Modeling and Simulation of Static and Dynamic Behavior of Pre-stressed Joints in Machine Tools using Relative-Bedding-Elements

有限元分析(FEA)是模拟机床静动态行为的重要工具。有限元分析中的单元使用形函数来近似其物理特性。通常使用线性或高次多项式函数。线性单元的应用具有数值简单的优点，但缺点是需要大量的单元才能保证足够的模型质量。另一方面，用高阶函数建模可以用更少的元素来实现这一点。在这种情况下，弹性关节的建模(即在机床中)提出了一个大规模的问题。最先进的关节模型有限地适用于模态和频率响应分析。因此，对静态和动态行为进行现实预测将是困难的。因此，他的研究项目的目的是开发和实践一种预应力弹性节点的建模方法，这种方法可以使当前使用的密集单元网格过时，并能够正确地与高次多项式有限元如梁和壳进行互操作。这样，目前使用离散弹簧-阻尼器单元、材料层或各种非线性接触模型描述的接头之间的差距应该被弥合。此外，由于系统的自由度明显变小，这种方法使得基于模型的刚度和阻尼参数的识别过程变得有效。在这里，项目要求的第一年是关于充分接受模型侧线性化应变连接中的刚度和阻尼值的实验证明。

The Finite Element Analysis (FEA) is an important tool for the simulation of static and dynamic behavior of machine tools. The elements in FEA use shape functions for approximation of their physical characteristics. Commonly linear or higher-polynomial functions are used. Application of linear elements has the advantage of numerical simplicity however they have the disadvantage of need for many elements for sufficient model quality. On the other hand modeling with higher order function can do this with much less elements. In this context the modeling of elastic joints (i. e. in machine tools) poses a large-scale issue. State of the art joint models are limited suited for modal and frequency response analysis. So a realistic prediction of static and dynamic behavior will be difficult. Therefore the intention of his research project is the development and practice of a modeling approach for pre-stressed elastic joints which makes currently used closely spaced element meshing obsolete and which correctly interoperates with higher-polynomial finite elements - like beams and shells. In this way, the present gap between current descriptions of joints using discrete spring-damper-elements, layers of material or various non-linear contact models should be closed. Furthermore this method enables an efficient model-based identification process of stiffness and damping parameters because the systems degree of freedom becomes significantly smaller. Here the requested first year of the project deals with the experimental proof of sufficient acceptance to the model side linearization of stiffness and damping in strained joints.