Application of the synergistic concept in determining the CNC program for turning
Introduction. One of the dynamically developing areas of increasing the efficiency of CNC machines is associated with the use of the synergetic concept in determining the CNC program. The principle of compression-expansion of the dimensionality of the state space is used. Subject. On the example of the workpiece machining, the stiffness parameters of which are a function of the toolpath, all stages of control synthesis, which ensures the mutual consistency of dynamic subsystems, including the cutting process, are described in the paper. The aim of the work is to determine asymptotically stable machine actuator toolpath, given by CNC program parameters, from the set of paths, for which the condition of minimum wear intensity is fulfilled. Method and methodology. Mathematical modeling of the controlled cutting system, which is based on the principle of compression-expansion state space, is presented. When the dimension of the state space is expanded, the model of the dynamic cutting system includes all elements from the CNC system that programs the motion of the actuating elements to the elastic deformations of the tool, which interacts with the workpiece through the connection formed by the cutting process. The dynamic coupling integrates the subsystems into a single coupled control system. In this space, the desired shaping motion path of the tool tip relative to the workpiece is constructed, which should be the attractor of the entire state space. The transformation of the desired motion path into an attractor characterizes the procedure of compressing the dimensionality of the state space. It is supposed that it is possible to control the motion trajectories of the actuators within the bandwidths of the servomotors. Results and discussion. The analysis of the stability of the cutting process is performed; the example of the efficiency of a NC program on the basis of the synergetic paradigm is presented. It is shown that by coordinating the external control with the internal dynamics of the system it is possible to increase the efficiency of a part production up to two times in machine time.