3.1 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. 3(a-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. 4(a-d).
Considering the dispersion between the different pinion gears during rolling-sliding contact fatigue, Fig. 4(a-d), the Weibull’s statistical analysis was the function selected for distributing the results and evaluate the pinions 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 LC50 parameter. This parameter is used to define the rolling-sliding contact fatigue failure probability, allowing a comparative analysis of fatigue performance [27, 55]. 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, 56]. This procedure was applied to the results presented in Fig. 4(a-d), and in Fig. 5 is shown the Weibull diagram, followed by the LC50 results.
Weibull’s statistical analysis confirms that nitrided gears with 76, 24 and 5 vol.% N2 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.% N2 (best condition) had a probability of 87.1% and 94.4% of having a higher pitting wear resistance than nitrided gears with 76 and 5 vol.% N2. Nitrided gears with 5 vol.% N2 lasts less than nitrided gears with 24 and 76 vol.% N2, due to the flank hardness being smaller and the compound layer thickness being extremely thin. The difference in performance of nitrided gears with 24 and 76 vol.% N2 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.% N2 is less than nitrided gears with 24 vol.% N2. Rakhit [57] recommends that the compound layer not exceed 12.7 µm so that the gears support loads and avoid spalling of the surface layer. Table 4 shows that the compound layer thickness of nitrided gears with 76 vol.% N2 has 15.0 µm, and this may have contributed to the spalling of the surface layer of these gears, see Fig. 3(h).
Figure 6(a-d) show the macrophotographs of the radial section of the pinion’s teeth after rolling-sliding contact fatigue. The darker edges of Fig. 6(b-d) that outline the pinions teeth, represent the case depth (~ 300 µm) reached by plasma nitriding. All groups of gears indicate the sub-surface cracks, nucleation, and propagation during the rolling-sliding contact fatigue. In general, the sub-surface cracks have large dimensions, Table 4, which are usually associated with material removal by spalling. Plasma nitriding influences the direction and mode of crack propagation. Figure 6(b, d) reveals that most of the sub-surface cracks in the flanks of the nitrided gears with 5 and 76 vol.% N2 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, 38]. The repetitive stress cycles generated by the contact between the corresponding parts lead to the formation of cracks and subsequently component failure [16, 58, 59]. Figure 7 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 [26, 27, 37]. 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, 60]. 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) [61]. Finally, when the flank collapses (4), part of the material is removed from the surface [62].
The cracks found in the gears occur in areas very close to the surface, causing many these cracks, with the course of the propagation stage, to reach the surface, leading the formation of damage by pitting or spalling [28–31]. 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 gear’s investigated, hiding the original mechanisms of damage creation. Nitrided gears with 24 vol.% N2 (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 Image J software. It is evident that cracks in nitrided gears with 5 and 76 vol.% N2 occur at higher depths than even non-nitrided gears, and that the lowest depth occurs in nitrided gears with 24 vol.% N2. 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 that the nitrided gears.
Table 4
Performance of pinions to rolling-sliding contact fatigue.
Groups of gears | Compound layer thickness (µm) | Case depth (µm) | Surface hardness (HV0.1) | Load cycles estimate* | Average crack depth (µm) |
Non-nitrided | - | - | 376 ± 35 | 2.8 ± 0.5x105 | 102 ± 86 |
5 vol.% N2 | 1.2 ± 0.3 | 327 ± 66 | 690 ± 128 | 1.0 ± 0.5x106 | 430 ± 95 |
24 vol.% N2 | 10.7 ± 1.4 | 299 ± 55 | 1045 ± 59 | 2.7 ± 0.7x106 | 56 ± 14 |
76 vol.% N2 | 15.0 ± 1.6 | 345 ± 36 | 1102 ± 118 | 1.5 ± 0.5x106 | 227 ± 99 |
*Load cycles estimate for 4% pitted area.
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 to 84 µm. In this study, only the nitrided gears with 24 vol.% N2 showed damage with depths within this range. Figure 6(b, d) shows the damaged of non-nitrided and nitrided gears with 5 and 76 vol.% N2 occurred at greater depth.
3.2 Roughness Evolution During the Rolling-Sliding Contact Fatigue
Several studies [17, 36, 63] have been carried out to verify the effect of surface roughness on rolling-sliding contact fatigue [64]. Martins et al. [16] found an analogy 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 (Ra, Rq and Rz) with the wear of the flanks, Fig. 8(a-c), and the spacing parameter (Rsm) was measured, to understand the pitting damage evolution by contact regions, Fig. 8(d-f). Figure 8(a-f) show the average roughness of non-nitrided and nitrided gears with 5, 24 and 76 vol.% N2, in the manufacturing condition, after running-in and steady-state. The roughness height parameters reduce their amplitude after the running-in period, Fig. 8(a-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 [38]. Figure 8(d-f) show in the spacing parameters by contact region that the pitting damage in the end steady-state are greater in the dedendum and pitch line regions.
3.3 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. 9(a-d) that the film parameters are always lower after the end steady-state spur gears 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 10(a-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 steady-state. 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. 10(a-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.% N2 than nitrided gears with 5 and 24 vol.% N2. In general, pitting wear damage occurs faster in conditions where the friction coefficient is higher (in this case was in the non-nitrided gears). Lubricants are used to reduce the friction between the contacts [30, 65]. When the film parameter finds its lowest values because of loading, Fig. 9(a-d), the friction coefficient shows an inverse behavior, Fig. 10(a-d), showing that the lubricating film is of paramount importance with respect to friction between the bodies. The EHD lubrication regime is the most common for the gearing region of the gears [66, 67], but when the oil film breaks, the lubrication regime becomes the lubrication limit, where almost the entire load is supported mainly by the asperities [68].
3.4 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, 64, 69].
Figure 11(a) show 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 11(b) 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. 11(c). 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 12(a, b) shows the state of maximum shear stresses calculated considering the surface perfectly smooth 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. 2(a), and represent the average of three teeth per analyzed condition. An interesting fact is noted when evaluating Fig. 12(a, 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 steady-state due to increased load.
The roughness had no significant influence on the fact that nitrided gears with 24 vol.% N2 presented higher pitting wear resistance than nitrided gears with 76 vol.% N2. Non-nitrided and nitrided gears with 5 vol.% N2 lasts less due the lower hardness, however, nitrided gears with 24 and 76 vol.% N2, despite having greater surface hardness, they have different resistance to pitting wear. The performance difference of nitrided gears with 24 and 76 vol.% N2 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.% N2 is lower than the compound layer of nitrided gears with 24 and 5 vol.% N2. 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.% N2 have a very thin compound layer, while nitrided gears with 76 vol.% N2 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 analyzes do not consider the roughness during the contact between the gear teeth, Fig. 12(a, b). Macroscopic analysis shows that the maximum depth of shear stress or the depth where sub-surface cracks should propagate in pitch line, addendum and dedendum regions would be 194.5, 132.3 and 128.2 µm, using a torque of 302.0 N.m, but according to Ding et al. [31] the damage of the non-nitrided gears should be at a depth of the surface between 60 to 84 µm, considering the hypothesis that the spalling depth on surfaces in contact is 0.25 to 0.35 of the half contact width.
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. 12(c, 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. 12(a, b). The maximum crack propagation depth values shown in Fig. 12(c, d) would exist if the material were hard enough to withstand the stresses shown in Fig. 12(a, b).
3.5 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. The contact stresses analysis and their relationship with the wear of gear flanks is not a simple task, as it depends on several factors [17, 25, 26, 35, 38] such as: (i) material, (ii) contact stresses level, (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.% N2 due to the increased nitrogen composition. Nitrided gears with 24 and 76 vol.% N2 have higher surface hardness than nitrided gears with 5 vol.% N2, but the fracture toughness of the compound layer of nitrided gears with 76 vol.% N2 is lower than nitrided gears with 5 and 24 vol.% N2, Fig. 13(a), since it has more ε-Fe2-3(C)N [3, 11]. Figure 13(b) shows that non-nitrided and nitrided gears with 5 vol.% N2 last less as the flank hardness is lower.
Table 4 indicates that the difference in performance of nitrided gears with 24 and 76 vol.% N2 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.% N2 have a very thin compound layer, while nitrided gears with 76 vol.% N2 have a higher compound layer. Rocha et al. [70] showed that residual stresses become more tensile in the compound layer with increasing thickness. When a thicker compound layer above 12.7 µm are produced [57], the chances of spalling on the surface of the flanks increase.
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, 38]. 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 [38, 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 Calabokis et al. [32] shows 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 shearing tensions are also higher and the cracks originate closer to the surface [26, 43], see Fig. 14(a, b). Although nitrided gears with 24 vol.% N2 (best condition) show the same level of shear stress than nitrided gears with 76 vol.% N2, Fig. 14(a), they have a larger end thicker film at the end of the rolling-sliding contact fatigue, which gives it greater protection, see Fig. 15(a).
Figure 14(a) show 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.% N2 had higher performance than nitrided gears with 5 and 76 vol.% N2. Nitrided gears with 5 vol.% N2 last less because of the hardness and the compound layer thickness. However, nitrided gears with 76 vol.% N2 last less than nitrided gears with 24 vol.% N2, since the fracture toughness of the compound layer of nitrided gears with 76 vol.% N2 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. 14(a). The nitrided gears with 24 vol.% N2 (best condition), despite having the same level of shear stress as nitrided gears with 76 vol.% N2, Fig. 14(a), have a greater film thickness at the end of the rolling-sliding contact fatigue, which gives it greater protection, see Fig. 15(a). Non-nitrided gears have higher shear stresses at the end of the rolling-sliding contact fatigue than plasma nitrided gear groups, Fig. 14(a), 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. 15(b).
Two types of damage were identified on the flank surfaces after rolling-sliding contact fatigue: large fatigue craters (spalling) [3, 31] and small, dispersed craters on the flanks (pitting) [3, 9, 32]. Figure 3(a-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 and 76 vol.% N2, while pitting wear damage was predominantly manifested in nitrided gears with 24 vol.% N2. The occurrence of some spalling damage on nitrided flanks with 24 vol.% N2, but in a smaller amount. Likewise, in the begin periods of rolling-sliding contact fatigue, pitting damage is also evident in non-nitrided and nitrided gears with 5 and 76 vol.% N2, see Fig. 4(a-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 and 76 vol.% N2), Fig. 14(b), are usually associated with material removal by spalling. Most sub-surface cracks in nitrided gears with 5 and 76 vol.% N2 showed uncontrolled growth at great depths during the propagation period, and in many cases caused the removal of the entire nitrided surface, Fig. 6(b, 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. 14(b). Despite this, it is evident that the cracks in nitrided gears with 24 vol.% N2 occur at lower depths than the other conditions investigated, even with the number of cycles being much higher than the other conditions, Fig. 14(b).
Hamilton et al. [72] and Terrin et al. [73] found that when friction is present in the nonconforming 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.% N2 and for the non-nitrided gears, as the average crack depths shown in Fig. 14(b) are smaller than the crack depth calculated by the Hertz model [47]. Despite the non-nitrided gears showing higher levels of damage, those nitrided gears with 5 and 76 vol.% N2, 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.% N2. For nitrided gears with 76 vol.% N2, 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. 5 that non-nitrided and plasma nitrided gears with 5 vol.% N2 has lower pitting wear resistance than the plasma nitrided gears with 24 and 76 vol.% N2. The nitrided gears with 24 vol.% N2 (best condition) had a life ten times longer than non-nitrided gears, because the non-nitrided gears have lower hardness, Fig. 13(b). Although nitrided gears with 5 vol.% N2 have higher toughness in the compound layer due to the monophasic layer with the γ’-Fe4N phase, they last less than other nitriding conditions due to lower hardness, Fig. 13(a). Previous works [3, 11–14] show the fragility of nitrided gears with 76 vol.% N2 is associated with its microstructural characteristics, such as high compound layer thickness, a biphasic compound layer of ε-Fe2-3(C)N and γ’-Fe4N, lower toughness, porosity and dark regions in the diffusion zone (associated with the precipitation of chromium nitrides), see Fig. 6(d). According to Dalcin et al. [3], nitrided gears with 24 vol.% N2 last longer due to a best combination of surface hardness, fracture toughness, residual stresses, compound layer thickness and phases on surface.