Correlation between roughness, film thickness, and friction coefficient with pitting wear resistance of spur gears

This research aims to examine the relationship between roughness, film thickness, and friction coefficient in relation to pitting wear resistance during the rolling-sliding contact fatigue of forged and plasma-nitrided gears. In the present work, forged gears in continuous cooling bainitic steel were manufactured and plasma nitrided with three sets of N2-H2 gas mixtures, containing 5 vol%, 24 vol%, and 76 vol% N2. The present investigation evaluated the contact analysis between gears from the macroscopic point of view and the microscopic. At the same time, the evolution of roughness and pitting damage area after each test stage was monitored. The study determined the stress field after each loading cycle and correlated the regions of higher stresses with surface and sub-surface fatigue. Weibull’s statistical approach showed that nitrided gears with 24 vol% N2 exhibit the most reduced pitting wear rates among the gears tested. This outcome is attributed to the optimal balance of surface hardness, fracture toughness, compound layer depth, and surface phases. The most pitting damage occurred in the dedendum and pitch line regions, being the regions that reported the greatest Hertz contact pressure. This is due to the rolling direction being opposed to the friction force in the dedendum region. This paper shows that pitting wear intensifies with increasing roughness, but this same behavior was not observed between the wear evolution and the maximum shear stress field in the sub-surface. Another interesting fact is that nitrided gears with 24 vol% N2 (best condition) have a greater film thickness at the end of the rolling-sliding contact fatigue, which gives it greater protection, less friction, and pitting wear. In general, the cracks were observed in areas very close to the surface and, with the course of the propagation stage, reached the surface, causing the formation of damage by pitting or spalling.


Introduction
Thermomechanical processing using continuous cooling after forging is an established method for producing bainitic steels, mainly because of the elimination of energy-intensive additional heat treatment processes [1][2][3][4].Thermomechanical processing of low-carbon bainitic steels is used to obtain a bainitic microstructure with good mechanical strength and toughness by continuous cooling after forging without the need of further heat treating, thus reducing manufacturing costs [1,5,6].However, hot forging parameters can significantly influence the microstructure in the forged material [3][4][5]7].The cooling is usually employed in an uncontrolled manner in the industrial sector, which can be detrimental to the resulting microstructural morphology and, consequently, the component properties [1,3,6,8].
Plasma nitriding is a thermochemical treatment applied mainly to iron alloys to improve wear resistance [3,[9][10][11][12].The nitrided phases formed during the plasma nitriding process to obtain the mechanical strength and hardness of the compound layer and diffusion zone are highly impacted by the steel microstructure, and mainly the plasma nitriding parameters such as times, temperatures, and gas mixture compositions [3,[11][12][13][14][15].The compound layer provides an extremely hard surface as required in gears normally working at high speed [3].These applications require teeth with high root and flank stiffness to improve bending fatigue and low friction, the conditions to enable smooth running and wear resistance [9,10].The relatively low-temperature process prevents dimensional distortion, eliminating postmachining work [9,10,13].Furthermore, the precise control of the compound layer properties makes the plasma nitriding process a valuable technique for these applications [3,11,12].
The surface finishing has a strong influence on the gear life [16,17], as roughness behaves as a stress concentration factor for crack initiation [18][19][20][21]; therefore, it is important to take it into consideration when analyzing the gear flank wear.The pitting wear resistance of rolling-sliding contacts depends on different factors [9,[22][23][24], such as stress and elastoplastic strain, material properties, physicochemical properties of lubricant, surface roughness, residual stress, and contact kinematics.The surface cracks could be initiated near the deformed surface zone, in the region of maximum cyclic shear stress caused by rolling-sliding contact fatigue [25][26][27].The crack propagation can result in damage by pitting and/or spalling [3,[28][29][30][31].
The friction force causes changes in the stress field generated by the contact between bodies, thus exerting a great influence on the pitting damage due to rolling-sliding contact fatigue [25,26,32].Lubrication is aimed at introducing a low-shear strength film [33], which ends up weakening the resistance of these joints, thus reducing friction [33].Therefore, the use of lubricants will reduce the wear rate [34], and this will be a direct function of the type of lubrication [25,33,35].The roughness obtained after the manufacturing process [36,37] can be considered a determining factor in the performance of gears [17,21,38], as it causes punctual stresses to be changed and also influences the form of lubrication as the thickness changes of the lubricating film [23][24][25].This paper comprehends the global observation of contact stress level [19,25], tooth profile type [39], relative contact speed [25,32], roughness [19,20], and lubrication conditions [34,35,40] and aims to monitor all these factors during rollingsliding contact fatigue.
In the previous paper [3], the use of bainitic steel for forged gear applications and the suitability of different plasma nitriding treatments have been evaluated under lubricated rolling-sliding and pitting wear conditions.Forged gears were characterized before and after the nitriding, concerning the phase composition, microstructure, microhardness, fracture toughness, and residual stress states.Experimental results indicated that the wear resistance of DIN 18MnCrSiMo6-4 bainitic steel, especially pitting wear resistance, can be greatly improved by means of controlled forging and plasma nitriding.The improved pitting wear resistance of nitrided steel was attributed to the combination of high surface hardness, the compound layer microstructure, fracture toughness of the compound layer, and high compressive stresses in the diffusion zone.
The present investigation aims to examine the relationship between roughness, film thickness, and friction coefficient in relation to pitting wear resistance during the rolling-sliding contact fatigue of forged and plasma-nitrided gears.The present work evaluated the contact analysis between gears from the macroscopic and microscopic points of view.At the same time, the evolution of roughness and pitting damage area after each test stage was monitored.The study determined the stress field after each loading cycle and correlated the regions of higher stresses with surface and sub-surface fatigue.This paper shows that pitting wear intensifies with increasing roughness, and that the cracks occur in areas very close to the surface, but with the course of the propagation stage, reach the surface, causing the formation of damage by pitting or spalling.

Gear materials
The material used in the manufacturing of pinion gears was a low-carbon continuous cooling bainitic steel (0.19% C, 1.35% Mn, 1.14% Cr, 1.16% Si, 0.26% Mo, and 0.06% Ni), manufactured by Steel Tech in Switzerland.The forged material's mechanical properties (average values) are as follows: 999 MPa yield strength, 1.116 MPa tensile strength, and 14% elongation.The chemical analysis of the bainitic steel was measured by optical emission spectrometry, while the mechanical properties were measured by tensile tests.
The gears were manufactured according to the processing route proposed by Dalcin et al. [3].Briefly, pinion gears went through stages of hot forging and controlled cooling, machining, grinding, polishing, cleaning, and pulsed plasma nitriding.Pulsed plasma nitriding treatments were conducted at 500 °C with three sets of N 2 -H 2 gas mixtures, containing 5 vol%, 24 vol%, and 76 vol% N 2 , and times of 30 h, 20 h, and 15 h, to develop a nitrided case of approximately 300 µm depth.
In the present investigation, the phases on the surface of the gears and residual stress were examined using X-ray diffraction.X-ray diffraction was carried out using a XRD M -Research Edition diffractometer (GE Seifert Charon model) equipped with a Meteor 1D fast line position sensitive detector.Phase analysis on the flank surface and compressive residual stresses in the diffusion zone of pinion gears were measured according to the methodology presented by Dalcin et al. [3].
The fracture toughness (K IC0 ) of the nitrided layer was measured according to the model proposed by Nolan et al. [41].In this study, the indentations were made on a Vickers Instron hardness tester (Tukon 2100B model), with loads of 1 kgf, 5 kgf, 10 kgf, 20 kgf, 30 kgf, and 50 kgf, respectively.The images of the impressions generated by the indenter were registered using an Olympus optical microscope (GX-51 model).The dimensions of the diagonals and Palmqvist cracks were measured in ImageJ software.
Surface Vickers microhardness measurements of the pulsed plasma-nitrided samples' surfaces and Vickers microhardness profiles of the cross-sections were obtained with a Struers microhardness tester (Duramin model).The determination of the nitrided layer depth was carried out based on the microhardness profiles and following the recommendations established in the DIN 50 190 standard [42].The macrostructure of the pinion teeth was recorded in an Olympus stereoscopic microscope (SZX10 model), and the cross-sectional microstructural images were obtained by an Olympus metallurgical microscope (BX51M model).The compound layer thickness was measured using the ImageJ software.
Table 1 summarizes the main results of the materials characterization before and after pulsed plasma nitriding.Briefly, the compound layer thickness, case depth, phases on surface, surface hardness, fracture toughness estimate (K IC0 ), and compressive residual stresses in the diffusion zone of pinion gears were measured according to the methodology presented by Dalcin et al. [3].According to previous works [3,11], nitrided surfaces with 76 vol% N 2 and with 24 vol% N 2 produced biphasic layers of ε-Fe 2-3 (C)N and γ'-Fe 4 N phases, with a preponderance of ε-Fe 2-3 (C)N for 76 vol% N 2 and more γ'-Fe 4 N for 24 vol% N 2 .However, on the nitrided surfaces with 5 vol% N 2 , a monophasic layer with the γ'-Fe 4 N phase was formed in the compound layer [3,11].
In general, the compound layer thickness increases with the treatment time and with increased nitrogen concentration [3,11,12].The mechanical properties of the diffusion zone influence the fracture properties of the compound layer, since the diffusion zone provides support for the surface compound layer [13,14,41].Table 1 shows that the nitrogen-rich gas composition increases the surface hardness and promotes a decrease in the fracture toughness of the compound layer, since it has more ε-Fe 2-3 (C)N [3,11].Plasma-nitrided gears with 76 vol% N 2 have higher compressive residual stresses in the diffusion zone than nitrided gears with 5 vol% and 24 vol% N 2 , due to the higher hardness gradient associated with higher nitrogen concentration [3].

Rolling-sliding contact fatigue and damage characterization
Rolling-sliding contact fatigue was performed using a standard FZG test rig, with type-C spur gears.This equipment was designed, manufactured, and assembled by Koda [43] at Federal University of Technology-Paraná.This rig is known as FZG, in attribute to their concept inventors, the laboratory Forschungsstelle für Zahnräder und Getriebebau at the Technical University of Munich.
A detailed description of the test rig is given in the DIN 14635-1 standard [44].In this specific case, 12 pairs of FZG type-C spur gears were manufactured and tested to produce pitting damage.Each gear pair to be tested have a pinion with 16 teeth and a wheel with 24 teeth.To produce accelerated wear on the gear teeth flank, it is common to use gears with a modified profile [3,25,45].The geometric characteristics of type-C spur gears tested throughout this work are shown in Table 2.The spur gears were manufactured with two different steels: (i) carburized DIN 20MnCr5 ferriticpearlitic steel (wheel gears) and (ii) plasma-nitrided DIN 18MnCrSiMo6-4 bainitic steel (pinion gears).The spur gears (pinion and wheel) were manufactured according to the procedures described in Dalcin et al. [3].In this study, two loading stages are applied: (i) the running-in (k6) period and (ii) the steady-state period (k9) (see Table 2).All tests were performed with the driven    half-height of the gear pair; however, the lubricant oil recirculated and passed through a filter during the rolling-sliding contact fatigue.After testing each gear pair, the lubricant oil used was removed and replaced by new oil to avoid that debris generated in one test would affect the next one.The evolution of pinion pitting damage was monitored after the end of each stage of the rolling-sliding contact fatigue, and after reaching the pitting failure criterion, the test was interrupted.The failure criterion was the occurrence of more than 4% pitted area on one pinion tooth.The quantification of the area affected by the damage was determined from flank images, using the procedure adopted by Dalcin et al. [3].
A damage rate was established to have a comparison parameter between the groups of gears studied in relation to their resistance to pitting wear.The damage rate relates the fraction of pinion gear-damaged area by pitting and/ or spalling and the number of cycles for each pinion gear tested.As it is impossible to interrupt the rolling-sliding contact fatigue at the exact moment when 4% damage to the flanks occurs, the experimental results were interpolated to find a second-order polynomial function which was used to calculate/estimate the number of cycles where 4% damage should happen.The estimated number of cycles is less than the number of cycles during rolling-sliding contact fatigue, because the pitted area quickly exceeded the test stop criterion, even making scheduled stop every 0.348 × 10 6 cycles.
Crack propagation and pitting wear on the pinion teeth flank wear were also evaluated.The cuts shown in Fig. 2a were initially made in the pinions with the objective of extracting teeth from the gear hub.The teeth were cut in the radial and axial direction on a Buehler precision cutting machine (IsoMet 4000 model).The cut parts (Fig. 2b) were mounted in bakelite (Fig. 2c), and then the sequential sanding steps were performed with sandpaper of increasing grit numbers (#100, #220, #320, #400, #600, #1200), and finally, they were polished with a 3-µm diamond paste and chemically attacked in 3% Nital.An Olympus optical microscope (BX51M model) revealed the macrostructure, microstructure, and cracks generated in the sub-surface of the pinion gear teeth.

Roughness evolution during the rolling-sliding contact fatigue
The roughness of the pinion teeth flank was measured on a Taylor Hobson profilometer (Surtronic S-128 model), and the roughness parameters R a , R q , R z , and R sm were calculated based on ISO 4287 [47].The parameters R z and R q were used to relate the height of the peaks with tooth wear; in addition, R q was used to determine the film thickness parameter (which suggests the type of regime in each region of the tooth analyzed).The R a parameter was used to monitor the average roughness, while the R sm parameter established the spacing between peaks of the gear flank asperities at each stage of the FZG wear test.
According to ISO 4288 standard [48], there are two different situations when selecting the cutoff value necessary to perform a roughness measurement: when the part profile is aperiodic and when it is periodic.Due to the topographic characteristics of the pinion gear teeth, measurements were made using the configuration for periodic roughness profile.When the profile is periodic, as in the case of gear flanks, the cutoff value depends on the distance between the grooves (R sm ) left by the advance of the machining tool.This classification results from the requirement that the limiting wavelength be at least 2.5 times greater than the distance between the grooves and a maximum of 8 times.In this study, the average distance between grooves (R sm ) was determined by measuring ten grooves to determine the average spacing.As the average distance between the grooves was between 0.1 and 0.32 mm, a cutoff of 0.8 mm and a measuring length of 4.0 mm were used.In this case, a measuring length (l m ) of 4.0 mm, a polynomial filter of second degree to remove the form, and a cutoff of 0.8 mm to separate roughness from waviness were set on the profilometer.
Pinion roughness evolution after the end of each test period was monitored, following the procedures shown in Fig. 3a and b.In this specific case, three teeth of each pinion gear were randomly chosen to follow the roughness on the flanks of the contact surface of the teeth to understand the pitting wear mechanisms.The roughness data were collected after the manufacturing stage of the pinions and after each rolling-sliding contact fatigue stage.The average values of the roughness parameters for addendum, pitch line, and dedendum contact regions were measured according to procedures shown in Fig. 3b.

Gear contact macroscopic analysis
The macroscopic contact analysis along the tooth flank in k6 and k9 load conditions (Table 2) was performed with EngCalc educational software developed by Muraro and Reisdorfer Junior [49] to perform calculations related to the contact between spur cylindrical gears.The contact stress distribution between the gear teeth is based on an analytical solution of Hertz theory, considering the contact between the teeth flanks equivalent to "non-conformal" contact between two cylinders [50].Analysis of the maximum Hertz pressure, oil film parameter (λ), friction coefficient (µ), and sliding rate along the calculations of the teeth profile of modified type-C gears was performed following the procedure proposed by Muraro et al. [25] and Palma Calabokis et al. [32].Software input parameters are listed in Table 3. Figure 3a represents the contact points (04, 09, and 12) along the gear flank in the addendum (AD), pitch diameter (PD), and dedendum (DD) regions.The parameters calculated along the involute gear profile were as follows: (i) pinion curvature radio, (ii) rolling speed, (iii) sliding speed, (iv) normal force distribution, (v) maximum Hertzian stress, (vi) contact area width, (vii) lubricant film thickness, and (viii) friction coefficient.

Gear contact microscopic analysis
Microscopic contact analysis was performed with a MatLab® code developed and adapted by the authors.The used  calculation method was first proposed by Seabra and Berthe [19], who evaluate the influence of waviness and roughness on stress distribution for a Hertzian contact.In this paper, the contact condition was simplified by considering a rough pinion surface and a smooth wheel surface.The simplification highlights the influence of roughness measured on the pinion flanks compared to the damaged surface images taken [32].MatLab routine input data were calculated using EngCalc software [49].The points of each roughness profile chosen for the MatLab analysis were indicated in Fig. 3a and b.In this paper, the following information was calculated: (i) maximum shear stress according to Tresca and von Misses and their respective sub-surface coordinates, (ii) Hertzian width, (iii) Hertzian pressure, and (iv) maximum normal stress.
The equivalent stresses in non-conformal contacts can be formed from the coordinate stresses using various stress hypothesis: (i) distortion energy hypothesis, (ii) shear stress hypothesis, and (iii) alternating shear stress hypothesis [20,51,52].The shear stress hypothesis (Tresca) will be used to set up the stress field on the face of the tooth, as suggested by Palma Calabokis et al. [32], because the aim is to compare the locations on the pinion flank where the stresses are higher with the regions where the pitting is more intense.Input data for the MatLab® code shown in Table 3 were obtained through the macroscopic calculations performed in the EngCalc software.

Weibull's statistical analysis
Weibull's statistical analysis was used to analyze the pitting wear resistance of pinion gears.To support this choice, Eq. (1) proposed by Tiryakioğlu et al. [53] was used.The critical value for the determination coefficient ( R 2 0.05 ) depends only on the number of samples (n).If the critical correlation coefficient (R 2 ) is greater than or equal to R 2 0.05 , it can be said with 95% confidence that the data can be modeled by a Weibull distribution.
The probability distributions were calculated using the Weibull + + ® software.In each curve plotted on the Weibull diagram, n = 3 samples were used.The R 2 for this sample number calculated with Eq. ( 1) is equal to R 2 0.05 = 0.76.For distributions with n < 20, it is recommended to plot the curves using the X regression method (RRX) [54].The use of the confidence interval is fundamental for the material life analysis, especially in small sample size [26,27,55].The confidence interval shows a plausible range of variation that the value of the parameter of interest can assume.ReliaSoft [56] recommends to calculate the small sample confidence interval using the likelihood ratio.3 Results and discussion

Rolling-sliding contact fatigue and damage characterization
The prior approach to the pitting damage concerns its aspect and how it progresses along the time.In general, the first change in the surface is characterized by the appearance of small portions of material that have been removed along the dedendum.From the moment the damage begins to evolve, the amount of damage grows along the dedendum and/or pitch line regions.In the final stage of the rolling-sliding contact fatigue, the increased damage quickly exceeds the failure criterion (see Fig. 4a-h).The evolution is not simultaneous for all the pinion's teeth flank [27]; therefore, the damage evolution of the pinion flanks over time is presented in Fig. 5a-d.
Considering the dispersion between the different pinion gears during rolling-sliding contact fatigue (Fig. 5a-d), Weibull's statistical analysis was the function selected for distributing the results and to evaluate the pinion's performance.The percentage levels of failure probability are attributed to the ranking, also considering the number of pinion gears in the group [27].The failure probability was taken together with the corresponding useful life to compose the Weibull diagram.The plotted points were used to extract a regression line.The point at which this regression line crosses the 50% probability of failure level defines the LC 50 parameter.This parameter is used to define the rolling-sliding contact fatigue failure probability, allowing a comparative analysis of fatigue performance [27,57].The 50% limit is a countermeasure to compensate for the high dispersion of a small sample size, which reduces the repeatability of the low and high levels of failure probability [27,58].This procedure was applied to the results presented in Fig. 5a-d, and in Fig. 6, the Weibull diagram is shown, followed by the LC 50 results.
Weibull's statistical analysis confirms that nitrided gears with 76 vol%, 24 vol%, and 5 vol% N 2 were 99.3%, 99.9%, and 94.8% likely to have a higher pitting wear resistance than non-nitrided gears.Nitrided gears with 24 vol% N 2 (best condition) had a probability of 87.1% and 94.4% of having a higher pitting wear resistance than nitrided gears with 76 vol% and 5 vol% N 2 .Nitrided gears with 5 vol% N 2 lasts less than nitrided gears with 24 vol% and 76 vol% N 2 , due to the flank hardness being smaller and the compound layer thickness being extremely thin.The difference in performance of nitrided gears with 24 vol% and 76 vol% N 2 is associated with fracture toughness and compound layer thickness since the surface hardness and case depth are similar (Table 1).
Table 1 shows that the fracture toughness of the compound layer of nitrided gears with 76 vol% N 2 is less than that of nitrided gears with 24 vol% N 2 .Rakhit [59] recommends that the compound layer should not exceed 12.7 µm so that the gears can support loads and avoid spalling of the surface layer.Table 4 shows that the compound layer thickness of nitrided gears with 76 vol% N 2 has 15.0 µm, and this may have contributed to the spalling of the surface layer of these gears (see Fig. 4h).
Figure 7a-d shows the macrophotographs of the radial section of the pinion's teeth after rolling-sliding contact fatigue.The darker edges of Fig. 7b-d 4), which are usually associated with material removal by spalling.Plasma nitriding influences the direction and mode of crack propagation.Figure 7b and d reveals that most of the sub-surface cracks in the flanks of the nitrided gears with 5 vol% and 76 vol% N 2 showed uncontrolled growth and at great depths during the propagation period and, in many cases, caused the removal of the entire nitrided surface.
During the rolling-sliding contact fatigue between surfaces with dissimilar curvature radius, the load is applied over a small contact area, resulting in high contact pressures [25,32,39].The repetitive stress cycles generated by the contact between the corresponding parts lead to the formation of cracks and, subsequently, component failure [16,60,61].Figure 8 shows in a schematic way how the crack propagation mechanism occurs in the pinion flanks.Due to the rolling force, an increase in the maximum shear stress occurs at the flank sub-surface and consequently promotes the nucleation of cracks in the sub-surface [25][26][27].The sub-surface cracks are unified by coalescence and spread rapidly with an orientation parallel to the surface, stimulated by shear forces [27,29].The shear propagation mode (1) is not maintained for a long time, because the crack seeks a less energy propagation path, offered by the opening mode (2) that promotes the propagation of the crack towards the surface [27,31,62].From the moment the crack reaches the surface, its opposite end exceeds the critical intensity factor and, with that, it starts to express an uncontrolled growth, which leads to the branching effect (3) [63].Finally, when the flank collapses (4), part of the material is removed from the surface [64].The cracks found in the gears occur in areas very close to the surface, causing these many cracks, with the course of the propagation stage, to reach the surface, leading to the formation of damage by pitting or spalling [28][29][30][31].Many radial and axial cracks are located in the dedendum and close to the pitch diameter [25,32].The orientations of the axial cracks in the sub-surface of the gear's teeth are in the same direction of the frictional force in dedendum regions.The pitting damage evolution of each surface at the end of the rolling-sliding contact fatigue is very uneven among the gears investigated, hiding the original mechanisms of damage creation.Nitrided gears with 24 vol% N 2 (best condition) showed a smaller number of cracks and without great depths, causing less pitting damage, even resisting several fatigue cycles much higher than the other investigated groups.
The average measurements of the crack depths over the radial and axial section of the pinion's teeth are shown in Table 4.The cracks were revealed in an optical microscope and measured using the ImageJ software.It is evident that cracks in nitrided gears with 5 vol% and 76 vol% N 2 occur at higher depths than even non-nitrided gears, Fig. 8 The crack is sub-surface originated and propagates outwards the surface, and when the opposite extremity finally collapses, the material is removed.Adapted from Ding and Gear [64] and Rego [27] and that the lowest depth occurs in nitrided gears with 24 vol% N 2 .It is not possible to statistically establish whether nitriding influenced the depth of cracks in the gear's teeth, due to the greater number of cycles to be carried out on plasma-nitrided gears.The crack depth would probably be greater, if the non-nitrided gears reached the number of cycles of the nitrided gears.
After the first pitting is formed, the apparent contact area decreases and the region of the maximum shear stress becomes deeper, and with a few more cycles, it is spalling [27].The spalling depth on surfaces in contact can be estimated to be 0.25 to 0.35 of half the contact width [31]; therefore, the damage of non-nitrided gears should occur with a surface depth between 60 and 84 µm.In this study, only the nitrided gears with 24 vol% N 2 showed damage with depths within this range.Figure 7b and d shows the damaged of non-nitrided and nitrided gears with 5 vol% and 76 vol% N 2 occurred at greater depth.

Roughness evolution during the rolling-sliding contact fatigue
Several studies [17,38,65] have been carried out to verify the effect of surface roughness on rolling-sliding contact fatigue [66].Martins et al. [16] found an analogy of the wear of the flanks with the roughness peaks in the dedendum region.In general, when two surfaces are pressed against each other, their apparent contact area is easily calculated by macrogeometry; however, their real contact area is affected by the roughness present on their surfaces.The rough edges of one flank will initially contact the edges of the other flank, and the contact area will be extremely small.The resulting stresses from asperity are extremely high and can easily exceed the compressive flow limit of the material.As the contact pressure between the two flanks is increased, the asperity points give in and widen until the combined area is sufficient to reduce the average stress to a sustainable level, i.e., something like the compressive penetration of the less resistant material.The pinion's roughness was monitored to relate the height parameters (R a , R q , and R z ) with the wear of the flanks (Fig. 9a-c), and the spacing parameter (R sm ) was measured, to understand the pitting damage evolution by contact regions (Fig. 9d-f).Figure 9a-f shows the average roughness of non-nitrided and nitrided gears with 5 vol%, 24 vol%, and 76 vol% N 2 , in the manufacturing condition, after running-in and steady-state.The roughness height parameters reduce their amplitude after the running-in period (Fig. 9a-c), due to the conformation of roughness peaks during rolling-sliding contact fatigue.The smallest roughness was recorded in non-nitrided gears, because in these cases, the surface hardness is lower, and the tendency is for these flanks to suffer greater plastic deformation [3].
The roughness values after the end steady-state increased in all parameters evaluated.This increase in average roughness is due to the presence of pitting damage on the gear flanks.The flank roughness after the test depends on the number of cycles of each gear and its final state (presence of pitting and/or spalling, and cracks); therefore, they cannot be directly compared between the tested conditions [39]. Figure 9d-f shows in the spacing parameters by contact region that the pitting damage in the end steady-state is greater in the dedendum and pitch line regions.

Influence of macroscopic gear contact on pitting wear
The film parameter (λ) at the contact point of spur gears is a parameter that might explain the influence of the different surface roughness on the pitting wear damage of the gears under study.It is observed in Fig. 10a-d that the film parameters are always lower after the end steadystate spur gear contact, making the loading conditions more severe.The film parameter (λ) results demonstrate the elastohydrodynamic (EHD) lubrication regime in the steady-state, for all contact conditions.The running-in period aims at equalizing the contact area and stabilizing some parameters, such as the friction coefficient [25].Figure 11a-d shows the friction coefficient along all contact points during meshing, based on the diametral pinion position.During the running-in, there is a drop in the friction coefficient when compared to the steadystate.This fact is related to the reduction of the contact pressure of the flank during the beginning period of the rolling-sliding contact fatigue.Along the contact path, the friction coefficient declines in the region between the root and the top of the gear.However, it is observed in Fig. 11a-d that the friction values show a plateau in the region between the LSPTC and HPSTC points.
It is verified that the friction coefficient is higher for nitrided gears with 76 vol% N 2 than nitrided gears with 5 vol% and 24 vol% N 2 .In general, pitting wear damage occurs faster in conditions where the friction coefficient is higher (in this case, it was in the non-nitrided gears).Lubricants are used to reduce the friction between the contacts [30,67].When the film parameter finds its lowest values because of loading (Fig. 10a-d), the friction coefficient shows an inverse behavior (Fig. 11a-d), showing that the lubricating film is of paramount importance with respect to the friction between the bodies.The EHD lubrication regime is the most common for the gearing region of the gears [68,69], but when the oil film breaks, the lubrication regime becomes the lubrication limit, where almost the entire load is supported mainly by the asperities [70].

Influence of microscopic gear contact on pitting wear
To correlate the roughness profiles measured on the pinion contact flank in the end state of manufacture and after the rolling-sliding contact fatigue, it was necessary to consider the stresses generated due to the roughness of the surface in contact.In this study, the roughness of the wheel was not considered.The measured roughness of the pinions was inserted as input parameters to analyze the contact stresses.The roughness peaks tend to decrease until a certain test time; however, this value increases drastically after the pitting damage spread over the surface, as already observed by other researchers [30,66,71].
Figure 12a shows the stress peaks generated due to the contact between the wheel and the pinion roughness peaks after the rolling-sliding contact fatigue.In general, pinion roughness peaks provided an increase in peak stress [32].Figure 12b shows the gear profile before and after a load is applied between the smooth wheel and the rough pinion after the end steady-state.The roughness peaks cause an increase in stress since the load is concentrated in small areas [32], causing, in general, a higher strain in these points.Another effect of the strain caused by the roughness peaks is on the location of the maximum shear stresses (Fig. 12c).The maximum shear stress has shifted to the contact surface [32].Its location coincides with the position of the biggest rough spots.All of these factors contribute to increased pitting wear damage in these regions [9].
Figure 13a and b shows the state of maximum shear stresses calculated considering the perfectly smooth surface and considering its roughness for the spur gears tested.The results include the addendum, pitch line, and dedendum regions.The measurement was performed at points 04 (addendum), 09 (pitch diameter), and 12 (dedendum) (Fig. 3a) and represented the average of three teeth per analyzed condition.An interesting fact is noted when evaluating Fig. 13a and b.In the addendum (point 04), there is a decrease in stress peaks on the pitch diameter (point 09) and the dedendum (point 12) regions, respectively.This can be explained by the fact that wear is higher in the dedendum and pitch line regions.High stresses indicate that the roughness is high, as the surface is imperfect due to the action of the pitting wear mechanisms, and once the stresses start to rise, they tend to wear the gears more.Maximum shear stresses are lower at running-in and higher at steadystate due to increased load.
The roughness had no significant influence on the fact that nitrided gears with 24 vol% N 2 presented higher pitting wear resistance than nitrided gears with 76 vol% N 2 .Nonnitrided and nitrided gears with 5 vol% N 2 last less due the lower hardness; however, nitrided gears with 24 vol% and 76 vol% N 2 , despite having greater surface hardness, have different resistance to pitting wear.The performance difference of nitrided gears with 24 vol% and 76 vol% N 2 is associated with fracture toughness of the compound layer (Table 1), once that the fracture toughness of the compound layer of nitrided gears with 76 vol% N 2 is lower than the compound layer of nitrided gears with 24 vol% and 5 vol% N 2 .Another fact that had an influence on the pitting wear resistance of nitrided gears may be related to the compound layer thickness.As shown in Table 4, nitrided gears with 5 vol% N 2 have a very thin compound layer, while nitrided gears with 76 vol% N 2 have a very thick compound layer, and this may have contributed to the spalling of these gears.
The maximum shear stresses are lower than the microscopic analyzes in which it considers the measured roughness values, since the macroscopic analyses do not consider the roughness during the contact between the gear teeth (Fig. 13a, b).Macroscopic analysis shows that the maximum depth of shear stress or the depth where The depth of the maximum shear stress occurs in the pitch line, but the greatest wear tends to happen in the dedendum due to the sliding rate being greater in this region [25].Shear stresses are higher, and cracks originate closer to the surface [26], when considering the influence of friction and flank roughness (microscopic analysis) (Fig. 13c, d).High stresses indicate that the roughness is high, as the surface is imperfect due to the action of the pitting wear, and once the stresses start to rise, the gears tend to wear more (Fig. 13a,  b).The maximum crack propagation depth values shown in Fig. 13c and d would exist if the materials were hard enough to withstand the stresses shown in Fig. 13a and b.

Final discussion
Rolling-sliding contact fatigue tests were carried out on the gears to evaluate the potential of the forged DIN 18MnCrSiMo6-4 steel and the performance of pulsed plasma-nitrided layers with different gas mixture compositions.Analysis of the contact stresses and their relationship with the wear of gear flanks is not a simple task, as it depends on several factors [17,25,26,35,39] such as (i) material, (ii) level of contact stresses, (iii) type of teeth profile, (iv) contact speed, and (v) lubrication conditions.In this case, as previously reported [3], a gradual variation in the flank surface properties occurs as the hardness, residual stress state, and nitride phases change towards the tooth core.
The case depth is similar between nitrided gear groups, but the compound layer is thicker in the nitrided gears with 76 vol% N 2 due to the increased nitrogen composition.Nitrided gears with 24 vol% and 76 vol% N 2 have higher surface hardness than nitrided gears with 5 vol% N 2 , but the fracture toughness of the compound layer of nitrided gears with 76 vol% N 2 is lower than nitrided gears with 5 vol% and 24 vol% N 2 (Fig. 14a), since it has more ε-Fe 2-3 (C)N [3,11].Figure 14b shows that non-nitrided and nitrided gears with 5 vol% N 2 last less as the flank hardness is lower.
Table 4 indicates that the difference in performance of nitrided gears with 24 vol% and 76 vol% N 2 is associated with the fracture toughness of the compound layer, since the surface hardness is similar in these cases.Another fact shown in Table 1 that influenced the pitting wear resistance of nitrided gears may be related to the compound layer thickness and the residual stresses state.Nitrided gears with 5 vol% N 2 have a very thin compound layer, while nitrided gears with 76 vol% N 2 have a higher compound layer.da Silva Rocha et al. [72] showed that residual stresses become more tensile in the compound layer with increasing thickness.When a thicker compound layer above 12.7 µm is produced [59], the possibility of spalling on the surface of the flanks increases.
In rolling-sliding contact fatigue, the pitting wear resistance depends on several factors, such as elastoplastic stress and deformation, material properties, physicochemical properties of the lubricant, roughness, residual stress state, and contact kinematics [3,22,30,32,39].The maximum Hertz pressure at the center of the contact varies depending on the normal force and the variation of the equivalent radius of curvature along the engagement line [39,71].In FZG type-C gears, the maximum pressure occurs at the lowest point of single tooth contact (LPSTC) [25,32].
Muraro et al. [25] and Palma Calabokis et al. [32] show that the sliding rate is higher in the pinion dedendum region.Therefore, this fact also contributes to a more intense loading severity.In the dedendum region, in addition to the kinematic characteristics with rolling-sliding in the same direction [25], the shear stresses are also higher and the cracks originate closer to the surface [26,45] (see Fig. 15a,  b).Although nitrided gears with 24 vol% N 2 (best condition) show the same level of shear stress than nitrided gears with 76 vol% N 2 (Fig. 15a), they have a larger end thicker film at the end of the rolling-sliding contact fatigue, which gives it greater protection (see Fig. 16a).
Figure 15a shows that the maximum shear stress occurs in the regions of the pitch line and dedendum regions at the end of the rolling-sliding contact fatigue.The increase in shear stresses in these regions occurs due to the wear of the flanks increasing the roughness.The non-nitrided gears have a lower hardness than the nitrided gears group; therefore, the pitting wear damage occurred more quickly under these conditions.Roughness had no significant influence on whether nitrided gears with 24 vol% N 2 had higher performance than nitrided gears with 5 vol% and 76 vol% N 2 .Nitrided gears with 5 vol% N 2 last less because of the hardness and the compound layer thickness.However, nitrided gears with 76 vol% N 2 last less than nitrided gears with 24 vol% N 2 , since the fracture toughness of the compound layer of nitrided gears with 76 vol% N 2 is lower, and the compound layer thickness is very high, and this may have contributed to the early spalling of the surface layer of these gears.
In the dedendum region, in addition to the kinematic characteristics with rolling-sliding [25], the shear stresses are higher at the end of the rolling-sliding contact fatigue (Fig. 15a).The nitrided gears with 24 vol% N 2 (best condition), despite having the same level of shear stress as nitrided gears with 76 vol% N 2 (Fig. 15a), have a greater film thickness at the end of the rolling-sliding contact fatigue, which gives it greater protection (see Fig. 16a).Non-nitrided gears have higher shear stresses at the end of the rolling-sliding contact fatigue than plasmanitrided gear groups (Fig. 15a), due to the high presence of pitting damage on the flanks.In these cases, the lubricating film thickness is smaller, and consequently, the friction coefficient is higher than plasma-nitrided gear group (Fig. 16b).
Two types of damage were identified on the flank surfaces after rolling-sliding contact fatigue: large fatigue craters (spalling) [3,31] and small craters (pitting) [3,9,32].Figure 4a-h present images of the flank damage of the four tested gear groups.In general, spalling damage was predominantly present on the flank of non-nitrided and nitrided gears with 5 vol% and 76 vol% N 2 , while pitting wear damage was predominantly manifested in nitrided gears with 24 vol% N 2 .The occurrence of some spalling causes damage on nitrided flanks with 24 vol% N 2 , but in a smaller amount.Likewise, in the beginning periods of rolling-sliding contact fatigue, pitting damage is also evident in non-nitrided and nitrided gears with 5 vol% and 76 vol% N 2 (see Fig. 5a-d).
During the rolling-sliding contact fatigue, all gears showed the crack formation, nucleation, and sub-surface propagation.In general, sub-surface cracks that have large dimensions (non-nitrided and nitrided gears with 5 vol% and 76 vol% N 2 ) (Fig. 15b) are usually associated with material removal by spalling.Most sub-surface cracks in nitrided gears with 5 vol% and 76 vol% N 2 showed uncontrolled growth at great depths during the propagation period and, in many cases, caused the removal of the entire nitrided surface (Fig. 7b, d).However, it is not possible to state statistically whether plasma nitriding influenced the crack depth in gear teeth, due to the greater number of cycles being performed on nitrided gears.The crack depth would likely be higher, if the non-nitrided gears reached the same number of cycles as the nitrided gears (Fig. 15b).Despite this, it is evident that the cracks in nitrided gears with 24 vol% N 2 occur at lower depths than the other conditions investigated, even with the number of cycles being much higher than the other conditions (Fig. 15b).
Hamilton and Goodman [73] and Terrin et al. [60] found that when friction is present in the non-conforming contact, the position of the maximum shear stress approaches the surface with an increase in the friction coefficient.Therefore, the crack depths observed in the gear teeth are consistent for the nitrided gears with 24 vol% N 2 and for the non-nitrided gears, as the average crack depths shown in Fig. 15b are smaller than the crack depth calculated by the Hertz model [50].Despite the non-nitrided gears showing higher levels of damage, those nitrided gears with 5 vol% and 76 vol% N 2 showed even higher depth cracks than those calculated by the Hertz model.This can be explained by the fact that the surface hardness and the thickness of the compound layer are very reduced in nitrided gears with 5 vol% N 2 .For nitrided gears with 76 vol% N 2 , this occurred due to the compound layer thickness being very high, the fracture toughness of the compound layer is lower and the fact that compositions rich in nitrogen are prone to embrittlement of the diffusion zone, as reported by Rocha et al. [74].
Weibull's statistical analysis confirms in Fig. 6 that nonnitrided and plasma-nitrided gears with 5 vol% N 2 have lower pitting wear resistance than the plasma-nitrided gears with 24 vol% and 76 vol% N 2 .The nitrided gears with 24 vol% N 2 (best condition) had a life ten times longer than non-nitrided gears, because the non-nitrided gears have lower hardness (Fig. 14b).Although nitrided gears with 5 vol% N 2 have higher toughness in the compound layer due to the monophasic layer with the γ'-Fe 4 N phase, they last less than other nitriding conditions due to lower hardness (Fig. 14a).Previous works [3,[11][12][13][14] show the fragility of nitrided gears with 76 vol% N 2 is associated with its microstructural characteristics, such as high compound layer thickness, a biphasic compound layer of ε-Fe 2-3 (C)N and γ'-Fe 4 N, lower toughness, porosity, and dark regions in the diffusion zone (associated with the precipitation of chromium nitrides) (see Fig. 7d).According to Dalcin et al. [3], nitrided gears with 24 vol% N 2 last longer due to a best combination of surface hardness, fracture toughness, residual stresses, compound layer thickness, and phases on surface.

Conclusions
1. Weibull's statistical analysis confirms that the nitrided gears with 24 vol% N 2 had a pitting wear resistance higher than the other gears, due to a better combination of surface hardness, fracture toughness, compound layer thickness, and phases on surface.Another interesting fact is that nitrided gears with 24 vol% N 2 have a greater film thickness at the end of the rolling-sliding contact fatigue, which gives it greater protection, less friction, and pitting wear.2. It was found that most pitting damage occurred in the dedendum and pitch line regions, being the regions that reported the greatest Hertz contact pressure.This is due to the rolling direction being opposed to the friction force in the dedendum region.The behavior of the roughness parameters was similar in the pitch line and dedendum regions.3. The roughness tends to decrease its magnitude in the beginning stages of rolling-sliding contact fatigue, and as the test progresses, its values increase abruptly showing the formation of damage by pitting and/ or spalling.The roughness has a great influence on the contact stress generated and pitting wear, but the roughness had no significant influence on the fact that nitrided gears with 24 vol% N 2 have higher resistance to pitting wear than nitrided gears with 76 vol% N 2 .4. The film parameters (λ) are always lower after the rolling-sliding contact fatigue, thus making loading conditions more severe.The film parameter (λ) demonstrates that the lubrication regime, in the region of the pitch line (region in which pure rolling occurs), is the limit (or borderline).In general, small surface craters known as pitting were found in the three groups of plasma-nitrided gears.Despite this, the nitrided gears with 5 vol% and 76 vol% N 2 showed spalling after a certain number of cycles.5. Most radial cracks are in the dedendum and close to the pitch line region.The cracks were observed in areas very close to the surface and, with the course of the propagation stage, reached the surface, causing the formation of damage by pitting or spalling.
pinion rotating at 1450 rpm.With this configuration, each test hour represents 0.87 × 10 5 cycles on the pinion.During the running-in period (0.174 × 10 6 cycles), the gears are loaded with a torque of 135.3 Nm, and the oil temperature is maintained at 60 °C.After the running-in period, the oil temperature is increased to 90 °C and the gears are loaded with a torque of 302.0 Nm during 0.348 × 10 6 cycles.

Figure 1
shows the methodology used in the FZG wear tests.The loaded gears are lubricated with LUBRAX GL 5 90 lubricant oil.The main properties of the LUBRAX GL 5 90 lubricant oil are shown in Table 2.During the rolling-sliding contact fatigue, the lubricant oil bath reaches approximately

Fig. 2
Fig. 2 (a) Representation of the gear teeth showing the cuts carried out in the preparation of the sample.(b) Identification of the radial and axial sections.(c) Procedure for assembling samples in bakelite prior to preparation for metallography analysis

Fig. 3
Fig. 3 (a) Schematic representation of the tooth contact points of a straight tooth gear.LPSTC, lowest point of single tooth contact; HPSTC, highest point of single tooth contact.Contact points 04 (addendum), 09 (pitch diameter), and 12 (dedendum) are chosen for contact analysis calculation.Adapted from Palma Calabokis et al. [32].(b) Selected points for measuring roughness in the radial direction: 1-3, addendum; 4-6, pitch line; and 7-9, dedendum that outline the pinion's teeth represent the case depth (~ 300 µm) reached by plasma nitriding.All groups of gears indicate the sub-surface

Fig. 6
Fig.6 Weibull's statistical analysis to determine the failure probability of the investigated gears

Fig. 9
Fig. 9 Average roughness of pinion gears.(a) R a , (b) R q , (c) R z , (d) R sm addendum, (e) R sm pitch line, and (f) R sm dedendum, in different periods of rolling-sliding contact fatigue

Fig. 10
Fig. 10 Film parameter (λ) along the pinion gear tooth profile at the beginning of rolling-sliding contact fatigue and after the running-in and steady-state.(a) Non-nitrided, (b) nitrided with 5 vol% N 2 , (c) nitrided with 24 vol% N 2 , and (d) nitrided with 76 vol% N 2

Fig. 11
Fig. 11 Friction coefficient (µ) along the pinion gear tooth profile at the beginning of rolling-sliding contact fatigue and after the running-in and steady-state.(a) Non-nitrided, (b) nitrided with 5 vol% N 2 , (c) nitrided with 24 vol% N 2 , and (d) nitrided with 76 vol% N 2

Fig. 12
Fig. 12 Rough versus smooth surface contact analysis.(a) Hertzian pressure distribution for perfectly smooth contact (black line) and real contact pressure (blue line).(b) Smooth wheel and rough pinion profiles prior loading and after loading.(c) Distribution of the maximum shear stress according to Tresca

Fig. 13
Fig. 13 State of maximum shear stresses calculated considering the perfectly smooth surface and roughness of tested gears after (a) running-in and (b) end steady-state.Maximum depth of shear stresses on the flank of tested gears after (c) running-in and (d) end steady-state

Fig. 15 (Fig. 16
Fig. 15 (a) Maximum shear stress (torque 302.0 Nm) considering the roughness of the flanks by contact region versus the number of cycles.(b) Average crack depth versus the number of cycles

Table 1
Compound layer thickness, case depth, phases on surface, surface hardness, fracture toughness estimate (K IC0 ), and compressive residual stresses in the diffusion zone of pinion gears

Table 2
EngCalc software input parameters for the calculation of Hertz stress in gears Representation of the methodology used in FZG wear tests

Table 3
Input data for the

Table 4
Performance of pinions to rolling-sliding contact fatigue a Load cycles estimate for 4% pitted area Groups of gears Compound layer thickness (µm) Case depth (µm) Surface hardness (HV 0.1 ) Load cycle estimate a Average crack depth (µm)