Friction measurements are performed on the ball-on-disk tribometer MTM2 from PCS Instruments Ltd., London, United Kingdom. Figure 1 shows a schematic representation of the test chamber. The ball is loaded via a leaf spring so that it is pressed against the face of the disk. The ball and disk are driven independently, so that various rolling-sliding conditions can be adjusted. The frictional force in the EHL contact between the two specimens is measured by a load cell located at the driving shaft of the ball. In this study, a 3/4 inch diameter ball is paired with a disk. Both test specimens are made of 100Cr6 (AISI 52100) with polished surfaces. Tactile roughness measurements are performed transversally to the running track of the ball and disk and give a root mean square surface roughness of the ball of Rq₁ = 10.5 nm and a corresponding disk roughness of Rq₂ = 9.0 nm. As shown in Section 4.3, this results in fluid film lubrication regime with fully separated surfaces for almost all of the operating conditions under consideration. The tests are conducted in a fully-flooded lubricant chamber. The lubricant temperature ϑ O i l is controlled by heaters embedded in the pot of the test chamber and is measured in the lubricant sump next to the disk.

For each friction curve, the slide-to-roll ratio SRR is varied from 0.0 (pure rolling) to 1.0 at constant mean speed v_m . The SRR is defined as the ratio of sliding speed v_g to mean speed v_m S R R = v g v m , where the sliding speed v_g is the difference between the speed of the ball 1 and the speed of the disk 2. The mean speed v_m is the mean of the surface speed of ball 1 and disk 2: v g = v 1 − v 2 v m = v 1 + v 2 2 .

For the friction measurements, the “unidirectional traction step” of MTM2 software is used. Hence, the measured coefficients of friction correspond to the mean value for negative and positive SRR.

EHL film thickness measurements are performed on an optical EHL tribometer using thin film colorimetric interferometry (Hartl et al., 1997). It is also a ball-on-disk tribometer. The EHL tribometer has been manufactured by Brno University of Technology (BUT) and has already been used in earlier studies with water-containing lubricants (Yilmaz et al., 2019a). Figure 2 shows the schematic representation of the EHL tribometer. The following description is based mainly on the works of Omasta et al. (2018) and Yilmaz et al. (2019a).

In the EHL tribometer a disk is loaded via a dead weight lever mechanism against a one inch diameter ball. The ball and disk are each individually driven by a speed-controlled electric motor to allow continuous variation of the speeds. In this study, the disk is made of sapphire and the ball of 100Cr6 (AISI 52100). The surfaces of both specimens are polished to achieve a surface roughness Ra <0.01 µm. The mean speed v_m , sliding speed v_g and SRR are defined identically as for the MTM2 tribometer (see Section 2.1). The ball rotates in a temperature-controlled lubricant reservoir, which supplies the contact between disk and ball. The lubricant temperature ϑ o i l is measured by a thermocouple directly located in the inlet zone of the EHL contact.

For evaluation of EHL film thickness, the interference pattern within the contact is tracked by an industrial microscope and evaluated using thin film colorimetric interferometry. Details on the measurement principle can be found in references (Hartl et al., 1997; Omasta et al., 2018).

Three water-containing lubricants with different water content are considered. A polyalphaolefine oil is considered as a reference. All lubricants are of grade ISO VG 22. The water-containing lubricants are based on water-soluble PAGs. The constant viscosity grade is achieved by different PAG chain lengths. Furthermore, additives such as extreme-pressure, anti-wear, foam inhibitor, anti-freeze and corrosion protection are added. The water contents under consideration were determined by Karl-Fischer titration and are 8 wt% for PAGW_{8 wt%}, 20 wt% for PAGW_{20 wt%} and 40 wt% for PAGW_{40 wt%}. The water content of 8 wt% represents an azeotropic state resulting from the hygroscopic properties of water-soluble PAGs. The maximum water content of 40 wt% was chosen because literature shows very poor lubricant film formation capability for higher water content. The reference PAO-05 was also considered by Yilmaz et al. (2019a). The properties of all investigated lubricants are listed in Table 1.

The speed and contact pressure are varied while maintaining a constant oil temperature of ϑ O i l = 40 °C and are listed in Table 2. On the MTM2, mean speed v_m and slide-to-roll ratio SRR are varied for three Hertzian contact pressures p_H , while on the EHL tribometer only the mean speed v_m is varied under constant load and pure rolling conditions.

On the MTM2 tribometer, for each mean speed under consideration, the system is heated up to ϑ O i l = 40°C under no-load and SRR = 0.0 conditions to ensure a quasi-stationary temperature distribution. Then the load is applied and friction curves are recorded as a function of SRR. The first test sequence is conducted at a contact pressure of p_H = 1200 N/mm². In doing so, the mean speed is stepwise decreased from v_m = 2.5…1.0 m/s. The second and third test sequence are conducted at contact pressures of p_H = 1000 N/mm² and 800 N/mm². The coefficients of friction shown in Section 3 and Section 4 represent the mean value obtained for positive and negative SRR (see Section 2.1). For material pairings with similar thermal effusivity, the kinematic conditions in terms of negative or positive SRR have a negligible effect on the coefficient of friction (Liu et al., 2020).

On the optical EHL tribometer, for each mean speed under consideration, the system is heated up to ϑ O i l = 40°C under no-load conditions to ensure a quasi-stationary temperature distribution. Then the load is applied and the lubricant film thickness measured while increasing the mean speed incrementally from v_m = 0.5 to 2.0 m/s. Each lubricant film thickness presented in Section 3 and Section 4 represents the mean arithmetic value of three single measurements. Evaluation of measurement repeatability gives a maximum deviation of 3.3 nm for PAO-05, 12.6 nm for PAGW_{8 wt%}, 6.4 nm for PAGW_{20 wt%} and 7.7 nm for PAGW_{40 wt%}, respectively.

For water-containing lubricants, the evaporation of water needs to be prevented or controlled within specified limits to avoid a change in properties. The tribometer design and test procedure have a significant influence. For the water-containing lubricants PAGW_8wt%, PAGW_20wt% and PAGW_40wt%, the high ratio of lubricant volume to free surface in combination with relatively long heating and conditioning periods in the optical EHL tribometer can cause water evaporation. The actual measurement of the film thickness only takes about 5 minutes per lubricant. Therefore, the EHL tribometer is first calibrated and heated up with a flushing PAGW until the desired steady-state oil temperature has been achieved. Then a separate metallic vessel is heated up on a hotplate to the desired oil temperature and the water-containing lubricant is filled in. Due to the high thermal mass of the vessel, the small volume of lubricant (about 50 ml) is heated up immediately. In the next step, the flushing PAGW in the EHL tribometer is removed and replaced by the fresh tempered PAGW. The test procedure is then started immediately to prevent evaporation. In contrast to the EHL tribometer, the MTM2 tribometer has a more closed design with much shorter heating periods and testing times. Therefore, no flushing lubricants were used. Note that, in addition to evaporation, water absorption can also occur depending on the temperature and relative humidity (Zhang et al., 2012; Chen et al., 2013). For PAO-05, both the MTM2 and EHL tribometer are calibrated and heated up to the desired oil temperature without additional measures.

Friction characteristic results for the considered lubricants are presented in Section 3.1.1. The influence of contact pressure is presented in Section 3.1.2, and that of mean speed in Section 3.1.3.

Figure 6 shows the measured central film thickness h_c plotted against the mean speed v_m for the investigated lubricants at p_H = 1200 N/mm² and ϑ O i l = 40°C for pure rolling conditions (SRR = 0.0). The measured film thickness is plotted in double-logarithmic scale.

For all investigated lubricants, the central film thickness increases nearly linear when plotted against the mean speed in double-logarithmic scale. All lubricants are capable of forming a lubricant film. This was also observed by Yilmaz et al. (2019a) for water-containing PAGs and for water-containing glycerol by Shi et al. (2014). The film thickness decreases the higher the water content. Thus, PAGW_8wt% shows the maximum and PAGW_40wt% the minimum central film thickness. The reference oil PAO-05 exhibits only a slightly higher central film thickness than the water-containing lubricant PAGW_8wt%. Figure 7 shows typical measured interferograms for p_H = 1200 N/mm², v_m = 2.0 m/s and ϑ O i l = 40°C.

All interferograms exhibit the typical film thickness distribution known for EHL point contacts. The central film thickness h_c is located in the middle of the contact, which is surrounded by a horse-shoe shape constriction of minimum film thickness. Note that each interferogram has its own color bar as the interference pattern depends on the refractive index of the lubricants. Thereby, the refractive index reduces the higher the water content (see Table 1) as also shown by Shi et al. (2014) for water-containing glycerol.

The experimental results of Section 3.1 clearly show the potential of EHL friction reduction with PAGWs. For evaluation, a mean coefficient of friction µ ¯ was calculated for each measured friction map. First, the mean coefficient of friction is evaluated for each friction curve at constant mean speed v_m : µ ¯ v m = ∫ S R R = 0.0 S R R = 1.0 µ S R R , v m d S R R .

Second, the mean values µ ¯ v m are averaged for all seven considered mean speeds: µ ¯ = 1 7 ( µ ¯ 1 m s + … + µ ¯ 2.5 m s ) .

Figure 8 shows the calculated mean coefficients of friction µ ¯ for each contact pressure in comparison of the lubricants under consideration.

For all PAGWs, a drastic reduction in the evaluated mean coefficient of friction µ ¯ in comparison to PAO-05 is observed. For PAGW_8wt% with the lowest water content, a mean friction reduction of between 73% and 81% is observed. For PAGW_20wt% and PAGW_40wt% with higher water content an even more pronounced reduction of maximum 91% and 95% is found, whereby there is no linear trend in friction reduction with increasing water content. The contact pressure exhibits only a subordinate influence on friction reduction with PAGWs.

The experimental results in Section 3.1 also show that the characteristics of friction curves with PAGWs differ strongly from the ones with PAO-05. The coefficient of friction increases slightly degressively for PAGW_8wt% and almost linearly as a function of SRR for PAGW_20wt% and PAGW_40wt%, as reported in literature (Yilmaz et al., 2019a; Burbank et al., 2020). Yilmaz et al. (2019a) found steadily increasing coefficients of friction with slip ratio on a twin-disk tribometer. Flattening of the friction curves at higher speeds was attributed to the thermal effects of bulk heating.

The literature review in Section 1 shows that the low friction of water-containing lubricants is mainly attributed to layers that shear easily in the lubricant film or to low effective contact viscosity due to small pressure-viscosity coefficients. The low frictional heating within the contact for the considered PAGWs can explain the almost negligible thermal regime under the considered operating conditions. The effective contact viscosity of the PAGWs is related to the derived pressure-viscosity coefficients (see Section 4.2), which are significantly lower than those of PAO-05. The lower effective viscosity results in lower shear stress and hence lower friction. Consequently, the influence of speed and contact pressure becomes less dominant the higher the water content. The study clearly shows the strong influence of the water content on friction for similar kinematic viscosity. The underlying mechanisms resulting in superlubricity cannot be finally declared.

The experimental results of Section 3.2 clearly demonstrate the ability of water-containing PAGs for lubricant film formation. For evaluation, Figure 9 shows the mean central film thickness h c ¯ evaluated for each lubricant averaged over all considered mean speeds. While h c ¯ for PAGW_8wt% is only 8% lower than for PAO-05, h c ¯ is reduced by 37% for PAGW_20% and 56% for PAGW_40wt%.

The measured EHL film thickness under pure rolling conditions discussed in Section 3.2 allows a backwards calculation of the pressure-viscosity coefficient α p 40 ° C for the investigated lubricants. In doing so, the Hamrock and Dowson equation (Hamrock and Dowson, 1976) for central film thickness in EHL point contacts is used: h c = 2.69 ∙ G 0.53 ∙ U 0.67 ∙ W − 0.067 1 − 0.61 e − 0.73 k with

k = 1.03 ( R y R x ) 0.64 and ( R y R x ) = 1 for circular point contacts.

The dimensionless parameters for material (G), speed (U) and load (W) are given by G = α p ∙ E ´ , U = η ϑ O i l ∙ v m E ´ ∙ R x   a n d W = F N E ´ ∙ R x 2 .

As all parameters for G, U and W except α p are known, the film thickness equation can be solved for α p . The calculation is based on the exponential curve fits of all measurement points per lubricant in Figure 6, see also (Shi et al., 2014; Yilmaz et al., 2019a). Table 3 shows the derived pressure-viscosity coefficients α p 40 ° C for the investigated lubricants.

For the water-containing PAGs, α p 40 ° C decreases from 5.9 1/GPa for PAGW_8wt% to 4.1 1/GPa for PAGW_20wt% to 3.0 1/GPa for PAGW_40wt%. Besides water content, also the different PAG chain lengths of the water-containing PAGs influence the pressure-viscosity coefficient. The lower the pressure-viscosity coefficient, the lower is the EHL film thickness, which shifts the transition from fluid film to mixed lubrication to lower speeds, depending on the surface roughness. The reference oil PAO-05 shows α p 40 ° C = 12.2 1/GPa. The calculated pressure-viscosity coefficients of all considered PAGWs are generally in the range reported in literature (Schmidt et al., 2006; Shi et al., 2014; Yilmaz et al., 2019a).

The pressure-viscosity coefficient of PAO-05 is approximately twice that of PAGW_8wt%. However, the central film thickness is only slightly higher (see Figure 10). This can be attributed to the higher density (approx. + 35 %) of PAGWs compared to PAO-05, which supports film formation, because the speed parameter U depends on the dynamic viscosity. Considering the reduction in the mean coefficient of friction of PAGW_8wt% by 81% compared to PAO-05 (see Figure 8), this is an interesting aspect in respect of EHL contact design.

The derived pressure-viscosity coefficients α p 40 ° C allow the calculation of EHL minimum and central film thicknesses for the friction measurements performed on the MTM tribometer. Considering the optical EHL tribometer, mixed lubrication can be directly excluded by the measured interferograms. The lubrication regime can be estimated by the relative film thickness λ r e l λ r e l = h m ( R q 1 2 + R q 2 2 ) with h_m calculated according to Hamrock and Dowson (1976). For λ r e l > 3, fluid film lubrication can be assumed. As the film thickness is lowest for the lowest mean speed, the investigated value of v_m = 1.0 m/s on the MTM2 tribometer is considered. Table 4 shows the calculated central (h_c ) and minimum film thickness h_m as well as λ r e l for v_m = 1.0 m/s and p_H = 1200 N/mm². The lowest film thickness is calculated for PAGW_40wt% with λ r e l = 2.6, which is only slightly lower than the threshold for fluid film lubrication. Hence, the measured friction curves represent mainly the fluid friction in fluid film lubrication.

EHL friction and film thickness are strongly influenced by the water content of PAGWs. As a summary of the results, Figure 10 shows the mean coefficient of friction µ ¯ (1 m/s) as a function of the calculated minimum film thickness h_m at a mean speed v_m = 1.0 m/s and contact pressure p_H = 1200 N/mm². The lowest coefficient of friction is associated with the lowest minimum film thickness. Thus, low water content in PAGWs results in higher lubricant film thickness but also higher friction and vice versa. However, superlubricity is achieved even for PAGW_8wt%. Depending on the friction, film thickness and cooling requirements of a specific tribosystem, the water content of PAGWs can be chosen accordingly. If a given tribosystem operates at low speed and features a high surface roughness, the water content can be chosen low to support elastohydrodynamic lubricant film formation and to avoid wear. If a given tribosystem operates at higher speed and features a low surface roughness, the water content can be chosen high to use the full potential of friction reduction. Note, that the friction results correspond to the fluid film lubrication regime (see Section 4.3). The friction results for boundary and mixed lubrication might be considerably different.