Efficient Static and Dynamic Modelling of Machine Structures with Large Linear Motions

Mechatronic structures deform under static and dynamic loads. These deformations lead to deviations at the tool center point (TCP), affecting the reachable accuracy and/or productivity of the machines. The scope of this work is the comparison of calculations and measurements of different static and dynamic errors on a dynamic test bench. A reduced-order modelling approach is applied for the test bench modelling. It uses a combination of modal condensation and moment-matching methods with Krylov subspaces. The different modelling steps and requirements are presented. The same model is used for all static and dynamic evaluations presented within this paper. Static deformations, leading to roll and pitch deviations at the TCP of the test bench structure, are simulated using the described modelling methodology and validated by inclination measurements. The modal behavior of the system is investigated by calculation and compared to the measurements at a single axes position. The spatial change of the frequency response functions of the modelled system is investigated further, by calculation and measurement of the velocity open-loop FRFs of one axis for different machine configurations. In addition, a transient trajectory simulation is performed and compared to the Heidenhain KGM and encoder measurements. The large variety of comparisons shows the efficient applicability of the modelling environment MORe.