CHAPTER 5: DEVELOPMENT OF NUMERICAL MODEL FOR TIRE/ROAD NOISE ON POROUS PAVEMENT
5.1 Issues Considered in Modeling Tire/Road Noise on Porous Pavement
Similar to skid resistance, tire/road noise on porous pavements is a complex phenomenon involving various mechanisms. It is a combination of tire vibration
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effect and aerodynamic effect (Sandberg and Ejsmont, 2002; Bernhard and McDaniel, 2005). The former is a result of pavement texture, tire rotation and frictional force, among which the radian excitation induced by pavement texture is the most significant cause of the structure-borne noise. The latter includes air pumping, groove resonance and air resonant radiation, which are more relevant to the air movements between tire tread and pavement surface. The model developed in this study aims to focus on tire wall vibration which is the dominant noise generation mechanism under most traveling conditions (Kim et al., 2007). The other noise generation mechanisms can be covered in the simulation model through a calibration process. Finite element method (FEM) and boundary element method (BEM) are used to formulate the generation and propagation of noise respectively. In the simulation of tire/road noise on porous pavements, problems presented in below subsections should be properly considered.
5.1.1 Pavement Surface Texture
Pavement surface texture induces tire wall vibration and affects the friction at tire-pavement interface. It is important to appropriately represent pavement surface texture in the numerical simulation of tire/road noise. The major challenge lies in the randomness of texture profile and the small scale of texture characteristics. In this work, the spectral analysis in accordance with the technique outlined by ISO 13473-4 standard (ISO, 2008) is adopted to derive the pavement texture spectra from the raw texture profile data measured by high-speed laser profilometers. Specifically, discrete Fourier transform (DFT) method is performed to derive texture spectra. This analysis makes it possible to capture the characteristics of surface asperity distribution (Miller et al., 2012). The DFT is defined by:
1 2 , 0
1 N j Nk i
k i win
i
Z Z e
N
(5.1)
181 where Zk is the texture amplitude in the narrow band k, Zi,win is the windowed profile elevation at the discrete point i, and j is the imaginary unit (j2 = -1).
The power spectral density (PSD) can be determined from the DFT results of each narrow band and the total power of a fractional-octave-band is obtained through a summation of all the narrow band power within the window. The pavement texture profile level can then be calculated by:
2 ,
, 10 log 2p 10 log 2 tx
ref ref
Z a
L a a
(5.2)
where Ltx,λ is the texture profile level (dB) of the fractional-octave-band with a center wavelength λ, Zp,λ is the power within the fractional-octave band, αλ is the root mean square of texture amplitude, and αref is the reference texture amplitude, 10-6 m. In this study, both the 1/3-octave and 1/12-octave bands are used in the representation of texture spectrum.
5.1.2 Rolling Tire Vibration
Most of the tire/road noise generation mechanisms result from tire rotation, especially the tire wall vibration. Tire-pavement interaction is the most important source of rolling tire vibration. Tire deformation and its pre-stress status significantly affect its vibration characteristics and therefore, have to be properly reproduced in the modeling of tire/road noise. Modal analysis is one of the most extensively used methods in tire vibration analysis, and the natural frequencies and mode shapes are fundamental descriptions of tire vibration characteristics. Modal analysis and mode superposition technique are adopted in this study to analyze the rolling tire vibration.
5.1.3 Acoustic-Structure Coupling
Tire/road noise phenomenon involves acoustic radiation and scattering by an elastic structure (i.e. the tire) submerged in an infinite fluid medium (i.e. the air). The interaction between tire walls and surrounding air is an important feature in tire/road
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noise modeling. Since the influence of air acoustic pressure on tire wall vibration is negligible and the purpose of the model is for noise prediction, a one-way coupling scheme is adequate for the tire-air interaction. The coupling algorithm transforms the tire vibration velocities or accelerations to the boundary of fluid domain which serve as the radiation source in the acoustic model. This can be realized through the vibro- acoustic transfer vectors (VATV) approach.
5.1.4 Sound Propagation in Free Space
Sound is essentially a sequence of pressure wave propagating in compressible medium, such as air. During propagation, sound waves may be reflected, refracted or attenuated by the medium. The behavior of sound propagation is generally affected by the relationship between density and pressure. The medium viscosity also affects the motion of sound waves and determine the rate at which sound is attenuated. The propagation is also influenced by the motion of the medium itself. Numerical formulations of sound propagation behaviors in the air should be developed to estimate the sound level at a distance from source. Acoustic transfer vector (ATV) concept could be adopted to formulate the relationship between boundary vibration and acoustic pressure field.
5.1.5 Acoustic Absorption of Porous Pavement
Past experimental studies have identified porous pavement as an effective engineering solution to tire/road noise (Bérengier et al ., 1997; Praticò and Anfosso- Lédée, 2012). It reduces noise through its acoustic absorption property. Sound energy dissipates when it propagates through the porous pavement layer, primarily due to viscous and thermal effects resulting from the compression and expansion of the air within the pore structure. Sound absorption depends on the complicated pore structure within porous mixtures and the acoustical properties of its materials (i.e.
aggregates, binders and additives). It is crucial and essential for the tire/road noise
183 numerical modeling to appropriately represent the acoustic absorption of porous pavements.
Four of the critical issues (pavement surface texture, rolling tire vibration, acoustic-structure coupling and sound propagation in free space) have already been studied and included into some dense-graded pavement tire/road noise simulation models by the literature (Brinkmeier and Nackenhorst, 2008; Kropp et al., 2012).
Similar concepts are adopted in this research study. However, the acoustic properties of porous pavements have not been appropriately considered in existing tire/road noise models (Anfosso-Lédée et al., 2007). This research therefore focuses on integrating the acoustic properties of porous pavements into the numerical tire/road noise prediction model to properly evaluate the noise reduction effects on porous pavements. The modeling of acoustic absorption can be approached by either a phenomenological model or a microstructural model, both of which will be discussed in the next section.