Steady State Rolling and Dynamic Response of a Tire at Low Frequency

Authors: Md Monir Hossain, Anne Staples, Kuya Takami, Tomonari Furukawa

Abstract:

Tire noise has a significant impact on ride quality and vehicle interior comfort, even at low frequency. Reduction of tire noise is especially important due to strict state and federal environmental regulations. The primary sources of tire noise are the low frequency structure-borne noise and the noise that originates from the release of trapped air between the tire tread and road surface during each revolution of the tire. The frequency response of the tire changes at low and high frequency. At low frequency, the tension and bending moment become dominant, while the internal structure and local deformation become dominant at higher frequencies. Here, we analyze tire response in terms of deformation and rolling velocity at low revolution frequency. An Abaqus FEA finite element model is used to calculate the static and dynamic response of a rolling tire under different rolling conditions. The natural frequencies and mode shapes of a deformed tire are calculated with the FEA package where the subspace-based steady state dynamic analysis calculates dynamic response of tire subjected to harmonic excitation. The analysis was conducted on the dynamic response at the road (contact point of tire and road surface) and side nodes of a static and rolling tire when the tire was excited with 200 N vertical load for a frequency ranging from 20 to 200 Hz. The results show that frequency has little effect on tire deformation up to 80 Hz. But between 80 and 200 Hz, the radial and lateral components of displacement of the road and side nodes exhibited significant oscillation. For the static analysis, the fluctuation was sharp and frequent and decreased with frequency. In contrast, the fluctuation was periodic in nature for the dynamic response of the rolling tire. In addition to the dynamic analysis, a steady state rolling analysis was also performed on the tire traveling at ground velocity with a constant angular motion. The purpose of the computation was to demonstrate the effect of rotating motion on deformation and rolling velocity with respect to a fixed Newtonian reference point. The analysis showed a significant variation in deformation and rolling velocity due to centrifugal and Coriolis acceleration with respect to a fixed Newtonian point on ground.

Keywords: Natural frequency, rotational motion, steady state rolling, subspace-based steady state dynamic analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316389

References:

[1] K. Iwao and I. Yamazaki, “A study on the mechanism of tire/road noise,” J. SAE Review 17 , vol. 2, 1996, pp.139–144.
[2] S. Kim, W. Jeong, Y. Park and S. Lee, “Prediction method for tire air-pumping noise using a hybrid technique,” J. Acoustical Society of America 119, vol. 6, 2006, pp. 3799–3812.
[3] U. Sandberg and J. Ejsmont, Tyre/Road Noise Reference Book. Kisa, Sweden, 2002.
[4] K. Larsson and W. Kropp, “A high-frequency three-dimensional tyre model based on two coupled elastic layers,” J. Sound and vibration, 2002, pp. 889–908.
[5] W. Kropp, K. Larsson, F. Wullens, P. Andersson, F. Becot and T. Beckenbauer, “The modeling of tire/road noise–a quasi three dimensional model,” in Proc. Inter–noise, Hague, Netherlands, 2001.
[6] M. Matsubara, D. Tajiri, T. Ise and S. Kawamura, “Vibrational response analysis of tires using a three-dimensional flexible ring-based model,” J. of Sound and Vibration 408, 2017, pp.368-382.
[7] W. Kropp, “Structure-borne sound on a smooth tyre,” J. Applied Acoustics 26, vol. 3, 1989, pp. 181-192.
[8] R. Lehoucq, D. Sorensen and C. Yang, Arpack users guide: solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods, SIAM, 1998.
[9] C. Diaz, P. Kindt, J. Middelberg, S. Vercammen, C. Thiry, R. Close and J. Leyssens, “Dynamic behaviour of a rolling tyre: Experimental and numerical analyses,” J. Sound and Vibration 364, 2016, pp.147-164.
[10] Z. Bai, J. Demmel, J. Dongarra, A. Ruhe and H. Vorst, Templates for the solution of algebraic eigenvalue problems: a practical guide. Philadelphia:SIAM, 2000.
[11] U. Nackenhorst, “The ALE-formulation of bodies in rolling contacttheoretical foundations and finite element approach, Computer Methods,”J. Applied Mechanics and Engineering, 2004, pp. 4299-4322.
[12] Y. J. Kim and J. S. Bolton, “Effects of rotation on the dynamics of a circular cylindrical shell with applications to tire vibration, ” J. Sound and vibration 275, 2003, pp. 605-621.
[13] Abaqus, Abaqus Documentation, Dassault Systmes, RI, USA, 2016.