Analytical Model of Tire Cavity Resonance and Coupled Tire/Cavity Modal Model

Abstract The acoustic resonance of the air cavity in the tire/wheel assembly may be a contributor to vehicle interior noise through the structure-borne noise transmission path. This problem has been examined in the past using approximate closed form solutions (based on plane wave theory for a two-tube model) and numerically, using FEA. The coupling between the cavity resonance and structural resonance of the wheel may result in higher levels of interior noise as noted previously. The two primary goals of this paper are (1) to develop simple analytical models to gain fundamental understanding of some observed phenomena and for a quick estimation of cavity resonance frequency to assist in the design process, and (2) to develop tire modal models incorporating the acoustic cavity to predict coupled system natural frequencies and response. An improved analytical model for accurate calculation of acoustic cavity resonance frequencies of a static, unloaded tire is developed using variational principles. The sensitivities of the cavity resonance frequencies to tire width and aspect ratio are examined. For the case of a loaded tire, an improved analytical formulation based on plane wave propagation (for linearly varying cross-sectional area) is developed. Deformed structure geometry from FEA is used as input to the analytical model. The FEA-based methodology used in the tire/cavity coupling analysis is as follows: The tire structural modes are calculated, ignoring the effect of the acoustic cavity. The tire cavity modes are calculated using deformed cavity geometry only. Next, the structural/acoustic coupling matrix is calculated. Finally, a coupled cavity-structure modal model is generated from modal mass and stiffness of the tire/wheel assembly, the cavity modal matrices, and the coupling matrix. This process is an improvement over conventional tire modal models, which only include structural modes.