Finite Element Modelling of Off-Road Tyres

Abstract

Most tyre models developed to date require a fair amount of data before an accurate representation of the tyre can be obtained. This study entails the development of a simplified, yet accurate, non-linear Finite Element (FE) model of an “off-road” tyre to study the behaviour of the tyre due to radial loading conditions. The study aims to develop a FE tyre model that can solve fast and be accurate enough to be used in multibody dynamic vehicle simulations. A model that is less complex than conventional detailed FE models is developed. The work explores the use of superimposed finite elements to model the varying stiffness in the respective orthogonal directions of the sidewall and tread of the tyre. Non-linear elements defined by Neo-Hookean or Ogden models and elements with different linear orthogonal stiffnesses are superimposed onto each other to simulate the global material properties of the tread and the sidewall of the tyre investigated. The geometry of the tyre studied was measured experimentally using laser displacement transducers and digital image correlation techniques. Material properties of segments of the tyre were obtained by performing tensile tests on samples. Since the rubber slipped against the clamps during the experiment, deformation of the segments was also measured using digital image correlation. These geometrical and material properties were used as input to develop a finite element model of an “off-road” tyre. Measurements were conducted using laser displacement transducers, load cells mounted to actuators, etc. to obtain accurate sidewall deformation profiles and global radial load vs. displacement curves for different radial loading conditions. The data obtained from the results was used to validate the tyre model developed. Numerous analyses are performed with different combinations of moduli of elasticity in the respective orthogonal directions of the sidewall stiffness and the tread to investigate its influence on the global behaviour of the tyre model. The main focus of the project was to develop a tyre model from data obtained from laser and photogrammetry measurements in a laboratory that accurately represents tyre behaviour due to radial forces. A finite element model that can simulate the effect of radial forced and obstacles on a tyre was developed. The use of two subsets of elements, superimposed onto each other to simulate global material properties of the rubbers, steel wires, polyester and nylon threads, was investigated. The combination of material properties that gave the best fit for all the load cases investigated were determined. The finite element model correlated well with the load vs. displacement graphs and sidewall displacement profiles determined experimentally. The solving time is still fairly high and is still not quite suitable for real-time dynamic simulation. However, it solves faster than more complex tyre models where details of steel wires, etc. are included in the model. For future studies it is recommended that different element types be investigated in the tyre model. The study proves that equivalent material properties can be used to simulate the composite properties of the materials in tyres. Most tyres can be divided into a few regions that each has its own material structure right through the region. These regions can be characterized by simple tests and the input can be used as a first estimation of the tyre’s material properties for the model. Accurate validation criteria should be used to validate the tyre model if time does not allow for excessive testing of the material properties of all the rubber, steel wires, polyester threads, etc. Geometric displacement data at various loading conditions can be used for validation of the tyre model. The model developed can be used to investigate the effect of different stiffnesses and other material changes in the sidewall or tread of a tyre. Useful insight can be obtained from the finite element model developed for dynamic simulation where the force vs. global displacement data is important.