MODELLING OF CHANGES IN SURFACE TOPOGRAPHY IN DRY SLIDING CONDITIONS

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1 T R I B O L O G I A 61 Andrzej DZIERWA *, Rafał REIZER ** MODELLING OF CHANGES IN SURFACE TOPOGRAPHY IN DRY SLIDING CONDITIONS MODELOWANIE ZMIAN STRUKTURY GEOMETRYCZNEJ POWIERZCHNI W WARUNKACH TARCIA SUCHEGO Key words: surface topography, modelling, wear, friction force Słowa kluczowe: struktura geometryczna powierzchni, modelowanie, zużycie, siła tarcia Abstract Metrology of surface topography is presently so developed that, in some ways, we can predict the surface behaviour of the one part in co-operation with another element. We can single out two main approaches to the modelling of surface texture. In the first one, the modelling does not take into account the conditions of the technological or operational formation of the surface, while in the second, more complicated approach, modelling takes into account the real conditions of forming the surface. In this work, tribological tests were carried out in dry sliding conditions, and the analytical methodology of wear * ** Rzeszow University of Technology, Department of Manufacturing and Engineering, al. Powstańców Warszawy 8, Rzeszów, Poland, tel. (17) , adktmiop@prz.edu.pl. University of Rzeszow, Centre for Innovative Technologies, Faculty of Mathematics and Natural Sciences, ul. Rejtana 16C, Rzeszów, Poland, tel. (17) , rreizer@ur.edu.pl.

2 62 T R I B O L O G I A determination in such conditions was worked out, and the results obtained using these two methods were compared. Tribological tests were conducted using a T-11 pin-on-disc tester (with ball-on-disc configuration) according to ASTM G 99 standard. A steel disc of hardness 40 HRC (made from 42CrMo4 steel) was put in contact with a ball of 6.35 mm diameter. The hardness of bearing ball was 62±2 HRC. The rotating speed of the discs was 300 [rpm]. The finishing treatments of the discs were the processes of grinding, polishing, milling, and slide burnishing. Finishing treatment of all surfaces was prepared in other to obtain the value of Sa parameter lower than 0.5 µm. A parallel, analytical procedure for the determination of the wear value of surface topography was worked out and the results obtained using the procedures were compared with the results of experimental studies. INTRODUCTION Changes in elements of mechanisms, caused by friction forces and physicochemical phenomena, are defined as a wear. Since the wear usually leads to a reduction in functionality and machine life, it should be prevented. It is aimed at elimination or minimization of the wear effects. Counteraction should start at the design stage. Then we are able to select such forms of tribological sets like materials and lubrication in order to minimize wear during operation. Apart from the structural prevention of wear, there is also a technological way to prevent it. These can be achieved by using the following [L. 1 3]: Heat treatment (surface hardening); Thermochemical treatment (e.g., nitrogen hardening, carburizing, cyaniding, chromizing); Plastic forming (e.g., hammering, burnishing); or, Coatings (e.g., chemical nickel plating, phosphating). Surface topography plays an important role in this case. It has an impact on many functional properties, such as fatigue strength, wear resistance, corrosion resistance, resistance to flow, and impermeability [L. 4]. At present, engineers have many tools for the assessment and simulation such relationships mainly 2D and 3D parameters of surface roughness (according to ISO and ISO 4278 standard). Surface topography modelling is a field of surface engineering with high development perspective. One can single out two basic approaches to modelling of surface topography [L. 5]. In the first one, the modelling does not take into account the conditions of the technological or operational formation of the surface. In the second approach, which is a more complicated approach, modelling takes into account the real conditions of forming the surface [L. 6 7]. The second approach provides the ability to analyse the effect of the technological and operational forming conditions on the surface topography of machines. An example of this approach is the modelling of a machined surface

3 T R I B O L O G I A 63 or worn surface. Approximations obtained using the second approach are usually worse than those using the first method [L. 8 10]. In the presented work, tribological tests in dry sliding conditions were carried out, and a numerical model to determine the cross-sectional area of wear in presented conditions was produced, and the results obtained using modelling and experimental tests were compared. EXPERIMENTAL Tribological tests were conducted using a T-11 pin-on-disc tester (with ball-ondisc configuration) according to ASTM G 99 standard. A steel disc of hardness 40 HRC (made from 42CrMo4 steel) was put in contact with a ball of 6.35 mm diameter. The hardness of ball bearing was 62±2 HRC. Rotating speed of the discs was 300 [rpm]. Finishing treatment of the discs were processes of grinding, polishing, milling, and various kinds of slide burnishing (burnishing element was made from Al 2 O 3 or 100Cr6). The sliding burnishing process was made in order to obtain similar values of the Sa parameter (arithmetical mean height of the surface), but different values remained of other surface topography parameters. Finishing treatment of all surfaces was made in other to obtain the value of Sa parameter lower than 0,5 µm. The sliding distance of all samples was m (test duration was 30 min), and the sliding diameter was 10 mm. Dry sliding tests were done at a sliding speed of m/s and a normal load of 9.81 N. All tests were repeated at least 3 times. During the tests, the friction force was monitored as a function of time. The wear of disc was determined after the dry sliding tests by means of surface topography analysis, using white light interferometer Talysurf CCI Lite with vertical resolution 0.01 nm. The measuring area (3.3 mm x 3.3 mm) contained 1024 x 1024 points. The profiles were perpendicularly taken to the wear track in four positions, 90 0 apart. Then, using the interferometer software (TalyMap Gold 6.0) the resulting records were computed and averaged. In the next step, the wear volumes of the disc samples were calculated according to the formula (1). Table 1 presents selected surface topography parameters of the tested samples [L. 11]. V 3 = m d S [ mm ] (1) where: d diameter of the wear track [mm], S cross-sectional area of wear [mm 2 ]. Then numerical model to calculate a cross-sectional area of disc wear and, consequently, to calculate the volumetric wear was devised. The simplified algorithm for the proposed model is presented in Fig. 1.

4 64 T R I B O L O G I A Table 1. Selected surface topography parameters of tested samples Tabela 1. Wybrane parametry SGP wybranych powierzchni Finishing treatment Parameter Sa [µm] Str Ssk Sal [mm] grinding polishing milling burnishing K1 (ball Al 2 O 3 ) burnishing K2 (ball 100Cr6) burnishing H1 (ball Al 2 O 3 ) burnishing H2 (ball 100Cr6) START Load: Profile of raw surface dedicated to investigation pp Pq parameter of ball surface Pq b Correlation length of the profile of ball surface KL b Depth of cross-sectional area of wear H Generate the shape of ball pb Generate the roughness profile pv bs = pv + pb If pp bs Y Iteration repeated for all profile ordinates pp and bs N pw = pp pw = bs STOP Fig. 1. Flowchart of worn profile modelling Rys. 1. Uproszczony algorytm modelowania profilu zużycia

5 T R I B O L O G I A 65 The shape of the ball pb is generated up to the height of the chord. Roughness profile pv is generated based on parameters Pq b and KL b, according to the algorithm described in [L. 12]. Its basic assumptions are as follows: In a first step, the shape of autocorrelation function of modelled profile is generated, based on the input parameters Rq and β (correlation length) using equation (2): where: k = 1, 2, k ( k) = Rq 3 R z exp (2) β In the next step, Power Spectral Density (Sz) function is computed based on the autocorrelation shape. Finally, a profile with desired Rq and β parameters is generated using equation (3): z t n = = 1 kt S z exp i2π φ k + k = 0 n (3) where: t=0, 1, 2,..., (n-1), n = 1, 2, 3,..., φ k set of independent random phases uniformly distributed between 0 and 2 φ k and φ k =-φ N-k ; φ 0 =φ N/2 =0. The shape of ball pb and roughness profile pv are added together. Then, these results are applied to the profile of raw surface pp for investigation. In the next step, separate ordinates (i) are compared. If bs (i) pp (i) then ordinates of resulting profile pw (i) = bs (i), and if bs (i) > pp (i), then the ordinates of resulting profile pw (i) = pp (i). The modelling process of roughness profiles was developed using MATLAB software. The results of the calculation of volumetric wear obtained by modelling the cross-sectional area of wear were compared to experimental results.

6 66 T R I B O L O G I A RESULTS AND DISCUSSION Table 2 presents the results of the investigations. For each surface type, the mean values of the wear volume of the disc samples VD, estimated distance to steady value of friction force (DSS), and average value of friction force after obtained steady-state condition F av, are presented. Table 2. Results of tribological tests Tabela 2. Wyniki badań tribologicznych Finishing treatment V [mm 3 ] Measured value DSS [m] F av [N] grinding polishing milling burnishing K1 (ball Al 2 O 3 ) burnishing K2 (ball 100Cr6) burnishing H1 (ball Al 2 O 3 ) burnishing H2 (ball 100Cr6) The largest volumetric wear was observed for the sample H2. It was m 3. It corresponded to the highest average value of the friction force after tests F av. 8.9 N. The sliding distance to obtain steady-state conditions was 8.5 m. As can be seen from Table 2, the shortest way to achieve a stable value of the friction force was obtained for the polished and burnished H1 samples. It was 7.8 and 7.9 m, respectively. The lowest value of wear volume was obtained in the case of the milled sample, and it was mm 3. This sample was also characterized by the lowest average value of the friction force F av = 7.2 N and the longest distance (26.3 m), to obtain steady state condition DSS. The differences in the value of wear volume between samples with the smallest and the largest wear was evident, and it was over 300%. In the case of average value of the friction force, the spread of results was between 7.2 N (milled sample) and 8.9 N (burnished sample H2. The wear of the investigated surfaces under dry sliding contact was dominated by plastic deformation and abrasive wear. Table 3 presents a comparison of the measured wear volumes after tribological tests and wear volumes obtained based on the presented numerical model. Table 3 also shows the percentage differences between obtained values of volumetric wear. Figure 2 presents selected worn surface profiles obtained for burnished sample K2. Figure 2a shows the cross-sectional area of wear measured after the tribological tests, while Figure 2b shows the cross-sectional area of wear obtained by modelling in accordance with the procedure shown on Fig. 1.

7 T R I B O L O G I A 67 Figure 2 presents the values of the surface roughness (according to [L. 13]) for both variants. a) Rp = 4.31 [µm] Rv = 3.48 [µm] Rz = 7.79 [µm] Rc = 4.53 [µm] Rt = 10.4 [µm] Ra = 1.32 [µm] Rq = 1.73 [µm] Rsk = Rku = 4.02 b) Rp = 3.34 [µm] Rv = 3.80 [µm] Rz = 7.14 [µm] Rc = 7.25 [µm] Rt = 9.0 [µm] Ra = 1.19 [µm] Rq = 1.57 [µm] Rsk = Rku = 3.12 Fig. 2. Cross-sectional area of worn profile of burnished sample K2, (a) measured profile, (b) modelled profile Rys. 2. Pole powierzchni zużytej próbki nagniatanej K2, a) profil zmierzony, b) profil zamodelowany Analysing the obtained results, one can see the high similarity of the values of wear volume in the case of burnished samples K1, K2, H1, and the milled sample. In these conditions, the differences in wear volumes after tribological

8 68 T R I B O L O G I A tests and the modelled wear volumes was 9.4%. Differences in other variants were less than 15%. Table 3. Wear volume comparison of experiment and model Tabela 3. Zużycie objętościowe porównanie eksperymentu z modelem Finishing treatment V zm [mm 3 ] Measured value V mod [mm 3 ] Difference [%] grinding polishing milling burnishing K1 (ball Al 2 O 3 ) burnishing K2 (ball 100Cr6) burnishing H1 (ball Al 2 O 3 ) burnishing H2 (ball 100Cr6) It is noticeable that the differences smaller than 9% concerned in samples where the value of Sa parameter was between mm. Larger differences were found in samples with a surface roughness slightly higher, as in the case of burnished sample H2 and ground sample as well as in the case of the smoothest surface (polished), where the Sa parameter amounted to µm. Moreover, surface roughness parameters were subjected to comparative evaluation. The greatest similarity was obtained for such parameters as Rv maximum valley depth of the roughness profile, Rz maximum height of the roughness profile, Ra arithmetic mean deviation of the roughness profile, and Rq root mean square deviation of the roughness profile. For these parameters, the absolute error between the surface roughness obtained after tribological tests and the surface roughness obtained by modelling did not exceed 9%. On the other hand, differences between such parameters as Rp, Rt, and Rc were up to 20-25%. CONCLUSIONS Due to the ability to process a simulation of machining, friction, and wear, the role of surface topography modelling is constantly increasing. The application of the original algorithm for modelling the roughness profile of a wear surface allowed us to model the volumetric wear and compare the results to the volumetric wear obtained after tribological tests, and we found that the differences were not more than 9% (for 4 variants) and not more than 15% for the other variants. Anisotropic samples (Str<0.2) with an arithmetical mean height of the surface smaller than 0.5 µm were used in the tests. Especially beneficial results of modelling were obtained in the range of the Sa parameter between µm.

9 T R I B O L O G I A 69 In the case of surface roughness parameters, a high similarity between parameters obtained after tribological tests and those obtained by modelling were observed for parameters like Ra, Rq, Rv, and Rm; however, the similarities were lower for parameters like Rp, Rt, and Rc. Undoubtedly, further research should focus on reducing the errors of these parameters. REFERENCES 1. Blicharski M., Inżynieria powierzchni, WNT, Warszawa Lawrowski Z., Tribologia, Tarcie zużywanie smarowanie, Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław Dzierwa A., Charakterystyka właściwości tribologicznych stali 36NiCrMo16 po procesie kulowania, Mechanik nr 11, 2014, Grzesik W., Wpływ topografii powierzchni na właściwości eksploatacyjne części maszyn, Mechanik, nr 8 9, 2015, Reizer R., Pawlus P., Przegląd metod modelowania struktury geometrycznej powierzchni, Zeszyty naukowe Politechniki Rzeszowskiej, nr 278, seria Mechanika z. 82, Uchidate M., Yanagi K., Yoshida I., Shimizu T., Iwabuchi A., Generation of 3-D random topography datasets with periodic boundaries for surface metrology algorithms and measurement standards, Proceedings of the 12th Conference on Metrology and Properties of Engineering Surfaces, Rzeszów 2009, Wu J.-J., Simulation of non-gaussian surfaces with FFT, Tribology International, 27, 2004, Pawlus P., Reizer R., Dzierwa A., Surface topography of chromium coatings after pneumatic ball peening, Key Engineering Materials, , 2008, Reizer R., Pawlus P., Galda L., Grabon W., Dzierwa A., Modeling of worn surface topography formed in a low wear process, Wear, , 2012, Fang L., Cen Q., Sun K., Liu W., Zhang X., Huang Z., FEM computation of groove ridge and Monte Carlo simulation in two-body abrasive wear, Wear, 258, 2005, PN-EN ISO :2012 Specyfikacje geometrii wyrobów (GPS) Struktura geometryczna powierzchni: Przestrzenna Część 2: Terminy, definicje i parametry struktury geometrycznej powierzchni. 12. Wu J.-J., Simulation of rough surfaces with FFT, Tribology International, 33, 2000, PN-EN ISO 4287:1999 Specyfikacje geometrii wyrobów Struktura geometryczna powierzchni: metoda profilowa Terminy, definicje i parametry struktury geometrycznej powierzchni. Streszczenie Metrologia stereometrycznych cech powierzchni jest już na tyle rozwinięta, że w pewnym stopniu można przewidzieć zachowanie się powierzchni danej części we współpracy z innym elementem oraz stopień spełnienia przez nią założonych funkcji podczas eksploatacji. Można wyodrębnić dwa zasadni-

10 70 T R I B O L O G I A cze podejścia do modelowania struktury geometrycznej powierzchni. Pierwszym z nich jest modelowanie nieuwzględniające warunków technologicznego lub eksploatacyjnego kształtowania powierzchni. Natomiast drugim, bardziej skomplikowanym podejściem, jest modelowanie odzwierciedlające rzeczywiste warunki tworzenia powierzchni. W prezentowanej pracy przeprowadzono badania tribologiczne w warunkach tarcia suchego, opracowano analityczną metodykę określania zużycia w takich warunkach oraz porównano wyniki otrzymane oboma metodami. Badania tribologiczne przeprowadzono na testerze tribologicznym T-11 zgodnie ze standardem określonym w normie ASTM G 99. Skojarzenie tribologiczne stanowiła nieruchoma kulka łożyskowa o twardości 62±2 HRC i tarcza obracająca się z zadaną prędkością obrotową równą 300 obr./min. Tarcze wykonane zostały ze stali 42CrMo4 o twardości 40±2HRC. Obciążenie podczas testów wynosiło 10 N. Obróbką wykańczającą tarcz były różne rodzaje obróbki wykańczającej (szlifowanie, frezowanie, docieranie, polerowanie, nagniatanie ślizgowe), przy czym w każdym z wymienionych przypadków średnie arytmetyczne odchylenie nierówności powierzchni Sa było niższe niż 0,5 µm. Równolegle opracowano analityczną procedurę określania wielkości zmian struktury geometrycznej powierzchni na skutek tacia i porównano otrzymane z niej wyniki z wynikami otrzymanymi z badań eksperymentalnych.