24th International Colloquium Tribology - January 2024 127 Power Loss in High-Speed Angular Contact Ball Bearings Lúcia B. S. Pereira 1 , Justino A. O. Cruz 2 , Pedro M. T. Marques 2 , Stephane Portron 2 , Jorge H. O. Seabra 1 , Carlos M. C. G. Fernandes 1 1 Universidade do Porto, Faculdade de Engenharia, Departamento de Engenharia Mecânica, Porto, Portugal, 2 INEGI - Universidade do Porto, Unidade de Tribologia Vibrações e Manutenç-o Industrial, Porto, Portugal 1. Introduction The electrification of vehicles brings new challenges to gear transmissions and Angular Contact Ball Bearings (ACBB) become a mechanical solution to fulfil speed and load requirements more efficiently [1]. The focus of this work is to measure the torque loss in highspeed ACBB for different operating conditions of speed, load and temperature, lubricated by a low viscosity Automatic Transmission Fluid (ATF) [2]. The ACBB torque losses are also calculated using the SKF model [3]. The correlation between torque loss calculations and measurements allowed improving the accuracy of the model predictions. An equation is proposed for the coefficient of friction in ACBB. 2. Materials and methods The tests are performed with a pair of spindle ACBBs, from FAG ® , with reference B7206-E-T-P4S-UL, as presented in Table 1. These are super precision single row ACBB with solid outer and inner rings, ball and cage assemblies and solid window cages. They have high load carrying capacity and high rigidity [4]. The ACBBs are lubricated with low viscosity high performance synthetic lubricant, Eni Rotra ATF VI that follows the requirements of GM’s DEXRON ™ VI standard [2], as presented in Table 2. This is an Automatic Transmission Fluid (ATF) that meets the requirements for EV applications, having low electrical conductivity, high cooling capability and low volatility [5]. Figure 1 shows the ACBB test rig [6]. It consists on a test and drive rolling bearing assemblies (1, 5) with their shafts coupled to a torque sensor (2, 3, 4), as shown in Figure 1. The driving transmission (6) is composed by an electric motor and a belt system (transmission ratio 3: 1) connected to the driving rolling bearing assembly (5). A temperature control unit keeps the oil supplied to the test chamber (1) at constant temperature. The oil temperature inside the test chamber (1) is measured by a PT100 thermocouple (6), shown in Figure 2. A type K thermocouple (7) measures the temperature of the oil flowing back [6]. The ACBBs are loaded axially, using waved washers (Borrelly C3P72), allowing axial loads between 510 N and 3-570-N [6]. Tests are performed at low and high speeds, for temperatures between 40°C and 80°C, as presented in Table 3. Temperatures of the ACBB outer ring and of the oil are measured in several locations (see Figure 2). 3. SKF torque loss model The SKF torque loss model considers that the total frictional moment is the sum of four components, as presented in equation (1): Table 1: B7206-E-T-P4S-UL ACBB. Dimension Desig. Value Unit Bore diameter d 30 mm Outside diameter D 62 mm Width B 16 mm Contact angle α 25 / Dynamic load rating C 22 100 N Static load rating C0 9 900 N Fatigue load limit Pu 1 050 N Limit speed oil lubrication n 36 000 rpm Table 2: Eni Rotra ATF VI synthetic lubricant. Property Unit Method Typical value Colour / / red Density @ 15°C kg m -3 ASTM D 4052 850 Viscosity @ 100-°C mm 2 s -1 ASTM D 445 5.7 Viscosity Index / ASTM D 2270 150 Viscosity @ -40-°C mPa s ASTM D 2983 10 400 Thermoviscosity °C -1 (100°C) 0.0179 Piezoviscosity Pa -1 (40°C) 1.9 × 10 -9 Table 3: Axial loads and oil sump temperatures. Temperature Axial Load Fa/ N Low-speed tests High-speed tests T/ °C 2040 2550 3570 2040 2550 3570 40 X X 50 X 60 X X X 70 80 X X X Figure 1: ACBB test rig. Figure 2: ACBB test assembly and temperature measurement locations in the ACBB. 128 24th International Colloquium Tribology - January 2024 Power Loss in High-Speed Angular Contact Ball Bearings M SKF = M rr + M sl + M drag + M seal (1) where M SKF (N mm) is the total frictional moment, M rr is the rolling frictional moment, M sl is the sliding frictional moment, M drag is the frictional moment of drag losses, churning, splashing and M seal is the frictional moment of the seals (in N mm) [3]. The SKF model establishes that the sliding coefficient of friction m sl is defined by equation (2), where f bl is the weighting factor, m bl is the coefficient of friction in boundary film lubrication, and m EHD is the coefficient of friction in full-film lubrication, m sl = f bl ∙ m bl + (1 − f bl ) ∙ m EHD (2) The SKF model also establishes that the weighting factor f bl is defined by equation (3) f bl = {exp [C bl ∙ (n ∙ n ) 1.4 ∙ d m ]} -1 (3) The seals torque losses are calculated using the Simrit model [6], given by equation (4), where T VD is the seal torque loss (N mm) and d sh is the shaft diameter (mm), T VD = C seal ∙ d 2 sh (4) The constants C bl and C seal (= 5.66 × 10 -2 ) are optimized, correlating the measured and calculated ACBB torque losses. 4. Torque loss measurements Figure 3 presents the torque loss measurements at low speeds (between 100 rpm and 2000 rpm). As expected, when the axial load increases the torque loss also increases, even if the oil temperature decreases. At very low speed the torque loss tends to the starting torque which is dependent on the applied axial load. These torque loss measurements are used to optimize the weighting lubrication factor, f bl , of the SKF model, where the constant C bl becomes 4.30 × 10 -8 . For high rotational speeds, n ≥ 3,000 rpm, the value of f bl becomes null (fullfilm lubrication). Figure 4 presents the torque loss measurements (a) and the ACBB temperatures (b) at high speeds (Fa = 3570 N, T-=-80°C). As Figure 4 shows, the correlation between measured and predicted torque losses is quite good (R 2 = 0.93). This correlation is obtained through the optimization of the coefficient of friction under full-film lubrication, m EHD , which can be defined by equations (5) and (6): (5) (6) 5. Conclusion As a general trend, the rolling moment (M rr ) and the drag moment (M drag ) increase when the speed increases, whatever the axial load and lubricant temperature. At higher loads, the sliding torque (M sl ) remains almost constant, independently of the speed and oil temperature. At lower loads, the sliding torque (M sl ) increases slightly when the speed increases. Acknowledgements - FCT PhD programme NORTE-69-2015-15 - supported by NORTE 2020, under European Social Fund - NORTE- 08-5369-FSE-000027; - LAETA under project UID/ EMS/ 50022/ 2020. Figure 3: Torque loss measurements at low speeds. Figure 4: Torque loss (a) and ACBB temperatures (b) at high speeds (Fa = 3570 N, T = 80-°C): test measurements vs. model predictions. References [1] Berker Bilgin et al., Making the case for electrified transportation. IEEE Trans. on Transportation Electrification, 1(1): 4-17. [2] Roy Fewkes et al., General motors DEXRONR-VI globalservice-fill specification. SAE Technical Paper, 2006. [3] SKF. Rolling Bearings Catalogue. October 2018. [4] Schaeffler Technologies AG Co. KG. Super Precision Bearings, November 2019. [5] Tom Hong-Zhi Tang et al., Lubricants for (hybrid) electric transmissions. SAE I. J. of Fuels and Lubricants, 6(2): 289-294, 2013. [6] Lúcia B. S. Pereira, Power loss in high-speed angular contact ball bearings, MSc Dissertation, Engineering Faculty, University of Porto, Portugal, July 2023.