Transient Analysis of Tyre Friction Generation Using a Brush Model with Interconnected Viscoelastic Bristles

Abstract

DOI: 10.1243/146441905X9908Abstract: An analysis of the mechanism of tyre contact force generation under transient conditions is presented. For this purpose, two different versions of a brush model are used, both with inertial and viscoelastic properties. The first model consists of independent bristles, while the second, with a more realistic scenario, introduces viscoelastic circumferential connections between the sequential bristles, which affect the lateral degrees of freedom. Friction between the tyre and the ground follows an experimentally verified stick -slip law. For the model with independent bristles, the state of each bristle at any instant of time depends only on the state of the same bristle at a previous time step. In the second model, the instantaneous state depends on the state of the same bristle at the preceding time step, as well as on the state of the two adjacent bristles at the same time. Simulation results reveal the differences between the two models and most importantly show how transient friction force generation may differ substantially from steady state predictions. The findings suggest that transient tyre behaviour should not be attributed solely to the contributions of the flexible belt and carcass. On the contrary, the observed transience in the neighbourhood of the contact patch should also be taken into account.

The simulation of in-plane tyre modal behaviour: a broad modal range comparison between analytical and discretised modelling approaches

“…In many cases, the vertical load distribution is assumed to be an analytical function of the position along the contact, with the parabola being the favourable choice for simple analysis [2]. In an effort to improve accuracy, simplified physical contact models are used to capture the changes in the size of the contact and the associated vertical distribution, as shown in [18].…”

“…Stick-slip friction, common in tyre-road interaction [18,23], as well as other non-linearities, theoretically impose a rather broad-band excitation. In practice, such a wide frequency range is not present in the actual carcass response, due to energy dissipation reasons, but this cannot the only basis upon which a frequency cut-off limit is decided for a tyre model aiming to simulate modal/shear-force interactions.…”

“…This combined simulation approach is found in the commercially available FTire model [21], or the advanced contact representation described in [39] and [38]. The requirement for the accurate capture of the contact behaviour and friction-related phenomena, such as stick-slip, has led to the separate treatment of the contact using finer discretization levels than those required for modal representation ( [18]). …”

A Modal-Based Derivation of Transient Pressure Distribution Along the Tyre-Road Contact

“…For computational efficiency reasons, though, the contact pressure field is not usually calculated as part of the computation algorithm but artificially superimposed as an input to the friction calculation sub-model ( [17], SWIFT model described 1 in [18]). Analytical parabolic/trapezoidal shaped vertical pressure distribution is the common assumption along the contact length when the friction potential has to be calculated, as in [19]. This approach is believed to moderate the transient validity and potential of the model, in comparison to studies where the contact pressure field is incorporated in the simulation process [20].…”

“…The nature of the developed algorithm and the qualitative conclusions on the acceptable reduction level enable the future transformation of the modelling approach into a physical shear force generation simulation tool with acceptable computational demands. The present state of the research may offer guidelines for the application of modal expansion/reduction method in various tyre models, the transient nature of which imposes the real time calculation of the contact interaction stresses [8,19]. The huge computational load of such discretized approaches can be significantly reduced without major sacrifice of the prediction accuracy.…”