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

Abstract

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 inteifaces 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 substructtirally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system.

Rapid Evaluation for Position-Dependent Dynamics of a 3-DOF PKM Module

“…Investigation based on a "virtual prototyping" technique using FEM model of the machine is an alternative solution [13]. However, structure dynamic analyses for full machine finite element models, which are typically on the order of 1,000,000 DOFs or more, are computationally expensive [14,15]. Therefore, the analytical or semianalytical dynamic modeling method is needed for rapid evaluation.…”

“…The substructures will be incompatible for the further assembling of substructure models [7,14]. As shown in Figure 4, to make the incompatible substructure synthesis possible, a virtual condensation node representing only a subset of interface nodes within the closed frame is defined; all interface nodal DOFs u are represented by the condensation node DOFs u using constraint equations without any interface reduction.…”

“…To ensure that the condensation node represents the average motion of the contacting interface, the weight factors for each DOF are chosen proportional to the part of the interface area that its node represents, as shown in [14]. r is the position vector from to the th node.…”

Model reduction methods for cylindrical structures in reactor internals considering the fluid–structure interaction

“…Email: pnch@yonsei.ac.kr buildings, and industrial structures [3][4][5]. The principal advantage of these methods is that the accuracy of the results is maintained, while the computational costs are reduced significantly.…”

Axis Position Dependent Dynamics of Multi-axis Milling Machines

“…According to [13], modal parameters can be interpolated to describe the dynamics of a work piece, whose dynamic properties change remarkably, when material is removed. Law and his colleagues [14] set up a reduced three axis milling machine model that can be moved to different positions. Based on this model Frequency Response Functions (FRFs) are determined for different axes positions and are fed to frequency domain stability simulations.…”