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

Abstract This paper presents a new framework for modeling machine tool dynamics, aiming to enable their integration in 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 implementation of the proposed framework is demonstrated through a case study in which the generated model interfaces with a 3D printer controller to adaptively produce optimal trajectories that compensate for structural vibrations during printing. Bidirectional digital–physical communication 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.