Geodesic
Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 26 (2018) no. 5, pp. 20-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

Aim. The aim of the investigation is to study the evolutionary properties changes of the dynamic cutting system and the bifurcation of the attracting sets of the deformation displacement of the tool due to the irreversible transformation of the energy input in coupling tool-processing are considered. Method. The mathematical modeling of the evolutionary system in form of the integro-differential functionally related systems is indicated, and the problem of bifurcation of the deformation displacement of the tool relatively to detail in the processing of evolution is considered. The example of the bifurcation and their influence on output properties of the processing. Novelty. In contrast to previously done researches in which the changes of this properties are determined by the set variations of the system parameters, for example, the rigidity of the workpiece, the evolution of the parameters is considered in the article as the natural process caused by the irreversible transformations of the energy in the cutting area. In this case the parameters of the dynamics (which is formed by the processing) depend on the phase work trajectories and the power of the irreversible transformations in the interface knots between the tool sides and the detail, and in the zone of the chip formation. Therefore the dynamic link parameters are considered as depending on the trajectories of the work and the power of the irreversible transformation in marked areas. Thus on the one side the parameters depend on these trajectories, on the another side their changing acts the work and the power of the irreversible transformation. Discussion. The important general regularities of the control of the processing on metal-cutting machines are not considered earlier. Their consist in coordination of the external control, for example, the NPC with the internal dynamic system changing evolutionarily. Their discussed here.
Keywords: dynamic system softheturning, system evolution, bifurcation of the attracting sets of the deformational displacement, Volterra operator. 
@article{IVP_2018_26_5_a2,
     author = {V. L. Zakovorotnyj and V. E. Gvindzhilija},
     title = {Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {20--38},
     publisher = {mathdoc},
     volume = {26},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2018_26_5_a2/}
}
TY  - JOUR
AU  - V. L. Zakovorotnyj
AU  - V. E. Gvindzhilija
TI  - Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties
JO  - Izvestiya VUZ. Applied Nonlinear Dynamics
PY  - 2018
SP  - 20
EP  - 38
VL  - 26
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVP_2018_26_5_a2/
LA  - ru
ID  - IVP_2018_26_5_a2
ER  - 
%0 Journal Article
%A V. L. Zakovorotnyj
%A V. E. Gvindzhilija
%T Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties
%J Izvestiya VUZ. Applied Nonlinear Dynamics
%D 2018
%P 20-38
%V 26
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVP_2018_26_5_a2/
%G ru
%F IVP_2018_26_5_a2
V. L. Zakovorotnyj; V. E. Gvindzhilija. Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 26 (2018) no. 5, pp. 20-38. http://geodesic.mathdoc.fr/item/IVP_2018_26_5_a2/