An Efficient Third-Order Full-Discretization Method for Prediction of Regenerative Chatter Stability in Milling

Abstract

The prediction of regenerative chatter stability has long been recognized as an important issue of concern in the field of machining community because it limits metal removal rate below the machine’s capacity and hence reduces the productivity of the machine. Various full-discretization methods have been designed for predicting regenerative chatter stability. The main problem of such methods is that they can predict the regenerative chatter stability but do not efficiently determine stability lobe diagrams (SLDs). Using third-order Newton interpolation and third-order Hermite interpolation techniques, this study proposes a straightforward and effective third-order full-discretization method (called NI-HI-3rdFDM) to predict the regenerative chatter stability in milling operations. Experimental results using simulation show that the proposed NI-HI-3rdFDM can not only efficiently predict the regenerative chatter stability but also accurately identify the SLD. The comparison results also indicate that the proposed NI-HI-3rdFDM is very much more accurate than that of other existing methods for predicting the regenerative chatter stability in milling operations. A demonstrative experimental verification is provided to illustrate the usage of the proposed NI-HI-3rdFDM to regenerative chatter stability prediction. The feature of accurate computing makes the proposed NI-HI-3rdFDM more adaptable to a dynamic milling scenario, in which a computationally efficient and accurate chatter stability method is required.

A precise and efficient updated third-order full-discretization approach for chatter stability analysis of the milling process

“…The results show that the suggested approach merges quicker than Insperger and Stepan's SDM [6,7] and Dong et al's UNIM [21], while it performs the same convergence rate as the Huang et al's NI-HI-3rdFDM [24]. (3) Concerning the computational efficiency, the proposed PE3rdFDM is always faster than Insperger and Stepan's SDM [6,7] and Huang et al's NI-HI-3rdFDM [24]. Because it separates the whole tooth passing period into free vibration and forced vibration, which significantly avoids the unnecessary discretization process within the free vibration period.…”

“…Stepan's SDM [6,7] and Huang et al's NI-HI-3rdFDM [24] for the same m value. There is a requirement for fewer discrete time periods, especially in non-full immersion milling circumstances.…”

“…The suggested approach's performance is compared to previously published approaches (e.g., Insperger and Stepan's SDM [6,7], Dong et al's UNIM [21] and Huang et al's NI-HI-3rdFDM [24]). To provide a fair comparison, the identical processing settings from Ref.…”

“…To comprehensively access the prediction accuracy of Insperger and Stepan's SDM [6,7], Dong et al's UNIM [21], Huang et al's NI-HI-3rdFDM [24] and the proposed PE3rdFDM, the following tests take the milling processes at / e aD = 0.05, 0.1, 0.2, 0.5, 0.7 and 1.0. SAE and AMRE are calculated in every milling condition to verify the high-accuracy performance of the proposed approach.…”

“…Finally, the transition matrix is established and Floquet theory [32] is utilized to determine SLDs. Comparisons are conducted over the updated third-order fulldiscretization approach [24], the updated numerical integration approach [21], and the remarkable semidiscretization approach [6]. According to the results, the proposed strategy performs more accurately at predicting milling stability.…”