Mapping model of structure nonlinearity and feedrate for predicting chatter stability in robotic milling

The study presents an innovative method for predicting stability lobe diagrams (SLDs) by explicitly incorporating the nonlinear dynamics of robotic milling systems. A frequency-domain decomposition (FDD)-based technique has been devised to systematically identify a comprehensive set of nonlinear frequency response functions (FRFs), from which a systematic mapping relationship between modal parameters, cutting forces, and feedrate is developed. Through this mapping, the complex governing equation of robotic milling is subsequently transformed into a more tractable form to predict SLDs. The significant advancement lies in that a decoupled formulation between modal parameters and excitation forces is established for the first time, thereby simplifying SLD analysis. It also offers the following two advantages over existing methods: (i) enhanced sensitivity in identifying the feedrate-dependent transition between regenerative chatter (RC) and low-frequency chatter (LFC), and (ii) substantial enhancement in the prediction accuracy of SLDs. Experimental results demonstrate that increasing feedrate shifts the RC-LFC transition point toward higher spindle speed regions, with more distinct variation patterns under strong-stiffness conditions. The proposed method achieves an average prediction accuracy of 89.48%, thereby effectively verifying its capability to enhance both the sensitivity and reliability of SLD predictions in robotic milling processes.