CN115782480B - Rolling tire structure noise time domain prediction method - Google Patents
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Abstract
The invention discloses a rolling tire structure noise time domain prediction method, which comprises the steps of performing conformal retraction on the surface of a tire model to establish a conformal surface, arranging a plurality of equivalent sources on the conformal surface, and solving time domain acceleration at each node of the surface of the tire model; establishing a transfer function between each node and the equivalent source intensity according to the position relation between the equivalent source point and the tire surface time domain acceleration node; solving equivalent source strengths at any position on the conformal surface inside the tire model at each moment according to a transfer function based on an offline interpolation method; and (3) the ground reflection influence is calculated in the obtained sound transmission relation by using a mirror image source method, and the noise field of the external structure of the tire is calculated by establishing the transmission relation between the external sound field of the tire and the equivalent source. According to the invention, the equivalent source surface is conformal with the surface of the tire model, and the influence of the ground reflection effect is considered, so that an accurate and efficient tire structure noise prediction process is realized.
Description
Technical Field
The invention relates to the technical field of sound field prediction in the noise field, in particular to a rolling tire structure noise time domain prediction method.
Background
Predicting vibration acoustic radiation of a tire structure has been an important focus of attention of scientific research institutes and tire enterprises at home and abroad. The prediction methods widely used at present are a finite element method and a boundary element method. But most existing methods are directed to stationary tires. Since the stationary state is not the actual condition of the tire, the calculated radiated sound field is different from the actual one. The dynamic simulation method of the rolling tire structure is continuously perfected, the simulation precision is continuously improved, and the attention of students is drawn to how to calculate the acoustic radiation of the rolling tire structure by utilizing the dynamic simulation results.
In recent years, with respect to dynamic simulation and acoustic radiation of a rolling tire, scholars have proposed a concept of associating vibration in a lagrangian coordinate system with vibration in an euler coordinate system by using coordinate system mapping. The existing coordinate system mapping methods are three, namely, the vibration response mapping method in the Lagrangian coordinate system and the Euler coordinate system is realized through the adjustment of the grid node numbers. This method is in fact an artificial rearrangement of the calculation results in the rotation coordinate system, which has a certain difficulty in popularizing the method to engineering applications. And secondly, mapping from a Lagrange coordinate system to an Euler coordinate system is realized by adopting wave number domain-frequency domain transformation. The method is actually an angle frequency domain interpolation method, and requires grid nodes to form a plurality of circles of complete circumferences to perform Fourier transformation of circumferential angles, so that the ground reflection effect cannot be considered. Finally, a hybrid Lagrangian-Euler Method (MLE) is used to solve the problem of vibration data mapping in two coordinate systems. The MLE method is essentially a time domain spatial interpolation method with strong adaptability, but at each moment, projection judgment and interpolation are needed to be carried out on each static tire grid node, the calculation complexity is high, and in addition, numerical errors exist in the spatial interpolation process.
The prior art has the defects that the research on the time domain prediction of the structural noise of the rolling tire is still insufficient, and a plurality of problems to be solved exist, such as the influence caused by the ground reflection when the tire structure is contacted with the ground cannot be considered; or the numerical implementation process is too complex, a large amount of interpolation calculation is required, and a certain numerical error is inevitably introduced in the calculation, so that the accuracy of a numerical result is reduced.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and adopts a rolling tire structure noise time domain prediction method to solve the problems in the prior art.
A method of rolling tire structural noise time domain prediction comprising:
s1, performing conformal retraction on the surface of a tire model to establish a conformal surface, setting a plurality of equivalent sources on the conformal surface, and solving time domain acceleration at each node of the surface of the tire model;
S2, establishing a transfer function between each node and the equivalent source intensity according to the position relation between the equivalent source point and the tire surface time domain acceleration node;
step S3, solving equivalent source strengths at any position on the conformal surface inside the tire model at each moment according to a transfer function based on an offline interpolation method;
And S4, accounting the ground reflection influence in the obtained sound transmission relation by using a mirror image source method, and calculating to obtain the noise field of the external structure of the tire by establishing the transmission relation between the external sound field of the tire and the equivalent source.
As a further aspect of the invention: the specific steps of the step S1 include:
Acquiring an actual tire model, dispersing the tire model surface by adopting a triangular unit, and performing conformal retraction along the normal vector direction of the tire model surface unit to obtain a conformal surface, wherein the retraction size is 0.5c x dt, and c represents the sound velocity and dt represents the sampling time interval;
Setting M nodes on the surface of the tire model, and obtaining time domain acceleration of each node on the surface of the tire model by adopting a numerical simulation technology;
n equivalent sources corresponding to M nodes are arranged in the tire model, and the time domain acceleration is used as the input quantity of the time domain equivalent sources, wherein N is less than or equal to M.
As a further aspect of the invention: the specific steps of the step S2 include:
obtaining the superposition of sound fields generated by N equivalent sources on the inner side of the tire according to the equivalent source theory;
obtaining time domain acceleration of the surface according to the tire model, and reversely obtaining time domain equivalent source strength, wherein the formula is as follows:
Wherein a (r m, t) represents the time domain acceleration value of the mth tire surface node; ρ represents the acoustic medium density; c represents the sound velocity; r mn is the distance between the mth node and the nth equivalent source, (X m,ym,zm) represents the spatial position of the mth node in the Cartesian coordinate system, (x n,yn,zn) represents the spatial position of the nth equivalent source point in the Cartesian coordinate system; n represents a unit normal vector of the tire surface; q (r n,τmn) represents the time domain source intensity of the nth equivalent source inside the tire; r n represents the nth equivalent source; τ mn represents the delay time, and τ mn＝t-Rmn/c; τ represents the delay time.
As a further aspect of the invention: the specific steps of the step S3 include:
S31, carrying out interpolation processing on the time domain equivalent source intensity by adopting a linear interpolation function, and reversely obtaining the time domain equivalent source intensity at any moment, wherein the formula is as follows:
Wherein i represents the sampling time discrete point number; j represents the delay time discrete point number; t i denotes the i-th discrete sampling step; The method comprises the steps that when sound waves are sent out for an nth equivalent source, the sound waves are received by an mth node at a time t i; τ j is the jth discrete delay step; τ j＝τ1+(j-1)Δτ,τ1＝t1-Rmin/c; Δτ represents a delay time interval; r min represents the minimum distance between all equivalent sources and nodes; q (r n,τj) is the time domain source strength of the nth equivalent source at time t at time τ j; Is based on A linear interpolation function for the parameter;
The formula based on the linear interpolation function Φ k (τ) with delay τ as a parameter is:
Obtaining linear interpolation functions phi (tau mn) according to the linear interpolation functions phi k (tau) respectively;
Obtaining tire acceleration of M nodes at time t i, and obtaining a characterization formula of time domain equivalent source intensity by interpolation:
Where a i is a time domain acceleration vector consisting of m=1, 2, …, a (r m,ti) of M; q j is a time-domain equivalent source strong vector consisting of n=1, 2, …, Q (r n,τj) of N; Is composed of An M multiplied by N dimension transfer matrix is formed;
S32, solving the time domain equivalent source intensity at any moment in the tire structure through the process, and sequentially solving the time domain equivalent source intensity at any moment from the initial time step:
In the method, in the process of the invention, The superscript "+" indicates taking the pseudo-inverse of the transfer matrix; q j denotes a time domain source intensity vector composed of Q (r n,τj).
As a further aspect of the invention: the specific steps of the step S4 include:
According to the time domain equivalent source intensity of each moment on the surface of the tire model and the transfer relation between the equivalent source and any node, predicting the time domain sound field of the tire structure noise, the real-time sound field prediction formula with the ground reflection effect is as follows:
Wherein p (r m,ti) represents the time domain sound pressure generated at the mth measurement point at time t i; r rn represents a mirror source taking n equivalent sources; r rmn represents the Euclidean distance between the mirror image source of the nth equivalent source and the mth measuring point, an (X rn,yrn,zrn) represents the spatial position of the mirror source of the nth equivalent source in the Cartesian coordinate system, and y n＝-yrn.
Compared with the prior art, the invention has the following technical effects by adopting the technical scheme:
the method is directly completed in the time domain, overcomes the defect that the actual working condition of the tire cannot be effectively analyzed based on frequency domain transformation, and can realize an accurate and efficient noise prediction process of the complex tire structure.
The theoretical technology of the method is a time domain equivalent source method, and the numerical calculation is directly carried out on the complex tire model by establishing the conformal surface, so that the numerical model is closer to an actual tire model, the numerical solving process is simpler, and the actual tire structural noise can be described more accurately.
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The following detailed description of specific embodiments of the invention refers to the accompanying drawings, in which:
FIG. 1 is a schematic diagram of the steps of a prediction method according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of an acceleration input signal that accounts for Gaussian white noise in accordance with an embodiment of the present disclosure;
FIG. 3 is a schematic view of the spatial distribution of equivalent source points on a conformal surface using actual tire model surface nodes and structures in accordance with an embodiment of the present disclosure;
FIG. 4 is a space-time cloud image of a sound field of a tire structure on a predicted surface obtained by solving a theoretical formula;
FIG. 5 is a spatiotemporal cloud image of a tire structure sound field on a predicted surface obtained by solving in accordance with an embodiment of the present disclosure;
FIG. 6 is a space-time cloud image of a tire structure sound field on a predicted surface, which is obtained by solving a theoretical formula without considering ground reflection;
Fig. 7 is a theoretical sound pressure diagram of a time domain of a 10 th measurement point in a tire structure sound field in an analysis time period and a time domain sound pressure diagram obtained by adopting the method of the application in the embodiment of the application;
FIG. 8 is a theoretical sound pressure graph of a time domain of a 100 th measuring point in a tire structure sound field in an analysis time period and a time domain sound pressure graph obtained by adopting the method of the application in the embodiment of the application;
Fig. 9, 10 and 11 are cloud diagrams of spatial distribution of sound pressure at time t=68Δt in the disclosed embodiment of the application.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the embodiment of the invention, the prediction method solves the time domain acceleration of each node on the surface of the tire by arranging an equivalent source in the tire; establishing a transfer relation between time domain acceleration at each node on the tire surface at any moment and each equivalent source intensity; sequentially solving the time domain source strengths of all equivalent sources at any moment point in the tire; according to the obtained time domain source intensity of each equivalent source at any moment and the transfer relation between the equivalent source and any measuring point, calculating to obtain the time domain sound field of the tire structural noise, thereby realizing the real-time prediction process of the tire structural noise. The equivalent source surface is conformal with the tire surface, and the influence caused by the ground reflection effect can be considered, so that the accurate and efficient noise prediction process of the complex tire structure can be realized.
Referring to fig. 1, in an embodiment of the present invention, a method for predicting structural noise time domain of a rolling tire includes:
S1, performing conformal retraction on the surface of a tire model to establish a conformal surface, setting a plurality of equivalent sources on the conformal surface, and solving time domain acceleration at each node of the surface of the tire model, wherein the method specifically comprises the following steps:
Acquiring an actual tire model, dispersing the tire model surface by adopting a triangular unit, and performing conformal retraction along the normal vector direction of the tire model surface unit to obtain a conformal surface, wherein the retraction size is 0.5c x dt, and c represents the sound velocity and dt represents the sampling time interval;
Setting M nodes on the surface of the tire model, and obtaining time domain acceleration of each node on the surface of the tire model by adopting a numerical simulation technology;
n equivalent sources corresponding to M nodes are arranged in the tire model, and the time domain acceleration is used as the input quantity of the time domain equivalent sources, wherein N is less than or equal to M.
Step S2, establishing a transfer function between each node and the equivalent source intensity according to the position relation between the equivalent source point and the tire surface time domain acceleration node, wherein the specific steps comprise:
obtaining the superposition of sound fields generated by N equivalent sources on the inner side of the tire according to the equivalent source theory;
obtaining time domain acceleration of the surface according to the tire model, and reversely obtaining time domain equivalent source strength, wherein the formula is as follows:
Wherein a (r m, t) represents the time domain acceleration value of the mth tire surface node; ρ represents the acoustic medium density; c represents the sound velocity; r mn is the distance between the mth node and the nth equivalent source, (X m,ym,zm) represents the spatial position of the mth node in the Cartesian coordinate system, (x n,yn,zn) represents the spatial position of the nth equivalent source point in the Cartesian coordinate system; n represents a unit normal vector of the tire surface; q (r n,τmn) represents the time domain source intensity of the nth equivalent source inside the tire; r n represents the nth equivalent source; τ mn represents the delay time, and τ mn＝t-Rmn/c; τ represents the delay time.
Step S3, solving equivalent source strengths at any position on the conformal surface inside the tire model at each moment according to a transfer function based on an offline interpolation method, wherein the method specifically comprises the following steps:
S31, carrying out interpolation processing on the time domain equivalent source intensity by adopting a linear interpolation function, and reversely obtaining the time domain equivalent source intensity at any moment, wherein the formula is as follows:
Wherein i represents the sampling time discrete point number; j represents the delay time discrete point number; t i denotes the i-th discrete sampling step; The method comprises the steps that when sound waves are sent out for an nth equivalent source, the sound waves are received by an mth node at a time t i; τ j is the jth discrete delay step; τ j＝τ1+(j-1)Δτ,τ1＝t1-Rmin/c; Δτ represents a delay time interval; r min represents the minimum distance between all equivalent sources and nodes; q (r n,τj) is the time domain source strength of the nth equivalent source at time t at time τ j; Is based on A linear interpolation function for the parameter;
The formula based on the linear interpolation function Φ k (τ) with delay τ as a parameter is:
Obtaining linear interpolation functions phi (tau mn) according to the linear interpolation functions phi k (tau) respectively;
Obtaining tire acceleration of M nodes at time t i, and obtaining a characterization formula of time domain equivalent source intensity by interpolation:
Where a i is a time domain acceleration vector consisting of m=1, 2, …, a (r m,ti) of M; q j is a time-domain equivalent source strong vector consisting of n=1, 2, …, Q (r n,τj) of N; Is composed of An M multiplied by N dimension transfer matrix is formed;
S32, solving the time domain equivalent source intensity at any moment in the tire structure through the process, and sequentially solving the time domain equivalent source intensity at any moment from the initial time step:
In the method, in the process of the invention, The superscript "+" indicates taking the pseudo-inverse of the transfer matrix, and introducing a regularization method in the inversion process of each time step to control instability in order to inhibit the amplification of error by the pathogenicity of the inversion matrix. Q j denotes a time domain source intensity vector composed of Q (r n,τj).
S4, using a mirror image source method to calculate the external structural noise field of the tire by establishing a transmission relation between the external sound field of the tire and an equivalent source, wherein the method comprises the following specific steps of:
According to the time domain equivalent source intensity of each moment on the surface of the tire model and the transfer relation between the equivalent source and any node, predicting the time domain sound field of the tire structure noise, the real-time sound field prediction formula with the ground reflection effect is as follows:
Wherein p (r m,ti) represents the time domain sound pressure generated at the mth measurement point at time t i; r rn represents a mirror source taking n equivalent sources; r rmn represents the Euclidean distance between the mirror image source of the nth equivalent source and the mth measuring point, an (X rn,yrn,zrn) represents the spatial position of the mirror source of the nth equivalent source in the Cartesian coordinate system, and y n＝-yrn.
In this embodiment, the time domain acceleration signals on each node are obtained by adopting numerical simulation calculation according to the actual running condition of the tire.
The method according to the invention is tested as follows:
Setting the tire rotation linear speed as an input quantity, wherein the tire rotation linear speed is 60km/h, and calculating to obtain an excitation frequency f r as follows:
Wherein: v 0 represents the tire rotation linear velocity, h represents the tire height, and d represents the tire inner surface diameter. The time sampling frequency is f=12.8 kHz, 128 sampling points are sampled in total, and the calculated time length is the time of one rotation of the tire. The time domain acceleration signals of all nodes on the surface of the tire are given by the following modes:
In order to simulate the actual measurement conditions, gaussian white noise with a signal-to-noise ratio of 30dB is added to the acceleration signal, and the generated Gaussian white noise graph is shown in FIG. 2, wherein b1 represents the original signal and b2 represents the signal to which the Gaussian white noise is added.
The tire surface nodes and internal equivalent source locations shown in FIG. 3 are schematically represented by tire model 205/55R16, the tire parameters are: width 0.205m, inner surface radius 0.2901m; setting related parameters: air density ρ=1.21 kg/m 3, sound speed in air 344m/s; wherein the solid line represents the inner surface of the tire, the solid circle dotted line represents a node on the surface of the tire, and the solid square dotted line represents an equivalent source point location.
And a space-time cloud picture of the tire structure sound field on the predicted surface obtained by solving the theoretical formula is shown in fig. 4. The sound pressure prediction plane is a plane at 0.3m in the z direction, the plane coordinate information is-0.5 m in the x direction, the space point interval is-0.5 m in the y direction. The theoretical sound pressure on the prediction plane is obtained by adopting a sound radiation calculation formula of a rotating point source.
FIG. 5 shows a spatiotemporal cloud image of a tire structure sound field on a predicted surface obtained by solving the method of the invention.
FIG. 6 shows a space-time cloud image of a tire structure sound field on a predicted surface obtained by solving a theoretical formula when ground reflection is not considered; FIGS. 4, 5 and 6 show that the contour diagrams of the sound pressure of the measuring points of the sound field of the structure at each moment are consistent, which shows the correctness and effectiveness of the method of the invention; meanwhile, the influence of ground reflection on the sound field prediction of the tire structure can be found, and the influence of the ground reflection on the noise field of the tire can be considered.
The analysis time periods shown in fig. 7 and fig. 8 are (-0.5 m, -0.05m,0.3 m) and (-0.3 m,0.25m,0.3 m) of the time domain theoretical sound pressure results of the measuring points in the sound field of the tire structure in the analysis time period and the time domain sound pressure results obtained by adopting the method of the invention, wherein a solid line is a curve a1 which is a theoretical sound pressure signal, a hollow round dotted line is a curve a2 which is a time domain sound pressure signal, and a solid triangular dotted line is a curve a3 which is a sound pressure signal which does not consider ground reflection. From the curve results, the method can be used for predicting the time domain sound field well, and the method can consider the influence of ground reflection.
The tire noise field spatial distribution cloud at time t=68Δt shown in fig. 9, 10 and 11; wherein the time point is selected to be t=68Δt; from fig. 8, 9 and 10, it can be seen that the time domain sound field distribution obtained by the method of the present invention is consistent with the sound field distribution obtained by the theoretical time domain, and that the ground reflection has a certain influence on the noise field when predicting the sound field of the tire structure.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the spirit and scope of the invention as defined by the appended claims and their equivalents.
Claims (1)
1. A method for predicting the time domain of structural noise of a rolling tire, comprising:
Step S1, performing conformal retraction on the surface of a tire model to establish a conformal surface, setting a plurality of equivalent sources on the conformal surface, and solving time domain acceleration at each node of the surface of the tire model, wherein the specific steps comprise:
Acquiring an actual tire model, dispersing the tire model surface by adopting a triangular unit, and performing conformal retraction along the normal vector direction of the tire model surface unit to obtain a conformal surface, wherein the retraction size is 0.5c x dt, and c represents the sound velocity and dt represents the sampling time interval;
Setting M nodes on the surface of the tire model, and obtaining time domain acceleration of each node on the surface of the tire model by adopting a numerical simulation technology;
setting N equivalent sources corresponding to M nodes in the tire model, and taking time domain acceleration as input quantity of the time domain equivalent sources, wherein N is less than or equal to M;
step S2, establishing a transfer function between each node and the equivalent source intensity according to the position relation between the equivalent source point and the tire surface time domain acceleration node, wherein the specific steps comprise:
obtaining the superposition of sound fields generated by N equivalent sources on the inner side of the tire according to the equivalent source theory;
obtaining time domain acceleration of the surface according to the tire model, and reversely obtaining time domain equivalent source strength, wherein the formula is as follows:
Wherein a (r m, t) represents the time domain acceleration value of the mth tire surface node; ρ represents the acoustic medium density; c represents the sound velocity; r mn is the distance between the mth node and the nth equivalent source, (X m,ym,zm) represents the spatial position of the mth node in the Cartesian coordinate system, (x n,yn,zn) represents the spatial position of the nth equivalent source point in the Cartesian coordinate system; n represents a unit normal vector of the tire surface; q (r n,τmn) represents the time domain source intensity of the nth equivalent source inside the tire; r n represents the nth equivalent source; τ mn represents the delay time, and τ mn＝t-Rmn/c; τ represents a delay time;
Step S3, solving the equivalent source intensity at any position on the conformal surface inside the tire model at each moment according to a transfer function based on an offline interpolation method, wherein the specific steps comprise:
S31, carrying out interpolation processing on the time domain equivalent source intensity by adopting a linear interpolation function, and reversely obtaining the time domain equivalent source intensity at any moment, wherein the formula is as follows:
Wherein i represents the sampling time discrete point number; j represents the delay time discrete point number; t i denotes the i-th discrete sampling step; The method comprises the steps that when sound waves are sent out for an nth equivalent source, the sound waves are received by an mth node at a time t i; τ j is the jth discrete delay step; τ j＝τ1+(j-1)Δτ,τ1＝t1-Rmin/c; Δτ represents a delay time interval; r min represents the minimum distance between all equivalent sources and nodes; q (r n,τj) is the time domain source strength of the nth equivalent source at time t at time τ j; Is based on A linear interpolation function for the parameter;
The formula based on the linear interpolation function Φ k (τ) with delay τ as a parameter is:
Obtaining linear interpolation functions phi (tau mn) according to the linear interpolation functions phi k (tau) respectively;
Obtaining tire acceleration of M nodes at time t i, and obtaining a characterization formula of time domain equivalent source intensity by interpolation:
Where Ai is a time domain acceleration vector consisting of m=1, 2, …, a (r m,ti) of M; qj is a time-domain equivalent source strong vector consisting of q (r n,τj) of n=1, 2, …, N; Is composed of An M multiplied by N dimension transfer matrix is formed;
S32, solving the time domain equivalent source intensity at any moment in the tire structure through the process, and sequentially solving the time domain equivalent source intensity at any moment from the initial time step:
In the method, in the process of the invention, The superscript "+" indicates taking the pseudo-inverse of the transfer matrix; qj represents a time domain source intensity vector composed of q (r n,τj);
S4, using a mirror image source method to calculate the external structural noise field of the tire by establishing a transmission relation between the external sound field of the tire and an equivalent source, wherein the method comprises the following specific steps of:
According to the time domain equivalent source intensity of each moment on the surface of the tire model and the transfer relation between the equivalent source and any node, predicting the time domain sound field of the tire structure noise, the real-time sound field prediction formula with the ground reflection effect is as follows:
Wherein p (r m,ti) represents the time domain sound pressure generated at the mth measurement point at time t i; rrn represents a mirror source taking n equivalent sources; r rmn represents the Euclidean distance between the mirror image source of the nth equivalent source and the mth measuring point, an (X rn,yrn,zrn) represents the spatial position of the mirror source of the nth equivalent source in the Cartesian coordinate system, and y n＝-yrn.
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| CN107284149A (en) * | 2016-03-02 | 2017-10-24 | 通用汽车环球科技运作有限责任公司 | Utilize the system and method for radar remote monitoring |
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| US4727501A (en) * | 1987-02-27 | 1988-02-23 | The Uniroyal Goodrich Tire Company | Method of simulating tire tread noise and apparatus |
| WO2002052298A1 (en) * | 2000-12-22 | 2002-07-04 | Pirelli Pneumatici S.P.A. | System and method for measuring kinematic parameters of a tyre during the running of a vehicle |
| JP5183970B2 (en) * | 2007-05-30 | 2013-04-17 | 東洋ゴム工業株式会社 | Prediction method of cavity resonance of pneumatic tire |
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