Abstract
Nowadays, the dynamic cutting system is represented in the form of two subsystems — tool and workpiece, interacting through a nonlinear relationship formed by the cutting process. Such a representation determines the importance of studying the dynamics of the cutting process as the main factor influencing the efficiency of machines, the trajectories of the executive elements of which are set by CNC and are provided with high accuracy. However, in order to improve the efficiency of cutting, it is necessary to align the trajectories of the executive elements are defined by CNC with the changing dynamics of cutting, which introduces deviations in the program-defined trajectories. Purpose of this article is to consider the dependence of the dynamics of the cutting process on the spatial orientation of the cutting tool elasticity and the regenerative effect, and to find out the effect of the proposed dependence on the efficiency of the cutting process. All the issues discussed in the article are analyzed using the example of external shaft turning. Methods. The study is based on the methods of mathematical modeling and experimental dynamics. In contrast to the known studies, the dependence of the turnover lag time on the oscillatory displacements in the direction of the cutting speed, as well as the influence of the positive feedback formed in this case, is taken into account. In addition, changes in the sign of the internal feedback from the direction of deformations, as well as the influence of the regenerative effect on the generated attracting sets of deformations are taken into account. Results. Dependence of the system evolution on the elements of the stiffness matrix at different spindle speeds is disclosed. The properties of the system evolution depending on the ratio of the spindle rotation frequency and the eigenfrequencies of the tool subsystem, as well as the spatial distribution of the stiffness are studied. Conclusion. The frequency and time characteristics of the system are discussed. Conclusion is made about the possibility of efficiency increasing of the cutting process based on the coordination of the CNC program with the dynamic properties of the system.
Highlights
The dynamic cutting system is represented in the form of two subsystems — tool and workpiece, interacting through a nonlinear relationship formed by the cutting process
Such a representation determines the importance of studying the dynamics of the cutting process as the main factor influencing the efficiency of machines, the trajectories of the executive elements of which are set by CNC and are provided with high accuracy
In order to improve the efficiency of cutting, it is necessary to align the trajectories of the executive elements are defined by CNC with the changing dynamics of cutting, which introduces deviations in the program-defined trajectories
Summary
Свойства системы можно раскрыть на основе использования следующей модели (рис. 1) [10, 22, 44, 49]: d2X dX m dt. Свойства системы можно раскрыть на основе использования следующей модели Где ρ — давление в [кг/мм2]; ζ — параметр крутизны в [с/мм]; μ — безразмерный коэффициент; T (0) — параметр, определяющий запаздывание сил. Если равновесие X* = {X1*, X2*, X3*}T Тогда вариации положения инструмента относительно следа вызывают образование сил Φ(t) и Φ(t)(1), действующих на главную и вспомогательную задние грани. Здесь положительное направление определяется по направлению сближения передней αΣ и задней α1Σ граней. Причем углы определяются в сечениях (A−A1), нормальных к режущим лезвиям Так как задние углы есть величины малые, то имеем выражения для дополнительных сил ΦX = {ΦX1 , ΦX2 ΦX3 }T ∈ R(3) в функции ТИЭС и X. Эти свойства эволюции отличаются от рассмотренных в работах [48, 50]
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