The Effect of Disc Surface Topography on the Dry Gross Fretting Wear of an Equal-Hardness Steel Pair

Experimental investigations were carried out with an Optimol SRV5 tribological tester in a flat-on-sphere scheme. The balls co-acted with the discs in a gross sliding fretting regime. The balls and discs were made from the same steel with a very similar hardness. Tests were conducted at 25–35% relative humidity, 30 °C, and a constant normal load and number of cycles (18,000). The discs had different textures after various machining treatments. It was found that the total wear level of the tribological assembly was proportional to the disc surface amplitude. The influence of the disc roughness on the coefficient of friction was evident only for the smallest stroke of 0.1 mm, and the frequency of oscillation affected this dependency.


Introduction
Fretting is the motion between two contacting parts when the sliding amplitude is small. When the amplitude of oscillation is larger than the radius of elastic contact, reciprocating sliding occurs [1]. Depending on the normal load, the following regimes can be recognized when the sliding amplitude increases: stick, partial slip and gross slip [2][3][4]. Varenberg et al. [5,6] introduced the slip index, which is a criterion to define various fretting regimes. For a low displacement amplitude, a partial slip occurs. When the sliding amplitude is higher, but smaller than a Hertzian contact radius, a gross slip takes place [7]. Fretting regimes are related to the kinds of damage; a material loss occurs in a gross slip, but cracking occurs in a partial slip. Various types of wear occur during fretting: abrasion, adhesion, oxidation and surface fatigue [8].
In fretting, wear oxide debris is formed. Wear particles can have two contrary influences on wear loss; beneficial or harmful [9,10]. Varenberg et al. [8] found that wear debris for dominant adhesion diminished, while for prevailing abrasion, it simplified material loss. Wear debris is also related to the coefficient of friction [11]. Diomidis and Mischler [12] found that an increase in the stroke caused increases in the sizes of wear particles when the fretting stroke increased. During fretting of steel elements, the created wear particles are non-cohesive and loose; therefore, they can be removed without difficulty [13].
Many variables (about 50) affect fretting wear [14,15]; a stroke, a normal force, a frequency and surface hardness seem to be the most important.
Fretting wear is proportional to the stroke [16,17]. It was found that when the amplitude of displacement increased, the friction coefficient also increased. Decreasing the normal load reduced the volumetric wear. However, increasing the contact pressure reduced the sliding amplitude, leading to operating in the partial slip regime [18]. Kalin et al. [19] performed dry fretting tests with silicon carbide against bearing steel counterparts. The wear volume increased exponentially with the amplitude.  50 45 Surface topographies of machined and worn counterparts were measured by a Talysurf CCI Lite scanning coherent interferometer (Taylor Hobson, Leicester, UK). The measured areas were 3.3 × 3.3 mm 2 , and sampling intervals in perpendicular directions were 3.2 µm. The average value of the Ra parameter of machined balls was 0.15 µm. Discs were prepared by various methods including polishing (P), lapping (L), milling (M), grinding (G) and vapour blasting (VB). Tribological tests of anisotropic disc topographies (M and G) were conducted perpendicularly to lays (main directions). The wear volume V tot of the whole tribological system was computed as Equations (1)-(3): where volumes (V disc+ ) and (V ball+ ) were buildups or materials transferred; volumes (V disc− ) and (V ball− ) were lost materials [13,32]. The wear levels of discs were assessed only after surface leveling, and a digital filtration was not used. Before the calculation of wear levels of the balls, their curvatures were eliminated using spheres. Table 2 shows selected surface topography parameters of discs before wear: the root mean square height Sq, the texture aspect ratio Str, the autocorrelation length Sal, the skewness Ssk, the kurtosis Sku and the root mean square slope Sdq [46]. Figure 1 shows contour maps of the disc surfaces. after finish milling were larger than those of discs after grinding. The roughness heights of polished P and lapped L samples were the lowest. The surfaces after milling had deterministic characters, while other surfaces had random characters. The surfaces of worn counterparts were examined by scanning electron microscope (SEM) fitted out with an energy dispersive spectrometry (EDS) analyser. Table 3 lists the results of the fretting tests. It shows the volumetric wear levels of discs and balls, and the mean and final coefficients of friction. There were 18,000 cycles, corresponding to a test duration of 15 min for the frequency of 20 Hz, and 6 min for the frequency of 50 Hz. When the  Figure 1. Contour maps of disc surfaces: after vapour blasting VB1 and VB2, after milling M1 and M2, after grinding G1 and G2, after polising P and after lapping L.

Results and Discussion
The heights (Sq) and slopes (Sdq) of isotropic (the Str parameter in the range: 0.85-0.87) vapour-blasted surfaces VB1 and VB2 were the biggest. The surface height of the sample VB2 after finish vapour blasting was smaller. Anisotropic samples after finish milling M1 and M2 had radial structures, but after grinding G1 and G2, they had one-directional structures. Amongst the anisotropic surfaces, the M1 sample was the roughest and had the largest autocorrelation length Sal. The height of the finish ground surface G2 was smaller than that of the rough ground G1 texture. The heights of the milled M2 and ground G1 samples G1 were similar. The correlation lengths of samples after finish milling were larger than those of discs after grinding. The roughness heights of polished P and The surfaces of worn counterparts were examined by scanning electron microscope (SEM) fitted out with an energy dispersive spectrometry (EDS) analyser. Table 3 lists the results of the fretting tests. It shows the volumetric wear levels of discs and balls, and the mean and final coefficients of friction. There were 18,000 cycles, corresponding to a test duration of 15 min for the frequency of 20 Hz, and 6 min for the frequency of 50 Hz. When the frequency was 20 Hz, the average value of the largest friction coefficient (COF 50-900 ) was estimated after removal of the early parts of the results (rapid growths of the coefficient of friction) before 50 s of the test, while the final value (COF 600-900 ) was assessed as the mean from the last five minutes of the test. When the frequency was set to 50 Hz, COF 50-360 characterized the mean and COF 300-360 characterized the final friction coefficient.  The maximum surface elastic contact pressure p o was calculated by Equation (4) [47]:

Results and Discussion
The radius of elastic contact length a was computed by the following Equations (5) and (6) [47]: where: When the normal force was 45 N, the Hertzian radius of contact a was 0.114 mm; it was higher than the largest amplitude of oscillation (0.1 mm), and therefore fretting occurred. In this case, the maximum elastic contact pressure p 0 was 1652 MPa.
The variation of the friction coefficient was typically not higher than 0.03. Scatters of total volumetric wear were usually not higher than 14% for assemblies with the same disc samples. Table 3 lists the results of experimental investigations.
In test A, the wear of the discs was typically higher than the wear of the balls, but the sliding pair with the roughest disc sample VB1 was the exception. The final friction coefficient COF 600-900 was similar for various assemblies; however, the average friction coefficient COF 50-900 was the smallest for the sliding pair containing the polished disc P of the lowest roughness height. The friction coefficient initially increased and then obtained a stable value typically after 15,000 cycles ( Figure 2a). The total volumetric wear level was proportional to the disc surface height determined by the Sq parameter; the coefficient of linear correlation was 0.95 ( Figure 3a). 2b). The smallest friction coefficient was achieved for the assembly containing the disc after lapping L, while the highest coefficient was acheived for sliding pairs with discs after polishing P, milling M1, and grinding G2. A decrease in the amplitude of oscillation from 0.1 (test A) to 0.075 mm caused a reduction in volumetric wear, but had a marginal effect on the coefficient of friction. Total wear was proportional to the standard deviation of the disc height; the linear coefficient of correlation was 0.85 ( Figure 3b).  Figure 4 shows the runs of the maximum coefficients of friction during tests C for sliding pairs containing all selected discs. The shapes of the presented curves are similar to those obtained in tests A and B. In all analysed cases, the wear levels of the balls were much lower than the wear levels of the discs. Similar to the assemblies analysed, the previous wear of the system was proportional to the disc roughness height (Figure 5a). The average coefficients of friction were higher for bigger disc topography heights (Figure 5b). The roughest disc sample VB1 led to the highest total wear level and  In test B, for the sliding pair containing disc VB1, the wear rate of the disc was lower than that of the ball. For different sliding pairs, the opposed situation was observed. The wear of the balls was inversely proportional to the wear of the discs. Similarly to test A, the friction coefficient after initial sharp growth, increased slowly and obtained a stable value in most cases after 15,000 cycles (Figure 2b). The smallest friction coefficient was achieved for the assembly containing the disc after lapping L, while the highest coefficient was acheived for sliding pairs with discs after polishing P, milling M1, and grinding G2. A decrease in the amplitude of oscillation from 0.1 (test A) to 0.075 mm caused a reduction in volumetric wear, but had a marginal effect on the coefficient of friction. Total wear was proportional to the standard deviation of the disc height; the linear coefficient of correlation was 0.85 ( Figure 3b). Figure 4 shows the runs of the maximum coefficients of friction during tests C for sliding pairs containing all selected discs. The shapes of the presented curves are similar to those obtained in tests A and B. In all analysed cases, the wear levels of the balls were much lower than the wear levels of the discs. Similar to the assemblies analysed, the previous wear of the system was proportional to the disc roughness height (Figure 5a). The average coefficients of friction were higher for bigger disc topography heights (Figure 5b). The roughest disc sample VB1 led to the highest total wear level and the average friction coefficient COF     In test D, contrary to the results analysed previously, the average wear rates of the balls were similar to those of the discs. The assembly with the roughest disc VB1 led to the biggest, while the smoothest disc P, led to the smallest wear volume of the tribological system. The wear of the balls and the total wear were proportional to the disc roughness height. The highest coefficient of friction was obtained for the roughest sample VB1, while the smallest was obtained for sample M2 after milling. The friction forces increased during tests and obtained steady values typically after 9000 cycles (Figure 6a). A reduction in the contact pressure for the same frequency of oscillations (test C) caused a slight wear decrease and growth in the friction coefficient.  In test E, the wear of the balls was typically lower than the wear of the discs, but assemblies with VB1 and G1 discs were the exceptions. Similar to other tests, the volumetric wear was proportional to the disc roughness height. The total wear of the sliding pair with the roughest disc sample VB1 was the biggest, but with the smoothest disc P, it was the lowest. The wear of the balls was inversely related to the wear of the discs. The highest mean friction coefficient was obtained for the sliding pair with the polished sample of the smallest height P, while the smallest was obtained for the assemblies with ground samples G1 and G2. It is interesting that the M2 sample after milling led to comparatively high frictional resistance, contrary to test D carried out at the same load and smaller frequency of oscillation. Similar to test D, the friction coefficient after early fluctuations typically obtained stable values after 9000 cycles (Figure 6b). A growth in the frequency of oscillations for the same load of 15 N (test D) caused wear reduction and growth in the friction coefficient. smoothest disc P, led to the smallest wear volume of the tribological system. The wear of the balls and the total wear were proportional to the disc roughness height. The highest coefficient of friction was obtained for the roughest sample VB1, while the smallest was obtained for sample M2 after milling. The friction forces increased during tests and obtained steady values typically after 9000 cycles (Figure 6a). A reduction in the contact pressure for the same frequency of oscillations (test C) caused a slight wear decrease and growth in the friction coefficient. In test E, the wear of the balls was typically lower than the wear of the discs, but assemblies with VB1 and G1 discs were the exceptions. Similar to other tests, the volumetric wear was proportional to the disc roughness height. The total wear of the sliding pair with the roughest disc sample VB1 was the biggest, but with the smoothest disc P, it was the lowest. The wear of the balls was inversely related to the wear of the discs. The highest mean friction coefficient was obtained for the sliding pair with the polished sample of the smallest height P, while the smallest was obtained for the assemblies with ground samples G1 and G2. It is interesting that the M2 sample after milling led to comparatively high frictional resistance, contrary to test D carried out at the same load and smaller frequency of oscillation. Similar to test D, the friction coefficient after early fluctuations typically In test F, except for assembly with the vapour-blasted VB1 sample, the wear rates of the discs were larger than the wear rates of the balls. The wear of the balls was inversely proportional to the wear of the discs. In most cases, the negative wear levels of the balls were obtained, which means that build-ups or material transfers were formed. The total wear level of the assembly with the roughest VB1 sample after vapour blasting was the largest, but with the smoothest P sample after polishing, it was the smallest. As a result, the total wear and wear rates of the balls were proportional to the Sq parameter of the disc textures. It is also interesting that the roughest disc sample VB1 yielded the smallest coefficient of friction from all analysed assemblies. In this case, the scatter of the average friction coefficient did not coincide with scatters corresponding to the other sliding pairs, except for the assembly containing the milled M1 specimen. Disc sample M2 after milling led to the highest mean friction coefficient. Figure 7 presents values of the maximum friction coefficient runs for sliding pairs with all and chosen discs in test F. The coefficient of friction after initial abrupt growth was stable between 2000 and 7000 cycles and then increased as the test progressed. The results presented in Figure 7b (the lowest friction coefficient of the assembly with VB1 disc) are different from those shown in Figure 4b obtained for the same normal load and smaller frequency of oscillations (test C). However, the change in the frequency for the same normal load caused a marginal change in total wear volume.
An increase in the normal load for the same frequency of oscillations (test E) led to wear growth and a reduction in the coefficient of friction. the assembly containing the milled M1 specimen. Disc sample M2 after milling led to the highest mean friction coefficient. Figure 7 presents values of the maximum friction coefficient runs for sliding pairs with all and chosen discs in test F. The coefficient of friction after initial abrupt growth was stable between 2000 and 7000 cycles and then increased as the test progressed. The results presented in Figure 7b (the lowest friction coefficient of the assembly with VB1 disc) are different from those shown in Figure 4b obtained for the same normal load and smaller frequency of oscillations (test C). However, the change in the frequency for the same normal load caused a marginal change in total wear volume. An increase in the normal load for the same frequency of oscillations (test E) led to wear growth and a reduction in the coefficient of friction.  Figure 8 shows fretting loops for the sliding pair with a lapped L disc. One can observe changes in the relative displacements without changes in the coefficients of friction during the analysis of the fretting loops corresponding to tests A, B, C. After comparing fretting loops obtained after tests C and D, as well as F and E, it is evident that a reduction in the load led to growth in the friction coefficient and a change in the loop shape corresponding to a higher value of the slip index. An increase in the frequency from 20 (tests A, B, C and D) to 50 Hz (tests E and F) led to changes in fretting loop shapes (smaller stability of the coefficient of friction at a higher frequency). Figure 8 shows fretting loops for the sliding pair with a lapped L disc. One can observe changes in the relative displacements without changes in the coefficients of friction during the analysis of the fretting loops corresponding to tests A, B, C. After comparing fretting loops obtained after tests C and D, as well as F and E, it is evident that a reduction in the load led to growth in the friction coefficient and a change in the loop shape corresponding to a higher value of the slip index. An increase in the frequency from 20 (tests A, B, C and D) to 50 Hz (tests E and F) led to changes in fretting loop shapes (smaller stability of the coefficient of friction at a higher frequency).  Figures 9 and 10 show contour maps of vapour-blasted VB1 and polished P discs and contacted balls, respectively, after various tests. It is evident that smaller volumetric wear occurred for the sliding pair containing the P disc compared to the VB1 disc. For assembly with VB1, the disc wear of  Figures 9 and 10 show contour maps of vapour-blasted VB1 and polished P discs and contacted balls, respectively, after various tests. It is evident that smaller volumetric wear occurred for the sliding pair containing the P disc compared to the VB1 disc. For assembly with VB1, the disc wear of the disc was typically lower than the wear of the ball, contrary to the assembly with the P disc. Wear of co-acting pairs had an abrasive-adhesive character. Plastic deformation also occurred on the vapour-blasted VB1 disc surface. the disc was typically lower than the wear of the ball, contrary to the assembly with the P disc. Wear of co-acting pairs had an abrasive-adhesive character. Plastic deformation also occurred on the vapour-blasted VB1 disc surface.  The influence of the disc surface texture on the frictional resistance was evident mainly at the lowest amplitude of motion (0.05 mm), when wear of the disc was comparatively low. The effect of the disc surface texture on the friction coefficient depended on the frequency of oscillation. For the normal force of 45 N and the frequency of 20 Hz (test C), the highest disc roughness (VB1 sample) The influence of the disc surface texture on the frictional resistance was evident mainly at the lowest amplitude of motion (0.05 mm), when wear of the disc was comparatively low. The effect of the disc surface texture on the friction coefficient depended on the frequency of oscillation. For the normal force of 45 N and the frequency of 20 Hz (test C), the highest disc roughness (VB1 sample) led to the largest mean coefficient of friction; however, the opposed tendency occurred for the same load and the frequency of 50 Hz (test F). For the lower normal force of 15 N, a similar effect of frequency on friction force was not as apparent; however, in test E (frequency of 50 Hz), the highest mean friction coefficient was obtained for the assembly containing the disc P with the smallest height.
The total wear rate was proportional to the height of the disc surface, determined by the value of the Sq parameter, independently of the operating conditions. In tests A, C, D, E and F, the total wear of assembly with the roughest vapour-blasted VB1 sample was the highest, it was the smallest with the smoothest polished specimen P. This performance probably resulted from the fact that rougher surfaces, of higher plasticity indices [48,49], have a larger tendency to plastic deformation and hence wear. Tracks of the plastic deformation were found on the VB1 disc surface after tribological tests ( Figure 9). The wear level of balls was typically smaller than of discs, but the assembly with the roughest VB1 disc was the exception.
Previously, experiments were conducted using the same tester [50]. Steel balls made of 100Cr6 steel of 60 HRC hardness contacted discs of various surface topographies made of 42CrMo4 steel of 40 HRC hardness under the same conditions as in the tests A, B, C. In the previous tests the resistance to motion was the smallest when the movement of the ball was orthogonal to the main direction of the finished milled disc surface. These results were probably related to formation of the layer of oxidized wear particles on the disc surface and the smaller wear of discs compared to the wear of balls. However, in the present tests, this effect disappeared. Oxidised abrasive particles were embedded into both counterparts (Figures 11 and 12). A low coefficient of friction of assembly with the milled disc surface M2 was achieved only in test D. An increase in hardness of the disc compared to the results presented in [50] led to a smaller role of the oxidized debris layer, and hence, smaller wear of the tribological system and typically smaller wear of the balls compared to that of discs. A decrease in total wear of a sliding pair due to a decrease in hardness differences was found in the other works [14,31]. led to the largest mean coefficient of friction; however, the opposed tendency occurred for the same load and the frequency of 50 Hz (test F). For the lower normal force of 15 N, a similar effect of frequency on friction force was not as apparent; however, in test E (frequency of 50 Hz), the highest mean friction coefficient was obtained for the assembly containing the disc P with the smallest height. The total wear rate was proportional to the height of the disc surface, determined by the value of the Sq parameter, independently of the operating conditions. In tests A, C, D, E and F, the total wear of assembly with the roughest vapour-blasted VB1 sample was the highest, it was the smallest with the smoothest polished specimen P. This performance probably resulted from the fact that rougher surfaces, of higher plasticity indices [48,49], have a larger tendency to plastic deformation and hence wear. Tracks of the plastic deformation were found on the VB1 disc surface after tribological tests (Figure 9). The wear level of balls was typically smaller than of discs, but the assembly with the roughest VB1 disc was the exception.
Previously, experiments were conducted using the same tester [50]. Steel balls made of 100Cr6 steel of 60 HRC hardness contacted discs of various surface topographies made of 42CrMo4 steel of 40 HRC hardness under the same conditions as in the tests A, B, C. In the previous tests the resistance to motion was the smallest when the movement of the ball was orthogonal to the main direction of the finished milled disc surface. These results were probably related to formation of the layer of oxidized wear particles on the disc surface and the smaller wear of discs compared to the wear of balls. However, in the present tests, this effect disappeared. Oxidised abrasive particles were embedded into both counterparts (Figures 11 and 12). A low coefficient of friction of assembly with the milled disc surface M2 was achieved only in test D. An increase in hardness of the disc compared to the results presented in [50] led to a smaller role of the oxidized debris layer, and hence, smaller wear of the tribological system and typically smaller wear of the balls compared to that of discs. A decrease in total wear of a sliding pair due to a decrease in hardness differences was found in the other works [14,31]  A decrease in the stroke led to wear reduction. A reduction in the contact pressure led to growth in the friction coefficient and a reduction in the wear volume. An increase in the frequency of oscillation led to an increase in the coefficient of friction and a reduction in volumetric wear only when a lower normal force was applied (15 N). Similar results were obtained for different hardness of counterparts [51]. A decrease in the stroke led to wear reduction. A reduction in the contact pressure led to growth in the friction coefficient and a reduction in the wear volume. An increase in the frequency of oscillation led to an increase in the coefficient of friction and a reduction in volumetric wear only when a lower normal force was applied (15 N). Similar results were obtained for different hardness of counterparts [51].

Conclusions
For equal-hardness pairs, the wear of the disc was typically higher than that of the ball. Total wear of the tribological system was proportional to the disc roughness height. The influence of the disc surface texture on the friction coefficient was substantial only for the smallest stroke of 0.1 mm. The frequency of oscillation had an effect on this dependence. For the normal load of 45 N and the frequency of 20 Hz, the highest disc roughness corresponded to the largest mean coefficient of friction; however, after increasing the frequency to 50 Hz, the biggest disc amplitude led to the smallest frictional resistance.
A reduction in the amplitude of oscillation decreased wear but had marginal influence on the coefficient of friction. The friction coefficient increased and total wear decreased due to a reduction in the normal load. When the frequency increased, wear decreased and the friction coefficient increased. These effects were visible only when a lower normal load was applied.