An improved numerical integration method for predicting milling stability with varying time delay

Varying time delay (VTD) plays an important role in governing the state of chatter vibration in low radial immersion milling. Meanwhile, numerical integration method (NIM) has been proven a highly efficient method in predicting milling stability lobe diagram (SLD) where a constant time delay (CTD) should be assumed as one tooth passing period. In this paper, an improved numerical integration method (INIM) is proposed, focusing on how to extend this efficient method to the condition that VTD has to be considered in low radial immersion milling. Based on an equivalent description of VTD, an offset matrix is constructed to modify the Floquet transition matrix. Thus, the distributions of SLD and system oscillations can be updated simultaneously with the effect of VTD. Then, a chatter excitation test (CET) method for low radial immersion milling is introduced so that SLD can be extracted directly by analyzing the machined surface structure, and the lobe-drifting effect of the SLD can be revealed visually. Comparing the extracted SLDs with the predictions, the accuracy of the proposed INIM can be validated due to the capability of bridging the gap between the lobe-drifting effect and VTD, while the traditional NIM with CTD is powerless. The improvement of the proposed INIM has also been validated by comparing with a peripheral milling test provided in a published literature.