Numerical Analysis Of States Of Strain
And Stress Of Material During Machining
With A Single Abrasive Grain
Author(s)
L. Kukielka, J. Kustra & K. Kukielka
Abstract
In papers [4, 7], a mathematical model was derived of a single-grain machining
process in conditions of centreless continuous grinding. This model comprises
discrete equations of the object’s motion and heat transfer together with initial
and boundary conditions. In this paper, an effective solution of these equations
has been presented. The manner of a partial linearization of the incremental
motion equations has been shown, which allows for an application of an explicit
method of integration, which makes use of an approximation with the method of
central differences. As a result of this, it is possible to calculate vectors of
displacements and temperature at the end of a given step on the basis of values
concerning the previous step. For this method, an adequate algorithm of the
solution of motion equations has been developed with the assumptions of
Rayleigh’s proportional damping. Its application has been developed in the
system of the ANSYS finite element method, which allows for a complex time
analysis of the states of displacements, strains and stresses occurring in the set
(which consists of an object, an abrasive grain and a binding agent, both for
spatial and flat states). Numerical computations of the process of the object’s
material strain have been conducted with the use of two methodologies. The first
one requires an introduction of boundary conditions for displacements in the
contact area determined in modeling investigation, while the second requires a
proper definition of the contact zone through the introduction of finite elements
of TARGET and CANTACT types, without the necessity of introducing
boundary conditions. It is evident from the analyses conducted that forecasting
of the physical properties of the surface layer in the centreless continuous
grinding processes may occur on the basis of analyses of thermal phenomena and
the state of strains in the machining zone. An analysis of machining with a model
abrasive grain is the first stage towards a proper design and control of this
complex technological process.
Keywords
Related Book
Other papers in this volume
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