Constitutive rubber model suitable for rolling resistance simulations of truck tyres

Abstract

Tyres are a vital vehicle component forming an interface between a vehicle and the road, enabling the generation of braking, steering and traction forces. However, they also generate rolling resistance which researchers have tried to minimise through the years for environmental and economic reasons. Despite numerous attempts to model rolling resistance of tyres there still does not seem to exist a simple, flexible and accepted way of modelling rolling resistance in the time domain as well as parametrising models in an easy and accessible way. This study explores a simple and intuitive way of parametrising a hyperviscoplastic parallel rheological framework. In the experimental part of this study, rubber samples with various amounts of carbon black filler are extracted from a truck tyre section and tested using dynamic mechanical analysis. The test data was used to parametrise the material model. The model consists of Mooney-Rivlin hyperelasticity, 40 Prony elements and 8 perfectly plastic elements with Ogden hyperelasticity. The paper introduces a method to obtain a large number of parameters using only six tuneable parameters, which simplifies the tuning of the model drastically. The parametrised model is suitable for tyre rolling resistance simulations with frequency and strain amplitude dependency of the storage and loss modulus. A wide range of strain amplitudes and frequencies can be covered with the proposed method and it is possible to achieve a good fit for the storage and loss modulus values with the benefit of only a few tuneable parameters. Additional Prony or plastic networks do not increase the amount of tuneable parameters. Moreover, the method can be used to parametrise the material using manual iterations which is generally not possible for a parallel rheological framework with such a large amount of parameters.