Basic Non-Linearity in Machining Chatter

An analysis is presented of chatter in machining including the consideration of the basic non-linearity of the process which is due to the fact that with increased vibration the tool starts to move outside of the cut for a part of the cycle. The analysis is carried out in the time domain, by computer simulation. Both turning and milling are considered. In the latter case the varying directional orientation is fully respected. In the analysis the mode coupling self excitation is demonstrated. For turning the method does not reveal any new conclusions. But for milling it illustrates the gradual boundary of stability and shows that stability may be 2 to 3 times wrongly calculated by the methods known and used so far. The results are important for the formulation of acceptance tests of milling machines.