A Low-Order Trigonometric Parametric Model for Predicting Pose-Dependent Dynamics and Multimodal Chatter Stability of Milling Robots

Accurate and efficient prediction of pose-dependent structural dynamics and chatter stability is essential for improving the vibration behavior of milling robots. This paper proposes a mechanism-guided low-order trigonometric parametric model and a corresponding identification procedure for predicting pose-dependent frequency response functions and multimodal chatter stability of milling robots from limited modal data. Specifically, a pose-dependent dynamic model of the milling robot is established using the extended transfer matrix method, incorporating spatial elastic joints, rigid links, and a rigid spindle structure. Based on this mechanism model, a low-order trigonometric parametric representation is derived through numerical analysis as a combination of unknown constant matrices and joint-angle-dependent basis functions, ensuring model identifiability while maintaining prediction accuracy for low-order modal dynamics. To identify the model parameters from limited drive-point experimental modal analysis data, sparse ridge regression combined with bootstrap resampling is employed to enhance robustness against measurement noise and unmodeled dynamics. Furthermore, the identified robot modes and tool modes are integrated into a unified state-space formulation to account for multimodal effects in chatter stability prediction. Simulation analysis, modal experiments, and robotic milling tests are conducted to validate the proposed model. The results demonstrate that the proposed method provides accurate predictions of pose-dependent frequency responses and reliable chatter stability boundaries. The experimental results further reveal that robotic milling stability is governed by the combined effects of robot structural modes and tool modes, rather than by the lower envelope of individual modal stability limits.