Experimental study of a titan grade 2 surface topography prepared by abrasive waterjet cutting is performed using methods of the spectral analysis. Topographic data are acquired by means of the optical profilometr MicroProf®FRT. Estimation of the areal power spectral density of the studied surface is carried out using the periodogram method combined with the Welch´s method. Attention is paid to a structure of the areal power spectral density, which is characterized by means of the angular power spectral density. This structure of the areal spectral density is linked to the fi ne texture of the surface studied.Eksperimentalna studija površine titana klase 2 dobivene abrazivnim rezanjem vodenim mlazom je provedena korištenjem metode spektralne analize. Topografski su podaci prikupljeni pomoću optičkog profi lometra MicroProf®FRT. Procjena površinske snage spektralne gustoće je provedena periodogram metodom u kombinaciji sa Welch metodom. Pozornost je posvećena površinskoj snazi spektralne gustoće koja je karakterizirana pomoću kutnih spektara gustoće snage. Struktura površinskog spektra gustoće je povezana sa istraživanom fi nom teksturom površine

D. Kozak

J. Valíček

K. Brillová

M. Ohlídal

S. Hloch

Ž. Ivandić

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39METALURGIJA 51 (2012) 1, 39-42K. BRILLOVÁ, M. OHLÍDAL, J. VALÍČEK, S. HLOCH, D. KOZAK, Ž. IVANDIĆEVALUATION OF ABRASIVE WATERJET PRODUCED TITAN SURFACES TOPOGRAPHY BY SPECTRAL ANALYSIS TECHNIQUES Received - Prispjelo: 2011-01-28Accepted - Prihvaćeno: 2011-04-20Original Scientifi c Paper – Izvorni znanstveni radISSN 0543-5846METABK 51(1) 39-42 (2012)UDC – UDK 620.197.6:544.62=111Experimental study of a titan grade 2 surface topography prepared by abrasive waterjet cutting is performed using methods of the spectral analysis. Topographic data are acquired by means of the optical profi lometr MicroProfFRT. Estimation of the areal power spectral density of the studied surface is carried out using the periodogram method combined with the Welch´s method. Attention is paid to a structure of the areal power spectral density, which is characterized by means of the angular power spectral density. This structure of the areal spectral density is linked to the fi ne texture of the surface studied. Key words: Abrasive waterjet cutting, Surface topography, Spectral analysisAnaliza topografi je površina titanove legure nakon rezanja vodenim mlazom pomoću spektralne analize. Eks-perimentalna studija površine titana klase 2 dobivene abrazivnim rezanjem vodenim mlazom je provedena korištenjem metode spektralne analize. Topografski su podaci prikupljeni pomoću optičkog profi lometra MicroProfFRT. Procjena površinske snage spektralne gustoće je provedena periodogram metodom u kombinaciji sa Welch metodom. Pozor-nost je posvećena površinskoj snazi spektralne gustoće koja je karakterizirana pomoću kutnih spektara gustoće snage. Struktura površinskog spektra gustoće je povezana sa istraživanom fi nom teksturom površine.Ključne riječi: Rezanje abrazivnim vodenim mlazom, površinska topografi ja, spektralna analiza INTRODUCTIONOver the last decades, research and engineering practice have been characterized by the development of non-traditional methods of material machining. Various machining technologies of high-speed cutting by using of liquid jets can be included in this category. Whereas, the technology of high-speed jet machining itself is well defi ned, the studies of abrasive waterjet (AWJ) quality parameters in the depth of produced cuts are still desir-able. The attempt to defi ne the depth of zone where the AWJ - produced surface is yet satisfactory for usual ma-chinery practice has been done e.g. by Hashish [1,2]. Guo suggested the classifi cation of cutting zones by means of the surface roughness spectral analysis and the same problem has been solved also by a wavelet-based topography analysis [3,4]. Surface irregularities in the form of striation were studied in [5–7], where also the quantitative surface roughness data were presented. The most widespread tool used in practice for a surface roughness measurement is a stylus profi lometer. Its main drawbacks are an ability of only 2-D assessment of a surface topography and a contact with the surface, which can cause a destruction of certain surfaces and K. Brillová, Institute of Physical Engineering, Brno University of Tech-nology, Czech Republic, M. Ohlídal, Institute of Physic, VŠB-Technicala University of Ostrava, Czech Republic, J. Valíček, S. Hloch, Faculty of Manufacturing Technologies TU Košice with a seat in Prešov, Slovakia, D. Kozak, Ž. Ivandić, Mechanical Enginnering Faculty J. J. Strossmayer University of Osijek, Slavonski Brod, Croatiamisinterpretation of data measured. Aforementioned drawbacks of the 2-D assessment of a surfaces quality lead to needs of a new generation of instruments ena-bling a non-contact 3-D assessment of a surface quality (it is along a selected area of the surface). Such an in-strument is the optical profi lometer MicroProf  FRT (Fries Research & Technology GmbH).We shall focus our attention to the spectral analysis of surface 3D topographic data obtained by means of the optical profi lometer MicroProf  FRT from titan surfaces generated by abrasive waterjet.  AREAL POWER SPECTRAL DENSITY OF A RANDOM FUNCTIONIt is interesting to apply spectral analysis of a sur-face topography to surfaces generated by AWJ cutting. These surfaces are of a random character. It is possible to select individual zones of the surface in which the surface function can be considered as a stationary (i.e. there is not any change of the surface character within the whole individual zone) and ergodic (i.e. we can evaluate features of the whole surface topography with-in the individual zone from an individual suffi ciently large realization of the surface within the zone) 2D ran-dom function. We shall confi ne our attention only to the so called transition zone. The reason is that the surface quality within this zone is changing from suffi cient to defi cient from the viewpoint of engineering production 40  METALURGIJA 51 (2012) 1, 39-42K. BRILLOVÁ et al.: EVALUATION OF ABRASIVE WATERJET PRODUCED TITAN SURFACES TOPOGRAPHY BY SPECTRAL...requirements. Considering the surface under study as a random function we have to describe the surface by means of mean quantities derived from amplitude Fou-rier spectra of its realizations or, as usually, from squares of these spectra in the frequency domain (so called en-ergy or power spectra of the surface realizations). We shall describe a non-limited (i.e. defi ned along the whole plane x, y) realization of the random surface under study by the surface function z=z (x, y) in the coordinate sys-tem Oxyz, where z is the height of the surface with re-spect to the plane x, y in the point [x, y]. Hence, the function z=z (x, y) is the realization of a stationary and ergodic random function zr≡{z(x, y)}  selected by a process of a measurement. The function  z=z (x, y) is defi ned along the whole plane x, y. But we acquire in-formation on the function z=z (x, y) only from a fi nite region X, Y of the plane x, y by the measurement. So we deal with the function zX,Y=zX,Y(x, y)defi ned as follows: ( ) ( )( ) otherwiseyxzYyXxforyxzyxzYXYX0,,,,,=≤∧≤=   (1)This function has the Fourier integral( ) ( ) ( )[ ] dydxyfxfiyxzffZ yxYXyxYX ∫ ∫∞∞−∞∞−+−= 2exp,, ,,   (2)Then it is possible to defi ne the areal power spectral density (APSD) of the function z=z (x, y)  as follows  ( )=∞→∞→XYZffP YXYXyx2,lim,  (3)APSD of the whole random function zr is defi ned as: ( )=∞→∞→XYZffPYXYXyxzr2,lim,  (4)where the symbol 〈 〉 denotes the mean of the surface realizations population. The quantity Pzr(fx, fy) indicates in what way the mean power of the studied surface is distributed within the frequency domain. We shall use it for the characterization of surfaces generated by AWJ. The characterization of the surface topography within the transition zone along an individual surface profi le can be also performed by means of amplitude – fre-quency analysis (2D surface evaluation) [8-10]. More advanced approach is the surface topography charac-terization by means of the discrete fast Fourier trans-form (DFFT) [11-13] of 2D data (maps of surface heights) within the zone. According to our best knowl-edge the application of the areal data spectral analysis has not been used for a topography characterization of surfaces generated by the AWJ cutting yet.ANGULAR POWER SPECTRAL DENSITYIt is possible to characterize the shape of APSD by means of the angular power spectral density (AnPSD) of the function [11]. To defi ne this quantity it is neces-sary to transform APSD (see Equation 4) into polar co-ordinates within the frequency domain. ( ) ( ),, rzryxzr fPffP → ,where( ) ( ) =+===xyyxrryrx fffffffff arctg,,sin,cos 22Then AnPSD is defi ned as follows [11]: ( ) ( )( )rfr dffPPr∫=max0, , (5)where 0 ≤ θπ and frmax (θ) is a maximum spatial fre-quency contained in the section of APSD given by the angle θ. We can describe a distribution of the power of the studied random function along individual directions within the frequency plane by this quantity.PERIODOGRAM ANGULAR POWER SPECTRAL DENSITY ESTIMATIONWe cannot analyze infi nite number of possible real-izations of the infi nite function zr. It leads to the fact that our result must be only the estimation of APSD from Equation (4) as  21,,2,,1 ∑=≅QqqYXqYX ZQZ  (6)where Q is the number of realizations available. Hence, we can approximately express Equation (4) as follows: ∑=∆∆∆∆≅∆∆QqqYXzr yxMNyNlxMkZQyNlxMkP12,, ,1,, (7)where 0 ≤ k ≤ M – 1; 0 ≤ l ≤ M – 1.Using the relation (7) we employ so called periodo-gram method of the determination of the ASPD estima-tion of the random function zr.WELCH’S METHODCalculation of the right side of Equation (7) can be carried out in several ways. We selected the Welch’s method. Within the framework of this method we re-solve the measured domain of the given realization into a suffi cient number of mutually overlapping sub-do-mains ZX’,Y (xm’,, ym‘). Then we carry out weighting the surface function in each sub-domain by a chosen weight-ing function w(xm’,, ym‘). Thereafter we determine the following expression for each the weighted sub-domain denoted by the indices q’:  yxNMyNlxMkZ qYXw∆∆∆∆''2'',',',,' (8) for 0 ≤ k ≤ M´ – 1; 0 ≤ l ≤ N´– 1, M´M, N´NThe symbol ∆∆ yNlxMkZ qYXw '',',', ,'  in Eq. (8) 41METALURGIJA 51 (2012) 1, 39-42K. BRILLOVÁ et al.: EVALUATION OF ABRASIVE WATERJET PRODUCED TITAN SURFACES TOPOGRAPHY BY SPECTRAL...denotes the Fourier transform of the surface function weighted by the function w(m'∆, n'∆y) within the se-lected q' th domain X', Y'. In conclusion we calculate the arithmetic average of Q' spectra of weighted surface function within all sub-domains ∑= ∆∆∆∆='1''2'',',',''' ,1 QqqYXwW yxNMyNlxMkZQP  (9)Considering the assumption of the function zr ergo-dicity the term (9) is equivalent to the arithmetic aver-age of the given number of fi nite realizations of zr . The term (9) is the resulting statistical estimate of the APSD defi ned by Equation (4).  ∑− ∆∆∆∆==∆∆≅∆∆QqqYXwWzryxNMyNlxMkZQyNlxMkPyNlxMkP1''2'',',',''''''' ,1,, (10)As regards to the discrete form of the term (5) for AnPSD we used an appropriate numerical algorithm for their calculation.RESULTSThe 3D matrix of surface heights measured by the optical profi lometer MicroProf  FRT on a typical titan grade 2 surface prepared by AWJ cutting under condi-tions listed in Tab.1 is presented in Figure 1. The evaluation of the surface topography has been done within the transition zone marked by the white rectangle. The estimate of the APSD obtained by men-tioned procedure is presented in Figure 2. This fi gure shows contours of the APSD for the sake of clearness. Two lines in the fi gure represent the directions in which AnPSD is reaching its maximum for low (the solid line) and high spatial frequencies (the dashed line). The head-ing angles of both the lines equal the angular coordi-nates θ of the normalized AnPSD maximum for low and high spatial frequencies. Values of those maxima AnPSD angular coordinates are as follows: θml = (174,9±0,3)°, θmh = (158,6±0,2)°These values were obtained from 10 independent procedures of the parameters evaluation; their random uncertainties are of 95 % confi dence level.DISCUSSIONWe can interpret the difference between θml and θmh  in the following way. The topography of the surface studied shows typical striation (see Figure 1). With re-gard to dimensions of this striation they contribute to the APSD within the low spatial frequencies region (the smallest contour in Figure 2) In accordance with the theorem of similarity, which is valid for the Fourier transform [10], we can state that the main orientation of this striation is perpendicular to the solid line in Figure 2. For the same reasons we can also state that there is a fi ne texture corresponding to high spatial frequencies in the surface topography, the main orientation of which is slightly rotated with respect to the direction of the sur-face striation. In the case presented the difference be-tween these directions is ∆θ = θml – θmh= (16,3±0,3)°. It can be explained by a supposed mechanism of the sur-face generation. The abrasive water jet creates surface striation as the main feature of the surface topography in transition and so called rough zones. Inside an indi-vidual groove the turbulent fl ow of the abrasive water jet originates a fi ne texture in the surface topography with a prevailing direction different from the prevailing direction of the surface striation. This proposed mecha-nism is supported by the detailed study of the surface topography by means of optical microscopy which has been carried out too.Figure 1  Digital map of the typical titan grade 2 surface topography produced by AWJ cutting (Optical profi lometer MicroProf  FRT)Figure 2 Contours of the APSD of the surface from Figure 1 within the transition zone (semilogarithmic scale). Solid line –direction of surface striation, dashed line – direction of the fi ne surface texture.42  METALURGIJA 51 (2012) 1, 39-42K. BRILLOVÁ et al.: EVALUATION OF ABRASIVE WATERJET PRODUCED TITAN SURFACES TOPOGRAPHY BY SPECTRAL...CONCLUSIONIn this paper we studied a titan grade 2 surface to-pography prepared by abrasive waterjet cutting. Topo-graphic data were acquired by optical profi lometer Mi-croProf  FRT. We focused our attention to the transi-tion surface zone. Using APSD and AnPSD we found that an abrasive water jet creates besides striation also a fi ne texture inside individual grooves. These two com-ponents of the surface topography show different pre-vailing directions which were determined by means of the angular coordinate of the maximum of the normal-ized AnPSD. We explained this fact by the proposed mechanism of AWJ surface generation, i. e. by a turbu-lent fl ow of the abrasive water jet inside an individual surface groove. We can conclude that the spectral analy-sis of surfaces generated by AWJ provide results useful for topography characterization of such surfaces. These results can be used for an optimization of the AWJ ma-chining process.AcknowledgementsThis work was supported by the Grant Agency of Czech Republic under contract No. 101/09/0650 and by the Ministry of Education, Youth and Sports of Czech Republic under contract MSM 0021630518. REFERENCES[1] Hashish, M.: Modeling Study of Metal Cutting with Abra-sive Waterjets. Trans. of the ASME, Journal of Eng. Mat&Tech, 106(1984)1[2] Hashish, M.: Pressure Effect in Abrasive – Waterjet (AWJ) Machining. Trans. of the ASME, Journal of Eng. Mat&Tech., 106(1984)7[3] Guo, N. S.: Schneidprozess und Schnittqualität beim Was-serabrasiusstrahl – schneiden. VDI Verlag, 1994[4]  Raja, J. et al. Recent advances in separation of roughness, Waviness and Form, Precision Engineering: Journal of the International Societies for Precision Engineering and Na-notechnology 26 (2002) 222–235.[5] Chen, F., L. et al. Improving the cut surface qualities using different controlled nozzle oscillation techniques, Interna-tional Journal of Machine Tools and Manufacture 42 (2002) 717–722.[6] Lemma, E. Optimising the AWJ cutting process of ductile materials using nozzle oscillation technique, International Journal of Machine Tools and Manufacture 42 (2002) 781–789.[7] Hloch S et al. Experimental study of surface topography created by abrasive waterjet cutting. In: Strojarstvo. 49(2008)4, 303-309[8] Valíček J, Hloch S. Optical measurement of surface and topographical parameters investigation created by abrasive waterjet. In: International Journal of Surface Science and Engineering. 3(2009)4, 360-373[9] Valíček J, Hloch S. Using the acoustic sound pressure level for quality prediction of surfaces created by abrasive wate-rjet. In: The International Journal of Advanced Manufactu-ring Technology. 48(2010)1-4, 193-203[10] Valíček J, Hloch S, Kozak D. Surface geometric parame-ters proposal for the advanced control of abrasive waterjet technology. In: The International Journal of Advanced Ma-nufacturing Technology. 41(2009)3-4, 323-328[11] Brigham, E., O. The Fast Fourier Transform and its appli-cation, Prentice-Hall, Upper Saddle River, 1988.[12] Bracewell, R.N. The Fourier Transform and its Applica-tions, 3rd ed., McGraw-Hill Companies, Boston, 2000[13] Mainsah, E. et al. Metrology and Properties of Engineering Surfaces, Kluwert Academic Publishers, Dordrecht, 2001Note:  Responsible translator: Željka Rosandić, Faculty of Mechanical Engineering in Slavonski Brod, University of Osijek, Slavonski Brod, Croatia 

Analiza topografije površina titanove legure nakon rezanja vodenim mlazom pomoću spektralne analize

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