Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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A Semi-analytical Investigation into the Dynamics of the Abrasive Machining of Deep Cylindrical Holes Accounting for the Memory Effects in the Frictional Interaction

Author(s):

Aleksandra Viktorovna Grezina

N.Lobachevskii National State University of Nignii Novgorod
Nizhny Novgorod, Gagarina Prospect,23
candidate of physical and mathematical sciences
associate professor

aleksandra-grezina@yandex.ru

Vladimir Semenovith Metrikin

N.Lobachevskii National State University of Nignii Novgorod
Nizhny Novgorod, Gagarina Prospect,23
candidate of physical and mathematical sciences
associate professor

v.s.metrikin@mail.ru

Adolf Grigorevith Panasenko

N.Lobachevskii National State University of Nignii Novgorod
Nizhny Novgorod, Gagarina Prospect,23
candidate of physical and mathematical sciences
associate professor

a.g.panasenko@yandex.ru

Abstract:

In this paper we present a semi-analytical methodology of the mathematical modelling of abrasive machining of deep cylindrical holes. The modelling accounts for the memory effects in the frictional interaction which governs the process. The mathematical model is presented in the form of a non-autonomous system of differential-difference equations of variable structure. The model is investigated using the mapping of the Poincare surface, boundaries of which vary in time in accordance with the functional dependence of the coefficient of static friction. To this end we developed an original semi-analytical approach to identify the fixed points that correspond to periodic motions of an arbitrary complexity. The obtained bifurcation diagrams enabled an in-depth analysis of the main regimes of abrasive machining in the presence of memory effects in the frictional interaction. These regimes are not present when the memory effects are unaccounted for. The mechanism of the existence of not perfectly smooth surfaces resulting from the honing of cylindrical surfaces (as observed in physical experiments) is discovered.

Keywords

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