Determination of optimal coordinates for switching processing cycles on metal-cutting machines

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 1 monotonous decreases in both the cutting speed and, to an even greater extent, the longitudinal feed rate correspond to the matching condition. Therefore, a new problem for the subject area is formulated to ensure the economic optimality of processing: to determine the coordinates of the tool subsystem changeover for the minimal costs of manufacturing a batch of parts. The given mathematical tools, algorithms and proven necessary optimality conditions can solve this problem. An example of changing the optimal coordinates of the tool subsystem changeover showed that they depend on the ratio of the machine tool’s minute cost during the actual cutting process to the cost of replacing and changeover of the cutting tool. As the cost of switching increases, their number decreases, and the cutting path increases in each cycle. The number of switches and the cutting path are also affected by the degradation intensity of the processing, which is characterized by the parameter  . It is affected by irreversible energy transformations at the interface of the tool fl ank face with the workpiece. They depend both on the elastic-dissipative properties of subsystems interacting at cutting, the evolutionarily changing parameters of the dynamic coupling formed by cutting, and on uncontrolled disturbances, for example, spindle beats. Moreover, as we showed earlier [8-10], the trajectories of irreversible energy transformations along the cutting path can have a high sensitivity to small variations in the system parameters and the parameters of uncontrolled disturbances. The developed technique was tested at Helicopter Service Company, JSC when turning the MI-29 helicopter shaft of the hydraulic system fi tting made of 08Kh15N24V4TR steel. Without dwelling on the details, we note that using the practical recommendations consistent with the evolution of the MEUT as well as optimal algorithms for switching processing cycles yielded the following results: according to the traditional program there were 3 processed parts between the changeover of tool systems; according to the adapted program, there were 8 parts; the average machine time for processing one part increased by 1.7 times. The stated costs for the production of a batch of 100 parts decreased by 1.3 times. Importantly, the given ef fi ciency is obtained by software methods without changing the tool and processing conditions. The developed methodology and mathematical tools can be extended to solving problems of controlling other types of evolutionary processing [37]. Conclusion Creating a CNC program with regard to the alignment of the trajectories of the machine’s executive units and the evolutionary changes in the properties of the cutting process requires taking into account the fact that the cutting speed and the corresponding feed rate tend to decrease as the tool wear develops. Therefore, the tool changeover coordinate along the cutting path should be determined for the ef fi ciency of processing. This coordinate is selected on the basis of minimizing the costs for manufacturing a batch of parts. A mathematical simulation of the process is proposed to implement the choice of coordinates; the necessary optimality conditions are stated and a method for calculating the optimal coordinates for tool changeover is proposed. The optimal switching coordinates are shown to correspond to equal minimum cutting speeds in the direction of the tooltip motion. They depend on the ratio of the machine time cost to the cost of changing tools (the cost of switching processing cycles). The paper presents the results of numerical simulation and industrial testing of the developed algorithms. They demonstrate that software methods can increase the cost ef fi ciency of processing by 1.2-1.3 times, even without changing the properties of tools, the state of machines, and others parameters. References 1. Haken H. Information and self-organization: a macroscopic approach to complex systems. Amsterdam, Elsevier, 2006. 258 p. ISBN 978-3-540-33021-9. DOI: 10.1007/3-540-33023-2. 2. Prigogine I., George C. The second law as a selection principle: the microscopic theory of dissipative processes in quantum systems. Proceedings of the National Academy of Sciences of the United States of America , 1983, vol. 80, pp. 4590–4594. 3. Kolesnikov A.A. Prikladnaya sinergetika: osnovy sistemnogo sinteza [Applied synergetics: fundamentals of system synthesis]. Taganrog, SFU Publ., 2007. 384 p.