Partition of the workspace for machine tool based on position-dependent modal energy distribution and clustering algorithm

The natural frequencies and damping ratios of machine tool structure vary with the change of the machining position in the machining space. When the stiffness distribution of the whole machine structure is not uniform, some position change will further lead to the change of weak components of the structure. In order to detail the position-dependent dynamics of the machine tool, the change of structure dynamics caused by the change of position is divided into two types: one is both the modal parameters and structural weakness change, and the other is that only the modal parameters change, while the weakness remains unchanged. The entire workspace can be divided into different subareas according to whether the weakness changes. In the same subarea, only the modal parameters change and the weakness remains unchanged. In the different subareas, the weakness of whole machine tool structure changes. The change of structural weakness influences the vibration characteristics of the machine tool and the dominant modes of vibration. Hence, the partition of machining space according to the change of structural weakness is helpful to more accurately analyze the position-dependent dynamics and vibration characteristics of the machine tool. Firstly, this paper presents the method of modal energy distribution to analysis position-dependent structural weakness and the principle of the clustering to divide the workspace. A simulation example is given to verify the effectiveness of the method. Then, the clustering partition of the workspace for a gantry machining center is conducted with the presented method. Finally, the cutting tests are performed to verify the change of the vibration dominant mode of machine tool at different subareas.