Substructure Coupling of a Machine Tool in Arbitrary Axis Positions Considering Local Linear Damping Models

Virtual prototypes, e.g., finite element models, are commonly used to reduce the development times of a new machine tool generation. However, the accuracy of these models is often limited by their representation of damping effects and the possibility to efficiently simulate the dynamic behavior in different axis positions. This paper shows the changing local damping distribution within a single-axis machine tool configuration for different axis positions. Based on this investigation, an approach to accurately model the position-dependent dynamics, while keeping the calculation times small, is presented. The virtual model of the machine is divided in several substructures, which consider the local damping behavior of each dissipation source. The reduced mass, stiffness, and damping matrices are coupled in the desired machine position by using multipoint constraints, which are generated at the desired machine position after the reduction of the substructures. Four different approaches to apply multipoint constraints on reduced substructures are compared, followed by an investigation of their influencing parameters. The most promising approach is compared with a model without local damping representation as well as a model without substructuring. By considering the local damping effects within the finite element model and coupling the reduced models of each component in arbitrary axis positions, an efficient analysis and optimization of the dynamic behavior of a machine tool over the whole workspace can be conducted.