An example of an acoustic calculation of an office ventilation system. Acoustic calculations. Reduced sound load from fan operation

Ventilation systems are noisy and vibrate. The intensity and area of ​​sound propagation depends on the location of the main units, the length of the air ducts, the overall performance, as well as the type of building and its functional purpose. The calculation of noise from ventilation is designed to select the mechanisms of operation and the materials used, in which it will not go beyond the normative values, and is included in the design of ventilation systems as one of the points.

Ventilation systems consist of separate elements, each of which is a source of unpleasant sounds:

  • For a fan, this can be a blade or a motor. The blade makes noise due to a sharp pressure drop on one side and the other. Engine - due to breakdown or improper installation. Refrigeration units make noise for the same reasons, plus improper compressor operation.
  • Air ducts. There are two reasons: the first is vortex formations from the air hitting the walls. We talked about this in more detail in the article. The second is a hum in places where the cross section of the duct changes. Problems are solved by reducing the speed of gas movement.
  • Building construction. Side noise from vibrations of fans and other installations transmitted to building elements. The solution is carried out by installing special supports or gaskets to dampen vibrations. illustrative example- air conditioning in the apartment: if outdoor unit is not fixed at all points, or the installers forgot to put protective gaskets, then its operation may cause acoustic discomfort to the owners of the installation or their neighbors.

Transfer Methods

There are three sound propagation paths, and in order to calculate the sound load, you need to know exactly how it is transmitted in all three ways:

  • Airborne: noise from operating installations. Distributed both inside and outside the building. The main source of stress for people. For example, a large store, air conditioners and refrigeration units which are located on the back of the building. Sound waves propagate in all directions to nearby houses.
  • Hydraulic: Noise source - liquid pipes. Sound waves are transmitted over long distances throughout a building. It is caused by a change in the size of the pipeline section and a malfunction of the compressor.
  • Vibrating: source - building construction. Caused by improper installation of fans or other parts of the system. It is transmitted throughout the building and beyond.

Some specialists use scientific research from other countries in their calculations. For example, there is a formula published in a German magazine: it calculates the sound generation by the walls of an air duct, depending on the speed of the air flow.


Measuring method


It is often required to measure the permissible noise level or vibration intensity in already installed, operating ventilation systems. The classical method of measurement involves the use special device"Sound level meter": it determines the strength of the propagation of sound waves. The measurement is carried out using three filters that allow you to cut off unwanted sounds outside the studied area. The first filter - measures the sound, the intensity of which does not exceed 50 dB. The second is from 50 to 85 dB. The third is over 80 dB.

Vibrations are measured in Hertz (Hz) for several points. For example, in the immediate vicinity of the noise source, then at a certain distance, then at the most distant point.

Norms and rules

The rules for calculating noise from ventilation operation and the algorithms for performing calculations are specified in SNiP 23-03-2003 "Protection from noise"; GOST 12.1.023-80 “System of labor safety standards (SSBT). Noise. Methods for establishing the values ​​of noise characteristics of stationary machines.

When determining the sound load near buildings, it must be remembered that the standard values ​​are given for intermittent mechanical ventilation and open windows. If closed windows and a forced air exchange system capable of providing the design multiplicity are taken into account, then other parameters are used as norms. The maximum noise level around the building is increased to the limit, which allows maintaining the normative parameters inside the building.

Sound load requirements for residential and public buildings depend on their category:

  1. A is the best condition.
  2. B - comfortable environment.
  3. B is the noise level at the limit limit.

Acoustic calculation

It is used by designers to determine noise reduction. The main task of acoustic calculation is to calculate the active spectrum of sound loads at all points determined in advance, and compare the obtained value with the normative, maximum allowable. If necessary, reduce to established standards.

The calculation is carried out according to the noise characteristics of the ventilation equipment, they must be indicated in the technical documentation.

Settlement points:

  • direct installation site of the equipment;
  • adjoining premises;
  • all rooms where the ventilation system operates, including basements;
  • rooms for transit applications of air channels;
  • places of inlet supply or exhaust outlet.

Acoustic calculation is performed according to two main formulas, the choice of which depends on the location of the point.

  1. The calculation point is taken inside the building, in the immediate vicinity of the fan. Sound pressure depends on the power and number of fans, wave directionality and other parameters. Formula 1 for determining octave sound pressure levels from one or more fans looks like this:

where L Pi is the sound power in each octave;
∆L pomi - decrease in the intensity of the noise load associated with the multidirectional movement of sound waves and power losses from propagation in the air;

According to formula 2, ∆L is determined by mi:

where Фi is the dimensionless factor of the wave propagation vector;
S is the area of ​​a sphere or hemisphere that captures the fan and the calculation point, m 2;
B is the constant value of the acoustic constant in the room, m 2 .

  1. The settlement point is taken outside the building in the surrounding area. The sound from operation propagates through the walls of the ventilation shafts, grilles and the fan housing. It is conditionally assumed that the noise source is a point one (the distance from the fan to the calculated position is an order of magnitude greater than the size of the apparatus). Then the octave noise pressure level is calculated by formula 3:

where L Pocti - octave power of the noise source, dB;
∆L Pneti - loss of sound power during its propagation through the duct, dB;
∆L ni - sound radiation directivity index, dB;
r - length of the segment from the fan to the calculation point, m;
W is the angle of sound radiation in space;
b a - reduction of noise intensity in the atmosphere, dB/km.

If several sources of noise act on one point, for example, a fan and an air conditioner, then the calculation method changes slightly. You can’t just take and add up all the sources, so experienced designers go the other way, removing all unnecessary data. The difference between the largest and the least intense source is calculated, and the resulting value is compared with the standard parameter and added to the level of the largest.

Reduced sound load from fan operation


There is a set of measures that allow leveling the noise factors from the operation of the fan that are unpleasant to the human ear:

  • Choice of equipment. A professional designer, unlike an amateur, always pays attention to the noise from the system and selects fans that provide standard microclimate parameters, but at the same time without a large power margin. Presented on the market wide range of fans with silencers, they well protect against unpleasant sounds and vibrations.
  • Choice of installation location. Powerful ventilation equipment is mounted only outside the serviced premises: it can be a roof or a special chamber. For example, if you put a fan in the attic in panel house, then the residents on the top floor will immediately feel discomfort. Therefore, only roof fans are used in such cases.
  • Selection of the speed of air movement through the channels. Designers proceed from acoustic calculation. For example, for a classic air duct 300×900 mm, it is no more than 10 m/s.
  • Vibration isolation, sound isolation and shielding. Vibration isolation involves the installation of special supports that dampen vibrations. Soundproofing is carried out by pasting the cases with a special material. Shielding involves cutting off a sound source from a building or room using a shield.

The calculation of noise from ventilation systems involves finding such technical solutions when the operation of the equipment will not interfere with people. This is a complex task requiring skills and experience in this area.


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Acoustic calculation produced for each of the eight octave bands of the auditory range (for which noise levels are normalized) with geometric mean frequencies of 63, 125, 250, 500, 1000, 2000, 4000, 8000 Hz.

For central systems ventilation and air conditioning with branched air duct networks, it is allowed to carry out acoustic calculation only for frequencies of 125 and 250 Hz. All calculations are performed with an accuracy of 0.5 Hz and the final result is rounded to the nearest whole number of decibels.

When the fan operates in efficiency modes greater than or equal to 0.9, the maximum efficiency 6 = 0. If the fan operation mode deviates by no more than 20% of the maximum efficiency, 6 = 2 dB is taken, and with a deviation of more than 20% - 4 dB.

It is recommended to reduce the level of sound power generated in the air ducts, to take the following maximum air speeds: in the main air ducts of public buildings and auxiliary premises of industrial buildings 5-6 m/s, and in branches - 2-4 m/s. For industrial buildings, these speeds can be increased by a factor of 2.

For ventilation systems with an extensive network of air ducts, acoustic calculation is done only for the branch to the nearest room (at the same permissible noise levels), at different noise levels - for the branch with the lowest permissible level. Acoustic calculation for air intake and exhaust shafts is done separately.

For centralized systems ventilation and air conditioning with an extensive network of air ducts, the calculation can only be done for frequencies of 125 and 250 Hz.

When noise enters the room from several sources (from supply and exhaust grilles, from units, local air conditioners, etc.), several design points are selected at workplaces closest to the noise sources. For these points, octave sound pressure levels are determined from each noise source separately.

With different regulatory requirements for sound pressure levels during the day, acoustic calculation is performed at the lowest permissible levels.

The total number of noise sources m does not include sources that create in calculated point octave levels are 10 and 15 dB below the standard ones, with their number not exceeding 3 and 10, respectively. The throttling devices for fans are also not taken into account.

Several supply or exhaust grilles from one fan evenly distributed throughout the room can be considered as one source of noise when noise from one fan penetrates through them.

When several sources of the same sound power are located in the room, the sound pressure levels at the selected design point are determined by the formula

Acoustic calculations

Among the health issues environment Noise control is one of the most important. In large cities, noise is one of the main physical factors that shape the conditions of the environment.

Growth of industrial and housing construction, rapid development various kinds transport, increasing use in residential and public buildings of sanitary and engineering equipment, household appliances led to the fact that the noise levels in the residential areas of the city became comparable to the noise levels at work.

The noise regime of large cities is formed mainly by road and rail transport, which makes up 60-70% of all noise.

The increase in air traffic, the emergence of new powerful aircraft and helicopters, as well as rail transport, open metro lines and shallow metro have a noticeable impact on the noise level.

At the same time, in some large cities, where measures are being taken to improve the noise situation, noise levels are decreasing.

There are acoustic and non-acoustic noises, what is the difference between them?

Acoustic noise is defined as a set of sounds of different strength and frequency, resulting from the oscillatory motion of particles in elastic media (solid, liquid, gaseous).

Non-acoustic noise - Radio-electronic noise - random fluctuations of currents and voltages in radio-electronic devices, arise as a result of uneven emission of electrons in electrovacuum devices (shot noise, flicker noise), uneven processes of generation and recombination of charge carriers (conduction electrons and holes) in semiconductor devices, thermal motion of current carriers in conductors (thermal noise), thermal radiation of the Earth and the earth's atmosphere, as well as planets, the Sun, stars, the interstellar medium, etc. (cosmic noise).

Acoustic calculation, noise level calculation.

In the process of construction and operation of various facilities, noise control problems are an integral part of labor protection and protection of public health. Machines can act as sources vehicles, mechanisms and other equipment. Noise, its magnitude of impact and vibration on a person depends on the level of sound pressure, frequency characteristics.

Normalization of noise characteristics is understood as the establishment of restrictions on the values ​​of these characteristics, at which the noise affecting people should not exceed acceptable levels regulated by the current sanitary standards and rules.

The objectives of the acoustic calculation are:

Identification of noise sources;

Determination of their noise characteristics;

Determination of the degree of influence of noise sources on normalized objects;

Calculation and construction of individual zones of acoustic discomfort of noise sources;

Development of special noise protection measures that provide the required acoustic comfort.

The installation of ventilation and air conditioning systems is already considered a natural need in any building (whether residential or administrative), acoustic calculation should be performed for rooms of this type. So, if the noise level is not calculated, it may turn out that the room has a very low level of sound absorption, and this greatly complicates the process of communication between people in it.

Therefore, before installing a ventilation system in a room, it is necessary to carry out an acoustic calculation. If it turns out that the room is characterized by poor acoustic properties, it is necessary to propose a series of measures to improve the acoustic situation in the room. Therefore, acoustic calculations are also performed for the installation of household air conditioners.

Acoustic calculation is most often carried out for objects that have complex acoustics or have high requirements for sound quality.

Sound sensations arise in the hearing organs when they are exposed to sound waves in the range from 16 Hz to 22 thousand Hz. Sound propagates in air at a speed of 344 m/s in 3 seconds. 1 km.

The value of the hearing threshold depends on the frequency of perceived sounds and is equal to 10-12 W/m 2 at frequencies close to 1000 Hz. The upper limit is the pain threshold, which is less dependent on frequency and lies within 130 - 140 dB (at a frequency of 1000 Hz, intensity 10 W / m 2, sound pressure).

The ratio of intensity level and frequency determines the sensation of sound volume, i.e. sounds that have different frequencies and intensities can be assessed by a person as equally loud.

When perceived sound signals against a certain acoustic background, the effect of signal masking can be observed.

The masking effect can be detrimental to acoustic indicators and can be used to improve the acoustic environment, i.e. in the case of masking a high-frequency tone with a low-frequency one, which is less harmful to humans.

The procedure for performing acoustic calculation.

To perform an acoustic calculation, the following data will be required:

Dimensions of the room for which the calculation of the noise level will be carried out;

The main characteristics of the premises and its properties;

Noise spectrum from the source;

Characteristics of the barrier;

Distance data from the center of the noise source to the acoustic calculation point.

In the calculation, the sources of noise and their characteristic properties are first determined. Next, on the object under study, points are selected at which calculations will be carried out. At selected points of the object, a preliminary sound pressure level is calculated. Based on the results obtained, a calculation is performed to reduce noise to the required standards. Having received all the necessary data, a project is carried out to develop measures that will reduce the noise level.

Properly performed acoustic calculation is the key to excellent acoustics and comfort in a room of any size and design.

Based on the performed acoustic calculation, the following measures can be proposed to reduce the noise level:

* installation of soundproof structures;

* the use of seals in windows, doors, gates;

* the use of structures and screens that absorb sound;

*implementation of planning and development of the residential area in accordance with SNiP;

* the use of silencers in ventilation systems and air conditioning systems.

Carrying out acoustic calculation.

Work on the calculation of noise levels, assessment of acoustic (noise) impact, as well as the design of specialized noise protection measures, should be carried out by a specialized organization with a relevant area.

noise acoustic calculation measurement

In the simplest definition, the main task of an acoustic calculation is to estimate the noise level, created by the source noise at a given design point with the established quality of the acoustic impact.

The acoustic calculation process consists of the following main steps:

1. Collection of the necessary initial data:

The nature of noise sources, their mode of operation;

Acoustic characteristics of noise sources (in the range of geometric mean frequencies 63-8000 Hz);

Geometric parameters of the room in which the noise sources are located;

Analysis of the weakened elements of the enclosing structures, through which the noise will penetrate into the environment;

Geometric and soundproof parameters of weakened elements of enclosing structures;

Analysis of nearby objects with the established quality of acoustic impact, determination of permissible sound levels for each object;

Analysis of distances from external noise sources to normalized objects;

Analysis of possible shielding elements on the path of sound wave propagation (buildings, green spaces, etc.);

Analysis of weakened elements of enclosing structures (windows, doors, etc.), through which noise will penetrate into normalized premises, identification of their soundproofing ability.

2. Acoustic calculation is made on the basis of existing guidelines and recommendations. Basically, these are “Methods of calculation, standards”.

At each calculated point, it is necessary to sum up all available noise sources.

The result of the acoustic calculation are certain values ​​(dB) in octave bands with geometric mean frequencies of 63-8000 Hz and the equivalent value of the sound level (dBA) at the calculated point.

3. Analysis of the calculation results.

The analysis of the results obtained is carried out by comparing the values ​​obtained at the calculated point with the established Sanitary Standards.

If necessary, the next step in the acoustic calculation can be the design of the necessary noise protection measures that will reduce the acoustic impact at the calculated points to an acceptable level.

Carrying out instrumental measurements.

In addition to acoustic calculations, it is possible to calculate instrumental measurements of noise levels of any complexity, including:

Measurement of noise impact of existing ventilation and air conditioning systems for office buildings, private apartments, etc.;

Carrying out measurements of noise levels for attestation of workplaces;

Carrying out work on instrumental measurement of noise levels within the framework of the project;

Carrying out work on instrumental measurement of noise levels as part of technical reports when approving the boundaries of the SPZ;

Implementation of any instrumental measurements of noise exposure.

Conducting instrumental measurements of noise levels is carried out by a specialized mobile laboratory using modern equipment.

Timing of acoustic calculation. Terms of performance of work depend on volume of calculations and measurements. If it is necessary to make an acoustic calculation for projects of residential buildings or administrative facilities, then they are performed on average 1 - 3 weeks. Acoustic calculation for large or unique objects (theaters, organ halls) takes more time, based on the provided source materials. In addition, the number of studied noise sources, as well as external factors, largely affect the life.

2008-04-14

The ventilation and air conditioning system (VAC) is one of the main sources of noise in modern residential, public and industrial buildings, on ships, in sleeping cars of trains, in various salons and control cabins.

Noise in UHKV comes from the fan (the main source of noise with its own tasks) and other sources, propagates through the duct along with the air flow and is radiated into the ventilated room. Noise and its reduction are influenced by: air conditioners, heating units, air control and distribution devices, design, turns and branching of air ducts.

Acoustic calculation of UHVW is carried out in order to optimally select all necessary funds noise reduction and determination of the expected noise level at the design points of the room. Traditionally, active and reactive silencers have been the main means of reducing system noise. Soundproofing and sound absorption of the system and premises is required to ensure compliance with the norms of permissible noise levels for humans - important environmental standards.

Now, in the building codes and regulations of Russia (SNiP), which are mandatory for the design, construction and operation of buildings in order to protect people from noise, an emergency situation has developed. In the old SNiP II-12-77 "Protection from noise", the method of acoustic calculation of the SVKV of buildings is outdated and therefore was not included in the new SNiP 23-03-2003 "Protection from noise" (instead of SNiP II-12-77), where it is still at all is absent.

So the old method is deprecated and the new one is not. The time has come to create a modern method of acoustic calculation of SVKV in buildings, as is already the case with its own specifics in other, previously more advanced in acoustics, areas of technology, for example, on ships. Consider three possible ways acoustic calculation, as applied to SVKV.

The first method of acoustic calculation. This method, which is established purely on analytical dependencies, uses the theory of long lines, known in electrical engineering and referred here to the propagation of sound in a gas filling a narrow pipe with rigid walls. The calculation is made under the condition that the pipe diameter is much less than the sound wave length.

For a rectangular pipe, the side must be less than half the wavelength, and for round pipe- radius. It is these pipes in acoustics that are called narrow. So, for air at a frequency of 100 Hz, a rectangular pipe will be considered narrow if the section side is less than 1.65 m. In a narrow curved pipe, sound propagation will remain the same as in a straight pipe.

This is known from the practice of using speech tubes, for example, for a long time on steamships. Typical scheme long line of the ventilation system has two defining quantities: L wH is the sound power coming into the discharge pipeline from the fan at the beginning of the long line, and L wK is the sound power coming from the discharge pipeline at the end of the long line and entering the ventilated room.

The long line contains the following characteristic elements. They are R 1 sound inlet, R 2 active silencer, R 3 sound insulated tee, R 4 sound insulated jet silencer, R 5 sound insulated butterfly valve, and R 6 sound insulated outlet. Sound insulation here refers to the difference in dB between the sound power in the waves incident on a given element and the sound power radiated by this element after the waves have passed through it further.

If the sound insulation of each of these elements does not depend on all others, then the sound insulation of the entire system can be estimated by calculation as follows. The wave equation for a narrow pipe has the following form of the equation for plane sound waves in an unbounded medium:

where c is the speed of sound in air and p is the sound pressure in the pipe, related to the vibrational speed in the pipe according to Newton's second law by the relation

where ρ is the air density. The sound power for plane harmonic waves is equal to the integral over the cross-sectional area S of the duct over the period of sound vibrations T in W:

where T = 1/f is the period of sound vibrations, s; f is the oscillation frequency, Hz. Sound power in dB: L w \u003d 10lg (N / N 0), where N 0 \u003d 10 -12 W. Within the specified assumptions, the sound insulation of a long line of a ventilation system is calculated using the following formula:

The number of elements n for a specific SVKV can, of course, be greater than the above n = 6. Let us apply the theory of long lines to the above characteristic elements of the air ventilation system to calculate the values ​​of R i .

Inlet and outlet openings of the ventilation system with R 1 and R 6 . The junction of two narrow pipes with different areas cross sections S 1 and S 2, according to the theory of long lines, are an analogue of the interface between two media with normal incidence of sound waves on the interface. The boundary conditions at the junction of two pipes are determined by the equality of sound pressures and vibrational velocities on both sides of the connection boundary, multiplied by the cross-sectional area of ​​the pipes.

Solving the equations obtained in this way, we obtain the energy transmission coefficient and the sound insulation of the junction of two pipes with the above sections:

An analysis of this formula shows that at S 2 >> S 1 the properties of the second tube approach those of the free boundary. For example, a narrow pipe open into a semi-infinite space can be considered, from the point of view of the soundproofing effect, as bordering on a vacuum. For S 1<< S 2 свойства второй трубы приближаются к свойствам жесткой границы. В обоих случаях звукоизоляция максимальна. При равенстве площадей сечений первой и второй трубы отражение от границы отсутствует и звукоизоляция равна нулю независимо от вида сечения границы.

Active noise suppressor R2. Sound insulation in this case can be approximately and quickly estimated in dB, for example, according to the well-known formula of engineer A.I. Belova:

where P is the perimeter of the passage section, m; l is the silencer length, m; S is the cross-sectional area of ​​the silencer channel, m 2 ; α eq is the equivalent sound absorption coefficient of the lining, depending on the actual absorption coefficient α, for example, as follows:

α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

α eq 0.1 0.2 0.4 0.5 0.6 0.9 1.2 1.6 2.0 4.0

It follows from the formula that the sound insulation of the channel of the active silencer R 2 is the greater, the greater the absorption capacity of the walls α eq, the length of the silencer l and the ratio of the channel perimeter to its cross-sectional area П/S. For the best sound-absorbing materials, for example, the PPU-ET, BZM and ATM-1 brands, as well as other widely used sound absorbers, the actual sound absorption coefficient α is presented in.

Tee R3. In ventilation systems, most often the first pipe with a cross-sectional area S 3 then branches into two pipes with cross-sectional areas S 3.1 and S 3.2. Such a branch is called a tee: through the first branch, sound enters, through the other two it passes further. In general, the first and second pipes may be comprised of a plurality of pipes. Then we have

The sound insulation of a tee from section S 3 to section S 3.i is determined by the formula

Note that due to aerohydrodynamic considerations in tees, they strive to ensure that the cross-sectional area of ​​the first pipe is equal to the sum of the cross-sectional area in the branches.

Reactive (chamber) noise suppressor R4. The chamber silencer is an acoustically narrow pipe with a cross section S 4 , which passes into another acoustically narrow pipe of large cross section S 4.1 with a length l, called a chamber, and then again passes into an acoustically narrow pipe with a cross section S 4 . Let us use the theory of the long line here as well. Replacing the characteristic impedance in the well-known formula for the sound insulation of a layer of arbitrary thickness at normal incidence of sound waves by the corresponding reciprocals of the pipe area, we obtain the formula for the sound insulation of a chamber silencer

where k is the wave number. The sound insulation of a chamber silencer reaches its greatest value at sin(kl)= 1, i.e. at

where n = 1, 2, 3, … Frequency of maximum sound insulation

where c is the speed of sound in air. If several chambers are used in such a silencer, then the sound reduction formula must be applied sequentially from chamber to chamber, and the total effect is calculated by applying, for example, the boundary conditions method. Efficient chamber silencers sometimes require large overall dimensions. But their advantage is that they can be effective at any frequency, including low frequencies, where active jammers are practically useless.

The zone of large sound insulation of chamber silencers covers repeating fairly wide frequency bands, but they also have periodic sound transmission zones that are very narrow in frequency. To increase efficiency and equalize the frequency response, a chamber silencer is often lined on the inside with a sound absorber.

damper R 5 . The damper is structurally a thin plate with an area S 5 and a thickness δ 5, clamped between the flanges of the pipeline, the hole in which the area S 5.1 is less than the inner diameter of the pipe (or other characteristic size). Soundproofing such a throttle valve

where c is the speed of sound in air. In the first method, the main issue for us when developing a new method is the assessment of the accuracy and reliability of the result of the acoustic calculation of the system. Let us determine the accuracy and reliability of the result of calculating the sound power entering the ventilated room - in this case, the values

Let us rewrite this expression in the following notation for the algebraic sum, namely

Note that the absolute maximum error of an approximate value is the maximum difference between its exact value y 0 and approximate y, that is, ± ε= y 0 - y. The absolute maximum error of the algebraic sum of several approximate values ​​y i is equal to the sum of the absolute values ​​of the absolute errors of the terms:

Here the least favorable case is adopted, when the absolute errors of all terms have the same sign. In reality, partial errors can have different signs and be distributed according to different laws. Most often in practice, the errors of the algebraic sum are distributed according to the normal law (Gaussian distribution). Let us consider these errors and compare them with the corresponding value of the absolute maximum error. Let us define this quantity under the assumption that each algebraic term y 0i of the sum is distributed according to the normal law with the center M(y 0i) and the standard

Then the sum also follows the normal distribution law with mathematical expectation

The error of the algebraic sum is defined as:

Then it can be argued that with a reliability equal to the probability 2Φ(t), the error of the sum will not exceed the value

At 2Φ(t), = 0.9973, we have t = 3 = α and the statistical estimate at almost maximum reliability is the error of the sum (formula) The absolute maximum error in this case

Thus ε 2Φ(t)<< ε. Проиллюстрируем это на примере результатов расчета по первому способу. Если для всех элементов имеем ε i = ε= ±3 дБ (удовлетворительная точность исходных данных) и n = 7, то получим ε= ε n = ±21 дБ, а (формула). Результат имеет совершенно неудовлетворительную точность, он неприемлем. Если для всех характерных элементов системы вентиляции воздуха имеем ε i = ε= ±1 дБ (очень высокая точность расчета каждого из элементов n) и тоже n = 7, то получим ε= ε n = ±7 дБ, а (формула).

Here, the result in the probabilistic estimation of errors in the first approximation can be more or less acceptable. So, the probabilistic estimation of errors is preferable, and it should be used to select the “ignorance margin”, which is proposed to be used in the acoustic calculation of the SVKV to ensure that the permissible noise standards are met in a ventilated room (this has not been done before).

But the probabilistic estimation of the result errors also indicates in this case that it is difficult to achieve high accuracy of the calculation results by the first method even for very simple circuits and a low-velocity ventilation system. For simple, complex, low- and high-speed UTCS circuits, satisfactory accuracy and reliability of such a calculation can be achieved in many cases only by the second method.

The second method of acoustic calculation. On ships, a calculation method has long been used, based partly on analytical dependencies, but decisively on experimental data. We use the experience of such calculations on ships for modern buildings. Then, in a ventilated room served by one j-th air distributor, the noise levels L j , dB, at the design point should be determined by the following formula:

where L wi is the sound power, dB, generated in the i-th element of the UCS, R i is the sound insulation in the i-th element of the UCS, dB (see the first method),

a value that takes into account the influence of the room on the noise in it (in the construction literature, sometimes B is used instead of Q). Here r j is the distance from the jth air distributor to the design point of the room, Q is the sound absorption constant of the room, and the values ​​χ, Φ, Ω, κ are empirical coefficients (χ is the near field influence coefficient, Ω is the spatial radiation angle of the source, Φ is the factor directivity of the source, κ is the coefficient of violation of the diffuseness of the sound field).

If m air diffusers are placed in the room of a modern building, the noise level from each of them at the calculated point is equal to L j , then the total noise from all of them must be below the noise levels acceptable for a person, namely:

where L H is the sanitary noise standard. According to the second method of acoustic calculation, the sound power L wi generated in all elements of the UHCS, and the sound insulation R i that takes place in all these elements, for each of them is preliminarily determined experimentally. The fact is that over the past one and a half to two decades, the electronic technology of acoustic measurements, combined with a computer, has greatly progressed.

As a result, enterprises producing SVKV elements must indicate in passports and catalogs the characteristics L wi and R i measured in accordance with national and international standards. Thus, the second method takes into account the noise generation not only in the fan (as in the first method), but also in all other elements of the UHCS, which can be significant for medium- and high-speed systems.

In addition, since it is impossible to calculate the sound insulation R i of such system elements as air conditioners, heating units, control and air distribution devices, therefore, they are not in the first method. But it can be determined with the required accuracy by standard measurements, which is now done for the second method. As a result, the second method, unlike the first one, covers almost all SVKV schemes.

And, finally, the second method takes into account the influence of the properties of the room on the noise in it, as well as the values ​​\u200b\u200bof noise acceptable to a person according to the current building codes and regulations in this case. The main disadvantage of the second method is that it does not take into account the acoustic interaction between the elements of the system - interference phenomena in pipelines.

The summation of the sound power of noise sources in watts, and the sound insulation of elements in decibels, according to the indicated formula for the acoustic calculation of UHCS, is valid only, at least, when there is no interference of sound waves in the system. And when there is interference in pipelines, then it can be a source of powerful sound, on which, for example, the sound of some wind musical instruments is based.

The second method has already been included in the textbook and guidelines for building acoustics course projects for senior students of St. Petersburg State Polytechnic University. Failure to take into account interference phenomena in pipelines increases the "margin for ignorance" or requires, in critical cases, experimental refinement of the result to the required degree of accuracy and reliability.

For the choice of "margin of ignorance", as shown above for the first method, the probabilistic error estimate is preferable, which is proposed to be used in the acoustic calculation of the SVKV of buildings to ensure that the permissible noise standards in the premises are met when designing modern buildings.

The third method of acoustic calculation. This method takes into account interference processes in a narrow pipeline of a long line. Such accounting can dramatically improve the accuracy and reliability of the result. For this purpose, it is proposed to apply for narrow pipes the "method of impedances" of Academician of the Academy of Sciences of the USSR and the Russian Academy of Sciences Brekhovskikh L.M., which he used when calculating the sound insulation of an arbitrary number of plane-parallel layers.

So, let us first determine the input impedance of a plane-parallel layer with a thickness δ 2 , whose sound propagation constant γ 2 = β 2 + ik 2 and acoustic impedance Z 2 = ρ 2 c 2 . Let us denote the acoustic resistance in the medium in front of the layer from where the waves fall, Z 1 = ρ 1 c 1 , and in the medium behind the layer we have Z 3 = ρ 3 c 3 . Then the sound field in the layer, with the omission of the factor i ωt, will be a superposition of waves traveling in the forward and reverse directions, with sound pressure

The input impedance of the whole system of layers (formula) can be obtained by a simple (n - 1)-fold application of the previous formula, then we have

Let us now apply, as in the first method, the theory of long lines to a cylindrical pipe. And thus, with interference in narrow pipes, we have the formula for sound insulation in dB of a long line of a ventilation system:

The input impedances here can be obtained both, in simple cases, by calculation, and, in all cases, by measurement on a special installation with modern acoustic equipment. According to the third method, similarly to the first method, we have the sound power coming from the discharge air duct at the end of a long UHVAC line and entering the ventilated room according to the scheme:

Next comes the evaluation of the result, as in the first method with a "margin of ignorance", and the sound pressure level of the room L, as in the second method. Finally, we obtain the following basic formula for the acoustic calculation of the ventilation and air conditioning system of buildings:

With the calculation reliability 2Φ(t)=0.9973 (practically the highest degree of reliability), we have t = 3 and the error values ​​are 3σ Li and 3σ Ri . With reliability 2Φ(t)= 0.95 (high degree of reliability) we have t = 1.96 and the error values ​​are approximately 2σ Li and 2σ Ri . With reliability 2Φ(t)= 0.6827 (engineering reliability assessment) we have t = 1.0 and the error values ​​are equal to σ Li and σ Ri The third method, directed to the future, is more accurate and reliable, but also more complex - it requires high qualifications in the fields of building acoustics, probability theory and mathematical statistics, and modern measuring technology.

It is convenient to use it in engineering calculations using computer technology. It, according to the author, can be proposed as a new method of acoustic calculation of the ventilation and air conditioning systems of buildings.

Summing up

The solution of urgent issues of developing a new method of acoustic calculation should take into account the best of the existing methods. A new method of acoustic calculation of the UTCS of buildings is proposed, which has a minimum "margin of ignorance" BB, due to the inclusion of errors by the methods of probability theory and mathematical statistics and the consideration of interference phenomena by the impedance method.

The information about the new calculation method presented in the article does not contain some of the necessary details obtained by additional research and work practice, and which constitute the author's "know-how". The ultimate goal of the new method is to provide a choice of a set of means to reduce the noise of the ventilation and air conditioning system of buildings, which increases, in comparison with the existing one, the efficiency, reducing the weight and cost of HVAC.

Technical regulations in the field of industrial and civil construction are not yet available, therefore, developments in the field, in particular, noise reduction in UHV buildings are relevant and should be continued at least until such regulations are adopted.

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  4. Khoroshev G.A., Petrov Yu.I., Egorov N.F. Fighting fan noise // M .: Energoizdat, 1981.
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  6. Bogolepov I.I. Industrial soundproofing. Foreword by acad. I.A. Glebov. Theory, research, design, manufacture, control // Leningrad, Shipbuilding, 1986.
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  9. Noise reduction in buildings and residential areas. Ed. G.L. Osipova and E.Ya. Yudin. - M.: Stroyizdat, 1987.
  10. Building regulations. Noise protection. SNiP II-12-77. Approved by the Decree of the State Committee of the Council of Ministers of the USSR for Construction of June 14, 1977 No. 72. - M.: Gosstroy of Russia, 1997.
  11. Guidance for the calculation and design of noise attenuation of ventilation installations. Developed for SNiPu II-12–77 by organizations of the Research Institute of Building Physics, GPI Santekhpoekt, NIISK. - M.: Stroyizdat, 1982.
  12. Catalog of noise characteristics of technological equipment (to SNiP II-12-77). Research Institute of Construction Physics of the Gosstroy of the USSR // M .: Stroyizdat, 1988.
  13. Construction norms and rules of the Russian Federation. Noise protection. SNiP 23-03-2003. Adopted and put into effect by the resolution of the Gosstroy of Russia dated June 30, 2003 No. 136. Date of introduction 2004-04-01.
  14. Soundproofing and sound absorption. A textbook for university students studying in the specialty "Industrial and civil engineering" and "Heat and gas supply and ventilation", ed. G.L. Osipov and V.N. Bobylev. - M.: AST-Astrel Publishing House, 2004.
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  16. Bogolepov I.I. Building acoustics. Foreword by acad. Yu.S. Vasilyeva // St. Petersburg. Polytechnic University Press, 2006.
  17. Sotnikov A.G. Processes, devices and systems of air conditioning and ventilation. Theory, technology and design at the turn of the century // St. Petersburg, AT-Publishing, 2007.
  18. www.integral.ru Firm "Integral". Calculation of the external noise level of ventilation systems according to: SNiP II-12-77 (part II) - "Guidelines for the calculation and design of noise attenuation of ventilation installations." St. Petersburg, 2007.
  19. www.iso.org is an Internet site that contains complete information about the International Organization for Standardization ISO, a catalog and an online standards store through which you can purchase any currently valid ISO standard in electronic or printed form.
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  23. Federal Law of May 1, 2007 No. 65-FZ “On Amendments to the Federal Law “On Technical Regulation”.

Description:

The norms and regulations in force in the country stipulate that the projects must provide for measures to protect against noise of equipment used for human life support. Such equipment includes ventilation and air conditioning systems.

Acoustic calculation as a basis for designing a low-noise ventilation (air conditioning) system

V. P. Gusev, doctor of tech. sciences, head. noise protection laboratory for ventilation and engineering equipment (NIISF)

The norms and regulations in force in the country stipulate that the projects must provide for measures to protect against noise of equipment used for human life support. Such equipment includes ventilation and air conditioning systems.

The basis for the design of sound attenuation of ventilation and air conditioning systems is acoustic calculation - a mandatory application to the ventilation project of any object. The main tasks of such a calculation are: determination of the octave spectrum of airborne, structural ventilation noise at the calculated points and its required reduction by comparing this spectrum with the permissible spectrum according to hygienic standards. After the selection of construction and acoustic measures to ensure the required noise reduction, a verification calculation of the expected sound pressure levels at the same design points is carried out, taking into account the effectiveness of these measures.

The materials given below do not claim to be complete in the presentation of the method of acoustic calculation of ventilation systems (installations). They contain information that clarifies, supplements or reveals in a new way various aspects of this technique using the example of the acoustic calculation of a fan as the main source of noise in a ventilation system. The materials will be used in the preparation of a set of rules for the calculation and design of noise attenuation of ventilation installations for the new SNiP.

The initial data for acoustic calculation are the noise characteristics of the equipment - sound power levels (SPL) in octave bands with geometric mean frequencies of 63, 125, 250, 500, 1000, 2000, 4000, 8000 Hz. For indicative calculations, corrected sound power levels of noise sources in dBA are sometimes used.

The calculated points are located in human habitats, in particular, at the place where the fan is installed (in the ventilation chamber); in rooms or in areas adjacent to the installation site of the fan; in rooms served by a ventilation system; in rooms where air ducts pass in transit; in the area of ​​​​the air intake or exhaust device, or only the air intake for recirculation.

The calculated point is in the room where the fan is installed

In general, sound pressure levels in a room depend on the sound power of the source and the directivity factor of noise emission, the number of noise sources, the location of the design point relative to the source and the enclosing building structures, and the size and acoustic qualities of the room.

The octave sound pressure levels generated by the fan (fans) at the installation site (in the ventilation chamber) are equal to:

where Фi is the directivity factor of the noise source (dimensionless);

S is the area of ​​an imaginary sphere or part thereof surrounding the source and passing through the calculated point, m 2 ;

B is the acoustic constant of the room, m 2 .

The calculated point is located in the room adjacent to the room where the fan is installed

The octave levels of airborne noise penetrating through the fence into the isolated room adjacent to the room where the fan is installed are determined by the soundproofing ability of the noisy room fences and the acoustic qualities of the protected room, which is expressed by the formula:

(3)

where L w - octave sound pressure level in the room with a noise source, dB;

R - isolation from airborne noise by the enclosing structure through which the noise penetrates, dB;

S - area of ​​the building envelope, m 2 ;

B u - acoustic constant of the insulated room, m 2 ;

k - coefficient that takes into account the violation of the diffuseness of the sound field in the room.

The calculated point is located in the room served by the system

The noise from the fan propagates through the air duct (air duct), partially attenuates in its elements and penetrates into the serviced room through the air distribution and air intake grilles. Octave levels of sound pressure in a room depend on the amount of noise reduction in the air duct and the acoustic qualities of this room:

(4)

where L Pi is the sound power level in the i-th octave radiated by the fan into the air duct;

D L networki - attenuation in the air channel (in the network) between the noise source and the room;

D L remember - the same as in formula (1) - formula (2).

Attenuation in the network (in the air channel) D L R network - the sum of the attenuation in its elements, sequentially located along the sound waves. The energy theory of sound propagation through pipes assumes that these elements do not influence each other. In fact, a sequence of shaped elements and straight sections form a single wave system, in which the principle of attenuation independence in the general case cannot be justified on pure sinusoidal tones. At the same time, in octave (wide) frequency bands, standing waves created by individual sinusoidal components compensate each other, and therefore the energy approach, which does not take into account the wave pattern in air ducts and considers the flow of sound energy, can be considered justified.

Attenuation in straight sections of air ducts made of sheet material is due to losses due to wall deformation and sound emission to the outside. The decrease in the sound power level D L R per 1 m of the length of straight sections of metal air ducts, depending on the frequency, can be judged from the data in Fig. one.

As can be seen, in rectangular ducts, the attenuation (lowering SAM) decreases with increasing sound frequency, while that of a circular duct increases. In the presence of thermal insulation on metal air ducts, shown in fig. 1 values ​​should be approximately doubled.

The concept of attenuation (reduction) of the sound energy flow level cannot be identified with the concept of a change in the sound pressure level in the air duct. As a sound wave travels through a channel, the total amount of energy it carries decreases, but this is not necessarily due to a decrease in the sound pressure level. In a narrowing channel, despite the attenuation of the total energy flow, the sound pressure level can increase due to an increase in the sound energy density. Conversely, in an expanding duct, the energy density (and sound pressure level) can decrease faster than the total sound power. The attenuation of sound in a section with a variable cross section is equal to:

(5)

where L 1 and L 2 are the average sound pressure levels in the initial and final sections of the channel section along the sound waves;

F 1 and F 2 - cross-sectional areas, respectively, at the beginning and end of the channel section.

Attenuation at bends (in elbows, bends) with smooth walls, the cross section of which is less than the wavelength, is determined by the reactance of the additional mass type and the appearance of higher order modes. The kinetic energy of the flow at the turn without changing the cross section of the channel increases due to the resulting non-uniformity of the velocity field. The square turn acts like a low pass filter. The amount of noise reduction at a turn in the plane wave range is given by an exact theoretical solution:

(6)

where K is the modulus of the sound transmission coefficient.

For a ≥ l /2, the value of K is equal to zero, and the incident plane sound wave is theoretically completely reflected by the channel rotation. The maximum noise reduction is observed when the turning depth is approximately half the wavelength. The value of the theoretical modulus of the coefficient of sound transmission through rectangular turns can be judged from Fig. 2.

In real designs, according to the data of the works, the maximum attenuation is 8-10 dB, when half the wavelength fits in the channel width. With increasing frequency, the attenuation decreases to 3-6 dB in the region of wavelengths close in magnitude to twice the channel width. Then it again smoothly increases at high frequencies, reaching 8-13 dB. On fig. Figure 3 shows the noise attenuation curves at channel turns for plane waves (curve 1) and for random, diffuse sound incidence (curve 2). These curves are obtained on the basis of theoretical and experimental data. The presence of a noise reduction maximum at a = l /2 can be used to reduce noise with low-frequency discrete components by adjusting the channel sizes at turns to the frequency of interest.

Noise reduction on turns less than 90° is approximately proportional to the angle of the turn. For example, the noise reduction on a 45° turn is equal to half the noise reduction on a 90° turn. On curves with an angle of less than 45°, noise reduction is not taken into account. For smooth bends and straight bends of air ducts with guide vanes, the noise reduction (sound power level) can be determined using the curves in Fig. 4.

In branching channels, the transverse dimensions of which are less than half the wavelength of the sound wave, the physical causes of attenuation are similar to the causes of attenuation in elbows and bends. This attenuation is determined as follows (Fig. 5).

Based on the medium continuity equation:

From the pressure continuity condition (r p + r 0 = r pr) and equation (7), the transmitted sound power can be represented by the expression

and the reduction in the sound power level at the cross-sectional area of ​​the branch

(11)

(12)

(13)

With a sudden change in the cross section of a channel with transverse dimensions less than half-wavelengths (Fig. 6 a), a decrease in the sound power level can be determined in the same way as with branching.

The calculation formula for such a change in the channel cross section has the form

(14)

where m is the ratio of the larger cross-sectional area of ​​the channel to the smaller one.

The reduction in sound power levels when the channel sizes are larger than the non-planar half-wavelengths due to a sudden narrowing of the channel is

If the channel expands or gradually narrows (Fig. 6 b and 6 d), then the decrease in the sound power level is equal to zero, since there is no reflection of waves with a length shorter than the channel dimensions.

In simple elements of ventilation systems, the following reduction values ​​​​are taken at all frequencies: heaters and air coolers 1.5 dB, central air conditioners 10 dB, mesh filters 0 dB, the junction of the fan to the air duct network 2 dB.

Reflection of sound from the end of the duct occurs if the transverse dimension of the duct is less than the length of the sound wave (Fig. 7).

If a plane wave propagates, then there is no reflection in a large duct, and we can assume that there are no reflection losses. However, if an opening connects a large room and an open space, then only diffuse sound waves directed towards the opening, the energy of which is equal to a quarter of the energy of the diffuse field, enter the opening. Therefore, in this case, the sound intensity level is attenuated by 6 dB.

Characteristics of directivity of sound emission by air distribution grilles are shown in fig. eight.

When the noise source is located in space (for example, on a column in a large room) S = 4p r 2 (radiation in a full sphere); in the middle part of the wall, floors S = 2p r 2 (radiation into the hemisphere); in a dihedral angle (radiation in 1/4 sphere) S = p r 2 ; in the trihedral angle S = p r 2 /2.

The attenuation of the noise level in the room is determined by formula (2). The calculated point is selected at the place of permanent residence of people closest to the noise source, at a distance of 1.5 m from the floor. If the noise at the design point is created by several gratings, then the acoustic calculation is made taking into account their total impact.

When the source of noise is a section of a transit air duct passing through the room, the initial data for the calculation according to formula (1) are the octave sound power levels of the noise emitted by it, determined by the approximate formula:

(16)

where L pi is the sound power level of the source in the i-th octave frequency band, dB;

D L' Рneti - attenuation in the network between the source and the transit section under consideration, dB;

R Ti - sound insulation of the structure of the transit section of the air duct, dB;

S T - surface area of ​​the transit section, which goes into the room, m 2 ;

F T - cross-sectional area of ​​the duct section, m 2 .

Formula (16) does not take into account the increase in the density of sound energy in the duct due to reflections; the conditions for the incidence and passage of sound through the duct structure are significantly different from the passage of diffuse sound through the enclosures of the room.

Settlement points are located on the territory adjacent to the building

Fan noise propagates through the air duct and is radiated into the surrounding space through a grill or shaft, directly through the walls of the fan housing or an open pipe when the fan is installed outside the building.

When the distance from the fan to the calculated point is much larger than its dimensions, the noise source can be considered as a point source.

In this case, the octave sound pressure levels at the calculated points are determined by the formula

(17)

where L Pocti is the octave level of the sound power of the noise source, dB;

D L Pseti - total reduction of the sound power level along the path of sound propagation in the duct in the considered octave band, dB;

D L ni - sound radiation directivity indicator, dB;

r - distance from the noise source to the calculated point, m;

W - spatial angle of sound emission;

b a - sound attenuation in the atmosphere, dB/km.

If there is a row of several fans, grilles or other extended noise source of limited dimensions, then the third term in formula (17) is taken equal to 15 lgr .

Structural noise calculation

Structural noise in rooms adjacent to ventilation chambers occurs as a result of the transfer of dynamic forces from the fan to the ceiling. The octave sound pressure level in the adjacent isolated room is determined by the formula

For fans located in the technical room outside the ceiling above the isolated room:

(20)

where L Pi is the octave sound power level of airborne noise emitted by the fan into the ventilation chamber, dB;

Z c - total wave resistance of the elements of vibration isolators, on which the refrigeration machine is installed, N s / m;

Z lane - input impedance of the ceiling - the carrier plate, in the absence of a floor on an elastic base, the floor plate - if available, N s / m;

S - conditional floor area of ​​the technical room above the isolated room, m 2;

S = S 1 for S 1 > S u /4; S = S u /4; with S 1 ≤ S u /4, or if the technical room is not located above the isolated room, but has one common wall with it;

S 1 - the area of ​​​​the technical room above the isolated room, m 2;

S u - area of ​​the isolated room, m 2;

S in - the total area of ​​​​the technical room, m 2;

R - own insulation of airborne noise by overlapping, dB.

Determination of required noise reduction

The required reduction in octave sound pressure levels is calculated separately for each noise source (fan, fittings, fittings), but at the same time, the number of noise sources of the same type in terms of the sound power spectrum and the magnitude of the sound pressure levels created by each of them at the calculated point are taken into account. In general, the required noise reduction for each source should be such that the total levels in all octave frequency bands from all noise sources do not exceed the permissible sound pressure levels .

In the presence of one noise source, the required reduction in octave sound pressure levels is determined by the formula

where n is the total number of noise sources taken into account.

In the total number of noise sources n, when determining D L tri the required reduction in octave sound pressure levels in urban areas, all noise sources that create sound pressure levels at the design point that differ by less than 10 dB should be included.

When determining D L tri for design points in a room protected from ventilation system noise, the total number of noise sources should include:

When calculating the required fan noise reduction - the number of systems serving the room; noise generated by air distribution devices and fittings is not taken into account;

When calculating the required noise reduction generated by the air distribution devices of the considered ventilation system, - the number of ventilation systems serving the room; the noise of the fan, air distribution devices and fittings is not taken into account;

When calculating the required noise reduction generated by shaped elements and air distribution devices of the considered branch, the number of shaped elements and chokes, the noise levels of which differ from one another by less than 10 dB; the noise of the fan and grilles is not taken into account.

At the same time, the total number of noise sources taken into account does not take into account noise sources that create at the design point the sound pressure level 10 dB lower than the permissible one, if their number is not more than 3 and 15 dB less than the permissible one, if their number is not more than 10.

As you can see, acoustic calculation is not an easy task. The necessary accuracy of its solution is provided by acoustic specialists. The efficiency of noise suppression and the cost of its implementation depend on the accuracy of the performed acoustic calculation. If the value of the calculated required noise reduction is underestimated, then the measures will not be effective enough. In this case, it will be necessary to eliminate the shortcomings at the operating facility, which is inevitably associated with significant material costs. If the required noise reduction is overestimated, unjustified costs are laid directly into the project. So, only due to the installation of silencers, the length of which is 300-500 mm longer than required, additional costs for medium and large objects can amount to 100-400 thousand rubles or more.

Literature

1. SNiP II-12-77. Noise protection. Moscow: Stroyizdat, 1978.

2. SNiP 23-03-2003. Noise protection. Gosstroy of Russia, 2004.

3. Gusev V.P. Acoustic requirements and design rules for low-noise ventilation systems // ABOK. 2004. No. 4.

4. Guidance for the calculation and design of noise attenuation of ventilation installations. Moscow: Stroyizdat, 1982.

5. Yudin E. Ya., Terekhin AS Fighting the noise of mine ventilation installations. Moscow: Nedra, 1985.

6. Noise reduction in buildings and residential areas. Ed. G. L. Osipova, E. Ya. Yudina. Moscow: Stroyizdat, 1987.

7. Khoroshev S. A., Petrov Yu. I., Egorov P. F. Control of fan noise. Moscow: Energoizdat, 1981.