Error Correction Methods for Accurate Analysis of Milling Stability Based on Predictor–Corrector Scheme

Chatter vibration in machining operations has been identified as one of the major obstacles to improving surface quality and productivity. Therefore, efficiently and accurately predicting stable cutting regions is becoming increasingly important, especially in high-speed milling processes. In this study, on the basis of a predictor–corrector scheme, the following three error correction methods are developed for milling stability analysis: the Correction Hamming–Milne-based method (CHM), the Correction Adams–Milne-based method (CAM) and the Predictor–Corrector Hamming–Adams–Milne-based method (PCHAM). Firstly, we employ the periodic delay differential equations (DDEs), which are usually adopted to describe mathematical models of milling dynamics, and the time period of the coefficient matrix is divided into two unequal subintervals based on an analysis of the vibration modes. Then, the Hamming method and the fourth-order implicit Adams–Moulton method are separately utilized to predict the state term, and the Milne method is adopted to correct the state term. Based on local truncation error, combining the Hamming and Milne methods creates a CHM that can more precisely approximate the state term. Similarly, combining the fourth-order implicit Adams–Moulton method and the Milne method creates a CAM that can more accurately approximate the state term. More importantly, the CHM and the CAM are employed together to acquire the state transition matrix. Thereafter, the effectiveness and applicability of the three error correction methods are verified by comparing them with three existing methods. The results demonstrate that the three error correction methods achieve higher prediction accuracy without sacrificing computational efficiency. Compared with the 2nd SDM, the calculation times of the CHM, CAM and PCHAM are reduced by around 56%, 56% and 58%, respectively. Finally, verification experiments are carried out using a CNC machine (EMV650) to further validate the reliability of the proposed methods, where ten groups of cutting tests illustrate that the stability lobes predicted by the three error correction methods exhibit better agreement with the experimental results.