The development of the CFD model for the 41513219

This number represents the bearing reference code.

The interaction of the fluid with the boundaries of the domain in CFD analysis is defined by BCs. Therefore, appropriate BCs play a significant role in accurately replicating the physical conditions in the CFD environment. In this paper, the most appropriate BCs for velocity, relative pressure, and grease volume fraction were applied to respective patches as shown in Table .

Rigid mesh motion (RMM) model was implemented to ensure the mesh rotation around the bearing axis as single, undeformable entity. In the present study, the mesh rotational speed was set to the same rotational speed as that of the cage. Therefore, movingWallVelocity BCs were applied to cage to ensure zero relative velocity (no slip) between walls of cage and mesh. The rotatingWallVelocity BCs were applied to inner ring and outer ring. Inner ring was rotated around a fixed axis (bearing axis) with the same rotational speed as that of shaft, whereas, outer ring was set as stationary. In the 360° model, the cage was divided into two separate patches corresponding to both the rows of the bearing, and the boundary conditions were applied separately to each. The inner ring and outer ring were each treated as single continuous patches covering both rows of the bearing, and their respective boundary conditions were imposed uniformly over the entire surfaces. The conical rollers exhibit combined motion, i.e., spinning about their own axis (dynamic axis) and rotating around the bearing axis (fixed axis). To replicate this complex combination of motion, a new custom BC, named conicalWallVelocity was applied to each roller in both the rows, as their own axes of rotation were unique. The zeroGradient BCs corresponded to the conditions where the respective variables were not changing in perpendicular direction to the boundary faces. Non-conformal faces with different mesh structures were connected via cyclicAMI (Arbitrary Mesh Interface) BCs. Gravitational effects are significant and are taken into account in this study. Since the bearing is tilted, the components of gravitational acceleration are resolved accordingly and applied to the bearing.

In this study, the case was considered multiphase, incompressible, laminar, and isothermal. The flow velocities involved in target domain are significantly lower than speed of sound; therefore, grease and air phases were treated as incompressible. The most appropriate solver available in OpenFOAM^® is interFoam for solving these conditions. This solver uses the VoF model to solve multiphase flows, and hence it was used in the present study. The numerical stability, convergence, and computational efficiency were ensured by limiting the Courant number (Co) to less than 1. A first-order implicit Euler scheme was used for time discretization, whereas a Gauss gradient scheme was used for computing spatial gradients.

To validate the numerical model, experiments were first conducted using a custom-designed test rig at the Machine Elements, Gears and Tribology (MEGT) laboratory, as shown in Fig. . The test rig consisted of a hydrostatic frictionless support bearing, a horizontal shaft, thermocouples for temperature monitoring, an electric motor, locking assemblies, a loading module, and the test bearing. The test bearing was subjected to an axial load of 3.7 kN to ensure proper roller kinematics, prevent roller skidding, and maintain stable rolling conditions during the experiments. A high-speed camera was installed to capture the real-time evolution of the grease film inside the bearing through direct optical access to the bearing interior.

The validation experiments were performed using a 32224-XL TRB (key geometric parameters in Table ). The bearing was operated at a rotational speed of 500 rpm, while the grease temperature was 25 °C. A grease filling ratio corresponding to 25 % of the total bearing volume was applied prior to the experiments. During operation, the high-speed camera recorded the temporal evolution of the grease film and lubricant distribution inside the bearing for subsequent comparison with the numerical predictions.

Figure  shows the initial grease filling condition inside the bearing. The thick black fluid visible in Fig. a represents the grease in the experimental setup. In the experimental images, the red-highlighted regions indicate the observed grease film, as shown in Figs. –.

After one complete rotation of the inner ring, the grease distribution recorded by the high-speed camera is presented in Fig. a. A thicker grease film is observed in the upper and lower regions of the bearing, as indicated by the dotted red lines, suggesting localized grease accumulation in these regions. This behavior indicates the initial redistribution of grease caused by roller-induced shear and circumferential transport within the bearing cavity. Figure a illustrates the grease distribution after two complete rotations of the inner ring, where grease accumulation is predominantly observed within the lower half of the bearing. The observed downward migration of grease can be attributed to the combined effects of gravity and the progressive displacement of lubricant by the rotating rollers. After the third and fourth rotations, the grease progressively spreads throughout the entire bearing, as clearly shown in Figs. a and a. This behavior suggests the formation of a more distributed grease film resulting from continuous churning, roller–raceway interaction, and lubricant recirculation within the bearing.

The experimentally observed grease flow behavior was subsequently reproduced using CFD simulations for validation purposes. The same bearing configuration and operating conditions used in the experiments were implemented in the numerical model, including the rotational speed, grease filling ratio, and grease temperature. Although the geometry of the validation bearing differs from that of the wind turbine main bearing investigated in this study, both configurations are TRBs and therefore exhibit similar rolling kinematics and grease transport mechanisms. The objective of the validation is therefore not to demonstrate complete geometric similarity but rather to verify the capability of the proposed numerical framework to reproduce the dominant grease redistribution mechanisms under comparable local geometric and dynamic conditions.

To support this comparison, two local geometric parameters governing grease transport were evaluated. The circumferential packing density of the rolling elements is defined as 13Φr=NrowdRπDp, where Nrow is the number of rollers in one row, dR is the mean roller diameter. This parameter represents the fraction of the pitch circumference occupied by the rolling elements and therefore characterizes the periodic passages available for grease transport. In addition, the normalized radial position of the roller row is expressed as 14Πp=Dp-DiDo-Di, where Di and Do denote the bore and outer diameters, respectively. This parameter describes the relative radial location of the rolling elements within the bearing envelope and is relevant to the confinement of the lubricant.

The corresponding geometric similarity parameters are summarized in Table . Although the two bearings differ significantly in their overall dimensions, the circumferential packing density and the normalized radial position are in close agreement. This suggests that the local geometric features governing grease transport are well represented in the validation bearing, thereby supporting its suitability for assessing the grease redistribution mechanisms investigated in the present study.

Dynamic similarity was assessed using both the Reynolds and Froude numbers. The Reynolds number was calculated as 15Re=UcdRν, where Uc is the cage translational velocity, and ν is the kinematic viscosity of the grease. The Froude number was calculated as 16Fr=UcgdR, where g is the gravitational acceleration. The Reynolds numbers are approximately 28.4 for the validation bearing and 29.5 for the wind turbine main bearing, indicating that both configurations operate within a comparable Reynolds-number regime and therefore exhibit a similar balance between inertial and viscous forces. The Froude numbers are 1.43 and 2.32 for the validation and wind turbine bearings, respectively. The difference in Froude number reflects the substantially different bearing size and operating speed of the two configurations. Nevertheless, the comparable local geometric characteristics together with the similar Reynolds-number regime indicate that the dominant grease transport mechanisms are well represented by the validation bearing.

The computational mesh for the 32224-XL TRB was generated using the blockMesh utility in OpenFOAM^®. The CFD-predicted grease distributions corresponding to the experimental operating conditions are shown in Figs. b–b. After the first rotation of the inner ring, the numerical model predicts localized grease accumulation within the upper and lower regions of the bearing, consistent with the experimentally observed grease redistribution shown in Fig. a. After two rotations, the CFD results reproduce the predominant grease accumulation within the lower half of the bearing, indicating the combined influence of gravity and roller-induced lubricant displacement. Following the third and fourth rotations, the numerical model captures the progressive spreading and recirculation of grease throughout the bearing cavity, in good agreement with the experimental observations. Overall, the qualitative comparison between the numerical and experimental results demonstrates strong agreement in the evolution and spatial distribution of the grease film, thereby supporting the validity of the proposed modeling approach.

It should be noted that the present experimental validation is limited to the transient evolution and spatial distribution of the grease film qualitatively. The experiments validate the capability of the proposed CFD model to reproduce the observed grease redistribution behavior.

In this study, the grease filling ratio within the bearing was varied while keeping the rotational speed and other operating conditions constant. It is important to note that when the bearing is initially installed in the wind turbine, it is fully flooded with grease. However, during operation, grease continuously exits through the outlet ports. Although a re-lubrication pump supplies fresh grease to the bearing, the grease filling ratio remains below 50 % of the total volume for most of the operational period. Therefore, the selected grease fill ratios were provided by the industrial partner, reflecting practical operating scenarios. These conditions are summarized in Table . The rotational speed chosen corresponds to the rated speed of the wind turbine. All simulations were carried out for one full rotation of the cage due to computational resource limitations, utilizing 24 cores of a high-performance computing (HPC) cluster. One full rotation of the cage corresponds to approximately 7.1 s of simulated time at the rated operating speed. The simulation of this interval required about 35 d of wall-clock time for a single run.

The grease filling ratio for Simulation 3 (21 % of the bearing volume) is considered the most critical condition, as it represents the lowest practical grease level. This level lies just below the outlet port, beyond which the grease volume cannot further decrease due to the port's positioning. This outlet port is closed during operation; therefore, it has not been modeled.

To gain further insight into understanding the behavior of grease within the bearing, an additional simulation was performed to examine the grease settling behavior after the bearing rotation stops following operation. The simulation was carried out for operating conditions, i.e., 45 % filling ratio, 0 rpm, and a temperature of 40 °C. The grease distribution after one complete rotation of cage was taken from the results of simulation 1. At this point, the bearing was brought to a stop (0 rpm), and the grease temperature was maintained at 40 °C. The system was then monitored to observe the redistribution of grease as it gradually settled back toward its pre-rotation state. These operating conditions were designed to replicate a real-world scenario, such as a wind turbine shutdown, to assess how long it would take for the grease to migrate back to the lower region of the bearing under gravity-driven effects.

In this study, the grease filling ratios were kept below 50 % of the total volume of the bearing’s lubricating chamber to better represent critical operating conditions. The total volume of bearing's lubricating chamber is 0.035 m3. Figure  depicts the respective grease filling ratios for the three simulations.

The grease distribution inside the bearing after one complete rotation of the cage is shown in Fig. . As observed in Fig. , the upper region of the bearing exhibits signs of grease starvation, with noticeably less lubricant compared to the lower region for all the three grease filling ratios. This phenomenon is attributed mainly to the influence of gravity.

The disparity in grease distribution is further illustrated in Fig. , which provides a clearer comparison between the top and bottom sections for the three simulations. For 45 % grease filling ratio (Fig. a), the wetted volume of the upper part of the bearing is 0.004 m3, whereas the lower part has a wetted volume of 0.011 m3 – approximately 41 % greater than that of the upper region. For 35 % grease filling ratio (Fig. b), the wetted volume of the upper part of the bearing is 0.003 m3, whereas the lower part has a wetted volume of 0.009 m3 – approximately 36 % greater than that of the upper region. For 21 % grease filling ratio (Fig. c), the wetted volume of the upper part of the bearing is 0.001 m3, whereas the lower part has a wetted volume of 0.006 m3 – approximately 25.6 % greater than that of the upper region.

The tilt of the bearing also influences the grease distribution behavior. To analyze this effect, the two rows of the bearing were separated, and the corresponding grease distribution was captured for each filling ratio as shown in Fig. . The total volume of the lubrication chamber for each row is 0.017 m3. After one complete rotation of cage, the wetted volume in the MFS row is 0.009 m3, whereas the hub side (HS) row has a wetted volume of 0.007 m3 for 45 % grease filling ratio (Fig. a). This indicates that the MFS row retains approximately 8.5 % more grease than the HS row. For 35 % ratio, the wetted volume in the MFS row is 0.007 m3, whereas the HS row has a wetted volume of 0.005 m3 indicating approximately 7.9 % more grease in the MFS row (Fig. b). Similarly for 21 % grease filling ratio, the difference between the wetted volume in MFS and HS row is 6.53 % (Fig. c). The results of grease distribution by volume (m3) are summarized in Table .

Figure  illustrates the asymmetric distribution of grease over time. Initially, both rows exhibit equal grease occupancy, as the local stresses remain below the grease yield stress, causing it to behave like a solid, while the bearing tilt of 5° alone is insufficient to induce flow. However, once rotation begins, the grease volume in the MFS row (i.e., the row toward which the bearing is tilted) gradually increases, accompanied by a corresponding decrease in the HS row. This behavior can be attributed to the influence of centrifugal forces, which drive the grease radially outward. Due to the bearing tilt, this outward flow is biased toward the MFS row, resulting in a pressure build-up in that region. This pressure build up gives rise to an interesting phenomenon of grease redistribution that begins to occur after a certain period of time shown in Fig. . As the pressure in the MFS row increases, a sufficient pressure gradient is established between the two rows. This gradient drives the grease back toward the HS row, counteracting the centrifugal bias. Eventually, a steady state is reached in which a dynamic equilibrium exists between the centrifugal-driven flow and the pressure-induced backflow. At this stage, the net grease flow between the rows becomes negligible and the grease distribution stabilizes. This redistribution process and the resulting equilibrium are quantitatively captured by the grease occupancy evolution shown in Fig. , which provides a clear measure of the redistribution dynamics. In addition, Fig.  presents the grease occupancy in each row, normalized with respect to the corresponding initial grease occupancy. Specifically, for each row, the grease volume at a given time is divided by the initial grease volume in that same row, which is taken as the reference value; this normalization is applied independently for each grease filling ratio. This normalization highlights the extent of asymmetric grease distribution between rows for each grease filling ratio. This indicates that asymmetric grease distribution tends to become more pronounced as the grease filling ratio decreases. At lower grease volumes, the grease is more susceptible to centrifugal forces, which preferentially bias its migration toward the MFS row.

Figure  illustrates the temporal evolution of the grease film angle (θ) for three different grease filling ratios. The angles are measured with respect to the bottommost part of the bearing (i.e., θ=0°), and represent the extent to which the grease progresses toward the topmost region (θ=180°) under rotation. The initial grease levels in the rotating direction (positive x axis) are approximately 82, 62, and 36° for the 45 %, 35 %, and 21 % filling ratios, respectively. The wetted surfaces were evaluated using the information provided by VoF model. In particular, the VoF formulation supplies both the grease volume fraction, αgrease, which describes the local phase distribution within each computational cell, and the direction of the grease–air interface through the gradient of the volume fraction field. Exploiting this information, the grease-covered area on each cell face was estimated, enabling the reconstruction of the wetted area on the relevant boundary surfaces. These quantities were subsequently used in a post-processing step to distinguish and quantify the boundary regions in contact with grease from those exposed to air.

Figure a presents the grease film evolution on the MFS inner raceway. It is evident that, for all three filling ratios, the grease film progresses up to the topmost region of the bearing. However, the time required to reach this position varies with the filling ratio, with higher ratios achieving full coverage more rapidly. The corresponding distribution on the HS inner raceway is shown in Fig. b. In this case, the 45 % and 35 % filling ratios allow the grease film to reach the top region, similar to the MFS. However, for the 21 % filling ratio, the grease front diminishes significantly and fails to reach the upper portion, indicating a thinning film and potentially inadequate lubrication in this area.

Figure c shows the grease progression on the MFS outer raceway. Only the 45 % filling ratio provides sufficient grease volume to reach the topmost section. For the 35 % and 21 % cases, the upper region remains starved. This behavior can be attributed to the fact that the outer raceway is stationary and, therefore, does not contribute to the centrifugal transport of grease. As a result, the grease tends to remain with the rotating inner raceway and rollers, limiting its migration toward the outer raceway – especially under low grease volumes. Finally, Fig. d illustrates the HS outer raceway. In this case, none of the three filling ratios succeed in delivering grease to the top region, leaving it starved throughout the simulation. This consistent starvation across all cases emphasizes the asymmetric grease distribution resulting from the bearing’s tilt and the centrifugal-biased flow towards the MFS side.

It is important to note that in cases where the grease fails to reach the topmost region, the limited amount of grease causes the front to gradually disappear over time. After a certain point, the grease becomes too sparse to form a continuous layer, instead breaking into small dispersed droplets. As a result, it is not possible to extract a well-defined angle of progression beyond this stage. Therefore, data beyond this point were excluded from the graph, as no coherent front exists to track angular progression reliably. The bump observed only for the 45 % filling ratio on the outer raceway reflects a sensitive regime characterized by transient grease accumulation and redistribution.

Figures  and  illustrate the velocity fields in cross-sectional slices taken from planes perpendicular to the bearing axis for the MFS and HS rows, respectively. The velocity field is shown only in grease-dominated regions by applying a grease volume fraction threshold of αgrease of 0.5 or above in the cell. The figures reveal clear differences in the spatial distribution and intensity of grease motion between the different filling ratios. Higher velocities are observed primarily in regions adjacent to the roller surfaces, highlighting the dominant role of squeeze-induced motion, while grease adhering to the inner and outer raceways satisfies the no-slip boundary condition. With increasing filling ratio, the extent of regions exhibiting significant grease motion increases, indicating enhanced internal grease flux within the bearing.

The pumping effect induced by the rollers, resulting from their tapered geometry, is the displacement of grease in a favorable direction. Figures  and , corresponding to the MFS and HS rows, respectively, show the axial velocity field in grease-dominated regions. Owing to the tapered geometry, one side of each roller exhibits axial velocity towards the bearing bore, while the other side shows axial velocity away from bearing bore, leading to an asymmetric axial velocity distribution.

On the MFS (Fig. ), negative axial velocity indicates flow away from bearing bore, whereas positive axial velocity represents flow towards bearing bore. On the HS, the sign convention is opposite (Fig. ), where positive axial velocity represents flow away from bearing bore, while negative axial velocity represents flow towards bearing bore. In the regions between the rollers, the grease displays coherent axial velocities with a consistent directional bias. Since these regions are not directly attached to the roller surfaces, the observed motion cannot be explained solely by local displacement effects. Instead, it indicates a preferential axial transport of grease, supporting the presence of a pumping tendency arising from the tapered roller geometry and the imposed kinematics. This bidirectional flow pattern highlights the role of tapered rollers (pumping effect) in driving lubricant circulation across the bearing rows.

The pressure field developed due to grease flow over the roller surfaces and inner raceway is illustrated in Fig. . Higher pressure regions are observed in areas with greater lubricant accumulation which is evident from Fig. . For 45 % grease filling ratio (Fig. a), the pressure developed inside the bearing is higher as compared to 35 % and 21 % filling ratios (Fig. b and c, respectively). Notably, steep pressure gradients occur near the contact interfaces between the rollers and raceways, which can be attributed to the squeezing effect of the lubricant in these narrow gaps. Similar pressure profiles were found by in their study.

The pressure distribution on the bearing seals is of particular importance, as it directly affects the potential of lubricant leakage. The threshold of the pressure for the seal of bearing under investigation is 0.5 bar. Figure  presents the pressure profiles on both the MFS and HS seals for the three grease filling ratios. The left column corresponds to the MFS seal, while the right column shows the HS seal. It is evident that the pressure on the seals is highest for the 45 % grease filling ratio (Fig. a), followed by 35 % and 21 % (Figs. b and c respectively), indicating that increased grease volume leads to greater sealing pressure and potentially a higher risk of leakage. Figure  presents the temporal evolution of the maximum total pressure acting on the seals for the different grease filling ratios. The reported pressure corresponds to the total pressure experienced by the seals, including hydrostatic as well as rotational (centrifugal and dynamic) contributions. For all filling ratios, the pressure initially decreases as the grease redistributes within the bearing during the early stages of rotation. When the grease reaches the top region and subsequently starts its downward motion, the pressure increases due to the combined effects of grease accumulation toward the bottom region of the bearing and dynamic contributions, with hydrostatic and inertial pressure contributions acting together to support the load. The magnitude of the maximum seal pressure increases with grease filling ratio; however, this increase remains smooth and does not exhibit any over-linear amplification. Importantly, in all cases the maximum pressure remains well below the sealing pressure limit of 0.5 bar, indicating that seal integrity is maintained and that pressure-driven leakage is unlikely for the investigated operating conditions.

Another important aspect of the lubrication phenomenon inside the bearing is the settling behavior of grease after the bearing stops rotating. To investigate this, a dedicated simulation was performed following the operational scenario described in Sect. .

The grease distribution across the top and bottom sections of the bearing after 40 s is illustrated in Fig. , and the temporal evolution of the settling process is presented in Fig. . It is observed that approximately 98 % of the grease volume settled back to the lower region of the bearing within 40 s. It is worth noting that at 40 °C, the kinematic viscosity of the grease decreases to approximately 470 mm2s-1, which is considerably low for grease. This significant reduction in viscosity facilitates a much faster settling of the grease within the bearing.