According to the dynamic model of machine tool system and
the dynamic cutting forces model,the analytical modeling of
chatter vibration including the linear and nonlinear analys is will
be investigated.Moreover,the analytical SLD,which offer an
effective prediction for selecting the stable and unstable cutting
conditions for chatter vibration,will be obtained using the time
domain semi-discrete method [33]. And the corresponding solutions
of the dynamic model are also obtained using the Matlab function dde23 [34].