Rapid prediction method for tire radiation noise on porous ground

Abstract

The invention discloses a rapid prediction method for tire radiation noise on a porous ground, and relates to the technical field of sound field prediction methods in the noise field. The theoretical basis of the method is a half-space boundary element method and a fast multi-pole algorithm. In the prediction process, firstly, a triangular unit is used for carrying out grid division on the tire surface, a required tree structure is divided according to unit nodes, and the normal vibration speed of each node on the tire surface is input. A half-space Green function is expanded into a series form by using a fast multipolar algorithm, and the implementation steps of the fast multipolar algorithm are simplified according to the characteristics of a half-space tree structure. And then, according to the obtained unknown quantity and the transfer relationship between the half-space boundary element method and any field point, sound field distribution of the tire radiation noise is calculated. According to the method, rapid prediction of the tire structure noise is realized, the influence caused by porous ground reflection is considered by using the half-space Green function, and implementation steps are simplified through the half-space rapid multi-pole algorithm, so that the accuracy and high efficiency of prediction are ensured.

Description

Technical Field

[0001] The invention relates to the technical field of sound field prediction methods in the field of noise, and in particular to a method for quickly predicting tire radiation noise on porous ground. Background Art

[0002] Predicting the acoustic radiation of tire structure vibration has always been the focus of research institutes and tire companies at home and abroad. However, most of the existing work is oriented towards the situation of flat ground. But in actual situations, the natural ground surface is usually porous, which means that only a part of the sound waves will be reflected on the ground, while the rest will be absorbed due to the interaction between the sound waves and the ground surface. In order to improve the accuracy of the sound field prediction in this half-space acoustic problem, it is necessary to introduce an accurate ground model for sound radiation calculation.

[0003] At present, the widely used methods for predicting half-space acoustic radiation are finite element method, finite difference method and boundary element method. Among them, finite element method and finite difference method are in-domain methods. They need to discretize the entire acoustic domain and solve the acoustic wave equation based on these discrete points. Although this method can provide more detailed field distribution information, it also brings a certain computational burden. For example, although the finite element method can adapt to complex geometric structures well and can flexibly adjust the grid density to improve local accuracy. However, for half-space problems, especially those involving porous ground, the finite element method may require very fine grid division to accurately capture the reflection and absorption characteristics of sound waves, which undoubtedly increases the computational cost. The finite difference method discretizes the partial differential equation and replaces the derivative with the difference quotient to solve the original equation at a series of discrete points. The advantage of this method is that it is relatively simple to implement and easy to understand and program. However, for scenes with inhomogeneous media or complex geometric shapes, the finite difference method may require a dense grid to ensure the accuracy of the solution. Especially when dealing with half-space problems, the porous nature of the ground requires the model to accurately reflect the changes in the actual boundary conditions, which places higher requirements on the grid. In contrast, the boundary element method, as a boundary method, only needs to discretize the boundary of the problem, rather than the entire domain. This method reduces the size of the computational domain, thereby reducing the amount of calculation. In addition, the boundary element method can accurately describe the porous characteristics of the ground by using the half-space Green's function, which is suitable for dealing with acoustic problems with complex boundary conditions.

[0004] In summary, for the prediction of sound radiation of rolling tire structures, scholars have proposed a variety of solution techniques that can be used to predict the sound field of tire radiation, including finite element method, finite difference method and boundary element method. These methods have improved the accuracy of prediction to a certain extent and provided a powerful tool for understanding the acoustic behavior of tires during movement. However, the existing research on the prediction of radiated noise of tires on porous ground is still insufficient, and there are many problems that need to be solved. On the one hand, the complex characteristics of porous ground make it difficult to directly apply traditional simulation methods used in free field environments to half-space conditions. On the other hand, due to the dynamic changes of the contact surface between the tire and the ground and its influence on the propagation path of sound waves, it becomes more complicated to accurately predict the radiated noise of tire structures on porous ground. Therefore, how to develop a more accurate prediction method for tire radiated noise based on the characteristics of porous ground has become an urgent problem to be solved in the current research field; in view of this, the present invention proposes a rapid prediction method for tire radiated noise on porous ground. Summary of the invention

[0005] The purpose of the present invention is to propose a rapid prediction method for tire radiated noise on porous ground to solve the problems raised in the background technology. The present invention is suitable for quickly and accurately evaluating the vibration and acoustic radiation of tire structures on porous ground, and effectively combines the advantages of the half-space boundary element method and the fast multipole algorithm, which not only improves the prediction speed, but also ensures the accuracy of the prediction.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A fast prediction method for tire radiated noise on porous ground includes the following contents:

[0008] S1. Discretize the tire structure surface using triangular elements to ensure that all mesh elements are located above the porous pavement model; divide the boundary elements of the tire structure into two parts according to the distance from the node, where the part close to the node is recorded as the near-field grid, and the part far from the node is recorded as the interaction and far-field grid;

[0009] S2, using the traditional boundary element method to establish the acoustic transfer relationship of the near-field grid obtained by dividing in S1;

[0010] S3, using the fast multipole boundary element method to establish the acoustic transfer relationship between the interaction and far-field grids obtained in S1;

[0011] S4. Based on the operations described in S2 and S3, the unknown main variables are solved, and further combined with the established acoustic transfer relationship to realize the prediction of the radiated noise of the tire on the porous ground.

[0012] Preferably, S2 specifically includes the following contents:

[0013] Based on the traditional boundary element method, the traditional boundary element integral equation for sound radiation prediction is obtained by integrating the Helmholtz equation. The obtained equation is further discretized to obtain:

[0014]

[0015] Among them, v n (x) represents the normal vibration velocity value of the tire surface at point x; ρ represents the density of the acoustic medium; c represents the speed of sound; ω represents the circumferential frequency; k = ω / c; R(θ) represents the distance from x to the edge of the triangle; Γ\Γ x Indicates that the triangular cell boundary Γ does not include Γ x ; n represents the unit normal vector of the tire surface; G(x,y) is the half-space Green's function, and its expression is:

[0016]

[0017] The last two terms of the half-space Green's function G r (x,y) means considering the porous characteristics of the ground, and its expression is:

[0018]

[0019] g(x,y) represents the Green's function of the entire space, and its expression is:

[0020]

[0021] r = |xy| represents the Euclidean distance between x and y; y (y 1 ,y 2 ,-y 3 ) is y(y 1 ,y 2 ,y 3 ), (y 1 ,y 2 ,y 3 ) represent the x, y, and z coordinates of the y point respectively; y ζ (y 1 ,y 2 ,-y 3 +iζ) is the mirror node of y considering the porous characteristics of the ground; ζ is the point coordinate considering the impedance effect; γ=ik / z 0 , z 0 =z p / (ρc),z p satisfy The infinite integral in formula (3) is solved by the Gauss-Laguerre integration method; the Gauss-Laguerre integration points and weights are determined based on the roots of the Laguerre orthogonal polynomial; assuming there are N integration points, the integral is approximately expressed as:

[0022]

[0023] Among them, A i is the corresponding weight, x i is the integration point; the integration points and weights are obtained by solving the roots of the Laguerre polynomial and using the obtained roots to calculate the corresponding weights; the Laguerre polynomial is defined as:

[0024]

[0025] The root of each polynomial is in the interval (0,∞), and its corresponding weight A i Calculated by the following formula:

[0026]

[0027] Where n represents the order of the Laguerre polynomial, L n+1 represents the Laguerre polynomial of order n+1.

[0028] Preferably, the normal vibration velocity of each node on the tire surface is obtained by numerical simulation technology and input into formula (1) as an input condition.

[0029] Preferably, S3 specifically includes the following contents:

[0030] According to the fast multipole algorithm, the acoustic transfer relationship in the far-field lattice is approximated by series expansion of the Green's function; the multi-level expansion form of the full-space Green's function is:

[0031]

[0032] According to formula (8) and using the mirror relationship between nodes, the expansion of the half-space Green's function G(x, y) is obtained:

[0033]

[0034] In formula (9), O represents the series expansion point; the upward arrow represents the vector formed by two points; the following coordinate relationship O(O) is used in equations (8) and (9): 1 ,O 2 ,O 3 ), O (O 1 ,O 2 ,-O 3), O ζ (O 1 ,O 2 ,-O 3 +iζ); express The complex conjugate of and Defined as and j n and denote the n-order first-kind spherical Bessel and Hankel functions, respectively; is a spherical harmonic function, r, θ and φ are vectors The three spherical coordinates of ; the formula of spherical harmonics is expressed as:

[0035]

[0036] Where l is a non-negative integer, which represents the order of the spherical harmonic function; m is an integer, which represents the degree of the spherical harmonic function; P l m represents the associated Legendre polynomials, defined as:

[0037] Preferably, the S4 specifically includes the following contents:

[0038] In the near-field grid, the unknown variable μ is obtained by using equation (1) or by combining equation (1) and equation (9) in the interactive and far-field grids. According to the boundary element method, the acoustic variables at each node on the tire surface and the transfer relationship between the acoustic variables and any measuring point are expressed as follows:

[0039]

[0040] In formula (11), the half-space Green's function G(x, y) is used to consider the influence of ground reflection; mn It represents the Euclidean distance between the mth unit node and the nth measuring point, and its expression is as follows:

[0041] r mn =R mn +R rmn +R rimn (12)

[0042]

[0043] Among them, (x 1n ,x 2n ,x 3n ),(y 1n ,y 2n ,y 3n ) represent the coordinates of the measuring points and unit nodes respectively.

[0044] Preferably, when predicting tire radiation noise on porous ground, the noise reflection contribution of the porous ground is considered, and the ground reflection contribution is obtained by solving the image source method.

[0045] Compared with the prior art, the present invention provides a method for quickly predicting tire radiation noise on porous ground, which has the following beneficial effects:

[0046] (1) The present invention takes into account the actual characteristics of porous ground and can more accurately simulate the propagation behavior of sound waves in a half-space environment, especially in the case of interaction between tires and the ground, thereby improving the accuracy of sound radiation prediction.

[0047] (2) Compared with the traditional full-space prediction method, the present invention is optimized for the actual working environment (i.e., half-space conditions), making it suitable for a wider range of real-world application scenarios, especially in road noise control and tire design optimization.

[0048] (3) Through improved algorithms or models, the present invention can reduce the demand for computing resources, simplify the calculation process, speed up the simulation, and make large-scale simulation tasks more feasible while ensuring prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a method for rapidly predicting tire radiation noise on porous ground proposed by the present invention;

[0050] Figure 2 The simplified tire model and position diagram used in Example 1 of the present invention;

[0051] Figure 3 The absolute sound pressure distribution diagram is calculated by using the rapid prediction method for tire radiation noise on porous ground proposed by the present invention as mentioned in Example 1 of the present invention;

[0052] Figure 4 The absolute sound pressure distribution is calculated by using the finite element method mentioned in Example 1 of the present invention. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0054] The present invention proposes a method for rapid prediction of tire radiated noise on porous ground. First, the surface of the tire structure is meshed, and triangular units are used for discretization to ensure that all mesh units are located above the porous road surface model. Then, the triangular units divided from the tire surface are divided into near field and far field parts according to the distance from the nodes on the tire surface. For the near field part, the traditional boundary element method is used to establish the transfer relationship between the nodes for solution; while for the far field part, the fast multipole method is used to approximate the transfer relationship between the nodes. Subsequently, a simplified fast multipole expansion formula is derived based on the expansion of the half-space Green's function. The mirror relationship is used to avoid directly calculating the expansion coefficient in the mirror domain, thereby simplifying the implementation steps of the fast multipole algorithm. Finally, the acoustic variables on the unit obtained by the above solution and the sound field transfer relationship are used to realize the rapid prediction of tire radiated noise on porous ground. The half-space Green's function is used in the sound transfer relationship to take into account the influence of ground reflection, thereby improving the accuracy of the prediction. A preferred embodiment of the present invention is described in detail below in conjunction with the accompanying drawings, specifically including the following contents.

[0055] Embodiment 1:

[0056] See also Figure 1 The present invention proposes a rapid prediction method for tire radiation noise on porous ground, which includes the following contents:

[0057] S1. Discretize the tire structure surface using triangular elements to ensure that all mesh elements are located above the porous pavement model; divide the boundary elements of the tire structure into two parts according to the distance from the node, where the part close to the node is recorded as the near-field grid, and the part far from the node is recorded as the interaction and far-field grid;

[0058] S2. Use the traditional boundary element method to establish the acoustic transmission relationship of the near-field grid obtained in S1; specifically, the following contents are included:

[0059] Based on the traditional boundary element method, the traditional boundary element integral equation for sound radiation prediction is obtained by integrating the Helmholtz equation. The obtained equation is further discretized to obtain:

[0060]

[0061] Among them, v n (x) represents the normal vibration velocity value of the tire surface at point x; ρ represents the density of the acoustic medium; c represents the speed of sound; ω represents the circumferential frequency; k = ω / c; R(θ) represents the distance from x to the edge of the triangle; Γ\Γ x Indicates that the triangular cell boundary Γ does not include Γ x; n represents the unit normal vector of the tire surface; G(x,y) is the half-space Green function, and its expression is:

[0062]

[0063] The last two terms of the half-space Green's function G r (x,y) means considering the porous characteristics of the ground, and its expression is:

[0064]

[0065] g(x,y) represents the Green's function of the entire space, and its expression is:

[0066]

[0067] r = |xy| represents the Euclidean distance between x and y; y (y 1 ,y 2 ,-y 3 ) is y(y 1 ,y 2 ,y 3 ), (y 1 ,y 2 ,y 3 ) represent the x, y, and z coordinates of the y point respectively; y ζ (y 1 ,y 2 ,-y 3 +iζ) is the mirror node of y considering the porous characteristics of the ground; ζ is the point coordinate considering the impedance effect; γ=ik / z 0 , z 0 =z p / (ρc),z p satisfy The infinite integral in formula (3) is solved by the Gauss-Laguerre integration method; the Gauss-Laguerre integration points and weights are determined based on the roots of the Laguerre orthogonal polynomial; assuming there are N integration points, the integral is approximately expressed as:

[0068]

[0069] Among them, A i is the corresponding weight, x i is the integration point; the integration points and weights are obtained by solving the roots of the Laguerre polynomial and using the obtained roots to calculate the corresponding weights; the Laguerre polynomial is defined as:

[0070]

[0071] The root of each polynomial is in the interval (0,∞), and its corresponding weight A i Calculated by the following formula:

[0072]

[0073] Where n represents the order of the Laguerre polynomial, L n+1 represents the n+1 order Laguerre polynomial;

[0074] The normal vibration velocity of each node on the tire surface is obtained by numerical simulation technology and is input into equation (1) as an input condition;

[0075] S3, using the fast multipole boundary element method to establish the acoustic transfer relationship between the interaction and far-field grids obtained in S1; specifically including the following contents:

[0076] According to the fast multipole algorithm, the acoustic transfer relationship in the far-field lattice is approximated by series expansion of the Green's function; the multi-level expansion form of the full-space Green's function is:

[0077]

[0078] According to formula (8) and using the mirror relationship between nodes, the expansion of the half-space Green's function G(x, y) is obtained:

[0079]

[0080] In formula (9), O represents the series expansion point; the upward arrow represents the vector formed by two points; the following coordinate relationship O(O) is used in equations (8) and (9): 1 ,O 2 ,O 3 ), O (O 1 ,O 2 ,-O 3 ), O ζ (O 1 ,O 2 ,-O 3 +iζ); express The complex conjugate of and Defined as and j n and denote the n-order first-kind spherical Bessel and Hankel functions, respectively; is a spherical harmonic function, r, θ and φ are vectors The three spherical coordinates of ; the formula of spherical harmonics is expressed as:

[0081]

[0082] Where l is a non-negative integer, which represents the order of the spherical harmonic function; m is an integer, which represents the degree of the spherical harmonic function; P l m represents the associated Legendre polynomials, defined as:

[0083] Preferably, the S4 specifically includes the following contents:

[0084] In the near-field grid, the unknown variable μ is obtained by using equation (1) or by combining equation (1) and equation (9) in the interactive and far-field grids. According to the boundary element method, the acoustic variables at each node on the tire surface and the transfer relationship between the acoustic variables and any measuring point are expressed as follows:

[0085]

[0086] In formula (11), the half-space Green's function G(x, y) is used to consider the influence of ground reflection; mn It represents the Euclidean distance between the mth unit node and the nth measuring point, and its expression is as follows:

[0087] r mn =R mn +R rmn +R rimn (12)

[0088]

[0089] Among them, (x 1n ,x 2n ,x 3n ),(y 1n ,y 2n ,y 3n ) represent the coordinates of the measuring points and unit nodes respectively;

[0090] When predicting tire radiation noise on porous ground, the noise reflection contribution of porous ground is considered, and the ground reflection contribution is obtained by the image source method.

[0091] S4. Based on the operations described in S2 and S3, the unknown main variables are solved, and further combined with the established acoustic transfer relationship to realize the prediction of the radiated noise of the tire on the porous ground.

[0092] Based on the above content, the present invention uses the method in this paper and the finite element method to calculate the absolute sound pressure distribution at 100 Hz. Figure 2-4As shown in the figure, the tire model is set to a radius of 0.3105m, a width of 0.195m, and the contact point between the tire and the ground is set to the coordinate origin. From the results in the figure, it can be seen that the two methods are in good agreement, but the finite element method requires 245530 degrees of freedom, while the method in this paper only requires 5988 grids. Therefore, the method in this paper can not only maintain high accuracy, but also reduce the number of grids.

[0093] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for rapid prediction of tire radiated noise on porous ground, characterized in that: It includes the following: S1. Discretize the tire structure surface using triangular elements to ensure that all mesh elements are located above the porous pavement model; divide the boundary elements of the tire structure into two parts according to the distance from the node, where the part close to the node is recorded as the near-field grid, and the part far from the node is recorded as the interaction and far-field grid; S2, using the traditional boundary element method to establish the acoustic transfer relationship of the near-field grid obtained by dividing in S1; S3, using the fast multipole boundary element method to establish the acoustic transfer relationship between the interaction and far-field grids obtained in S1; S4. Based on the operations described in S2 and S3, the unknown main variables are solved, and further combined with the established acoustic transfer relationship to realize the prediction of the radiated noise of the tire on the porous ground.

2. The rapid prediction method of tire radiation noise on porous ground according to claim 1 is characterized in that: The S2 specifically includes the following contents: Based on the traditional boundary element method, the traditional boundary element integral equation for sound radiation prediction is obtained by integrating the Helmholtz equation. The obtained equation is further discretized to obtain: Among them, v n (x) represents the normal vibration velocity value of the tire surface at point x; ρ represents the density of the acoustic medium; c represents the speed of sound; ω represents the circumferential frequency; k = ω / c; R(θ) represents the distance from x to the edge of the triangle; Γ\Γ x Indicates that the triangular cell boundary Γ does not include Γ x ; n represents the unit normal vector of the tire surface; G(x,y) is the half-space Green's function, and its expression is: The last two terms of the half-space Green's function G r (x,y) means considering the porous characteristics of the ground, and its expression is: g(x,y) represents the Green's function of the entire space, and its expression is: r = |xy| represents the Euclidean distance between x and y; y (y1,y2,-y3) is the mirror node of y(y1,y2,y3), (y1,y2,y3) represents the x,y,z coordinates of y respectively; y ζ (y1,y2,-y3+iζ) is the mirror node of y considering the porous characteristics of the ground; ζ is the point coordinate considering the impedance effect; γ=ik / z0, z0=z p / (ρc),z p satisfy The infinite integral in formula (3) is solved by the Gauss-Laguerre integration method; the Gauss-Laguerre integration points and weights are determined based on the roots of the Laguerre orthogonal polynomial; assuming there are N integration points, the integral is approximately expressed as: Among them, A i is the corresponding weight, x i is the integration point; the integration points and weights are obtained by solving the roots of the Laguerre polynomial and using the obtained roots to calculate the corresponding weights; the Laguerre polynomial is defined as: The root of each polynomial is in the interval (0,∞), and its corresponding weight A i Calculated by the following formula: Where n represents the order of the Laguerre polynomial, L n+1 represents the Laguerre polynomial of order n+1.

3. The rapid prediction method of tire radiation noise on porous ground according to claim 2 is characterized in that: The normal vibration velocity of each node on the tire surface is obtained by numerical simulation technology and is input into equation (1) as an input condition.

4. The rapid prediction method of tire radiation noise on porous ground according to claim 3 is characterized in that: The S3 specifically includes the following contents: According to the fast multipole algorithm, the acoustic transfer relationship in the far-field lattice is approximated by series expansion of the Green's function; the multi-level expansion form of the full-space Green's function is: According to formula (8) and using the mirror relationship between nodes, the expansion of the half-space Green's function G(x,y) is obtained: In formula (9), O represents the series expansion point; the upward arrow represents the vector formed by two points; the following coordinate relationship O(O1,O2,O3) is used in equations (8) and (9), O (O1,O2,-O3), O ζ (O1, O2, -O3 + iζ); express The complex conjugate of and Defined as and j n and denote the n-order first-kind spherical Bessel and Hankel functions, respectively; is a spherical harmonic function, r, θ and φ are vectors The three spherical coordinates of ; the formula of spherical harmonics is expressed as: Where l is a non-negative integer, which represents the order of the spherical harmonic function; m is an integer, which represents the degree of the spherical harmonic function; P l m represents the associated Legendre polynomials, defined as:

5. The rapid prediction method of tire radiation noise on porous ground according to claim 4 is characterized in that: The S4 specifically includes the following contents: In the near-field grid, the unknown variable μ is obtained by using equation (1) or by combining equation (1) and equation (9) in the interactive and far-field grids. According to the boundary element method, the acoustic variables at each node on the tire surface and the transfer relationship between the acoustic variables and any measuring point are expressed as follows: In formula (11), the half-space Green's function G(x, y) is used to consider the influence of ground reflection; mn It represents the Euclidean distance between the mth unit node and the nth measuring point, and its expression is as follows: r mn =R mn +R rmn +R rimn (12) Among them, (x 1n ,x 2n ,x 3n ),(y 1n ,y 2n ,y 3n ) represent the coordinates of the measuring points and unit nodes respectively.

6. The rapid prediction method of tire radiation noise on porous ground according to claim 1, characterized in that: When predicting tire radiated noise on porous ground, the noise reflection contribution of porous ground is considered, and the ground reflection contribution is obtained by the image source method.

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