A multi-scale approach on the transient dynamics of rolling tires
|Bearbeitung:||Prof. Dr.-Ing. Udo Nackenhorst, M.Sc. Anuwat suwannachit|
|Förderung durch:||This work is supported by German Ministry for Economics within the “Leiser Straßenverkehr 2” program|
Computational techniques for the prediction of transient dynamic response of tires rolling on rough road surface have been developed since couple of years, see [Proj. MB]. A staggered approach is suggested, where in the first step the nonlinear stationary rolling process is solved within a relative-kinematic ALE-description, for the current state of the art see [Proj. MZ]. Based on this result an eigenvalue-analysis is performed for the prestressed gyroscopic system [Proj. MB]. The operational vibration of tire/road system is computed by a modal superposition technique. In the final step, sound radiation is analyzed by an infinite element approach, which is done in close co-operation with the Technical University of Hamburg-Harburg. During the validation procedure, a special sensitivity of the model chain with respect to the excitation function has been observed. A key question is how deep the tread rubber penetrates into the rough surface in dependency of rolling speed. Therefore, a weekly coupled two-scale approach is introduced. The overall procedure is sketched in figure 1.
Figure 1: Schematic sketch on the overall simulation procedure
The tire/road contact is approximated by a representative part of the tread rubber discretized with fine spatial resolution such that the road roughness is resolved in a suitable manner. This model is loaded with the pressure distribution obtained from the stationary rolling approach in a cyclic manner, such that a transient dynamic rolling process is simulated. A Newmark-type schema is introduced for the transient dynamic analysis.
Figure 2: Tire model and tread rubberstrip in contact with road surface
Figure 3: Time dependent loading with computed contact pressure distribution
The material properties of the tread rubber are described by a nonlinear constitutive model including damage and viscoelastic effects within a large deformation framework. A good agreement between the simulation and experimental results from a uniaxial tension test is shown in figure 4. Moreover, the dynamic stiffening at moderate frequencies can also be predicted, as seen from the comparison between the blue and red dot line (average stiffness) at each operational point in figure 5. The blue curve represents large loading cycle under very low excitation frequency and the red cycles correspond to the hysteresis curves at different static working points under harmonic excitation.
Figure 4: Quasi-static uniaxial tension test (carbon black-filled rubber)
Figure 5: Dynamic stiffening
An enveloping surface profile, which is the trace of the deepest penetration occurred, is computed and consequently reconstructed to be used for the excitation of the modal tire model. In figure 6, the original contact surface topology is compared with the computed envelopes corresponding to different rolling speeds. A particular filter function has to be determined in order to obtain the envelopes of the entire road surface. A good agreement between the envelopes computed by dynamic problem and that by using the filter function is shown in figure 7.
Figure 6: Computed envelopes in dependency of the rolling speed
Figure 7: Original contact surface, computed envelope and envelope determined by using a filter function
However, under high frequency excitation the technical rubber used in tire industry is usually characterized by complex modulus, as well as damping. More sophisticated material models have to be derived when a broad frequency range is considered and new tests have to be designed to adjust the constitutive parameters, see [Proj. AS].