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Article

Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses

1
LabECAM, ECAM LaSalle Campus de Lyon, University of Lyon, 69321 Lyon, France
2
INSA Lyon, CNRS, LaMCoS, UMR5259, 69621 Villeurbanne, France
3
CETIM, 60300 Senlis, France
4
NTN Europe, 74010 Annecy, France
*
Author to whom correspondence should be addressed.
Lubricants 2024, 12(11), 362; https://doi.org/10.3390/lubricants12110362
Submission received: 20 September 2024 / Revised: 18 October 2024 / Accepted: 19 October 2024 / Published: 23 October 2024
(This article belongs to the Special Issue Tribological Characteristics of Bearing System, 2nd Edition)

Abstract

:
This study investigates the power losses of rolling element bearings (REBs) lubricated using an oil bath. Experimental tests conducted on two different deep-groove ball bearings (DGBBs) provide valuable insights into the behaviour of DGBBs under different oil levels, generating essential data for developing accurate models of power losses. Observations of the oil bath dynamics reveal the formation of an oil ring at high oil levels, as observed for planetary gear trains, leading to modifications in the oil flow behaviour. The experiments demonstrate that oil bath lubrication generates power losses comparable to injection lubrication when the oil level is low. However, as the oil level increases, so do the power losses due to increased drag within the bearing. This study presents a comprehensive model for calculating drag losses. The proposed drag power loss model accounts for variations in oil level and significantly improves loss predictions. A comparison of existing models with the experimental results shows good agreement for both bearings, demonstrating the effectiveness of the developed model in accounting for oil bath height in loss calculations.

1. Introduction

Energy consumption is particularly high in the transportation sector, accounting for about 28% of all energy produced globally, with 75% of this energy used by road vehicles. Many moving parts still lose about a third of their energy due to friction and wear [1,2]. Reducing friction and optimising lubrication significantly contributes to the energy performance of mechanical components. In this context, driven by the increasing electrification of vehicles, high rotational speeds are achieved. This implies greater power losses in mechanical transmissions. Rolling element bearings (REBs) have become key elements in high-performance electric motor systems [3], but they are also significant sources of losses in mechanical transmissions, especially at high speeds [4]. While the sources of losses related to the load applied to the bearings are well known, the origin of load-independent losses is less obvious, but could be explained by hydrodynamic phenomena [5] at moderate speeds, whereas drag effects are predominant at higher speeds [4].
Several studies on REB power losses have been performed and led to the development of global models such as the Harris [6] and SKF [7] models. But some works on oil-jet-lubricated REB power losses demonstrated that these global models need some correction [4,5,8,9]. Power losses can also be calculated by a local model for each local source: sliding [10,11], hydrodynamic rolling [12,13,14,15,16], and drag [17,18,19]. The sliding contribution is important at high radial load, but is quite low under limited load. Hydrodynamic rolling has two components: the first is load-dependent and occurs in the loaded contacts in the REB, while the second is independent of the load and occurs in the unloaded contacts [5,12,13,14,20]. Power losses due to the shearing of lubricant in the cage is frequently neglected for normal operating conditions [21,22,23]. For injection lubrication, drag power loss is calculated for aligned spheres moving in oil–air mixtures [24,25]. The oil–air volume fraction calculation is based on Parker’s work [25] and has been modified by Niel [4,26]. This drag power loss model has been validated through experiments [4,24]. This contribution has also been widely studied through numerical tests as computational fluid dynamics [26,27,28,29].
However, most of these studies considered oil-jet-lubricated REBs. Only a few studies on power losses in oil-bath-lubricated DGBBs exist. Since lubrication does not impact sliding or hydrodynamic rolling as long as the contacts are fully flooded, only the drag power loss is reconsidered to adapt the model from injection to oil bath lubrication. SKF already takes into account lubrication in its drag loss model. Oil bath lubrication is primarily considered with the height of the bath, and a demonstration was presented by Morales [30]. When the REB is lubricated by injection, the height must be fixed at half the diameter of the lowest rolling element, and the drag torque obtained must be multiplied by two [7]. The Harris model originally proposed one value of f 0 according to the REB and lubrication types [6]. For example, the value of parameter f 0 for a DGBB is 4.0 and 2.0, respectively, for injection and oil bath [6]. According to global models, passing from injection to oil bath lubrication should halve the load-independent power losses of REBs. The Schaeffler company suggested modifying the load-independent component M 0 from the Harris model according to the lubrication used [31]. Two different f 0 values are proposed between injection and oil bath lubrication for each bearing series. In the case of oil bath lubrication, this parameter is multiplied by a coefficient proportional to the height of the bath. In the study by Peterson et al. [32], REB power losses were measured under different operating conditions and a method to isolate drag losses was proposed. By subtracting the results from two tests at different oil bath levels, with one very low, it is possible to obtain a drag loss difference, and then study that power loss source experimentally.
In the context of oil bath lubrication, Peterson et al. demonstrated that when the oil level is high, an oil ring is formed [32]. Hannon et al. presented results related to the quantity of oil in an oil-bath-lubricated bearing, showing a phenomenon of oil aspiration into the bearing and the beginning of ring formation, although these tests were conducted at low speeds [33]. This phenomenon of oil ring formation has also been observed in splash-lubricated epicyclic gear trains [34]. This particular flow pattern within the bearing when an oil bath is employed must have an impact on the churning power losses, and this raises the question of the suitability of existing models for correctly predicting these losses.
The aim of this study was to provide a better understanding of churning power losses in oil-bath-lubricated deep-groove ball bearings through experimental results and to propose a model to predict this source of dissipation by considering the oil level. First, the experimental study of oil-bath-lubricated REBs with a limited radial load applied is presented. The test rig used, the procedure, and the two DGBBs tested are described, followed by power loss measurements. The influence of lubrication type and oil bath level on the REB power losses are depicted. Then, a new drag loss model is developed. Finally, this drag power loss model is added to the Harris model and compared to measurements.

2. Experiments on Power Loss in Rolling Element Bearings

2.1. Test Rig and Test Procedure

Niel et al. [4] developed a test bench for studying both the power losses and the thermal behaviour of rolling element bearings under different operating conditions. A scheme of the test bench is given in Figure 1 and a photo of the measurement region is given in Figure 2. A more detailed presentation is available in references [5,20], but the test apparatus and the measurement protocol are briefly introduced here.
The test bench comprises a motor rotating a shaft equipped with a torque meter positioned between two bellows couplings. The signal is measured with strain gauges, and the information is transmitted by induction. The torque meter is followed by two support blocks (in black in Figure 2) surrounding the measuring block containing the REB to be studied. Identical bearings in the two support blocks are lubricated by an oil bath with the same oil level. As they generate resistive torque, one must be able to estimate it whatever the operating condition. A specific calibration campaign was therefore conducted, including three radial loads (1, 3, and 5 kN) at rotational speeds from 3200 rpm to 9700 rpm, during which the outer ring temperature of each bearing in the blocks and the total power were measured. This allowed the formulation of the four-support block torques based on both the load and the rotational speed to be proposed. During the experiment, once the tested bearing has been placed in the measurement block and the rotational speed and the load specified, (i) the torque meter measures the total torque on the shaft line, (ii) the torque generated by the bearings located in the two blocks is evaluated using the calibration formulation, and (iii) the torque generated by the tested bearing is estimated from the subtraction of the two previous torque values. A flowchart illustrates this procedure in Figure 3. A radial load can be applied to the measurement block using a hydraulic cylinder. No axial load was applied in this study. Labyrinth seals or lip seals can be installed in the blocks, with the latter mainly used in oil bath lubrication tests where the oil level is significant.
In this study, rotational speed evolves from 3200 rpm to 12,100 rpm, and a radial load, corresponding to 7% of the static capacity ( C o ) of the tested bearings, is applied to avoid cage slipping and vibrations. The temperature of the outer ring (OR) of each DGBB, the external surface of the measurement block, and the ambient air are measured with type K or type T thermocouples. The temperature of the oil bath is measured when the tested DGBB is lubricated by oil bath lubrication. The temperature of the inner ring (IR) of the DGBB in the measurement block is measured by telemetry. The range and precision of the sensors are summarised in Table 1.
In the case of oil bath lubrication, oil evacuations of the block can be closed to have an oil sump at the bottom of the block. The amount of oil in the bath is adjusted using a gauge on the block indicating the oil sump height.
Test campaigns were conducted on two bearing references (6311 and 6208) to study the losses of DGBBs lubricated through oil bath lubrication. For each tested bearing, four oil levels were applied. The oil level was defined in relation to the number of immersed balls under non-rotating conditions. To achieve this, it was decided that the static bearing be placed in such a position that a single ball was at its lowest point (Figure 4). This position is in accordance with the recommendation given by bearing manufacturers when they suggest the oil level (i.e., half the diameter of the lowest rolling element). The lowest level corresponds to a half-immersed ball (0.5 B), and then increases with one fully immersed ball (1 B), three immersed balls (3 B), and half of the immersed DGBB (0.5 R) (Figure 4).

2.2. Bearing Geometry

The two DGBBs depicted in Figure 5, with references 6311 and 6208, were tested. The dimensions of the tested bearings are provided in Table 2. The internal geometry was known for both tested bearings. Some information provided by the manufacturers is given in their catalogues such as the outer diameter d o , the inner diameter d i , the mean diameter d m (equal to ( d o + d i ) / 2 ), the width B , and the static load rating C o . Additional information about the internal geometry, given by the bearing manufacturer, is provided in Table 2 such as the ball diameter D and the number of balls Z . The relative space L / D between the balls is given as L = π d m / Z   .
Bearing 6311 was chosen for its large dimensions, especially the ball diameter, which highlights load-independent power losses such as drag. Bearing 6208, on the other hand, is smaller and closer to the target industrial application. For example, the ratio of the volumes of the bearings is 3.8 with the volume expressed as V = π · d o 2 d i 2 · B / 4 , and the ball diameter ratio is 1.73.
The cages have identical designs for both bearings, with only their dimensions being different. They are asymmetrical plastic cages adapted to high speed.
As previously explained, both bearings were oil-bath-lubricated and the oil level varied. The oil properties are defined in Table 3. Several experimental campaigns were carried out to test these two bearings. The influence of various parameters was observed and measured.

2.3. Power Loss Measurement Results

The lubrication mode can influence bearing power losses, as the phenomena related to oil flow are different. Therefore, several models for calculating bearing losses predict differences depending on lubrication modes. As mentioned in the introductory section, some models suggest an increase in power losses when the bearing is lubricated by injection rather than oil bath, whereas a decrease is pointed out by others. To verify these hypotheses, tests were conducted with the oil-bath-lubricated DGBBs 6311 and 6208, with an oil level corresponding to a half-submerged ball. Indeed, the SKF model suggests that the drag power loss will be half of that obtained for an oil-jet-lubricated REB. The results of the tests were then compared with measurements obtained in injection tests from [5], carried out using the same test rig and procedure and under equivalent operating conditions. Power losses from different tests were compared at the same DGBB temperature, defined by the mean of OR and IR temperatures. The losses between the two lubrication modes were the same for each bearing and rotational speed, contrary to the predictions of the existing global models (Figure 6).
The mean relative difference between injection losses and oil bath losses was less than 10.2% for both bearings. The errors were less than the measurement uncertainty. Some observations made in injection tests [5] are therefore still valid when DGBBs are oil-bath-lubricated with a half-submerged ball, such as speed or load influences.
Only a low oil bath level was previously considered. Then, tests with different oil levels were conducted. As mentioned previously, the oil bath level is relative to the number of submerged rolling elements, ranging from a half-submerged ball (industry recommendation) to a half-submerged DGBB. DGBBs 6311 and 6208 were tested at 6400 rpm and for each immersion level. One mainly notices at first that the larger bearing (i.e., 6311) leads to higher power losses considering identical mean temperature, which was probably due to the bigger size of the rolling elements. The losses increase with the oil level in the DGBB (Figure 7 and Figure 8). Moving from a half-submerged ball to a fully submerged ball and then to three submerged balls corresponds to an increase in power losses of 7.5% and between 11% and 20%, respectively, for both DGBBs. When half of the bearing is submerged, the losses increase between 24% and 36%.
This increase in power losses is assumed to have no influence on the friction coefficient and therefore on sliding power losses, nor on hydrodynamic rolling power losses, as the lubrication remains fully flooded. These power loss differences are only due to the increase in the amount of oil in the block and in the DGBB cavity. However, the current models do not consider the oil level in their formulations, and this could lead to significant differences between measurements and predictions from these models. The purpose of the present investigation was to add a term considering the oil level to the classical model.
Oil bath lubrication generates losses close to those obtained by injection when the bath height is relatively low, i.e., 0.5 B. The results and models of an injection-lubricated DGBB [5] can therefore be reused in oil bath lubrication. However, these models must be modified to work in the case of higher oil levels. Based on these experimental results, the study of power losses in an oil-bath-lubricated REB can, thus, be separated into two cases: the losses of a bearing with low submersion, as recommended by manufacturers and industrials; and the case with higher oil levels. The next section presents a model developed to consider drag losses according to the oil level.

3. Drag Loss Model

Fluid dynamic drag power losses are due to the displacement of rolling elements within a fluid. In the case of an isolated sphere moving in an infinite medium, drag power losses are expressed by [17]:
P d r a g = 1 2   ρ   A   C D   u 3
with the density ρ , the sphere velocity u , the reference area A , and the drag coefficient C D depending on the Reynolds number Re defined by the following equation:
R e = u   D ν
where D is the sphere diameter, u is the tangential speed of the sphere, and v is the kinematic viscosity of the fluid. Drag losses also occur in ball bearings [6,24,35,36].

3.1. Low Submersion Level

When the oil bath level is low, and when the DGBB rotates, the bath in the block can remain static, but the oil in the DGBB is assumed to be mixed with air due to the regular passage of the balls, thus forming an oil mist. This mixture of oil and air is such that it can be considered homogeneous. The rolling elements are then moving in a mixture whose physical and rheological properties are mainly defined by its oil volume fraction X [18,24,25,35]. The properties of the mist, such as the effective density ϱ eff and the dynamic viscosity η eff , read [37]:
ϱ eff = ϱ oil X + ϱ air 1 X
η e f f = 1 X m η a i r + X m η o i l 1
with X m the mass fraction of oil in the mixture such that X m = X · ϱ oil / ϱ eff . The calculation of drag power losses in a lubricated ball bearing can be written as:
P d r a g = 1 2   Z   ρ e f f   C D   A   ω c d m 2 3
where Z is the number of balls, ω c is the cage rotation speed that drives the rolling elements, d m is the average diameter of the bearing, and A is the cross-sectional area perpendicular to the flow modified by the cage thickness.
The drag coefficient C D must be estimated for bearing applications. A numerical model integrating three rolling elements with periodicity conditions and the different relative movements was developed, considering the displacement and rotation of the balls in the fluid [27]. This coefficient was determined numerically using the CFD (Computational Fluid Dynamics) method for the two bearings studied, at different speeds and for several oil fractions within the bearing [27] (Figure 9). The drag coefficient is expressed as a function of the Reynolds number. A drag coefficient law was defined using simulation results and is valid for the two bearings tested over a speed range from 3200 rpm to 12,100 rpm (Figure 9):
C D = K ·   R e   3.52 + 0.23
with the constant K = 4.89 × 10 17 . This expression is only valid for 4.0 × 10 3 < R e < 2.2 × 10 4 . If R e is greater than 2.2 × 10 4 , C D = 0.13 . Otherwise, this formula has not been verified. One observes that the relative difference equals 10% at maximum.
This formula will be used for the calculation of the drag coefficient, itself used in the estimation of drag losses.
To estimate the physical properties of a mixture (Equations (3) and (4)), one needs to know its oil volume fraction within the DGBB. This fraction is defined by both the oil and DGBB volumes, V b a t h and V t o t a l , respectively. Thus, a simplified analytical model was developed to calculate the oil volume in the bearing, the number of submerged balls, and the available volume in each bearing. This model is based on the bearing geometry and the static oil level. When one increases the oil level value in the DGBB cavity, the ratio between the volume occupied by the fluid and the total volume corresponding to the oil volume fraction is estimated. The results were verified with CAD models (Figure 10), and an error on the bath volumes below 5% was obtained.
The amount of oil in the DGBB is estimated from the static bath level, and the oil fraction of the air–oil mixture X is thus defined by:
X = V bath / V total
with V bath and V total representing the volume of the bath at rest in the bearing and the total volume available in the bearing, respectively. The estimation of the oil volume fraction using the static bath level is debatable, since when the DGBB rotates, the oil located in the cavity is expelled by centrifugal effects and is replaced by the oil from the sump. Therefore, the volume occupied by the oil in the cavity must be different from the one considering static bath. The air–oil fraction might be higher for a rotating bearing due to oil replenishment from the surrounding oil bath. This replenishment for low oil levels has been neglected. This fraction is assumed constant for a fixed oil bath level. The drag power losses can, therefore, be evaluated using Equations (3)–(7).

3.2. High Submersion Level

When the oil level is high, the oil bath behaviour can be different. Peterson et al. [32] and Hannon et al. [33] observed, for example, an initiation or the formation of an oil ring in the DGBB cavity. This was also the case in the present study when the DGBB was half-submerged (0.5 R). This phenomenon was also observed by Boni et al. [34] in splash-lubricated epicyclic gear trains [34]. A bearing [32] and an epicyclic gear train [34], both oil-bath-lubricated, exhibit similar phenomena and flows (Figure 11). This allows for an analogy to be drawn between these two systems, which have a similar architecture, with the ring and sun gears corresponding to the rings of a DGBB, the planets to the rolling elements, and the planet-carrier to the cage (Figure 12).
This analogy allows us to draw inspiration from studies conducted on epicyclic gear trains lubricated by an oil bath. An oil ring is not necessarily observed, and a condition for its formation has been developed by Boni et al. [34] based upon both (i) a relation between Froude and Reynolds numbers and (ii) a critical bath volume V crit . above which an oil ring can form. The former criterion is always met within the speed and temperature ranges of the tests with DGBB s 6311 and 6208. The critical volume corresponds to the volume of oil such that if the oil ring existed, it would at least be in contact with the periphery of the satellite carrier.
The drag power loss calculation must be modified when an oil ring is present in the DGBB cavity so that only the contribution of oil in the ring is considered: the properties of pure oil are used, ρ eff = ρ oil , in Equation (5), and the cross-sectional area is calculated based on the oil ring thickness h relative to the rolling elements. The air drag is neglected, and the drag coefficient is always determined from relationship (6).

3.3. Drag Power Loss Model Formulations

Drag power losses are then expressed by two distinct equations depending on the presence of a ring:
V < V c r i t   : P d r a g = 1 2   Z   ρ eff X   C D   A ω c d m 2 3
V   V c r i t   :   P d r a g = 1 2   Z   ρ oil   C D   A h ω c d m 2 3
An example of drag loss calculation for the 6311 and 6208 DGBB s (at 6400 rpm with oil at 50 °C) depending on the relative oil level is given in Figure 13. The marks on the curves correspond to immersions 0.5 B, 1 B, 3 B, and 0.5 R. The transition from an air–oil mixture to an oil ring is visible, since a sudden increase in power losses occurs for a relative level equal to 0.491 and 0.422, respectively, for the 6311 and 6208 bearings. This value corresponds to an immersion greater than three submerged balls for the two tested bearings. The oil quantity can, however, vary without modifying the number of balls in the bath over a small level range; the plateau is visible in Figure 10b. The model result coincides with the experimental observations: an oil ring forms when the bearing is half-immersed.
It is possible to experimentally isolate the drag power losses due to the increase in oil level by subtracting the power losses obtained for large heights from the power losses of the tests with a half-submerged ball [32]. Thus, the difference in drag losses is measurable. Figure 14 shows the difference in the measured drag losses at 6400 rpm compared to those calculated by the developed drag model. The drag power losses predicted by the model are consistent with the experimentally estimated values. Negative values were found for the 6208 bearing, which can be explained by the very low orders of magnitude of the power losses and the high uncertainty. The absolute error of the power losses calculated by the model compared to the experimental power losses is less than the measurement uncertainty (26.8 W) for each oil level.
The existing power loss models can be used with the proposed drag power loss model considering the oil quantity in the bearing. This model provides good results compared to measurements at both low and high immersions. In the case of very high oil levels, an analogy with epicyclic gear trains was made and showed the formation of an oil ring on the outer ring. This phenomenon was considered in the drag modelling. This drag loss model can, thus, be added to the global Harris model or a local model to better take into account the oil bath height in the calculation.

4. Comparison of Harris Model with Experiments

Since the local model and the Harris model give very close results once the f 0 parameter is experimentally adjusted [5], only the Harris model is presented here, to which the previously presented drag power loss model is added. The f 0 values for DGBBs 6311 and 6208 are, respectively, 1.65 and 1.40. The results of this model were compared to the measurements made during tests on the 6311 and 6208 bearings for several oil levels. The addition of drag in the Harris model allows the oil level to be considered in the power loss calculation (Figure 15). Moreover, one clearly observes that the curves obtained at different oil levels remain parallel when the mean temperature increases, highlighting the poor influence of the viscosity on the added drag loss. The relative error is less than 7.5% for the 6311 DGBB and less than 11.5% for the 6208 bearing for less than three submerged balls, and 16.2% for half of the submerged 6208 DGBB. The results from the model were also compared with the measured power losses of the 6311 DGBB at two different rotating speeds (8000 rpm and 9700 rpm) and various oil levels (Figure 16). These results are still in good agreement with the experiments, with the mean relative error equal to 6.9%. When the rotation speed and the oil level equal 9700 rpm and 0.5 B, respectively (Figure 16), one notices a considerable decrease in the power losses with the mean temperature followed by 500 W constant value from 20 °C to 45 °C, which was not observed for the other curves. Since the oil level is low, it is not due to the drag power. Therefore, this behaviour might be connected to hydrodynamic effects in the contact. However, it has been demonstrated in previous investigations [20] that the contact temperature has a significant role in the lubrication regime. Therefore, the mean temperature cannot be used here to consider this fact.

5. Conclusions

This study investigated the power losses of lightly loaded DGBBs, focusing on the influence of lubrication mode, particularly oil bath lubrication (i.e., churning power losses). The experiments conducted on bearings 6311 and 6208 revealed insights into the behaviour of bearings under different oil levels, providing valuable data for modelling power losses. The measured power losses for DGBBs lubricated by an oil jet or an oil bath with a low oil level were equivalent under the same operating conditions. For higher oil levels, the power losses increased. The observations of the oil bath and the development of a drag loss model have enhanced our understanding of the factors affecting bearing performance. The oil bath had two different behaviours depending on the oil quantity. An oil–air mixture was assumed in the DGBBs for low levels, while an oil ring was observed for important oil volumes, as already found for epicyclic gear trains [34]. Hence, a drag loss model that is based on the oil level was proposed that significantly improves the accuracy of loss predictions compared to existing models. Overall, this research contributes to the optimisation of bearing design and lubrication strategies, essential for improving energy efficiency in transportation systems. This study only focused on DGBB power losses, but thermal aspects can also be included. Ring temperatures between the different lubrication processes could be compared and predicted with a thermal network, for example [4,24,38,39,40].

Author Contributions

Conceptualisation, F.d.C.d.V., Y.M., C.C. and F.V.; methodology, F.d.C.d.V., Y.M., T.T., C.C. and F.V.; software, F.d.C.d.V.; validation, F.d.C.d.V., Y.M., T.T., C.C. and F.V.; formal analysis, F.d.C.d.V., Y.M., C.C., F.V., L.A. and C.F.; investigation, F.d.C.d.V., Y.M., C.C., F.V., L.A. and C.F.; writing—original draft preparation, F.d.C.d.V.; writing—review and editing, F.d.C.d.V., Y.M., C.C. and F.V.; All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the first author.

Acknowledgments

The authors are grateful to Association Nationale de la Recherche et de la Technologie (ANRT) (CIFRE No. 2020/1522). The authors would like also to thank both CETIM and NTN Europe for their financial support.

Conflicts of Interest

Luc Amar was employed by the company CETIM. Charlotte Fossier was employed by the company NTN Europe. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Scheme of the test bench.
Figure 1. Scheme of the test bench.
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Figure 2. Photograph of the test bench and the blocks.
Figure 2. Photograph of the test bench and the blocks.
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Figure 3. Flowchart of the measurement protocol (N, rotational speed; Q, radial load; OR: outer ring).
Figure 3. Flowchart of the measurement protocol (N, rotational speed; Q, radial load; OR: outer ring).
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Figure 4. Representation of the four oil levels applied to bearing 6311.
Figure 4. Representation of the four oil levels applied to bearing 6311.
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Figure 5. Bearing 6311 (left) and 6208 (right).
Figure 5. Bearing 6311 (left) and 6208 (right).
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Figure 6. Comparison of bearing losses between injection and oil bath lubrication with half-submerged ball ((a) 6311 DGBB at several mean temperatures; (b) 6208 DGBB at 50 °C).
Figure 6. Comparison of bearing losses between injection and oil bath lubrication with half-submerged ball ((a) 6311 DGBB at several mean temperatures; (b) 6208 DGBB at 50 °C).
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Figure 7. Influence of oil level on losses of bearing 6311 at 6400 rpm.
Figure 7. Influence of oil level on losses of bearing 6311 at 6400 rpm.
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Figure 8. Influence of oil level on losses of bearing 6208 at 6400 rpm.
Figure 8. Influence of oil level on losses of bearing 6208 at 6400 rpm.
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Figure 9. Drag coefficient versus Reynolds number.
Figure 9. Drag coefficient versus Reynolds number.
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Figure 10. Evolution of (a) bath volume in the bearing and (b) number of submerged balls depending on the relative oil level.
Figure 10. Evolution of (a) bath volume in the bearing and (b) number of submerged balls depending on the relative oil level.
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Figure 11. Photos of (a) a bearing [32] (reprinted from [32], copyright (2024), with permission from Elsevier) and (b) an oil-bath-lubricated epicyclic gear train [34].
Figure 11. Photos of (a) a bearing [32] (reprinted from [32], copyright (2024), with permission from Elsevier) and (b) an oil-bath-lubricated epicyclic gear train [34].
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Figure 12. Analogy between an epicyclic gear train (left) and a bearing (right).
Figure 12. Analogy between an epicyclic gear train (left) and a bearing (right).
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Figure 13. Calculation of drag losses of bearings at 50 °C and 6400 rpm.
Figure 13. Calculation of drag losses of bearings at 50 °C and 6400 rpm.
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Figure 14. Calculation of drag losses of bearing (a) 6311 and (b) 6208 at 50 °C and 6400 rpm.
Figure 14. Calculation of drag losses of bearing (a) 6311 and (b) 6208 at 50 °C and 6400 rpm.
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Figure 15. Comparison of measurements and Harris model with drag for bearings (a) 6311 and (b) 6208, with various immersion levels at 6400 rpm (for curves, the higher they are, the higher the level of immersion).
Figure 15. Comparison of measurements and Harris model with drag for bearings (a) 6311 and (b) 6208, with various immersion levels at 6400 rpm (for curves, the higher they are, the higher the level of immersion).
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Figure 16. Comparison of measurements and Harris model with drag for bearing 6311 with various immersion levels at 8000 rpm and 9700 rpm (for curves, the higher they are, the higher the level of immersion).
Figure 16. Comparison of measurements and Harris model with drag for bearing 6311 with various immersion levels at 8000 rpm and 9700 rpm (for curves, the higher they are, the higher the level of immersion).
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Table 1. Characteristics of sensors on the test bench.
Table 1. Characteristics of sensors on the test bench.
SensorsRangeAccuracy
Torque meter0 Nm to 10 Nm0.02 Nm
Thermocouple−40 °C to +125 °C0.5 °C
Load0 kN to 20 kN0.4%
Table 2. Characteristic and dimensions of the studied bearings.
Table 2. Characteristic and dimensions of the studied bearings.
CharacteristicDGBB 6311DGBB 6208
d o 120 mm80 mm
d i 55 mm40 mm
d m 87.5 mm60 mm
D 20.6 mm11.9 mm
Z 89
B 29 mm18 mm
C o 45 kN17.8 kN
L / D 1.661.76
Table 3. Oil properties.
Table 3. Oil properties.
Kinematic Viscosity
at 40 °C (cSt)
Kinematic Viscosity
at 100 °C (cSt)
Density
at 15 °C (kg/m3)
36.67.8864.6
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MDPI and ACS Style

de Cadier de Veauce, F.; Marchesse, Y.; Touret, T.; Changenet, C.; Ville, F.; Amar, L.; Fossier, C. Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses. Lubricants 2024, 12, 362. https://doi.org/10.3390/lubricants12110362

AMA Style

de Cadier de Veauce F, Marchesse Y, Touret T, Changenet C, Ville F, Amar L, Fossier C. Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses. Lubricants. 2024; 12(11):362. https://doi.org/10.3390/lubricants12110362

Chicago/Turabian Style

de Cadier de Veauce, Florian, Yann Marchesse, Thomas Touret, Christophe Changenet, Fabrice Ville, Luc Amar, and Charlotte Fossier. 2024. "Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses" Lubricants 12, no. 11: 362. https://doi.org/10.3390/lubricants12110362

APA Style

de Cadier de Veauce, F., Marchesse, Y., Touret, T., Changenet, C., Ville, F., Amar, L., & Fossier, C. (2024). Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses. Lubricants, 12(11), 362. https://doi.org/10.3390/lubricants12110362

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