Numerical
analysis of nonlinear contact problem in
processes
of
rolling and grinding
Remigiusz Błaszków,
Leon Kukiełka, Radosław Patyk, Mariusz Wojtalik
Technical University of Koszalin
ul. Racławicka 15 - 17, 75 - 620 Koszalin, Poland
The article consists of two chapters: The first
concerns determination of the contact problem. Also there are described
processes of burnishing rolling and centreless grinding. There is presented the
algorithm of solving the contact problem using the Finite Elements Method based
on updated Lagrange method. The algorithm for the solution of the dynamic
problem was using the EXPLICIT method.
In
the second chapter there are included two examples of numerical analysis of the
contact problem. The first example presents the procedure of modelling of
burnishing rolling process. The second example presents the procedure of
modelling of the centreless grinding process. The obtained results in both
cases allow to analyse the change of quantities in time. Numerical modelling
allows to determine-with specified accuracy - the distribution of contact
pressure, intensity of stress, intensity of strain and more. Measuring these
phenomena in the contact zone is impossible at present.
Introduction
In the
work [1, 2] there is presented the variational equation of movement of objects
being in contact. The resulting variational equation was discretized using the
Finite Elements Method and the arrangement of equations was obtained. In this
work there is presented the algorithm of solving the contact problem and the
discrete equation using the EXPLICIT method. Also there are presented examples
of practically applying the obtained algorithm for numerical analysis of the
contact problem using the ANSYS program. The analysis took into account two technological
processes: burnishing rolling and centreless grinding.
The phenomena described accompany the
burnishing rolling and centreless grinding operations. In literature, various
problems are connected with these processes of metal working.
Burnishing is a process by which a smooth hard
tool (using sufficient pressure) is rubbed on the metal surface (Fig.1a). This
process flattens the high spots by causing plastic flow of the metal. The edges
of sheet metal can be smoothed out by pushing the sheet metal through a die
that will exert a compressive force to smooth out the blanked edge and the
burrs caused by the die break. Burnishing rolling improves the finish and size
of surfaces of revolution such as cylinders and conical surfaces. Both internal
and external surfaces can be burnished using an appropriate tool. Burnishing
improves the surface finish, surface hardness, wear-resistance, fatigue and
corrosion resistance [1, 3, 4]. An example of the profile ("plateau") after burnishing and photo of microstructure with
visible wedge of hardening is presented on Fig. 2.
Fig.
1.
Fig. 2. Profile of roughness after burnishing
(a), metallographic specimen (b).
Centreless grinding is a grinding
operation, where the object isn't mounted to the machine tool elements
(Fig.1b). Grinded object is "free" placed between two grinding wheels-grinding
and leading, placed on the work-rest blade. Grinding wheel used in the process
of centreless grinding is built of 3 main parts: entry-in shape of one or two
cones, cylindrical-central part of the grinder, and output-shaped most often as
relief cone. Its main aim is cutting the material of the object. The second
grinder in the process, called shield or leading grinder is built as grinding
tool. It does not cut, but by selecting the parameters it turns the worked
object into rotation and line feed. This rotational and line feed movement of
worked object, necessary for working is an effect of little inclination of axis
of leading wheel (about angle of 1,5 - 6) and it is a result of forces of
friction occuring between tool and worked object [5].
The process of
centreless grinding proceeds as follows: object put between grinders is gripped
between entry cone of the grinding wheel and leading grinding wheel. As a
result of axial displacement of worked object there proceeds the process of
cutting of allowance material. The process proceeds until total removal of
allowance, to the end of conical part of the grinder. In the cylindrical part
worked object is finally shaped-it is formed to final dimensions and to final
roughness of surface. In the conical part the worked object is free relocated
[5, 6, 7,].
Particular
attention should be paid to the following issues: the geometrical structure of
an object's surface after its previous processing, the deformation mechanism of
an inequality in the burnishing process, the durability of a burnishing element
(tool) in the time of the process, the state of the displacement rate and the
deformation rate of the surface layer material during the burnishing process
and the size of the areas of contact zones. From the investigations results,
that the profile of roughness before burnishing should be determined, regular
and periodic. The publications [1, 2, 4, 7-14] contain a modern method of burnishing
rolling and centreless grinding modeling with the use of the mechanic contact.
These concern the contact problem of an ideally rigid body with a deformable
body (elasto - plastic or rigid-plastic), for the cases of the occurrence of
very small plastic deformations - comparable to an elastic deformation.
Conclusions
The paper presents the algorithm of solving the
contact problem using a step-by-step incremental procedure. Also there is
presented the dynamic explicit method (DEM) for solving discrete equation of
movement, formulated with updated Lagrangian, in the increments of
displacement. Applying step-by-step procedure allows solving the contact
problems characterized by partial knowledge of the boundary conditions.
Also there are presented two examples of
applying this method: analysis of burnishing rolling and grinding using single
grain.
In
result of experimental research and numerical analysis one ascertained three
qualitatively dif-ferent cases of deformations of asperity dependent only on
the angle of inclination of the sides.
1. For angles Q³500,
the deformation of the material occurs only within the heights of asperity. The
depressions of the asperities do not move upwards. Core of material stays not deformed.
2. For angles
17,50<Q<500 follows enlargement of zone of plastic deformations,
which embrace also core. Depressions of asperities move upwards.
3. For angles Q£17,50 the
settlement of the surface is the result of the deformations of inequalities and
of the core of material. The value of lowering the vertex of an asperity is
equal to the values for which its depression moves up. The final layer does not
have surfaces with discontinuities of material.
The obtained results
of calculations permit to qualify dependencies between the geometry of asperity
and state of deformations and stress in the surface layer. This is necessary to
estimate the residual stress and displacement after burnishing rolling.
The application of
described algorithm for single grain cutting provides a complex time analysis
of displacement, strains and stresses occurring in the object. It is possible
to analyse of course of physical phenomena in the contact zone of grain with
chip and in the contact zone of grain with worked object for different
conditions of process realization: geometry of grain, friction conditions in the
stick zone and more.
Numerical results clearly show from the
analyses that physical properties of the surface layer in the process of
centreless grinding could be predicted by analyses of phenomena and strain
states in the grinding zone.
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