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Simulation environment for sensor-enhanced tires - SENSE

Subject Area Applied Mechanics, Statics and Dynamics
Polymer Materials
Term from 2018 to 2022
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 392015269
 
Final Report Year 2024

Final Report Abstract

Simulation approaches for the tire manufacturing process as well as for tire force estimation in sensor enhanced tires have been developed in the course of this Sino-German joint research project. At THU, an intelligent tire system prototype was developed to measure accelerations and consequently estimate forces acting on the tire in different directions. A MEMS accelerometer was used as a sensor, which is convenient for installation, reliable and robust enough to withstand the hard environment inside the tire. Moreover, a universal force estimation scheme has been established depending on tire rolling kinematics and using a mixed Lagrangian-Eulerian formulation. The vertical force is approximated based on an analytical model, while the lateral force is estimated based on the tire beam model. Though the longitudinal tire force estimation still needs further research, the feasibility and robustness of the proposed schemes are tested and validated at different conditions. The work at the ISD focused on simulating the manufacturing process of tires. As a first step to achieve this goal, a material model was developed, which can describe rubber materials in its green form (before vulcanization) and in its cured form (after vulcanization), as well as during the vulcanization process itself. In this model, the degree of vulcanization of rubber is characterized by an evolution law depending on the temperature and the curing time. A simple coupling between the vulcanization process and the mechanical response has been proposed, where the green rubber model already contains the cured rubber model. Green rubber is considered as a visco-hyperelastic material, while the cured rubber as a hyperelastic material. The transformation from green to cured rubber occurs through an inelastic evolution law, in analogy to viscoplastic models. The increase of the degree of vulcanization gradually deactivates a viscous dashpot until the material becomes purely hyperelastic. The second step to achieve reliable tire manufacturing simulations was the development of a finite element model to characterize polymeric tire cords and to simulate the changes in tire dimensions during the Post Cure Inflation (PCI) process. A finite strain rebar element is formulated to include the 1D cord material into 3D tire simulations. A material model to describe thermally induced shrinkage strains is developed, where a temperature, stress and time dependent evolution law is proposed. The law also distinguishes between recoverable and unrecoverable shrinkage, which is important for Nylon 66 cords. Furthermore, mechanical creep is considered using a viscoelastic rheological model and the temperature effect on elastic constants is considered using a thermal dependency function. The stiffness reduction and recovery observed due to shrinkage and creep processes are also accounted for by a stiffness variation variable. The proposed polymeric cord material model is compared to experiments conducted for Nylon 66 and PET cords. Shrinkage under several stress levels, shrinkage force and tensile tests are simulated with good agreement to experimental results. It is also found that including thermal shrinkage in cord material models can reproduce the difference in tire dimensions observed between PCI and no-PCI tires. Another key achievement in this project is the development of a rigorous arbitrary Lagrangian-Eulerian framework for thermomechanical simulations of viscoplastic problems. An ALE scheme based on tracking both the material and the spatial configurations has been used, which proved to provide a more appropriate way to incorporate rubber hyperelasticity and multiplicative finite strain inelasticity, with no remapping required for the elastic variables. In addition, the operator split of the ALE solution into smoothing, advection and Lagrangian steps leads to an efficient simulation with minimal increase in computational time, as well as it allows the straightforward incorporation of already available Lagrangian elements. The smoothing step is based on solving a fictitious hyperelasticity problem to optimize both the material and spatial meshes. This avoids the need of geometric rezoning procedures, which become complex in 3D applications. One more benefit of tracking the material mesh is that it can be used to remap the history variables by an implicit particle tracking scheme, which does not depend on the number of history variables or requires the evaluation of spatial gradients of these variables. A new IGA framework to model rolling tires is also introduced using closed unclamped B-splines in order to achieve a fully continuous representation of geometry and field variables. The high order continuity allows a straightforward evaluation of accelerations in a local coordinate system. Radial, circumferential and lateral accelerations obtained by the IGA scheme are compared to the experimental data and can be employed to calibrate and improve the analytical models propped by THU. The algorithms, codes and techniques achieved in this project have two main potential areas of application. The first area is vehicle embedded software, where real-time tire forces monitoring can be deployed based on the schemes proposed by THU. The second area of application is the optimization of tire design and manufacturing using the FE simulation tools developed at ISD. Collaboration with industrial partners to transfer the knowledge is already on the agenda as the next focus of future research work.

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