An Analysis Approach For The Tire Cavity Resonance With The Boundary Element Method

Tire noise which has poor controllability is a key factor affecting the vehicle NVH performance.Then,suppressing the tire noise undoubtedly does well in improving the comfort of the drivers and the passengers.Knowing that the pipe resonance noise and the cavity resonance noise play main roles in the tire noise,they will be fully studied in this thesis.The pipe size of the tire pattern and the porous material pasted on the inner tire surface directly determine the resonance noise level of the pipe and the cavity.Thus,the pipe size design and the porous material selection become vital issues of controlling the tire pipe resonance noise and the cavity resonance noise,respectively.In the analysis of the pipe and the cavity resonance,the eigenfrequency is a key parameter whose real part is the resonant frequency of the acoustic cavity and the imaginary one represents the external radiation or the damping loss of the acoustic cavity.Obviously,the imaginary part can be used as an index evaluating the noise control.Each eigenfrequency of the pipe and the cavity can be numerically obtained by the boundary element method(BEM),as has been done in this thesis.While it should be noticed that a nonlinear eigenproblem(NEP)is generally formed due to the frequency-dependent coefficient matrix using the BEM and it is unfortunately hard to solve directly.So,a contour integral method and an acoustic eigenvalue analysis approach based on the BEM are simultaneously proposed to calculate the eigenfrequencies of the pipe and the cavity.This thesis conducts research on the acoustic eigenvalue analysis approach based on the BEM around the pipe resonance noise and the cavity resonance noise.The main contents include:The spurious eigenfrequency problem contained in the eigenvalue problem analysis will be fully investigated in the eigenvalue analysis of the exterior,interior,multiplyconnected as well as the multi-domain acoustic eigenvalue problems corresponding to the tire pipe and tire cavity analysis model.The influence of the different boundary integral equations on the true and the spurious eigenfrequencies in the numerical results under different boundary conditions is analyzed.Meanwhile,the occurrence mechanism of the spurious eigenfrequency is analyzed,and the method of removing the spurious eigenfrequencies is given combined with the Burton-Miller method.Based on the above,the proposed method is further applied to investigate the pipe size thereby controlling the tire pipe resonance noise and selecting porous materials to suppress the cavity resonance noise.In the analysis of the pipe resonance,the method is applied to study the 2D pipe resonance,and its effectiveness is verified by analyzing the tire pipe resonance.In addition,the reliability of the method in analyzing tire pipe resonance is verified by numerical simulations and experiments.At the same time,the depth and length on the pipe resonance is analyzed using the absolute values of the imaginary part of the eigenfrequencies and further provide theoretical guarantees for optimizing the tire cavity resonance noise based on size design.In the analysis of the cavity resonance,the impedance boundary condition is introduced to replace the porous material pasted on the inner surface,the numerical results are greatly deviated from the experimental results.Furthermore,a new eigenvalue analysis method for analyzing the resonance of tire cavity with porous materials pasted on the inner surface,namely the acoustic eigenvalue analysis method based on multi-domain boundary element method is proposed.In the method,the multi-domain boundary element method is used to model the tire lined with porous material on the inner surface.The porous material and the other regions of the cavity separately correspond to the equivalent fluid and the domain.The system equations are constructed by the continuity condition of the interface between the air domain and the equivalent fluid domain.Apart from that,the 2D tire cavity model with analytical solution is used to verify the effectiveness of the method in the study of tire cavity resonance and the reliability of this method in analyzing tire cavity resonance is also verified combined with the simulations and experiments.In the end,the effects of porous materials with different flow resistivities,thicknesses,and widths on the suppression of tire cavity resonance noise are compared and discussed,which provide theoretical guarantees for selecting appropriate porous materials to suppress tire cavity resonance noise.Based on the above research,this thesis systematically studies the spurious eigenfrequency of the BEM and the noise problems of the pipe resonance and the cavity resonance,which provides theoretical guarantees for the low noise tire design.