Dynamic substructuring of machine tools considering local damping models

Dynamic substructuring is widely known and applied for different types of systems to divide a structure into subsystems while considering the dynamic influences of the coupled structure. For complex systems such as machine tools, substructuring becomes more difficult. Nevertheless, dividing a machine tool into substructures allows for a more efficient optimization of machine tool design regarding different machine positions. Recent substructuring approaches for machine tools focus on the modelling of mass and stiffness properties while lacking proper local damping models for each component. Damping is usually added after the coupling of the individual components by using measured or empirical values for the overall system in the current state. Therefore, a real prototype of the machine is needed to predict accurate results for the system behavior. This paper proposes a substructuring approach, which includes the local damping of each dissipation source on the substructure level. Each substructure is modelled using viscous and hysteretic damping models for the individual damping sources followed by a Craig-Bampton-reduction of the substructure. The reduced mass, stiffness and damping matrices are coupled in the desired machine position to predict the behavior of the machine tool structure. The hysteretic damping is thereby transformed using equivalent viscous damping values to allow for a simulation of the machine's dynamic behavior in the time domain. The results of this substructure coupling approach are compared to a standard mode acceleration approach of the non-substructured machine tool, which needs to be recalculated for every machine position or design changes to individual components. Furthermore, the influence of the frequency range on the substructure reduction results is evaluated. It is shown, that the presented coupling approach is in high accordance with traditional reduction approaches. With this modelling approach, the dynamic behavior of a machine tool can be predicted at different machine positions without measuring the damping values on real prototypes or using simplified empirical values. This leads to new optimization possibilities in the design process of machine tools and thus to enhanced machine tool performance.