg

Description

Technical field

The invention relates to measuring equipment and is intended to measure the frequency response of complex conductivity, resonance and antiresonance frequencies, quality factor, as well as parallel capacitance in the resonance frequency range and at a frequency much lower than the fundamental resonance frequency. The invention can be used in testing and control of piezoelectric elements (PE), as well as for determining the electrophysical parameters of piezoelectric materials.

State of the art

The task of operational measurement of the characteristics of piezoelectric elements and piezoelectric transducers and control of their parameters in a dynamic mode is relevant both at the stages of development and production, and during operation. The systems used for these purposes, based on standard measuring instruments, have low productivity. In addition, due to their weight and size characteristics, they are unsuitable for monitoring the characteristics of converters on mobile carriers during their testing and during routine maintenance.

There is a method of determining the electrophysical parameters of a piezoelectric material (Industry standard OCT II 0444-87. Piezoceramic materials. Technical conditions. - M .: Elektrostandart. 1987. C 49) / 1 /, according to which the resonance and antiresonance frequencies of PE of a certain shape and size are determined by voltage measurements on an auxiliary load resistor connected to PE in series. The measuring circuit contains a sinusoidal signal generator, resistive divider, PE, load resistor, voltmeter.

By smoothly changing the frequency of the generator, the resonance and antiresonance frequencies are determined respectively by the maximum and minimum voltmeter readings.

The disadvantage of this method is the low accuracy, high complexity and duration of measurements.

Means for monitoring the parameters of piezoelectric transducers are also known from the prior art.

A device for measuring the impedance of a multilayer piezoelectric actuator located in a mechanical system (WO 2012149649 (A1), IPC F02M 51/00; G01R 27/02; G01R 31/00, 2012-11-08) / 2 /, contains a signal generator that generates a voltage signal with a frequency greater than the resonant frequency of the piezoelectric drive, a voltage sensor, a current sensor and a computer. The piezoelectric actuator mechanically responds to current and voltage signals. The computer is connected to a voltage sensor and a current sensor and is programmed to calculate the impedance value from the measured voltage and current values.

Known automatic measuring system for monitoring piezoelectric materials (TW 200933163 (A), IPC G01R 27/02, G01R 27/28, 2009-08-01) / 3 /, based on the amplitude-phase method of measuring the parameters of the resonant frequency, antiresonance frequency, electromechanical characteristics. The measuring system comprises a control computer, a functional generator, a piezoelectric element, a data acquisition board, and a display.

System for monitoring the structural integrity of objects (Structural integrity monitoring system including wireless electromechanical impedance measurement US 6768312 6 IPC G01N 29/09; G01N 29/12; CL US 324/525; 324/509, 2004-07-27) / 4 / contains a piezoelectric sensor to which a resistor is connected in series. A system for determining the structural state of an object includes: a piezoelectric sensor, which is configured to be mounted on a test object; a resistive element connected in series with the piezoelectric sensor; signal shaper, voltage drop meter at the sensor; a transmitter that transmits the processed signal; and a remotely located interface that receives the transmitted signal and provides an output of the sensor resistance based on the processed signal and a conclusion about the structural state of the monitored object. The main disadvantage of this method is the physical and mathematical incorrectness of the method of determining the impedance.

There is a method of determining the quality factor of a piezoelectric element (RU 2499234, 6 IPC G01H 13/00, G01H 1/06) / 5 /, according to which oscillations of the piezoelectric element in the resonance region are excited by exposing it to an electric sinusoidal voltage with a variable frequency, at the same time, the active component of conductivity and perform its differentiation. On the frequency response of the derivative of the active component of the conductivity, measure the frequency corresponding to the maximum value of the derivative, and measure the value of the derivative at the maximum frequency. On the frequency response of the active component of conductivity, the value of the active component of conductivity is measured at the frequency of the maximum derivative and the quality factor is calculated by the formula.

However, the differentiation of the active component of the conductivity in the presence of noise and interference leads to an increase in measurement error, since any interference is differentiated with the signal. In addition, the use of information on the active component of conductivity at a single frequency reduces the repeatability of the results.

. Частотная зависимость полной (комплексной) проводимости пьезоэлемента $$\dot{Y}(ƒ)$$

, измеренная в достаточно широкой области частот, охватывающей резонансный промежуток, содержит полную информацию о механической колебательной системе ПЭ и его электрических свойствах на данной моде колебаний. Она используется для определения основных параметров ПЭ, таких, как резонансная ƒ_r и антирезонансная ƒ_а частоты, механическая добротность Q, эффективный коэффициент электромеханической связи (/1/, стр. 74-75).The most informative is the amplitude-phase method of measuring the frequency response of complex conductivity $$\dot{Y}(ƒ)$$

. Frequency dependence of the total (complex) conductivity of a piezoelectric element $$\dot{Y}(ƒ)$$

, measured in a fairly wide frequency range, covering the resonance gap, contains complete information about the mechanical vibrational system of PE and its electrical properties in this mode of vibration. It is used to determine the main parameters of PE, such as resonant ƒ _r and antiresonance ƒ _a frequencies, mechanical Q factor, effective coefficient of electromechanical coupling (/ 1 /, pp. 74-75).

на заданной частоте ƒ определяют по формуле:In the amplitude-phase method, a circuit containing a sinusoidal signal generator, a frequency meter, a phase meter and a voltmeter is used. Harmonic signal u ₀ (t) = A ₀ cos (2πƒt + φ ₀₎ with a frequency of ƒ and known amplitude A ₀ from the oscillator output is fed to the series connected resistor with a known resistance value r ₀ and the pattern PE, exciting thereby forced mechanical PE fluctuations at the frequency of the applied voltage. The measuring signal u (t) = A ₁ cos (2πƒ + φ ₁ ) is recorded at the junction of the sample with the resistor and the phase difference φ = φ ₀ -φ _{1 is} measured with a phase meter and the signal amplitude A _{1 with a} voltmeter. The frequency response of the complex conductivity of the PE is measured at each individually set frequency of the sinusoidal signal, which is controlled by a frequency meter. The value of complex conductivity $$\dot{Y}(ƒ)$$

at a given frequency ƒ is determined by the formula:

. Однако это условие невыполнимо в широком диапазоне частот, полностью включающем резонансный промежуток ПЭ.where i ² = -1 is the imaginary unit. The nominal load resistance r _{0 is} selected from the condition of the approximate equality of the amplitudes of the voltages across the resistor and PE, i.e. $$r_{}$$$${}_0\approx |\dot{Y}(ƒ){|}^{-\mathrm{one}}$$

. However, this condition is not feasible in a wide frequency range that completely includes the resonance gap of PE.

The disadvantages of the amplitude-phase method are as follows:

- the error in setting the frequency, as well as measuring the amplitudes and phase difference, is determined by the time of excitation of the PE, and to reduce it, it is necessary to increase the measurement time at each frequency, and with it

the measurement time as a whole, which may be unacceptable in the conditions of output or input control of PE;

- PE conduction module in the resonance interval varies within a wide range (up to 2-3 orders of magnitude), which requires an individual selection of the resistance r ₀ on different frequencies and use a resistor with a fixed nominal value reduces the accuracy of measurements.

The closest in technical essence to the claimed invention is a digital method for measuring the parameters of piezoceramic elements and piezoelectric materials (N.M. Ivanov, V.L. Zemlyakov, Yu.K. Miloslavsky. New means of measuring the parameters of piezoceramic elements and piezoelectric materials. Engineering Journal of the Don. No. 3. 2013) / 7 /, taken as a prototype of the present invention. The functional diagram of the equipment for implementing the prototype method (Fig. 1) contains a computer and RAM 1 connected to it, a digital-to-analog converter, a digital-to-analog converter, a low-pass filter, a low-pass filter, a four-terminal measuring device containing a resistor and a PE connected in series, and a two-channel analog-to-digital converter ADC1 and ADC2, made according to the scheme with a common master oscillator, and a buffer RAM memory RAM2 connected to a computer. Analog signal processing is reduced to analog filtering and signal amplification operations. The operations of the prototype method are as follows:

- form in the computer a sample of the values of the digital pulse excitation signal s _{n of} volume N, n∈ [0, N-1], according to the formula

where A is the amplitude of the digital signal, F _d is the sampling frequency, ƒ ₀ and ƒ ₁ are the specified minimum and maximum boundaries of the frequency range in which measurements are performed; convert the values of the digital pulse excitation signal s _n into an analog pulse excitation signal with voltage u ₀ (t), the instantaneous frequency of which increases linearly from ƒ ₀ to ƒ ₁ during the pulse duration. The voltage u ₀ (t) is supplied to the measuring four-terminal network containing a resistor and PE connected in series;

и $$\dot{U}(ƒ)$$

на частотах ƒ_k=kF_d/N, k∈[0, N/2];- supply voltage u ₀ (t) together with the measuring voltage u ₁ (t), taken at the point of connection of the resistor and PE, to the input of a two-channel analog-to-digital converter (ADC), and then through a buffer storage device to the host computer, where they undergo a discrete Fourier transform, resulting in two complex arrays of length 1 + N / 2 each, corresponding to the values $${\dot{U}}_0(ƒ)$$

and $$\dot{U}(ƒ)$$

at frequencies ƒ _k = kF _d / N, k∈ [0, N / 2];

- calculate the values of the complex conductivity of PE by the formula:

- determine from the measurement results the capacitance at a low frequency, the resonance frequency and antiresonance as the frequencies of the maximum and minimum of the conductivity modulus, the width of the resonance curve at half power and the quality factor of PE as the ratio of the resonance frequency to this width.

The disadvantages of the prototype method are as follows:

- the use of a single load resistor in the entire resonance gap, due to the pulsed nature of the exciting signal, and, as a result, low accuracy in determining the frequency of antiresonance and quality factor;

- the equality of the duration of registration of the measuring signal and the pulse duration of the exciting signal, which does not allow to record the response of PE after the completion of the exciting signal.

Disclosure of invention

, которая использует всю совокупность измеренных значений комплексной проводимости ПЭ.The technical result of the present invention is to increase the accuracy of measuring the complex conductivity of PE by introducing a pause between the moment of completion of the exciting pulse signal and the moment of completion of registration of the measuring signal, as well as improving the accuracy of determining the resonance frequencies, antiresonance and quality factor of the piezoelectric element by fractional rational approximation of the dependence

, which uses the entire set of measured values of the complex conductivity of PE.

и

обоих сигналов, вычисляют и запоминают множество значений комплексной проводимости

пьезоэлемента на каждой дискретной частоте ƒ в пределах изменения частоты возбуждающего сигнала.The technical result is achieved by the fact that the digital method of measuring the parameters of the piezoelectric elements includes the action of the excitation signal u ₀ (t) on the piezoelectric element connected in series with a resistor having a given resistance r ₀ , registration of the measuring signal u (t) at the junction of the piezoelectric element with the resistor, formation a computer a predetermined number N of digital values pulsed excitation signal with linear frequency modulation, the instantaneous frequency of which varies from ₀ to ƒ ƒ _1, wherein ƒ ƒ ₀ and ₁ - the minimum and m ksimalnaya frequency range in which the measurements are performed covering a resonance interval for a predetermined fashion piezoelectric element formed by a digital pulse signal of the vibration is converted into an analog pulse excitation signal u ₀ (t), synchronously convert excitation signal u ₀ (t) and the measurement signal u (t) to digital form, restore and store complex discrete spectra

and

of both signals, calculate and store many complex conductivity values

a piezoelectric element at each discrete frequency ƒ within the limits of the frequency variation of the exciting signal.

According to the invention, the pulse excitation signal has a duration of T ₁ = T ₀ -τ, where τ is the pause time between the end of the linear frequency modulated signal and the moment of registration of digital signals, the time of registration of digital signals is T ₀ , the resonance frequency ƒ _r , antiresonance frequency ƒ _a piezoelectric element, and the quality factor Q, and the value of the parallel capacitance C ₀ of the resulting set by it a rational approximation of the frequency dependence of complex conductivity values complex th canonical conduction equivalent circuit in a resonance frequency interval.

Another difference is that the pause duration for recording the complete response of the piezoelectric element to the pulsed excitation signal is chosen from the condition τ> Q _max / ƒ ₀ , where Q _max is the upper limit of the Q factor.

The introduction of a pause between the moment of completion of the exciting pulse signal and the moment of completion of the registration of the measuring signal allows the registration of free vibrations of PE, which increases the accuracy of complex conductivity measurements. Improving the accuracy of determining resonance and antiresonance frequencies, as well as the quality factor of a piezoelectric element, is achieved by using an ADC with a number of discharges of at least 14 and determining these frequencies from the parameters of the canonical equivalent PE circuit, which are found from all measured values of the complex conductivity by their fractional rational approximation, and not by the values of the module or conductivity components in separate frequency positions, as in the prototype method.

List of drawings

FIG. 1. Functional diagram of the formation and registration of the exciting u ₀ (t) and measuring u (t).

FIG. 2. The block diagram of the operations of the digital method for measuring the parameters of piezoelectric elements.

FIG. 3. The shape of the exciting pulse signal u ₀ (t) with linear frequency modulation.

FIG. 4. The waveform of the signal of the measuring voltage u (t).

FIG. 5. The amplitude discrete spectra of the signals of the exciting u ₀ (t) (1) and measuring u (t) (2) voltages.

.FIG. 6. Frequency dependence of the active component of the measured complex conductivity $$\dot{Y}(ƒ)$$

.

.FIG. 7. The frequency dependence of the reactive component of the measured complex conductivity $$\dot{Y}(ƒ)$$

.

.FIG. 8. The frequency dependence of the measured complex conductivity module $$\dot{Y}(ƒ)$$

.

FIG. 9. The canonical equivalent piezoelectric circuit used to determine the resonance frequency, antiresonance frequency, quality factor and parallel capacitance in the resonant frequency range.

(1), активной $$\mathrm{Re}(\dot{Y}(ƒ))$$

(2) и реактивной $$\mathrm{Im}(\dot{Y}(ƒ))$$

(3) составляющих комплексной проводимости и результаты их обработки.FIG. 10. Screen form of module measurement results $$\left|\dot{Y}(ƒ)\right|$$

(1) active $$\mathrm{Re}(\dot{Y}(ƒ))$$

(2) and reactive $$\mathrm{Im}(\dot{Y}(ƒ))$$

(3) components of complex conductivity and the results of their processing.

и $$\dot{U}(ƒ)$$

обоих цифровых сигналов. В блоке 5 вычисляются значения комплексной проводимости $$\dot{Y}({ƒ}_j)$$

ПЭ на каждой дискретной частоте ƒ_j, которая попадает в полосу частот возбуждающего сигнала. Для определения параметров ПЭ в блоке 6 выполняется процедура дробно-рациональной аппроксимации множества значений комплексной проводимости $$\dot{Y}({ƒ}_j)$$

частотной зависимостью проводимости канонической эквивалентной схемы (фиг. 9), которая содержит соединенные параллельно емкость С₀ и последовательную резонансную RLC-цепочку (колебательный контур). В блоке 7 по результатам процедуры дробно-рациональной аппроксимации восстанавливаются частота резонанса ƒ_r, частота антирезонанса ƒ_a, добротность Q и параллельная емкость С₀.The operation of the method is illustrated by a flowchart (Fig. 2). The formation of the required number of N values of the digital pulse excitation signal is performed in a computer (block 1). In block 2, the digital signal is converted into an analog pulse excitation signal u ₀ (t) of duration T ₀ = NΔt, where Δt is the sampling period using a digital-to-analog converter and a low-pass filter. An analog pulse excitation signal u ₀ (t) is supplied to the measuring four-terminal network, and the measuring voltage u (t) is recorded at the connection point of the resistor and PE. In block 3, the excitation signal u ₀ (t) and the measuring signal u (t) are synchronously converted to digital signals. In block 4, digital signals undergo a discrete Fourier transform using the FFT algorithm, resulting in the restoration of complex discrete spectra $${\dot{U}}_0(ƒ)$$

and $$\dot{U}(ƒ)$$

both digital signals. In block 5, the complex conductivity values are calculated $$\dot{Y}({ƒ}_j)$$

PE at each discrete frequency ƒ _j , which falls into the frequency band of the exciting signal. To determine the parameters of PE in block 6, the procedure of fractional rational approximation of the set of values of complex conductivity $$\dot{Y}({ƒ}_j)$$

the frequency dependence of the conductivity of the canonical equivalent circuit (Fig. 9), which contains a capacitance C ₀ connected in parallel and a series resonant RLC chain (oscillatory circuit). In block 7, according to the results of the fractional rational approximation procedure, the resonance frequency ƒ _r , antiresonance frequency ƒ _a , Q factor Q, and parallel capacitance C _{0 are} restored.

The operations of the method are performed as follows.

1. Form in a computer a sample of the values of the digital pulse excitation signal s _{n of} volume N, n∈ [0, N-1], according to the formula

where A is the amplitude of the digital signal, Δt is the sampling period, ƒ ₀ and ƒ ₁ are the minimum and maximum boundaries of the frequency range in which measurements are performed, θ (t) is the Heaviside step function, equal to zero for t <0, and unity otherwise case. The pulse excitation signal has a total duration T ₀ = NΔt, which coincides with the duration of the registration of the measuring signal and the excitation signal. The duration of the excitation signal, during which the instantaneous frequency of the signal runs from ƒ ₀ to ƒ ₁ , is T ₁ = T ₀ -τ, where τ is the pause duration during which the voltage of the excitation signal is zero. A pause is entered to register the PE response signal after the supply of the exciting voltage is stopped, i.e. response of free vibrations of PE.

The pause duration is selected from the condition τ> Q _max / ƒ ₀ , where Q _max is the upper limit of the Q factor measurement, to ensure registration of the complete response of the piezoelectric element to the pulse excitation signal. In this case, the amplitude of the response signal of free vibrations of PE decreases no less than e ^π ≈ 23 times.

2. Convert the values of the digital pulse excitation signal s _n into an analog pulse excitation signal with voltage u ₀ (t), the duration of which is T ₀ , the instantaneous frequency increases linearly from ƒ ₀ to ƒ ₁ over a period of time of duration T ₁ , and within a pause the amplitude of the exciting signal is zero. Voltage u ₀ (t) is fed to the measuring quadripole, comprising serially connected resistor and PE. The shape of the exciting pulse signal u ₀ (t) with linear frequency modulation is shown in FIG. 3.

3. Convert the voltage u ₀ (t) and the measuring voltage u (t), which is recorded at the connection point of the resistor and PE, into samples of a digital pulse excitation signal U ₀ (nΔt) and samples of a digital measuring signal U (nΔt) using a two-channel ADC whose channels operate strictly synchronously from a single master oscillator. The waveform of the signal of the measuring voltage u (t) is shown in FIG. 4. The failure in FIG. 4 corresponds to the passage of the instantaneous frequency of the pulse excitation signal in the vicinity of the resonance frequency of the PE. The oscillogram also shows damped oscillations of the PE after the termination of the excitation voltage.

, $$\dot{U}({ƒ}_k)$$

, ƒ_k=k/(NΔt), k∈[0, N/2]. Для этого используют алгоритм БПФ. Число отсчетов N задают, исходя из требуемого разрешения Δƒ=1/(NΔt) дискретного Фурье-анализа по частоте. Амплитудные дискретные спектры $$\left|{\dot{U}}_0({ƒ}_k)\right|$$

и $$\left|\dot{U}({ƒ}_k)\right|$$

представлены на фиг. 5, из которой следует, что сигнал u₀(t) имеет близкий к равномерному спектр в заданном диапазоне частот (ƒ₀, ƒ₁), за пределами которого его значения малы, а спектр сигнала u(t) имеет глубокий провал на частоте резонанса.4. Convert the digital excitation signal U ₀ (nΔt) and the measuring signal U (nΔt) into samples of signals of complex discrete spectra $${\dot{U}}_0({ƒ}_k)$$

, $$\dot{U}({ƒ}_k)$$

, ƒ _k = k / (NΔt), k∈ [0, N / 2]. To do this, use the FFT algorithm. The number of samples N is set based on the required resolution Δƒ = 1 / (NΔt) of the discrete Fourier analysis in frequency. Amplitude Discrete Spectra $$\left|{\dot{U}}_0({ƒ}_k)\right|$$

and $$\left|\dot{U}({ƒ}_k)\right|$$

presented in FIG. 5, from which it follows that the signal u ₀ (t) is close to a uniform spectrum in a predetermined frequency range (ƒ _0, ƒ _1), beyond which its value is small, and the spectrum of u (t) signal has a deep notch at the resonance frequency .

5. Calculate the values of the complex conductivity of PE at frequencies ƒ _j, falling within the interval (ƒ _0, ƒ _1), according to the formula:

, реактивной составляющей $$\mathrm{Im}(\dot{Y}(ƒ))$$

и модуля $$\left|\dot{Y}(ƒ)\right|$$

комплексной проводимости иллюстрируются фиг. 6, 7, 8 соответственно.Characteristic frequency dependences of the active component $$\mathrm{Re}(\dot{Y}(ƒ))$$

reactive component $$\mathrm{Im}(\dot{Y}(ƒ))$$

and module $$\left|\dot{Y}(ƒ)\right|$$

complex conductivity are illustrated in FIG. 6, 7, 8, respectively.

и частот ƒ_j поступают в блок дробно-рациональной аппроксимации измеренных значений $${\dot{Y}}_j$$

частотной зависимостью комплексной проводимости канонической эквивалентной схемы $${\dot{Y}}_0(ƒ)$$

(фиг. 9), которая состоит из соединенных параллельно емкости С₀ и последовательной резонансной RLC-цепочки. Этой эквивалентной схемой ПЭ описывается в резонансном промежутке частот (Пьезоэлектрические резонаторы. Справочник. Под ред. П.Е. Кандыбы и П.Г. Позднякова. - М.: Радио и связь. 1992. С 42) /8/. Комплексная проводимость канонической эквивалентной схемы $${\dot{Y}}_0(ƒ)$$

вычисляется по формуле:6. Formed arrays of complex conductivity values $${\dot{Y}}_j=\dot{Y}({ƒ}_j)$$

and frequencies ƒ _j enter the fractional rational approximation block of the measured values $${\dot{Y}}_j$$

frequency dependence of the complex conductivity of the canonical equivalent circuit $${\dot{Y}}_0(ƒ)$$

(Fig. 9), which consists of a capacitance C ₀ connected in parallel and a series resonant RLC chain. This equivalent circuit describes the PE in the resonant frequency range (Piezoelectric resonators. Handbook. Edited by PE Kandyba and PG Pozdnyakov. - M .: Radio and communications. 1992. With 42) / 8 /. Complex conductivity of the canonical equivalent circuit $${\dot{Y}}_0(ƒ)$$

calculated by the formula:

,

, $$Q=R^{-1}\sqrt{L/C}$$

- соответственно параллельная емкость, частоты резонанса и антирезонанса, добротность канонической эквивалентной схемы, R, C, L - эквивалентные параметры (соответственно активное сопротивление, емкость и индуктивность) динамической ветви канонической эквивалентной схемы. Задачу дробно-рациональной аппроксимации решают методом итерированного веса (Н.Н. Калиткин. Численные методы. - М.: Наука. 1978. С 64) /9/. Для определения частот ƒ_r, ƒ_a, добротности Q и параллельной емкости С₀ выполняют, согласно методу итерированного веса, следующие действия.where C ₀ , $${ƒ}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="00000066.png,00000069.png"\; state="\{\{state\}\}">r</figure-callout>}}^2=2\pi {(LC)}^{-\mathrm{one}}$$

,

, $$Q=R^{-\mathrm{one}}\sqrt{L/C}$$

- respectively, parallel capacitance, resonance and antiresonance frequencies, quality factor of the canonical equivalent circuit, R, C, L - equivalent parameters (respectively, resistance, capacitance and inductance) of the dynamic branch of the canonical equivalent circuit. The problem of fractional rational approximation is solved by the iterated weight method (NN Kalitkin. Numerical methods. - M .: Nauka. 1978. P 64) / 9 /. To determine the frequencies ƒ _r , ƒ _a , the quality factor Q and the parallel capacitance C ₀ , the following actions are performed according to the iterated weight method.

1. Set the value of the variable c and assume c ₁ = c.

2. Define small (~ 10 ^-5 ÷ 10 ^-8 ) numbers ε ₁ and ε ₂ .

3. Set the values of the array ρ _j = 1.

4. Set the values of the vector ξ: ξ ₀ = 0, ξ ₁ = 0, ξ ₂ = 0.

.5. Calculate the array of values $${\dot{y}}_j=2\pi i{ƒ}_{j}c$$

.

с элементами6. Form the matrix $$\dot{A}$$

with elements

с элементами $$b_j={\rho }_j{ƒ}_j^2({\dot{Y}}_j-{\dot{y}}_j)$$

.7. Vector form $$\dot{b}$$

with elements $$b_j={\rho }_j{ƒ}_j^2({\dot{Y}}_j-{\dot{y}}_j)$$

.

, где знак (·)^H обозначает эрмитово сопряжение.8. Form the matrix $$\mathrm{Re}({\dot{A}}^H\dot{A})$$

, where the sign (·) ^H denotes Hermitian conjugation.

.9. Form a vector $$\mathrm{Re}({\dot{A}}^H\dot{b})$$

.

. 10. Find a three-dimensional vector x, solving a system of three linear equations with three unknowns $$\mathrm{Re}({\dot{A}}^H\dot{A})x=\mathrm{Re}({\dot{A}}^H\dot{b})$$

.

с компонентами11. Calculate the vector $$\dot{F}$$

with components

12. Determine the new value of the variable with:

.13. Calculate the new array values $${\rho }_j={\left|{ƒ}_j^2-i{ƒ}_j{x}_0-x_2\right|}^{-\mathrm{one}}$$

.

14. Check the conditions | x-ξ | / | x |> ε ₁ and | s-s ₁ | / s> ε ₂ .

15. Assume with ₁ = c, ξ = x and return to step 5 if the conditions are met.

16. Complete the process, considering the result achieved if the conditions are not met.

, частоту антирезонанса

, добротность $$Q=\sqrt{x_2}/x_0$$

и параллельную емкость С₀=с в резонансном промежутке частот.17. Determine the resonance frequency $${ƒ}_r=\sqrt{x_2}$$

frequency of antiresonance

, quality factor $$Q=\sqrt{x_2}/x_0$$

and a parallel capacitance C ₀ = c in the resonant frequency span.

на частоте заполнения радиоимпульса F определяют по формуле (5), а параллельную емкость на низкой частоте рассчитывают по формуле $$C=\mathrm{Im}(\dot{Y}(F))/2\pi F$$

и полагают c=ηC, где η∈[0.7, 1].The initial value of the variable c is found from additional measurements of the parallel capacitance C at a low frequency when the PE is excited by a segment of a harmonic signal, which is also performed by the claimed method, since the radio pulse is a special case of a signal with linear frequency modulation with the matching values ƒ ₀ = ƒ ₁ = F of its initial and final frequencies. Conductivity value $$\dot{Y}(F)$$

at the filling frequency of the radio pulse F is determined by the formula (5), and the parallel capacitance at a low frequency is calculated by the formula $$C=\mathrm{Im}(\dot{Y}(F))/2\pi F$$

and put c = ηC, where η∈ [0.7, 1].

Thus, an increase in the accuracy of measuring the parameters of PE is achieved through the use of a digital method for determining the complex conductivity upon excitation of PE by a pulse signal with linear frequency modulation, the duration of which is less than the duration of the registration of the measuring signal and the excitation signal. The measured frequency dependence of the complex conductivity is used to extract resonance, antiresonance, and Q factors from all its samples by the method of fractional rational approximation, in contrast to the prototype, in which the duration of the excitation of the PE and the registration of the measuring signal are the same, and the characteristic frequencies and Q factor are determined by separate values integrated conductivity module.

, активной $$\mathrm{Re}(\dot{Y}(ƒ))$$

и реактивной $$\mathrm{Im}(\dot{Y}(ƒ))$$

составляющих комплексной проводимости и результаты их обработки представлен на фиг. 10. Экспериментальный образец измерительного комплекса успешно прошел испытания.The inventive method is implemented in an automated measuring complex, which is located in a case-type case and consists of a measuring unit and a personal computer. An example of a screen with the measurement results of the module $$\left|\dot{Y}(ƒ)\right|$$

active $$\mathrm{Re}(\dot{Y}(ƒ))$$

and reactive $$\mathrm{Im}(\dot{Y}(ƒ))$$

components of complex conductivity and the results of their processing are presented in FIG. 10. The experimental sample of the measuring complex has been successfully tested.

Information sources

1. Industry standard OCT II 0444-87. Piezoceramic materials. Technical conditions - M .: Elektrostandart, 1987.

2. WO 2012149649 (A1), IPC F02M 51/00; G01R 27/02; G01R 31/00, 2012-11-08.

3. TW 200933163 (A), IPC G01R 27/02, G01R 27/28, 2009-08-01.

4. US 6768312, 6 IPC G01N 29/09; G01N 29/12; class US 324/525; 324/509, 2004-07-27.

5. RU 2499234, 6 IPC G01H 13/00, G01H 1/06, publ. 11/20/013.

6. Piezoceramic transducers. Directory. Ed. S.I. Pugacheva. - L .: Shipbuilding. 1984. C 144-147.

7. N.M. Ivanov, V.L. Zemlyakov, Yu.K. Miloslavsky. New means of measuring the parameters of piezoceramic elements and piezomaterials. Engineering Herald of the Don. T. 26. No. 3. 2013 is a prototype.

8. Piezoelectric resonators. Directory. Ed. P.E. Kandyba and P.G. Pozdnyakova. - M .: Radio and communication. 1992.S. 42.

9. N.N. Kalitkin. Numerical methods. - M .: Nauka, 1978.C 64.

Claims (2)

1. A digital method for measuring the parameters of piezoelectric elements, including the action of the excitation signal u ₀ (t) on the piezoelectric element connected in series with a resistor having a given resistance r ₀ , registration of the measuring signal u (t) at the point of connection of the piezoelectric element with a resistor, the formation of a specified the number N of values of a digital pulse excitation signal with linear frequency modulation, the instantaneous frequency of which varies from ƒ ₀ to ƒ ₁ , where ƒ ₀ and ƒ ₁ are the minimum and maximum frequencies of the range in which m measurements are performed, covering a resonance interval for a predetermined fashion piezoelement oscillations generated digital pulse signal is converted into an analog pulse excitation signal u ₀ (t), synchronously convert excitation signal u ₀ (t) and the measurement signal u (t) in digital form, is reduced and remember complex discrete spectra

and

of both signals, calculate and store many complex conductivity values

a piezoelectric element at each discrete frequency ƒ within the frequency range of the exciting signal, characterized in that the pulse excitation signal has a duration T ₁ = T ₀ -τ, where τ is the pause time between the end of the linear frequency modulated signal and the moment the digital signals are recorded, at this time, the registration of digital signals is equal to T ₀ , the resonance frequency ƒ _r , the antiresonance frequency пь _a and the Q factor of the piezoelectric element, as well as the value of the parallel capacitance C ₀ from the obtained set of complex values are determined xn conductivity by its fractional rational approximation by the frequency dependence of the complex conductivity of the canonical equivalent circuit in the resonant frequency range. 2. A method according to claim 1, characterized in that for recording a full response pulse on the piezoelectric element drive signal pause duration is chosen from the condition τ> Q _max / ƒ _0, where Q _max -. Q upper limit of measurement.

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