Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Order Models

Dynamic response of a machine tool structure varies along the tool path depending on the changes in its structural configurations. The productivity of the machine tool varies as a function of its frequency response function (FRF) which determines its chatter stability and productivity. This paper presents a computationally efficient reduced order model to obtain the FRF at the tool center point of a machine tool at any desired position within its work volume. The machine tool is represented by its position invariant substructures. These substructures are assembled at the contacting interfaces by using novel adaptations of constraint formulations. As the tool moves to a new position, these constraint equations are updated to predict the FRFs efficiently without having to use computationally costly full order finite element or modal models. To facilitate dynamic substructuring, an improved variant of standard component mode synthesis method is developed which automates reduced order determination by retaining only the important modes of the subsystems. Position-dependent dynamic behavior and chatter stability charts are successfully simulated for a virtual three axis milling machine, using the substructurally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system.