Optimization of cutting wedge geometry for a plastic disintegrator tool.
Cernecky, Jozef ; Brodnianska, Zuzana
1. INTRODUCTION
In the paper we focus on the visualization of stress and
deformation states during plastic dividing by a cutting wedge of a
disintegrator tool by the method of holographic interferometry. Our aim
is to achieve the distribution of stress in the area of disintegration
of plastic. We are interested in the optimal geometry of a cutting wedge
from the viewpoint of spending the least energy to disintegrate. One of
the indicators is also stress and deformation states during entering of
the cutting edge into plastic. The findings achieved from the
interferometric measurements can serve to optimize geometry of a cutting
wedge for a plastic disintegrator.
2. EXPERIMENT
To carry out an experimental research we used an experimental
device illustrated in Fig.1. An important part of the equipment was a
tool of disintegrator (4), whose cutting wedge entered the sample of
plastic material (3). The force acting in the place of material dividing
by a cutting wedge was derived via weights (2) fixed to an arm (1). The
device allows variable setting of the strength of the acting force
(Cernecky & Pivarciova, 2007).
[FIGURE 1 OMITTED]
Deformations which occurred as an effect of entering the cutting
wedge into the plastic (rubber sealing board of the NR/SBR type) in the
initial stage corresponded to the case of one axis loaded by a pressure
force (Guinea et. al., 2004).
To find out the stress and deformation states we used the method of
holographic interferometry, which enables to visualize micro shifts in
interaction of a tool's cutting wedge with the plastic (Jones &
Wykes, 1989).
Formation of interference fringes which can be interpreted in a
qualitative and quantitative way will be shown by the micro shifts.
However, the qualitative analysis itself can provide us with
understanding of stress and deformation states which appear during
opening of a micro-crack (Sirohi, 1993).
The used method will picture not only spreading of the crack in the
plastic, but also directions and amounts in loading of the tool. We used
a singular solution in the following form during experimental
determination of coefficients of stress intensity [K.sub.I]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The coefficient of the tension intensity was determined from the
equation:
[K.sub.I] = [sigma][square root of a x [pi] (4)
where r is distance of the isopach from the crack, a is dimension
of the crack, [theta] is angle of the isopach depending on r, a is total
stress (loading), [[sigma].sub.xx], [[sigma].sub.yy], [[sigma].sub.xy]
are main stresses in the direction of the axis x, y, xy.
Considering that singular solutions take into account only the
first member of a row their validity is limited to only very surrounding
of the crack root (Balas & Szabo, 1994).
3. RESULTS AND DISCUSSION
In our paper we focused on the comparison and assessment of two
geometries of a cutting wedge (CW) of a disintegrator. Cutting wedges A
and B were loaded by the same weight of 50 g on an arm of 130 mm. Based
on stress and deformation states in the material we searched for an
optimal geometry of a cutting wedge of a disintegrator tool during
dividing of plastic.
In the paper we focused only on initial state of entering of the
cutting edge into plastic. To find out this we used the method of
holographic interferometry which enables to visualize shifts in the
material even for very small loadings.
Fig. 2 shows interferograms of cutting wedges A, B obtained by the
double-exposure method, while the first one was formed by superposition of the object wave and the reference wave before deformation of the
object and the second exposure after the deformation of the object.
This method gave us a double-exposure holographic interferogram
which presents the state of object at the moment of the second exposure.
It is possible to observe changes in the number of interference fringes
(isopaches) with the changes of loading. With a bigger change of loading
we can observe higher density of fringes. To analyze stress and
deformation states CW A we chose isopaches with the initial distance (at
0[degrees]) [r.sub.3] = 3,1 mm, [r.sub.4] = 4,1 mm and [r.sub.5] = 5,5
mm (Fig. 3a).
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Cutting wedge B has a different geometry than a cutting wedge A
which is manifested in the shape and density of interference fringes and
so that enabled us to determine which geometry of a cutting tool is
better.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
To analyze stress and deformation states of CW B we chose isopaches
with the initial distance (at 0[degrees]) [r.sub.3] = 6,7 mm, [r.sub.4]
= 14,3 mm, [r.sub.5] = 28,16 mm (Fig. 3b). The value of stress
[[sigma].sub.xx], [[sigma].sub.yy] for the distances [r.sub.3],
[r.sub.4], [r.sub.5] was calculated according to the equations (1), (2).
Similarly, we can calculate the value of stress [[sigma].sub.xy]
according to the relation (3). To be able to find out the values of
stress it was necessary to calculate the coefficients of the tension
intensity K according to the relation (4).
Graphic development of stress [[sigma].sub.xx] for CW A and CW B is
pictured in Fig. 4 and graphic development of stress [[sigma].sub.yy]
for CW A and CW B is obvious from Fig. 5.
The findings suggest that the stress [[sigma].sub.xx] and
[[sigma].sub.yy] is for CW B lower than for CW A, so it can be
established that geometry of CW A is better.
4. CONCLUSION
In our paper we used the method of holographic interferometry
(microscopic method) to determine stress and deformation states. Based
on the stress and deformation states in plastic we compared the optimal
geometry of a cutting wedge during dividing of plastic.
We obtained the distribution of stresses in the zone of dividing
from interferometric measurements. The stress field in the area of
interaction of cutting wedge and plastic consisted of the stress field
of the plastic and the stress field of the tool, which is proved by the
shapes of interference fringes on both bodies.
The stress values were determined by singular solutions. The
cutting wedge A had higher values of stresses [[sigma].sub.xx],
[[sigma].sub.yy] at the same loading than the cutting wedge B in the
area of crack root, which is evident from the Fig. 4, 5. It was possible
to observe changes in the number of interference fringes with the
changes of loading. The higher loading was, the higher density of
fringes was produced.
We also focused on a qualitative analysis of interferogram pictures
based on which we can observe spreading of the crack in plastic as well
as directions and values of loadings in the tool. The used
double-exposure method enables us gradually record changes which are
constantly increasing in one direction so that the following referential
states are gradually recorded as the states of former changes.
5. ACKNOWLEDGEMENTS
The part of the topic dealt with is a part of VEGA 1/0498/10 grant
project called "Application of holographic interferometry in
research of boundary layer in heat transfer appliances".
6. REFERENCES
Balas, J.; Szabo, V. (1994). Holographic interferometry in
experimental mechanics, Prentice Hall PTR, ISBN 9780-1339-5369-5, USA
Cernecky, J.; Pivarciova, E. (2007). Possibilities and prospects of
holography. Izdatel'stvo Fzevskogo gosudarstvennogo techniceskogo
universiteta, Fzevsk, ISBN 978-5-7526-03037, Russia
Guinea, G. V; Rojo, F. J. & Elices, M. (2004) Stress intensity
factors for internal circular cracks in fibers under tensile loading.
Engineering Fracture Mechanics, Vol. 71, No. 3, february 2004, 365--377,
ISSN 0013--7944
Jones, R.; Wykes, K. (1989). Holographic and speckle interferometry. A discussion of the theory, practice and application of
the technique. Cambridge University Press, 2nd edition, ISBN
0-521-34878-1, United Kingdom
Sirohi R. S. (1993). Speckle Metrology. Marcel Dekker, Inc., New
York, ISBN 0-8247-8932-6, USA
