Stability analysis in turning with variable spindle speed based on the reconstructed semi-discretization method

Chatter is a harmful phenomenon in metal cutting process. The turning process with variable spindle speed is an effective means for chatter suppression. In this paper, the reconstructed semi-discretization method (RSDM) is used to analyze the stability in turning process with variable spindle speed which is constructed as the dynamic model of delay differential equations with varying delay term (VDDE). Firstly, the dynamic model in turning with variable spindle speed is established. Secondly, stability analysis of VDDE based on the RSDM is introduced. For the turning process with variable spindle speed, the RSDM has been proved to be more calculation speed without reducing calculation accuracy than the well-accepted semi-discretization method (SDM) via an example of single degree of freedom turning. Finally, three types of chatter, period-one, flip, and secondary Hopf bifurcations are discussed in detail based on the RSDM. The proposed method is a good alternative method to the stability analysis in turning with variable spindle speed.

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