# A Fast Approach to Optimize Trad Pattern Shape for Tire Noise Reduction
## Results and Conclusions
### The Validation of the Tire Noise Prediction Method  
In this research, to calculate the tire noise accurately, the footprint profile was calculated using FE software ABAQUS 6.14. The simplified tread pattern was modeled, which has sufficient accuracy in analyzing the tire's steady state [43]. The tire reinforcement was modeled by the rebar layer, the rubber material was modeled as incompressible hyperelasticity, and the Yeoh constitutive model was used in this simulation. The tire three-dimensional model was generated with symmetrical model generation technology, and the load and inflation pressure are consistent with those of the noise test. Figure 7b shows the footprint profile of a 225/60 R18 tire at a speed of 60 km/h. In this study, the leading edge of the footprint profile was used. We assume that each pattern element produces a unit pulse, resulting in a weight function that remains constant along the tread meridian direction. Thus, the \(\gamma\) can be simplified to 1.0. The excitation force was obtained by moving the leading edge along the tread pattern, resulting in a total of 2048 data points. The predicted and measured 1/3-octave sound pressure levels (dB(A)) are shown in Figure 8.  
It is clear from Figure 8 that the predicted result is in good agreement with the measured noise for frequencies over 800 Hz. In this range, the tire/road noise is primarily determined by the local deformations occurring at the leading and trailing edges of the tire's footprint; these local deformations arise due to the impact of tread blocks during tire rotation. In contrast to the urban road traffic noise experiment [44], and to further validate the correlation between the experiment results and our prediction of external noise, our study followed the pass-by noise testing process outlined in ECE R117 [45]. During this test, the vehicle was driven along a designated test track following the centerline denoted as C-C in Figure 9, and two target microphones were placed on both sides of the track to measure the noise levels. These microphones were placed in the middle of the track 7.5 m away from the vehicle's centerline at a height of 1.2 m. Subsequently, the maximum sound pressure level was recorded while the test vehicle was coasting. To obtain the final result for a reference speed, we conducted a linear regression analysis. If the discrepancy between the measurements from the left and right microphones exceeded 1 dB (a), the test result was deemed invalid and necessitated retesting. Finally, the sound pressure level (dB(A)) at a velocity of 80 km/h was calculated. Figure 6: Measured 1/3-octave-band sound pressure levels at various velocities. Four different trend patterns, denoted as A, B, C, and D, were selected for the experiment, while the tire size and structural design of 205/60 R16 were kept the same. Figure 7c shows the contact patch at a speed of 80 km/h. The evaluation results of the pass-by noise experiment are presented in Figure 10 where the predicted results are compared with the measured results. In this analysis, the predicted results were calculated using the 1/3-octave dB(A) range from 800-2000 Hz, which specifically covers the pattern impact  
Figure 8: Comparison of predicted and measured 1/3-octave sound pressure (dB(A)) at a velocity of 60 km/h. Figure 7: Simulation results of tire footprint profile. (**a**) Process of calculating excitation force of pattern; (**b**) footprint of 225/60 R18 at a velocity of 60 km/h on drum; (**c**) footprint of 205/60 R16 at a velocity of 80 km/h on a flat surface. noise range. The predicted values agree well with the test noise in terms of overall trends. This level of agreement is highly advantageous, as it facilitates the initial evaluation of pattern design. While the specific values may not match perfectly, this is mainly due to the test results of the pass-by noise experiment being influenced by environmental factors [46], road conditions, and the motion state of vehicles [47].