Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting

Zakovorotny, V. L.; Lukyanov, Alexander; Gubanova, Alexandra A.; Hristoforova, Veronica V.

doi:10.1016/j.jsv.2016.01.020

Cited by 27 publications

(9 citation statements)

References 13 publications

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“…The solution to this problem, in our opinion, is in the application of the existing scientific approaches to the description of the interconnected complex, nonlinear dynamics of the cutting process, taking into account the regenerative nature of self-excitation of vibrations under processing [ 17 , 18 , 19 , 20 , 21 ]. At the same time, we understand that this dynamic in the cutting process state space has pronounced nonlinear properties [ 22 ], including points of the bifurcation (rebuilding) of the cutting system [ 23 ].…”

Section: Introductionmentioning

confidence: 99%

Turning Tool Wear Estimation Based on the Calculated Parameter Values of the Thermodynamic Subsystem of the Cutting System

Lapshin

2021

Materials

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Today, modern metalworking centers are not yet able to reliably assess the degree of wear of the tool used in metal cutting. Despite the fact that a large number of methods for monitoring the service life of the tool have been developed, this issue still remains a difficult task that needs to be solved. Idea: The article proposes a new, previously unused method for estimating the power of a cutting wedge in metalworking. The aim of the study is to develop a method for indirectly estimating the tool wear rate based on a consistent model of intersystem communication that describes the force, thermal and vibration reactions of the cutting process to the shaping movements of the tool. Research methods: The study consists of experiments on a measuring stand and a homemade measuring complex. It also uses the Matlab mathematical software package for processing and graphical interpretation of data obtained during experiments. The results show that the proposed method of estimating the current tool wear is applicable for the interpretation of experimental data. Statistically, the modified Voltaire operator of the second kind models the temperature more accurately; at the peak, this method is three times more accurate than the other.

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Section: Introductionmentioning

confidence: 99%

Turning Tool Wear Estimation Based on the Calculated Parameter Values of the Thermodynamic Subsystem of the Cutting System

Lapshin

2021

Materials

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“…Для подсистемы (13) (14) После очевидных преобразований имеем закон синергетического управления в координатах состояния системы:…”

Section: реализация синергетического подходаunclassified

“…Исследования в этой области многочисленны. Они рассматривают устойчивость, свойства притягивающих множеств деформационных смещений [12,13], их бифуркации [14,15], а также отображения в геометрической топологии поверхности. Их исследования ограничены случаем, когда не принимается во внимание взаимосвязь управляемых от ЧПУ траекторий исполнительных элементов и свойств динамической системы.…”

Section: Introductionunclassified

Synergetic approach to machining control of lathe group machines

Zakovorotny¹,

Zakovorotny

Гвинджилия³

et al. 2019

Science Intensive Technologies in Mechanical Engineering

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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.

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“…Принимается во внимание запаздывание вариаций сил при изменениях площади среза [29,[41][42][43][44][45][46]. Учитываются нелинейные зависимости сил резания и трения от скоростей и смещений [47][48][49][50][51][52][53][54]. Рассмотрено параметрическое самовозбуждение [55][56][57].…”

Section: Introductionunclassified

The study of vibration disturbance mapping in the geometry of the surface formed by turning

Zakovorotny,

Gvindjiliya

2024

Metal Working and Material Science

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Introduction. The development of virtual digital models of the machining process on metal-cutting machines is a dynamically developing direction of increasing the efficiency of machine-building production. Such models include subsystems of parts quality prediction. Accuracy and validity of its work directly depends on the built model of dynamic cutting system, which is perturbed by force noise, the sources of which have different physical origin. In addition, the autonomous dynamic system itself is a generator of various attracting sets of deformations, such as limit cycles or chaotic attractors. Taking into account various nonlinear transformations in the properties of the dynamics of the cutting process allows increasing the adequacy of the model to the real process and is an actual task in the construction of simulation modeling systems of the dynamics of surface machining by cutting. Study object. Our earlier studies allow us to determine the geometry corresponding to the deformation trajectories of the surface formed by cutting. However, the adequacy of the mapping of the calculated trajectories to the geometry estimates remains not quite clear. The proposed paper focuses on achieving an adequate mapping of calculated as well as measured strain trajectories into the geometric topology of the part. The aim of the work is to evaluate the mapping of vibration perturbations of the system into the geometry of the surface formed by cutting. Method and methodology. The research is of experimental-theoretical nature. The content of the research includes the study of the correspondence of frequency characteristics obtained on the model and in real machining. The main attention is paid to the mapping of deformations to the part geometry. For this purpose, the paper considers the coherence functions between the strain functions and the part profile. Results and Discussion. It is shown that the conditioning of these transformations has a limited frequency range in which the explanation of the variable components of the generated relief is statistically significant. Mathematical modeling of the dynamic cutting system based on the mechanics of interaction between tool and workpiece allows adequate prediction of the macro geometry of the part formed by cutting. The obtained mathematical tools can be used to create systems for predicting the geometry of the machined surface.

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Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting

Cited by 27 publications

References 13 publications

Turning Tool Wear Estimation Based on the Calculated Parameter Values of the Thermodynamic Subsystem of the Cutting System

Turning Tool Wear Estimation Based on the Calculated Parameter Values of the Thermodynamic Subsystem of the Cutting System

Synergetic approach to machining control of lathe group machines

The study of vibration disturbance mapping in the geometry of the surface formed by turning

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