Device, system and method for exploring sound production problem of airflow sound source

Abstract

The invention discloses a device, system and method for exploring the sound production problem of an airflow sound source, and the device comprises a first case, the interior of the first case is fixedly connected with a first switch, the two sides of the first switch are provided with sound insulation sleeves, and the interior of each sound insulation sleeve is sleeved with an air pump; the system comprises an audio processing module, a motor control module and a simulation module. The method comprises the following steps: step 1, COMSOL simulation; 2, building an experimental device; step 3, carrying out a pre-experiment; step 4, theoretical analysis; step 5, experimental verification; step 6, practical application; through theoretical derivation and experiments, related physical laws of fundamental tone, overtone and background noise of whistling sound source sound production are verified, and defects in overtone and background noise research in the prior art are made up; according to the device, by drawing the spectrogram, the physical law in the experiment process can be visually displayed, and the device can generate low-noise high-air-volume airflow and is more suitable for teaching research.

Description

Technical Field

[0001] The present invention relates to the field of acoustic technologies, and specifically to a device, a system, and a method for exploring the sound generation problem of an air flow sound source. Background Art

[0002] Modulated air flow sound sources are widely used in electric vertical sirens, air defense sirens, etc. As a modulated air flow sound source, a siren consists of an air flow and a rotating disk with circular holes. In the prior art, there are various studies on the sound generation mechanism of sirens. For example, some studies use the basic principles of gas dynamics and the law of conservation of energy to draw a set of graphs of the air flow pressure characteristics of modulated air flow sound sources; some studies perform numerical calculations on other shaped holes based on circular holes to explore the sound power under different hole shapes; some studies discuss the driving power of the motor in a modulated air flow sound source according to Bernoulli's equation, and use software to explore the sound field characteristics of modulated air flow sound sources, etc. However, the focus of the above studies is on the discussion of the fundamental frequency and sound power of the modulated air flow sound source. There is a lack of research on the overtones and background noise in the modulated air flow sound source in the prior art. At the same time, the existing experimental devices for modulated air flow sound sources cannot visually display physical laws during use, are not suitable for use as teaching instruments, and the air flow noise is relatively large during the use of the existing experimental devices for modulated air flow sound sources, which has a strong interference on experiments. Therefore, there are certain limitations in its practical application. Therefore, it is of great significance for teaching and research to develop a device that can deeply study the sound generation mechanism of modulated air flow sound sources and overcome these limitations. Summary of the Invention

[0003] The purpose of the present invention is to provide a device, a system, and a method for exploring the sound generation problem of an air flow sound source, so as to solve the problems raised in the above background art.

[0004] To achieve the above purpose, the present invention provides the following technical solution: A device for exploring the sound generation problem of an air flow sound source includes a first chassis. A first switch is fixedly connected inside the first chassis. Sound insulation sleeves are arranged on both sides of the first switch. An air pump is sleeved inside the sound insulation sleeves, and the first switch is electrically connected to the air pump. An air outlet pipe penetrates and is fixedly connected to the first chassis, and the output end of the air pump is conductively connected to the input end of the air outlet pipe. A second chassis is arranged on one side of the first chassis. A second switch is fixedly connected inside the second chassis. The second switch is electrically connected to a power adapter. The power adapter is electrically connected to a numerical control power supply. The numerical control power supply is electrically connected to a development board. The development board is electrically connected to a driving board and a touch screen. The driving board is electrically connected to a brushless motor. A disk is fixed to the output end of the brushless motor. A plurality of through holes are evenly distributed on the disk, and the output end of the air outlet pipe is arranged at the top of the through holes.

[0005] Preferably, the power adapter, the numerical control power supply, the development board, the driving board, and the touch screen are all fixedly connected to the second chassis.

[0006] Preferably, a computer is provided on the other side of the first chassis. The computer is electrically connected to a microphone, and the microphone is disposed on one side of the disc. A machine cover is provided on the top end of the first chassis, and a sound insulation sponge is fixedly connected to the inner wall of the first chassis, and a sound insulation board is fixedly connected to the sound insulation sponge.

[0007] Preferably, the input end of the air outlet pipe is conductively fixed with a confluence pipe, and the input end of the confluence pipe is conductively fixed to the output end of the air pump.

[0008] A system for exploring the problem of airflow sound source sound production includes an audio processing module, a motor control module, and a simulation module. The audio processing module and the simulation module are provided on the computer, and the motor control module is provided on the development board.

[0009] Preferably, the audio processing module uses MATLAB software, and the simulation module uses COMSOL software.

[0010] A method for exploring the problem of airflow sound source sound production includes the following steps: Step 1, COMSOL simulation; Step 2, building an experimental device; Step 3, pre-experiment; Step 4, theoretical analysis; Step 5, experimental verification; Step 6, practical application;

[0011] Among them, in the above Step 1, first use the simulation module to establish a model with the cross-sectional area of the air outlet equal to the area of the disc for simulation, and then use the actual radius of the air outlet for simulation to simulate the process of airflow passing through a single through-hole when the disc is stationary, understand the entire physical process of the airflow passing through the perforated disc, and infer from this that the disturbance of the rotating disc to the airflow is the main reason for the sound emitted by the airflow sound source.

[0012] Among them, in the above Step 2, design and build an experimental device according to the inference result of Step 1.

[0013] Among them, in the above Step 3, install the disc on the output end of the brushless motor, set different speeds of the brushless motor, start the air pump and the brushless motor, use the microphone to collect the sound information of the perforated disc, and import the sound file into the audio processing module. The audio processing module draws a spectrogram, analyzes the spectrogram, and determines according to the analysis result that the sound information of the perforated disc consists of fundamental tone, overtones, and background noise, and finds that the aperture and speed have an impact on the sound frequency and amplitude.

[0014] Among them, in the above Step 4, based on the analysis result of the spectrogram in Step 3, perform mathematical modeling on the fundamental tone, overtones, and background noise of the perforated disc.

[0015] Among them, in the above Step 5, conduct an experiment based on the experimental device built in Step 2 to verify the mathematical model established in Step 4.

[0016] In the above step six, based on the mathematical model verified in step five and combined with the audio frequency comparison table of C key and traditional Chinese pentatonic tones, the number of holes and rotation speed required for different tones are calculated, and a disc with the corresponding number of holes is made to obtain a musical instrument.

[0017] Preferably, in the step 2, building the experimental device specifically includes: connecting two four-hole air pumps to the air outlet pipe through a confluence pipe, establishing an electrical connection between the first switch and the air pump, establishing an electrical connection between the second switch, the power adapter, the CNC power supply, the development board and the driver board in sequence, establishing an electrical connection between the driver board and the brushless motor, establishing an electrical connection between the development board and the touch screen, installing a motor control module on the development board, establishing an electrical connection between the microphone and the computer, installing an audio processing module in the computer, and producing discs with different numbers of holes, materials and thicknesses.

[0018] Preferably, in step 4, mathematical modeling of the fundamental tone is specifically performed as follows:

[0019] t=T·z

[0020]

[0021] Where t represents the time taken for the disk to rotate one circle, T represents the effective interaction time between each through hole and the airflow, z represents the number of through holes, ω represents the angular velocity of the disk rotation, and n represents the rotation speed of the disk. The result obtained by combining the two equations is as follows:

[0022]

[0023] The effective interaction time T between each hole and the airflow can also be expressed as the period of sound generation, and the sound can be obtained from it:

[0024] f=z·n

[0025] Where n represents the rotation speed per second. If n represents the rotation speed per minute, the above formula becomes:

[0026]

[0027] The above formula indicates that the fundamental frequency of the disc's sound is equal to the number of through holes multiplied by the disc's rotation speed per second;

[0028] The mathematical modeling of overtones is as follows:

[0029]

[0030] Among them, p is the pressure caused by the fluctuation of the airflow element, A(t) is the ventilation area of ​​the through hole, ρ is the density of air, and u is the vibration displacement of the airflow element;

[0031] The area \(A(t)\) on both sides of the above equation can cancel each other out and is finally simplified to the wave equation, which is expressed in polar coordinates as:

[0032]

[0033] In polar coordinates, the two-dimensional Laplace operator can be expressed as:

[0034]

[0035] Set the radius of the through hole to \(r1\), and then there should be:

[0036]

[0037] where \(\varphi(\omega,z,t)\) is the boundary condition of the airflow acting on the disc;

[0038] Use the method of separation of variables to solve again Separate \(t\) from \(r\) and \(\theta\) in the sound pressure \(p\):

[0039] \(p((r,\theta),t)=b(r,\theta)T(t)=R(r)\Theta(\theta)T(t)\)

[0040] Solve for \(b(r,\theta)\) and substitute the above equation Equation A can be obtained:

[0041]

[0042] And in the polar coordinates of the through hole, there is a periodic boundary condition:

[0043] \(\Theta(\theta)=\Theta(\theta + 2\pi)\)

[0044] Substitute the periodic boundary condition into Equation A and solve to get:

[0045]

[0046] Substitute the above equation into \(p((r,\theta),t)=b(r,\theta)T(t)=R(r)\Theta(\theta)T(t)\), and at this time the sound pressure can be expressed as:

[0047]

[0048] Solve the above equation, where \(\omega\) k changes in form, and the expression is as follows:

[0049]

[0050] According to the boundary condition \(\varphi(\omega,z,t)\) and the fundamental frequency expression \(f = z\cdot n\), it can be obtained:

[0051] \(\omega\) k= 2(k - 1)π·nz

[0052] The relationship between the overtone and the fundamental tone is as follows:

[0053] f k = (k - 1)f

[0054] The mathematical modeling of the background noise is specifically as follows:

[0055] First, solve the force exerted by the air flow on the disc. The air flow is simplified as a cylindrical fluid with a certain velocity. According to the momentum theorem, we have:

[0056] FΔt = mv2 - mv1

[0057] The air flow with a certain velocity transported to the disc will exert a force on it. This force will cause the disc to vibrate up and down. Since the air flow cylinder diffuses after colliding with the disc, the velocity of the air flow in the x-axis direction is 0, that is, v2 = 0. Then FΔt = -mv1, where m represents the mass of the air flow, which is equal to the product of the density and the volume. The expression is as follows:

[0058] m = ρ·ΔV

[0059] The volume ΔV of the air flow is equal to the product of the bottom area S of the air column and the length Δl. The expression is as follows:

[0060] ΔV = S·Δl

[0061] The length Δl of the air column is equal to the velocity v1 of the air flow multiplied by the action time Δt of the air flow on the disc. The expression is as follows:

[0062] Δl = v1·Δt

[0063] Then we have:

[0064]

[0065] The above formula indicates that the direction of the force on the disc is opposite to v1, and the magnitude is From this, it can be known that the disc is affected by a force proportional to the square of the air flow velocity. Under the action of the force, the disc vibrates to generate noise;

[0066] The essence of the disc vibration problem is to solve the fourth-order differential equation under the boundary conditions. The expression is as follows:

[0067]

[0068] In the formula, D is the flexural rigidity of the disc, w, ρ1, h, and ω are the displacement perpendicular to the disc, the disc density, the disc thickness, and the vibration frequency of the disc respectively. Let the radius of the disc be r1. Since the object under study is a disc, polar coordinates are used for processing. At this time, the two-dimensional Laplace operator is also:

[0069]

[0070] Solve the above fourth-order differential equation using the boundary conditions. Since the center of the disk is fixed on the brushless motor, we have:

[0071] w(r,θ)| r＝0 = 0

[0072] And in the polar coordinate system of the through-hole, there are periodic boundary conditions:

[0073] w(r,θ) = w(r,θ + 2π)

[0074] When dealing with polar coordinates, the displacement function of the disk in each direction can be decomposed into radial and tangential forms. Solving the fourth-order differential equation at this time, the displacement function of the disk can be obtained as:

[0075]

[0076] where J k (x) is the Bessel function of the k-th order, λ km is the first m positive roots of J k (x) = 0, and the coefficient A km is the amplitude of the disk vibration.

[0077] Preferably, in step five, the experiment specifically includes the following steps:

[0078] 5.1 Fundamental frequency experiment: Extract the fundamental frequencies of disks with five different numbers of holes at each rotational speed, record them as the actual values of the fundamental frequencies, substitute the rotational speed data into the fundamental frequency expression, solve for the theoretical values of the fundamental frequencies, and at the same time record the rotational speed, number of holes, theoretical and actual values of the fundamental frequencies. Plot the actual values of the fundamental frequencies of the five disks at each rotational speed against the rotational speed data and perform linear fitting to verify the quantitative relationship between the fundamental frequency and the rotational speed and the number of holes;

[0079] 5.2 Overtone frequency experiment: Ignore the background noise in the spectrogram, only consider the fundamental and overtone frequencies, record the overtone frequencies of the disk at each rotational speed, analyze the overtone frequency and fundamental frequency data, and verify the integer multiple relationship between the overtone frequency and the fundamental frequency;

[0080] 5.3 Noise problem experiment: Select a disk, first record the spectrogram of the disk vibrating and making sound when there is no air flow, then record the spectrogram when air flow is passed, compare the amplitude and the situation of new spectral lines of the two, analyze the influence of air flow on the noise generated by the disk vibration, use Tracker software to record the displacements of the disk along the central plane in the x-axis and y-axis directions before and after passing air flow, and depict the change of the disk vibration;

[0081] 5.4 Experiments on Different Materials and Thicknesses: Select discs with different materials, different thicknesses, and the same number of holes, conduct experiments at the same rotational speed, record the spectrograms, and analyze the effects of different materials and thicknesses on the fundamental frequency, overtone frequency, and noise;

[0082] 5.5 Experimental Summary: Calculate the error of the fundamental frequency, analyze the error conditions under different rotational speeds and materials, find out the reasons for the error, summarize the experimental results, verify the correctness of the theoretical derivation, determine the relationships between the fundamental frequency, overtone frequency and various factors, as well as the relationship between the disc vibration and noise. Among them, the fundamental frequency error E is:

[0083]

[0084] In the formula, f 理 is the theoretical value, f 实 is the actual value, n is the number of holes, and z is the rotational speed.

[0085] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention verifies the relevant physical laws of the fundamental tone, overtone, and background noise of the steam whistle sound source through theoretical derivation and experiments, making up for the deficiencies in the research of overtones and background noise in the prior art; The device of the present invention can visually display the physical laws in the experimental process by drawing spectrograms, and the device can generate a high-air volume airflow with low noise, which is more suitable for teaching research. Description of the Drawings

[0086] Figure 1 is the three-dimensional structural schematic diagram of the device of the present invention;

[0087] Figure 2 is the three-dimensional sectional structural schematic diagram of the first chassis of the present invention;

[0088] Figure 3 is the three-dimensional sectional structural schematic diagram of the second chassis of the present invention;

[0089] Figure 4 is the system structural block diagram of the present invention;

[0090] Figure 5 is the method flow chart of the present invention;

[0091] Figure 6 is the software interface diagram of the motor control module;

[0092] Figure 7 is the COMSOL simulation diagram of the model with the cross-sectional area of the air holes equal to the area of the disc;

[0093] Figure 8 is the COMSOL simulation diagram of the airflow passing through a single through-hole when the disc is stationary;

[0094] Figure 9It is the sound spectrum diagram of a disc with 12 holes;

[0095] Figure 10 It is the sound spectrum diagram of a disc with 18 holes;

[0096] Figure 11 It is the program interface diagram of the audio processing module;

[0097] Figure 12 It is the sound spectrum diagrams of five discs;

[0098] Figure 13 It is the sound spectrum diagrams of two discs at 1250 revolutions per minute before and after processing;

[0099] Figure 13 (a) It is the spectrum diagram before processing when the number of holes is 6;

[0100] Figure 13 (b) It is the sound spectrum diagram that only retains the center frequency when the number of holes is 6;

[0101] Figure 13 (c) It is the sound spectrum diagram that only retains the center frequency when the number of holes is 12;

[0102] Figure 13 (d) It is the sound spectrum diagram that only retains the center frequency when the number of holes is 12;

[0103] Figure 14 It is the sound spectrum diagram of a disc with 18 holes at 24.5 r / s before and after introducing air flow;

[0104] Figure 14 (a) It is the sound spectrum diagram when no air flow is introduced;

[0105] Figure 14 (b) It is the sound spectrum diagram after introducing air flow;

[0106] Figure 15 It is the change diagram of the disc vibration before and after introducing air flow;

[0107] Figure 15 (a) It is the vibration broken line diagram of the disc perpendicular to the rotation direction;

[0108] Figure 15 (b) It is the vibration broken line diagram of the disc along the rotation direction;

[0109] Figure 16 It is the sound spectrum diagrams of discs made of different materials;

[0110] Figure 16 (a) It is the sound spectrum diagram of a fiberglass disc;

[0111] Figure 16 (b) It is the sound spectrum diagram of a white resin disc;

[0112] Figure 16 (c) Sound spectrum diagram of a black nylon disc;

[0113] Figure 16 (d) Sound spectrum diagram of a yellow high-toughness resin disc;

[0114] Figure 17 Sound spectrum diagrams of discs made of materials with different thicknesses;

[0115] Figure 17 (a) Sound spectrum diagram of a red PLA disc with a thickness of 1.5 mm;

[0116] Figure 17 (b) Sound spectrum diagram of a black PLA disc with a thickness of 3.0 mm;

[0117] Figure 17 (c) Sound spectrum diagram of a white PLA disc with a thickness of 2.5 mm.

[0118] In the figure: 1. First chassis; 11. Machine cover; 12. Sound insulation sponge; 13. Sound insulation board; 14. First switch; 15. Sound insulation sleeve; 16. Air pump; 17. Confluence pipe; 18. Air outlet pipe; 2. Brushless motor; 3. Disc; 31. Through hole; 4. Microphone; 5. Computer; 6. Second chassis; 61. Second switch; 62. Power adapter; 63. Numerical control power supply; 64. Development board; 65. Driver board; 66. Touch screen; 7. Audio processing module; 8. Motor control module; 9. Simulation module. Detailed implementation manner

[0119] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0120] Please refer to the attached Figure 1 - attached Figure 3, an embodiment provided by the present invention: a device for exploring the problem of airflow sound source generation, including a first chassis 1, a first switch 14 is fixedly connected inside the first chassis 1, sound insulation sleeves 15 are arranged on both sides of the first switch 14, an air pump 16 is sleeved inside the sound insulation sleeves 15, and the first switch 14 is electrically connected to the air pump 16. An air outlet pipe 18 is fixedly penetrated through the first chassis 1, and the output end of the air pump 16 is conductively connected to the input end of the air outlet pipe 18. A second chassis 6 is arranged on one side of the first chassis 1. A second switch 61 is fixedly connected inside the second chassis 6. The second switch 61 is electrically connected to a power adapter 62. The power adapter 62 is electrically connected to a numerical control power supply 63. The numerical control power supply 63 is electrically connected to a development board 64. The development board 64 is electrically connected to a drive board 65 and a touch screen 66. The drive board 65 is electrically connected to a brushless motor 2. The output end of the brushless motor 2 is fixed with a disc 3. A plurality of through holes 31 are evenly distributed on the disc 3, and the output end of the air outlet pipe 18 is arranged at the top of the through holes 31. The first switch 14 and the second switch 61 are used to control the power on and off. The sound insulation sleeves 15 are used to reduce the noise of the air pump 16. The air pump 16 is used to generate airflow. The air outlet pipe 18 is used to transport the airflow. The power adapter 62 is used to convert alternating current into direct current. The numerical control power supply 63 is used to precisely adjust the output voltage, current and power. The development board 64 is used to control the brushless motor 2. The drive board 65 is used to drive the brushless motor 2. The touch screen 66 is used for human-computer interaction. The brushless motor 2 is used to drive the disc 3. The disc 3 and the through holes 31 form a siren; the power adapter 62, the numerical control power supply 63, the development board 64, the drive board 65 and the touch screen 66 are all fixedly connected to the second chassis 6; A computer 5 is arranged on the other side of the first chassis 1. The computer 5 is electrically connected to a microphone 4, and the microphone 4 is arranged on one side of the disc 3. A machine cover 11 is arranged at the top of the first chassis 1. A sound insulation sponge 12 is fixedly connected to the inner wall of the first chassis 1. A sound insulation board 13 is fixedly connected to the sound insulation sponge 12. The computer 5 is used to process data. The microphone 4 is used to collect audio information. The machine cover 11 is used to close the first chassis 1. The sound insulation sponge 12 and the sound insulation board 13 are used to reduce the noise of the air pump 16; The input end of the air outlet pipe 18 is conductively fixed with a confluence pipe 17, and the input end of the confluence pipe 17 is conductively fixed to the output end of the air pump 16. The confluence pipe 17 is used to connect the air outlet pipe 18 and the air pump 16.

[0121] Please refer to the appendix Figure 4 , an embodiment provided by the present invention: a system for exploring the problem of airflow sound source generation, including an audio processing module 7, a motor control module 8 and a simulation module 9. The audio processing module 7 and the simulation module 9 are arranged on the computer 5. The motor control module 8 is arranged on the development board 64. The audio processing module 7 is used to process audio information. The motor control module 8 is used to adjust motor parameters. The simulation module 9 is used to conduct simulation experiments; The audio processing module 7 uses MATLAB software, and the simulation module 9 uses COMSOL software.

[0122] Please refer to the appendixFigure 5 -Attached Figure 17 , Table 1-Table 5, an embodiment provided by the present invention: a method for exploring the sound generation problem of airflow sound source, comprising the following steps: step 1, COMSOL simulation; step 2, building an experimental device; step 3, preliminary experiment; step 4, theoretical analysis; step 5, experimental verification; step 6, practical application;

[0123] In the above step 1, the simulation module 9 is first used to establish a model in which the cross section of the air outlet is equal to the area of ​​the disc 3 for simulation, and then the actual air outlet radius is used for simulation to simulate the process of airflow passing through a single through hole 31 when the disc 3 is stationary, so as to understand the entire physical process of airflow passing through the perforated disc 3, and it is inferred that the disturbance of the airflow caused by the rotating disc 3 is the main reason for the sound of the airflow sound source;

[0124] In the above step 2, according to the inference result of step 1, an experimental device is designed and built. The specific steps of building the experimental device are as follows: two four-hole air pumps 16 are connected to the air outlet pipe 18 through the confluence pipe 17, the first switch 14 is electrically connected to the air pump 16, the second switch 61, the power adapter 62, the CNC power supply 63, the development board 64 and the driver board 65 are electrically connected in sequence, the driver board 65 is electrically connected to the brushless motor 2, the development board 64 is electrically connected to the touch screen 66, the motor control module 8 is installed on the development board 64, the microphone 4 is electrically connected to the computer 5, the audio processing module 7 is installed in the computer 5, and the discs 3 with different numbers of holes, materials and thicknesses are produced;

[0125] In the above step 3, the disc 3 is installed at the output end of the brushless motor 2, the brushless motor 2 is set to different speeds, the air pump 16 and the brushless motor 2 are started, the microphone 4 is used to collect the sound information of the disc 3 with holes, and the sound file is imported into the audio processing module 7, the audio processing module 7 draws a spectrogram, analyzes the spectrogram, and determines that the sound information of the disc 3 with holes is composed of fundamental tone, overtone and background noise according to the analysis result, and finds that the aperture and the speed have an influence on the sound frequency and amplitude;

[0126] In the above step 4, based on the analysis result of the spectrogram in step 3, mathematical modeling is performed on the fundamental tone, overtones and background noise of the perforated disc 3, wherein the mathematical modeling of the fundamental tone is specifically as follows:

[0127] t=T·z

[0128]

[0129] Where t represents the time taken for the disk 3 to rotate one circle, T represents the effective interaction time between each through hole 31 and the airflow, z represents the number of through holes 31, ω represents the angular velocity of the disk 3, and n represents the rotation speed of the disk 3. The result obtained by combining the two equations is as follows:

[0130]

[0131] Moreover, the effective action time T of each through-hole 31 with the airflow can also be expressed as the period of sound generation, and thus the sound can be obtained therefrom:

[0132] f = z·n

[0133] Wherein, n represents the rotational speed per second. If n represents the rotational speed per minute, the above formula becomes:

[0134]

[0135] The above formula indicates that the fundamental tone frequency of the disc 3 sounding is equal to the number of through-holes 31 multiplied by the rotational speed of the disc 3 per second;

[0136] Specifically, the mathematical modeling of overtones is as follows:

[0137]

[0138] Wherein, p is the pressure caused by the airflow micro-element fluctuation, A(t) is the ventilation area of the through-hole 31, ρ is the density of air, and u is the vibration displacement of the airflow micro-element;

[0139] The area A(t) on both sides of the above formula can be cancelled out with each other, and finally it is simplified to a wave equation, which is expressed in the polar coordinate system as:

[0140]

[0141] In the polar coordinate system, the two-dimensional Laplace operator can be expressed as:

[0142]

[0143] Assume that the radius of the through-hole 31 is r1, and at this time, there should be:

[0144]

[0145] Wherein, φ(ω,z,t) is the boundary condition of the airflow acting on the disc 3;

[0146] Use the method of separation of variables to solve again Separate t from r and θ in the sound pressure p:

[0147] p((r,θ),t) = b(r,θ)T(t) = R(r)Θ(θ)T(t)

[0148] Solve b(r,θ) and substitute the above formula into it Formula A can be obtained:

[0149]

[0150] And in the polar coordinate system of the through-hole 31, there are periodic boundary conditions:

[0151] Θ(θ) = Θ(θ + 2π)

[0152] Substitute the periodic boundary conditions into Equation A and solve to obtain:

[0153]

[0154] Substitute the above equation into p((r,θ),t) = b(r,θ)T(t) = R(r)Θ(θ)T(t). At this time, the sound pressure can be expressed as:

[0155]

[0156] Solve the above equation, where ω k changes in form, and the expression is as follows:

[0157]

[0158] According to the boundary conditions φ(ω,z,t) and the fundamental frequency expression f = z·n, it can be obtained that:

[0159] ω k = 2(k - 1)π·nz

[0160] Then the relationship between the overtone and the fundamental tone is:

[0161] f k = (k - 1)f

[0162] The mathematical modeling of the background noise is specifically as follows:

[0163] First, solve the force exerted by the air flow on the disk 3. Simplify the air flow into a cylindrical fluid with a certain velocity. According to the momentum theorem, it can be obtained that:

[0164] FΔt = mv2 - mv1

[0165] The air flow with a certain velocity transported to the disk 3 will exert a force on it, and this force will cause the disk 3 to vibrate up and down. Since the air flow cylinder diffuses after colliding with the disk 3, the velocity of the air flow in the x-axis direction is 0, that is, v2 = 0. Then FΔt = -mv1, where m represents the mass of the air flow, which is equal to the product of the density and the volume, and the expression is as follows:

[0166] m = ρ·ΔV

[0167] The volume ΔV of the air flow is equal to the product of the bottom area S of the air column and the length Δl, and the expression is as follows:

[0168] ΔV = S·Δl

[0169] The length Δl of the air column is equal to the velocity v1 of the air flow multiplied by the action time Δt of the air flow on the disk 3, and the expression is as follows:

[0170] Δl = v1·Δt

[0171] Then there is:

[0172]

[0173] The above formula indicates that the force direction on the disk 3 is opposite to v1, and the magnitude is It can be seen from this that the disk 3 is affected by a force proportional to the square of the air flow velocity. Under the action of the force, the disk 3 vibrates to generate noise;

[0174] The essence of the vibration problem of the disk 3 is to solve the fourth-order differential equation under the boundary conditions, and the expression is as follows:

[0175]

[0176] In the formula, D is the flexural rigidity of the disk 3, w, ρ1, h, ω are the displacement perpendicular to the disk 3, the density of the disk 3, the thickness of the disk 3, and the vibration frequency of the disk 3 respectively. Let the radius of the disk 3 be r1. Since the object under study is the disk 3, polar coordinates are used for processing. At this time, the two-dimensional Laplace operator is also:

[0177]

[0178] Using the boundary to solve the above fourth-order differential equation, since the center of the disk 3 is fixed on the brushless motor 2, there is:

[0179] w(r,θ)| r＝0 = 0

[0180] And in the polar coordinate system of the through hole 31, there are periodic boundary conditions:

[0181] w(r,θ) = w(r,θ + 2π)

[0182] When using polar coordinates for processing, the displacement function of the disk 3 in each direction can be decomposed into radial and tangential forms. At this time, solving the fourth-order differential equation, the displacement function of the disk 3 can be obtained as:

[0183]

[0184] Among them, J k (x) is the k-order Bessel function, λ km is the first m positive roots of J k (x) = 0, and the coefficient A km is the vibration amplitude of the disk 3;

[0185] Among the above step 5, the experiment is carried out based on the experimental device built in step 2 to verify the mathematical model established in step 4, which specifically includes the following steps:

[0186] 5.1 Fundamental frequency experiment: Extract the fundamental frequencies of the disk 3 with five different numbers of holes at each rotational speed, record them as the actual values of the fundamental frequencies, substitute the rotational speed data into the fundamental frequency expression to solve the theoretical values of the fundamental frequencies, and record the rotational speed, number of holes, theoretical values and actual values of the fundamental frequencies at the same time, as shown in Table 1. Plot the actual values of the fundamental frequencies of the five disks 3 at each rotational speed against the rotational speed data and perform linear fitting to verify the quantitative relationship between the fundamental frequency and the rotational speed and the number of holes;

[0187] 5.2 Overtone frequency experiment: Ignore the background noise in the spectrogram, only consider the fundamental and overtones, record the overtone frequencies of the disk 3 at each rotational speed, as shown in Table 2, analyze the overtone frequency and fundamental frequency data to verify the integer multiple relationship between the overtone frequency and the fundamental frequency;

[0188] 5.3 Noise problem experiment: Select a disk 3, first record the spectrogram of the disk 3 vibrating and generating sound when no air flow is passed, then record the spectrogram when air flow is passed, compare the amplitude and the situation of new spectral lines between the two, analyze the influence of air flow on the noise generated by the vibration of the disk 3, use Tracker software to record the displacements of the disk 3 along the central plane in the x-axis and y-axis directions before and after passing air flow, and depict the vibration change of the disk 3;

[0189] 5.4 Experiments with different materials and thicknesses: Select disks 3 with different materials and different thicknesses but the same number of holes, conduct experiments at the same rotational speed, record the spectrograms, and analyze the influence of different materials and thicknesses on the fundamental frequency, overtone frequency and noise;

[0190] 5.5 Experiment summary: Calculate the fundamental frequency error, as shown in Table 3, analyze the error situations under different rotational speeds and materials, find out the reasons for the errors, use a 10-hole white PLA disk with a thickness of 2.5 mm, set the rotational speed to 1750 revolutions, repeat the fundamental frequency experiment 8 times to measure and calculate the error as shown in Table 4, summarize the experimental results, verify the correctness of the theoretical derivation, determine the relationships between the fundamental frequency, overtone frequency and various factors, and the relationship between the vibration of the disk 3 and the noise. Among them, the fundamental frequency error E is:

[0191]

[0192] In the formula, f 理 is the theoretical value, f 实 is the actual value, n is the number of holes, and z is the rotational speed;

[0193] Among them, in the above step six, based on the verified mathematical model in step five, combined with the audio frequency comparison tables of C major and the five-tone scale of traditional Chinese music, as shown in Table 5, calculate the number of holes and rotation speed required for different tones, and fabricate a disc 3 with the corresponding number of holes to obtain the musical instrument.

[0194] Table 1 Fundamental Tone Frequencies of White PLA Material with z = 6 (a)

[0195]

[0196] Table 1 Fundamental Tone Frequencies of White PLA Material with z = 6 (b)

[0197]

[0198] Table 1 Fundamental Tone Frequencies of White PLA Material with z = 6 (c)

[0199]

[0200] Table 2 Overtone Frequencies of White PLA Material with z = 6 (a)

[0201]

[0202] Table 2 Overtone Frequencies of White PLA Material with z = 6 (b)

[0203]

[0204] Table 2 Overtone Frequencies of White PLA Material with z = 6 (c)

[0205]

[0206] Table 3 Experimental Error

[0207]

[0208]

[0209] Table 4 Experimental Uncertainty

[0210]

[0211] Table 5 Audio Frequency Comparison Table of C Major

[0212]

[0213] Working principle: When using the present invention, the disc 3 is installed on the brushless motor 2, and the output end of the air outlet pipe 18 is vertically aligned with the through hole 31, the microphone 4 is aligned with the disc 3, and is connected to the computer 5 through a data cable. The first switch 14 and the second switch 61 are connected to the power supply. The second switch 61 on the second chassis 6 is turned on, and the current is delivered to the numerical control power supply 63 through the power adapter 62. The numerical control power supply 63 is adjusted to 24V, and the numerical control power supply 63 delivers the current to the development board 64. The motor control module 8 is used through the touch screen 66 to adjust the brushless motor 2 to the specified speed. The brushless motor 2 is started through the drive board 65. The first switch 14 is turned on, and the air pump 16 generates an air flow. The air flow is input into the air outlet pipe 18 through the confluence pipe 17. The air flow blown out by the air outlet pipe 18 acts on the rotating disc 3 to generate sound. The recording software of the computer 5 is used for recording. After the recording is completed, the brushless motor 2 and the air pump 16 are turned off. The audio processing module 7 is used to process the audio to obtain a spectrogram; among them, the sound insulation sponge 12, the sound insulation board 13 and the sound insulation sleeve 15 are all used to reduce the working noise of the air pump 16, the machine cover 11 is used to enclose the first chassis 1 to reduce noise, and the simulation module 9 is used for simulation experiments.

[0214] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be regarded as limiting the claimed claims.

Claims

1. An apparatus for exploring the problem of sound generation by air flow sound sources, comprising a first chassis (1), characterized in that: A first switch (14) is fixedly connected inside the first chassis (1). Sound insulation sleeves (15) are arranged on both sides of the first switch (14). An air pump (16) is sleeved inside the sound insulation sleeve (15), and the first switch (14) is electrically connected to the air pump (16). An air outlet pipe (18) is fixedly penetrated through the first chassis (1), and the output end of the air pump (16) is conductively connected to the input end of the air outlet pipe (18). A second chassis (6) is arranged on one side of the first chassis (1). A second switch (61) is fixedly connected inside the second chassis (6). The second switch (61) is electrically connected to a power adapter (62). The power adapter (62) is electrically connected to a numerical control power supply (63). The numerical control power supply (63) is electrically connected to a development board (64). The development board (64) is electrically connected to a drive board (65) and a touch screen (66). The drive board (65) is electrically connected to a brushless motor (2). A disk (3) is fixed to the output end of the brushless motor (2). A plurality of through holes (31) are evenly distributed on the disk (3), and the output end of the air outlet pipe (18) is arranged at the top of the through hole (31).

2. The device for exploring the problem of airflow sound source sound production according to claim 1, characterized in that: The power adapter (62), the numerical control power supply (63), the development board (64), the drive board (65), and the touch screen (66) are all fixedly connected to the second chassis (6).

3. The device for exploring the problem of airflow sound source sound production according to claim 1, wherein: A computer (5) is arranged on the other side of the first chassis (1). The computer (5) is electrically connected to a microphone (4), and the microphone (4) is arranged on one side of the disk (3). A machine cover (11) is arranged at the top of the first chassis (1). A sound insulation sponge (12) is fixedly connected to the inner wall of the first chassis (1). A sound insulation board (13) is fixedly connected to the sound insulation sponge (12).

4. The device for exploring the problem of airflow sound source sound production according to claim 1, characterized in that: The input end of the air outlet pipe (18) is conductively fixed with a confluence pipe (17), and the input end of the confluence pipe (17) is conductively fixed to the output end of the air pump (16).

5. A system for exploring the problem of airflow sound source sound production, comprising an audio processing module (7), a motor control module (8), and a simulation module (9), characterized in that: The audio processing module (7) and the simulation module (9) are arranged on the computer (5), and the motor control module (8) is arranged on the development board (64).

6. The system for exploring the problem of airflow sound source sound production according to claim 5, wherein: The audio processing module (7) uses MATLAB software, and the simulation module (9) uses COMSOL software.

7. A method for exploring the problem of sound generation by an air flow sound source, comprising the following steps: Step 1, COMSOL simulation; Step 2, build an experimental device; Step 3, pre-experiment; Step 4, theoretical analysis; Step 5, experimental verification; Step 6, practical application; characterized in that: In the above step 1, first use the simulation module (9) to establish a model with the cross-sectional area of the air outlet hole equal to the area of the disk (3) for simulation, and then use the actual radius of the air outlet hole for simulation to simulate the process of air flow passing through a single through hole (31) when the disk (3) is stationary, understand the entire physical process of the air flow passing through the perforated disk (3), and infer from this that the disturbance of the air flow caused by the rotating disk (3) is the main reason for the sound emitted by the air flow sound source; In the above step 2, according to the inference result of step 1, design and build an experimental device; In the above step 3, the disk (3) is installed at the output end of the brushless motor (2), the brushless motor (2) is set to different speeds, the air pump (16) and the brushless motor (2) are started, the microphone (4) is used to collect sound information of the perforated disk (3), and the sound file is imported into the audio processing module (7), the audio processing module (7) draws a spectrogram, and the spectrogram is analyzed. According to the analysis result, it is determined that the sound information of the perforated disk (3) is composed of fundamental tone, overtone and background noise, and it is found that the aperture and the speed have an influence on the sound frequency and amplitude; In the above step 4, based on the analysis result of the spectrogram in step 3, a mathematical model is constructed for the fundamental tone, overtones and background noise of the perforated disc (3); In the above step 5, an experiment is conducted based on the experimental device built in step 2 to verify the mathematical model established in step 4; In the above step six, based on the mathematical model verified in step five, combined with the C key and the audio frequency comparison table of the traditional Chinese pentatonic tones, the number of holes and the rotation speed required for different tones are calculated, and a disc (3) containing the corresponding number of holes is made to obtain the musical instrument.

8. A method for exploring the problem of airflow sound source sound production according to claim 7, characterized in that: In the step 2, the experimental device is specifically constructed as follows: two four-hole air pumps (16) are connected to the air outlet pipe (18) through a confluence pipe (17), the first switch (14) is electrically connected to the air pump (16), the second switch (61), the power adapter (62), the CNC power supply (63), the development board (64) and the driver board (65) are electrically connected in sequence, the driver board (65) is electrically connected to the brushless motor (2), the development board (64) is electrically connected to the touch screen (66), a motor control module (8) is installed on the development board (64), a microphone (4) is electrically connected to the computer (5), an audio processing module (7) is installed in the computer (5), and discs (3) with different numbers of holes, materials and thicknesses are manufactured.

9. A method for exploring the problem of airflow sound source sound production according to claim 7, characterized in that: In the step 4, mathematical modeling of the fundamental tone is specifically performed as follows: t=T·z Wherein t represents the time taken for the disk (3) to rotate one circle, T represents the effective action time of each through hole (31) and the airflow, z represents the number of through holes (31), ω represents the angular velocity of the disk (3) rotation, and n represents the rotation speed of the disk (3). The result obtained by combining the two equations is as follows: The effective interaction time T between each through hole (31) and the airflow can also be expressed as the sound generation period, and the sound can be obtained from it: f=z·n Where n represents the rotation speed per second. If n represents the rotation speed per minute, the above formula becomes: The above formula indicates that the fundamental frequency of the sound produced by the disc (3) is equal to the number of through holes (31) multiplied by the rotation speed of the disc (3) per second; The mathematical modeling of overtones is as follows: Wherein, p is the pressure caused by the fluctuation of the airflow microelement, A(t) is the ventilation area of ​​the through hole (31), ρ is the density of air, and u is the vibration displacement of the airflow microelement; The areas A(t) on both sides of the above equation can cancel each other out, and finally simplify to the wave equation, which is expressed in the polar coordinate system as follows: In polar coordinates, the two-dimensional Laplace operator can be expressed as: Assuming the radius of the through hole (31) is r1, then: Among them, φ(ω, z, t) is the boundary condition of the airflow acting on the disk (3); Solve again using the method of separation of variables Separate t from r and θ in the sound pressure p: p((r, θ), t) = b(r, θ)T(t) = R(r)Θ(θ)T(t) Solve for b(r,θ), substitute the above equation into We can obtain Equation A: And in the polar coordinate system of the through hole (31), there are periodic boundary conditions: Θ(θ) = Θ(θ + 2π) Substitute the periodic boundary condition into Equation A and solve to obtain: Substitute the above formula into p((r, θ), t) = b(r, θ)T(t) = R(r)Θ(θ)T(t), and at this time the sound pressure can be expressed as: Solve the above equation, where ω k changes in form, and the expression is as follows: According to the boundary condition φ(ω, z, t) and the fundamental tone frequency expression f = z·n, it can be obtained: ω k = 2(k - 1)π·nz Then the relationship between the overtone and the fundamental tone is: f k = (k - 1)f The specific mathematical modeling of the background noise is as follows: First, solve the force of the airflow acting on the disk (3). Simplify the airflow into a cylindrical fluid with a certain velocity. According to the momentum theorem, we can get: FΔt = mv2 - mv1 The airflow with a certain velocity transported to the disk (3) will exert a force on it, and this force will cause the disk (3) to vibrate up and down. Since the airflow cylinder diffuses after colliding with the disk (3), the velocity of the airflow in the x-axis direction is 0, that is, v2 = 0, then FΔt = -mv1. In the formula, m represents the mass of the airflow, which is equal to the product of the density and the volume, and the expression is as follows: m = ρ·ΔV The volume ΔV of the airflow is equal to the product of the bottom area S of the air column and the length Δl, and the expression is as follows: ΔV = S·Δl The length Δl of the air column is equal to the velocity v1 of the airflow multiplied by the acting time Δt of the airflow on the disk (3), and the expression is as follows: Δl = v1·Δt Then there is: The above formula indicates that the direction of the force on the disk (3) is opposite to v1, and the magnitude is It can be seen from this that the disk (3) is affected by a force proportional to the square of the air flow velocity. Under the action of the force, the disk (3) vibrates to generate noise; The essence of the vibration problem of the disk (3) is to solve the fourth-order differential equation under the boundary conditions, and the expression is as follows: In the formula, D is the flexural rigidity of the disk (3), w, ρ1, h, ω are the displacement perpendicular to the disk (3), the density of the disk (3), the thickness of the disk (3), and the vibration frequency of the disk (3) respectively. Let the radius of the disk (3) be r1. Since the object under study is the disk (3), polar coordinates are used for processing. At this time, the two-dimensional Laplace operator is also: Use the boundary to solve the above fourth-order differential equation. Since the center of the disk (3) is fixed on the brushless motor (2), there is: w(r, θ)| r＝0 = 0 And in the polar coordinate system of the through hole (31), there are periodic boundary conditions: w(r, θ) = w(r, θ + 2π) When using polar coordinates for processing, the displacement function of the disk (3) in each direction can be decomposed into radial and tangential forms. At this time, solve the fourth-order differential equation, and the displacement function of the disk (3) can be obtained as: Among them, J k (x) is the Bessel function of the k-th order, and λ km is the first m positive roots of J k (x) = 0, and the coefficient A km is the amplitude of the vibration of the disc (3).

10. A method for exploring the problem of airflow sound source sound production according to claim 7, characterized in that: In the fifth step, the experiment specifically includes the following steps: 5.1 Fundamental tone frequency experiment: Extract the fundamental tone frequencies of the disks (3) with five different numbers of holes at each rotational speed, record them as the actual values of the fundamental tone frequencies, substitute the rotational speed data into the fundamental tone frequency expression, solve the theoretical values of the fundamental tone frequencies, and at the same time record the rotational speed, the number of holes, the theoretical values and the actual values of the fundamental tone frequencies. Plot the actual values of the fundamental frequencies of the five disks (3) at each rotational speed against the rotational speed data and perform linear fitting to verify the quantitative relationship between the fundamental tone frequency and the rotational speed and the number of holes; 5.2 Overtone frequency experiment: Ignoring the background noise in the spectrogram and only considering the fundamental tone and overtones, record the overtone frequencies of the disk (3) at various rotational speeds, analyze the overtone frequency and fundamental frequency data, and verify the integer multiple relationship between the overtone frequency and the fundamental frequency; 5.3 Noise problem experiment: Select a disk (3). First, record the spectrogram of the sound generated by the vibration of the disk (3) when no air flow is passed. Then, pass air flow and record the spectrogram. Compare the amplitude and the situation of new spectral lines between the two, analyze the influence of the air flow on the noise generated by the vibration of the disk (3), and use the Tracker software to record the displacements of the disk (3) along the central plane in the x-axis and y-axis directions before and after the air flow is passed, and depict the vibration changes of the disk (3); 5.4 Experiments on different materials and thicknesses: Respectively select disks (3) with different materials, different thicknesses and the same number of holes, conduct experiments at the same rotational speed, record the spectrograms, and analyze the influence of different materials and thicknesses on the fundamental frequency, overtone frequency and noise; 5.5 Experiment summary: Calculate the fundamental frequency error, analyze the error situations under different rotational speeds and materials, find out the reasons for the errors, summarize the experimental results, verify the correctness of the theoretical derivation, determine the relationships between the fundamental frequency, overtone frequency and various factors, and the relationship between the vibration of the disk (3) and the noise. Among them, the fundamental frequency error E is: where f 理 is the theoretical value, f 实 is the actual value, n is the number of holes, and z is the rotational speed.

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