Effect of state-dependent time delay on dynamics of trimming of thin-walled structures

Trimming of cantilever thin-walled structures is commonly seen in aerospace industry, including trimming of blades. Trimming with helix angle tools can cause the vibration of the thin-walled workpiece along the tool-axis, which may disturb the time delay between cutting by the current and previous teeth. The time delay dependent on the vibration state makes the stability analysis of trimming process challenging. This paper is the first attempt to uncover the effect of state-dependent time delay of the trimming process caused by workpiece vibration on chatter stability. Modeling of the cutter-workpiece interactions, state-dependent time delay and the dynamic chip generation mechanism are presented. A time-domain numerical algorithm with an improved stability metrics is constructed to analyze the trimming stability behaviors. We found that the two dominant states can occur, namely, period-n instabilities with time-varying time delay and stability with constant time delay. A focused experimental study was carried out to calibrate this new finding. This study reveals the way the workpiece vibration affects the time delay and stability in the trimming process.