Spectral analysis is a signal processing method that allows you to identify the frequency composition of a signal. There are known methods for processing a vibration signal: correlation, autocorrelation, spectral power, cepstral characteristics, calculation of kurtosis, envelope. The most widespread is spectral analysis as a method of presenting information, due to the unambiguous identification of damage and understandable kinematic relationships between ongoing processes and vibration spectra.

A visual representation of the composition of the spectrum is provided by a graphical representation of the vibration signal in the form of spectrograms. Identifying the pattern of amplitudes and vibration components makes it possible to identify equipment malfunctions. Analysis of vibration acceleration spectrograms makes it possible to recognize damage at an early stage. Vibration velocity spectrograms are used in monitoring advanced damage. The search for damage is carried out at predetermined frequencies of possible damage. To analyze the vibration spectrum, the main components of the spectral signal are identified from the following list.

1. Turnover frequency– rotation speed of the drive shaft of the mechanism or frequency of the working process – the first harmonic. Harmonics are frequencies that are multiples of the rotation frequency (), exceeding the rotation frequency by an integer number of times (2, 3, 4, 5, ...). Harmonics are often called superharmonics. Harmonics characterize faults: misalignment, shaft bending, damage to the coupling, wear of seats. The number and amplitude of harmonics indicate the degree of damage to the mechanism.

   The main causes of harmonics:

   • imbalance vibration of an unbalanced rotor manifests itself in the form of sinusoidal oscillations with the rotor rotation frequency, a change in the rotation frequency leads to a change in the oscillation amplitude in a quadratic relationship;
   • shaft bending, shaft misalignment - determined by increased amplitudes of even harmonics of the 2nd or 4th, manifested in the radial and axial directions;
   • turning the bearing ring on the shaft or in the housing can lead to the appearance of odd harmonics - the 3rd or 5th.
2. Subharmonics– fractional parts of the first harmonic (1/2, 1/3, 1/4, ... rotational speed), their appearance in the vibration spectrum indicates the presence of gaps, increased compliance of parts and supports (). Sometimes increased compliance and gaps in nodes lead to the appearance of one-and-a-half harmonics of 1½, 2½, 3½….revolution frequency ().

   

   

3. Resonant frequencies– frequencies of natural vibrations of mechanism parts. The resonant frequencies remain unchanged when the shaft rotation speed () changes.

   

4. Non-harmonic vibrations– at these frequencies damage to rolling bearings appears. In the vibration spectrum, components appear with the frequency of possible bearing damage ():
   • outer ring damage f nc = 0.5 × z × f time × (1 – d × cos β / D);
   • damage to the inner ring f vk = 0.5 × z × f vr × (1 + d × cos β / D);
   • damage to rolling elements f tk = (D × f time / d) ×;
   • separator damage f с = 0.5 × f time × (1 – d × cos β / D),

   Where f vr– shaft rotation speed; z number of rolling elements; d– diameter of rolling elements; β – contact angle (contact between the rolling elements and the treadmill); D– diameter of the circle passing through the centers of the rolling elements ().

   

   

   With significant development of damage, harmonic components appear. The degree of bearing damage is determined by the number of harmonics of a certain damage.

   Damage to rolling bearings leads to the appearance of a large number of components in the vibration acceleration spectrum in the region of the bearings’ natural frequencies of 2000…4000 Hz ().

   

5. Wave frequencies– frequencies equal to the product of the shaft rotation frequency and the number of elements (number of teeth, number of blades, number of fingers):

   f turn = z × f turn,

   Where z– the number of wheel teeth or the number of blades.

   Damage manifested at the tooth frequency can generate harmonic components as the damage progresses further ().

   

6. Side stripes– modulation of the process, appear with the development of damage to gears and rolling bearings. The reason for the appearance is a change in speed during the interaction of damaged surfaces. The modulation value indicates the source of excitation of the oscillations. Modulation analysis allows you to find out the origin and degree of development of damage (Figure 110).

   

7. Vibration of electrical origin usually observed at 50 Hz, 100 Hz, 150 Hz and other harmonics (). The frequency of vibration of electromagnetic origin disappears in the spectrum when the electrical energy is turned off. The cause of damage may be due to mechanical damage, for example, loosening of the threaded connections securing the stator to the frame.

   

8. Noise components, occur when jamming, mechanical contacts or unstable rotation speed. They are characterized by a large number of components of different amplitudes ().

   

If you have knowledge about the components of the spectrum, it becomes possible to distinguish them in the frequency spectrum and determine the causes and consequences of damage ().

(A)	(b)
(V)	(G)

a) spectrogram of the vibration velocity of a mechanism with a rotor imbalance and a first harmonic frequency of 10 Hz; b) vibration spectrum of a rolling bearing with damage to the outer ring - the appearance of harmonics with the frequency of rolling elements rolling along the outer ring; c) spectrogram of vibration acceleration corresponding to damage to the rolling bearings of the spindle of a vertical milling machine - resonant components at frequencies of 7000...9500 Hz; d) spectrogram of vibration acceleration during setting of the second type, a part processed on a metal-cutting machine

Rules for analyzing spectral components

1. A large number of harmonics characterizes greater damage to the mechanism.
2. The harmonic amplitudes should decrease as the harmonic number increases.
3. The amplitudes of subharmonics must be less than the amplitude of the first harmonic.
4. An increase in the number of side stripes indicates the development of damage.
5. The amplitude of the first harmonic should have a greater value.
6. The modulation depth (the ratio of the harmonic amplitude to the sideband amplitude) determines the degree of damage to the mechanism.
7. The amplitudes of vibration velocity components should not exceed the permissible values ​​accepted when analyzing the overall vibration level. One of the signs of significant damage is the presence in the vibration acceleration spectrum of components with values ​​greater than 9.8 m/s 2 .

For effective monitoring of technical condition, monthly monitoring of spectral analysis of vibration velocity components is necessary. There are several stages in the history of damage development:

(A)	(b)
(V)	(G)

a) good condition; b) initial imbalance; c) average level of damage; d) significant damage

One of the characteristic damages to the mechanism after long-term operation (10...15 years) is the non-parallelism of the supporting surfaces of the machine body and the foundation, while the weight of the machine is distributed over three or two supports. The vibration velocity spectrum in this case contains harmonic components with an amplitude of more than 4.5 mm/s and one and a half harmonics. Damage leads to increased compliance of the housing in one of the directions and instability of the phase angle during balancing. Therefore, non-parallelism of the machine body supports and the foundation, loosening of threaded connections, wear of bearing seats, increased axial play of bearings must be eliminated before balancing the rotor.

Variants of the appearance and development of one-and-a-half harmonics are presented in Figure 115. The small amplitude of the one-and-a-half harmonic is characteristic of the early stage of development of this damage (a). Further development can take two ways:

The need for repair arises if the amplitude of the one-and-a-half harmonic exceeds the amplitude of the reverse frequency (r).

(A)	(b)
(V)	(G)

a) early stage of damage development - small amplitude of one and a half harmonics; b) development of damage – increase in the amplitude of the one-and-a-half harmonic; c) development of damage – appearance of harmonics 1¼, 1½, 1¾, etc.;
d) the need for repairs – the amplitude of the one-and-a-half harmonic exceeds
reverse frequency amplitude

For rolling bearings, it is also possible to identify characteristic spectrograms of vibration acceleration associated with varying degrees of damage (Figure 116). A serviceable state is characterized by the presence of insignificant amplitude components in the low-frequency region of the spectrum under study, 10...4000 Hz (a). The initial stage of damage has several components with an amplitude of 3.0...6.0 m/s 2 in the middle part of the spectrum (b). The average level of damage is associated with the formation of an “energy hump” in the range of 2…4 kHz with peak values ​​of 5.0…7.0 m/s 2 (c). Significant damage leads to an increase in the amplitude values ​​of the components of the “energy hump” above 10 m/s 2 (g). The bearing should be replaced after the peak components begin to decrease. In this case, the nature of friction changes - sliding friction appears in the rolling bearing, the rolling elements begin to slip relative to the treadmill.

(A)	(b)
(V)	(G)

a) good condition; b) initial stage; c) average level of damage;
d) significant damage

Envelope Analysis

The operation of rolling bearings is characterized by the constant generation of noise and vibration in a wide frequency range. New bearings generate low noise and almost imperceptible mechanical vibrations. As the bearing wears out, so-called bearing tones begin to appear in vibration processes, the amplitude of which increases as defects develop. As a result, the vibration signal generated by a defective bearing can be represented, with some approximation, as a random amplitude-modulated process ().

The shape of the envelope and the depth of modulation are very sensitive indicators of the technical condition of a rolling bearing and therefore form the basis of the analysis. As a measure of technical condition, some programs use the amplitude modulation coefficient:

K m = (U p,max – U p,min) / (U p,max + U p,min).

At the beginning of the development of defects, bearing tones begin to appear in the “noise background”, which increase as the defects develop by approximately 20 dB relative to the level of the “noise background”. At later stages of development of the defect, when it becomes serious, the noise level begins to increase and reaches the level of bearing tones in an unacceptable technical condition.

The high-frequency, noise part of the signal changes its amplitude over time and is modulated by the low-frequency signal. This modulating signal also contains information about the condition of the bearing. This method gives the best results if you analyze the modulation not of a broadband signal, but first perform bandpass filtering of the vibration signal in the range of approximately 6...18 kHz and analyze the modulation of this signal. To do this, the filtered signal is detected, a modulating signal is isolated, which is fed to a narrow-band spectrum analyzer where the envelope spectrum is formed.

Small defects in the bearing are not able to cause noticeable vibrations in the region of low and medium frequencies generated by the bearing. At the same time, for modulating high-frequency vibration noise, the energy of the resulting impacts turns out to be quite sufficient; the method has a very high sensitivity.

The envelope spectrum always has a very characteristic appearance. In the absence of defects, it appears as an almost horizontal, slightly wavy line. When defects appear, discrete components begin to rise above the level of this fairly smooth line of a solid background, the frequencies of which are calculated from the kinematics and revolutions of the bearing. The frequency composition of the envelope spectrum makes it possible to identify the presence of defects, and the excess of the corresponding components above the background unambiguously characterizes the depth of each defect.

When diagnosing a rolling bearing using the envelope, it is possible to identify individual faults. The frequencies of the vibration envelope spectrum at which faults are detected coincide with the frequencies of the vibration spectra. When measuring using an envelope, it is necessary to enter the carrier frequency into the device and filter the signal (bandwidth no more than 1/3 octave).

Questions for self-control

1. For what diagnostic purposes is spectral analysis used?
2. How to determine the rotation frequency and harmonics?
3. In what cases do subharmonics appear in the vibration spectrum?
4. What properties do resonant frequencies have?
5. At what frequencies does damage to rolling bearings occur?
6. What signs correspond to damage to gears?
7. What is vibration signal modulation?
8. What signs indicate vibrations of electrical origin?
9. How does the nature of spectral patterns change during the development of damage?
10. When is envelope analysis used?

Studies of real vibrations of various LLs have shown that vibrations are random functions of time. Their statistical characteristics are determined by processing real vibration records. The purpose of the tests is to reproduce vibration on a vibration stand with specified statistical characteristics at control points of the test object. Since the results of natural vibration processing are used as specified statistical characteristics, random vibration tests most accurately reproduce the actual vibration state of the test product.

When organizing a random vibration test, two hypotheses are accepted:

1) about the normality of the law of distribution of random vibrations;

2) about the local stationarity of random vibrations.

The rationale for the first hypothesis is that the vibration state of a product can be considered as a superposition of various random processes generated by statistically independent sources. It should also be taken into account that if the vibration sensor is located in a place in the structure where its filtering properties are manifested, then the distribution law of the output signal of this sensor approaches normal.

The second hypothesis assumes that the statistical characteristics of vibration change rather slowly over time. This allows us to assume that some averaged characteristics calculated in a certain time interval provide an adequate description of the vibrational state in this period of time.

The properties of vibration as a stationary centralized normal process are completely determined in the general case by the covariance matrix or its Fourier transform - the matrix of spectral densities. In the frequency (scalar) case, the process is characterized by a correlation function or spectral density. Since the structures under test are multi-resonant dynamic systems with pronounced frequency-selective properties, the spectral characteristics (intrinsic and mutual spectra) are the most obvious and are of decisive importance for the test engineer. The random vibration test mode is determined by the spectral density of vibration acceleration, controlled at one point and in one direction, or the matrix of spectral densities when analyzing vector vibration.

Broadband vibration tests usually cover a frequency range of one to two decades. Random narrow-band vibration is excited and studied in a band of units or tens of hertz.

Broadband random vibration test. Broadband random processes with a given energy spectrum have become widespread as physical models of real vibration processes. The description of models of real vibration processes within the framework of correlation theory makes it possible to characterize the equivalence of reproduced and real vibrations by the degree of similarity of their energy spectra. In this case, the vibration reproduction path of the vibration testing complex must ensure the reproduction of mechanical vibrations with the required energy spectrum at the controlled point or in a set of controlled points of the object under study.

This test method involves simultaneously exciting all resonant frequencies of an object. A diagram of the setup for broadband random vibration testing is shown in Fig. 2.24.

The correct reproduction of vibration is prevented by the distorting influence of the vibration exciting means. Therefore, before testing it is necessary to correct or level the amplitude; frequency response of the vibration stand. During testing, stationary random vibrations are excited at the control points of the product. Their numerical characteristics must be close to the specified ones, which are determined based on the results of full-scale tests.

The broadband random vibration test method allows you to reproduce those numerical vibration characteristics of operating conditions that affect the reliability of the product under test. The spectral density of vibration accelerations was taken as a similarity criterion, since the probability of a product failure or disruption of its operating mode increases with an increase in the level of spectral vibration density.

The test program is specified in the form of a graph of the dependence of the spectral density on the frequency bands in which these measurements were carried out. This program is reproduced by a vibration stand at the control point of the product using energy spectrum shapers, which in general represent a source of a broadband random signal or white noise and a set of adjustable bandpass filters.

Narrowband random vibration test. The varying narrowband random vibration mode is intermediate between the wideband random vibration mode and the varying sinusoidal signal mode. The method is based on replacing the excitation of a broadband low-acceleration density with the excitation of a narrow-band high-acceleration density that slowly changes over a certain portion of the frequency range.

When properly adjusted, the method provides the same number of most important accelerations at a given level as the broadband vibration method. To reproduce the resonance conditions and loading of the test sample, narrowband vibration must have the same characteristics as broadband vibration. It is also necessary that the number of changes in the sign of the acceleration for any increase in the voltage level be the same.

This method has the following advantages:

1) the ability to obtain significant load levels using less powerful equipment;

2) the possibility of using simpler control equipment and, consequently, the use of less qualified personnel.

The main tasks are to determine the law of change in average frequency over time and the law of change in vibration depending on frequency. When determining these laws, they are based on the equivalence of narrow- and broadband random vibration tests. Such equivalence, for example, is established in fatigue strength tests, which require identical distribution of maximum and minimum loads under narrow- and broadband vibration. Identity occurs in the case when the average frequency f changes according to a logarithmic law, and the root-mean-square value of vibration acceleration is proportional to the square root of the frequency. For the convenience of assigning a test mode, a parameter γ is introduced, which is called the acceleration gradient:

where σ y is the root-mean-square value of vibration overload (in terms of acceleration in units of g = 9.81 m×s 2) with narrow-band excitation. If σ y must be proportional to , then the acceleration gradient in narrowband vibration tests is a constant value.

The test time for a logarithmic frequency change is determined as

where f y and f m are the testing time for narrow- and broadband vibration; p - scale factor; f in and f and are, respectively, the highest and lowest frequencies of the range in which scanning is performed. To reproduce the conditions of broadband vibration with uniform spectral density S 0 in the frequency band f in and F n (Fig. 2.25), the acceleration gradient is calculated using the formula

where kcf is the average transmission coefficient of the vibration system;

H 0 (p) - ee transfer function.

From expressions (2.52) and (2.53) it is clear that the narrow-band vibration test mode is determined by the coefficients p and q. The coefficient q can vary from 1.14 (for simple tests) to 3.3 (for accelerated tests).

The coefficient p varies accordingly within the range of 0.65 - 0.025.

In Fig. Figure 2.25a shows the spectral densities of narrowband and broadband vibrations. The slope of the dashed line (tgα), which determines the rate of increase in the spectral density as the average frequency f changes, is equal to the square of the acceleration gradient.

An important feature of such tests is the ability to automatically control the level of vibration loads (Fig. 2.25.6).

A narrow-band random process with a time-varying central frequency / is obtained using a white noise generator and an accompanying filter, the central frequency of which is changed by a frequency scanning drive (FSD). The rotation speed of the PSCh is adjustable within wide limits. The RMS value of narrow-band vibrations at the output of the vibration system is stabilized with the help of an automatic gain control (AGC) system. Signal back! communication, the AGC comes from the output of the vibrometric equipment (VA).

The increment of the root mean square value of the signal, proportional to the nal one, corresponds on a logarithmic scale to a slope of 3 dB per octave. Therefore, at the VA output (before the AGC input), a filter is turned on with an attenuation of 3 dB per octave. This ensures the constancy of the acceleration gradient when scanning the average frequency.

WHAT IS RANDOM VIBRATION?

If we take a structure consisting of several beams of different lengths and begin to excite it with a sliding sinusoid, then each beam will vibrate intensely when its natural frequency is excited. However, if we excite the same structure with a broadband random signal, we will see that all the beams will begin to sway strongly, as if all frequencies were simultaneously present in the signal. This is true and at the same time not true. The picture will be more realistic if we assume that for some period of time these frequency components are present in the excitation signal, but their level and phase change randomly. Time is the key point in understanding a random process. In theory, we should consider an infinite period of time to have a true random signal. If the signal is truly random, then it never repeats.

Previously, to analyze a random process, equipment based on bandpass filters was used, which isolated and evaluated individual frequency components. Modern spectrum analyzers use a Fast Fourier Transform (FFT) algorithm. A random continuous signal is measured and sampled in time. Then, for each time point in the signal, sine and cosine functions are calculated, which determine the levels of the frequency components of the signal present in the analyzed signal period. Next, the signal is measured and analyzed for the next time interval and its results are averaged with the results of the previous analysis. This is repeated until an acceptable averaging is obtained. In practice, the number of averagings can vary from two to three to several tens and even hundreds.

The figure below shows how the sum of sinusoids with different frequencies forms a signal of a complex shape. It may appear that the total signal is random. But this is not so, because the components have a constant amplitude and phase and vary according to a sinusoidal law. Thus, the process shown is periodic, repeatable and predictable.

In reality, a random signal has components whose amplitudes and phases vary randomly.

The figure below shows the spectrum of the sum signal. Each frequency component of the total signal has a constant value, but for a truly random signal, the value of each component will change all the time and spectral analysis will show time-averaged values.

frequency Hz V well 2 (g well 2)

The FFT algorithm processes the random signal during the analysis time and determines the magnitude of each frequency component. These values ​​are represented by root mean square values, which are then squared. Since we are measuring acceleration, the unit of measurement will be the overload gn sq, and after squaring it will be gn 2 sq. If the frequency resolution in the analysis is 1 Hz, then the measured quantity will be expressed as the amount of acceleration squared in a frequency range 1 Hz wide and the unit of measurement will be gn 2 /Hz. It should be remembered that gn is gn well.

The unit gn 2 /Hz is used in the calculation of spectral density and essentially expresses the average power contained in a frequency range 1 Hz wide. From the random vibration test profile, we can determine the total power by adding the powers of each 1 Hz wide band. The profile shown below has only three 1Hz bands, but the method in question can be applied to any profile.

frequency Hz (4 g 2 /Hz = 4 g rms 2 in each 1 Hz wide range) Spectral density, g rms 2 /Hz g sq g sq g well 2 g well 2 g sq g well 2 g 2 /Hz

The total acceleration (overload) gn of the RMS profile can be obtained by addition, but since the values ​​are root mean square, they are summed up as follows:

The same result can be obtained using a more general formula:

However, the random vibration profiles currently used are rarely flat and more like a cross-section of a rock mass.

Spectral density, g rms 2 /Hz (log scale) dB/oct. dB/oct. Frequency, Hz (log scale)

At first glance, determining the total acceleration gn of the shown profile is a rather simple task, and is defined as the root-mean-square sum of the values ​​of the four segments. However, the profile is shown on a logarithmic scale and the slanted lines are not actually straight. These lines are exponential curves. So we need to calculate the area under the curves, which is a much more difficult task. We will not consider how to do this, but we can say that the total acceleration is equal to 12.62 g rms.

Test methods for resistance to mechanical external
influencing factors of machines, devices and other technical products

VIBRATION TESTS WITH SEVERAL TYPES OF IMPACTS

IEC 60068-2-80:2005
Environmental testing - Part 2-80: Tests - Test Fi: Vibration - Mixed mode
(MOD)

Moscow Standardinform 2009

Preface

The goals and principles of standardization in the Russian Federation are established by Federal Law of December 27, 2002 No. 184-FZ“On technical regulation”, and the rules for applying national standards of the Russian Federation - GOST R 1.0-2004“Standardization in the Russian Federation. Basic provisions"

Standard information

1 PREPARED by the Open Joint-Stock Company “Scientific Research Center for Control and Diagnostics of Technical Systems” (JSC “NIC KD”) based on its own authentic translation of the standard specified in paragraph 4

2 INTRODUCED by the Technical Committee for Standardization TC 183 “Vibration and Shock”

3 APPROVED AND ENTERED INTO EFFECT by Order of the Federal Agency for Technical Regulation and Metrology dated December 18, 2008 No. 640-st

4 This standard is modified from the international standard IEC 60068-2-80:2005 “Tests for exposure to external factors. Part 2-80. Tests. Fi test. Vibration combining effects of different types" (IEC 60068-2-80:2005 "Environmental testing - Part 2-80: Tests - Test Fi: Vibration - Mixed mode") by introducing technical deviations, the explanation of which is given in the introduction to this standard.

The title of this standard has been changed from the title of this international standard to comply with GOST R 1.5-2004(clause 3.5)

5 INTRODUCED FOR THE FIRST TIME

Information about changes to this standard is published in the annually published information index “National Standards”,A text of changes and amendments- in the monthly published information indexes “National Standards”. In case of revision (replacement) or cancellation of this standard, the corresponding notice will be published in the monthly published information index “National Standards”. Relevant information, notices and texts are also posted in the public information system- on the official website of the Federal Agency for Technical Regulation and Metrology on the Internet

Introduction

This standard establishes a test method for vibration strength and vibration resistance of machines and equipment of all types, which during operation are exposed to broadband vibration of complex shapes.

The test method uses digital control systems to produce broadband random vibration in combination with harmonic and/or narrowband random vibration. To implement this method, mainly electrodynamic or hydraulic vibration stands are used.

The results of vibration tests depend on the qualifications of the personnel conducting them, which should be known to both the customer and the test performer. When drawing up a test procedure, vibration impacts of those types that correspond to the actual conditions of use of the product should be indicated as reproducible excitation.

In comparison with the international standard IEC 60068-2-80:2005, this standard has been supplemented with references in italics and indicating its place in the set of GOST 30630 standards, united by the general group heading “Test methods for resistance to external influences of machines, devices and other technical products "

NATIONAL STANDARD OF THE RUSSIAN FEDERATION

Date of introduction - 2010-01-01

1 area of ​​use

This standard applies to machines, instruments and other technical products of all types (hereinafter referred to as products) and establishes test requirements to verify their ability to withstand the effects of broadband vibration of complex shapes.

The purpose of the tests is to confirm the ability of the product to withstand vibration impacts established by standards or technical specifications for products (hereinafter referred to as regulatory documents), without significant damage (vibration strength tests) and deterioration of its operational characteristics (vibration resistance tests). In this case, it is recommended to use measurement data carried out in real conditions of use of the product when specifying reproducible vibration.

Tests carried out in accordance with this standard are capable of detecting fatigue damage resulting from exposure to complex broadband vibration to assess the suitability of the product. In addition, this standard may be used to demonstrate the mechanical strength of a product's design.

This standard is intended for use when testing samples of products that, during transportation or operation (for example, on an aircraft or spacecraft) may be subject to random vibration in combination with other types of random or deterministic influences, as well as when testing products in transport container, if the latter can be considered as an integral part of the product,

This standard is used in conjunction with GOST 30630.0.0, which establishes general requirements for testing for exposure to external factors.

2 Normative references

This standard uses normative references to the following standards:

3.9.1 average control averaging strategy: A method of determining the control signal by averaging each frequency component over all test points.

3.9.2 control By extreme value(extremal strategy): A method of determining a control signal by selecting an extreme value of the controlled parameter for each frequency component across all test points.

3.10 MAX/SUM: A method for specifying the spectral acceleration density (see 3.14) for narrowband random vibration reproduced under test conditions against a background of broadband random vibration.

Note - MAX means that the spectral acceleration density of the reproduced signal is an envelope of the superimposed spectral acceleration densities of broadband and narrowband random signals; SUM means that the spectral acceleration density of the reproduced signal is the sum of the spectral acceleration densities of broadband and narrowband random signals.

3.11 crest factor(crest factor): The ratio of the peak value to the root mean square value of the signal.

3.12 superposition strategy(super positional strategy): A strategy that defines a method for calculating the acceleration spectral density of the reproduced vibration for each frequency component from a given harmonic signal and the acceleration spectral density of a random signal.

3.13 peak width at minus level 3 dB(-3 dB bandwidth): The bandwidth between two points in a frequency response located at 0.708 of its maximum value, assuming that the frequency response in that frequency band describes the peak of a single resonance.

3.14acceleration spectral density (acceleration spectral density); SPU: A function of frequency, defined as the limiting ratio of the mean square value of the acceleration signal after it passes through a narrow-band filter, the geometric mean frequency of which coincides with the given one, to the filter bandwidth as the bandwidth tends to zero and the averaging time tends to infinity.

3.15 bias(bias error): Systematic error in estimating the acceleration spectral density of a random signal or the amplitude of a harmonic signal.

Note - For a random signal, the displacement is due to the finite frequency resolution of the signal, which is inherent in the processing method used, and for a harmonic signal (mixed with random noise) - to the finiteness of the averaging interval.

3.16 control signal acceleration spectral density control acceleration spectral density: Spectral acceleration density of the signal measured at a control point (real or imaginary).

3.17 control circuit(control system loop): An electronic path that allows you to perform a combination of the following operations:

Digitization of the signal at the control point;

Signal processing procedure;

3.20 Acceleration spectral density reproduction error(error acceleration spectral density): The difference between the specified acceleration spectral density and the acceleration spectral density of the control signal.

3.21 correction(equalization): A procedure for minimizing the error in reproducing the spectral density of acceleration.

3.22 roll off at high frequencies(final slope): Section of a given spectral acceleration density at frequencies higher f 2(see Figure 1).

3.23 frequency resolution(frequency resolution): The width of the frequency increment interval in terms of acceleration spectral density (expressed in hertz).

Note - This value is inversely proportional to the length of the signal record used in digital analysis. The number of increment intervals coincides with the number of spectral lines in a given frequency range.

3.24 observed acceleration spectral density indicated acceleration spectral density: An estimate of the acceleration spectral density at the analyzer's reading device, including instrumental error, random error, and offset.

3.25 roll off at low frequencies(initial slope): Section of a given spectral acceleration density at frequencies below f 1(see Figure 1).

3.26 instrumental error(instrumental error): The totality of errors introduced by each analog device of the input part of the control system and each analog device as part of the control system.

3.27 random error(random error): The error in estimating the acceleration spectral density, varying from one measurement to another and due to the finite signal averaging time and finite filtering bandwidth.

3.28 signal recording(record): A set of process samples taken at regular intervals, which is used when implementing the fast Fourier transform procedure.

3.29 reproducibility(reproducibility): The closeness of the results of measurements of the same quantity with the same value, carried out:

By different methods;

Using different measuring instruments;

Different operators;

At different points in time, the interval between which is significantly greater than the time of one measurement;

Different ways of using available testing and measurement tools.

Note - The term “reproducibility” is also used in cases where only one or more of the above conditions are taken into account.

3.30 rms value(root-mean-square value): The square root of the mean value of the square of the function over a given interval (for spectral density, this interval is the frequency band between f 1 And f 2- cm. ).

Note - In this test method, the root mean square value can be calculated for different types of excitation: a purely broadband random process, a combination of broadband random and harmonic processes ( SoR ) or a set of two random processes ( RoR ) - see (Appendix B).

3.31 controlled parameter(signal value): The value of the acceleration spectral density for the random component of the reproducible process or the amplitude for the harmonic component of the reproducible process.

3.32 standard deviation(standard deviation): Characteristic of a random time signal, which for a vibration signal coincides with the root-mean-square value (since the average value of the vibration signal is taken equal to zero).

3.33 statistical accuracy(statistical accuracy): The ratio of the true acceleration spectral density to the observed one.

Note - This characteristic is applied only to the random component of the reproducible process.

3.34 statistical degree of freedom(statistical degrees of freedom): A quantity characterizing the properties of the acceleration spectral density estimate obtained from random samples by the time averaging method, and depending on the frequency resolution and averaging time.

3.35 swing cycle(frequency) (sweep cycle): Move (sweep) through a given frequency range once in each direction (for example, from 5 to 500 Hz and back to 5 Hz).

Note - In contrast to the frequency sweep cycle, a single frequency sweep means movement across the frequency range in only one direction: towards increasing or decreasing frequency.

3.36 swing speed (frequency)(sweep rate): The rate of change in the frequency of a harmonic signal, measured in either octaves per minute (octave/min) or hertz per second (Hz/s).

3.37 true acceleration spectral density(true acceleration spectral density): Spectral density of acceleration acting on the sample.

4 General test requirements

4.1 Generalprovisions

The specified requirements for test equipment apply to all test equipment as a whole. In the case of an electrodynamic or hydraulic type vibration installation, this equipment includes a power amplifier, a vibration stand with a sample mounting device and a control system.

Vibration table vibrations in the given and transverse directions should either be checked before testing or controlled during testing using an additional channel in the control system. The regulatory document for testing must define the levels of reproduced vibration and the sequence of actions during testing.

The standardized test method includes the following steps (applied to excitation in each of the specified directions):

Exposure of the sample when exposed to vibration in a given mode;

Final measurements to re-determine the dynamic characteristics of the sample (see) and compare it with the result obtained at the initial measurement stage in order to identify possible mechanical damage.

If the dynamic behavior of the test object is well known or is not of interest, then the regulatory document may not establish requirements for the study of dynamic characteristics or establish them to a limited extent.

4.2 Control system

Test management requires the use of special software that allows data analysis and test control in different excitation modes.

The reproducible vibrations established by the regulatory document for testing at all points of attachment of the sample must be approximately the same and progressive. If the condition of identical vibrations at different attachment points cannot be met, multi-point test control is used.

The reproducible motion must have a Gaussian distribution for the random component and be harmonic for the periodic vibration component.

Transverse vibration is either checked before testing by exciting the sample with random or harmonic vibration, the level of which is established by a regulatory document, or is controlled during testing using an additional channel of the control system.

The value of the monitored parameter at each frequency at each test point and in each direction perpendicular to the direction of the main movement should not exceed the established value in the frequency range above 500 Hz, and in the frequency range up to 500 Hz should not exceed a level that is 3 dB below this set value. The rms value of the acceleration (over the entire frequency band) for any direction perpendicular to the specified direction of motion shall not exceed 50% of that value for the specified direction of motion. For example, for small-sized samples, a regulatory document may require that the value of the controlled transverse vibration parameter does not exceed the value of the same parameter for the reproduced movement, reduced by 3 dB.

For large specimens or large masses, it may be difficult to meet the lateral vibration limits over the entire test frequency range. Difficulties in meeting the established limits may also arise if the regulatory document requires testing to be carried out over a wide dynamic range. In this case, one of the following wordings must be used in the regulatory document: “lateral vibration exceeding a specified level must be recorded and indicated in the test report” or “lateral vibration control is not carried out.”

The sample must be fixed on the vibrating table in accordance with the requirements GOST 30630.0.0.

4.6 Measuring system

The characteristics of the measuring system must provide for the ability to verify the fulfillment of the condition that the true value of the vibration parameter at the control point in a given direction of movement does not exceed the established tolerance.

The accuracy of measurements is significantly influenced by the frequency response of the measuring circuit, which includes a vibration sensor, a matching device, and data collection and processing devices. The lower limit of the frequency range of the measuring system should not exceed 0.5 f 1, and the upper limit should not be less than 2 f 2(cm. ). In the specified frequency range, the amplitude-frequency response of the measuring system must be constant within ±5%.

5 Requirements for reproduced vibration

The test method specified in this standard involves exposing the specimen to broadband random vibration combined with either narrowband random vibration, harmonic vibration, or both. A regulatory document may stipulate that excitation by narrow-band random or harmonic vibration is carried out with a frequency swing in a given range. When conducting this type of testing, the following must be taken into account.

The regulatory document must establish a method for setting the degree of severity of test conditions for random vibration: MAX or SUM.

The acceleration spectrum can be:

Superposition of spectra of broadband random vibration, narrowband random vibration and harmonic components for control systems in which the harmonic signal is specified as a spectral line;

Superposition of spectra of broadband random vibration and narrowband random vibration, as well as independent harmonic oscillations for control systems in which a harmonic signal is generated continuously in the frequency domain.

Instrumental error in estimating the spectral density of acceleration at control and verification points in the frequency range from f 1 before f 2 should not exceed ±3 dB relative to the specified acceleration spectral density. This tolerance does not take into account random error and offset. The random error characteristics can be calculated from the test results.

RMS acceleration value in the range from f 1 before f 2, measured directly or obtained by calculation, should not differ by more than ±10% from the root mean square value for a given spectral acceleration density. This applies to the signal at both the real and imaginary test point.

These requirements may be difficult to meet at certain frequencies or for large samples or large masses. In this case, the regulatory document may establish wider tolerance limits.

The decline in the spectral density of acceleration at low frequencies should be no less than plus 6 dB/octave, and at high frequencies - no more than minus 24 dB/octave [see. (Appendix B)].

For sweep tests, the tolerances for the frequency-varying spectral components shall be the same as for the broadband vibration components. However, this may not be feasible at high swing speeds. In this case, tolerances for spectral components must be established in a regulatory document.

The instantaneous acceleration value at the control point should be distributed according to a law close to Gaussian, as shown in Figure 2. Confirmation of this should be obtained during the system calibration process. The type of signal distribution in the presence of a harmonic component is shown in.

σ - standard deviation

Figure 2 - Random signal, close to normal, with a given cutoff level

The cutoff of the driving signal must be at a level of at least 2.5 rms value (see). It is necessary to ensure that the time waveform at the test point contains peaks that exceed the specified rms value by at least 3 times, unless otherwise specified by the relevant regulatory document.

If a signal at an imaginary test point is used for control, the above requirement for the crest factor value applies to all test points whose signals are used to generate the control signal.

The distribution probability density is calculated based on a two-minute signal realization at the control point at the beginning, in the middle and at the end of the tests.

Statistical accuracy is determined through the number of statistical degrees of freedom Nd and confidence level (see Figure 3). The statistical number of degrees of freedom is determined by the formula

Nd = 2B e T a,

Where V e- frequency resolution, Hz;

T a- effective averaging time, s.

Meaning Nd should not be less than 120, unless another requirement is established by the relevant regulatory document.

If the regulatory document establishes confidence levels that must be observed during testing, the data in Figure 3 should be used to calculate statistical accuracy.

Figure 3 - Statistical accuracy of reproduction of the spectral density of acceleration depending on the number of degrees of freedom for different values ​​of confidence probability

Frequency resolution B e, Hz, depends on the maximum clock frequency of the control system controller and the number of lines in the signal spectrum P:

B e = f high/n,

Where f hjgh- maximum clock frequency of the control system controller, Hz, which must be at least twice as high f 2(cm. );

P- the number of spectral lines evenly spaced over the frequency range up to f hjgh .

The frequency resolution must be established by a regulatory document [see. also , item h)].

1 - purely harmonic signal; 2 - harmonic and random (SPU - 0.1 m 2 / s 3) signals; 3 - harmonic and random (SPU - 1 m 2 / s 3) signals; 4 - harmonic and random (SPU - 5 m 2 / s 3) signals; 5 - purely random signal (SPU - 5 m 2 / s 3)

Figure 4 - Probability density distribution of harmonic (amplitude 50 m/s 2 , frequency 120 Hz) and random (in the range from 20 to 200 Hz) signals, as well as their combinations

5.1.4.1 Combination of wideband and narrowband random signals V e chosen in such a way that:

One of the spectral lines coincided with f 1, and the first spectral line was located no higher than 0.5 f 1;

Two spectral lines determined the shape of the decay of the spectral acceleration density of the narrowband signal.

If the above requirements give two different values V e, then choose the smallest of them.

Note - Selection IN einvolves a compromise between the desire to better describe the excitation spectrum and the need to ensure the speed of the control system. Additionally, increasing the sweep speed may require higher frequency resolution to maintain control over the entire sweep frequency range.

5.1.4.2 Combination of harmonic and random signals

INe are chosen so that one of the spectral lines coincides with f 1, and the first spectral line was located no higher than 0.5 f 1.

The frequency swing of the harmonic signal should, if possible, be continuous. For control systems in which the frequency of the harmonic signal changes abruptly, V e should be no more than 0.1% f high.

When sweeping the frequency of a harmonic component reproduced against a background of random oscillations, a digital tracking filter is usually used to estimate its amplitude. This filter allows you to cut off a significant part of the random component. However, in any case, the amplitude estimate will contain a portion of random noise at frequencies located near the frequency of the harmonic signal. In addition, the greater the ratio of the acceleration spectral density of the random signal to half the square of the amplitude of the harmonic signal (also called the power ratio), the greater will be the proportion of this random error. Reducing the tracking filter bandwidth will reduce the random error, but this is accompanied by an increase in the number of samples over which averaging is performed.

If the sample has a sharp, high-Q resonance, increasing the number of samples leads to a significant shift in the response estimate.

Tolerances on the amplitude of harmonic components acting against the background of random vibration must be greater than the total error, which includes random error, offset, control circuit error and instrumental error.

Studies of the frequency response of the sample are carried out over the entire test frequency range in accordance with GOST 30630.1.1.

6 Severity of test conditions

The severity of the test conditions is determined by a combination of the following parameters:

Test frequency range;

Broadband vibration acceleration spectral density values;

Broadband vibration acceleration spectral density curve shape;

Frequency ranges of narrowband random vibration;

Harmonic components of vibration;

Frequency swing speed;

Duration of exposure to vibration.

The specified parameters must be determined by the relevant regulatory document in one of the following ways:

By choosing from the values ​​given in 6.1 - ;

Based on the known operating conditions of the product, if they give significantly different parameter values.

Note - When determining the levels of random or harmonic vibration from recordings of real observations, attention should be paid to the fact that the data compression methods used could significantly distort the amplitude ratios of the signals.

The limit values ​​of the test frequency range, which must be determined by the regulatory document, are recommended to be selected from a range of.... 1; 2; 5; 10; 20; 50. Lower limit value f 1 should not be less than 1 Hz, and the upper limit value f 2 should not be more than 5000 Hz.

The acceleration spectral density value in the range between f 1 And f 2(cm.) in (m/s 2) 2 /Hz selected from the series ... 1; 2; 5; 10. The minimum value is 0.01, the maximum is 100.

Note - If the spectral density of acceleration is expressed in terms of the unit of gravity accelerationgP, then for the purposes of this standard we acceptgP = 10 m/s 2.

For this test, the shape of the acceleration spectral density curve is defined as a flat-top portion (see ). In special cases, it is allowed for the acceleration spectral density function to have a different form. In this case, the type of this function must be defined in a regulatory document. If the test frequency range is divided into subranges, in each of which the acceleration spectral density is specified as a constant value, then the boundaries of the subranges and the values ​​of the acceleration spectral density should be selected from the values ​​​​given in 6.1.1 and 6.1.2. The corresponding regulatory document must also define the types of curves on the acceleration spectral density graph connecting the constant levels of this function in adjacent subranges.

The duration of vibration exposure, in minutes (hours or days), which must be established by a regulatory document, is recommended to be selected from the range ... 1; 2; 5; 10. with permissible error + 5%.

The regulation must specify the number of random vibration bands added to the background broadband vibration.

For each lane you need to set the following:

a) bandwidth (this should be not less than 0.5% and not more than 10% of the frequency range of broadband random vibration). The lower limit of the frequency band should not lie below twice the frequency resolution;

b) lower and upper limits of the sweep cycle;

c) the swing speed in octave/min or Hz/s or the time it takes to complete one swing cycle;

d) number of swing cycles or duration of exposure to narrowband vibration;

e) law of frequency change: linear or logarithmic;

f) initial direction of frequency change (increasing or decreasing);

g) the value of the acceleration spectral density within the band;

h) the strategy (SUM or MAX) used in selecting the acceleration spectral density value of narrowband vibration when combined with broadband vibration.

The regulatory document must establish the number of harmonic components that must be excited against the background of broadband random vibration. For these harmonic components the following must be determined:

a) whether their frequencies are multiples of each other or not and what are the phase relationships between them.

Note - Phase relationships are determined for the driving signal, and they may differ from the phase relationships in the acceleration signal due to distortions introduced by the transfer functions of the vibration stand, the mounting device and the sample itself;

b) lower and upper limits of the sweep cycle;

c) swing speed in octave/min or Hz/s or time to complete one cycle,

d) the initial direction of the frequency change (increasing or decreasing), as well as the start and end time of the influence of each component;

e) dependence of the change in the amplitude of each component on frequency;

f) the number of swing cycles or duration of exposure to each harmonic component;

g) frequency change law: linear or logarithmic;

h) frequency values ​​when excited by harmonic vibration at fixed frequencies;

i) amplitudes of components at fixed frequencies.

If frequency sweep is not used, the parameters specified in items b), c), d), f) and g) are not specified. The regulatory document must indicate which method of excitation by harmonic vibration is used.

7 Initial stabilization

The need for initial stabilization of the sample under conditions of vibration excitation and the conditions for this excitation must be determined by the relevant regulatory document.

8 Initial measurements

The sample must be subjected to visual inspection, dimensional control and performance testing as prescribed by the relevant regulatory document.

9 Testing

Tests are carried out in the sequence established by the regulatory document and include the following stages:

Initial study (if necessary) of the frequency response of the sample;

Excitation by low level vibration to perform the required settings;

Exposure in the established vibration excitation modes;

Final study (if necessary) of the frequency response of the sample.

Unless otherwise specified by the regulatory document, the sample is excited in turn in each of the preferred directions of vibration. The order in which the direction of excitation is selected, unless specifically stipulated by a regulatory document, does not matter. If the sample is tested in a position characteristic of its operating conditions, then a method for installing the sample in this position must be established.

The control signal must be obtained from measurements at one test point for single-point control or at several test points for multi-point control.

In the latter case, the regulatory document must establish one of the following management methods:

By average value;

Based on the average value with correction;

By maximum or minimum value.

With any control method, the control race is imaginary.

If a product intended for operation with vibration isolators must be tested without them, then for this purpose the degree of severity of the test conditions is changed accordingly. The regulatory document may indicate how the degree of severity of test conditions carried out without vibration isolators should be changed.

If prescribed by regulation, conduct a frequency response study at at least one point on the sample. The number of points for which the frequency response should be determined must be indicated in the regulatory document.

The study of the frequency response can be performed by exciting the sample with harmonic or random vibration in the test frequency range in accordance with GOST 30630.1.1. The level of arousal must be defined in a regulatory document.

The vibration level when studying the frequency response is chosen so that the sample response is weaker than when exposed to vibration in the main test mode, but sufficient to detect critical frequencies.

If research is carried out by exciting harmonic vibration, then the rate of change in frequency should not exceed one octave per minute. To more accurately determine the shape of the frequency response, the swing speed can be reduced. Unreasonably prolonged excitation by vibration at one frequency should be avoided.

When testing with random vibration excitation, it should be kept in mind that the excitation time must be sufficient to minimize random variations in response. The frequency resolution must be sufficient to satisfactorily describe the shape of the resonant peak. It is recommended that there be at least five spectral lines per peak width at minus 3 dB.

A regulatory document may require that during a frequency response study the sample operates in a specified mode. If the functioning of the sample prevents the determination of vibration characteristics, then additional studies of the frequency response are carried out with the sample not working. As a result of the study, all critical frequencies of a given sample must be determined and reflected in the test report.

9.3 Excitation by low level vibration

Before testing in the main mode, it may be necessary to excite the sample with random vibration at a lower level for preliminary analysis and signal correction. At this stage it is important to keep the acceleration spectral density at a minimum level.

The duration of preliminary excitation by random vibration can be as follows:

At 12 dB RMS acceleration below the set value: no time limit;

With an rms acceleration value 6 - 12 dB below the established one: no more than 1.5 times higher than the established exposure time in the main test mode;

With an rms acceleration value 0 - 6 dB below the established one: no more than 10% of the established dwell time in the main test mode.

The duration of preliminary excitation by random vibration should not be subtracted from the established duration of exposure to vibration during the main test mode.

9.4.1 General provisions

Sometimes, under real operating conditions, a product is exposed to quasi-periodic vibration caused by the operation of machines whose components (rotor blades, gears, propellers, pistons, etc.) perform reciprocating or rotational motion. If this form of impact is dominant, then it is characterized by broadband random vibration with the superposition of narrowband vibration or harmonic oscillations of a higher level.

9.4.2 Excitation by narrowband and broadband random vibration (SoR)

The sample is excited by background broadband vibration with the superposition of one or more narrow-band random vibrations with a swing of geometric mean frequencies.

The degree of severity of test conditions in this mode is determined by the parameters set in and.

In some cases, excitation is carried out without frequency swing. Then tests of this type differ little from tests according to GOST 30630.1.9. The need to use frequency sweep must be specified in the regulatory document.

9.4.3 Excitation by harmonic and broadband random vibration (SoR)

The sample is excited by broadband random vibration with the superposition of one or more harmonic oscillations with a swing of their frequencies.

The degree of severity of test conditions in this mode is determined by the parameters established in 6.1 and.

In some cases, excitation is carried out without frequency swing. Then the parameters specified in items b), c), d), f) and g) of subsection 6.3 are not determined. The need to use frequency sweep must be specified in the regulatory document.

9.4.4 Excitation by harmonic, narrowband random and broadband random vibration (SoRoR)

Excitation of the sample in this mode is a combination of the conditions in 9.4.2 and 9.4.3. The method of excitation must be determined in detail by the relevant regulatory document.

If a regulatory document requires an initial study of the frequency response of a sample, it may also require that similar studies be carried out after completion of tests in the main mode to compare with the results of the initial study and identify possible changes and damage to the sample. The final study of the frequency response is carried out in exactly the same way, at the same points and with the same excitation parameters as the initial one. The actions that need to be taken when discrepancies between the results of the initial and final studies are identified must be determined by the relevant regulatory document.

10 Intermediate measurements

If a regulatory document establishes that a sample must function during testing, then the same document may establish the need to measure the performance characteristics of the sample during its operation.

11 Final stabilization

The regulatory document may require that the sample be given some time to recover its characteristics (for example, temperature) after testing before making final measurements.

12 Final measurements

The sample must be subjected to visual inspection, dimensional control and performance testing in accordance with the requirements of the relevant regulatory document.

The same document must establish the criteria for accepting or rejecting the sample.

13 Information provided in the relevant regulatory document

	Section or subsection of this standard
a) Reproducible movement*
b ) Specimen attachment points*
c ) Lateral vibration
d ) Sample installation*
E) Tolerances
f ) Crest factor (cutoff level of the driving signal)*
g ) Statistical accuracy
h ) Frequency resolution
i ) Test frequency range*
j ) Spectral density of acceleration of broadband random vibration*
k ) Shape of the acceleration spectral density curve*
l ) Duration of exposure to vibration*
m ) Narrowband random vibration
n ) Harmonic vibration and frequency swing speed
o) Pre-exposure
p) Initial measurements*
q ) Multipoint control
d) Directions of vibration influence
s ) Initial and final frequency response studies
t ) Exposure and control of functioning
u ) Intermediate measurements
v ) Recovery
w ) Final measurements*

14 Information given in the test report

The test report must contain at least the following information:

1) Customer	(name of organization, address)
2) Testing laboratory	(name, address)
3) Report ID	(date of compilation, number)
4) Test data
5) Test type	(SoR, RoR, SoRoR)
6) Purpose of testing	(development tests, acceptance, etc.)
7) Test standard	(corresponding test method)
8) Description of the sample	(model, number, drawing, photo, parameters)
9) Sample installation	(type of fastening, drawing, photo, etc.)
10) Characteristics of vibration installation	(lateral vibration, etc.)
11) Measuring system, sensor location	(description, drawing, photo, etc.)
12) Instrumental error	(results of verifications, dates of verifications)
13) Management strategy	(multipoint control, SUM/MAX)
14) Initial, intermediate, final measurements
15) Required degree of severity of test conditions	(according to test specifications)
16) Real degree of severity of test conditions	(measurement points, degrees of freedom, spectra)
17) Test results	(sample condition)
18) Observations and actions during testing
19) Resume
20) Person who carried out the tests	(initials, surname, signature)
21) To whom are the test results sent?	(list of persons receiving the test report)

Note - If test results must be recorded, for example, in chronological order, indicating test parameters, observations made during tests, actions taken and measurement tables, then in these cases, as a rule, a test log is kept. The test log may be attached to the test report.

Appendix A
(informative)
General information about tests with a combination of different types of vibration influences

A.1 General provisions

Test methods for random and harmonic vibration are established by GOST 30630.1.9 and GOST 30630.1.2, respectively. This appendix discusses the features of tests in which a combination of the two indicated types of influences is used. Currently available digital control systems allow the implementation of the most complex control strategies for all possible combinations of random and harmonic signals. For example, the frequencies of different harmonics (as well as the geometric mean frequencies of narrow-band random processes) when the frequency swings can move towards each other and intersect. This complicates the mathematical description of processes and makes it difficult to ensure the required control accuracy, which requires making some compromise decisions.

A.2 Combination of wideband and narrowband (with a fixed geometric mean frequency) random signals

Vibration of this type is essentially no different from broadband random vibration considered in GOST 30630.1.9 and does not require modification of the test method.

Tolerances for narrowband spectra remain unchanged. Only the areas where the narrowband and broadband spectra intersect may require additional consideration. If these areas contain only one or two spectral lines, and the difference between the acceleration spectral density levels for broadband and narrowband vibration is large, then the tolerances in these areas may be increased to facilitate the reproduction of the required vibration, which should be reflected in the test report.

A.3 Combination of wideband and narrowband (frequency sweep) random signals

The main control problem when exciting this type of vibration is the need to coordinate the swing speed and the effective averaging time in the feedback circuit. If the swing speed is high and the averaging time is long, then the effect of blurring of spectral lines is observed, when energy from one spectral line “flows” into neighboring ones. In this case, the rectangular shape of the spectrum of the narrow-band signal is lost, and the control system can stop the test due to the fact that a number of spectral lines go out of tolerance.

The control system, forming a new spectral acceleration density at the output, performs averaging, for example exponential, over a sample of values ​​from the previous signal, which allows for control stability. The number of degrees of freedom taken into account depends on the gain in the feedback circuit - the lower its value, the longer the time interval required for a significant change in the estimate, i.e. the more stable the system works.

When sweeping a narrowband signal, the previous signal values ​​sampled by the estimation algorithm may be high enough to cause the acceleration spectral density estimate to exceed tolerance limits, causing the test to stop. This can be avoided by increasing the feedback ratio, which is equivalent to reducing the number of values ​​being averaged (reducing the effective averaging time in the feedback circuit), but this may result in loss of control stability.

Thus, in each specific case, it is necessary to determine some compromise value regarding the feedback coefficient.

If the laboratory has the appropriate equipment, it may be useful to record the vibration signal at the control point for its subsequent processing using various spectral analysis algorithms. This, of course, will not change the conditions of the tests that have already been completed, but will make it possible to clarify exactly what test conditions were implemented with the subsequent reflection of these conditions in the test report.

A.4 Combination of a wideband signal with a harmonic signal at a fixed frequency

Isolation by a control system of the harmonic component of a signal from its mixture with a broadband signal in general form is a difficult task. This task will be easier if the ratio of the amplitude of the harmonic signal to the rms value of the random signal is large. As this ratio decreases, the accuracy of the harmonic component can deteriorate, as shown in the following example.

Example - Three types of digital control systems were used for the study. The test parameters were unchanged in all cases.

Random vibration:

- frequency range: 10- 2000 Hz,

-acceleration spectral density level (constant): 0.005; 0.01;0.05 /Hz,

- frequency resolution (maximum possible): 1 Hz,

- number of degrees of freedom (maximum possible): 120,

Harmonic vibration:

- amplitude: 5 g n,

- frequency: 20; 160; 380 Hz.

During tests at a constant frequency of harmonic vibration, excitations were used at all possible combinations of acceleration spectral density level and harmonic signal amplitude for 60 s each.

The output of the control system was fed to a digital recorder with a sampling rate of 12.5 kHz. These data were transferred to a computer to calculate the spectral acceleration density. The following parameter values ​​were used in the computer analysis:

- frequency range: 10 - 2000 Hz,

- frequency resolution: 1 Hz,

- number of degrees of freedom: 120,

- sampling duration: 60 s.

Examples of calculating the acceleration spectral density graph for one of the control systems and different frequencies of excitation by harmonic vibration are shown in Figures A.1 and A.2.

Figure A.1 - Harmonic signal at a frequency of 160 Hz

Figure A.2 - Harmonic signal at 380 Hz

Table A.1 shows the acceleration spectral density at the geometric mean frequency of the frequency range for all measurements. Based on these values, the root-mean-square acceleration values ​​are calculated and the last column shows their deviations, as a percentage, from the theoretical value. This deviation can characterize the quality of reproduction of harmonic excitation. Since only RMS values ​​are compared, no conclusions can be drawn about the quality of the sine waveform reproduction.

To obtain information about how significant the deviation from periodicity is in the excited harmonic signal, the autocorrelation function was calculated for each 5-second interval of the vibration signal. Examples of such calculations for two different levels of background random noise are shown in Figure A.3.

1 - SPU:0.01 /Hz; 2 - SPU:0.005 /Hz

Figure A.3 - Autocorrelation function for a mixture of random noise with a harmonic signal at a frequency of 160 Hz

Table A.1 - Estimated spectral density of acceleration at the frequency of a harmonic signal in its mixture with a broadband random signal

Control system	/Hz	frequency Hz	RMS acceleration value,g n	Relative error, %
	0,005		3,56
			3,56
			3,56
	0,01		3,54
			3,57
			3,54
	0,05
			3,58
			3,56
	0,005		3,49
			3,52
			3,51
	0,01		3,49
			3,52
			3,53
	0,05		3,55
			3,53
			3,51
	0,005		3,51
			3,53
			3,54
	0,01
			3,54
			3,52
	0,05		3,52
			3,51
			3,58
			3,53
			3,54

After this, for each measurement the squared amplitudes were determined for time 5 T autocorrelation function, where T- period of the harmonic signal. These values ​​are shown in Table A.2. Deviations, as a percentage, from the theoretical value are given in the last column of this table.

Table A.2 - Estimated autocorrelation function A for a mixture of harmonic and wideband random signals

Control system	SPU of the broadband component, /Hz	frequency Hz	T, With	A 2 (5T),	Relative error, %
	0,005		0,05	12,45
			0,00624	12,71
			0,00264	12,65
	0,01		0,05	12,67
			0,00624	12,88
			0,00264	13,11
	0,05		0,05	13,37
			0,00624	11,98
			0,00264	13,23
	0,005		0,05	12,0
			0,00624	12,32
			0,00264	12,19
	0,01		0,05	11,97
			0,00624	12,85
			0,00264	12,3
	0,05		0,05	12,33
			0,00624	11,69
			0,00264	13,23
	0,005		0,05	12,14
			0,00624	12,3
			0,0028	12,33
	0,01		0,05	12,21
			0,00624	12,47
			0,0028	12,07
	0,05		0,05	12,01
			0,00624	13,63
			0,0028	10,71	14,3
Master harmonic signal (real)			0,05	12,37
			0,00624	12,48
			0,00277	12,49
			0,00262	12,49
Master harmonic signal (theoretical)			0,05	12,5
			0,00625	12,5
			0,00278	12,5
			0,00263	12,5

Such calculations are applicable only in the case when excitation occurs at a fixed frequency that exactly coincides with one of the spectral lines. If there is no such coincidence, then a power leak of the spectral peak is observed, which can reach 17% when this frequency falls exactly in the middle between the spectral lines. However, such an error is systematic and can be compensated using appropriate algorithms.

A.5 Combination of a wideband signal with a sweeping harmonic signal

What is stated in section A.4 also applies to this type of vibration. Moreover, if the frequency of the harmonic signal changes, a significant additional error may appear, mainly associated with the acceleration spectral density averaging algorithm, the use of which is designed only for a purely random signal. This algorithm does not allow estimating the amplitude of the harmonic component of a changing frequency. Therefore, it may be necessary to carry out an analysis in which the isolation of the harmonic component would be a separate step.

A.6 Combination of wideband and narrowband random signals with harmonic signals at fixed and varying frequencies

This form of excitation represents the most difficult case for analysis, since additional complexity is added not only by possible intersections of changing frequencies of harmonic components, but also by intersections of narrow-band components of a random signal.

It is recommended to use this type of stimulation only in cases of extreme necessity and only with the participation of experienced and qualified specialists. Otherwise, the reliability and reproducibility of test results may be questioned.

Ensuring reproducibility of test results is a challenging task. Due to the statistical nature of the random signal, the complex response of the sample, and the uncertainties of the analysis, it is impossible to predict with certainty whether the true acceleration spectral density applied to the sample will match the observed acceleration spectral density within specified tolerances. This requires complex and time-consuming analysis that cannot be performed in real time.

The characteristics of most digital control systems that can be used to conduct tests with a combination of vibration influences of different types are similar. By varying several selectable parameters of the control system, it is possible to obtain estimates of the statistical accuracy of the reproduced motion, characterized by the difference between the true and observed spectral acceleration densities. The final choice should allow this difference (without taking into account other sources of error) to be reduced to a minimum.

Correction of the initial acceleration spectral density is a recurrent procedure implemented using the feedback loop of the control system. Moreover, the effective signal averaging time in this procedure depends on several factors, such as the composition of the equipment, the transfer function of the system as a whole, the shape of the specified spectral acceleration density, the control algorithm and test parameters that must be selected before conducting these tests. Specified test parameters include maximum analysis frequency, frequency resolution, and signal cutoff level.

The random vibration control algorithm must provide a compromise between control accuracy and effective signal averaging time (the speed of the feedback circuit). High control accuracy implies an increase in the number of data used in the recurrent procedure and, accordingly, a decrease in the speed of the feedback circuit, i.e. slowing down the response to changes in the actual spectral density of acceleration. The control accuracy and speed of the feedback circuit are also affected by the selected frequency resolution. Typically, increasing the frequency resolution leads to increased control accuracy, but reduces the speed of the feedback circuit. To reduce the discrepancy between the true and observed spectral acceleration densities, it is necessary to select the optimal values ​​of the above parameters.

Studies of the frequency response of a sample provide important information about the nature of the interaction between the sample and the vibration stand. For example, such a study may reveal excessive vibration amplification by the sample holding device or a coincidence of resonances between the sample and the holding device.

This appendix primarily addresses issues related to the random component of excitation. Regarding the harmonic component of excitation (frequency swing, swing speed, use of tracking filters), you can follow the recommendations of GOST 30630.1.2.

B.2 Test requirements

B.2.1 Single-point and multi-point control

B.2.1.1 General

Compliance with test requirements is verified based on the values ​​of the controlled parameter obtained as a result of signal processing at the test point.

For rigid or small samples, such as equipment components, and if it is known that the influence of a sample rigidly mounted on a vibration stand on the dynamics of the system in the test frequency range is small, it is sufficient to perform measurements at one test point, which thereby becomes the control point dot.

In the case of large samples or complex shapes with widely spaced attachment points, one of the test points or an imaginary control point is used for control. In the latter case, the spectral acceleration density is calculated from signals at several test points. For complex or large samples, it is recommended to use signal control at an imaginary control point (see ).

B.2.1.2 Single point control

Measurements are carried out at one control point, and the value of the controlled parameter at each frequency is directly compared with the specified value.

B.2.1.3 Multipoint control

B.2.1.3.1 General

If it is necessary to implement multipoint control, choose one of two control strategies.

B.2.1.3.2 Average value control

This control strategy involves calculating the controlled parameter at each frequency for each test point, after which the arithmetic average over all test points is found for the calculated values ​​at each frequency.

The resulting arithmetic average values ​​are compared with the specified values ​​of the controlled parameter at each frequency.

B.2.1.3.3 Extreme value control

When choosing this control strategy, the values ​​of the controlled parameter at each frequency are determined as the extreme value in the totality of these parameters obtained for the signals at all test points. Thus, the values ​​of the controlled parameter by which control is carried out represent an envelope of the values ​​of the controlled parameter obtained for all test points.

B.2.2 Probabilistic characteristics

B.2.2.1 Distribution of instantaneous values

Distribution of instantaneous χ values of the specifying random signal must satisfy the normal law described by the formula

Where p(χ)- probability density of distribution of the instantaneous value of the setting signal;

σ - root mean square value (standard deviation) of the setting signal.

The average value of the random vibration signal is assumed to be zero.

The probability density distribution for a population of random signals and a combination of narrowband and wideband random signals is shown in . The probability density function for a combination of harmonic and random signals is shown in .

B.2.2.2 Crest factor

The crest factor characterizes the distribution of the excitation signal as the ratio of the maximum instantaneous signal value to the standard deviation (see also Figure 2).

This parameter can only be used in relation to the reference signal generated at the output of a digital test control system, since non-linearities in the entire system, including the power amplifier, shaker, fixture and test piece, can distort the waveform at the test point. The influence of these nonlinearities in a wide frequency range is, as a rule, impossible to eliminate.

In accordance with this standard, the crest factor must be at least 2.5 (see also). If a normally distributed drive signal has a cutoff level of 2.5 standard deviations, then approximately 99% of the signal will reach the power amplifier without distortion.

This standard assumes that the acceleration spectral density has a rectangular shape (flat top) and all frequency components are located in the range between frequencies f 1 And f 2(cm. ). However, in practice, the excited signal has a decrease in the spectral acceleration density in the low and high frequency regions. In order for the RMS value to remain as close to the target value as possible, these slopes must be quite steep. Typically the roll-off slope in the low frequency region is 6 dB/octave. If the value of the spectral density of acceleration at a point f 1 is large and the test setup's displacement tolerances are limited, this may require increasing the roll-off slope in the low-frequency region. Displacement calculations for a random signal are given in B.2.4.

Typically, the dynamic range for two adjacent acceleration spectral density lines when using a digital test control system is 8 dB. To achieve a steeper rolloff, it may be necessary to increase the frequency resolution (i.e., reduce the V e). If this is not feasible, and if increasing the slope does not allow the displacement values ​​to be reduced to an acceptable level, consider reducing the lower tolerance limit for the acceleration spectral density at low frequencies.

In the high-frequency region, there are no problems with ensuring the steepness of the rolloff. At frequencies higher f 2 the slope should be minus 24 dB/octave or less.

The root mean square value of acceleration, speed or displacement in the effective test frequency range is the square root of the sum of the root mean squares of the values ​​of these quantities in the corresponding subranges. Each of these subranges is determined by the value of the spectral acceleration density for

The above formulas are valid if on the graph of the spectral acceleration density, where both coordinates are given on a logarithmic scale, the shape of the spectral acceleration density is formed by straight lines. In this case, the decline M can be determined by the formula

and the peak value (subscript amp) - according to the formula

a amp , MM =CFa r .m.s.,R+aamp.S,

Where CF- crest factor, usually taken equal to three.

B.3 Test procedure

The purpose of vibration testing is to demonstrate the ability of a product to withstand vibration and function properly under a specified level of vibration excitation. Such testing shall be continued only for a time sufficient to enable the sample to demonstrate the specified capabilities over the specified frequency range. The duration of the vibration test, which determines the ability of a specimen to withstand the cumulative effects of vibration, such as the accumulation of fatigue or mechanical deformation, should be sufficient to provide the required number of cycles of changes in mechanical stress, even if the test duration does not meet the requirements.

When testing for vibration effects, equipment that is installed on vibration isolators under normal operating conditions is usually tested together with vibration isolators. If it is not possible to test equipment with its own vibration isolators, for example, if this equipment is mounted together with other equipment using a common fastening, it is permissible to carry out tests without vibration isolators, but under a different degree of severity of the test conditions, which must be defined in the relevant regulatory document. The degree of severity of the test conditions is adjusted taking into account the transfer properties of the vibration isolating system in each direction of vibration excitation. If the characteristics of vibration isolators are unknown, recommendations B.4.1 should be followed.

The appropriate regulatory document may require additional testing of the sample with the external vibration isolators removed or blocked to demonstrate compliance with certain minimum vibration resistance requirements. In this case, the regulatory document must indicate the degree of severity of the test conditions.

B.4 Equipment intended for use in conjunction with vibration isolators

B.4.1 Transfer properties of vibration isolators

Products that are installed on vibration isolators during operation can be tested without them, in particular when the dynamic characteristics of vibration isolators are unstable (for example, they change with temperature). In this case, the severity of the test conditions should be reduced taking into account the range of changes in the transmission coefficient of vibration isolators. When correcting the degree of severity of test conditions, the lower limit of the range for each direction of vibration is taken into account.

If there is no data on the transfer properties of vibration isolators, then the degree of severity of the test conditions should be the subject of agreement between the contractor and the customer.

B.4.2 Effect of temperature

Many vibration isolators contain materials whose properties depend on temperature. If the natural resonant frequency of a vibration isolator sample falls within the test frequency range, care should be taken in determining the dwell time during which a given excitation will be applied to the sample. In some cases, it is not advisable to subject the sample to prolonged excitation and breaks should be provided for its recovery. If the actual distribution of excitation time of a product at a given resonant frequency during operation is known, one should try to simulate it during testing. If this distribution is unknown, then tests should be carried out by limiting the duration of the excitation periods to avoid excessive heating of the sample.

B.5 Severity of test conditions

The specified test frequency ranges, spectral densities of acceleration of broadband and narrowband vibration, amplitudes of harmonic signals must be selected in such a way as to cover a wide range of conditions for the practical use of the product. If the product is intended to be used under strictly defined conditions, it is advisable to set the degree of severity of the test conditions based on the actual characteristics of the vibration impact under these conditions (when such characteristics are known).

If possible, the degree of severity of the test conditions should be selected, which is related either to the impacts to which the product may be subjected during transportation or operation, or to the design requirements for the product, if the purpose of the tests is to evaluate its strength properties.

When determining the degree of severity of test conditions, it is necessary to assess whether there is a need to prescribe them “with a margin” compared to the effects in real conditions of use.

AT 6 Equipment characteristics

The normative document may require that the sample perform during either all or part of the test as it would normally perform in practice.

If vibration can affect the on and/or off operations, for example by interfering with the operation of a relay, these operations should be performed several times during the test to ensure that they are performed reliably.

If the sole purpose of the test is to verify the resistance of a product to a specified vibration, then the functionality of the sample is assessed after completion of the test.

B.7 Initial and final measurements

Initial and final measurements are carried out to assess how the sample was affected by the vibration created during the testing process.

In addition to visual inspection, these steps may include electrical and mechanical measurements.

Keywords: vibration, vibration tests, vibration strength, vibration resistance, machines, instruments, measurements, frequency response, degree of severity of test conditions, broadband random vibration, narrowband random vibration, harmonic vibration

Depending on the nature of the vibrations, they differ:

deterministic vibration:

Changes according to the periodic law;

Function x(t), describing it, changes values ​​at regular intervals T(oscillation period) and has an arbitrary shape (Fig. 3.1.a)

If the curve x(t) changes over time according to a sinusoidal law (Fig. 3.1.b), then periodic vibration is called harmonic(in practice - sinusoidal). For harmonic vibration the following equation holds:

x(t) = A sin (wt), (3.1)

Where x(t)- displacement from the equilibrium position at the moment t;

A- displacement amplitude; w = 2pf- angular frequency.

The spectrum of such vibration (Fig. 3.1. b) consists of one frequency f = 1/T.

Fig.3.1. Periodic vibration (a); harmonic vibration and its frequency spectrum (b); periodic vibration as the sum of harmonic oscillations and its frequency spectrum (c)

Polyharmonic oscillation- a particular type of periodic vibration; :

Most common in practice;

A periodic oscillation by Fourier series expansion can be represented as the sum of a series of harmonic oscillations with different amplitudes and frequencies (Fig. 3.1.c).

Where k- harmonic number; - amplitude k- th harmonics;

The frequencies of all harmonics are multiples of the fundamental frequency of the periodic oscillation;

The spectrum is discrete (line) and is presented in Fig. 3.1.c;

It is often classified, with some distortions, as harmonic vibrations; the degree of distortion is calculated using harmonic distortion

,

where is amplitude i- harmonics.

Random vibration:

Cannot be described by precise mathematical relationships;

It is impossible to accurately predict the values ​​of its parameters at the nearest point in time;

It can be predicted with a certain probability that the instantaneous value x(t) vibration falls into an arbitrarily selected range of values ​​from to (Fig. 3.2.).

Fig.3.2. Random vibration

From Fig. 3.2. it follows that this probability is equal to

,

where is the total duration of the vibration amplitude in the interval during the observation time t.

To describe a continuous random variable, use probability density:

Formula ;

The type of distribution function characterizes the distribution law of a random variable;

Random vibration is the sum of many independent and slightly different instantaneous influences (subject to Gauss’s law);

Vibration can be characterized:

mathematical expectation M[X]– arithmetic mean of instantaneous values ​​of random vibration during the observation period;

general dispersion - the spread of instantaneous values ​​of random vibration relative to its average value.

If oscillatory processes with the same M[X] and differ from each other due to different frequencies, then the random process is described in the frequency domain (random vibration is the sum of an infinitely large number of harmonic oscillations). Here it is used power spectral density random vibration in the frequency band