Finite Element and Mesh-Free Simulation Environment for the Molding and Vulcanization of Rubber in Industrial Tire Production

在过去的几年里（2018-2021年），在研究项目SENSE中对轴对称汽车轮胎的成型和硫化过程的数值表示进行了深入的基础研究。在该项目中，申请人结构分析研究所（ISD）的Michael Kaliske教授开发了基于有限元法（FEM）的热机械轮胎成型模拟环境，重点是模拟从未硫化到最终硫化的轴对称轮胎的过程。基于有限元（FE）的模拟方法使用任意拉格朗日欧拉（ALE）描述来在绿色轮胎的模制期间跟踪材料点，以获得模制过程的表示（避免网格变形）。此外，已经开发了几种先进的热机械耦合材料模型来描述橡胶在其固化和未固化状态。然而，任意胎面花纹的模制仍然具有挑战性，这是由于在模制过程期间未固化橡胶的复杂几何形状、摩擦和材料流动（关于真实3D轮胎设计的数值稳定性和鲁棒性的问题）。这些开放的研究问题将是ISD和工业项目合作伙伴Continental Reifen Deutschland GmbH之间的转移项目的进一步发展步骤。该转移项目旨在联合收割机的基础学术研究和新产品的创新实现程序的优势，在不断变化的工业环境受到全过程链数字化。因此，该转让项目不仅将在SENSE项目内开发的模拟环境带入工业应用，（未硫化和硫化橡胶的材料模型，橡胶成型的ALE方法，工业专门知识交流）而且还将进一步促进用于具有任意胎面花纹的轮胎从其制造状态到其使用的高级数值描述和表示的数值方法的发展另一种数值方法是材料点法（MPM）。转移项目的其他新的研究方面解决了隐式MPM作为任意胎面花纹轮胎成型的无网格方法的开发和应用（胎面MPM模拟）在3D中，MPM在热力学框架中的公式化，耦合有限元法（轮胎主体）与MPM用于成型和硫化过程中的分析（制造阶段），以及提出FEM、MPM或ALE的材料行为的实现的策略，包括当前材料状态（非弹性、非线性）的描述。主要目标是开发一个强大的和数值稳定的模拟环境的成型和硫化轮胎的三维胎面花纹。

In the last years (2018-2021), intensive fundamental research on the numerical representation of the molding and the vulcanization process of axisymmetric, automotive tires has been carried out in the research project SENSE. Within this project, a thermo-mechanical tire molding simulation environment by the finite element method (FEM) focusing on the simulation of the process from the uncured to the final cured axisymmetric tire has been developed by the applicant Prof. Michael Kaliske at the Institute for Structural Analysis (ISD). The finite element (FE) based simulation approach uses an Arbitrary Lagrangian Eulerian (ALE) description to track the material points during the molding of the green tire to obtain a representation of the molding process (avoidance of mesh distortion). Furthermore, several advanced thermo-mechanically coupled material models have been developed to describe rubber in its cured and uncured state. However, the molding of arbitrary tread patterns is still challenging due to the complex geometry, friction and the material flow of the uncured rubber during the molding process (questions with respect to numerical stability and robustness for realistic 3D tire designs). These open research questions shall be further development steps of this transfer project between ISD and the industrial project partner Continental Reifen Deutschland GmbH. The transfer project aims to combine the strengths of fundamental academic research and innovative realization procedures of new products in a changing industrial environment subjected to digitalization of the whole process chain. Hence, the transfer project will not only bring to industrial application the simulation environment developed within the project SENSE (material model for unvulcanized and vulcanized rubber, ALE approach for rubber molding, exchange on industrial expertise) but will further contribute to the development of numerical methods for the advanced numerical description and representation of tires with arbitrary tread patterns from their manufacturing state to their service state by an alternative numerical method, the material point method (MPM). Additional new research aspects of the transfer project address the development and application of the implicit MPM as a mesh-free method for the molding of tires with arbitrary tread pattern (MPM simulation for tread) in 3D, the formulation of the MPM in the framework of thermo-mechanics, a coupling of FE methods (tire main body) with the MPM (tire tread) for the analysis during the forming and vulcanization process (manufacturing stage), and a strategy to propose an implementation of the material behavior for FEM, MPM or ALE including the description of the current material state (inelastic, nonlinear). The main objective is the development of a robust and numerically stable simulation environment for the molding and vulcanization of tires with 3D tread patterns.