DETERMINATION OF OPTIMAL TRAJECTORIES UNDER TREATMENT WITH ACCOUNT FOR CUTTING PROCESS DEVELOPMENT

Abstract

The task of selecting optimal coordinates of the switching cycles at which the controlled process performance attains a maximum is formulated. This is some refinement of the optimal control problem applied to the machining processes for the case when the treatment mode control providing stabilization of various cutting conditions occurs. A typical example of such a problem necessitating the treatment mode switching for deephole machining with twistdrills is given. The necessary optimum condition to which minimum velocity values equal among themselves correspond is proved. On this basis, a velocity calculation technique providing the time minimum is proposed. A concrete example for the case of deep pinhole machining (diameter — 2.15 mm, hole depth — 140 mm) is given. The obtained results are generalized in the case when problems on any evolutionary system control machining are solved.

Keywords

• optimal control
• cutting process
• evolutionary system.