Experimental Research and Significance Analysis of Advanced Interpolation Methods for Optimizing System State Items and Processing Parameters

The Finite-Difference Method (FDM) plays a pivotal role in the field of stability prediction, particularly in the modeling and stability analysis of cutting process dynamics. However, traditional approaches to optimizing the FDM often treat system state terms and time-delay terms as a monolithic entity, failing to explicitly distinguish between them, which leads to a lack of specificity in selecting optimization targets. In this study, an innovative approach is introduced by incorporating the third-order Newton interpolation method and the fourth-order Hermite interpolation method. By comparing the computational accuracy and convergence speed, it is found that the 3N-FDM (third-order Newton Finite-Difference Method) exhibits superior overall performance, and it is clearly pointed out that increasing the order does not always result in better outcomes. Additionally, this study selects different discretization numbers, denoted as m, for comparative analysis to thoroughly evaluate their impact on computational accuracy. Experimental validation demonstrates the high accuracy of the 3N-FDM. Through a one-way ANOVA (analysis of variance) of tool wear and workpiece surface roughness, it is revealed that changes in system state terms have the most significant impact on the feed rate f, followed by the cutting depth ap, and finally the spindle speed n. Based on the experimental results and analysis mentioned above, this study concludes that optimizing system state terms can more effectively explore the combined influences of processing parameters on processing quality, production efficiency, and tool wear.