Assessment of the Tribological Performance of Diamond-Like Carbon Coatings for Differential Shafts for Electric Vehicles

A wide range of electric vehicles has been developed and put in service over the last 10 years as a contribution from the car manufacturers to the decarbonization of the mobility sector. This technology created new challenges in terms of efficiency, reliability, and durability of the mechanical systems used in electric vehicles (EVs) [1]. In particular, transmission systems are subjected to enhanced mechanical and tribological stress. Two reasons for this are that EVs are usually heavier than internal combustion engine (ICE) vehicles and that electric engines generate by design higher torques in shorter shift ramps than internal combustion engines. Notably, in EVs, the maximum output torque of the electric motor is available upon start-up and the torque is delivered through a single-speed transmission to the wheels, thus creating an abrupt loading of the differential assembly, whereas in ICE vehicles, the torque generated by the engine is gradually transmitted to the differential assembly through a clutch. Differential assemblies use a set of gears to distribute the engine's torque between the wheels while allowing the wheels on the same axle to rotate at different speeds when the vehicle turns. The higher torque transmitted to the differential assembly results in an increase in the normal load applied to the contact between the differential shaft and the planet gear. Surface treatments traditionally used in such differential systems present some limitations when used in EV's transmission.

Diamond-like carbon (DLC) coatings have been used in the automotive industry since the late 1980s, initially in high-performance and racing engines due to their high hardness, low friction, and wear resistance [2]. Advancements in coating technologies allowed for more cost-effective production [3,4], enabling the use of DLC coatings in mass-produced vehicles. Today, DLC coatings are commonly applied to ICE components like cam tappets, piston pins, piston rings, and fuel injectors enabling reduced friction, improved fuel efficiency, and extended component life [5]. In this respect, DLC coatings are interesting surface treatment candidates to face the enhanced tribological stress applied to the differential shafts of EVs.

An experimental study was conducted to qualify the tribological performances of DLC coatings on the differential shaft for the differential shaft/planet gear lubricated contact. Beforehand, an analytical approach was used to identify the lubrication regimes in which the tribological system operates. It also enabled to design simplified but relevant test setup and test protocol. The tribological performance of two types of diamond-like carbon coatings was assessed and compared with an electroless nickel plating (e-nickel) which is commonly used for coating differential shafts in ICE vehicles. More precisely, the two DLC coatings were a hydrogenated amorphous carbon (a-C:H) and a non-hydrogenated tetrahedral amorphous carbon (ta-C). It has to be emphasized that, to increase the level of representativity of the tribological experiments, the defined test configuration involved the use of real components and commercially available coatings.

To evaluate the influence of the different contact parameters on the lubrication regime, analytical calculations were undertaken. Figure 1 presents a schematic diagram of a differential assembly and shows the relative positioning of the different components and their respective motion. When the vehicle is traveling in a straight line, there is no rotation of the planet gears around the differential shaft. When the vehicle turns, the planet gears rotate around the differential which enables the wheel to rotate at different speeds.

The above formula corresponds to a quasistatic loading condition when the vehicle starts and that assumes no friction losses in the transmission system and no friction between the tires and the road.

As stated in the literature [6,7], four lubrication regimes can be identified in full film lubrication depending on the fluid (iso-/piezo-viscous) and material (rigid/elastic) properties. The elasticity and pressure-viscosity parameters as defined by Johnson [6] were computed from various rotation speeds of the gear and various loads using the parameters presented in Table 1. The rotation speed values were between 1 and 500 rpm. In operating conditions, when the vehicle turns, the rotation speed of the gear on the differential is low, typically a few revolutions per minute, and can reach values up to about 10 rpm for sharp turns. High values of rotation speed (up to 500 rpm) were used because they correspond to operating conditions in which one of the wheels loses grip. The normal load values were between 1 and 60 kN and correspond to a low motor torque and a high motor torque, respectively. Given the data of Table 1, a normal load of 1 kN corresponds to a maximum Hertzian contact pressure of 30 MPa and a normal load of 60 kN to a maximum Hertzian contact pressure of 235 MPa.

The calculations of the elasticity and pressure-viscosity parameters showed that, if the full film lubrication assumption was verified, the shaft/gear contact operates in the transition regime between the piezo-viscous elastic and iso-viscous elastic regimes. As a consequence, the minimum oil film thickness h_min was calculated according to Myers' formula [8] using the data presented in Table 1 and the range of gear rotation speeds and normal loads mentioned previously. A value of composite RMS roughness R_qc of 0.3 µm was assumed, corresponding to values generally reached when the gear bore is initially ground, for the calculation of the Λ ratio.

Figure 2 presents the results of the calculations for a gear rotation speed between 1 and 500 rpm and a normal load between 1 and 60 kN. One can consider that when the Λ ratio is below 1 the boundary lubrication regime is likely, when the Λ ratio is between 1 and 3 mixed lubrication is likely, and when the Λ ratio is higher than 3, full film lubrication is likely [9]. The Λ ratio is used as a practical tool to get a rough assessment of the lubrication regime even though it was proven that it does not capture well all the interactions occurring in a lubricated rough contact [10–13].

From these calculations, it is shown that: (i) the gear/shaft contact operates mainly in the boundary lubrication regime and (ii) the lubrication regime is mainly affected by the differential rotation speed and is weakly affected by the load. This is due to the fact that oil film thickness is more dependent on the entrainment speed than on the load. This results in a larger exponent absolute value for the entrainment speed than that for the load in the oil film thickness formulas, such as the Dowson–Higginson formula [7] or Myers' formula [8]. The lubrication regime can be mixed only at high differential rotation speeds which corresponds to exceptional cases of loss of grip.

These analytical calculations provided a first understanding of the tribological behavior of the differential gear/shaft contact allowing to identify potential degradation scenarios. It was decided to design a simplified but relevant test setup and test protocol enabling to perform wear tests in boundary-lubricated conditions.

To improve the level of representativity, the test specimens were remachined from real differential shafts to fit into the experimental setup as presented in Fig. 3. Geometrical tolerances and shape defects of series production parts are in such applications less strict than any tribological samples specifically machined for laboratory testing. Since such differences could affect the actual contact pressure distribution due to the modification of the contact area, they might impact negatively the test results and conclusions.

The shafts used in this study have a nominal outer diameter of 22.2 mm. They were made of low-alloy steel 20CrMnTi and were case-hardened by gas carburizing to reach a minimum surface hardness of 58 HRC. The effective case-hardening depth was 1.1 mm. The three following coatings were deposited on the shaft for wear testing:

• Nickel-phosphorus (e-nickel) with a phosphorus content of 14 %at

• Hydrogenated amorphous carbon (a-C:H) with a hydrogen content of 20–25 %at

• Non-hydrogenated tetrahedral amorphous carbon (ta-C)

The nickel-phosphorus was deposited by electroless plating and then heat treated at 300–325 °C for 6 hours in an inert gas atmosphere to reach a surface hardness value of a minimum of 800 HV.

Prior to DLC coating, the shafts were polished to reach a roughness Ra of 0.01 µm. The a-C:H coating was deposited by plasma-enhanced chemical vapor deposition from a hydrocarbon gas. The ta-C coating was deposited by unfiltered arc-physical vapor deposition from graphite and postpolished to reach a roughness Ra of 0.01 µm.

Table 2 presents some of the main characteristics of the three coatings.

The rotating rings standing for the planet gear were made with a typical gear-type steel ISO standard 20MnCr5 which was case-hardened by low-pressure carburizing to reach a surface hardness of 58 HRC and a case-hardening depth of 0.8 mm. The initial bore surface roughness was obtained by grinding with a roughness parameter Ra between 0.19 and 0.24 µm and a roughness parameter Rq between 0.25 and 0.30 µm.

A specific test setup (Fig. 3) was designed to compare the tribological behavior of different coatings applied on the shafts. The shafts were rubbed against a steel ring that inner surface simulated the gear’s inner surface. These rings were designed in order to obtain and a line contact length of 2 mm thanks to two 1-mm wide shoulders machined inside the ring in order to increase the contact pressure and thus promote wear. Both the ring bore and shaft diameter were measured before the test to ensure that oil clearance was kept between 0.13 and 0.14 mm. This enabled to minimize variations in contact pressure: the maximum Hertzian contact pressure was between 280 and 290 MPa.

In the test setup, the shaft sample (remachined from a real differential shaft) is mounted into a steel sample holder. The normal load is applied through the sample holder thanks to a hydraulic cylinder. The ring sample is mounted into a housing connected to a shaft which is driven in rotation by an electric motor. The ring is driven in rotation thanks to a keyed assembly inside the housing. The contact kinematics of the planet gear/differential shaft application is therefore respected. Both normal and tangential friction forces are measured thanks to strain gauge sensors enabling to calculate the friction coefficient all along the test duration.

For the tests, a fully formulated lubricant was used. It was a commercial gearbox oil Tranself NFP of grade 75W80 (KV40 = 36 cSt, KV100 = 7.5 cSt) containing antiwear (AW) and extreme pressure (EP) additives. The test protocol was designed to promote wear: it is an 8-hour long test at a constant normal load of 8 kN and a constant rotation speed of 100 rpm. Due to limitations in the controller of the testbench, the 8-hour long test was performed in a series of four subsequent 2-hour sequences.

The wear tests were duplicated. The test parameters are summarized in Table 3.

The oil was heated up to 50 °C at the beginning of the test. Oil temperature was not regulated during the test and was left free to evolve according to how much power was dissipated by friction in the contact. At the end of the test, oil reached temperatures between 57 and 60 °C.

Referring back to Sec. 2.2, the theoretical minimum oil film thickness calculated from the Myers [1] formula is 0.12 µm in these tribological conditions. Considering the initial roughness of both the ring bore and coated shaft for the three coatings tested, the contact operated initially in the boundary lubrication regime as the Λ ratios were 0.3 and 0.5 for the e-nickel coating and the DLC coatings, respectively.

Observation of the wear scars on the shafts and rings was performed using optical microscopy and scanning electron microscopy (Hitachi S-3400N). Energy-dispersive X-ray spectroscopy (UltraDry EDS detector and pathfinder software from Thermo Fisher) was used to perform chemical analyses on tribofilms and wear scars.

Stylus profilometry (Form Talysurf PGI820 from Taylor Hobson) was used to measure the surface roughness of both shaft and ring before and after the test. Stylus profilometry was also used to perform wear depth measurements on the shafts.

Surface hardness and elastic modulus measurements of the two DLC coatings were made using a Fisher instrumented indentation tester (FISHERSCOPE HM2000, Helmut Fischer GmbH) equipped with a Vickers diamond tip. The measurements were performed at a load of 10 mN so that the indentation depth did not exceed 10% of the coating thickness. The surface hardness of the e-nickel coating was performed using a microhardness tester (MicroMet 6040, Buehler) equipped with a Vickers diamond tip. A weight of 50 g was chosen for hardness measurement of the e-nickel coating to minimize surface roughness effects and to keep the indentation depth below 10% of the coating thickness.

Figure 4 presents the evolution of the friction coefficient during the 8-hour long test for the three coatings. Given that the test was performed in a series of four 2-h sequences, friction peaks caused by restart are observed every 2 h. After the running-in period, the friction coefficient stayed mainly between 0.08 and 0.10 for all three coatings. In these testing conditions, the friction coefficient did not seem to be affected by the coating. This may be due to the fact that, for fully formulated oils containing AW/EP additives but no friction modifier additives, friction is, in the boundary lubrication regime, mainly governed by the shearing of the tribofilm formed on the steel rings (tribofilms formed on the steel rings are presented in Fig. 7).

Figure 5 presents the average wear depth of the coatings after the 8-hour test. None of the coatings were completely worn out at the end of the test. One-third of the e-nickel coating thickness was worn out. The two DLC coatings showed lower wear as less than 10% of the a-C:H coating thickness and less than 5% of the ta-C coating thickness were worn out, respectively. The lower wear of the two DLC coatings compared to the e-nickel coating is at least partly due to the higher hardness of DLC.

The optical microscopy observations of the wear tracks of the three shaft specimens are presented in Fig. 6. No flaking nor delamination of the coatings was observed. The rubbing surface of the DLC-coated shafts (a-C:H and ta-C) showed a smooth wear mechanism with a polished wear scar.

In addition, the rubbing surface of the ta-C coating showed some bluish coloration which is reminiscent of a tribofilm. Sulfur, phosphorus, and zinc were detected in EDS. These chemical elements came from the AW/EP additives of the oil.

No optically visible tribofilm was observed on a-C:H coating and EDS performed on the a-C:H coating did not detect sulfur, phosphorus, nor zinc. According to Bobzin et al. [15] and Vengudusamy et al. [16], the tribofilm formed from antiwear additives, such as ZDDP, on non-doped amorphous carbon coatings can be extremely thin, ranging from 10 to 30 nm, and show a patch-like structure, rather than a pad-like structure as usually observed on steel. This tribofilm typically adheres weakly to a-C:H coatings and can be easily removed using solvents [17]. After testing, the samples were cleaned with ethyl acetate and ethanol, meaning that any tribofilm that may have formed on the a-C:H coating would have been removed during the cleaning process. The tribofilm formed on ta-C may be more adherent and may explain the blueish coloration of the rubbed area on the ta-C coating.

The e-nickel shaft presented clear abrasion grooves (green arrows) and also tribofilm formed from AW/EP additives which appear as a multitude of small brownish spots (pad-like structure, see red arrows). Sulfur and zinc were detected in EDS (as well as phosphorus coming from both the coating and the AW/EP additives). As described by Ozimina et al. [18,19], antiwear additives such as ZDDP can adsorb and react on phosphorus nickel coatings. Even if the e-nickel surface showed tribofilm patches formed from the AW/EP additives, it did not prevent the material from wearing.

In lubricated environments, tribochemical reactions between additives and the coatings are to be considered. As seen above, the three coatings are able to tribochemically react with AW/EP additives from the oil but it is difficult to determine which coating is the more prone to react with AW/EP additives and to be protected from wear by the tribofilm formed. AW/EP additives used in oils are mostly designed to react with iron-based material and mainly steel. However, AW/EP additives such as ZDDP are also known to react with other metallic materials such as chromium or nickel. In particular, Homann et al. [20] investigated the reaction of ZDDP with both iron and nickel metal surfaces and showed that the reactions are similar. The e-nickel coating might therefore be more prone to react with AW/EP additives from the oil used than the two DLC coatings. Nonetheless, e-nickel showed the most wear at the end of the test.

No adhesive wear patterns were observed in optical microscopy; therefore, considerations of adhesion between the coatings and the steel rings are unlikely to explain the difference in the tribological behavior of the three coatings. Hence, the high hardness of the DLC coatings is probably the main factor explaining the good performance of DLC coatings compared to e-nickel.

Wear on the steel rings was not measurable. The valleys of the initial roughness were still observed after the test which means that wear on the steel rings was rather limited and mainly consisted of the removal of the roughness peaks. The limited wear of the steel rings is probably due to clear tribofilms formed from the AW/EP additives of the oil that were visible on the steel rings, as shown in Fig. 7. The appearance of the tribofilms differs in terms of color and structure. The tribofilm on the ring that was rubbed against ta-C shows a lighter color and a more band-like structure (less pad-like structure) along the rubbing direction than the tribofilms on the rings that were rubbed against a-C:H and e-nickel. This may be attributed to different tribofilm thicknesses.

EDS analyses revealed the presence of sulfur, phosphorus, and zinc and thus confirmed the origin of the tribofilms formed on the rings [21,22]. After the test, the roughness parameter Rq was 0.18–0.21 µm for the rings that rubbed against the e-nickel-coated shafts and was 0.13–0.15 µm for the rings that rubbed against the DLC-coated (a-C:H and ta-C) shafts. It is possible that the final roughness of the steel rings that rubbed against a-C:H and ta-C is lower than those that rubbed against e-nickel because of the higher hardness and higher abrasiveness of the DLC coatings compared to the e-nickel coating.

The Λ ratios calculated at the end of the test were 0.5 and 0.7–0.8 for the e-nickel coating and DLC coatings, respectively. For the DLC coatings, the Λ ratios calculated were very close to 1, which is conventionally the limit value between boundary and mixed lubrication; therefore, hydrodynamic effects may have influenced some of the observations performed. For example, it is possible that the values of friction coefficient are rather those of a mixed lubrication regime with mainly inter-asperity contacts than those of a clear boundary lubrication regime. However, it is unlikely that it contributed to the lower wear observed on the DLC-coated shafts compared to the e-nickel-coated shafts.

A combined analytical and experimental approach was proposed to evaluate the tribological performances of DLC coatings applied to EV differential shafts and compare them to a reference electroless nickel plating. The analytical calculations suggested that the planet gear/differential shaft contact operates mainly in the boundary lubrication regime except at high differential rotation speeds in which the lubrication regime could be mixed.

A test setup and a test protocol were therefore designed to perform wear tests in boundary-lubricated conditions. Specific attention was paid to the test specimen preparation by using real differential shafts to make the tribological test configuration as close as possible to the final running conditions of the differential system and to take into consideration the standard variation of the series production machining process.

After an 8-hour long test in the initial boundary lubrication regime, a third of the e-nickel coating thickness was worn out whereas the a-C:H and ta-C coatings showed that less than 10% and less than 5% of their respective thickness were worn out. The reduced wear observed with the two DLC coatings, compared to the e-nickel coating, can be attributed in part to the higher hardness of DLC. The rubbing surfaces of the DLC-coated shafts (both a-C:H and ta-C) exhibited a smooth wear mechanism, resulting in a polished wear scar. Additionally, the rubbing surface of the ta-C coating displayed a bluish coloration due to a tribofilm formed from AW/EP additives. In contrast, the e-nickel-coated shaft showed distinct abrasion grooves along with small colored spots of tribofilm. Wear on the steel rings was not measurable or negligible as the valleys of the initial roughness remained visible after testing, indicating that wear on the steel rings was primarily involving the removal of surface peaks. This limited wear is likely due to the presence of distinct tribofilms formed by the AW/EP additives of the fully formulated oil used in this study. Even though DLC coatings are known also for their low friction properties, they did not show a reduced friction compared to e-nickel in the tribological conditions of this study: the friction coefficient stayed mainly between 0.08 and 0.10 for all three coatings. This may be attributed to the shearing of the tribofilm formed on the steel rings.

DLC coatings (a-C:H and ta-C) demonstrated a strong wear resistance under testing conditions simulating the planet gear/differential shaft application compared to the standard electroless nickel solution and are therefore to be considered a suitable surface treatment to improve durability for this application in electric vehicles.

There are no conflicts of interest.

The authors attest that all data for this study are included in the paper.