RU2693539C2 - Method of measuring resonant frequency of acoustic resonator of gas thermometer - Google Patents

Abstract

FIELD: physics.SUBSTANCE: invention relates to the metrology. Method for measuring resonant frequency of an acoustic resonator of a gas thermometer, comprising the fact that the self-oscillation circuit is tuned to generate self-oscillations on the selected mode of the precision spherical resonator, filled with gas near one of resonance maxima, a cylindrical resonator is added to the feedback circuit, filled with the same gas and located at the same temperature as the spherical resonator, thereby providing conditions for occurrence of stable oscillations on the selected mode of the spherical resonator near the resonant maximum, adjusting the cylindrical resonator by adjusting its length to resonance maximum, coinciding with resonance maximum of spherical resonator so that on frequency of self-oscillations of spherical resonator to provide maximum gain in feedback circuit, change in the frequency of self-oscillations is used to determine the change in the thermodynamic temperature of the gas in the spherical resonator. Generation of oscillations at maximum of amplitude-frequency dependence is also provided and rectangular pulses of constant amplitude are supplied to exciting microphone, phase shift of which is adjusted depending on amplitude of signal from receiving microphone.EFFECT: technical result is higher accuracy, shorter measurement time.1 cl, 7 dwg

Description

In connection with the planned transition to a new thermodynamic scale, the need arises to develop temperature standards based on the laws of thermodynamics. An acoustic gas thermometer is recommended by the Consultative Committee on Temperature at MBMV as the primary primary means of measuring temperature for a temperature range from 4.2 K to 273.16 K, as well as for higher temperatures.

The invention relates to the field of measurement technology and can be used in the development of temperature standards of the 1st and 0th digits based on an acoustic gas thermometer in a wide temperature range. Important advantages of the method: the temperature standard reproduces the thermodynamic temperature; since the working substance is flow gas, the standard has a large calibration interval; There are no restrictions on the number of heating-cooling cycles; short measurement time.

An important task is to measure the resonant frequencies of the acoustic resonator of a gas thermometer. The amplitude-frequency dependencies in the resonance region determine the resonant frequencies corresponding to the modes of the natural oscillations of the resonator. Knowing the resonant frequencies, one can calculate with high accuracy the gas temperature in the resonator.

The temperature of the gas in the resonator and the oscillation frequency are related by the relation:

- резонансная частота для моды (

, n), М - молярная масса газа, R - универсальная газовая постоянная, р-давление гелия в резонаторе,

- численный коэффициент, соответствующий моде (

, n), коэффициенты А_-0.5, A_l, А₂ определяют вклад слагаемых зависящих от давления и обусловленных взаимодействием газа со стенками резонатора - А_-0.5, - наличием температурного слоя на границе газ- стенка - A_-1, - кулоновским взаимодействием молекул газа -A_1,, А₂; а=a _w[1+α(Т-T_w)], а - радиус резонатора с учетом изменения геометрических размеров резонатора от температуры, α - коэффициент линейного расширения меди, a_w - радиус резонатора при температуре тройной точке воды T_w.where T is the measured temperature

- the resonant frequency for the mode (

, n), M is the molar mass of a gas, R is the universal gas constant, p is the pressure of helium in the resonator,

- the numerical coefficient corresponding to the mode (

, n), the coefficients A _-0.5 , A _l , A ₂ determine the contribution of pressure-dependent components caused by the interaction of the gas with the walls of the resonator - A- _0.5 , - by the presence of a temperature layer at the gas-wall interface - A _-1 , - by the Coulomb interaction gas -A ₁ ,, A ₂ ; a = a _w [1 + α (T-T _w )], a is the resonator radius taking into account changes in the geometric dimensions of the resonator with temperature, α is the linear expansion coefficient of copper, and _w is the radius of the resonator at the temperature of the triple point of water T _w .

Measurement of the resonant frequency by known methods requires the use of special devices and takes a large amount of time per measurement [1]. For example, the measurement using a digital synchronous amplifier SR 830 by removing the amplitude-frequency dependencies takes about 10. Since measurements must be carried out at several gas pressures in the resonator, it can take dozens of minutes to take temperature measurements at one point. At the time of measurement, it is necessary to stabilize the temperature of the resonator, to ensure the absence of gradients and a constant gas composition. Moreover, in order that no impurities from desorption from internal surfaces appear in the gas, it is necessary to ensure a constant flow of gas through the resonator.

The most important technical result achieved, when using the claimed method, is the measurement efficiency, that is, the reduction of the measurement time from several minutes to 1 second.

The proposed method is as follows: the inclusion of a resonator in a self-oscillating circuit leads to the generation of oscillations at one of the resonant frequencies of a spherical resonator filled with gas, provided that the system gain for the signal shifted by 180 ° is greater than one. By adjusting the frequency filter and the phase shifter, the required resonant frequency is selected near the selected mode of the spherical resonator. The most accurate results (stable generation) are achieved if the generation is realized at higher harmonics near the resonant maximum, where there is a pronounced frequency dependence of the amplitude and phase shift or on radial modes. By choosing a generation scheme and a selection of its parameters, you can provide a comparable systematic error in determining the resonant frequency, and by reducing the measurement time to several seconds, you can get more data, reduce random errors and thereby reduce the total measurement error.

A method for measuring the thermodynamic temperature of a gas in an acoustic spherical resonator is that the resonant frequency is measured by the frequency of the circuit’s self-oscillations in the feedback circuit of which a precision-made spherical resonator is included, and a cylindrical resonator filled with the same gas is used as a narrow-band frequency filter. same temperature, pre-tuned so that one of its modes coincides in frequency with the selected mode of the spherical resonator in all m working temperature range.

The way to achieve the technical result is illustrated by drawings. FIG. 1 is a block diagram of a device for generating self-oscillations; FIG. 2 — Experimental setup for measuring resonance; FIG. 3 — Typical amplitude-frequency dependence; FIG. 4 - 7 - graphs of measured temperature dependences.

It is proposed to measure the resonant frequency of an acoustic resonator of a gas thermometer in a wide temperature range by including a spherical resonator 4 with microphones in the feedback circuit of a system consisting of amplifiers 1, 3 and 5, controlled phase shifter 7, and a frequency filter consisting of a cylindrical resonator with microphones 6 The second feedback loop, designed for generation at the maximum of the amplitude-frequency dependence, consists of an amplitude detector 8 and a controlled phase shifter 7.

Principle of operation:

- the system is tuned to self-oscillations on one of the resonant maxima of a precision spherical resonator filled with gas;

- to ensure stable oscillations, a cylindrical resonator is added to the feedback circuit, filled with the same gas and at the same temperature as the spherical resonator;

- by adjusting the length of the cylindrical resonator is tuned to one of the resonant maxima so that at the frequency of self-oscillations of the spherical resonator to provide the maximum gain in the feedback circuit;

- when the gas temperature in the resonators changes, the resonant maxima in the spherical and cylindrical resonator will be shifted the same, however, due to the different mode composition of the oscillations for the spherical and cylindrical self-oscillation resonators will only occur at the initial selected resonant maximum of the spherical resonator;

- a cylindrical resonator, which is tuned to one of the resonant maxima, so that at the frequency of self-oscillations of the spherical resonator to ensure maximum gain in the feedback circuit;

- to reduce the systematic error of determining the resonant frequency by ensuring the generation of oscillations at the maximum of the amplitude-frequency dependence, rectangular pulses of constant amplitude are fed to the excitation microphone using a pulse shaper 2, the phase shift of which is adjusted by the amplitude of the signal from the receiving microphone.

Experimental studies were conducted on a gas acoustic thermometer including:

- thermostat with a spherical resonator located inside the pressure chamber;

- system of self-oscillation realization and frequency measurement;

- a system for stabilizing the temperature of the resonator;

- a system for regulating the pressure and flow of helium gas;

- helium gas purification system.

The main elements of the experimental model of the measurement setup are the thermostat 10, in which insert 13 is lowered with an acoustic spherical resonator made of M1 copper with a radius of 49.8075 mm, a cylinder 14 with ultrahigh-purity helium gas of grade 7.0, a gas reducer 15 for ultra-pure gases FDM 500-16, cryogenic trap 12, lowered into a Dewar 11 with liquid helium. The temperature of the bottom of the resonator Temperature 1 and the upper temperature 2 is measured by two TSPN type platinum resistance thermometers connected to the MIT 8.15 multichannel precision temperature meter, position 18. The resonator is heated using a heating element and a controlled current source GPD-73303D, position 17. Temperature stabilization was carried out on a resistance thermometer Temperature 1 by a PID controller implemented in a program on a PC, position 16, to which MIT 8.15 is connected. Frequency was measured with an ASN-8326 frequency meter, position 9, also connected to a PC. On the resonator, there are two caps of microphone condenser MK-465. The SR 830 digital synchronous amplifier was used to analyze the amplitude-frequency characteristics of the resonator. Amplifiers 1, 3, 5 and phase shifter 7 are made on the basis of operational amplifiers from Texas Instruments and Analog Devices.

A typical amplitude-frequency dependence at a temperature of 0 ° C for a spherical resonator filled with helium, obtained using a digital synchronous amplifier SR 830, is shown in FIG. 3. Determining the resonance from the maximum in the traditional way gives a noticeable error of the order of ^10-4 . The use of mathematical methods significantly improves the accuracy of determining the resonant frequency, but this requires considerable time and special software.

Better stability is achieved at higher generation frequencies. With changes in the setting of the phase shifter, lasing was obtained at a frequency of 69680 Hz at a temperature of 27 ° C. The measured oscillation frequency stability is shown in FIG. four.

Stability of generation within one hour at a level of several millikelvinov is obtained using typical circuits and electronic components in a phase shifter, frequency filter and amplifier. In order to obtain greater stability in addition to ensuring a constant gas composition, the absence of temperature gradients in the resonator, stabilizing the gas pressure in the resonator, additional measures are necessary, for example, the choice of precision electronic components, improved thermal stabilization, etc. To ensure the same gas composition in the system during measurements and to ensure a constant gas composition when replacing the cylinder can be used a device for cleaning gas from impurities.

To confirm the efficiency of the method and formula (1), the dependence of temperature T on ƒ ² (ƒ is the frequency of generation of self-oscillations) was constructed using the experimental data obtained (Fig. 5).

The shown dependence of T on ƒ ² is given at p = 100 kPa. An estimate of the total standard uncertainty gives 10 mK,

Only the contribution of the oscillation stability during two days to the standard temperature measurement uncertainty was evaluated. The contribution was comparable to the influence of other factors. The estimate was 5 mK, which is quite consistent with expectations.

Estimates of the standard uncertainty of temperature measurement allow us to conclude that the method can be used in the development of temperature standards for the 1st and 0th digits

The measured temperature dependences with a stepwise change in temperature in this mode in a cavity filled with air are shown in FIG. 7

To determine the sensitivity of the method, we analyzed the stability and step effect in the form of heating and subsequent cooling of the lower part of the resonator at 5 mK. FIG. 6. From Fig. 6 it follows that the frequency change corresponds to a change in the temperature of the resonator with high accuracy.

To select the optimal conditions for the generation of self-oscillations, calculations of the amplitude-frequency dependences were used.

Conclusion: the possibility of relative measurements of the thermodynamic temperature at the resonant frequency of the acoustic resonator of a gas thermometer in self-oscillation mode with an error of 1 mK was demonstrated.

Information sources

1. S.M. SEDUCTOR, B.G. POTAPOV, KD Pilipenko, E.G. ASLANYAN, A.N. SCHIPUNOV Measurement of Boltzmann constant in a quasispherical acoustic resonator, Measuring equipment No. 7, 2017, p. 8-13.

Claims (1)

A method of measuring the resonant frequency of an acoustic resonator of a gas thermometer, which consists in the fact that the self-oscillating circuit is tuned to generate self-oscillations at one of the resonant maxima near the resonant frequency of the selected mode of a precision spherical resonator filled with gas; a cylindrical resonator filled with the same gas and located at the same temperature as the spherical resonator is added to the feedback circuit, thereby providing conditions for the occurrence of stable oscillations in the selected mode of the spherical resonator near the resonant maximum; adjusting the cylindrical resonator by adjusting its length to the resonant maximum, tuning is performed so that the frequency of one of the resonator modes coincides with the frequency of the selected spherical resonator mode in the entire working temperature range of the spherical resonator, and also to ensure the maximum gain in the spherical resonator frequency feedback circuit; by changing the frequency of self-oscillations determine the change in thermodynamic temperature of the gas in a spherical resonator; reduce the systematic error in determining the resonant frequency due to the fact that they generate oscillations at the maximum of the amplitude-frequency dependence and by supplying rectangular pulses of constant amplitude to the exciting microphone, the phase shift of which is adjusted depending on the amplitude of the signal from the receiving microphone.

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