A frequency-based substructuring approach to efficiently model position-dependent dynamics in machine tools

Structural deformations of machine tool components that translate and/or rotate relative to each other to realize tool motion results in tool point dynamics varying along the tool path. These changing dynamics interact with the cutting process and the control loop of the drives to limit machine performance, making it necessary to virtually characterize these interactions such as to guide design decisions. To facilitate rapid evaluation of these varying dynamics, this paper describes a generalized frequency-based substructuring approach that combines the position-invariant component level receptances at the contacting interfaces between substructures to obtain the position-dependent tool point response. Receptances at the contacting interfaces are approximated by projecting them to a point to facilitate a multiple point receptance coupling formulation. Complete machine behavior is represented by just a few sets of receptances, making the model computationally more efficient than full-order finite element models and other dynamic substructuring methods. Position-dependent dynamic behavior for a representative three axis milling machine is simulated and numerically verified. Rapid investigations of the varying dynamics assist in virtually characterizing machine performance before eventual prototyping.