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Jet cooling for rolling bearings: Flow visualization and temperature distribution
Applied Thermal Engineering 105 (2016) 217–224
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Jet cooling for rolling bearings: Flow visualization and temperature distribution Wei Wu ⇑, Chenhui Hu, Jibin Hu 1, Shihua Yuan Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Institute of Technology, Beijing 100081, PR China National Key Laboratory of Vehicular Transmission, Beijing Institute of Technology, Beijing 100081, PR China
h i g h l i g h t s Simulated and measured flow behaviours inside jet cooling ball bearings are given. The higher temperature appears at the lower oil volume fraction position. Average oil volume fraction in bearing cavity rises with a larger nozzle number. Temperature decreases with a larger nozzle number due to better cooling effect.
a r t i c l e
i n f o
Article history: Received 1 March 2016 Revised 23 May 2016 Accepted 24 May 2016 Available online 25 May 2016 Keywords: Ball bearings Jet cooling Efficient cooling Two-phase flow VOF CFD
a b s t r a c t To achieve an efficient cooling for the rolling bearing, a further investigation on cooling methods is necessary. The oil-jet cooling for high-speed ball bearings was investigated. The two-phase flow inside the ball bearing 7210 were analysed and verified through tests. The heat transfer was also considered. The circumferential air-oil distribution inside the bearing appears a periodic variation between two adjacent nozzles. The bearing temperature distribution is deeply affected by the air-oil distribution. The higher temperature always appears at the lower oil volume fraction position. The average oil volume fraction increases with a larger nozzle number. The nozzle number should be no more than four considering its effect on the oil volume fraction and the oil supply mechanism complexity. The nozzle number and the jet velocity have larger influences on the oil volume fraction when bearing speed is lower than 20,000 r/min. When bearing speed is larger than 40,000 r/min, the bearing speed affects the oil volume fraction much more than the multiple-nozzle oil-jet cooling mechanism parameters. The results are useful for the advanced precision cooling mechanism design of the rolling bearing. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Many industrial applications use impinging liquid jet to provide an effective mode of heat transfer, such as electrical motor [1], gearbox [2] and steel rolling [3]. For high-speed transmission systems, such as aircraft engines, turbomachinery, and drive trains, oil-jet is applied to the ball bearing cooling [4]. The automotive transmission is now focused toward higher efficiency and greater power density [5]. A higher rated speed is beneficial to the greater power density. However, it makes the ball bearing speed become higher. Further, coupled with the compact design of the automotive transmission, there is always no bearing chamber which has ⇑ Corresponding author at: Room 412, Building 9, Beijing Institute of Technology, Beijing 100081, PR China. E-mail addresses: [email protected] (W. Wu), [email protected] (J. Hu). 1 Address: Room 412, Building 9, Beijing Institute of Technology, Beijing 100081, PR China. http://dx.doi.org/10.1016/j.applthermaleng.2016.05.147 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
been commonly used in aero engines [6]. They put increasing demands on the operation condition maintenance of the ball bearing for the automotive transmission. The oil-jet cooling method of the rolling bearing is mainly used for the high-speed operation. The placement and number of nozzles, the jet velocity, the flow rate, and the removal of lubricant from the bearing and immediate vicinity are all important for satisfactory operation [7]. Through a small-diameter nozzle, the lubricant oil is injected into the bearing. The nozzle aims at the inner race and locates near the side face of the bearing. The lubricant oil is absorbed back to the oil tank and circulated by the hydraulic system. For the oil-jet ball bearing, some of the oil is used to lubricate the ball bearing and form lubricant film in ball raceway contacts. The film formation behaviour has been investigated by singlephase method [8,9]. A larger film thickness is useful to reduce the friction and the heat generated. However, the total energy that
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Nomenclature d n N p r tw Q T u
section circle diameter of bearing (m) rotary speed of the inner ring (r/min) number of nozzles (–) pressure (Pa) radial position (mm) unit tangent vector (–) flow rate (L/min) temperature (°C) volume fraction (–)
t x
velocity (m/s) circumferential azimuth angle (degree)
Subscript air inner oil outer
subscript subscript subscript subscript
of of of of
the the the the
air phase parameter (–) inner ring parameter (–) oil phase parameter (–) outer ring parameter (–)
Table 1 Technical data of the test apparatus.
Fig. 1. Multiple-nozzle oil-jet mechanism for the high-speed rolling bearing.
is dissipated by the friction is largely determined by the load and speed of the bearing [10]. For the high-speed and heavy-load operation, the bearing is at a higher temperature and larger amounts of lubricant oil flow are required for the cooling of the bearing [11]. The increase in flow requirements leads to larger capacity pumps and a higher agitation torque. A higher power loss of the engine
Apparatus and sensor
Technical data
Motorized spindle Temperature sensor Oil flow transducer Vibration transducer External radial force External axial force
0–15,000 r/min Pt1000, 70 to 500 °C FT-110, 1.0–10 L/min JHT-II-B, ±15 g Hydraulic loading, 0–30 kN Hydraulic loading, 0–30 kN
Table 2 Specifications of the test ball bearing. Bearing type
SKF 7210
Inner diameter (mm) Outer diameter (mm) Width (mm) Ball diameter (mm) Number of balls Contact angle (deg.)
50 90 20 12.186 14 40
(a) Rolling bearing flow behaviour experimental apparatus.
(b) Rolling bearing temperature distribution experimental apparatus. Fig. 2. Experimental apparatus.
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Fig. 3. Main geometric model and mesh diagram. Table 3 Grid independence test results of the average oil volume fraction. Nozzle
Mesh
Cells number
4000 r/min
10,000 r/min
Double-nozzle
Mesh1 Mesh2 Mesh3
103485 177290 254765
0.05539 0.05604 0.05658
0.02807 0.02873 0.02932
Quadruple-nozzle
Mesh1 Mesh2 Mesh3
104621 178778 256349
0.06166 0.06721 0.07194
0.04126 0.04874 0.04911
219
is caused. Regarding the oil flow through a bearing compartment, only a relatively small part of the oil is used to form a lubricant film. Most of the oil is used to provide sufficient cooling capability [4,12]. Besides, the heat dissipation characteristic and the oil-air flow characteristic in a bearing can be largely affected by parameters such as pockets shape and contact angle [13,14]. For this reason, a sufficient assessment of the flow around the ball bearing is helpful when the jet cooling performance is investigated. The multiple-nozzle oil-jet cooling is always used for the highspeed and heavy-load bearings. Zaretsky and co-researchers [15] indicate that the double-nozzle jet produces lower bearing temperatures than the single-nozzle jet for a given lubricant flow rate. The results are achieved by a high-speed, high-temperature bearing tester. Both the single-phase CFD computations [16,17] and the twophase CFD computations [18,19] have been applied on the bearing chamber flow investigation. It is because the flow pattern around the ball bearing is important for the bearing temperature forecast. Enhanced CFD modelling combined with laser Doppler anemometer measurements have also been developed for the bearing chamber flow analysis [20]. The quantitative results about the flow pattern have been obtained. To further analyse the heat transfer performance of the multiple-nozzle oil-jet cooling, the time
(a) Simulated results.
(b) Photograph of the single-nozzle and double-nozzle oil-jet flow fields. Fig. 4. Simulated and measured flow field of the ball bearing.
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consuming test is not enough and a quantitative analysis is also required. This paper investigates the performance of the multiplenozzle oil-jet cooling. Extensive simulated and tested results are given. The simulated flow characteristics inside the ball bearing are obtained and verified through the test. The parametric effects on the oil volume fraction and the bearing temperature are investigated. It aims to propose a quantitative and efficient method for the advanced precision cooling mechanism design of the highspeed bearing. 2. Multiple-nozzle oil-jet cooling method The configuration of the multiple-nozzle oil-jet cooling method is shown in Fig. 1. To investigate the flow behaviour and temperature distribution, two experimental apparatus have been constructed, as shown in Fig. 2. One is used to measure the flow behaviour inside the ball bearing, as shown in Fig. 2(a). No load is applied on the bearing in the flow behaviour experimental apparatus. The shaft of the tested ball bearing is horizontal. The maximum tested speed is 4500 r/min which is the rated speed of the driving motor. In the temperature distribution experimental apparatus, a hydraulic system is separately designed to apply the external radial and axial forces on the test bearing, as shown in Fig. 2(b). There are three temperature sensors attached to the outer ring of the test bearing. The symbol r is the radial coordinates and x is the circumferential azimuth angle. One more temperature sensor is mounted on the inner ring. A data acquisition system is also employed to collect and transfer the data to a computer for further analysis. The technical data of the temperature distribution experimental apparatus is presented in Table 1. Table 2 lists the specifications of the tested ball bearing. After the lubricant oil is injected into the ball bearing, the air-oil two-phase flow appears with the rotation of the bearing. To track the air-oil two-phase flow, the VOF method [21] for multiphase flow is used. The geometric reconstruction scheme from the work of Youngs is used to represent the interfaces, which is the most accurate one for interface tracking [22]. Considering the influence of the high-speed rotation and the swirl flow, the RNG k-e turbulence model is employed in the simulation. The RNG k-e models consider the influence of high strain rate, large curvature overflowing and other factors, which can improve the accuracy under rotational flow [23]. The mesh image of the main flow field is shown in Fig. 3. The flow field inside the bearing is divided by a tetrahedral unstructured mesh. The nozzles and the flow field of both sides of the bearing are divided by a structured hexahedral mesh. The sliding mesh plane was used at the edge of the flow field inside the bearing to complete the data transfer in the entire computation domain. To ensure the accuracy and validity of the numerical results, a careful check for the grid independence of the numerical solutions has been made. Three sets of mesh specifications have been adopted for the double-nozzle and quadruple-nozzle oil-jet flow field. The refinement of a mesh with about 2.5 times of the initial cells was chosen for the analysis. In Table 3, the calculated results of the average oil volume fraction with two different bearing speeds are given. Different mesh specifications yield similar results. The differences of the average oil volume fraction are smaller than 5%. The mesh density does not change the average oil volume fraction in any appreciable way. Further, the mass flow conservation between the inlets and the outlets was used as the calculation convergence condition. 3. Flow visualization and temperature variation Fig. 4 presents the end face air-oil distribution of the singlenozzle and double-nozzle oil-jet flow fields. The inner ring speed
is 4000 r/min. The flow rate is 0.15 L/min and the nozzle diameter is 0.5 mm. No load is applied on the bearing in the flow behaviour experiment. In the double-nozzle oil-jet flow field, two nozzles are symmetrically placed around the bearing. It can be seen that the air-oil distribution appears a periodic variation inside the bearing. In each distribution cycle, the oil volume fraction around the nozzle is larger than other areas and gradually decreases along the rotating direction. Compared with the single-nozzle jet, the airoil distribution period with the double-nozzle oil-jet becomes small in one cycle. The air-oil flow inside the ball bearing determines the bearing heat generated by the rolling elements drag [24]. It also affects bearing temperatures and oil-out temperatures [25,26]. It seems that the measured temperatures at three different positions of the outer ring have the same distribution with the circumferential oil volume fraction distribution, as shown in Fig. 5. The speed of the inner ring is 4000 r/min and the oil flow rate is 3.0 L/min. The axial load is 5.0 kN in the test. The single-nozzle jet is used with the No. 1 nozzle. Both the No. 1 nozzle and the No. 3 nozzle are used in the double-nozzle jet. The measured temperature of the outer ring has followed the same trend and becomes more homogeneous under the double-nozzle jet. Based on the oil-jet cooling mechanism optimization, the oil
(a) Results under the single-nozzle jet.
(b) Results under the double-nozzle jet. Fig. 5. Simulated average oil volume fraction and measured temperature of the outer ring.
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(a) Simulated results.
(b) Photograph of the flow field. Fig. 6. Flow field of the ball bearing of different speeds with double-nozzle oil-jet.
Fig. 8. Flow field inside the ball bearing with different number of nozzles.
Fig. 7. Simulated and measured temperatures of the ball bearing under different flow rates.
consumption can be reduced with the same cooling performance by increasing the utilization of the oil [27]. Further, a higher temperature appears at the lower oil volume fraction position. The air-oil distributions at the end face of different speeds are presented in Fig. 6. The oil almost full fills the bearing cavity including the space near the inner ring at 500 r/min. The oil loss appears in the vicinity of the outer ring. However, the oil mainly appears around the outer ring at 3000 r/min. The oil is used to provide sufficient cooling capability and control the bearing temperature by removing generated heat. Thus, the oil distribution has important effects on the bearing temperature distribution.
Fig. 9. Simulated temperatures of the ball bearing with different number of nozzles.
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Due to the centrifugal effect, the cooling effect on the inner ring becomes low, as the measured temperature presented in Fig. 7. The inner ring speed is 10,000 r/min. The axial load is 5.0 kN and the radial load is 10.0 kN in the test. The simulated temperature is calculated considering the oil volume fraction which is calculated by numerical simulations. With the increase of the oil flow, the heat transfer capability is enhanced. However, the churning loss also increases. As a result, the decreasing rate of the bearing temperature slows down at last. 4. Influence of operation parameters The air-oil distribution inside the bearing becomes more uniform with larger number of nozzles, as shown in Fig. 8. The speed of the inner ring is 10,000 r/min and the oil flow rate is 3.0 L/min in the calculation. It seems that the volume fraction of the oil phase inside the bearing increases. The oil volume fraction close to the nozzle is usually much more than other positions. It decreases along the rotation direction of the inner ring. The lowest volume fraction of the oil phase always appears in the inner ring, which makes the cooling effect on the inner ring becomes low. The outer ring temperature is lower than the inner ring, as shown in Fig. 9. The average bearing temperature decreases with the increase of the nozzle number. The temperature distribution of the inner ring is more uniform than the temperature distribution of the outer ring. The parametric results of the oil volume fraction can indicate the effect of different number of nozzles more directly. The uniformity of the oil volume fraction inside the bearing rises with the
(a) Oil volume fraction distributions around the circumference.
(b) Average oil volume fraction inside the rolling bearing. Fig. 10. Simulated results of the flow field with different nozzle numbers.
increase of the nozzle number, as shown in Fig. 10(a). Further, the average oil volume fraction also increases with the increase of the nozzle number, as shown in Fig. 10(b). More nozzles are helpful for achieving a better cooling effect on the bearing. However, a larger oil volume fraction results in a higher churning loss [28]. The oil supply mechanism also becomes more complex with a larger nozzle number. Further, the oil volume fraction increases slowly at last. Although the power loss caused by the air-oil mixture is not the main part of the energy loss of the high speed and heavy load bearing, the nozzle number should no more than four considering its effect on the oil volume fraction and the oil supply mechanism complexity. The number of nozzles has a large influence on the oil volume fraction inside the bearing when the bearing speed is lower than 20,000 r/min, as shown in Fig. 11(a). In the simulation, the number of nozzles increases while the nozzle diameter stays the same. The jet speed influences the oil volume fraction inside the bearing obviously at the low-speed stage, as shown in Fig. 11(b). With the increase of the bearing speed, the influence decreases. When the bearing speed exceeds 20,000 r/min, the jet speed is almost a negligible factor and the influence of the nozzle number is not obvious at the same time. At the high-speed stage, such as 40,000 r/min in the simulation, the increase of the nozzle number is not an efficient method to improve the cooling effect. It is because that the air-oil distribution inside the bearing tends to be uniform at the highspeed stage. Fig. 12 presents the average temperatures of the inner ring and the outer ring with different bearing speeds and oil jet velocities. It
(a) Oil volume fraction with different bearing speeds and nozzles.
(b) Oil volume fraction with different bearing speeds and oil jet velocities. Fig. 11. Simulated oil volume fraction under different bearing speeds and oil jet velocities.
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mechanism design for the high-speed rolling bearing. The cooling of the inner ring of the high speed rolling bearing needs a special mechanism to full use the lubricant oil [27,29]. 5. Conclusions and future work The multiple-nozzle oil-jet cooling method for high-speed ball bearings has been investigated. The flow field and the corresponding temperature distribution for the ball bearing 7210 are analysed by numerical simulation and tests. The following observations were made.
(a) Temperature with different bearing speeds.
(1) The circumferential air-oil distribution inside the bearing appears a periodic variation between two adjacent nozzles. The bearing temperature distribution is significantly affected by the oil volume fraction. The higher temperature appears at the lower oil volume fraction position. (2) The average oil volume fraction inside the bearing increases with a larger nozzle number. The uniformity of the oil volume fraction also becomes better. The nozzle number should be no more than four considering its effect on the oil volume fraction and the oil supply mechanism complexity. (3) When bearing speed is lower than 20,000 r/min, the nozzle number and the jet velocity have large influences on the oil volume fraction. When bearing speed is larger than 40,000 r/min, the bearing speed affects the oil volume fraction much more than the oil-jet mechanism parameter. For higher speed ball bearings, the cooling of the inner ring of needs a special mechanism to full use the lubricant oil. Further, a balance between the jet cooling effect and the oil supply mechanism complexity should also be considered. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 51305032).
(b) Temperature with different oil-jet velocities. Fig. 12. Simulated temperatures under different bearing speeds and oil jet velocities.
seems that the average temperature increases linearly with the increase of the bearing speed. The temperature has a strong correlation with the bearing speed. The rising trend of the temperature has an agreement with the experimental results [11] under 20,000 r/min. The nonlinear relation between the temperature and the bearing speed is not obvious in that speed range. With the increase of the oil jet velocity, the average temperatures of the inner ring and the outer ring increase, as shown in Fig. 12(b). It is because that the convective heat transfer capability is weakened with a lower oil volume fraction. The inner ring speed is 10,000 r/min and the oil flow rate is 3.0 L/min in the simulation. Compared with the variation of the inner ring temperature, the outer ring temperature changes much smaller since the cooling oil of the outer ring is mainly discharged by the centrifugal force. The bearing speed rather than the oil jet velocity and the nozzle number becomes the main factor that affects the oil volume fraction inside the bearing. The multiple-nozzle oil-jet requires a more complex mechanism than the single-nozzle jet. Further, the load of the bearing is not applied uniform. Thus, it is also important to optimise the nozzle position according to the load and the air-oil distribution for the oil-jet cooling ball bearing. The analysis of the flow field inside the bearing gives an opportunity to the efficient cooling
References [1] T. Davin, J. Pellé, S. Harmand, R. Yu, Experimental study of oil cooling systems for electric motors, Appl. Therm. Eng. 75 (1) (2015) 1–13. [2] T. Fondelli, A. Andreini, R.D. Soghe, B. Facchini, L. Cipolla, Volume of fluid (VOF) analysis of oil-jet lubrication for high-speed spur gears using an adaptive meshing approach, in: ASME Turbo Expo, 2015. [3] T.L. Fu, Z.D. Wang, Y. Li, J.D. Li, G.D. Wang, The influence of spray inclination angle on the ultra fast cooling of steel plate in spray cooling condition, Appl. Therm. Eng. 78 (2014) 500–506. [4] J. Aidarinis, D. Missirlis, K. Yakinthos, A. Goulas, CFD modeling and LDA measurements for the air-flow in an aero engine front bearing chamber, J. Eng Gas Turbo Power 133 (8) (2011) 082504. [5] J.B. Hu, W. Wu, M.X. Wu, S.H. Yuan, Numerical investigation of the air-oil twophase flow inside an oil-jet lubricated ball bearing, Int. J. Heat Mass Transf. 68 (2014) 85–93. [6] B. Chandra, K. Simmons, S. Pickering, S.H. Collicott, N. Wiedemann, Study of gas/liquid behavior within an aeroengine bearing chamber, J. Eng. Gas Turbo Power 135 (5) (2013) 051201. [7] S.I. Pinel, H.R. Signer, E.V. Zaretsky, Comparison between oil-mist and oil-jet lubrication of high-speed, small-bore, angular-contact ball bearings, Tribol. Tran. 44 (2001) 327–338. [8] S. Knauf, S. Frei, T. Richter, R. Rannacher, Towards a complete numerical description of lubricant film dynamics in ball bearings, Comput. Mech. 53 (2) (2014) 239–255. [9] G.E. Morales-Espejel, P.M. Lugt, H.R. Pasaribu, H. Cen, Film thickness in grease lubricated slow rotating rolling bearings, Tribol. Int. 74 (2014) 7–19. [10] K.S. Kim, D.W. Lee, S.M. Lee, S.J. Lee, J.H. Hwang, A numerical approach to determine the frictional torque and temperature of an angular contact ball bearing in a spindle system, Int. J. Prec. Eng. Manu. 16 (1) (2015) 135–142. [11] S. Jiang, H. Mao, Investigation of the high speed rolling bearing temperature rise with oil-air lubrication, J. Tribol. 133 (2) (2011) 021101. [12] C.H. Hager, G.L. Doll, R.D. Evans, P.J. Shiller, Minimum quantity lubrication of M50/M50 and M50/Si3N4 tribological interfaces, Wear 271 (9–10) (2011) 1761–1771.
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W. Wu et al. / Applied Thermal Engineering 105 (2016) 217–224
[13] K. Yan, Y. Wang, Y. Zhu, J. Hong, Q. Zhai, Investigation on heat dissipation characteristic of ball bearing cage and inside cavity at ultra high rotation speed, Tribol. Int. 93 (2015) 470–481. [14] A.A. Adeniyi, H.P. Morvan, K.A. Simmons, A multiphase computational study of oil-air flow within the bearing sector of aeroengines, in: ASME Turbo Expo, 2015. [15] E.V. Zaretsky, H. Signer, E.N. Bamberger, Operating limitations of high-speed jet-lubricated ball bearings, J. Lubr Technol. 98 (1) (1976) 32–39. [16] A. Glahn, S. Wittig, Two-phase air/oil-flow in aero engine bearing chambers: characterization of oil film flows, J. Eng. Gas Turbo Power. 118 (3) (1996) 578– 583. [17] A. Glahn, S. Busam, M.F. Blair, K.L. Allard, S. Wittig, Droplet generation by disintegration of oil films at the rim of a rotating disk, J. Eng. Gas Turbo Power. 124 (1) (2002) 117–124. [18] B. Chen, G.D. Chen, H.C. Sun, Y.H. Zhang, Effect of oil droplet deformation on its deposited characteristics in an aeroengine bearing chamber, J. Aero. Eng. 228 (2) (2014) 206–218. [19] M. Farrall, S. Hibberd, K. Simmons, D. Giddings, Prediction of air/oil exit flows in a commercial aero-engine bearing chamber, J. Aero. Eng. 220 (3) (2006) 197–202. [20] J. Aidarinis, A. Goulas, Enhanced computational fluid dynamics modeling and Laser Doppler anemometer measurements for the air-flow in an aero-engine front bearing chamber-part I, J. Eng. Gas Turbo Power 137 (8) (2015) 1–14.
[21] C. Hirt, B. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39 (1) (1981) 201–225. [22] M. Mohammadi, S. Shahhosseini, M. Bayat, Direct numerical simulation of water droplet coalescence in the oil, Int. J. Heat Fluid Flow. 36 (2012) 58–71. [23] J.L. Xiao, E.Q. Zhu, G.D. Wang, Numerical simulation of emergency shutdown process of ring gate in hydraulic turbine runaway, J. Fluid Eng. 134 (12) (2012) 124501. [24] J.P. Richardm, Comparison of predicted and experimental thermal performance of angular-contact ball bearings, NASA Technical Paper 2275, 1984. [25] J.P. Richard, Lubrication of rolling element bearings, NASA Technical Memorandum 81449 (1980). [26] Y. Miyakawa, K. Seki, M. Yokoyama, Study on the Performance of Ball Bearings at High DN Values, National Aerospace Lab, Tokyo, 1973. [27] K. Yan, J. Zhang, J. Hong, Y. Wang, Y. Zhu, Structural optimization of lubrication device for high speed angular contact ball bearing based on internal fluid flow analysis, Int. J. Heat Mass Transf. 95 (2016) 540–550. [28] B. Chandra, K. Simmons, S.H. Collicott, S. Pickering, N. Wiedemann, Study of gas/liquid behaviour within an aeroengine bearing chamber, in: ASME Turbo Expo, 2012. [29] M. Koyama, Minimum quantity and cooling jet lubricated angular contact ball bearings for machine tool, NTN Tech. Rev. 74 (2006) 24–27.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Jet cooling for rolling bearings: Flow visualization and temperature distribution Wei Wu ⇑, Chenhui Hu, Jibin Hu 1, Shihua Yuan Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Institute of Technology, Beijing 100081, PR China National Key Laboratory of Vehicular Transmission, Beijing Institute of Technology, Beijing 100081, PR China
h i g h l i g h t s Simulated and measured flow behaviours inside jet cooling ball bearings are given. The higher temperature appears at the lower oil volume fraction position. Average oil volume fraction in bearing cavity rises with a larger nozzle number. Temperature decreases with a larger nozzle number due to better cooling effect.
a r t i c l e
i n f o
Article history: Received 1 March 2016 Revised 23 May 2016 Accepted 24 May 2016 Available online 25 May 2016 Keywords: Ball bearings Jet cooling Efficient cooling Two-phase flow VOF CFD
a b s t r a c t To achieve an efficient cooling for the rolling bearing, a further investigation on cooling methods is necessary. The oil-jet cooling for high-speed ball bearings was investigated. The two-phase flow inside the ball bearing 7210 were analysed and verified through tests. The heat transfer was also considered. The circumferential air-oil distribution inside the bearing appears a periodic variation between two adjacent nozzles. The bearing temperature distribution is deeply affected by the air-oil distribution. The higher temperature always appears at the lower oil volume fraction position. The average oil volume fraction increases with a larger nozzle number. The nozzle number should be no more than four considering its effect on the oil volume fraction and the oil supply mechanism complexity. The nozzle number and the jet velocity have larger influences on the oil volume fraction when bearing speed is lower than 20,000 r/min. When bearing speed is larger than 40,000 r/min, the bearing speed affects the oil volume fraction much more than the multiple-nozzle oil-jet cooling mechanism parameters. The results are useful for the advanced precision cooling mechanism design of the rolling bearing. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Many industrial applications use impinging liquid jet to provide an effective mode of heat transfer, such as electrical motor [1], gearbox [2] and steel rolling [3]. For high-speed transmission systems, such as aircraft engines, turbomachinery, and drive trains, oil-jet is applied to the ball bearing cooling [4]. The automotive transmission is now focused toward higher efficiency and greater power density [5]. A higher rated speed is beneficial to the greater power density. However, it makes the ball bearing speed become higher. Further, coupled with the compact design of the automotive transmission, there is always no bearing chamber which has ⇑ Corresponding author at: Room 412, Building 9, Beijing Institute of Technology, Beijing 100081, PR China. E-mail addresses: [email protected] (W. Wu), [email protected] (J. Hu). 1 Address: Room 412, Building 9, Beijing Institute of Technology, Beijing 100081, PR China. http://dx.doi.org/10.1016/j.applthermaleng.2016.05.147 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
been commonly used in aero engines [6]. They put increasing demands on the operation condition maintenance of the ball bearing for the automotive transmission. The oil-jet cooling method of the rolling bearing is mainly used for the high-speed operation. The placement and number of nozzles, the jet velocity, the flow rate, and the removal of lubricant from the bearing and immediate vicinity are all important for satisfactory operation [7]. Through a small-diameter nozzle, the lubricant oil is injected into the bearing. The nozzle aims at the inner race and locates near the side face of the bearing. The lubricant oil is absorbed back to the oil tank and circulated by the hydraulic system. For the oil-jet ball bearing, some of the oil is used to lubricate the ball bearing and form lubricant film in ball raceway contacts. The film formation behaviour has been investigated by singlephase method [8,9]. A larger film thickness is useful to reduce the friction and the heat generated. However, the total energy that
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W. Wu et al. / Applied Thermal Engineering 105 (2016) 217–224
Nomenclature d n N p r tw Q T u
section circle diameter of bearing (m) rotary speed of the inner ring (r/min) number of nozzles (–) pressure (Pa) radial position (mm) unit tangent vector (–) flow rate (L/min) temperature (°C) volume fraction (–)
t x
velocity (m/s) circumferential azimuth angle (degree)
Subscript air inner oil outer
subscript subscript subscript subscript
of of of of
the the the the
air phase parameter (–) inner ring parameter (–) oil phase parameter (–) outer ring parameter (–)
Table 1 Technical data of the test apparatus.
Fig. 1. Multiple-nozzle oil-jet mechanism for the high-speed rolling bearing.
is dissipated by the friction is largely determined by the load and speed of the bearing [10]. For the high-speed and heavy-load operation, the bearing is at a higher temperature and larger amounts of lubricant oil flow are required for the cooling of the bearing [11]. The increase in flow requirements leads to larger capacity pumps and a higher agitation torque. A higher power loss of the engine
Apparatus and sensor
Technical data
Motorized spindle Temperature sensor Oil flow transducer Vibration transducer External radial force External axial force
0–15,000 r/min Pt1000, 70 to 500 °C FT-110, 1.0–10 L/min JHT-II-B, ±15 g Hydraulic loading, 0–30 kN Hydraulic loading, 0–30 kN
Table 2 Specifications of the test ball bearing. Bearing type
SKF 7210
Inner diameter (mm) Outer diameter (mm) Width (mm) Ball diameter (mm) Number of balls Contact angle (deg.)
50 90 20 12.186 14 40
(a) Rolling bearing flow behaviour experimental apparatus.
(b) Rolling bearing temperature distribution experimental apparatus. Fig. 2. Experimental apparatus.
W. Wu et al. / Applied Thermal Engineering 105 (2016) 217–224
Fig. 3. Main geometric model and mesh diagram. Table 3 Grid independence test results of the average oil volume fraction. Nozzle
Mesh
Cells number
4000 r/min
10,000 r/min
Double-nozzle
Mesh1 Mesh2 Mesh3
103485 177290 254765
0.05539 0.05604 0.05658
0.02807 0.02873 0.02932
Quadruple-nozzle
Mesh1 Mesh2 Mesh3
104621 178778 256349
0.06166 0.06721 0.07194
0.04126 0.04874 0.04911
219
is caused. Regarding the oil flow through a bearing compartment, only a relatively small part of the oil is used to form a lubricant film. Most of the oil is used to provide sufficient cooling capability [4,12]. Besides, the heat dissipation characteristic and the oil-air flow characteristic in a bearing can be largely affected by parameters such as pockets shape and contact angle [13,14]. For this reason, a sufficient assessment of the flow around the ball bearing is helpful when the jet cooling performance is investigated. The multiple-nozzle oil-jet cooling is always used for the highspeed and heavy-load bearings. Zaretsky and co-researchers [15] indicate that the double-nozzle jet produces lower bearing temperatures than the single-nozzle jet for a given lubricant flow rate. The results are achieved by a high-speed, high-temperature bearing tester. Both the single-phase CFD computations [16,17] and the twophase CFD computations [18,19] have been applied on the bearing chamber flow investigation. It is because the flow pattern around the ball bearing is important for the bearing temperature forecast. Enhanced CFD modelling combined with laser Doppler anemometer measurements have also been developed for the bearing chamber flow analysis [20]. The quantitative results about the flow pattern have been obtained. To further analyse the heat transfer performance of the multiple-nozzle oil-jet cooling, the time
(a) Simulated results.
(b) Photograph of the single-nozzle and double-nozzle oil-jet flow fields. Fig. 4. Simulated and measured flow field of the ball bearing.
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consuming test is not enough and a quantitative analysis is also required. This paper investigates the performance of the multiplenozzle oil-jet cooling. Extensive simulated and tested results are given. The simulated flow characteristics inside the ball bearing are obtained and verified through the test. The parametric effects on the oil volume fraction and the bearing temperature are investigated. It aims to propose a quantitative and efficient method for the advanced precision cooling mechanism design of the highspeed bearing. 2. Multiple-nozzle oil-jet cooling method The configuration of the multiple-nozzle oil-jet cooling method is shown in Fig. 1. To investigate the flow behaviour and temperature distribution, two experimental apparatus have been constructed, as shown in Fig. 2. One is used to measure the flow behaviour inside the ball bearing, as shown in Fig. 2(a). No load is applied on the bearing in the flow behaviour experimental apparatus. The shaft of the tested ball bearing is horizontal. The maximum tested speed is 4500 r/min which is the rated speed of the driving motor. In the temperature distribution experimental apparatus, a hydraulic system is separately designed to apply the external radial and axial forces on the test bearing, as shown in Fig. 2(b). There are three temperature sensors attached to the outer ring of the test bearing. The symbol r is the radial coordinates and x is the circumferential azimuth angle. One more temperature sensor is mounted on the inner ring. A data acquisition system is also employed to collect and transfer the data to a computer for further analysis. The technical data of the temperature distribution experimental apparatus is presented in Table 1. Table 2 lists the specifications of the tested ball bearing. After the lubricant oil is injected into the ball bearing, the air-oil two-phase flow appears with the rotation of the bearing. To track the air-oil two-phase flow, the VOF method [21] for multiphase flow is used. The geometric reconstruction scheme from the work of Youngs is used to represent the interfaces, which is the most accurate one for interface tracking [22]. Considering the influence of the high-speed rotation and the swirl flow, the RNG k-e turbulence model is employed in the simulation. The RNG k-e models consider the influence of high strain rate, large curvature overflowing and other factors, which can improve the accuracy under rotational flow [23]. The mesh image of the main flow field is shown in Fig. 3. The flow field inside the bearing is divided by a tetrahedral unstructured mesh. The nozzles and the flow field of both sides of the bearing are divided by a structured hexahedral mesh. The sliding mesh plane was used at the edge of the flow field inside the bearing to complete the data transfer in the entire computation domain. To ensure the accuracy and validity of the numerical results, a careful check for the grid independence of the numerical solutions has been made. Three sets of mesh specifications have been adopted for the double-nozzle and quadruple-nozzle oil-jet flow field. The refinement of a mesh with about 2.5 times of the initial cells was chosen for the analysis. In Table 3, the calculated results of the average oil volume fraction with two different bearing speeds are given. Different mesh specifications yield similar results. The differences of the average oil volume fraction are smaller than 5%. The mesh density does not change the average oil volume fraction in any appreciable way. Further, the mass flow conservation between the inlets and the outlets was used as the calculation convergence condition. 3. Flow visualization and temperature variation Fig. 4 presents the end face air-oil distribution of the singlenozzle and double-nozzle oil-jet flow fields. The inner ring speed
is 4000 r/min. The flow rate is 0.15 L/min and the nozzle diameter is 0.5 mm. No load is applied on the bearing in the flow behaviour experiment. In the double-nozzle oil-jet flow field, two nozzles are symmetrically placed around the bearing. It can be seen that the air-oil distribution appears a periodic variation inside the bearing. In each distribution cycle, the oil volume fraction around the nozzle is larger than other areas and gradually decreases along the rotating direction. Compared with the single-nozzle jet, the airoil distribution period with the double-nozzle oil-jet becomes small in one cycle. The air-oil flow inside the ball bearing determines the bearing heat generated by the rolling elements drag [24]. It also affects bearing temperatures and oil-out temperatures [25,26]. It seems that the measured temperatures at three different positions of the outer ring have the same distribution with the circumferential oil volume fraction distribution, as shown in Fig. 5. The speed of the inner ring is 4000 r/min and the oil flow rate is 3.0 L/min. The axial load is 5.0 kN in the test. The single-nozzle jet is used with the No. 1 nozzle. Both the No. 1 nozzle and the No. 3 nozzle are used in the double-nozzle jet. The measured temperature of the outer ring has followed the same trend and becomes more homogeneous under the double-nozzle jet. Based on the oil-jet cooling mechanism optimization, the oil
(a) Results under the single-nozzle jet.
(b) Results under the double-nozzle jet. Fig. 5. Simulated average oil volume fraction and measured temperature of the outer ring.
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(a) Simulated results.
(b) Photograph of the flow field. Fig. 6. Flow field of the ball bearing of different speeds with double-nozzle oil-jet.
Fig. 8. Flow field inside the ball bearing with different number of nozzles.
Fig. 7. Simulated and measured temperatures of the ball bearing under different flow rates.
consumption can be reduced with the same cooling performance by increasing the utilization of the oil [27]. Further, a higher temperature appears at the lower oil volume fraction position. The air-oil distributions at the end face of different speeds are presented in Fig. 6. The oil almost full fills the bearing cavity including the space near the inner ring at 500 r/min. The oil loss appears in the vicinity of the outer ring. However, the oil mainly appears around the outer ring at 3000 r/min. The oil is used to provide sufficient cooling capability and control the bearing temperature by removing generated heat. Thus, the oil distribution has important effects on the bearing temperature distribution.
Fig. 9. Simulated temperatures of the ball bearing with different number of nozzles.
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Due to the centrifugal effect, the cooling effect on the inner ring becomes low, as the measured temperature presented in Fig. 7. The inner ring speed is 10,000 r/min. The axial load is 5.0 kN and the radial load is 10.0 kN in the test. The simulated temperature is calculated considering the oil volume fraction which is calculated by numerical simulations. With the increase of the oil flow, the heat transfer capability is enhanced. However, the churning loss also increases. As a result, the decreasing rate of the bearing temperature slows down at last. 4. Influence of operation parameters The air-oil distribution inside the bearing becomes more uniform with larger number of nozzles, as shown in Fig. 8. The speed of the inner ring is 10,000 r/min and the oil flow rate is 3.0 L/min in the calculation. It seems that the volume fraction of the oil phase inside the bearing increases. The oil volume fraction close to the nozzle is usually much more than other positions. It decreases along the rotation direction of the inner ring. The lowest volume fraction of the oil phase always appears in the inner ring, which makes the cooling effect on the inner ring becomes low. The outer ring temperature is lower than the inner ring, as shown in Fig. 9. The average bearing temperature decreases with the increase of the nozzle number. The temperature distribution of the inner ring is more uniform than the temperature distribution of the outer ring. The parametric results of the oil volume fraction can indicate the effect of different number of nozzles more directly. The uniformity of the oil volume fraction inside the bearing rises with the
(a) Oil volume fraction distributions around the circumference.
(b) Average oil volume fraction inside the rolling bearing. Fig. 10. Simulated results of the flow field with different nozzle numbers.
increase of the nozzle number, as shown in Fig. 10(a). Further, the average oil volume fraction also increases with the increase of the nozzle number, as shown in Fig. 10(b). More nozzles are helpful for achieving a better cooling effect on the bearing. However, a larger oil volume fraction results in a higher churning loss [28]. The oil supply mechanism also becomes more complex with a larger nozzle number. Further, the oil volume fraction increases slowly at last. Although the power loss caused by the air-oil mixture is not the main part of the energy loss of the high speed and heavy load bearing, the nozzle number should no more than four considering its effect on the oil volume fraction and the oil supply mechanism complexity. The number of nozzles has a large influence on the oil volume fraction inside the bearing when the bearing speed is lower than 20,000 r/min, as shown in Fig. 11(a). In the simulation, the number of nozzles increases while the nozzle diameter stays the same. The jet speed influences the oil volume fraction inside the bearing obviously at the low-speed stage, as shown in Fig. 11(b). With the increase of the bearing speed, the influence decreases. When the bearing speed exceeds 20,000 r/min, the jet speed is almost a negligible factor and the influence of the nozzle number is not obvious at the same time. At the high-speed stage, such as 40,000 r/min in the simulation, the increase of the nozzle number is not an efficient method to improve the cooling effect. It is because that the air-oil distribution inside the bearing tends to be uniform at the highspeed stage. Fig. 12 presents the average temperatures of the inner ring and the outer ring with different bearing speeds and oil jet velocities. It
(a) Oil volume fraction with different bearing speeds and nozzles.
(b) Oil volume fraction with different bearing speeds and oil jet velocities. Fig. 11. Simulated oil volume fraction under different bearing speeds and oil jet velocities.
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mechanism design for the high-speed rolling bearing. The cooling of the inner ring of the high speed rolling bearing needs a special mechanism to full use the lubricant oil [27,29]. 5. Conclusions and future work The multiple-nozzle oil-jet cooling method for high-speed ball bearings has been investigated. The flow field and the corresponding temperature distribution for the ball bearing 7210 are analysed by numerical simulation and tests. The following observations were made.
(a) Temperature with different bearing speeds.
(1) The circumferential air-oil distribution inside the bearing appears a periodic variation between two adjacent nozzles. The bearing temperature distribution is significantly affected by the oil volume fraction. The higher temperature appears at the lower oil volume fraction position. (2) The average oil volume fraction inside the bearing increases with a larger nozzle number. The uniformity of the oil volume fraction also becomes better. The nozzle number should be no more than four considering its effect on the oil volume fraction and the oil supply mechanism complexity. (3) When bearing speed is lower than 20,000 r/min, the nozzle number and the jet velocity have large influences on the oil volume fraction. When bearing speed is larger than 40,000 r/min, the bearing speed affects the oil volume fraction much more than the oil-jet mechanism parameter. For higher speed ball bearings, the cooling of the inner ring of needs a special mechanism to full use the lubricant oil. Further, a balance between the jet cooling effect and the oil supply mechanism complexity should also be considered. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 51305032).
(b) Temperature with different oil-jet velocities. Fig. 12. Simulated temperatures under different bearing speeds and oil jet velocities.
seems that the average temperature increases linearly with the increase of the bearing speed. The temperature has a strong correlation with the bearing speed. The rising trend of the temperature has an agreement with the experimental results [11] under 20,000 r/min. The nonlinear relation between the temperature and the bearing speed is not obvious in that speed range. With the increase of the oil jet velocity, the average temperatures of the inner ring and the outer ring increase, as shown in Fig. 12(b). It is because that the convective heat transfer capability is weakened with a lower oil volume fraction. The inner ring speed is 10,000 r/min and the oil flow rate is 3.0 L/min in the simulation. Compared with the variation of the inner ring temperature, the outer ring temperature changes much smaller since the cooling oil of the outer ring is mainly discharged by the centrifugal force. The bearing speed rather than the oil jet velocity and the nozzle number becomes the main factor that affects the oil volume fraction inside the bearing. The multiple-nozzle oil-jet requires a more complex mechanism than the single-nozzle jet. Further, the load of the bearing is not applied uniform. Thus, it is also important to optimise the nozzle position according to the load and the air-oil distribution for the oil-jet cooling ball bearing. The analysis of the flow field inside the bearing gives an opportunity to the efficient cooling
References [1] T. Davin, J. Pellé, S. Harmand, R. Yu, Experimental study of oil cooling systems for electric motors, Appl. Therm. Eng. 75 (1) (2015) 1–13. [2] T. Fondelli, A. Andreini, R.D. Soghe, B. Facchini, L. Cipolla, Volume of fluid (VOF) analysis of oil-jet lubrication for high-speed spur gears using an adaptive meshing approach, in: ASME Turbo Expo, 2015. [3] T.L. Fu, Z.D. Wang, Y. Li, J.D. Li, G.D. Wang, The influence of spray inclination angle on the ultra fast cooling of steel plate in spray cooling condition, Appl. Therm. Eng. 78 (2014) 500–506. [4] J. Aidarinis, D. Missirlis, K. Yakinthos, A. Goulas, CFD modeling and LDA measurements for the air-flow in an aero engine front bearing chamber, J. Eng Gas Turbo Power 133 (8) (2011) 082504. [5] J.B. Hu, W. Wu, M.X. Wu, S.H. Yuan, Numerical investigation of the air-oil twophase flow inside an oil-jet lubricated ball bearing, Int. J. Heat Mass Transf. 68 (2014) 85–93. [6] B. Chandra, K. Simmons, S. Pickering, S.H. Collicott, N. Wiedemann, Study of gas/liquid behavior within an aeroengine bearing chamber, J. Eng. Gas Turbo Power 135 (5) (2013) 051201. [7] S.I. Pinel, H.R. Signer, E.V. Zaretsky, Comparison between oil-mist and oil-jet lubrication of high-speed, small-bore, angular-contact ball bearings, Tribol. Tran. 44 (2001) 327–338. [8] S. Knauf, S. Frei, T. Richter, R. Rannacher, Towards a complete numerical description of lubricant film dynamics in ball bearings, Comput. Mech. 53 (2) (2014) 239–255. [9] G.E. Morales-Espejel, P.M. Lugt, H.R. Pasaribu, H. Cen, Film thickness in grease lubricated slow rotating rolling bearings, Tribol. Int. 74 (2014) 7–19. [10] K.S. Kim, D.W. Lee, S.M. Lee, S.J. Lee, J.H. Hwang, A numerical approach to determine the frictional torque and temperature of an angular contact ball bearing in a spindle system, Int. J. Prec. Eng. Manu. 16 (1) (2015) 135–142. [11] S. Jiang, H. Mao, Investigation of the high speed rolling bearing temperature rise with oil-air lubrication, J. Tribol. 133 (2) (2011) 021101. [12] C.H. Hager, G.L. Doll, R.D. Evans, P.J. Shiller, Minimum quantity lubrication of M50/M50 and M50/Si3N4 tribological interfaces, Wear 271 (9–10) (2011) 1761–1771.
224
W. Wu et al. / Applied Thermal Engineering 105 (2016) 217–224
[13] K. Yan, Y. Wang, Y. Zhu, J. Hong, Q. Zhai, Investigation on heat dissipation characteristic of ball bearing cage and inside cavity at ultra high rotation speed, Tribol. Int. 93 (2015) 470–481. [14] A.A. Adeniyi, H.P. Morvan, K.A. Simmons, A multiphase computational study of oil-air flow within the bearing sector of aeroengines, in: ASME Turbo Expo, 2015. [15] E.V. Zaretsky, H. Signer, E.N. Bamberger, Operating limitations of high-speed jet-lubricated ball bearings, J. Lubr Technol. 98 (1) (1976) 32–39. [16] A. Glahn, S. Wittig, Two-phase air/oil-flow in aero engine bearing chambers: characterization of oil film flows, J. Eng. Gas Turbo Power. 118 (3) (1996) 578– 583. [17] A. Glahn, S. Busam, M.F. Blair, K.L. Allard, S. Wittig, Droplet generation by disintegration of oil films at the rim of a rotating disk, J. Eng. Gas Turbo Power. 124 (1) (2002) 117–124. [18] B. Chen, G.D. Chen, H.C. Sun, Y.H. Zhang, Effect of oil droplet deformation on its deposited characteristics in an aeroengine bearing chamber, J. Aero. Eng. 228 (2) (2014) 206–218. [19] M. Farrall, S. Hibberd, K. Simmons, D. Giddings, Prediction of air/oil exit flows in a commercial aero-engine bearing chamber, J. Aero. Eng. 220 (3) (2006) 197–202. [20] J. Aidarinis, A. Goulas, Enhanced computational fluid dynamics modeling and Laser Doppler anemometer measurements for the air-flow in an aero-engine front bearing chamber-part I, J. Eng. Gas Turbo Power 137 (8) (2015) 1–14.
[21] C. Hirt, B. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39 (1) (1981) 201–225. [22] M. Mohammadi, S. Shahhosseini, M. Bayat, Direct numerical simulation of water droplet coalescence in the oil, Int. J. Heat Fluid Flow. 36 (2012) 58–71. [23] J.L. Xiao, E.Q. Zhu, G.D. Wang, Numerical simulation of emergency shutdown process of ring gate in hydraulic turbine runaway, J. Fluid Eng. 134 (12) (2012) 124501. [24] J.P. Richardm, Comparison of predicted and experimental thermal performance of angular-contact ball bearings, NASA Technical Paper 2275, 1984. [25] J.P. Richard, Lubrication of rolling element bearings, NASA Technical Memorandum 81449 (1980). [26] Y. Miyakawa, K. Seki, M. Yokoyama, Study on the Performance of Ball Bearings at High DN Values, National Aerospace Lab, Tokyo, 1973. [27] K. Yan, J. Zhang, J. Hong, Y. Wang, Y. Zhu, Structural optimization of lubrication device for high speed angular contact ball bearing based on internal fluid flow analysis, Int. J. Heat Mass Transf. 95 (2016) 540–550. [28] B. Chandra, K. Simmons, S.H. Collicott, S. Pickering, N. Wiedemann, Study of gas/liquid behaviour within an aeroengine bearing chamber, in: ASME Turbo Expo, 2012. [29] M. Koyama, Minimum quantity and cooling jet lubricated angular contact ball bearings for machine tool, NTN Tech. Rev. 74 (2006) 24–27.