Proceedings of SerbiaTrib '13

each of which is measured by the length ε. Thefractal dimension can be calculated according toEq. (2):D=lnN(ε)/lnε. (2)Characterization of surface topography isimportant in applications involving friction,lubrication, and wear (Thomas, 1999). In general, ithas been found that friction increases with averageroughness. Roughness parameters are, therefore,important in applications such as automobile brakelinings and floor surfaces. The effect of roughnesson lubrication has also been studied to determine itsimpact on issues regarding lubrication of slidingsurfaces, compliant surfaces, and roller bearingfatigue. Finally, some researchers have found acorrelation between the initial roughness of slidingsurfaces and their wear rate. Such correlations havebeen used to predict the failure time of contactsurfaces. A section of standard length is sampledfrom the mean line on the roughness chart. Themean line is laid on a Cartesian coordinate systemwherein the mean line runs in the direction of the x-axis and magnification is the y-axis. The valueobtained with the formula on the right is expressedin micrometers (Om) when y=f(a).Fractal dimension1,9651,961,9551,951,9451,941,9351,935 mm/s4 mm/s3 mm/s1,9252 mm/s1,920 50 100 150 200 250RoughnessExperimental dataFitting curve with neural networkGraph 3. Relationship between fractal dimension androughness R a in specimens hardened at different speedsat 1000 °CFractal dimension21,991,981,971,961,951,941,934 mm/s5 mm/s3 mm/s2 mm/s1,9234 234 434 634 834 1034 1234 1434RoughnessExperimental dataFitting curve with neural networkGraph 4. Relationship between fractal dimension androughness R a in specimens hardened at different speedsat 1400 °C4. CONCLUSIONGraph 1. Arithmetical mean roughness (Ra)3. RESULTWe studied the relationship between the fractaldimension, parameters of the robot laser cell androughness (friction).The paper presents the use of fractal geometry todescribe the mechanical properties of robot laserhardened specimens. We use a relatively newmethod, fractal geometry, to describe thecomplexity of laser hardened specimens. The mainfindings can be summarized as follows:1. A fractal structure exists in the robot laserhardened specimens.2. We describe the complexity of the robot laserhardened specimens using fractal geometry.3. We have identified the optimal fractal dimensionof tool steel hardened with different robot laserparameters.4. We use the box-counting method to calculate thefractal dimension for robot laser hardenedspecimens with different parameters.REFERENCESGraph 2. Roughness od robot laser hardenendspecimens[1] B.B. Mandelbrot. The fractal geometry ofNature. New York: W.H. Freeman, p. 93, 1982.[2] P.V. Yasnii, P.O. Marushchak, I.V.Konovalenko, R.T. Bishchak, Computeranalysis of surface cracks in structuralelements, Materials Science 46, pp. 833-839,2008.13 th International Conference on Tribology – Serbiatrib’13 353