Development of a model order reduction method for the direct generation of time-discrete, low-dimensional models of machine tools

开发一种模型降阶方法，用于直接生成机床的时间离散、低维模型

• 批准号: 269396201
• 负责人: Professor Dr. Timo Reis
• 金额: --
• 依托单位: Fachgebiet Werkzeugmaschinen und Fertigungstechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/269396201?language=en
• 关键词: Development; model; order; reduction; method

The development of modern machine tools is under great innovation, time and cost pressure. With continuous growth of productivity demands, also the complexity of machine tools increases. There is a high demand for innovative methods of developing and testing, to handle with these challenges. It results in preventing expensive design- or development-failures of a physical prototype as well as reducing commissioning times at a later point in time. Therefore time-deterministic models are needed, on the one hand having a high model quality and on the other hand a solution at a predetermined time step. Due to the model size of typical finite element models, these time steps are not suitable for real-time computations. Consequently, there is a demand for adapted model order reduction to solve real time problems. Currently, no such automated procedure for the creation of real-time computable systems exists applicable for complex finite-element models. The subject of this research project is to develop a model order reduction method for the direct generation of time-discrete, low-dimensional models of machine tools. The main goal of the project is the automated and customized application specific provision of discrete-time, deterministic, reduced systems to real-time capable models of the dynamic behavior of machine tools. For this purpose an innovative model order reduction method will be developed, which provides a low-dimensional approximation for a fixed time step of an original model along with the associated error estimate and retaining inherent system properties (such as passivity, steady-state accuracy). The method is based on high-dimensional ordinary differential equations and differential-algebraic equations, which are provided by finite element models of machine tools or rather machine modules. Furthermore, the method allows for the consideration of the time step for real-time calculations. In addition, the error estimation serves as abort criterion allowing the automatic model order reduction. Through interdisciplinary cooperation of production engineering and mathematics to support this innovative process and shorten the development of mechatronic systems and as machine tool is provided. This method is used in the early stage of the development process as far as to the point of virtual commissioning. The method makes a major contribution to the creation of structural models and to the increase of the accuracy of these models.

现代机床的发展面临着巨大的创新、时间和成本压力。随着生产力需求的不断增长，机床的复杂性也随之增加。为了应对这些挑战，对创新的开发和测试方法的需求很高。它可以防止物理原型代价高昂的设计或开发失败，并减少以后的调试时间。因此，需要时间确定性模型，一方面具有高模型质量，另一方面具有预定时间步长的解。由于典型有限元模型的模型大小，这些时间步长不适合实时计算。因此，需要适应模型降阶来解决实时问题。目前，尚不存在适用于复杂有限元模型的用于创建实时可计算系统的自动化程序。该研究项目的主题是开发一种模型降阶方法，用于直接生成机床的时间离散、低维模型。该项目的主要目标是自动化和定制的应用程序特定提供离散时间、确定性、简化的系统到机床动态行为的实时模型。为此，将开发一种创新的模型降阶方法，该方法为原始模型的固定时间步长提供低维近似以及相关的误差估计并保留固有的系统属性（例如无源性、稳态精度）。该方法基于高维常微分方程和微分代数方程，这些方程由机床或更确切地说是机器模块的有限元模型提供。此外，该方法允许考虑实时计算的时间步长。此外，误差估计用作允许自动模型降阶的中止标准。通过生产工程和数学的跨学科合作来支持这一创新过程并缩短机电一体化系统和机床的开发时间。这种方法用于开发过程的早期阶段直至虚拟调试。该方法对结构模型的创建和这些模型精度的提高做出了重大贡献。