Evaluation of the influence of the reaction rate of the thermodynamic subsystem on the dynamics of the cutting process in metalworking

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 TECHNOLOGY speci fi ed requirements [1]. The vibration of the tool is caused by various factors, which are conveniently divided into two subgroups, the subgroup due to external in fl uence on the processing process, here there can be both machine vibrations and vibrations associated with the malfunction of the spindle group or tool wear [1-2]. The second group of factors, affecting the vibration mode of cutting in a metal-cutting machine, is the factors of self-excitation of the cutting system, which include the regenerative nature of vibrations during cutting, as well as the thermodynamic subsystem of the cutting system, which is also able to excite tool vibrations [3-4]. In the scienti fi c literature, it is customary to divide the vibrations that occur during cutting into three components: free vibrations, forced vibrations, and self-excited vibrations [5-7]. It should be noted that a lot has already been done to combat free and forced vibrations, and there are many positive results in this area [7-9]. As for the fl uctuations associated with the self-excitation of the cutting system, that is, the fl uctuations that consume energy from the external environment, today there are no unambiguous solutions. Therefore, the topic of minimizing self-excited vibrations during turning of metals is popular in scienti fi c research conducted in the world [10-15]. In the above works, the main focus is on the evaluation of the effect on tool fl uctuations, the so-called regenerative effect. It should be noted that this is quite well studied in the twentieth century and is described in the works of Hahn R. S., Tobias S. A. and Merritt H. E. [16- 18]. Many more modern authors note the possibility of establishing the chaotic nature of tool vibrations during vibration regeneration [19-21]. However, in general, it is noted that the main factor affecting the regenerative effect is the so-called time delay. For Russian scientists, the problem of trail cutting, as the basis for self-excitation of the cutting system, is not so important; many scienti fi c schools pay more attention to the analysis of the interrelated dynamics of the cutting process [22-25]. For example, in [26], the analysis of the dynamics of deformation vibrations of the tool is based on the connection, through a force reaction, of this deformation movement with the cutting elements of the CNC machine system. In the works of Soviet and Russian scientists, studying the vibration dynamics of the cutting process [27–31], it is noted that in the cutting process, in addition to the feedback on the cutting force, which takes into account the regeneration of vibrations during cutting along the “trace”, through changes in the area of the cut layer, a thermodynamic feedback is formed, which is also associated with the vibration activity of the tool, as well as with the wear of the wedge. In [32-34], the in fl uence of various factors on the dynamics of the cutting system is considered, where the most interesting, from our point of view, is the work [34], in which an interconnected model of the cutting system is proposed, in which the thermodynamic subsystem of the cutting system plays the most important role. The mathematical model of the thermodynamic subsystem presented in this paper, and fi rst described in [33], is based on the Volterra operator of the second kind, which, for the stationary case of the cutting system, is reduced to an aperiodic equation of the fi rst or, in the more complex case, of the second order. The dependence of this constant on the vibration energy and tool wear along the back face, revealed in these works, allows us to make conclusion about the possible non-stationary nature of the equation describing the relationship of the thermodynamic cutting system with the subsystem describing the cutting force. That is, what is meant here is the fact that such a constant can change during the processing of metals by cutting on a metal-cutting machine. Based on the considerations of the interconnectedness of the subsystems of the cutting system, such a non-stationarity of the time constant should lead to a change in the entire cutting system. To assess the in fl uence of changes in the time constant of the thermodynamic subsystem on the dynamics of the processing process, it is possible to simulate a simpli fi ed version of the mathematical model of the subsystem with already known models of the subsystems of deformational movements of the tool and the force response to the shaping movements of the tool from the side of the cutting process. In this regard, the aim of the work is to form a consistent model of the relationship between the subsystems that describe the force, heat and vibration reactions of the tool, which adequately describes the mechanism for reducing the vibration load on the cutting process.