Study of cutting force predictability, signal complexity of different end milling CWE stages with different modelling methods

Cutting force analysis in milling processes is essential for precision metal cutting as it contributes to understanding tool wear, optimising machining performance, and ensuring overall process stability. Numerous research papers have been published to describe modelling techniques that provide high-fidelity predictions, with recent developments highlighting the benefits of combining different methods. However, these approaches are relatively limited in their ability to predict over the wide frequency range needed to describe the tooth passing frequency (TPF) and its harmonics under varying working conditions or stages of cutter-workpiece engagement (CWE). This paper studies the prediction performance of different modelling techniques when considering wide-band noise under varying working conditions. The methods evaluated are the explicitly defined but difficult-to-parameterise Finite Element Method (FEM), Semi-Analytical Solutions (SAS), and Long Short-Term Memory (LSTM) networks, which are black-box deep learning methods incorporating time-based information. Since white-box models are still more readily adopted by industry, the paper also introduces a new post-processing model to improve the prediction accuracy of FEM and SAS based upon the Fourier Series of the TPF (FS-TPF). Over the observable range of 0 to 1500 Hz, the cutting force predictability was assessed in both the time and frequency domains using similarity of frequency distribution, Shannon entropy, and Kullback–Leibler (KL) divergence. Verification and analysis indicate that the cutting force predictability with FEM at “partial engagement” was the lowest, due to its lack of ability to describe TPF harmonics. In contrast, the LSTM model showed the best prediction performance across all tested working conditions. The new FS-TPF significantly increased FEM’s prediction accuracy by approximately 50% and improved SAS’s performance by 20%. Finally, a Deep Neural Network (DNN) is compared to the LSTM, suggesting that both methods are suitable for force prediction without encountering significant accuracy issues across the different stages of CWE. It was found that the key to increasing cutting force predictability to be generally applicable to all milling conditions is the capability to describe TPF harmonics across the different CWE stages in milling processes. The FS-TPF compensation can dramatically enhance the cutting force prediction accuracy of FEM and SAS, while the applied DL-LSTM and DNN models have successfully demonstrated their wide adaptability without requiring additional post-processing.