Synergetic approach to studying stability of form-building trajectories of climb milling by side edges of endmills (low cutting speed case)

Stability problems of the stationary trajectories of the tool elastic deformational displacement under the longitudinal endmilling are considered. In the moving coordinates which displacement is determined by the actuators motion, the stationary steady state is not an equilibrium point (as when turning), but some closed trajectory. The synergetic concept of the analysis of trajectories executed in two stages is used. At the first stage, the established stationary trajectories are calculated according to the offered technique. At the second stage, the stability of these trajectories is analyzed. A case, when the equation parameters in variations under the fixed trajectory can be considered constant within the system impulsive reaction, is considered. Features of the stationary trajectories formation are studied; conditions under which they converge to some steady trajectories are obtained. Besides, some general properties of the loss of balance are received. An example of analysis is cited, and recommendations for ensuring stability of a trajectory of the established form-building motions are given.