Meta-transfer learning for predicting position-dependent milling stability across varying overhang lengths under limited experimental data

Stability lobe diagram (SLD) serves as a pivotal reference in determining appropriate chatter-free milling parameters. The tool tip frequency response functions (FRFs), as crucial prerequisites for deriving theoretical SLDs, vary with the position and overhang length. The acquisition of tool tip FRFs under different machining positions and overhang lengths necessitates repeated time-consuming experiments or simulations. To guarantee the efficiency and accuracy in predicting SLDs, this paper puts forward a meta-transfer learning method utilizing a deep neural network to refine the prediction of stability limits with limited experimental data. Initially, a source overhang length is defined to perform the impact testing under adequate machining positions for acquiring tool tip dynamics and constructing a theoretical stability dataset. Fewer impact tests for a target overhang length are conducted under insufficient machining positions arranged through a proposed similarity-based sampling strategy, and a target stability dataset is constructed using limited tool tip FRFs. Secondly, the source dataset is updated by domain adaptation on the modal parameters with a multi-fidelity modeling. Subsequently, meta-learning is carried out on multiple meta-tasks randomly determined from the updated source dataset. The ultimately trained deep neural network during the meta-learning phase undergoes fine-tuning with the target dataset for predicting the stability limits at various machining positions. Finally, a three-axis vertical machining center is taken to conduct a detailed experimental validation. Comparative analyses indicate that the proposed methodology outperforms others in accurately predicting stability limits, even with a constrained number of labeled samples.