Non-linear elastic ring tyre model using the absolute nodal coordinate formulation

Abstract

In this investigation, a non-linear elastic ring tyre model is developed. The elastic deformation of the tyre belt is modelled using the finite element absolute nodal coordinate formulation that allows for describing large rotational motion and the non-linear inertia effects; the curved structure of the tyre belt; and moving boundary resulting from the tread and road interaction. Using a concept of elastic ring tyre models, the sidewall flexibility of a tyre is modelled using circumferential and radial springs and dampers defined between the belt and rim, while the tangential tyre force is modelled using friction elements defined at contact nodes defined within the curved belt elements. Numerical examples are presented in order to demonstrate the use of the flexible tyre model developed in this investigation. Good agreements are demonstrated in the tyre vibration characteristics obtained using the experiments and the proposed model. It is presented that the proposed tyre model can be used for assessing dynamic characteristics of tyres in high frequency ranges resulting from the interaction to uneven road surfaces.

Finite element modelling of off-road tyres for radial tyre model parameterization

“…A well-known empirical model is the Magic Formula (MF) tyre. The MF tyre requires a large amount of experimental data, but the model generates fast and accurate results once the necessary coefficients have been accurately identified [11,12,13]. The vertical forces in many empirical models are generated by using some form of contact model.…”

“…Rigid belt and flexible belt models, with linear or non-linear spring and damper elements, are typically used in this type of model [11,7]. Some models take tread geometry into account and employ multi-point tyre-terrain contact models.…”

Rigid-flexible coupling modelling and dynamic performance analysis of novel flexible road wheel

“…Another problem is that it is unable to deal with dynamic problems and can't be used for comfort and fatigue load analysis. Structure-based tire models, [21][22][23] which can reflect the structural characteristics of tires, are a popular development trend, but they are only applicable to pneumatic tires. The theoretical basis of these models can be considered as the ring model, that is, the tire is simplified to a ring on the basis of elasticity, the elastic foundation represents the sidewall stiffness, and the ring represents the belt of the tire.…”

Flexible multibody dynamics approach for tire dynamics simulation

“…The constant mass matrix of large deformable bodies not only leads to efficient solutions in nonlinear dynamics simulation, but also allows for the use of the non-incremental solution procedures utilized in general multibody dynamics computer algorithms. Using these important features and general motion description employed in the absolute nodal coordinate formulation, the structural beam and shell elements for modelling the detailed tire structures can be directly integrated into general multibody dynamics computer algorithms without resorting to ad hoc co-simulation procedures, and the flexible tire model based on the absolute nodal coordinate formulation was developed for multibody vehicle dynamics simulation by Sugiyama and Suda [31]. This in-plane tire model was further extended by Yamashita, et al for transient longitudinal tire dynamics simulation by integrating the with LuGre tire friction model that allows for capturing the friction-induced hysteresis for an in-plane longitudinal tire dynamics problem [32].…”

“…To measure the accuracy, error in solution is defined by a deviation of the vertical deflection at the force application point on the plate from that of the reference solution This has a significant impact on the computational efficiency for large scale problems including tire simulation. tire belt deformation can be modeled by an equivalent material model [31,32], such a simplified material model cannot be used for predicting the overall tire structural deformation in the three-dimensional analysis. This is attributed to the fact that the tire section property in both geometry and material is of crucial importance in characterizing the contact pressure distribution.…”