Friction and contact temperature in dry rolling-sliding contacts with MoS2-bonded and a-C:H:Zr DLC coatings

Gearboxes are usually lubricated with oil or grease to reduce friction and wear and to dissipate heat. However, gearbox applications that cannot be lubricated with oil or grease, for example in the space or food industry, are commonly lubricated with solid lubricants. Especially solid lubricants with a lamellar sliding mechanism like graphite and molybdenum disulfide (MoS2) or diamond-like carbon (DLC) coatings can enable very low coefficients of friction. This study investigates the friction and temperature behavior of surface coatings in rolling-sliding contacts for the application in dry lubricated gears. In an experimental setup on a twin-disk test rig, case-hardened steel 16MnCr5E (AISI5115) is considered as substrate material together with an amorphous, hydrogenated, and metal-containing a-C:H:Zr DLC coating (ZrCg) and a MoS2-bonded coating (MoS2-BoC). The friction curves show reduced coefficients of friction and a significantly increased operating area for both surface coatings. Due to the sufficient electrical insulation of the MoS2-BoC, the application of thin-film temperature measurement-known from lubricated contacts-was successfully transfered to dry rolling-sliding contacts. The results of the contact temperature measurements reveal pronounced thermal insulation with MoS2-BoC, which can interefere the sliding mechanism of MoS2 by accelerated oxidation. The study shows that the application of dry lubricated gears under ambient air conditions is challenging as the tribological and thermal behavior requires tailored surface coatings.


Introduction
Solid lubricants have become particularly important in the 1960s due to the space industry, since prevailing vacuum conditions obstruct the use of fluid lubrication. Nowadays, dry lubrication is generally also important in hygenic environments and in engineering designs with extreme lightweight or thermal requirements. It can present an ecological alternative to fluid lubricants in suitable applications. In gearboxes, dry lubrication omits the use of expensive seals and drastically reduces noload power losses (Höhn et al. 2009).
Solid lubricants with a lamellar sliding mechanism like graphite, molybdenum disulfide (MoS 2 ), and tungsten disulfide (WS 2 ) have been shown to reduce friction and wear. However, the tribological performance strongly depends on the environmental conditions ( (Gradt and Schneider 2016) and (Banerjee and Chattopadhyay 2014)) and the provision of the solid lubricants in the tribological system (Birkhofer and Kümmerle 2012). Investigations on the life time of dry lubricated bearings from (Schul 1997) show higher friction and wear of bonded compared to sputtered MoS 2 coatings. According to (Dienwiebel et al. 2004) and (Li et al. 2017), solid lubricants with lamellar sliding mechanism can reach the friction regime of superlubricity. (Hirano and Shinjo 1990) introduced this friction regime, which is attributed to coefficients of friction below μ ≤ 0.01. However, the requirements for achieving superlubricity are numerous and can only be observed on microscale (Berman et al. 2018). On a ball-on-disk tribometer under vacuum conditions, sputtered MoS 2 enabled coefficients of friction as low as 0.05 (Gradt and Schneider 2016). Investigations from (Gamyula et al. 1984) revealed coefficients of friction below 0.02 for MoS 2 -bonded coating on a ballon-disk tribometer. However, in contrast to graphite, significant relative humidity (RH) under ambient air conditions leads to an sharp increase in friction and wear for MoS 2 (Vazirisereshk et al. 2019). Metallic elements like chromium or titanium can be added to increase wear resistance, whereas there is no remarkable influence on frictional behavior according to (Banerjee and Chattopadhyay 2014) and (Gradt and Schneider 2016). Moreover, it is possible that high contact temperatures interfere with the sliding mechanism due to the oxidation of, e.g., MoS 2 to MoO 3 , which leads to a structural change of the lattice-layer structure (Zhang et al. 2011). Investigations from (Xu et al. 2003) reveal to increased wear for a MoS 2 -bonded coating at temperatures above 100°C compared to room temperature, which was attributed to oxidation of MoS 2 .
In addition to bonded coatings and pure solid lubricant layers, diamond-like carbon (DLC) coatings can also reduce friction and provide high wear resistance even at high loads. The mechanical and tribological properties of DLC coatings can be strongly influenced by the ratio of sp 2 -to sp 3 -bonded carbon, the hydrogen content and doping elements (Donnet and Erdemir 2008). Especially DLC coatings with high proportions of amorphous sp 2 carbon bonds and hydrogen (a-C:H) can result in ultra-low friction under dry lubrication. Investigations in high vacuum on a linear reciprocating pin-ondisk tribometer showed coefficients of friction as small as 0.005 for an a-C:H DLC coating (Fontaine et al. 2005). Also (Erdemir and Eryilmaz 2014) observed coefficients of friction in the range of 0.001 in a dry atmosphere on a ball-on-disk tribometer for a highly hydrogenated DLC coating. Such low coefficients of friction are attributed to superlubricity (Hirano and Shinjo 1990). However, the tribological properties of DLC coatings also depend strongly on environmental conditions, where the humidity of the ambient air plays a major role according to (Weihnacht et al. 2012) and(Schultrich andWeihnacht 2008). (Ronkainen et al. 1998) determined coefficients of friction of 0.15 < μ < 0.22 in ambient air with RH = 50 % on a pin-on-disk tribometer for a-C:H and a-C DLC coatings, which are similar to the results from (Donnet et al. 1994) at RH = 40 %. Investigations from ) on a twin-disk test rig under dry lubrication in ambient air showed coefficients of friction in the range of 0.10 < μ < 0.18 for a tetrahedral ta-C DLC coating. (Grossl 2007) and (Martens 2008) conducted experimental investigations on a gear test rig under dry lubrication in ambient air and showed improved durability of ta-C DLC-coated gears. Uncoated gears demonstrated significant scuffing failure after a short running time. The durability can be further increased by low-loss gear designs (Hinterstoißer et al. 2019).
The aim of this study is the evaluation of operating limits and the characterization of friction and temperature behavior of two different surface coatings for reliable operation of dry lubricated rolling-sliding contacts. Besides an amorphous, hydrogenated, and metal-containing a-C: H:Zr (ZrC g ) DLC coating, a MoS 2 -bonded coating (MoS 2 -BoC) based on polyimide is used. As the focus is put on transferability of load and kinematic conditions to gears, a twin-disk test rig is used. Besides friction and bulk temperature, the contact temperature is measured for MoS 2 -BoC using thin-film sensor technology in order to get insight into the shearing mechanism.

Experimental setup
The following sections describe the considered twin-disk test rig, the test disks for friction and contact temperature measurements, the operating conditions, and the thin-film sensor technology.
FZG twin-disk test rig Figure 1 shows the mechanical layout of the considered FZG twin-disk test rig, which was designed by (Stößel 1971). The description and formulations are mainly adopted from (Lohner et al. 2015) and (Reitschuster et al. 2020). Both test disks are press-fitted onto shafts that can be driven independently by two three-phase motors. Traction drives mounted between the motors and driving shafts allow a continuous variation of speed. The normal force F N in the disk contact is applied by a pneumatic cylinder via the pivot arm where the lower disk is mounted. The upper disk is mounted in a skid, which is attached to the frame by thin steel sheets. The skid is supported laterally by a load cell to ensure that the friction force F R in the disk contact for sliding velocities v g ≠ 0 m/s can be measured as a reaction force with hardly any displacement of the skid. Normal force F N , friction force F R , surface velocities v 1 and v 2 , and bulk temperature of the upper disk ϑ M are measured. ϑ M is recorded by a Pt100 resistance temperature sensor 5 mm below the surface of the disk. The coefficient of friction is calculated according to Eq. (1).
The sum velocity v ∑ is defined as the sum of the surface velocity of the upper disk v 1 and the surface velocity Hofmann et al. International Journal of Mechanical and Materials Engineering (2021) 16:9 Page 2 of 12 of the lower disk v 2 , whereas the sliding velocity v g is defined as the difference between the surface velocities v 1 and v 2 : The slip ratio s is defined as All experiments are carried out under line contact conditions with cylindrical disks having a diameter of 80 mm and a width of 5 mm according to Fig. 1.

Test disks
All test disks were made of case-hardened steel 16MnCr5E (AISI5115) with a surface hardness of 60 ± 2 HRC and a case hardening depth of CHD 550HV1 = 0.9 ± 0.2 mm. The preparation of the running surface was adapted to each coating process. ZrC g coated disks were peripherally ground and polished to an arithmetic mean roughness value Ra ≤ 0.01 μm to ensure high adhesion of the coating-bonding system. DLC coating graded zirconium carbide (ZrC g ) was deposited by middle frequency magnetron sputtering (mfMS) at the Surface Engineering Institute (IOT) RWTH Aachen University, Aachen, Germany. Thereby an industrial coating unit was used with two zirconium targets with a purity > 99.5 % and argon (Ar) and acethylene (C 2 H 2 ) as process and reactive gas. To avoid annealing effects of the casehardened steel, temperature during the physical vapor deposition (PVD) process was limited to 180°C. Further process parameters can be found in (Bobzin et al. 2015). The coating possesses of a crystalline zirconium interlayer on steel substrate and a graded zirconium carbide layer with increasing portions of carbon. The maximum carbon ratio is reached at the zirconium and hydrogen containing top layer with an amorphous structure a-C: H:Zr. Young's modulus E = 110 ± 12 GPa is lower compared to the steel substrate with E = 210 GPa. Total film thickness was t c = 3.2 μm. MoS 2 -BoC for friction measurements was applied by spraying at FUCHS LUBRI-TECH GmbH, Kaiserslautern, Germany, and consists of solid lubricant particles dispersed in an organic binder matrix. In order to increase adhesion between lacquer and substrate, a surface roughness of Ra ≈ 0.5 μm after hardening was chosen before coating as recommended by (Gamyula et al. 1984) and (Yukhno et al. 2001) for bonded coatings. For the coating process, the disks were heated up to 100°C, sprayed manually, and tempered in a convection oven for 1 h at 200°C. A total coating thickness of t c =15 ± 2 μm was measured with the magnetic induction test method according to DIN EN ISO 2178. For contact temperature measurements, a MoS 2 -BoC was used that consists of 70 wt.% polyimide as binder and 30 wt.% of MoS 2 and was applied at INM Saarbrücken, Germany. An identical coating process was applied. The total coating thickness was t c = 25 ± 5 μm. Figure 2 shows a representative uncoated, ZrC g coated and MoS 2 -BoC coated test disk before the test run. It can be seen that the optical appearance and roughness strongly depends on the preparation and coating method. The mfMS PVD coating technology leads to a slight increase in arithmetic roughness from Ra ≤ 0.01 μm to Ra = 0.03 μm, whereas MoS 2 -BoC considers a slight increase from Ra ≈ 0.5 μm to Ra = 0.61 μm. The MoS 2 solid lubricant particles of MoS 2 -BoC are visible due to the colored reflections of the light of the microscope.
All surface roughness measurements were performed in axial direction by a profile method according to DIN EN ISO 13565-1 to 13565-3 with a measured length of

Thin-film sensors
Besides infrared technology, thin-film sensors enable high-resolution contact temperature measurements. With these, resistance measurements take advantage of the high sensitivity of a suitable sensor material to a change in temperature or pressure during the transit of the thin-film sensor through a tribological contact. Initial pressure measurements in elastohydrodynamic (EHL) contacts on a twin-disk test rig with manganin sensors started in the 1960s in investigations of (Kannel et al. 1965). Since then, numerous authors have carried out contact temperature and pressure measurements in elastohydrodynamic contacts on model test-rigs with thin-film sensor technology, e.g., (Schouten 1973), (Baumann 1987), (Bauerochs 1989), (Kagerer and Königer 1989), and (Mayer 2013). Measurements on gears and bearings can only be found from a few authors like (Kagerer 1991) and (Kühl 1996). Whereas the thin-film sensor technology is highly developed for lubricated contacts with high fluid load portions, measurements in dry lubricated contacts remain unexplored. Within this study, thin-film sensors made of platinum were used for contact temperature measurements. The sensors were applied on zirconium dioxide (ZrO 2 ) disks to provide electrical insulation. A titanium adhesion layer with a thickness of approximate 40 nm on the ZrO 2 disks improved durability of the thin-film sensor. For both layers (titanium and platinum) ion beam sputtering was used. Figure 3 illustrates the considered sensor geometry, which has been successfully applied for EHL contact temperature measurements ( (Kagerer 1991), (Mayer 2013), (Ebner et al. 2020)). The manufacturing process consists of masking with photolithography technique and sputtering of the titanium bonding layer and platinum sensor respectively. The sensor height of the thin film sensor is 100-150 nm, which results in an ohmic resistance value of R S ≈ 120 Ω. A detailed description of the manufacturing process can be found in (Ebner et al. 2020). The ohmic resistance of platinum shows high sensitivity to temperature and weak influence of pressure. The ratio between the temperature and pressure coefficient α T and α P is high, which results  in high sensitivity of the measurand compared to the measuring method. Equation (5) shows the correlation of relative resistance change of platinum ΔR Pt /ΔR 0,Pt to temperature (ΔT) and pressure change (Δp).
During the transit of the thin-film sensor through the contact, temperature and pressure changes always occur simultaneously such that the pressure distribution has to be known to calculate the temperature rise ΔT. For the used platinum thin-film sensor, the temperature coefficient α T, Pt = 1.16•10 −3 1/K is two orders in magnitude higher than the pressure coefficient α p, Pt = − 1.10•10 −5 mm 2 /N.
For evaluation of the influence of MoS 2 -BoC on the contact temperature, Table 1 supplements the material data and thermophysical properties of steel, ZrO 2 , and polyimide. The latter approximates the properties of the MoS 2 -BoC. The thermal effusivity e represents the ability to transport heat by conduction and convection (also known as thermal inertia ) and is defined by Eq. (6).
Thereby, ρ describes the density, c p the specific heat capacity, and λ the thermal conductivity of the considered substrate or surface coating.

Operating conditions
Friction curves and bulk temperatures were measured for various operating conditions shown in Table 2. Each friction curve was recorded at a constant normal force of F N = 435 N, which corresponds to a Hertzian pressure of p H = 400 MPa for the contact of uncoated disks. For each considered sum velocity v ∑ , the slip ratio s was incrementally increased from s = 0 % to s = 50 %. All coefficients of friction μ and bulk temperatures ϑ M were recorded in quasi-stationary states characterized by a bulk temperature change Δϑ M /Δt ≤ 0.5 K/min. After reaching the maximum slip ratio of s = 50 %, the system was left at rest to cool down to room temperature before adjusting the next sum velocity v ∑ . Besides dry lubrication, reference measurements under oil injection lubrication were conducted with reference ISO VG100 mineral oil with 4 % of sulfur-phosphorus extreme pressure (EP) additive (FVA3A, (Laukotka 2007)). The oil was injected at a temperature ϑ oil = 40°C. To avoid damage, all friction curve measurements were aborted if the coefficient of friction exceeded μ = 0.5, or if the measured bulk temperature exceeded ϑ M = 160°C. Disks with the same surface finish according to Fig. 2 were paired. Each friction curve was measured twice with a new set of disks. The room was conditioned to 20°C and a relative humidity of RH = 40 − 50 %.
Contact temperature measurements were performed at constant sum velocity v ∑ = 2 m/s, but different loads and slip ratios s, as shown in Table 2. The considered normal forces were F N = {251, 446} N, which correspond to Hertzian pressures of the uncoated contact of p H = {300, 400} MPa. The slip ratio ranged from s = 0 % to s = 30 %. After adjusting each operating point, the disks were brought into contact at the considered normal force F N for about three seconds and six roll-overs from the thin-film sensor were tracked with a digital oscilloscope. This procedure was repeated once to achieve a total of twelve signals for each operating point.

Results
This section presents the experimental results divided into friction curves and contact temperature measurements.
Friction curve measurements Figure 4 shows the measured coefficients of friction μ and bulk temperatures ϑ M over the slip ratio s for a normal force of F N = 435 N and sum velocities v ∑ = {1, 2, 4} m/s. Both friction curves of the uncoated polished surface under dry lubrication show a degressive increase of the coefficient of friction for a sum velocity v ∑ = 1 m/s up to a slip ratio s = 20%. A higher slip ratio results in a rapid increase in the coefficient of friction. Thus, the tests were aborted and a stationary value could not be measured. The results correspond to investigations by (Ebner et al. 2018) and ) for uncoated surfaces under dry lubrication. Measured bulk temperatures increase only slightly with increasing slip ratio for  (Vazirisereshk et al. 2019). Corresponding bulk temperatures increase with increasing sum velocity and slip ratio due to rising frictional power in the disk contact. The first test run is aborted due to high friction force at a sum velocity v ∑ = 4 m/s and a slip ratio s = 50 %, the second test run did not reach the abortion criteria. The friction curves for DLC coating ZrC g reveal frictional behavior similar to MoS 2 -BoC. For a sum velocity v ∑ = 1 m/s, a sharp increase of the coefficient of  friction up to a slip ratio s = 5 % and a moderate decrease for higher slip ratios is observed for the first test run. The second test run shows its maximum coefficient of friction at a slip ratio s = 20 % before it decreases to a similar level as the first test run. At higher sum velocities, the profile of the friction curves reveals a sharp increase to a maximum coefficient of friction at a slip ratio of s = 2 and 5 %, after which a continuous decrease occurs. The decrease of the coefficient of friction with an increasing slip ratio can be attributed to a temperatureinduced structural transformation from carbon to graphite (Durst 2008) resulting in a lattice-layer structure. This transformation process is also observed in investigations on the frictional behavior of ta-C coatings by . The corresponding bulk temperatures increase with increasing sum velocity and slip ratio due to rising frictional power in the contact. The second test run is aborted due to high friction force at a sum velocity v ∑ = 4 m/s and a slip ratio s = 50%. The experimental results under oil injection lubrication with uncoated polished surfaces show significantly lower coefficients of friction and bulk temperatures. Despite the oil injection temperature of ϑ oil = 40°C, the bulk temperatures are lower for every operating condition due to heat convection into the surroundings. Compared to lubricated contacts, dry lubrication shows lower repetition accuracy and higher sensitivity to changes of the operating conditions, as seen in Fig. 4. Figure 5 shows optical scans and corresponding mean arithmetic roughness Ra of all investigated surfaces under dry lubrication after the second test run. Note that the abortion limit was reached for the uncoated surface and DLC coating ZrC g , which indicates that the operation area was exceeded, resulting in damage to the investigated surface. Despite the rise in surface roughness Ra, the uncoated surface shows brown discoloration, which may indicate oxidation processes. Similar observations by ) revealed the formation of Fe 2 O 3 on the uncoated steel running surface under dry lubrication through energy-dispersive X-ray spectroscopy (EDX) element analysis. Generally, high friction is associated with tremendous local temperature developments that can lead to accelerated oxidation processes. MoS 2 -BoC reveals a partial detachment of the bonded coating as the steel substrate becomes visible, whereas the surface roughness increases slightly to Ra = 1.01 μm. Clear changes can be observed for DLC coating ZrC g in the optical appearance and increase of surface roughness to Ra = 3.18 μm.

Contact temperature measurements
Measurements of contact temperatures were considered for MoS 2 -BoC. The polyimide matrix and solid lubricant particles are sufficient electrical insulators to not cause a short circuit between the contact pads of the thin-film sensor. Besides, MoS 2 -BoC is soft compared to the platinum of the thin-film sensor, which inhibits detachment of the sensor from the sensor disk. Figure 6 shows the contact temperature rise ΔT* above bulk temperature over the dimensionless gap length direction x/b H for MoS 2 -BoC at normal forces F N = {251, 446} N, sum velocity v ∑ = 2 m/s and slip ratios s = {0, 10, 20, 30} %. Thereby, the dimensionless gap length direction represents the sensor distance × normalized by the half Hertzian contact width b H in entraintment direction to enable a simpler visualization of different loads. All illustrated temperature profiles represent the mean value of up to twelve roll-overs. The signal scattering for F N = 251 N is less than 1.2 K at a slip ratio s = 20 %. For slip ratios of s = {0, 10} %, the temperature scatters between 0.1 K and 0.2 K. At a normal force of F N = 446 N, the scattering increases to a maximum of 6 K for a slip ratio of s = 30 %. The influence of pressure on the temperature profile was neglected (symbolized by * added to ΔT), which leads to underestimated temperature rises due to the negative pressure coefficient of platinum. As MoS 2 -BoC with coating thickness t c = 25 ± 5 μm affects contact pressure, a pressure correction based on p H for the uncoated disk contact cannot be easily applied. Investigations by (Elsharkawy et al. 2006) on the influence of coatings Young's modulus and thickness on pressure distribution reveal significant lower maximum contact pressures for soft coatings. For a ratio of Young's moduli between substrate (E s ) and coating (E c ), E s /E c = 20, and a coating thickness of 20 μm, the maximum contact pressure can be as low as half the value of the uncoated system. However, since no detailed simulations are available for the considered MoS 2 -BoC, no pressure correction was applied. The comparison of measured contact temperatures ΔT* is limited to the same normal force, although the maximum temperature change due to pressure is estimated to be small as the platinum sensor is much more sensitive to temperature as described in "Thin-film sensors" section. At a normal load of F N = 251 N, a maximum temperature rise ΔT Ã max = 0.5 K for pure rolling (curve a) was measured. This can be referred to hysteresis friction in the polyimide matrix and microslip. The temperature rise increases from ΔT Ã max = 3.5 K (curve b) up to ΔT Ã max = 6.2 K (curve c) for the highest investigated slip ratio s = 20 %. This can be referred to the increased sliding speed and hence friction power. Note that the coefficient of friction also increases slightly from μ = 0.046 (curve b) to μ = 0.054 (curve c). A similar pattern is observed at a normal load F N = 446 N. The temperature rise ΔT * also rises steadily with increasing slip ratio s. For pure rolling (curve a), the temperature rise is very small. For curve b, the temperature rise is Δ T Ã max = 3.1 K and for curve c, ΔT Ã max = 8.0 K. The max-imum temperature rise ΔT Ã max = 20.5 K is observed for curve d at s = 30 %. As for the lower normal force, the coefficient of friction increases slightly from curve b to d, from μ = 0.040 to μ = 0.050 to μ = 0.051.

Discussion
In the following section, the experimental results are discussed with focus on the tribological behavior and thermal performance of the considered surface coatings.

Tribological performance of surface coatings
The experimental results in "Friction curve measurements" section under dry lubrication demonstrate a reduction of friction and an increase of the operating area by the considered surface coatings MoS 2 -BoC and DLC coating ZrC g compared to plain steel contacts. At higher sum velocities v ∑ , an increase in the slip ratio s can result in reduced friction. The measured coefficients of friction between 0.1 < μ < 0.2 for DLC coating ZrC g correlate with the results from (Erdemir and Eryilmaz 2014) for an a-C:H DLC coating under ambient air conditions. The decrease in friction at higher slip ratio and sum velocities can be referred to the graphitization of amorphous carbon coatings. (Liu et al. 1996) conducted experiments on a pin-on-disk tribometer with similar load and sliding speeds as for the friction curves in Fig. 4 and observed a significant reduction of friction especially for high sliding. According to (Durst 2008), the graphitization starts from 300°C, which can occur locally at asperity contacts with high local pressures and flash temperatures. Also for the MoS 2 -BoC, the coefficients of friction are in agreement to further investigations. (Xu et al. 2003) performed experiments under ambient air conditions on a ball-on-disk tribometer with MoS 2 -BoC and epoxy resin as binder. For a relative humidity of RH = 50 % and room temperature (23°C), coefficients of friction between 0.1 < μ < 0.2 were measured. The coefficients of friction for contact temperature measurements in the "Contact temperature measurements" section are significantly lower than observed during friction curve measurements with MoS 2 -BoC in the "Friction curve measurements" section. Although the comparison is restricted with respect to different disk pairings, testing time has to be considered. While the contact temperature measurements lasted only a few seconds, the total running time for a friction curve measurement can be up to 2 h. (Gradt and Schneider 2016) observed continuously increasing coefficients of friction over running time for MoS 2 coatings on a ballon-disk tribometer. The results of friction curve measurements may indicate this behavior, since low coefficients of friction as low as μ = 0.05 to 0.1 were observed only for low slip ratios at a sum velocity of v ∑ = 1 m/s. For the sum velocity v ∑ = 1 m/s and the slip ratio s = 10 %, the measured coefficient of friction is μ = 0.09, whereas for the same sliding speed v g at a sum velocity of v ∑ = 2 m/s (s = 5%), the measured mean coefficient of friction is μ = 0.15. This indicates that ongoing interaction in the contact accompanied with wear in the contact zone interferes with the sliding mechanism of the MoS 2 -BoC. Note that also the bulk temperatures were higher during friction curve measurements, which may have an influence on the material properties of the polyimide binder matrix of the MoS 2 -BoC. Investigations from (Tsai et al. 2003) on the temperature dependency of vapor deposited polyimide reveal a linear decrease in Young's modulus with increasing temperature. Hence, the increasing bulk temperatures for higher sum velocities and slip ratios may affect the tribological performance significantly.
The recorded coefficients of friction during contact temperature measurements in the "Contact temperature measurements" section also show a decrease with higher load as known for solid lubricants with a lamellar sliding mechanism (Gustavsson et al. 2013). According to (Donnet and Erdemir 2008) and (Kazuhisa 2001), coefficients of friction for compounds with lamellar sliding mechanism correlate to the contact area and shear stresses between the sliding planes. However, there is no linear relationship between load and contact area resulting in decreasing coefficients of friction for higher loads as observed by (Gradt and Schneider 2016) and (Gustavsson et al. 2013).

Thermal performance of surface coatings
The investigations with dry lubrication show significantly higher coefficients of friction than the investigations with oil injection lubrication. This higher friction power accompanied with a poor heat dissipation results in higher bulk temperatures. The related higher level of contact temperatures under dry lubrication are amplified by thermal insulation effects observed by contact temperature measurements with MoS 2 -BoC.
To consider the influence of the thermophysical properties of MoS 2 -BoC (see Table 1) on contact temperature, the flash temperatures T Bl according to Blok (Blok 1937) are calculated by Eq. (7) for the material pairings ZrO 2 /steel and ZrO 2 /polyimide. Thereby, polyimide approximates the thermophysical properties of MoS 2 -BoC. F N represents the normal load, l eff the width of the contact, E´the reduced modulus, an R the radius of relative curvature. Index 1 refers to the upper disk (ZrO 2 ) and index 2 to the lower disk (steel or polyimide).
As the temperature penetration depth is in the range of only a few micrometer (Habchi 2014) and , the influence of the steel substrate on the flash temperature can be neglected. T Bl refers to the maximum contact temperature rise above bulk temperature and can thus be compared to the maximum temperature rise ΔT max measured for MoS 2 -BoC. Figure 7 shows the maximum temperature rise ΔT max measured for ZrO 2 /MoS 2 -BoC and the flash temperatures T Bl calculated for ZrO 2 /polyimide and ZrO 2 /steel.
The comparison between the measured and calculated values for ZrO 2 /MoS 2 -BoC and ZrO 2 /polyimide agree, with largest deviations at the slip ratio of s = 30 % at F N = 446 N. The calculated flash temperatures for ZrO 2 / steel are clearly lower than for the measured and calculated pair with the considered coating. This clearly indicates thermal insulation effects that are mainly caused by the low thermal effusivity of e = 486 J/(K ffiffi s p m 2 ) of the MoS 2 -BoC compared to steel with e = 12130 J/(K ffiffi s p m 2 ). Numerical simulations of Ziegltrum et al. ) reveal thermal insulation effects in lubricated steel/polymer contacts due to low thermal effusivity of polymers. Hence, especially the high proportions of polyimide binder matrix with its very low thermal conductivity (Benford et al. 1999) favors thermal insulation by MoS 2 -BoC, since the thermal conductivity of MoS 2 is only slightly lower compared to steel (Peng et al. 2016). Thermal insulation has also been observed with coatings under oil lubrication (e.g. (Björling et al. 2014) and (Ebner et al. 2020)). Thereby, in contrast to dry lubricated contacts, thermal insulation can result in a reduction in the coefficient of friction, as the contact viscosity is reduced by high contact temperatures. It should be Hofmann et al. International Journal of Mechanical and Materials Engineering (2021) 16:9 Page 9 of 12 noted that the absolute contact temperatures measured with MoS 2 -BoC are low in comparison for the considered operating conditions. This is mainly because the disks are in contact for approximately only twelve rollovers per operating point in order to avoid detachment and high wear of the platinum thin-film sensor. Hence, the measured bulk temperature is not quasi-stationary like for the friction curve measurements. Nevertheless, the observed thermal insulation with high contact temperature rises can affect the performance of MoS 2 -BoC since MoS 2 is sensitive to oxidation processes (Zhang et al. 2011). Investigations from (Xu et al. 2003) show significantly increased wear at temperatures above 100°C for MoS 2 -bonded coatings. Besides accelerated oxidation, high temperature levels can also result in reduced Young's modulus of the polymer binder matrix (Tsai et al. 2003). For DLC coatings, high contact temperatures can result in increased tribological performance as a structural change (graphitization) from sp 3 -to sp 2 -bonded carbon can occur.
It should be noted that no pressure correction was considered for the measured contact temperatures. For this and a detailed interpretation, numerical modelling can be applied to obtain the pressure and temperature distributions. In addition, the influence of the MoS 2 particles on the thermophysical properties of MoS 2 -BoC should be investigated, whereby the thermal conductivity of filled polymers can show an anisotropic behavior (Mamunya et al. 2002).

Conclusion
This study investigated the friction and temperature behavior of rolling-sliding contacts under dry lubrication. Two surface coatings with different coating technologies were considered on a twin-disk test rig. To classify the results, uncoated polished surfaces were tested under dry and oil injection lubrication. The main conclusions of this study with respect to rolling-sliding contacts add The bearable load level of uncoated steel surfaces under dry lubrication is very low. Surface coatings can significantly increase operating areas under dry lubrication. Friction and bulk temperatures are considerably higher compared to oil lubrication. Contact temperatures under dry lubrication can be measured by thin-film sensors for bonded coatings if the electrical insulation is sufficient. Low thermal effusivity of bonded coatings can result in thermal insulation effects that can accelerate oxidation processes.
This study demonstrates the challenge of reliable implementation of e.g. gears with rolling-sliding contacts under dry lubrication under ambient air conditions. Nevertheless, the potential of tailored surface coatings under dry lubrication becomes clear. The lubrication and failure mechanisms have to be investigated further.