Probabilistic Graphical Modeling for Machine Tool Dynamics With a Case Study in 3D Printer Vibration Compensation

Abstract This article presents a new framework for modeling machine tool dynamics to enable their integration into machine tool digital twins. The framework is formulated as a dynamic Bayesian network, in which model parameters, sensor and process observations, and decision variables are represented explicitly and updated sequentially using Bayesian inference. The framework incorporates a library of candidate models and enables model selection, uncertainty quantification, and physical system state estimation through probabilistic inference. These properties enable scalable digital twin creation at both the machine and fleet levels. The proposed framework is designed to be broadly adoptable across a wide range of machine tool dynamics problems. In this article, we demonstrate its implementation through a case study in feed-drive dynamics, where the generated model interfaces with a 3D printer’s controller to adaptively produce optimal trajectories that compensate for structural vibrations during printing. Bidirectional digital–physical communication loop is established and experimentally validated, confirming the framework’s ability to predict and adapt to system variations. Results indicate improved vibration compensation and enhanced surface quality under varying dynamic conditions in this case study, while computational challenges for enabling general implementation are discussed.