Towards Virtual NVH Performance Assessment of Tires: Prediction of Dynamic Tire/Road Contact and Hub Forces Using a Fully Predictive Efficient Simulation Approach

Since it is reported that environmental noise has negative effects on the public health in the European Union, the European Commission has set a road traffic noise reduction target of 10 dB(A) by 2020. As a result, vehicle manufacturers are continuously working towards refining their car designs to help reduce traffic noise. Tire/road noise is an important contributor to the overall road traffic noise and can be divided into two categories: exterior noise and interior noise. While exterior tire/road noise is mainly perceived by bystanders, interior tire/road noise is mainly perceived by the driver and passengers of a car.

In order to meet both the governmental and industry demands, tire manufacturers therefore strive to reduce both the exterior and interior tire/road noise. However, over 50 different performance criteria have to be taken into account when optimizing a passenger car tire. Due to the complex structure of a typical passenger car tire, most of these criteria are coupled: trying to enhance one performance by means of changing some design parameters may affect other performances. As a result, design engineers have to balance multiple performances simultaneously in a single design. An experimental approach is typically used during the tire design process to assess the different performances of a specific tire design. Several tire design prototypes, which represent different sets of design parameters, are built and tested. This approach has drawbacks in terms of costs of running the experiments, as well as the material costs, labor costs and the time needed to build and test several prototype tires. In order to cope with the increasing need to optimize multiple tire performances simultaneously, as well as shorter product development times, predictive numerical simulation techniques could be used, rather than timeconsuming experiments.

This work therefore proposes a fully predictive and efficient numerical methodology to assess the interior tire/road noise performance of a tire. More specifically, the dynamic tire/road contact- and hub forces arising from constant speed rolling over a coarse road surface are calculated and the frequency spectrum of the vertical hub force is used to determine the Noise, Vibration and Harshness (NVH) performance of a tire in the 0–400Hz frequency range. The NVH performance is used as an indicator for the interior noise performance of the tire. The proposed methodology consists of the following contributions to the state-of-the-art:

- Extension and description of Arbitrary Lagrangian Eulerian (ALE) formulation-based nonlinear structural Finite Element (FE) tire models to fully coupled nonlinear vibro-acoustic ALE FE tire models, including the use of the convected Helmholtz equation for the acoustic air cavity dynamics and a structural FE flexible rim model
- A constraint-based contact mechanics approach exploiting the ALE framework to model the rolling tire/coarse road interaction
- Application of nonlinear Model Order Reduction (MOR) to nonlinear vibro-acoustic ALE FE tire models, using an a priori calculated nonlinear modal reduction basis
- Application and extension of the a priori Multi-Expansion Modal (MEM) hyper-reduction method to the vibro-acoustic nonlinear ALE FE tire models

Comparing the experimental and numerical lead times, the proposed methodology is on average, without optimization of the software implementation, ten times faster than the experimental approach, i.e. hours/days instead of weeks. Two case studies are considered in this work to validate and showcase the potential of the proposed methodology. As a first case study, the effect of changing the inflation pressure on the vertical hub force spectrum of a tire design is investigated. As a second case study, four different tire designs are built and tested. The designs are ranked based on their NVH performance, using the vertical hub force frequency spectra. For both case studies, a good correspondence between experimental and numerical results can be observed. Using the numerical results, the same objective design decisions can be made as when using the experimental results, showcasing the potential use of the proposed methodology.

Given thus the shorter lead times and the good correspondence between experimental and numerical data, the proposed methodology could therefore be considered as a more time- and cost-efficient alternative than the current experimental approaches. Furthermore, the proposed methodology could be a starting point for a fully predictive and efficient holistic virtual tire design performance optimization methodology, allowing to simultaneously optimize multiple/all performances and to more efficiently explore a larger design space.