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. When testing at the control points of the product, stationary random vibrations are excited. Their numerical characteristics should be close to the specified ones, which are determined by 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.

Narrow band 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 tests, which require the distribution of maximum and minimum loads to be identical for narrow-band and broad-band vibration. Identity takes place in the case when the average frequency f changes according to the logarithmic law, and the root mean square value of vibration acceleration is proportional to the square root of the frequency . For the convenience of setting the test mode, the parameter γ is introduced, which is called the acceleration gradient:

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

The test time for a logarithmic change in frequency is defined as

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

where k cf is the average transmission coefficient of the vibration system;

H 0 (p) - ee transfer function.

It can be seen from expressions (2.52) and (2.53) 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 with a change in the average frequency f, 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 center frequency / is obtained using a white noise generator and an accompanying filter, the center frequency of which is changed by a frequency sweep drive (FSF). The rotation speed of the PSCh is adjustable within wide limits. The RMS value of the 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.

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 t.

To describe a continuous random variable, use probability density:

Formula ;

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

Random vibration - the sum of many independent and little different instantaneous effects (obeys the Gauss 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

When testing for vibration effects, the following test methods are most widely used:

Fixed frequency sinusoidal vibration method;

Sweeping frequency method;

Broadband random vibration method;

Narrowband random vibration method.

Sometimes tests are carried out in laboratory conditions for the effects of real vibration.

Fixed Frequency Sinusoidal Vibration Tests carried out by setting specified values ​​of vibration parameters at a fixed frequency. Tests can be carried out:

At one fixed frequency;

At a number of mechanical resonance frequencies;

At a number of frequencies specified in the operating range.

Tests at one fixed frequency f(i) for a given time t p with a certain acceleration (displacement) amplitude are ineffective. Because the likelihood that a product during operation or transportation is exposed to vibration at one frequency is very small. This type of testing is carried out during the production process to identify poor-quality soldered and threaded connections, as well as other manufacturing defects.

Tests using the fixed frequency method at mechanical resonance frequencies. The products under test require preliminary determination of these frequencies. The product under test is sequentially exposed to vibration at resonance frequencies, maintaining it in each mode for some time. Dignity This method is that tests are carried out at frequencies that are most dangerous for the tested electrical system. Disadvantage is the difficulty of automating the testing process, since during testing the resonant frequencies may change slightly.

Tests at a number of specified frequencies in the operating range It is advisable to carry out to determine the characteristics of the product at points in the operating frequency range. Theoretically, the interval between two adjacent frequencies is chosen to be no greater than the width of the resonant characteristic of the structural element. This is done in order not to miss the possible occurrence of resonance. In case of detection of resonant frequencies or frequencies at which deterioration of the controlled parameters of the product is observed, an additional shutter speed at this frequency is recommended to clarify and identify the causes of the discrepancy.

Sweeping frequency testing are carried out by continuously changing the vibration frequency towards its increase and then decrease. The main parameters characterizing the sweep frequency method are:

Time of one swing cycle T c;

Swing speed nk;

Test duration T p.

An important indicator of the sweep frequency method is the speed of the frequency sweep. Based on the fact that the range of high vibration frequencies (1000...5000 Hz) is much wider than the range of low vibration frequencies (20...1000 Hz), it follows that when the frequency swings at a constant speed within the operating range, the low frequency region will pass in less time, than the high frequency region. As a result, detection of resonances at low frequencies will be difficult. Therefore, usually the frequency change within the operating frequency range is carried out according to an exponential law.

f in =f 1 ×e kt,(3)

Where f in– vibration frequency at time t, Hz; f 1– lower frequency of the operating range, Hz; k is an exponent characterizing the swing speed.

When choosing a high swing speed, the properties of the tested ES will be assessed with large errors, because the amplitude of the resonant oscillations of the product will reach lower values ​​than at low speed, and omissions (non-detection) of resonances are also possible. When choosing a low swing speed, prolonged passage of the operating frequency range may cause damage to the test product at resonant frequencies and increase the test duration. The rate of change of frequency must be such that the time of frequency change in the resonant frequency band t D f was no less than the time it took for the vibration amplitude of the product to rise at resonance to a steady-state value t nar and the time of final establishment of the moving part of the measuring or recording device t y. Those. The rate of change of frequency will be limited by the following conditions:

t D f > t nar,(4)

t D f > t y .

The time for the vibration amplitude to rise at resonance to a steady-state value can be approximately calculated using the formula:

t ad =k 1 ×Q/f 0, (5)

Where f 0 – resonant frequency, Hz; Q - quality factor of the product; k 1 – coefficient that takes into account the increase in the time of amplitude rise to a steady-state value as a result of deviation of amplitude changes from the linear law.

Taking into account all of the above, the rate of change of frequency is calculated using the formula:

n k =2000×lg(2×Q+1/2×Q)/t D f ,(6)

Where t D f - selected in accordance with conditions (4). If the rate of change of frequency found by the formula exceeds 2 octaves/s, then it is still accepted as 2 octaves/s - this is the maximum maximum rate of change of frequency.

Broadband random vibration testing. In this case, simultaneous excitation of all resonances of the test product is realized, which makes it possible to identify their joint influence. Tightening the test conditions due to the simultaneous excitation of resonant frequencies reduces the test time compared to the sweeping frequency method.

The severity of broadband random vibration testing is determined by a combination of the following parameters:

Frequency range;

Spectral acceleration density;

Duration of the test.

The degrees of cruelty are shown in Table 5.1.

Table 5.1

TO merits This method includes:

Proximity to mechanical stress during actual operation;

The ability to identify all the effects of mechanical influence of various structural elements;

Shortest test duration.

TO shortcomings concerns the high cost and complexity of the equipment being tested.

Narrowband random vibration testing. This method is also called the frequency band scanning random vibration method. Random vibration in this case is excited in a narrow frequency band, the central frequency of which, according to an exponential law, slowly scans across the frequency range during the test.

This method is a compromise between the wideband and swept sine wave test methods.

For the random vibration test to be equivalent to the frequency band scan test and the broadband random vibration test, the following condition must be met:

g=s/(2×pi×f) 1/2 =const,(7)

where g is the acceleration gradient, g×с 1/2; s is the root mean square vibration acceleration in a narrow frequency band, measured at the control point, g; f is the center frequency of the band.

The degree of test severity in this case is determined by a combination of the following parameters:

Frequency range;

Scanning frequency bandwidth;

Acceleration gradient;

Test duration.

The value of the acceleration gradient is found by the formula:

g=0.22×S(f) 1/2 ,(8)

Where S(f) is the spectral density of vibration acceleration when tested by the method of broadband random vibration.

Related information.

WHAT IS RANDOM VIBRATION?

If we take a structure consisting of several beams of different lengths and start to excite it with a sliding sinusoid, then each beam will oscillate 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 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. Theoretically, we must consider an infinite time period to have a true random signal. If the signal is truly random, then it never repeats.

Previously, for the analysis of a random process, equipment based on band-pass filters was used, which singled out and estimated individual frequency components. Modern spectrum analyzers use the Fast Fourier Transform (FFT) algorithm. A random continuous signal is measured and sampled in time. Then, for each time point of the signal, the 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 or three to several tens or even hundreds.

The figure below shows how the sum of sinusoids with different frequencies form a complex waveform. It may appear that the total signal is random. But this is not so, because the components have a constant amplitude and phase and change according to a sinusoidal law. Thus, the process shown is periodic, repetitive 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 calculating the spectral density and essentially expresses the average power contained in a 1 Hz frequency band. From the random vibration test profile, we can determine the total power by adding the powers of each 1 Hz band. The profile shown below has only three 1 Hz bands, but the method in question applies to any profile.

frequency Hz (4 g 2 /Hz = 4g rms 2 in each 1 Hz band) 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 profile RMS can be obtained by addition, but since the values ​​are root-mean-square, they are summarized as follows:

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

However, the random vibration profiles currently in use are rarely flat and more like a sectional rock mass.

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

At first glance, the determination of the total acceleration gn of the shown profile is a rather simple task, and is defined as the rms sum of the values ​​of the four segments. However, the profile is shown on a logarithmic scale and the oblique 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. How to do this, we will not consider, but we can say that the total acceleration is equal to 12.62 g RMS.

Spectral analysis is a signal processing method that allows you to identify the frequency content of the signal. There are known methods of vibration signal processing: correlation, autocorrelation, spectral power, cepstral characteristics, calculation of kurtosis, envelope. The most widely used spectral analysis as a method of presenting information, due to the unambiguous identification of damage and understandable kinematic dependencies 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 referred to as 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 reasons for the appearance 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" over 10 m/s 2 ( d). Bearing replacement should be carried out after the beginning of the decrease in the values ​​of the peak components. At the same time, 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) the 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 the broadband frequency range. New bearings generate low noise and almost imperceptible mechanical vibrations. As the bearing wears, so-called bearing tones begin to appear in vibration processes, the amplitude of which increases with the development of defects. 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 the rolling bearing and therefore form the basis of the analysis. As a measure of the technical condition in some programs, the amplitude modulation coefficient is used:

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

At the beginning of the development of defects on the “noise background”, bearing tones begin to appear, which increase as the defects develop by approximately 20 dB relative to the level of the “noise background”. At the later stages of the development of the defect, when it becomes serious, the noise level begins to increase and reaches the value 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 a 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 carry out band-pass 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 and a modulating signal is selected, which is fed to a narrow-band spectrum analyzer where the envelope spectrum is formed.

Small bearing defects are not able to cause noticeable vibrations in the low and medium frequencies generated by the bearing. At the same time, for the modulation of high-frequency vibrational noise, the energy of the resulting shocks is quite sufficient, the method has a very high sensitivity.

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

Envelope diagnosis of a rolling bearing makes it 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?