Regulations are generalized on the synergetic theory of control for the case when the paths of shaping motions have a frequency structure exceeding considerably a pass band of servomotors which control a motion of executive elements. There is shown a simulator of the system and a dual optimization problem is under solution which is based on minimization of costs shown for manufacturing parts and for their accuracy support.

Заковоротный В. Л. и др. Влияние динамических свойств взаимодействующих подсистем на эволюцию Zakovorotny V. L. et al.. Effect of dynamic properties of interacting subsystems on evolution of selective transfer formation in friction units

Introduction. One of the ways to improve the accuracy of manufacturing parts by cutting is related to the control of elastic deformations of the tool and the workpiece. This is particularly true for slender parts, whose stiffness law along the tool path is given. In this case, the control parameter, as a rule, is the return flow rate, which affects the cutting forces, whose change causes variations in elastic deformations. To provide the specified accuracy of the diameter, it is required to coordinate the controlled trajectory of the feed drive speed with the feed rate and a priori given law of change in the stiffness of the workpiece or the law of variation of the cutting process parameters. To do this, it is required to determine the law of converting the engine speed into the feed rate, and, ultimately, into elastic deformations. This law depends on the stiffness of the mechanical part of the feed drive and the changing parameters of the cutting process.Materials and Methods. The paper presents mathematical modeling and, on its basis, analysis of the conversion of the feed rate into cutting forces, taking into account the final stiffness value of the mechanical part of the drive and the evolutionary parameters of the cutting process.  Results. It is shown that, starting from a certain critical value, the law of converting the feed rate into cutting forces becomes fundamentally dependent on the stiffness of the mechanical part of the drive. At the same time, there is an increase in time for setting a new force value when the feed rate varies, which affects the accuracy of providing forces that are consistent with the stiffness law of the part. The paper presents algorithms for calculating elastic deformations for a given stiffness law, as well as algorithms for calculating the trajectory of the feed rate at which the deformations remain constant. It is shown that the law of conversion is also affected by variations in the cutting parameters. Discussion and Conclusion. The frequency and time characteristics of the conversion are discussed. A conclusion is made about the accuracy of the diameter formed through cutting, depending on the stiffness of the mechanical part of the feed drive and on some parameters of the cutting process.