Computational techniques on the stochastic excitation of rolling tires from the rough road surface contact
Final Report Abstract
The project set out with the goal of refining the modal tire vibration finite element model of Brinkmeier (2007) in three distinct ways: by accounting for the mesoscale interaction of the tread rubber with the rough surface, by parametrizating the rough surface textures by relevant road surface characteristics and by incorporating viscoelastic effects within the linearized modal dynamics model. In regard of the mesoscale submodel, a parametrization of the random process representing the surface was thus developed which separates the influence of the inherent randomness of surface heights from the variation of the parameters governing the surface characteristics. It was found that this, together with an ergodic assumption allows for the use of a single realization of white noise input to the surface generation process which is kept constant throughout the entire parametric computation, thus eliminating the randomness from the problem. This surface description serves as an input to a pressure-dependent enveloping process simulation in the offline stage. Due to this description, a response surface of the envelope in the parameters can be obtained by using an adaptive and perhaps multi-level collocation approach such as the one suggested in Gates and Bittens (2015). During the further course of the project, the viscoelastic macroscale tire problem was resolved by applying the method for spinning structures outlined in Potter (2013), which takes the inelastic metric as a fundamental unknown, to a real threedimensional tire model in both the steady-state and linearized dynamics. At this stage in the project, it became apparent that a modal truncation approach as suggested in Brinkmeier (2007) is not well-suited to the viscoelastic problem due to the large number of decay modes within the relevant frequency range. We circumvented this problem by using the Fourier collocation method in obtaining periodic solutions to the linearized dynamics problem. Given a set of loading frequencies from the mesoscale model, the frequency response functions governing the linearized macroscale dynamics can be computed about a steady-state problem in the offline stage. In the online stage, the mesoscale envelope and the macroscale frequency response are combined to obtain a parametric on-line model.
Publications
-
MIASC: An adaptive approach to uncertainty quantification in discretized problems of reduced regularity. Part 1: Illustration of the method, ECCOMAS Congress 2016, Crete Island, Greece
Robert L. Gates, Maximilian R. Bittens, Udo Nackenhorst
-
MIASC: An adaptive approach to uncertainty quantification in discretized problems of reduced regularity. Part 2: Applications in bone remodeling and rough surface contact, ECCOMAS Congress 2016, Crete Island, Greece
Maximilian R. Bittens, Robert L. Gates, Udo Nackenhorst
-
Rough surface contact: improved efficiency and robustness through the incorporation of multi-freedom constraints, ICCCM 2017, Lecce, Italy
Robert L. Gates, Udo Nackenhorst
