GEOMETRICKÉ ZÁKONITOSTI VYTVÁRANIA OBROBENÉHO POVRCHU GEOMETRIC RELATIONS OF THE FORMATION OF A CUT SURFACE GEOMETRICKÉ ZÁKONITOSTI VYTVÁRANIA OBROBENÉHO POVRCHU GEOMETRIC RELATIONS OF THE FORMATION OF A CUT SURFACE

and r (cid:12) is a radius of the curving of the knife. The latest approaches illustrate the inaccuracy of this dependency. On the basis of the experimental measurements the authors analyse new relationships between cutting conditions and roughness of the cut surface. These enable to predict morfology of the cut surface to the accession of the semi-product in the production facilities and to select optimal cut conditions of the aspect of the required quality of the surface.

Závislosť drsnosti povrchu od reznej rýchlosti v c a hĺbke rezu a p , ktorá je Rz ϭ Rz(v c , a p ) sa geometricky nedá vyjadriť, pretože súvisí so zákonitosťami plastickej deformácie povrchu obrobku pri styku s rezným klinom. Takéto vzťahy sú však veľmi potrebné na optimalizáciu rezných podmienok. Jednou z ciest ich získania je experimentálne štúdium povrchu pri meniacich sa rezných pod-When assessing the roughness of the cut surface a simplified relationship is used representing the dependency of maximum deviation of a roughness and a representing feed in the form Rz ϭ ᎏ 8 where Rz is the roughness of the cut surface, f is a feed and r ⑀ is a radius of the curving of the knife. The latest approaches illustrate the inaccuracy of this dependency. On the basis of the experimental measurements the authors analyse new relationships between cutting conditions and roughness of the cut surface. These enable to predict morfology of the cut surface to the accession of the semi-product in the production facilities and to select optimal cut conditions of the aspect of the required quality of the surface.

Introduction
Increase of the working reliability of machining systems requires the increase in the quality of the cut surface components. Requirements to improve the quality of machined surface evolve searching for new technological means to solve this problem. Reserves are in utilization of relations of the process of the creation of the cut surface with the cutting slice.
It is generally known that the cut surface is theoretically generated by moving the cutting slice according to kinematics of the machine. The tip of the tool is reproduces on the cut of the workpiece where the plastic deformation of the cut and the tribologic correlations of the areas of tool and workpiece participate.The result is complicated form of the cut plane. When we think of only geometric relationships of the interaction the tool -the work, we can deduce simple relationship within the feed and the roughness of the cut surface, i. e. Rz ϭ Rz(f).
The dependence of the roughness of the surface on the cut speed v c and on the depth of the Rz ϭ Rz(v c , a p ) cut is impossible to be described geometrically, because it is related to the plastic deformation relationships of the surface while in touch with the cut slice. These relations are necessary to a great extent for optimum cutting conditions. One of the ways how to obtain them mienkach. Nasledujúce analytické vzťahy sú získané uvedeným spôsobom. Príspevok je parciálnym výsledkom riešenia grantovej úlohy VEGA 1/7446/20
is the experimental study of the surface in the variable cutting conditions. The following analytic relations are obtained by the presented method. The paper is a partial result of the solution of the grant work VEGA 1/7446/20.

Character of geometric creation of cutting surface
When we analyse an exact geometric relation between the knife of the tool and the cut surface it is possible to determine the roughness of the surface from the Fig. 1.
K modifikácii teoretických vzťahov pre drsnosť povrchu pristupuje aj ďalšia skutočnosť. Reálny tvar hrotu nemá presný kruhový in Fig. 2. The dependence is not parabolic, it is described by segments of the elipses, it reaches final values for the selected values of the parameter r ⑀ . Technically it means that in the moment when the relation for selected finishes r ⑀ there side cutting edge comes to feed. The relation (2a) represents more precisely the dependence Rz ϭ Rz(f) than the simplified relation (1).
In Fig. 3 there is a graph of the function Rz ϭ Rz(r ⑀ ). The system of dependencies is obtained by the following relation (2a) where we expect that the feed is a parameter. Dependencies are limited by the upper parameter. For r ⑀ approaching 0, Rz increases very quickly.
From the original and from the dependence (1) for the surface roughness of the cut it can be seen that Rz increases very quickly with incresing feed. Therefore any increase in feed has unfavorable effect on morphology of the cut surface. From the three dimensional graph of the function it would be possible to get the equivalent value Rz.
The producers of cutting tools produce cutting plates with a defined radius of the tip. As an example we can introduce a piece of ISO standard 1832 according to which, e. g. SANDVIK Coromant produce their goods, where for convertible lathe plates radiuses are defined r ⑀ ϭ 0.4; 0.8; 1.2; 1.6 and 2.4 mm. Apart from it, round plates are produced with radiuses of 8 and 12 mm. Further increase of the radius of the tip of knife is not applicable due to the expansion of active contact of cutting edge with workpiece and of inclination to the vibration of the technological system. Therefore, the improvement of the roughness of the surface need to be solved in a different way.
Another fact joins the modification of theoretical relations for the surface roughness. The real shape of the tip is not of accurate round profile and with the wear it changes considerably. It is mainly the creation of a hole in side edge according to Fig. 4