PREDICTION OF THE SPLIT IN THE FUNDAMENTAL AIR-CAVITY MODE OF LOADED TIRES IN THE PRESENCE OF ROLLING BASED ON EXPERIMENTAL OBSERVATIONS AND COMPUTATIONAL SIMULATIONS

Tire/road noise can be a dominant source of cabin and pass-by noise for electric vehicles owing to the absence of powertrain noise. To be specific, a tire’s air-cavity mode at around 200 Hz can contribute to vehicle interior noise due to the dynamic forces that mode can generate at the hub, causing a vibration that is transmitted through the suspension to the interior in the low-frequency range between 50 Hz and 300 Hz. In previous studies, it was found that a tire’s fundamental air-cavity mode, typically near 200 Hz for current passenger car tires, splits into two features when the tire is loaded. Since the deformed tire is no longer geometrically symmetric, separate fore-aft and vertical modes appear, the former mode appearing at a slightly lower frequency than the vertical mode. When the tire is loaded, the air channel in the bottom region of the tire is narrowed, hence effectively increasing the inertia in that region, and thus causing the fore-aft mode, which has a relatively large particle velocity in the bottom part of the tire, to have a lower natural frequency than the vertical mode. These modes are important because they can create dynamic force inputs to the suspension system and thus they can contribute to vehicle interior noise at the modal natural frequencies near 200 Hz. 

In the first part, measurements of the dispersion relations for a set of statically loaded tires were initially performed to investigate the range of magnitudes of the acoustical frequency split. Also, finite element analysis of a tire was deployed to model the dispersion in the vicinity of the fundamental air cavity mode between 100 Hz and 300 Hz, which reproduced acoustically both structural and acoustical patterns well in the dispersion relation. Splits ranging from approximately 3 Hz to 11 Hz at the rated load were identified, and it has also been found that the magnitude of the frequency split for a given tire shows a low-order polynomial relationship to the applied load. Moreover, a regression model was developed to predict the split in the fundamental cavity mode for other tires in the range of operation, which showed good agreement with the test results. Finally, dynamic forces occurring at the hub were evaluated quantitatively in simulation to demonstrate the large contribution of coupling between odd-numbered structural modes and the vertical acoustic mode which amplifies the vertical force. 

In the second part, the Tire Pavement Test Apparatus (TPTA) was used to measure force and acceleration at the hub of a rolling tire to obtain experimental observation related to the interaction between the separation in air-cavity mode and the force amplification at the hub. In the measurement, the amplification resulting from the split in air-cavity mode was observed from the hub force and acceleration data for all tested tires between 50 Hz and 300 Hz. Also, the measured data were quantitatively compared with simulation results by activating the gyroscopic effect through steady-state transport analysis, which demonstrated the possibility of estimating dynamic force at the hub numerically. Finally, a design optimization based on geometry and material properties was carried out to see whether it is possible to reduce the amplified force by adjustment of tire properties. Most importantly, the implication between decoupling and force reduction was proposed by comparing waveforms and force spectrum at different speeds. It was concluded that force reduction at the two cavity modes for a rolling tire on the road surface can be accomplished by decoupling each of the split modes with adjacent structural mode by changing speed to shift acoustical modes, followed as a secondary choice by modification of both in material and geometry, thus affecting the natural frequency in tire structure. Finally, a quantitative assessment was conducted for the simulated results, which showed equivalent accuracy in predicting spindle force to the counterpart analysis in the industry. It is beneficial to utilize the simplified model suggested here in terms of convenience in modeling and less computational effort.

In future work, a FE model needs to be elaborated by applying a microscopic model to reflect more realistic parameters such as curvature, thickness variation, and reinforcement with rubber to achieve good accuracy over a wide range of modal frequencies, relating to accuracy in modal behavior in the cross-sectional direction. Moreover, sound radiation analysis is planned to be implemented by using an analytical solution such as Helmholtz’s equation or commercial software (e.g., Actran, Wave6, etc.). To verify near-field sound radiation from the coupled response between tire structure and air-cavity, the OBSI (On Board Sound Intensity) method will also be introduced for the current TPTA equipment to facilitate sound measurement as well as the current, vibration, and force measurement, for instance.