The intensity of vibration impacts depends on the frequency. As a consequence, the entire range of vibration frequencies is divided into segments (frequency bands) and vibration levels are determined for each band separately. Octave bands are taken as standard frequency bands when assessing vibration safety, in which the ratio of the upper cutoff frequencies to the low frequencies is 2. Each octave band is usually denoted by the geometric mean of its cutoff frequencies.

Here f min - lower, and f max - upper cutoff frequency (Hz).

The degree of vibration sensation is assessed according to the Weber-Fechner law by a logarithmic relative value - the level of vibration velocity L v in decibels.

Here V- effective root-mean-square value of vibration velocity, m / s; V 0 - threshold vibration velocity equal to 5 * 10 -8 m / s.

The root-mean-square vibration velocity is approximately 1.4 less than the amplitude value.

Taking into account the relationship between vibration velocity and vibration acceleration, the Weber-Fechner law can be applied to assess the degree of vibration sensation using the vibration acceleration level.

Here a- effective root-mean-square value of vibration acceleration, m / s; a 0 - threshold vibration acceleration equal to 3 * 10 -4 m / s.

Vibrations of machines and mechanisms are complex vibrations that can be represented by the sum of harmonic vibrations. Vibration, like noise, is characterized by a spectrum in octave bands that can be represented graphically.

Vibration classification

According to the method of transmission to a person, vibration is divided into two groups.

1. General, which acts on the body of a sitting or standing person and is estimated in octave bands f= 2, 4, 8, 16, 31.5; 63 Hz.

2. Local, which is transmitted through the hands at frequencies f = 8, 16, 31.5; 63, 125, 250, 500, 1000 Hz.

According to the source of occurrence, vibration is divided into three categories:

1. Transport (mobile machines on the ground).

2. Transport and technological (cranes, loaders).

3. Technological (jobs).

According to the duration of the action, vibration is divided into the following categories.

1. Constant. Here, the value of the monitored parameter changes by no more than two times during the observation time;

2. Fickle. Here, the value of the monitored parameter changes by more than 2 times during the observation time of at least 10 minutes when measured with a time constant of 1 s.

Intermittent vibration can be oscillatory, intermittent and impulsive.

2.8. Vibration. The impact of vibration on a person and its regulation

When exposed to high levels of vibration, painful sensations and pathological changes in the body occur.

1. Painful sensations are caused by the resonance of internal organs, pain in the lower back appears, and with local vibration - vasospasm, numbness of the fingers and hands.

2. With prolonged exposure to vibration, the development of vibration disease is possible, the severe stage of which is incurable. Vibration has a negative effect on the central nervous system, headaches, dizziness, cardiac abnormalities, and disorders of the vestibular apparatus occur.

There are three stages of manifestation of vibration disease: initial (stage I), moderately pronounced (stage II) and pronounced (stage III).

Vibration disease belongs to a group of diseases, the effective treatment of which is possible only in the early stages. Restoration of impaired functions proceeds very slowly, and in especially severe cases, irreversible changes occur in the body, leading to disability.

Table 2.3.

The negative impact of vibration on humans

Type of changes in the body	Symptoms of changes	Vibration Impact Results
Functional Physiological	Increased fatigue Increased motor response time Increased visual reaction time Violation of vestibular reactions and coordination of movements Development of nervous diseases Dysfunction of the cardiovascular system Dysfunctions of the musculoskeletal system Damage to muscle tissue and joints Dysfunction of the organs of internal secretion Genital dysfunction	Decrease in labor productivity and quality of work The onset of vibration disease

Distinguish between technical and hygienic vibration regulation.

Technical regulation establishes the permissible values ​​of vibration characteristics of machines. The basis of hygienic regulation is formed by the criteria of human health when exposed to vibration, taking into account the intensity and severity of labor.

The normalized indicators of vibration load on the operator at workplaces during labor are as follows.

1) at constant vibration - spectral or frequency-corrected values ​​of the controlled parameter;

2) in case of non-constant vibration - the value of the vibration dose or the equivalent corrected value of the controlled parameter.

Frequency-corrected value of the monitored parameter U is determined by the following formula:

.

Here U i - the mean square value of the controlled parameter (vibration velocity or vibration acceleration) in i-th frequency band; n - the number of frequency bands in the standardized range; k i Is the weighting factor for i- th frequency band for the root-mean-square value of the controlled parameter (determined by GOST and SN).

Vibration dose D

.

Here U(t) Is the frequency-corrected value of the controlled parameter at the moment of time t;T- time of exposure to vibration.

Equivalent corrected value U eq is determined by the following formula:

.

Reducing vibration

Vibration mitigation classification

1. Reducing vibration at the origin. These funds are carried out during the design and construction of the machine. These include: alignment, dynamic balancing, changes in the nature of disturbing influences.

2. Organizational and technical measures, which include reducing the time of exposure to vibration by using remote control, shortening the working day, and arranging work breaks.

3. Collective protection means: vibration-insulating fasteners of mechanisms and workplaces, dynamic vibration damping, damping.

4. Personal protective equipment: vibration-resistant gloves and shoes.

To reduce vibration, rubber, spring or pneumatic vibration isolators are used, which reduce the dynamic force transmitted from the machine to the foundation.

Vibration isolation efficiency L vib(dB) is the difference in vibration levels on the foundation with rigid N f(dB) and elastic N e-mail(dB) machine fastening.

When choosing vibration isolators, two tasks are solved: achieving high vibration isolation and ensuring the reliability of the system.

Figure 2.16.

Dependence of the level of vibration isolation

on the ratio of the frequencies of free and forced oscillations of the system

With a decrease in the free vibration frequency, vibration isolation increases.

F 0 ,f v- frequency of free and forced oscillations, Hz.

When installing the machine on rubber vibration dampers, the f 0 = 20-50 Hz, and for spring - f 0 = 2-6 Hz, so the efficiency of spring vibration isolators is greater than rubber ones, especially in the low and medium frequency range.

When
the phenomenon of resonance arises. As a consequence, the installation of vibration isolators should be preceded by the stage of calculating their effectiveness.

The quality of vibration isolation is assessed by the transmission coefficient for vibration isolation  ... Coefficient  is the ratio of the vibration displacement amplitude S O(vibration velocity V O, vibration acceleration a O) of the protected object to the amplitude of the same value of the excitation source with harmonic vibration.

.

Here f c - the frequency of the driving force; f o - frequency of natural vibrations of the system on vibration isolators.

The frequency of natural vibrations of the system on vibration isolators is determined by the following formula:

.

Here x st - static displacement (sediment) of the vibration source (vibration-insulated machine) on vibration isolators under the action of gravity (cm).

Vibration isolators reduce vibration when
.

In addition to the coefficient  vibration isolation can be estimated by the following formula of the logarithmic value vibration isolation L:

.

This formula is a special case of the Weber-Fechner law.

2.9. Electromagnetic radiation

The frequency spectrum of electromagnetic oscillations reaches 10 21 Hz. It is subdivided into the area of ​​non-ionizing and ionizing radiation.

Non-ionizing radiation includes infrared, visible (light), ultraviolet and laser radiation. In hygienic practice, it also includes electric and magnetic fields.

Sources of electromagnetic fields are natural and man-made.

Natural sources include atmospheric electricity, solar radiation, electric and magnetic fields of the Earth, etc.

Man-made sources include transformers, electric motors, television equipment, power lines, computers, mobile phones, etc.

Electric and magnetic fields of the so-called industrial frequency (50 Hz) are usually considered.

The process of propagation of an electromagnetic field has the character of a wave, while harmonic oscillations of the strength of the electric E and magnetic H fields. Vectors E and H mutually perpendicular.

Wavelength λ (m) is related to the speed of propagation of oscillations with(m / s) and frequency f(Hz) ratio:

.

Here with= 3 * 10 8 m / s - the speed of propagation of electromagnetic waves in the air.

The direction of movement of the energy flow is determined by the Umov-Poiting vector - .

.

EMF causes an increased heating of human tissues, and if the thermoregulation mechanism does not cope with this phenomenon, then an increase in body temperature is possible. The thermal threshold is 100W / m2. ... Heat exposure is most dangerous for the brain, eyes, kidneys, intestines. Radiation can cause clouding of the lens of the eye (cataract).

Under the influence of EMF, microprocesses in tissues change, the activity of protein metabolism is weakened, reflexes are inhibited, blood pressure decreases, and as a result, headaches, shortness of breath, and sleep disturbances occur.

With constant work under conditions of chronic exposure to EMF exceeding the MPL, dysfunctions of the nervous, cardiovascular and respiratory systems, the digestive tract develop, and changes in the blood occur. With a predominantly local effect, sensations of itching, pallor and cyanosis of the skin, puffiness and tightness of the skin may appear.

Exposure to EMR is especially harmful to tissues with an underdeveloped vascular system or insufficient blood circulation (eyes, brain, kidneys, stomach, gallbladder and bladder).

The regulation of EMF of industrial frequency is carried out according to the maximum permissible levels of intensity of EMF with a frequency of 50 Hz, depending on the time spent in it. The regulation is regulated by the "Sanitary norms and rules for performing work under the influence of electric fields of industrial frequency" and GOST for the electric field, as well as SanPiN for an alternating magnetic field of 50 Hz in production conditions.

The norms establish the permissible tension values E(v / m) in the radio frequency range (3 * 10 4 -3 * 10 8 Hz), depending on the exposure time, separately for professional and non-professional activities, and in the ultrahigh frequency range, the intensity is normalized I(w / m2), which is numerically equal to the modulus of the Umov-Poyting vector .

Staying in an electric field with a strength of up to 5 kV / m inclusive is allowed throughout the working day. The permissible residence time in hours in an electric power supply with a voltage of 5-20 kV / m is calculated by the following formula:

.

Permitted stay in the electronic signature can be realized one-time or fractionally during the whole working day. The rest of the time, the electric power intensity should not exceed 5 kV / m. With an EF intensity of 20-25 kV / m, the residence time in an EF should not exceed 10 minutes. During the working day. The PDU of the electric drive intensity is set equal to 25 kV / m.

Maximum permissible values ​​of EP ( E before) MP ( H before) in the frequency range from 60 kHz-300 MHz at workplaces are set based on the permissible energy load and exposure time.

They can be determined by the following formulas:

,

where
- the maximum permissible values ​​of the energy load during the working day.

The degree and nature of the effect of EMR on the body are determined by the density of the energy flux, the frequency of radiation, the duration of exposure, the mode of irradiation, the size of the irradiated surface, the individual characteristics of the organism and the presence of accompanying factors.

Exposure of a person to an electrostatic field (static electricity) is associated with the flow of a weak current (several microamperes) through a person. In this case, there are no electrical injuries, however, a reflex reaction to current can lead to mechanical injury, fall, etc.

The most sensitive to ESP are the central nervous system, the cardiovascular system, and analyzers. The impact of ESP can manifest itself in irritability, headache, sleep disturbances, etc. There are also a kind of "phobias" caused by the fear of discharge.

Classification of methods for protecting a person from electromagnetic radiation

1. Professional medical selection. Persons under the age of 18, as well as those with diseases of the blood, cardiovascular system, eyes are not allowed to work with installations of electromagnetic radiation.

2. Organizational measures: protection by time and distance; safety signs.

3. Technical means aimed at reducing the level of EMF to permissible values ​​(reflective and absorbing screens, flat, mesh, shell).

4. Personal protective equipment (overalls, hoods, gowns made of metallized fabric, special glasses with glass coated with semiconductor tin).

Protection of workers from radiofrequency and ultra-high frequency range radiation

RF range: 3 * 10 4 -3 * 10 8 Hz.

Super high frequency range: 3 * 10 8 -3 * 10 12 Hz.

1. Intensity of electromagnetic radiation I(w / m 2) from a power source R ist(w) decreases with increasing distance R by dependence:

.

Therefore, the operator's workplace should be as far away from the source as possible.

2. Reflective screens are made of highly conductive metals: copper, aluminum, brass, steel. EMF creates in the screen the so-called. Foucault currents, which induce a secondary field in it, which prevents the penetration of the primary field into the screen material. Shielding efficiency L(dB) is determined by the following formula:

.

Here I,I 1 - intensity of EMF without screen and with screen; L= 50 - 100 dB.

3. Sometimes metal meshes are used for EMI shielding. Mesh screens are less effective than solid screens. They are used when it is required to reduce the intensity (power flux density) by 20 - 30 dB (100 - 1000 times).

4. Absorbing screens are made of radio-absorbing materials (rubber, foam rubber, fibrous wood).

5. Multilayer screens consist of sequentially alternating non-magnetic and magnetic layers. As a result, the waves are reflected multiple times, which leads to a high screening efficiency.

The most common source of electromagnetic radiation in everyday life and at work has recently become a computer.

The following factors of the negative impact of a computer on a person have been determined: static loads; load on vision; hypodynamia (violation of body functions, due to the limitation of motor activity, a decrease in the strength of muscle contraction); electromagnetic radiation; electric fields; psychological stress.

Sanitary standards establish the limit values ​​for the strength of the electric and magnetic fields when working on a PC.

For people who regularly use the computer, the following operating times are set.

The duration of work on a PC without interruption is no more than 2 hours.

The duration of work on the PC of teachers is no more than 4 hours a day.

The duration of work on the students' PC is no more than 3 hours a day.

In this case, the minimum distance from the eyes to the screen should not be less than 50 cm.

In case of violation of the established requirements, the following diseases appear.

1. Diseases of the organs of vision - 60%.

2. Diseases of the cardiovascular system - 60%.

3. Diseases of the stomach - 40%.

4. Skin diseases - 10%.

5. Computer disease (operator stress syndrome) - 30%.

Vibration- movement of a point (or body) around the starting position, repeating exactly at regular intervals (periodically). The simplest form of periodic oscillation is harmonic vibrations, the graph of which versus time is a sinusoid (see Figure 1). The time between two subsequent, exactly similar positions of the oscillating point (or body) is called oscillation period (T).

Frequency hesitation is related to the period through the ratio:

As for the magnitude of the fluctuation, it can be described, according to GOST 10816-1-99, by three main parameters: vibration displacement ( s ) , vibration velocity ( v ) and vibration acceleration ( a ) ... These parameters have certain mathematical relationships to each other when considering harmonic (simplest) oscillations. If the vibration of a point (or body) has a purely longitudinal vibration mode along one axis (NS) then instant displacement (vibration displacement) from the starting position can be described by a mathematical equation:

where is the angular frequency;

– maximum point offset(or body) from the starting position;

t- time.

Time offset change is speed (vibration velocity) movement of a point (or body). Therefore, oscillations can also be described in terms of speed (v)

Thus, vibration displacement can be converted into speed through differentiation.

Differentiation is accompanied by multiplication of amplitude by frequency, therefore vibration velocity amplitude at a certain frequency is proportional to the offset (s) multiplied by the frequency (f)... With a fixed displacement, the speed will double as the frequency increases, and if the frequency is increased by 10 times, the speed will increase by 10 times.

The change in the speed of movement of a point (or body) in time is acceleration (vibration acceleration) movement:

That is, in order to get acceleration from the speed, one more differentiation is necessary, which means another multiplication by the frequency. Therefore, the acceleration at a fixed offset will be proportional to the square of the frequency.

According to Newton's second law, force is equal to mass times acceleration. Therefore, for a given displacement, the force will be proportional to the square of the frequency. That is why on practice do not face oscillations, where large accelerations are accompanied by large displacements, there are simply no such very large forces that would be extremely destructive.

As can be seen from the above equations, the shape and period of the oscillation remains unchanged regardless of whether displacement, velocity, or acceleration are considered.

It should be noted that instantaneous values s, v, a differ in phase... So the speed is ahead of the displacement by phase angle 90 0 (in the equation) and acceleration advances the speed by a phase angle of 90 0 (in the equation). As a characterizing quantity, we used peak value of vibration amplitude, that is. Peak value application vibration amplitudes effective when considering harmonic (simplest) vibrations.

The values ​​of vibration displacement, vibration velocity and vibration acceleration in standard units are related by the following equations:

When considering oscillations (Fig. 2), other amplitude values ​​are used.

The average arithmetic absolute value the vibration amplitude characterizes the overall vibration intensity and is determined by the formula:

The average value of the oscillation amplitude is used when analyzing oscillations over a very long period of time (day, several days), mainly in stationary equipment monitoring systems. Therefore, this value is of no particular practical interest.

Another value of the vibration amplitude is root mean square (SKZ). RMS is an important characteristic of vibration amplitude. To calculate it, you need to square instantaneous values ​​of vibration amplitude, and average the resulting values ​​over time. To obtain the correct value, the averaging interval must be at least one oscillation period. After that, the square root is extracted and the RMS is obtained.

For purely harmonic vibrations(vibration contains only one vibration frequency) the relationship between peak, average and mean square amplitude values are determined by the following formulas:

In a more general form, these relationships can be described as follows:

Odds F f and F c are called the form factor and the crest factor, respectively. These coefficients give an idea of ​​the waveform of the vibration being studied.

For purely harmonic vibrations, these coefficients are:

The vibrations encountered in practice are not purely harmonic vibrations, although many of them may be periodic. Figure 3 shows an example of a typical fluctuation found in practice.

Having determined the peak, mean and root-mean-square values ​​of this vibration, as well as its coefficients of form and amplitude, you can get a lot of useful information and, as a result, say about the inharmonic nature of vibration. However, on the basis of this information, it is practically impossible to predict possible defects caused by vibration in the structural elements of a machine or mechanism. Therefore, you need to use other

Vibration parameters in various units of measurement can be recalculated not only according to the above formulas, but also with the help of vibration conversion calculators, which are offered by both foreign and domestic companies. In Figure 4, you see one of these calculators. To get acquainted with its work, you can download it to your disk and run it.

R.S. If any of you dear reader did not quite understand this article, because they are not at ease with mathematics, then I recommend that you first study this issue with the help of a book : . In this book, all the material is presented in ordinary language, without a single formula.

1. Vibration displacement, S Is the distance between the extreme points of movement of the vibrating element along the measurement axis. Vibration displacement is measured in linear units: in microns - microns; in millimeters - mm, for large values ​​of vibration displacement, for example, screens (1 mm = 1000 microns). The parameter that complements vibration displacement is the rotational speed. For example, the admissible value of vibration displacement is 20 µm at a speed of 1500 rpm and 10 µm at a speed of 3000 rpm.
   Vibration displacement is measured when low-frequency vibration occurs, the upper limit of the frequency spectrum is not more than 200 Hz. These measurements are relevant in construction vibroacoustics, when balancing rotors, when studying machines with small gaps between units and parts, when studying elastic deformations and predicting fatigue fractures.
2. Vibration speed,v - time derivative of vibration displacement. This parameter characterizes the power of the oscillatory (vibration) process aimed at destroying parts and characterizes the energy impact on the nodes of the controlled object (vibration energy E = m × V 2/2). Vibration velocity is the speed of movement of the controlled point of the equipment. Vibration velocity simultaneously takes into account the movement of the controlled point and the frequency of the vibrations that caused the vibration. Vibration velocity is measured in millimeters per second, mm / s.
   Vibration speed is measured in the frequency range 10 ... 1000 Hz. The level of vibration speed determines the technical condition of machines, their units and parts.
3. Vibration acceleration, and- time derivative of vibration velocity. The parameter characterizes the force of inertia that affects the object during vibration:
   F = m × a, where F - force of inertia; m - the mass of the object; a -vibration acceleration.
   Vibration acceleration is the acceleration of the movement of the controlled point of the equipment or the rate of change in speed. Vibration acceleration characterizes the force dynamic interaction of the unit's elements. Vibration acceleration is measured in meters per second squared, m / s 2, sometimes the unit of gravitational acceleration is used - g, 1 g = 9.8 m / s 2.
   Vibration acceleration is measured in the presence of vibration in a wide frequency range, from 50 to 10,000 Hz or more. These measurements are relevant for vibroacoustic diagnostics to assess the force of impacts and early detection of damage in rolling bearings and gears.
   Note: there is a rarely used vibration parameter - sharpness- the third derivative of the time displacement, dimension - km / s 3.
4. Frequency,f- characteristic of a periodic process, equal to the number of repetitions per unit of time, is inversely proportional to the period of oscillations:
   f = 1 / T, where T- period, time of a complete cycle of oscillations (s).
   The unit of measurement of frequency in the International System of Units (SI) is hertz (Russian designation - Hz; international - Hz), named after the German physicist Heinrich Hertz. One oscillation per second corresponds to 1 Hz.
   At a speed of 3000 rpm, the oscillation frequency is:
   f =n/ 60 = 3000 / 60 = 50 Hz .
   The vibration frequency allows you to identify the source of the vibration.
   Harmonic vibrations at different points of the machine, coinciding in frequency, are called synchronous. Synchronous oscillations differ from each other in amplitude and phase.
5. Oscillation phase, φ- determines the position of the characteristic point of fluctuations (maximum, minimum value or transition from negative to positive value) relative to the fixed position of the mark. Measured in degrees. It is used for balancing, examination of metal structures, diagnostics of mechanisms.
   Oscillations at two points that coincide in phase are called in-phase, and differing by 180 0 - antiphase... The phase shift of synchronous harmonic oscillations is the phase difference of two synchronous harmonic oscillations of harmonic oscillations at a given moment in time. This parameter is often used in vibration analysis.

For a harmonic oscillatory process, there are a number of features that characterize the relationship between displacement, speed and acceleration:

Example

For a rotary mechanism with a rotational speed of 3000 rpm (50 Hz), the vibration displacement value is fixed - 20 μm. Determine the corresponding values ​​of vibration velocity and vibration acceleration.

v= 2 π × f× S = 6.28 ×50 × 20 = 6,28 mm / s;
a = 2π× f× v= 6,28 × 50 × 6,28 = 1,97 m / s 2 .

Based on these relationships, it can be concluded that the relationships between displacement, speed, acceleration and frequency will be different. The displacement graph will be dominated by the low-frequency region, while the acceleration graph will be dominated by the high-frequency region, while the low-frequency region will be weakened ().

Vibration acceleration

Vibration velocity

Vibration displacement

The numerical values ​​of the levels of acceleration, speed and displacement in logarithmic coordinates (at the threshold values ​​according to ISO 1683) are equal only at one point - at a frequency of 159 Hz (). Vibration calibrators are tuned to this frequency. At this point, the vibration displacement value is 10 μm, the vibration velocity value is 10 mm / s, and the vibration acceleration value is 10 m / s 2.

The main characteristics of oscillatory processes

1. Peak value- is defined as the greatest deviation of the fluctuating value from the mean position x PEAK = Iх MAX I.
   Used as a component when measuring vibration acceleration. The peak value is effective in evaluating short-term mechanical shocks and so on. However, the peak value reflects only the maximum value of the investigated fluctuations, and not their temporal development.
2. - the average value of the measured data, characterizes the overall vibration intensity:
   where τ - the current value of the time coordinate, T- measurement period.
   The average value reflects the temporal development of the investigated oscillations, but its practical application is limited due to the fact that it has no direct connection with any physical value of these oscillations.
3. Root mean square(RMS) - the square root of the arithmetic mean or integral mean of the square of the fluctuating quantity in the period under consideration:
   To obtain the correct value, the averaging interval must be at least one oscillation period. Used when measuring vibration velocity. Recalculation of the values ​​of vibration acceleration, vibration velocity and vibration displacement, determined as a result of spectrum analysis, as a function of angular frequency ω , to the root-mean-square value of the vibration velocity is carried out according to the following formulas:
   
   It is possible to determine the root-mean-square value of vibration velocity by the maximum and minimum value of vibration velocity in the spectrum:
   The root-mean-square value takes into account the temporal development of the investigated oscillations and directly reflects the value associated with the signal energy and, therefore, the destructive power of these oscillations.
4. Crest factor or crest factor - peak ratio ( x PEAK) to rms ( x RMS) value: K PF = x PEAK / x RMS.
   The crest factor characterizes the development of damage. The peak-factor values ​​in the initial period of the mechanism operation are 3 ... 4. At the initiation of damage, the values ​​of the crest factor increase to 10 ... 15. An increase in the degree of damage reduces the values ​​of the crest factor to 3 ... 4 ().
   For harmonic vibrations: K PF = 1,41; x PEAK = A; x MEDIUM = 0,637A; x RMS = 0,707A.

1. Excess- the ratio of the fourth order torque to the square of the second order torque. The kurtosis determines the degree of deviation of the parameter from the normal distribution: b = m 4 / (m 2 ) 2 , where m 4 - moment of the fourth order; m 2 - moment of the second order.
   When determining the statistical moments, the following values ​​are used:
   - arithmetic mean - the sum of relative deviations;
   - variance - the sum of squares of relative deviations;
   - asymmetry - the sum of cubes of relative deviations;
   - peakedness - the sum of the fourth degree of relative deviations.
   The kurtosis values ​​are used to determine the development of various malfunctions of machine elements, since a deviation from the normal distribution is an unambiguous sign of a malfunction.

Relative vibration units- 20-fold decimal logarithms of the ratio of the measured value of the vibration parameter ( vMOD) to some initial level ( vSTART) and are measured in decibels (dB). For vibration velocity:

L v = 20 lg(vMOD/ vSTART) .

For vibration acceleration:

La = 20lg(a MOD / a START).

A 6 dB increase in level corresponds to a doubling of the amplitude, regardless of the original value. A 20 dB change in level means a tenfold increase in amplitude. For temporal realizations of vibration, linear units of measurement of the amplitude are always used: the instantaneous value of the signal can be negative, and therefore it cannot be logarithmized.

When using logarithmic characteristics, it is necessary to indicate the standard threshold level adopted when processing vibration values. According to the Rules of the Russian Maritime Register of Shipping and GOST 12.1.034-81, the threshold level is adopted: vSTART= 5 · 10 -5 mm / s; and NACH= 3 · 10 -4 m / s 2. According to GOST 30296-95: vSTART= 5 · 10 -8 m / s; and NACH= 1 · 10 -6 m / s 2. According to ISO 1683: vSTART= 1 · 10 -6 mm / s; and NACH= 1 · 10 -6 m / s 2; SSTART= 1 · 10 -6 microns.

Typically, an analog vibration time signal is digitized and used for spectral analysis in the frequency domain. The complexity of the temporal waveform, its interpretation is very difficult, therefore, the temporal waveform is often ignored. At the same time, the information that the temporal form can give is not available when considering the vibration spectrum.

For example, a random process (continuous noise) and a transient process associated with some irregular events have similar spectra, which, nevertheless, correspond to signals of a completely different nature, which is clearly seen from their temporal realizations. In the time domain, knocking of parts is easily discernible, leading to asymmetry in the waveform, which may be due to weakening of mechanical connections.

The examination of the vibration state of the PM-400 gearbox of the overhead crane movement mechanism was carried out when the equipment was operating in idle mode at an engine speed of 720 rpm. Dull knocks are observed during the operation of the gearbox. The values ​​of the general level of vibration velocity - 3.0 mm / s, vibration acceleration - 1.8 m / s 2. In the spectrogram of the vibration velocity of the bearing of the low-speed shaft of the gearbox (a), the tooth frequency of the second gear is represented by a component at a frequency of 31.5 Hz, with an amplitude of 0.2 mm / s. Recording a temporary vibration acceleration signal (b) made it possible to establish a possible cause of the malfunction - damage (nick) on the gear wheel of the low-speed shaft, which manifested itself as blows with the speed of the low-speed shaft. Confirmation of the diagnosis was obtained by visual examination and eliminated after mechanical treatment of the damaged tooth.

(a)

(b)

The measurement cycle contained 12 measurements, taking into account 800 lines in the spectrum - 9600 values, in addition, measurements of the temporal shape of the vibration signal - 4 × 16000 values ​​were carried out. From this data, two information messages were received: about the general level of vibration (corresponding to a satisfactory condition) and about the possible cause of the malfunction that was eliminated during repair.

The operation of electric motors is often accompanied by beats, which are well perceived by ear. These beats correspond to the slip frequency of the rotor or the difference between the rotor speed and the excitation frequency of the motor. The beat frequency is very low, sometimes below 0.1 Hz. Runout can also occur when closely spaced machines operate at slightly different speeds. It is better to observe the beats in the time domain of the vibration signal, since it takes a very long time and high resolution to calculate the spectral components at such low frequencies.

The difficulty of the analysis lies in the absence of rules for formalizing and processing temporary implementations of the parameters of fast processes. In many ways, this process is subjective and depends on the experience of a specialist. The spectral components of the vibration signal often remain practically unchanged due to the vibration signal averaging necessary to obtain a reliable estimate. Analysis of the actual signal provides additional information about the technical condition of the mechanism. The most effective use of the analysis of the temporal form of a vibration signal for diagnosing transient, non-stationary, shock processes. For this, periods of 30 ... 400 μs are used, the number of measurements is 10000 ... 16000 and more, the mode is without averaging.

Time Signal Analysis Rules

1. It is necessary to evaluate the repeatability of the parameters of the oscillatory process. Identical influences must correspond to the same realizations of vibration parameters. You can use a comparative analysis of the same type of processes at different points when using a two-channel vibration analyzer.
2. Evaluation of the signal symmetry relative to the zero (initial) vibration level. The presence of a symmetrical signal indicates a good condition (the ideal case is a sinusoidal mode of oscillation - absolutely symmetric), deviations - increase the degree of asymmetry. Diagnostic parameters for analysis are positive and negative values ​​of vibration amplitudes. The reasons for the asymmetry are the nonlinearity of the characteristics of the system, the anisotropy of the parts of the bearing assembly.
3. The most significant is the time that the system calms down after the disturbance. Systems with low stiffness and low damping properties will have a longer decay time. The reasons for the decrease in the rigidity and damping properties of the system should be determined. It is possible to assess the stability of the damping properties of a mechanical system by determining the vibration decrement as the natural logarithm of the ratio of two subsequent amplitudes:

The nature of vibration when changing the speed of rotation of the mechanism is also a diagnostic sign that requires analysis of time realizations:

1. If, when the speed is changed, the vibration increases in a linear relationship, the cause of damage is mechanical damage to the parts.
2. If, when the speed is changed, the vibration increases in a quadratic relationship, the cause of the damage is an imbalance in the rotor.
3. If the vibration increases exponentially when the speed changes, the cause of the damage is a crack in the body or base.
4. A sharp decrease in motor vibration when the power is turned off is a sign of damage caused by damage to the electrical part of the motor.
5. A gradual decrease in vibration when the machine is stopped is a sign of damage to the mechanical system.

Examples of temporary implementation of vibration acceleration of electric motor bearings are given on.

(a)

(b)

A - the amplitude of oscillations is about 14.0 m / s 2, oscillations with a period of 20 ms are clearly distinguished - the frequency of rotation of the engine shaft. b - the range of oscillations is about 30.0 m / s 2, on a long sample, individual shocks up to 63.0 m / s 2 are recorded, which are passed by the spectral analysis as a result of averaging. Time-domain analysis can detect the first signs of deviations at an earlier stage than spectral analysis.

GOST ISO 10816-1-97

INTERSTATE STANDARD

VIBRATION

CONTROL OF MACHINE STATUS BY MEASUREMENT RESULTS
VIBRATIONS ON NON-ROTATING PARTS

Part 1

GENERAL REQUIREMENTS

INTERSTATE STANDARD
FOR STANDARDIZATION, METROLOGY AND CERTIFICATION
Minsk

Foreword

1 DEVELOPED by the Russian Federation

INTRODUCED by the Technical Secretariat of the Interstate Council for Standardization, Metrology and Certification

2 ADOPTED by the Interstate Council for Standardization, Metrology and Certification (Protocol No. 11 dated April 25, 1997)

State name	Name of the national standardization body
The Republic of Azerbaijan	Azgosstandart
Republic of Armenia	Armgosstandart
Republic of Belarus	Gosstandart of Belarus
The Republic of Kazakhstan	Gosstandart of the Republic of Kazakhstan
Kyrgyz Republic	Kyrgyzstandart
The Republic of Moldova	Moldovastandart
Russian Federation	Gosstandart of Russia
The Republic of Tajikistan	Tajikgosstandart
Turkmenistan	Main State Inspectorate of Turkmenistan
The Republic of Uzbekistan	Uzgosstandart
	State Standard of Ukraine

3 This standard contains the full authentic text of the international standard ISO 10816-1-95 “Vibration. Monitoring the vibration state of machines by measuring vibration on non-rotating parts. Part 1: General guidance "

4 By the Decree of the State Committee of the Russian Federation for Standardization, Metrology and Certification No. 353 dated September 17, 1998, the interstate standard GOST ISO 10816-1-97 was put into effect as a state standard of the Russian Federation from July 1, 1999.

5 INTRODUCED FOR THE FIRST TIME

6 REDISSION. July 2009

Introduction

This International Standard is a basic normative document that provides general guidelines for the measurement and assessment of mechanical vibration in stator elements of machines, such as bearing pedestals. Requirements for vibration measurements and criteria for assessing the state of machines of specific types are set in standards for these machines, developed on the basis of this standard.

For many machines, the results of measurements of vibration of stator elements are sufficient for an adequate assessment of the conditions for the reliability of their operation, as well as the effect on the operation of neighboring units. However, for some machines, such as those with flexible rotors, vibration measurements on stationary parts may not be sufficient. In these cases, vibration measurements of rotating rotors are also carried out, i. E. reliable control should be based on the results of vibration measurements of both stator and rotor elements.

The results of vibration measurements can be used for operational control, acceptance tests, diagnostic and analytical studies. This standard is intended as a guide only for in-service vibration control and vibration measurements for acceptance testing of equipment.

The standard uses three main vibration parameters: vibration displacement, vibration velocity and vibration acceleration, and the procedure for establishing their limit values ​​is given. Compliance with the suggested guidelines should in most cases ensure satisfactory performance of the equipment.

INTERSTATE STANDARD

Vibration CONTROL OF MACHINE STATUS BY VIBRATION MEASUREMENTS ON NON-ROTATING PARTS Part 1. General requirements Mechanical vibration. Evaluation of machine vibration by measurements on non-rotating parts. Part 1. General guidelines

Date of introduction 1999-07-01

1 AREA OF USE

This International Standard specifies the general conditions and procedure for the determination and assessment of vibration conditions based on measurements carried out on the stator elements of machines. General assessment criteria based on the measurement of both the actual values ​​of vibration parameters and the values ​​of their changes, related to both in-service control and acceptance tests, should be established taking into account the need to ensure the following factors:

Safe continuous operation of the machine;

Absence of the influence of machine vibration on the operation of neighboring machines and mechanisms.

This standard applies to vibration generated by the machine itself and does not apply to vibration transmitted externally.

Angular vibration is outside the scope of this standard.

2 REFERENCES

4 VIBRATION MEASUREMENT

4.1 Measured characteristics

4.1.1 Frequency range

Vibration measurements should be made over a frequency range that covers the frequency spectrum of the machine. The width of the frequency range depends on the type of machine (for example, the frequency range required for evaluating the integrity of rolling bearings should include frequencies higher than for machines with sleeve bearings). Recommendations on the choice of the frequency range for specific types of machines should be given in the relevant standards, for example, for stationary steam turbine units - in GOST 25364.

Note - In past years, vibration monitoring was mainly associated with vibration measurement in a fixed frequency range of 10 ... 1000 Hz and an assessment of the root mean square value of vibration velocity in this range; requirements for appropriate measuring instruments are given in GOST ISO 2954. However, some types of machines may require measurements in a different frequency range and other vibration parameters.

4.1.2 Measured value

For the purposes of this standard, one of the following may be used as the measurand:

Vibration displacement, in micrometers (μm);

Vibration velocity, in millimeters per second (mm / s);

Vibration acceleration, in meters per second squared (m / s 2).

The order of use, cases of application and restrictions imposed on these values ​​are discussed in.

As a rule, for vibration measured over a wide frequency range, there are no simple relationships between vibration acceleration, vibration velocity and vibration displacement, as well as between peak and root mean square values ​​of vibration quantities. A brief analysis of the reasons for this is given in, which also gives some exact relationships between the above parameters for the case when the frequency components of vibration are known.

It should be clearly defined by which vibration parameter the vibration state is assessed: the range of vibration displacement, the mean square value of the vibration velocity, etc.

4.1.3 Vibration parameter values

The value of the vibration parameter for a specific position and direction of measurement is understood as the result of measurements carried out using equipment that meets the requirements.

As a rule, when controlling the broadband vibration of rotary-type machines, the rms value of the vibration velocity is used as the estimated parameter, since it is related to the vibration energy. In some cases, however, it is preferable to use other parameters: related to vibration displacement or vibration acceleration, or peak values ​​instead of rms values. In these cases, other criteria should be used, which are not always related by simple relationships with the criteria for the root-mean-square values ​​of the vibration velocity.

Typically, measurements are taken at various points in two or three mutually perpendicular directions, which makes it possible to obtain a set of vibration parameter values. The vibration level of a machine is understood as the maximum value of vibration measured at one specific point or group of points in selected directions, under certain conditions and steady state operation.

The vibration condition of many types of machines can be assessed by the vibration level for a single measuring point. However, for some machines this approach is unacceptable and vibration levels should be determined from independent measurements at a number of points.

4.2 Measuring points

Measurements should be carried out on bearings, bearing housings or other structural elements that are most responsive to dynamic forces and characterize the overall vibration condition of the machine. Typical examples of location of measurement points are shown in Figures 1a - 1e.

Drawingla- Measuring points on the bearing pedestal	Figure 16 - Measuring points on the bearing housing
Figure 1c - Measurement points on small electrical machines
Figure 1d - Measurement points on the engine	Figure 1e - Measurement points on a vertically installed machine

A complete assessment of the vibration state of large aggregates is given by the results of measurements at controlled points in three mutually perpendicular directions, as indicated in Figures 1a - 1e. As a rule, such completeness of measurements is required only for acceptance tests. In-service inspection usually takes one or two measurements in the radial direction [generally horizontal and / or vertical]. In addition, axial vibration measurements can additionally also be made, usually at the location of the thrust bearing.

The location of the measuring points for specific types of machines should be specified in the relevant standards for these types of machines.

4.3 Requirements for the condition of the machine during operational control

Operational control is carried out only when the machine is fully assembled on standard supports at the place of its operation.

4.4 Requirements for machine supports for acceptance tests

4.4.1 On-site

If acceptance tests are carried out on site, the rotors should be mounted on standard supports. In this case, it is important that all the main elements of the machine are assembled during the acceptance test; for prototype machines this requirement is mandatory, and for serial machines, if this is not possible, the evaluation criteria should be adjusted accordingly. The results of comparing the vibration state of machines of the same type installed on different foundations are comparable only if the dynamic characteristics of the foundations are similar.

4.4.2 On the test bench

It is necessary to create conditions under which the coincidence of the frequencies of the natural vibrations of the test setup with the rotational speed of the machine or with any of its powerful harmonics is excluded. It is generally assumed that this requirement is fulfilled if the horizontal and vertical vibration of the supporting elements of the foundation near the bearing supports does not exceed 50% of the vibration value of the corresponding bearing in the same direction. The test setup shall also not cause changes in the value of any of the fundamental natural frequencies of the machine in service. If support resonances cannot be eliminated, an acceptance test should be carried out on the fully assembled machine on site.

Acceptance tests of some classes of machines, such as small electrical machines, are carried out on a resilient base. In this case, the lowest natural frequencies of the machine-test support system, considered as a rigid body, should be less than 1/2 of the minimum excitation frequency. Adequate support conditions can be achieved by placing the machine on a resiliently supported foundation (base) or by free suspension on soft springs.

4.5 Operating conditions of the machine

Vibration assessment should be carried out after normal operating conditions have been reached. Additional measurements under different conditions should not be used to assess vibration conditions in accordance with.

The assessment of the influence of the vibration activity of the surrounding mechanisms on the vibration of a particular machine is carried out on the basis of the results of measurements on a stopped machine. If the measured vibration value exceeds ⅓ of the recommended limit value, measures should be taken to reduce this influence.

5 CONTROL EQUIPMENT

The design of instrumentation (hereinafter - hardware) should ensure its normal functioning under conditions of measurements (temperature environment, humidity, etc.). There should be a special pay attention mount the vibration transducer and make sure that the mount does not alter the vibration characteristics of the machine. Requirements for equipment designed to measure the root-mean-square value of vibration in the range of 10 ... 1000 Hz - according to GOST ISO 2954.

Currently, two types of instruments are most often used to control broadband vibration:

Devices containing a detector of the root-mean-square value and an indicator for reading the root-mean-square values ​​of the measured value;

Instruments containing either a rms detector or an averaging detector, but calibrated to read the peak-to-peak or amplitude of the oscillations; the calibration is based on the ratio between rms and peak values ​​for a pure sinusoidal signal.

If the vibration assessment is based on the measurement results of more than one quantity (displacement, speed, acceleration), the instruments used should provide measurement all these values.

The measuring system must provide for the possibility calibrations of all measuring path (preferably built-in calibration device) and have independent outputs for connecting additional analyzers, etc.

6 CRITERIA FOR ASSESSING THE VIBRATION STATE OF MACHINES

6.1 Types of criteria

Criteria of two types are considered, which apply to operational control and acceptance tests and are designed to assess the vibration levels of machines of various types. Criterion 1 is associated with the values ​​of the measured vibration parameters, and criterion 2 - with changes in these values ​​(regardless of the direction of changes).

6.2 Criterion 1

6.2.1 Vibration zones

Criterion 1 is related to the determination of the limits for the absolute value of the vibration parameter corresponding to the permissible dynamic loads on bearings and permissible vibration transmitted to the outside through the supports and the foundation. The maximum value obtained from the measurement at each bearing or support (i.e. the vibration level value - as defined in) is compared to the four zone boundaries established based on international research and operating experience. These zones are intended for a qualitative assessment of the vibration state of machines and making decisions on the necessary measures. A different (compared to the one below) the number of zones and their location can be used for machines of special types, which are considered in the relevant standards. The approximate values ​​of the boundaries of the zones are given in.

Zone A- As a rule, new machines that have just been put into operation fall into this zone.

Zone V- Machines entering this zone are usually considered suitable for further operation without time limits.

Zone WITH- Machines entering this area are usually considered unsuitable for long-term continuous operation. Typically these machines can operate for a limited period of time until a suitable repair opportunity arises.

Zone D- Vibration levels in this area are generally considered to be severe enough to cause damage to the machine.

The numerical values ​​of the boundaries of the zones mentioned are not intended to serve as technical conditions for acceptance tests, this is the subject of agreement between the manufacturer of the machine and the consumer. However, these boundaries can serve as a guide to avoid overly exaggerated and unrealistic requirements. In certain cases, for some types of machines, features may be set that will require changing the values ​​of the zone boundaries (up or down). The machine manufacturer should then generally explain the reason for these changes and, in particular, confirm that the machine should not be endangered by operating at higher vibration levels.

The vibration of a particular machine depends on its size, the dynamic characteristics of the vibrating parts, the installation method and the purpose. When choosing the zones of permissible vibration of the machine, it is also necessary to take into account the conditions affecting its vibration state. Regardless of the type of bearings, the root-mean-square value of the vibration velocity of stator elements (for example, bearing supports) of most types of machines, as a rule, adequately characterizes the operating conditions of the rotors, their effect on the supporting elements and adjacent mechanisms, as well as the state of the machines themselves in a wide range of operating speeds. However, for some machines, for example with very low operating speeds, the use of one parameter - the root-mean-square value of the vibration velocity - without taking into account the value of the operating speed, can legitimize unacceptable high vibration displacements, in particular, when oscillations with a revolving frequency dominate. On the other hand, applying the principle of constancy of vibration velocity to machines with high operating speeds or the presence of high-frequency spectral components of vibration excited by some parts of the machine, one can come to an unacceptably high level of vibration acceleration.

Taking into account the above, the acceptance criteria based on the use of the root-mean-square value of the vibration velocity should have the general form shown in Figure 2 (see also), which indicates the boundaries of the frequency range of measurements f u and f l and shown below the frequency; f x and higher frequency f y permissible value of vibration velocity is already a function of frequency f/ vibration. For the zone from f x before f y apply the criterion of constant vibration velocity - it is for this criterion that the values ​​of the boundaries are given. More precise definition of acceptance criteria and values f l, f u, f x and f y must be given in the standards for specific machine types.

The vibration of many machines contains a dominant frequency component, often at the shaft speed. For such machines, the admissible vibration values can be obtained from Figure 2 as values ​​for a given dominant frequency.

If, for a certain machine, a significant part of the vibration energy is concentrated outside the frequency range f x ...f y, the following solutions are possible:

a) In addition to measuring vibration velocity, measurements are carried out in a wide frequency band of vibration displacement (if the main part of the energy spectrum lies below f x) or vibration acceleration (if the main part of the energy spectrum lies above f y). The permissible values ​​of the parameters of vibration displacement or vibration acceleration are obtained from Figure 2, converting the values ​​of vibration velocity at the edges of the curves (i.e., in the ranges. f l… f x, f y… f u) to constant values ​​of vibration velocity and vibration acceleration, respectively. Vibration can be considered acceptable if it is such for all criteria (displacement, speed and acceleration).

b) With the help of a spectrum analyzer, all powerful frequency components are distinguished in the vibration spectrum and the values ​​of vibration displacement, vibration velocity and vibration acceleration are determined for them. After that, on the basis of the equation (), the equivalent value of the vibration velocity parameter is calculated; for frequency components below f x and higher f y, the weighting factors are taken in accordance with Figure 2. The final assessment is made on the basis of comparison with the values ​​of the boundaries in the range f x ...f y.

It should be borne in mind that, apart from the case of a single dominant component, direct comparison of the components of the frequency spectrum with the boundaries defined by the curves in Figure 2 will lead to erroneous conclusions.

c) A measuring device is used, the shape of the frequency response of which in the area where the vibration energy of the machine is concentrated coincides with the shape of the curves in Figure 2. The final assessment is also made on the basis of comparison with the values ​​of the boundaries in the range f x ...f y.

Additional guidance on defining zone boundaries is provided in. For some types of machines, it may be necessary to define the boundaries of zones other than those shown in Figure 2 (see, for example,).

6.3 Criterion 2

This criterion is based on the assessment of the change in the value of the vibration parameter in comparison with the preset reference value in the steady state operation of the machine. Significant changes (increase or decrease) in the value of the parameter of broadband vibration may require taking certain measures even in the case when the border of the zone WITH according to criterion 1 has not yet been achieved. Such changes can be sudden or build up gradually over time and indicate possible early damage to the machine or other malfunctions.

When using criterion 2, it is important that the measurements of the values ​​of vibration parameters to be subsequently compared should be carried out at the same position and orientation of the vibration transducer and approximately in the same operating mode of the machine. Obvious changes in the vibration parameter value, regardless of its overall value, must be identified to prevent a hazardous situation from occurring. The extent to which this change is significant should be defined in the relevant standards for specific machine types.

It should be borne in mind that some significant changes in the state of the machine can only be detected by monitoring individual spectral components (see).

6.4 Vibration limits

6.4.1 General Provisions

As a rule, for machines intended for long-term operation, limit vibration levels are set, exceeding which in a steady state of operation of the machine leads to the issuance of a WARNING or STOP signal:

WARNING — to draw attention to the fact that vibration or vibration changes have reached a certain level where remedial action may be required. As a rule, when a WARNING signal appears, the machine can be operated for a certain period of time while the causes of vibration changes are investigated and the set of necessary measures is determined.

STOP - to indicate the vibration level, exceeding which further operation may lead to damage. When the STOP level is reached, take immediate action to reduce vibration or stop the machine.

Due to the difference in dynamic loads and stiffness of the supports, different vibration limits can be set for different positions and directions of measurement. The definition of such levels for specific machine types should be given in the relevant standards.

6.4.2 Level setting WARNING

The level of WARNING can change significantly in the direction of increasing or decreasing from machine to machine. Typically, this value is set relative to some basic value obtained for each specific instance of the machine at a fixed position and direction of measurement based on accumulated operating experience.

It is recommended to set the WARNING level higher than the base value by a certain percentage, in percentage, of the value of the upper boundary of the zone V. If the baseline is low, the WARNING level may be below zone C.

In the event that no baseline has been defined, for example for new machines, the initial setting of the WARNING position should be done either based on experience with similar machines or by agreement. After some time, set a constant reference value and adjust the position WARNING accordingly.

If there has been a change to a permanent baseline (for example, due to a major overhaul of the machine), a corresponding change in position may be required. WARNING. Due to the difference in dynamic loads and stiffness coefficients of the supports, different levels of the machine can be set.

6.4.3 Setting the STOP level

The STOP level that is commonly associated with the need to maintain the mechanical integrity of a machine may depend on various design considerations used to enable the machine to withstand abnormal dynamic forces. Thus, this value will usually be the same for machines of similar design and will not be related to the base value, as was the case for the WARNING level.

Due to the variety of machines of different designs, it is not possible to give clear guidance for the exact setting of the STOP level. Usually the STOP position is set within the zones WITH or D.

6.5 Additional features

The control method considered in this basic standard is limited to assessing vibration over a wide frequency range without analyzing the frequency components or considering the vibration phase. In most cases, this is sufficient for acceptance testing and in-service inspection. However, when assessing the vibration state of certain types of machines, it is advisable to use the vector vibration representation.

The use of the vibration vector as a criterion is especially useful in detecting and identifying changes in the dynamic characteristics of a machine. Sometimes such changes cannot be detected under conditions of monitoring only the general level of broadband vibration. An example of such a situation is given in. However, it is outside the scope of this standard to establish a criterion based on the change in the vibration vector.

6.5.2 Vibration sensitivity

The vibration measured on a particular machine may vary depending on the mode of operation. In most cases, this effect of operating conditions is insignificant, but sometimes the sensitivity to the mode may be such that, while the vibration of a certain machine under certain operating conditions is recognized as acceptable, it may cease to be considered as such when these conditions change.

In cases where some aspects of vibration sensitivity are in doubt, agreement should be reached between the user and the manufacturer of the machine on the required scope of tests or on the methods of theoretical evaluation.

Special methods are used to assess the condition of roller bearing elements. This issue is considered in. The definition of evaluation criteria for these methods is outside the scope of this International Standard.

APPENDIX A
(reference)
RELATIONSHIP BETWEEN VARIOUS VIBRATION PARAMETERS

For many years and up to now, the vibration state of a wide class of machines has been successfully assessed by measuring the root-mean-square value of the vibration velocity. For vibration with a discrete composition of frequency components of known amplitude and phase and a small pedestal determined by random and shock processes, the main vibration parameters (for example, displacement, speed, acceleration, peak and root mean square values) are related by strictly defined mathematical relationships. The derivation of these dependencies is well known, and this appendix is ​​not intended to re-examine this aspect of the problem. However, a number of useful relationships are shown below.

Having determined by measurements the dependence of vibration velocity on time, its root-mean-square value can be calculated as follows:

where v r. m. s is the corresponding root-mean-square value;

v (t) - function of vibration velocity versus time;

T- the sampling period, which should be much greater than the period of any of the main frequency components contained in v (t).

Values ​​of vibration acceleration, velocity or displacement (respectively a j, v j, S j, j= 1, 2, …, n) is determined by analyzing the vibration spectra as a function of the angular frequency ( ω 1, ω 2, ..., ω n). If the mean square values ​​of the vibration velocity amplitudes are known v 1, v 2, ..., v n or rms values ​​of acceleration amplitudes a 1, a 2, … a n, the associated with them and characterizing the oscillatory process, the root-mean-square value of the vibration velocity is determined by the expression

Figure A.1 - Graph showing the relationship between acceleration, velocity and displacement for harmonic vibration

In the presence of only two significant vibration components that determine the beats of the mean square value of the vibration velocity between the maximum v max and minimal v min values, the root-mean-square value of vibration is approximately expressed as

where S f- the range of vibration displacement, microns;

v f is the root-mean-square value of the vibration velocity at the frequency f, mm / s;

ω f = 2π f- angular frequency.

The graph for recalculation is shown in Figure A.1.

APPENDIX B
(reference)
APPROXIMATE CRITERIA FOR ASSESSING THE VIBRATION STATE OF DIFFERENT TYPES MACHINES

This International Standard is the basic document for the development of guidelines for the measurement and assessment of machine vibration. Evaluation criteria for specific machine types should be specified in the respective separate standards. Table B.1 shows only temporary, approximate criteria that can be used in the absence of suitable regulatory documents. It can be used to determine the upper boundaries of the zones from A before WITH(see 5.3.1), expressed in rms values ​​of vibration velocity v r.m.s, mm / s, for machines of various classes:

Class 1 - Individual parts of motors and machines connected to the unit and operating in their normal mode (serial electric motors up to 15 kW are typical machines in this category).

Class 2 - Medium-sized machines (typical electric motors from 15 to 875 kW) without special foundations, rigidly mounted motors or machines (up to 300 kW) on special foundations.

Class 3 - Powerful prime movers and other powerful machines with rotating masses, mounted on solid foundations, relatively rigid in the direction of vibration measurement.

Class 4 - Powerful prime movers and other powerful machines with rotating masses installed on foundations that are relatively flexible in the direction of vibration measurement (for example, turbine generators and gas turbines with an output of more than 10 MW).

Table B.1- Approximate boundaries of zones for machines of various classes

v r.m., m / s	Class 1	Class 2	Class 3	Class 4
0,28	A	A	A	A
0,45
0,71
1,12	V
		V
	WITH		V
		WITH		V
	D		WITH
11,2		D f w)m,

where v r.m.s- permissible root-mean-square value of vibration velocity, mm / s;

v A is the root-mean-square value of the vibration velocity, which corresponds to the frequency range between f x and f y, mm / s;

G is a factor that defines the boundaries of zones (for example, a limit value for a zone A can be obtained by substitution G= 1.0; zone limit B: G = 2.56; zone limit WITH:G= 6.4). This factor may depend on the performance of the machine: speed, load, pressure, etc .;

f x,f y - the established boundaries of the frequency range, within which the criterion is determined on the basis of one value of the vibration velocity parameter (see), Hz;

where f- the frequency for which the root-mean-square value is determined, Hz;

k, t - given constants for machines of this type.

APPENDIX D
(reference)
VECTOR ANALYSIS OF VIBRATION CHANGES

The criteria for evaluating the vibration state of the machine are based on the measured level of steady-state vibration and any changes in this level. However, in some cases, vibration changes can only be recorded by analyzing individual frequency components. Such a technique for components with frequencies that are not multiples of the circulating frequency is at an early stage of development, therefore, it is not considered in this standard.

D.1 General

The broadband steady-state vibration signal obtained as a result of measurements has a complex character and consists of a number of harmonics. Each of these components is determined by its frequency, amplitude and phase relative to some known origin. Standard vibration control devices measure the integral signal level and do not separate it into individual frequency components. However, modern diagnostic devices are able to analyze a complex signal by determining the amplitude and phase of each component, which makes it possible to determine the probable causes of the abnormal vibration state of the machine.

Changes in individual frequency components, which can be significant, are not always reflected to the same extent in the value of general vibration, and, therefore, a criterion based on a change in general vibration is of limited use.

D.2 The importance of assessing the change in the vector

Figure D.1, which is a graph in polar coordinates, is used to simultaneously represent the modulus and phase of one of the frequency components of a complex vibration signal in vector form. Vector A 1 corresponds to the initial steady-state vibration state of the machine, characterized by the root-mean-square value of the vibration velocity of 3 mm / s and the phase angle of 40 °. Vector A 2 corresponds to the steady-state vibration state after some changes in the state of the machine and is determined by the root-mean-square value of the vibration velocity of 2.5 mm / s at a phase angle of 180 °. Figure D.1 shows that although the root-mean-square value of the vibration velocity decreased by 0.5 mm / s, the true change in vibration is characterized by the vector (A 2 - A 1), the modulus of which is 5.2 mm / s, which is 10 times greater than the value obtained by comparing the absolute values ​​of vibration.

Figure D.1 - Comparison of the difference of two vector harmonics of vibration with the difference of their modules

D.3 Control over the change in the vibration vector

The above example clearly shows the possibilities of observing the change in the vibration vector. However, we must not forget that the total vibration signal consists of a number of frequency components, for each of which it is possible to register a change in the vector. In addition, an unacceptable change in the vector for one of the components may be quite acceptable for the other. In this regard, in relation to this standard, which is mainly devoted to operational vibration control, it is not possible to establish a criterion for changing the vector of individual frequency components.

APPENDIX E
(reference)
SPECIAL METHODS FOR MEASURING AND ANALYSIS OF VIBRATION OF ROLLING BEARINGS

A simple method for determining vibration over a wide frequency range by monitoring the vibration acceleration of rolling bearing housings, as described in the main body of this standard, often provides sufficient information about the condition of these bearings. However, this simple method may not give good results in all cases. In particular, errors may occur when the resonant frequencies of the bearing fall within the measurement frequency range, or in the case of vibration from other sources, such as gearing.

As a result of these circumstances, it becomes necessary to use other measuring instruments and methods of analysis, which are developed specifically for rolling bearings. But none of the devices and methods is universal for all cases. Thus, it is impossible with the help of any method to diagnose all kinds of bearing defects, and if any method can successfully diagnose the main defects of a machine of a certain type, it may be completely unsuitable for a machine of another type. The resulting vibration characteristics depend on the type of bearing, the design of its supporting elements, measuring equipment and methods of processing the results. All these factors must be well studied, and only in this case can an objective method for assessing the condition of the bearings be developed. The choice of a suitable method requires special knowledge in terms of research methods, as well as the mechanisms to which they are applied.

Below is a brief description of some of the measuring instruments and analysis methods that have become prevalent. However, sufficient information is not available on the appropriate evaluation criteria suitable for use in the standards.

E.1 Analysis of initial data (measurement of general vibration)

There are a number of proposals on the use of simple measurements as an alternative to monitoring the root-mean-square value of vibration acceleration in order to diagnose the condition of rolling bearings, namely:

Measurement of peak acceleration;

Measurement of the ratio of the peak acceleration value to its root mean square value (crest factor);

Determination of the product of the measured root mean square and peak acceleration values.

E.2 Frequency analysis

The individual frequency components of the vibrational spectrum can be determined by applying various filters or spectral analysis. If sufficient data is available for a particular bearing type, the frequency components that characterize certain bearing defects can be determined by calculating and then compared with the corresponding components of the resulting vibration spectrum. Thus, it is possible not only to obtain information about the presence of defects, but also to diagnose them.

For a more accurate acquisition of the spectrum components associated with bearings, in the presence of extraneous vibrational influences (background), the methods of coherent averaging, adaptive noise suppression and extraction of the useful signal spectrum are quite effective. A relatively new method is the spectral analysis of the envelope of a vibration signal that has passed through a band-pass high-frequency filter.

A convenient variant of the spectral analysis method is to analyze the side bands of the main characteristic frequencies of the bearings (sum and difference frequencies), and not the components themselves at these frequencies. Cepstrum analysis (defined as the power spectrum versus the log power spectrum) can be used to investigate the sidebands, typically used to detect gear defects.

E.3 Shock pulse analysis method

There are a number of industrial measuring instruments based on the fact that defects in rolling bearings cause short, very high frequency pulses, commonly called shock pulses.

Due to the high steepness of shock pulses, their spectrum contains components at very high frequencies. These devices detect these high-frequency components and convert them into a value that is related to the condition of the bearings.

Another method is the spectral analysis of the envelope of shock pulses.

E.4 Other methods

Several inspection methods are available to detect bearing defects without measuring vibration. These methods are, in particular: analysis of acoustic noise, analysis of wear products (ferrography) and thermography. However, none of these methods can claim to be universally successful, and in some cases they are unacceptable.

Keywords: machines, vibration, measurement, assessment, vibration condition