Friction and camber influences on the static stiffness properties of a racing tyre

Abstract

Investigation of the stationary load-deflection behaviour of tyres reveals many details of the structure and the rubber to road friction properties. These characteristics are fundamental to the understanding of the behaviour of both the stationary and the rolling tyre. In connection with racing, tyre static stiffness characteristics are of interest as they reflect on the controllability of the vehicle to which they are fitted.In this paper, the construction of a finite element model capable of predicting the static tyre behaviour in great detail is presented. The model is validated against extensive experimental data, including contact pressure distributions and load-deflection characteristics. Static loading tests which involve variations in wheel camber angle and in the friction rules coupling tread rubber with the ground surface, are simulated with the tyre model. The results of the simulations reveal that a friction coefficient of 0.5 is sufficient to prevent sliding in static loading tests for this particular tyre. Lower levels of friction lead to tread sliding and reduced vertical tyre stiffness.Sliding is primarily lateral, leading to narrowing of the contact patch of the tyre. Narrowing also increases the local sidewall curvature which is part of the softening mechanism for both upright and cambered tyres. IntroductionTyre behaviour on a running car depends on carcass stiffness and rubber to road friction properties with complex interactions between them. In general terms, the small-effort behaviour primarily involves adhesion between tread rubber and ground surface and is dominated by carcass stiffness attributes, while the large-effort or near-limit behaviour has sliding of rubber relative to ground at its core. In the latter case, the behaviour is ruled by rubber to road friction forces. In racing, the main concern is with limit-behaviour but nevertheless, the small-effort demeanour is of interest, since it reflects on the controllability of the concerned vehicle.Many structural details of a tyre can be revealed by static load-deflection testing, in which the non-spinning tyre is loaded against a flat surface and detailed observations of deformations and stresses are made. If this kind of test is done in reality, many of the measurements needed are intricate and difficult but if the testing is virtual, no such difficulties arise. They are replaced by the need to develop a virtual tyre, the results from which can be taken to represent the real item.

Normal and shear forces in the contact patch of a braked racing tyre. Part 2: development of a physical tyre model

“…Based on the results from the previously-described experimental investigations [2] and the FE simulations presented in the first of this pair of papers [1], the widths of the non-contacting regions (or grooves) can be assumed to stay constant over the investigated operating range. As a consequence, the inner contacting regions (ribs 2 to 4) are considered to have a fixed width.…”

“…where: F z : vertical tyre load m AREA : coefficient which describes the slope of the load-contact area relationship constant term: accounts for initial nonlinearity at low vertical loads [2] …”

“…The contact stresses at the interface of a braked racing tyre with the ground surface have been studied in Part 1 of this article [1] with a previously-described and validated finite-element (FE) model [2]. Detailed investigation of the deflection behaviour of the rolling tyre provided novel insights into the interrelationship between the reinforcement layers (i.e., carcass) and the shear stress distribution within the contact patch.…”

Normal and shear forces in the contact patch of a braked racing tyre. Part 1: results from a finite-element model

“…As a result, local mesh refinement in the area of interest, i.e. the contact zone, is possible and the mesh of the virtual tyre model of the previous work [1] can be used here.…”

“…Using the finite element (FE) method, the construction of such a model was the subject of previous research. The created and validated full three-dimensional FE model is described in detail in [1]. In line with current research in the field of tyre simulations (e.g., [2,3]), this virtual tyre is developed further for the work here, which involves numerical tests of a braked tyre at different vertical loads, wheel camber angles and longitudinal slip ratios.…”