2.1 Simulation of Droplets on Stepped Wettability Surface
In situations where lubricant supply is limited, the unidirectional motion of oil droplets towards the lubrication track can enhance the lubrication performance of the bearing. Therefore, the implementation of enhanced oil replenishment techniques can improve the film thickness as well as the life and reliability of bearings under limited lubricant supply.
Initially, a preliminary study was conducted to examine the behavior of oil spreading on a stepped wettability surface. Computational fluid dynamics (CFD) was employed to simulate the unidirectional spreading effect of oil droplets on a striped track with an oleophobic-oleophilic-oleophobic structure (referred to as ST). Fig. 1 illustrates the model used for oil droplet flow simulation. The model featured a spherical oil droplet positioned 0.05 mm above the center of the striped track, with a radius of 0.4 mm and a volume of approximately 0.268 μL. The track width was 0.4 mm. The computational domain had dimensions of 4 mm × 4 mm × 4 mm, divided into cells with an element size of 0.0346 mm. The origin of the coordinate axes was located at the centerline of the track, with the y-axis perpendicular to the track and the z-axis representing the direction of the falling oil droplet.
The simulation was performed using the FLUENT package, which solves the three-dimensional Navier-Stokes and continuity equations using a volume of fluid (VOF) model. This model solved a single Navier-Stokes equation and the continuity equation for two phases: air and oil. Furthermore, it solved an additional VOF advection equation in which a variable α denoting the volume fraction of one of the phases was introduced. A value of α = 1 indicated that the cell was filled with one phase (in this case, oil), while α = 0 specified that the cell was filled with the other phase (air). The interface between the phases was tracked using the condition 0 < α < 1. The variables and properties of each computational cell were characterized by the volume average values of the phases. The three-dimensional Navier-Stokes, continuity, and VOF advection equations [24] employed to solve the droplet falling onto the plane problem are as follows:
where v = (u, v, w) and p represent the velocity vector and pressure, respectively; ρ and μ denote the average density and viscosity of the fluid in the computational cell. The vector κ = (0, 0, 1) represents the unit vector in the z-direction; f is a volume force term originated from surface tension and interface curvature. The oil droplet falls freely from its initial position, and the boundary condition is that the outlet pressure is equal to atmospheric pressure. The simulation time step was set to be 1e-5 s.
The oil droplet flow process was utilized to illustrate the behavior of oil droplets on a stepped wettability track. Understanding the dewetting behavior of lubricants provides insight into their replenishment capability. Fig. 2 demonstrates that the PAO4 oil droplet exhibited preferential spreading in the entrainment direction of the striped track compared to the original surface, as observed from the bottom of the model. The oleophobic areas on either side of the lubrication track caused the oil to be pushed back as it was forced out of the lubrication track at the exit of the bearing contact area. During the rolling process in a bearing, increased oil spreading along the entrainment direction helps improve lubrication and stability. The time-dependent curve of the spreading length indicated that PAO4 oil droplets provide a more adequate oil supply in the entrainment direction. The spreading speed was found to be related to the difference in wettability gradient between the oleophobic and oleophilic areas.
Lubricating oils with high viscosity exhibit reduced replenishment capabilities due to greater drag. To investigate this, simulations were conducted using PAO4, PAO6 and PAO40 droplets of the same size to simulate the spreading process on a ST plane. As shown in Fig. 3(a), PAO40 and PAO6 required more time to spread in the entrainment direction compared to PAO4, which spreads quickly. The curves illustrate that oil droplets with higher viscosity require more time to spread. In particular, oil droplets that fall off the ST centerline cannot be replenished in time, as depicted in Fig. 3(b). When PAO4 droplets are located more than 0.8 mm from the centerline, they are unaffected by the designed stepped wettability in the experiment. Therefore, deviation distance (s) and oil viscosity limit oil replenishment.
Fig. 4 presents the contact angles of PAO4 droplets on different directions of the striped lubrication track on a steel plate. Various types of PAO oils were utilized to demonstrate the impact of the stepped wettability of the striped track, as indicated in Table 1. As the viscosity of the lubricant used in the experiments increased, the droplets tended to spread more evenly in x- and y-directions. Additionally, the aspect ratio of droplets in both directions decreased as viscosity increased, which is consistent with the simulation results.
Table 1 Lubricants properties
PAO oils
|
Viscosity @22 ℃
(mPa.s)
|
Density @22 ℃
(kg/m3)
|
Contact angles (°) (amount: 2 μL)
|
Aspect ratio
|
Steel surface
|
AF coating
|
x-direction
|
y- direction
|
PAO4
|
25.1
|
819
|
8.75
|
64.15
|
58.08
|
44.18
|
1.37
|
PAO6
|
50.2
|
828
|
15.37
|
64.52
|
59.26
|
48.86
|
1.29
|
PAO40
|
935.5
|
838
|
26.91
|
65.90
|
64.09
|
54.21
|
1.25
|
PAO100
|
2800.0
|
847
|
28.32
|
67.91
|
64.76
|
56.39
|
1.24
|
2.2 Lubrication Enhancement under Limited Lubricant Supply
When a bearing experiences severe starvation, oil pools typically separate completely on two sides of the bearing contact. Enhancing the replenishment of oil around the contact area becomes crucial to improve lubrication. Therefore, it is of utmost importance to enhance the replenishment performance under severe lubrication conditions in bearings.
To examine the effect of stepped wettability, the oil film thickness was measured using a multi-point optical lubricating film thickness test rig (shown in Fig. 5) in a controlled environment at a temperature of 20 ± 1° and a humidity of 65 ± 5%. A thrust ball bearing with an adjustable number of rolling balls was used, and the film thickness was measured using optical interferometry [25]. In the experiments, three balls were positioned at 120° intervals for testing. The film thickness measurements were averaged from three repeated tests, with a total load of 90 N applied to the three balls. The lubricant used was PAO series oil with a volume of 0.5 μL, and the diameter of the steel ball was 25.4 mm.
The multi-point optical lubricating film thickness test rig allows for the observation of the oil replenishment process. The oleophobic domain was created using a commercial anti-fingerprint (oleophobic) coating and had a constant width of ST (d = 0.4 mm). The track radius was 60 mm to the rotating center of the glass disc.
Fig. 6(a) illustrates the impact of stepped wettability on the formation of different viscous PAO oil pools under limited lubricant supply conditions at a speed of 64 mm/s. The images in the left and right columns depict the bearing contacts using different PAOs with the untreated glass disc surface and the stepped wettability surface, respectively. As the balls undergo repeated roll-overs, the oil in the lubrication track is forced to move towards both sides. Due to the limited supply condition, no oil pool forms at the inlet of the bearing contacts on the untreated disc, indicating a state of oil starvation. The effect of stepped wettability is evident from the presence of inlet oil pools and the formation of classical horse-shoe shaped elastohydrodynamic lubrication (EHL) interferometry images, particularly with low-viscosity oils.
Fig. 6(b) displays two graphs showing the film thickness and speed of PAO4 and PAO100 with and without stepped wettability (SW) on the glass disc surface. Overall, the lubricating film thickness generated using the disc with SW is greater than that with the untreated disc (without SW), attributed to improved oil replenishment on the track through SW. The effect of enhanced replenishment is particularly significant for the viscous PAO100. The film thickness increases considerably as the speed increases, especially evident in the results of PAO4. Only the tests with the untreated glass disc exhibit a decrease in the rate of film thickness increase at high speeds. Notably, the film thickness curve of PAO100 with the SW disc significantly decreases at the speed of 130 mm/s. The replenishment rate is low for the high viscosity of PAO100. At high speeds, the time between two consecutive bearing roll-overs is so short that the replenishment is insufficient to form a thick lubricating film. The insets in Fig. 6(b) show the SW tracks of PAO4 and PAO100 at 64 mm/s. The replenishment of PAO4 is noticeably better than that of PAO100. PAO100 features intact oil ridges on both sides of the track, whereas PAO4 readily replenishes the lubrication track. High-viscosity lubricants are generally preferred for bearing lubrication because they can form a thicker lubricating film. However, under limited lubricant supply conditions, the oil replenishment capacity decreases as the viscosity of the lubricating oil increases, as indicated by the simulation results in Fig. 3(a). Therefore, enhancing oil replenishment is crucial when using high-viscosity lubricating oils.
The size of the inlet pool is characterized by the distance of the meniscus from the bearing contact zone, referred to as the inlet distance (as marked in Fig. 6(a)). The distance indicates the level of starvation resulting from insufficient lubrication. Fig. 7 illustrates the inlet distance of different PAO oils at a speed of 64 mm/s, demonstrating an inverse relationship between viscosity and oil supply at the inlet. Stepped wettability effectively improves the oil supply conditions.
2.3 Friction Torques of Bearings
This study presents a novel approach to reduce the friction torque in bearings by utilizing a striped chemical pattern with stepped wettability [22]. The inner ring surface of a self-aligning bearing (1204, dimensions: 47×20×14 mm) was patterned using a striped pattern. The manufacturing process involved disassembling the bearing to create the pattern on the inner ring. The steel components of the bearing were thoroughly cleaned using petroleum ether, ethanol, and deionized water through ultrasonic cleaning for a duration of 10 min. The cages were cleaned with ethanol and then sprayed with deionized water. Subsequently, all cleaned parts were dried with nitrogen. The manufacturing process is illustrated in Fig. 8. The lubrication track of the inner ring was covered with masking tape cut into a regular striped pattern. After heating the ring to 60 °C, an AF (oleophobic) coating was sprayed onto the unmasked areas, followed by heat cured at 90 °C to fix the silane on the lubrication track. The uncoated stripes represented the original steel surface, which exhibited strong wettability due to its oleophilic nature. In contrast, the coated areas displayed weak wettability, resulting in stepped wettability on both sides of the lubrication track. This led to the creation of a new type of bearing with a unique inner ring, referred to as a replenishment-augmented rolling element bearing (RaREB).
After assembly, four bearings were simultaneously evaluated using a bearing tester, where the bearings were installed on the main shaft of the bearing tester, as shown in Fig. 9.
Fig. 10 displays the friction torque testing machine, capable of measuring the friction torque and temperature rise for four bearings simultaneously. The load cell had a measuring range of 0-500 N and the test speed range was 0-3000 rpm. The experiments aimed to evaluate the performance of the new bearings under two conditions: limited lubricant supply (LLS) and fully flooded lubricant supply (FFL). For the LLS condition, 20 μL of PAO4 oil and 400 μL of 1# lithium-based grease (with PAO4 as the base oil) were used. In contrast, for the FFL condition, the required oil volume was estimated based on the selected bearing size [26], and each bearing was supplied with over 4 mL of lubricant.
Fig. 11 and Fig. 12 present the typical results obtained from tests conducted with the original bearings under FFL and LLS conditions. The tests were performed steadily, with the torque increasing as the speed increased as shown in Fig. 11. All tests ran for 3000 seconds, and the measured torque values of the complete set of bearings during the last 500 seconds (depicted as the pink area in Fig. 11) were averaged to obtain the representative torque for each speed. The presented friction torque is the average of three repeated tests. Fig. 12 displays the torque-speed curves for different loads under LLS conditions using the original bearings. As the load increased, the friction torque also increased due to the higher load-induced frictional torque.
The friction torque results of the RaREB bearings and the original bearings under FFL and LLS conditions are presented in Fig. 13. The effect of the proposed surface pattern on the bearing performance is more pronounced in the LLS condition than in the FFL condition. Experiments with sufficient oil supply showed that for both types of bearings, the bearing friction torque gradually increased with speed and reached a steady value probably for temperature accumulation (Fig. 13(a)). The difference between the two bearings was not significant under FFL conditions. Under LLS conditions, the bearing friction was reduced due to lower agitation resistance. Moreover, the RaREB bearings exhibited lower friction torque than the original bearings (Fig. 13(b)) probably due to improved oil replenishment, which reduces the likelihood of frictional surface contact.
To assess the reliability of the RaREB bearings, 1# lithium-based grease (with PAO4 as the base oil) was selected as the lubricant for testing the bearing’s friction torque. Under limited grease supply, 50 μL of grease was provided to each row of bearings, resulting in a total grease supply of 400 μL. The results of the friction torque versus speed curves (Fig. 14(a)) indicate that the RaREB bearings exhibited better reduction of friction. The bearing temperature-speed curves (Fig. 14(b)) show differences at high speeds, which affected the viscosity of the lubricant. As the temperature increased, the oil separation rate of the grease also increased. With same oil separation rate, the separated oil in the RaREB bearings could be promptly replenished to the lubrication track. However, the original bearings would lose the separated oil, resulting in insufficient oil in the contact area and leading to high friction torque.
In summary, the design of a stripe-patterned surface with stepped wettability on the inner ring of a bearing resulted in improved lubrication under limited lubricant supply, thereby enhancing the lifespan of the bearing.