Thirumal Alagu Palanichamy, doctoral researcher at IBNM, Leibniz Universität Hannover, explains how the University, in collaboration with Continental Tyres, has found a way to accurately simulate tire tread deformation with less computational power, thanks to the Arbitrary Lagrangian Eulerian steady-state relative kinematic framework.
Please tell us about the newly developed approach to tread pattern simulation.
This research has been undertaken using the expertise available at the Institute of Mechanics & Computational Mechanics (IBNM) at Leibniz Universität Hannover, as part of a collaboration with Continental Tyres. The goal of the project is to develop an efficient method for the simulation of tires with a detailed tread pattern. A fully Lagrangian framework can be used, however this takes a huge amount of time due to the overall fine model description, and it takes many revolutions to reach a steady state.
The Arbitrary Lagrangian Eulerian (ALE) steady-state relative kinematic framework is the most widely used in rolling tire/road contact simulation. To give an insight into this framework, consider that the tire is fixed. With a sophisticated mapping technique, the tire is rotated. The advantage of this is that the tire mesh is not rotated in an authentic way, which creates a stationary footprint of the tire mesh. This means that local mesh refinement only at the contact region and the rest of the model is defined coarsely, which is computationally more efficient. Another advantage is the direct steady state due to time independent formulation. The major limitation of an ALE relative kinematic framework is that it cannot be applied to tires with a detailed tread pattern.
We have developed an efficient approach coupling ALE with a Lagrangian kinematic framework.
How have you developed the coupling of the tread pattern with the tire base structure using kinematic constraints?
The tire structure is decomposed into body and tread pattern, so that the body is axisymmetric and can be combined within the ALE kinematic framework, and the tread pattern is defined in the Lagrangian framework. The numerical gluing is done using the kinematic constraints, which state that there is no relative movement between the material points in the tread pattern and to the corresponding projection points in the ALE body.
The projected points in the ALE body are now rotating with angular velocity and due to the constraints, the tread pattern will follow these points. Thus, the necessary displacement and velocity continuity at the interface is established, along with the transfer of forces between them (two-way coupling). To maximise the advantages of this framework, adaptive mesh refinement or adaptive coupling of the tread pattern can be carried out. Adaptive coupling means the switching on and off of the kinematic constraints near the contact region and away from the contact region.
What have been the key challenges and how have you overcome these?
The challenge arises in the gluing step due to the geometric incompatibility. The lateral varying cross-section in the tire and the discretisation with lower order elements leads to penetration of the tread pattern with the ALE body in the initial configuration. This would result in an initial error in the gluing step. The problem could be tackled by defining the interface with higher order elements, which would reduce the error in an acceptable range. Another challenge is the implementation of adaptive coupling in the tread pattern. This is something we are currently working on.
What’s next for this research?
The next step is to include viscous heating of the rubber. To do so, the thermal interactions have to be coupled between the ALE body and tread, which is similar to the mechanical problem. We also need to perform numerical validation of this framework and compare the benefits with present methods. Another promising area of research is adaptive mesh refinement of the tread pattern, which enables accurate extraction of the contact forces.
This interview originally appeared in the November 2018 issue of Tire Technology International.
Thirumal Alagu Palanichamy will give a presentation titled An efficient approach for the simulation of tires with detailed tread pattern at the Tire Technology Expo Conference. Click here to book your delegate pass.