RU2415387C1 - Method to analyse oscillations - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: proposed method comprises measuring solid body deformation and plotting deformation and deformation speed vs test duration, deformation speed and amount. Note here that, to prove random occurrence of deformation speed fluctuation, obtained time dependence of deformation speed is processed by means of direct Fourier transform with subsequent representation of random process power spectrum in log-log grid. In case the dependence of random process power on frequency obeys the following relations: S=S(0) at ω<ω₀, S~ω^-n at ω>ω₀, where ω, ω₀ are oscillation frequencies on running light wave and that reflected by mirror, respectively, n=2H1+1 (H1 - Hurst constant) corresponds to spectral power S in frequency range ω<ω₀, then it may be concluded that flicker-noise origin belongs in random process of solid body deformation speed fluctuation occurrence.

EFFECT: analysis of oscillations using laser Doppler strain metre.

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Description

The invention relates to the field of optical vibrometry and can be used in optical instrumentation, laser flowmetry, the development of devices for measuring the flow of liquids and gases.

A known method of researching oscillations [1. Oscillation research method: RF Patent No. 2097710, IPC G01H 1/08 (Application No. 94029365/28 of 1994.08.05)], in which the radiation of the source is directed to the object under study, a signal is generated from the phase-shifted waves, which are the reference and reflected from the studied object, - measure the spectrum of the output signal, using several fixed values of the amplitudes of the harmonics judge the object under study. When generating a signal, the distance between the source and the object under study is changed, respectively, changing the magnitude of the phase shift. The signal spectrum is taken at each change in distance, fixing in each of them a harmonic with a maximum amplitude and a frequency corresponding to it, frequencies among them with a minimum and a maximum value are selected, and the oscillations are judged by the proposed relations. In addition, when generating the signal, the change in the distance between the source and the object under study is set within the range of values greater than λ / 2, and the oscillation amplitude is determined.

The disadvantages of this method are the low information content of the processing method of the obtained experimental information, the periodic mode of measuring the deformation of the object.

These shortcomings are due to the processing technique of the obtained signal spectrum, based on considering only the harmonics with the maximum amplitude and the corresponding frequency and the subsequent analysis of the obtained frequency sample corresponding to each change in distance, and choosing among the obtained frequency sample with maximum and minimum values.

A known method of measuring the periodic law of motion [2. A method for measuring the periodic law of motion of a vibrating surface: RF Patent No. 2101686, IPC G01H 1/04 (Application No. 96100261/28 of 1996.01.05)], which includes the formation of an array of points of intersection of the zero level with an electric signal at each vibration period. Next, a step-by-step calculation of the values of the law of motion of the vibrating surface z (t) at these points within each interval between adjacent zero-level intersections is performed. At the boundaries of the intervals, the calculation results are stitched together with continuity.

The disadvantages of this method are the low informativeness of the method of processing the obtained experimental information, the periodic nature of the measurement process, the complex procedure for processing the obtained data, based on the assumption of a predetermined periodic nature of the movement of the investigated object.

These shortcomings are caused by the method of studying vibrations, based on the formation of an array of points of intersection of the zero level with an electric signal at each oscillation period, step-by-step calculation of the values of the law of motion of the vibrating surface at these points within each interval between adjacent intersections of the zero level and subsequent stitching of the results of calculations taking into account the condition continuity.

A known method of checking the technical condition of tank engines [3. Device for checking the technical condition of tank engines. Application No. 94020038 dated 1994.06.01, IPC F41H 7/02; F02B 1/00], which is based on the fact that when changing vibration parameters using a laser interferometer, its radiation intensity changes depending on the relative position of the laser and the measurement object. Moreover, the number of periods N of fluctuations in the intensity of laser radiation for one period of vibration of the object determines how much the object has moved. The number N is determined by the formula (1):

where f is the frequency of the intensity of the laser radiation; F is the reference frequency (the oscillation frequency of the investigated object). Thus, the amplitude of vibration displacement is reduced to determining the ratio of frequencies f and F; a signal with a frequency f is generated at the output of the laser photodetector, and a signal with a reference frequency F is from a reference frequency generator.

The disadvantages of this method [3] are the need for a frequency standard, the periodic nature of the measurement of the deformation of the test object, the low informativeness of the registration method and the complex procedure for processing experimental deformation.

These shortcomings are due to the method of measuring vibrations proposed in [3], based on a consideration of the total number of periods of fluctuations in the intensity of laser radiation for one period of oscillation of the object under study induced by the reference frequency generator. However, the analysis of the entire frequency spectrum that occurs in an oscillating object is not performed; analysis of experimental data is reduced to considering the deformation behavior at only one frequency, which significantly depletes the information about the deformation properties of the studied object.

The closest in technical essence to the claimed method is a method for the study of fluctuations [4. Yakushev P.N., Peschanskaya N.N. // Interferometric method for determining relaxation transitions in polymers below the glass transition temperature // GSSSD Method. - 1991], based on the use to study the laws of deformation of solids of a laser Doppler deformometer with the following technical characteristics:

a) range of strain rates: 10 ^-2 ÷ 10 ^-10 m / s;

b) deformation range: 10 ^-6 ÷ 10 ^-2 m;

c) the “division price” on the deformation scale ΔD = λ / 4, where λ is the wavelength of the He-Ne laser radiation (at λ≈0.63 μm, the value ΔD≈0.15 · 10 ^-6 m);

т.е. она в основном определяется нестабильностью по частоте лазерного излучения и погрешностей измерительных приборов;d) the error in measuring strain ε and strain rate

those. it is mainly determined by the instability in the frequency of laser radiation and the errors of measuring instruments;

d) measurement temperature range: 77 ÷ 473 K (there is no fundamental difficulty in expanding ΔT; the set temperature is maintained with an accuracy of ± 0.1%);

e) the duration of the experiment is from 1 to 10 ⁴ s;

g) the value of the acting stresses - from 1 to 150 MPa, - can be set with an accuracy of ± 2%.

The optical scheme of the laser Doppler deformometer is based on the Michelson interferometer (Figure 1), consisting of a laser 1, mirrors 2, 8, 9, a polarizer 3, photodetectors 4, 5, translucent mirrors 6, 7 and associated with the installation for studying the creep of the studied samples of solid tel. Mirror 2 is rigidly connected with a movable grip that tracks the deformation of the sample during loading. Reflected by a moving mirror, beam b undergoes a Doppler frequency shift:

where ω, ω ₀ are the frequencies of the transmitted and reflected light waves from the mirror, respectively. In the simplest case, when the mirror is perpendicular to the incident light beam and moves parallel to itself, there is a “longitudinal Doppler effect”.

In this case, the frequency of reflected light can be determined by the formula:

где

- скорость перемещения зеркала 2 (10^-3-10^-9 м/с). Поскольку v<<c, получим:where c is the speed of light, v is the speed of movement of the light source (imaginary):

Where

- the speed of movement of the mirror 2 (10 ^-3 -10 ^-9 m / s). Since v << c, we get:

As a result of the interference of two light waves, a new wave is obtained - the “beat wave”, the intensity of which oscillates with a frequency Δω - the “beat frequency”. Let the intensities of the incident and reflected light beams - I ₁ and I ₂ , then the intensity of the resulting light flux:

Obviously, at cos (Δωt) = 1, the maximum light intensity recorded by the registration system is observed. Let the frequency of repetition of maxima of the intensity of the beats v = Δω / 2π; then, given the fact that ω ₀ = 2πc / λ, we obtain:

where λ is the wavelength of the light source. For a laser with a wavelength of 633 nm, the frequency range is ≈0.3 · (10 ⁴ ÷ 10 ^-4 ) s ^-1 , which can be experimentally recorded. The expression for the speed of movement of the mirror:

To estimate the displacement, ε _a , we obtain by integrating (7):

where N is the number of complete fluctuations in the intensity of the beat wave.

In the circuit shown in FIG. 1, rays b and c undergo the same number of refractions and reflections. Then, by the formula (6), for I ₁ = I ₂ , we obtain:

Therefore, the intensity of the output beam varies from 0 to 4I ₁ .

Thus, the known method for the study of fluctuations [4] includes the following stages:

a) periodic recording of the deformation interferogram on a paper information carrier (recorder tape). In this case, the frequency value is selected averaged over 5 ÷ 10 vibrations, at random points corresponding to deformations, measured independently on a setup for studying the creep of solids;

b) formulas (8, 9) determine the magnitude of the deformation and the creep rate;

-ε» и «ε-t» и определяют деформацию, соответствующую величине «предела вынужденной эластичности ε_в».c) according to the data obtained, creep curves are constructed in the coordinates “

-ε "and" ε-t "and determine the deformation corresponding to the value of the" limit of elastic elasticity ε _in ".

The disadvantages of this method [4] are the low information content, the periodic nature of the measurement of the strain and creep rate, the inability to study in detail the fluctuations in the creep rate of the test sample (Figure 3).

These shortcomings are due to the processing technique of the output signal recorded from photodetectors 4, 5, based on the predominant consideration of interference maxima, processing of the obtained data using formulas (7) ÷ (9), as well as the low level of application of information technology methods and modern approaches to random analysis processes.

An object of the invention is:

elimination of the indicated drawbacks, namely, low information content, a periodic measurement mode, the impossibility of an effective analysis of creep rate fluctuations during the experiment, as well as an increase in the information content of the method for studying deformation interferograms by direct Fourier transform of the experimentally established time dependence of the deformation rate and application of flicker noise spectroscopy to interpret the resulting power spectrum of a random process of occurrence of fluctuations second strain rate.

To achieve this goal in a method that includes measuring the deformation of samples of solids using a laser Doppler strainmeter (Figure 1), we also used the direct Fourier transform method for processing the data of the deformation experiment, and the methodology of flicker noise spectroscopy to interpret the obtained numerical vectors of experimental data .

Flicker noise spectroscopy [5. Timashev S.F. // Flicker noise spectroscopy: information in chaotic signals. - M .: Fizmatlit, 2007 .-- 248 p .; 6. Timashev S.F. // Informational significance of chaotic signals: flicker noise spectroscopy and its applications // Electrochemistry. - 2006. - T.42. No. 5. - S.480-524] is a phenomenologically method for extracting information contained in chaotic signals produced by open complex, including natural systems of different nature. The essence of the flicker-noise spectroscopy method is to give informational significance to the irregularities of the analyzed signals - bursts, jumps, kinks of derivatives of various orders at each spatio-temporal level of the hierarchical organization of the studied systems and to establish correlation relationships in the sequence of fixed values of the studied dynamic variables. The main difference between flicker noise spectroscopy and other methods for analyzing chaotic signals is the introduction of information parameters characterizing the components of the signals under study in different frequency ranges, and the implementation of the necessary procedures for isolating such parameters. According to the methodology of flicker noise spectroscopy, the individual features of the evolution of complex systems are manifested primarily in the low-frequency components of the produced signals, reflecting a specific set of eigenfrequencies and initiated by external influences, interference contributions of such resonances. Against the background of this type of low-frequency “envelopes,” there are inevitably more high-frequency chaotic (“noise”) components, the genesis of which is far from always clear. However, in the sequence of these high-frequency chaotic (“noise”) components, information-specific correlation relationships specific to each system are almost always revealed. Therefore, only by sequentially isolating the contributions of such components of complex signals in different frequency ranges and introducing the appropriate parameterization, it is possible to most adequately assess the state of the system under study, the dynamics of changes in the state of its subsystems, including under external influences.

It is the application of the methodology of flicker noise spectroscopy to the analysis of numerical data vectors obtained as a result of a deformation experiment that allows us to take into account the contributions of various factors that influence the deformation process, and thus increase the information content of studying the deformation behavior of solids using a laser Doppler deformometer. Thus, the goal of the invention is achieved - to increase the information content of deformation tests using a laser Doppler deformometer.

The invention is illustrated by drawings, where:

Figure 1 - optical diagram of the interferometric prefix: 1 - laser; 2, 8 - mirrors; 3 - polarizer; 4, 5 - photodetectors; 6, 7 - translucent mirrors; 9 - direction of movement.

Figure 2 is a fragment of a deformation interferogram recorded during the study of the initial stages of deformation of a sample of polymethyl methacrylate, γ-irradiated up to 160 kGy in vacuum, at room temperature. Sampling rate - 0.1 s. The magnitude of the load is 8 MPa, the test temperature is room temperature.

Figure 3 - dependence of the strain (1) and strain rate (2) of a sample of polymethyl methacrylate, γ-irradiated up to 160 kGy in vacuum, at room temperature, on the duration of the mechanical test. Sampling rate - 0.1 s. The magnitude of the load is 8 MPa, the test temperature is room temperature.

Figure 4 - block diagram of the switching device for collecting data with a laser Doppler deformometer in unipolar mode (A - microcontroller; B - pulse generator): 10 - trigger; 11 - multiplexers; 12 - input / output switch; 13 - source of a pulse output signal; 14 - 32 input channels of an analog signal; 15 - grounding. U _in - analog signal of the input voltage coming from the photodetectors (4, 5 in FIG. 1). U _signal - a sequence of voltage pulses with a frequency of up to 10 ⁵ Hz, obtained by converting the input analog signal in multiplexers and in the source of voltage signal pulses.

5 is a user interface of a program for receiving experimental data.

6 is a user interface of a data processing program.

7 is a power spectrum of a deformation process of a sample of polymethyl methacrylate, γ-irradiated up to 160 kGy in vacuum, at room temperature. Sampling rate - 0.1 s. The magnitude of the load is 8 MPa, the test temperature is room temperature.

Fig - dependence of the spectral power of the deformation process of a sample of polymethyl methacrylate, γ-irradiated up to 160 kGy in vacuum, at room temperature, on the frequency in a double logarithmic scale. Sampling rate - 0.1 s. The magnitude of the load is 8 MPa, the test temperature is room temperature.

Case Studies

The subject of the test. PMMA samples (GOST 17622-72) with a diameter of 3 mm, a height of 6 mm, in an amount of 10 pieces.

The purpose of the test. Investigation of the deformation behavior of PMMA samples subjected to vacuum (up to 10 ^-5 mm Hg), radiation exposure (γ radiation of the ⁶⁰ Co isotope (energy 1.25 MeV) dose - 160 kGy, dose rate - 3 Gy / s) . Storage and exposure temperature - room temperature. Heat treatment - heating to 373 K and rapid (over a period of time <1 min) cooling to 273 K.

Test conditions and procedure. To register the creep of PMMA samples, a laser Doppler deformometer was used, which was a displacement (Michelson) interferometer coupled to a creep measuring device in uniaxial compression mode (Figure 1).

Deformation tests were carried out at room temperature, in air, atmospheric pressure - 760 mm Hg. The value of the applied voltage is 7 ÷ 8 MPa, the duration of the test is not more than one hour. The deformation of PMMA samples was investigated in compression mode.

Before testing, the dimensions of the samples were measured using a micrometer with an accuracy of ~ 0.005 mm. Depending on the specified voltage (taking into account the diameter of the sample and the transmission coefficient of the installation for measuring creep) by the formula (11), the value of the load P was determined:

where σ, MPa is the value of the voltage applied to the sample, k is the value of the transmission coefficient of the system of levers of the installation (k = 30). Before conducting the experiment, instead of a sample (for a given σ), a template made of hardened steel U10 with a height equal to the height of the sample was placed in the apparatus and the initial position of the shoulder of the curly lever was set. Thus, errors that could arise due to differences in the initial position of the curly lever at different stresses and deformation of the parts of the creep measuring apparatus were removed. Then the test PMMA sample was placed in the installation and loading was carried out for 1-2 s.

The strain was measured using the registration system associated with the loading mechanism of the installation, recording the deviation of the indicator arrow at certain time intervals. To determine the strain by the number of divisions n by which the indicator arrow deviates, we used the formula (12):

where l ₀ is the height of the sample. The error in measuring the total strain in this case is determined by half the division price on the chart tape and is 0.15%.

For continuous recording of deformation and creep rate during the deformation, an interferometric attachment was used (Figure 1), a computerized system for recording, storing and processing experimental information using a data acquisition device (DRC) and a personal computer (Figure 4-6) was introduced into the registration system with a sampling rate of up to 10 ⁵ measurements per second.

As follows from Figure 1, the probe laser beam (a) is divided by a translucent mirror 7 into two equally intense light beams, one of which (c) is directed to a fixed mirror 8, and the other (b) to a movable mirror 2. On a translucent mirror 7, both beams (c and b) are again connected into one (cb). The total beam of interfering rays (cb) is sent to the measuring photodetector 4. Using a translucent mirror 6, part of the original laser light beam (light beam d) is sampled in the comparison photodetector 5.

During the deformation of the sample, mirror 2 moves with the punch, and the light flux reflected from it changes the frequency (beam b) due to the Doppler effect. The interference of the light beam c, reflected from the stationary mirror 8, and the light beam b, which experienced a Doppler shift, leads to the appearance of low-frequency beats in the intensity of the light flux (cb), which in the photodetector 5 are converted into an analog electrical signal. An example of a deformation interferogram, which is an analog electrical signal from photodetectors 4, 5, recorded on paper, is shown in Figure 2.

To carry out computer processing, the received signal is fed to the DRC (Figure 4), operating in a unipolar mode, which consists of: A - a microcontroller including a trigger 10, multiplexers 11, an “Input / Output” switch 12, B - an output pulse generator signal including a source output voltage 13 connected to the microcontroller 32 input pulses by an analog signal channel 14. in operation, the DRC needs to be grounded input signal 15. The analog voltage U _Rin, supplied on photodetectors 4, 5 (Figure 1), via the DRC is converted into a pulse train _signal U output voltage with a frequency ^{of 5} to 10 Hz, which is then fed to a personal computer equipped with relevant software-software for receiving and processing the signal (5 , 6). The registered numerical vector is formed as a result file, which is placed in the computer's memory. During the deformation experiment, the formation of the result file is performed every 20 seconds.

Test results. Figure 3 shows the dependences of the strain and strain rate on the duration of the compression test of a PMMA sample γ-irradiated up to 160 kGy at room temperature, obtained using a computer system for processing deformation data. On the time dependence of the strain rate (Fig.3, 2), one can clearly observe fluctuations in the strain rate of the polymer.

The appearance of fluctuations in the creep rate can be considered as a random process. To prove the nature of the random process of the occurrence of strain rate fluctuations and establish its parameters, the obtained numerical vector of the deformation data was converted using the direct Fourier transform (Fig. 7) and the real part of the obtained power spectrum of the deformation process was presented in double logarithmic coordinates (Fig. 8).

As follows from Fig, the spectral power of a random process of fluctuations in the strain rate has the following properties:

S = S (0) for ω <ω ₀ ,

S ~ ω ^-n for ω> ω ₀ ,

where n = 2H ₁ +1 (H ₁ is the Harst constant [6, 7]). Random processes of this kind are called flicker noise [6, 7]. The random process parameters determined from Fig. 8 are shown in the table.

Parameters of the random process of occurrence of fluctuations in the strain rate of PMMA γ-irradiated up to 160 kGy Parameter log (S (0)), rel. units T ₀ s n H ₁ Value 3,7 51.0 1.80 ± 0.09 0.40 ± 0.05

The parameter S (0) corresponds to the spectral power S in the frequency range ω <ω ₀ (ω ₀ is the boundary frequency corresponding to the beginning of the region of variation of S); T ₀ = 1 / 2πω ₀ - correlation time, s. To establish the physical meaning of T ₀ , additional research is needed; presumably, this is the average relaxation time of regions of the polymer sample in which strain jumps and creep rates are localized. The Harst constant characterizes the degree of deviation of the random process under consideration from Brownian motion (in this case, H ₁ = 0.5).

Thus, the use of the flicker-noise spectroscopy method for processing experimental information on the deformation behavior of a PMMA sample helps to identify the features of the deformation of this polymer.

The present invention allows 10 ² ÷ 10 ³ times to increase the information content of the method of recording deformation of solids by a laser Doppler deformometer, to automate the process of registration, storage and processing of experimental information, apply the methodology of flicker noise spectroscopy to interpret the results of deformation tests. The identification of the features of deformation of solids at the nano- and microlevels will make it possible to improve the quality of the prediction of the service life of various equipment objects under extreme operating conditions, which is a qualitative advantage of the proposed patent.

Claims (1)

A method for studying vibrations using a laser Doppler deformometer, including measuring the deformation of a solid and plotting the dependences of deformation and strain rate on the duration of the test, the strain rate on the strain value, characterized in that the obtained time dependence of the strain rate is processed using a direct Fourier transform with subsequent representation of the spectrum power of the random process in double logarithmic coordinates, and in the case if awn power frequency random process obeys the following relations:
S = S (0) for ω <ω ₀ ,
S ~ ω ^-n for ω> ω ₀ ,
where ω, ω ₀ are the oscillation frequencies of the transmitted and reflected from the mirror light waves, respectively,
n = 2H1 + 1 (H1 - Harst constant),
the parameter S (0) corresponds to the spectral power S in the frequency range ω <ω ₀ ,
it is concluded that the flicker-noise nature of the random process of the occurrence of fluctuations in the rate of deformation of a solid body.

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