From road excitation to spindle forces in frequency domain: Linearization of the rolling tire

The tire plays a fundamental role in the generation of acoustically perceptible driving noise and vibrations inside the vehicle. An essential part of these vibrations is induced by the road excitation and transferred via the tire into the vehicle. There are two basic ways to study NVH behavior: Simulations in time and frequency domains. The system can be simulated using a transient simulation method with the disadvantage of high simulation and process turnaround times. Alternatively, a linearization around a stationary state is performed and solved in frequency domain with fast numerical schemes. Modelling the tire transfer behavior in frequency domain requires special attention to the rotation of the tire. This paper shows the approach taken by the authors to include the transfer behavior in the frequency range up to 250 Hz from geometric road excitations to resulting spindle forces in frequency domain. Special care has been used in the modelling of local road excitations. The road surface travels through the contact area, contact points on the same line of travel will experience the same road excitation, but with a time delay. This paper validates the derived NVH tire model by comparison with appropriate transient simulations of the base transient model.