The stability analysis of separated feed ultrasonic milling

The full-discretization method introduced by Ding has high computational efficiency without loss of any numerical precision regardless of low and high radial depth of cut for the stability analysis of ordinary milling operation in time domain. Contrast to ordinary milling, it exists the separation phenomenon between each cutter tooth and the workpiece in feed ultrasonic milling operation. So before analyzing the system stability by the full-discretization method, the contact state between the cutter tooth and the workpiece should be made clear. In this paper, the trajectory method is proposed by the authors to judge the contact state between the cutter tooth and the workpiece. The stability analysis is developed for separated feed ultrasonic and ordinary end milling operations by the above methods and is validated via time domain simulations and experiments for both operations. The analyses show excellent agreement with both the time domain simulations and the experiments. Further, several end milling experiments were conducted that demonstrate the result ultrasonic vibration in feed direction can suppress chatter in machining operations.