With practical physical immersion depth as their joint, the relations between the oil distribution characteristics and the associated no-load power losses for splash-lubricated orthogonal face gears are explored and quantified in this paper. Firstly, a theoretical analytical model is proposed to estimate the churning losses of an isolated face gear considering all the preceding parameters, along with a numerical model of a face gear stirring oil developed based on the sliding mesh strategy. Then the accuracy and correctness of the computational fluid dynamics method are verified with experiments in terms of oil flow behavior and no-load losses. Finally, the physical immersion depth is determined by leveraging the image processing technique and substituted into the theoretical model replacing the static depth with an improvement of prediction accuracy. Last but not least, this practical immersion depth acts as a link to facilitate the communication between the oil distributions and the no-load power losses within the gearboxes.
HeathGFFillerRRTanJ. Development of face gear technology for industrial and aerospace power transmission. Mesa Arizona: Boeing Company, 2002.
2.
FillerRRHeathGFSlaughterSC, et al.Torque splitting by a concentric face gear transmission. American Helicopter Society 58th Annual Forum 2002.
3.
HeathGFSlaughterSCFisherDJ, et al.Helical face gear development under the enhanced rotorcraft drive system program. 67th Annual Forum and Technology Display (Forum 67) 2011; (AHS 2011-000270).
4.
LiuHWeiTZhouJ, et al.Research on characteristics of splash lubrication and power losses of reducer based on MPS method. Lubr Sci2023; 35(8): 596–615.
5.
HandschuhMGunerAKahramanA. An experimental investigation of windage and oil churning power losses of gears and discs. Proc IMechE, Part J: J Engineering Tribology2023; 237: 163–177.
6.
QuibanRChangenetCMarchesseY, et al.Experimental investigations about the power loss transition between churning and windage for spur gears. J Tribol-T ASME2021; 143: 024501.
7.
DiabYVilleFHoujohH, et al.Experimental and numerical investigations on the air-pumping phenomenon in high-speed spur and helical gears. Proc IMechE, Part C: J Mechanical Engineering Science2005; 219: 785–800.
8.
TalbotDKahramanASeetharamanS. A helical gear pair pocketing power loss model. J Tribol-T ASME2014; 136: 021105.
9.
GorlaCConcliFStahlK, et al.Hydraulic losses of a gearbox: CFD analysis and experiments. Tribol Int2013; 66: 337–344.
10.
FondelliTAndreiniADa SogheR, et al.Numerical simulation of oil jet lubrication for high speed gears. Int J Aerosp Eng2015; 2015. https://doi.org/10.1155/2015/752457
11.
KellerMCKromerCCordesL, et al.CFD study of oil-jet gear interaction flow phenomena in spur gears. Aeronaut J2020; 124: 1301–1317.
12.
DaiYChenXYangD, et al.Impulse power loss in orthogonal face gear–numerical and experimental results. Eur Phys J Plus2023; 138: 88.
13.
YangJLinTJiangL. Experimental and simulation analysis on windage power loss of herringbone gear pair. J Tribol-T ASME2023; 145(8): 084201.
14.
DaiYZhangYYZhuX. Generalized analytical model for evaluating the gear power losses transition changing from windage to churning behavior. Tribol Int2023; 185: 108572.
15.
WeiKLuFBaoH, et al.Mechanism and reduction of windage power losses for high speed herringbone gear. Proc IMechE, Part C: J Mechanical Engineering Science2023; 237: 2014–2029.
16.
ChangenetCVelexP. A model for the prediction of churning losses in geared transmissions-preliminary results. J Mech Design2007; 129: 128–133.
17.
ChangenetCLeprinceGVilleF, et al.A note on flow regimes and churning loss modeling. J Mech Design2011; 133: 121009.
18.
SeetharamanSKahramanAMoorheadM, et al.Oil churning power losses of a gear pair: experiments and model validation. J Tribol-T ASME2009; 131: 022202.
19.
LaruelleSFossierCChangenetC, et al.Experimental investigations and analysis on churning losses of splash lubricated spiral bevel gears. Mech Ind2017; 18: 412.
20.
BardayDFossierCChangenetC, et al.Investigations on drive axle thermal behaviour: power loss and heat-transfer estimations. SAE Int J Engines2018; 11: 55–66.
21.
QuibanRChangenetCMarchesseY, et al.Churning losses of spiral bevel gears at high rotational speed. Proc IMechE, Part J: J Engineering Tribology2020; 234: 172–182.
22.
DaiYMaFZhuX, et al.Development of an analytical model to estimate the churning power losses of a spiral bevel gear. Tribol Int2020; 151: 106536.
23.
ZhuXDaiY. Development of an analytical model to predict the churning power losses of an orthogonal face gear. Eng Sci Technol2023; 41: 101383.
24.
ZhuXDaiYMaF. CFD Modelling and numerical simulation on windage power loss of aeronautic high-speed spiral bevel gears. Simul Model Pract Th2020; 103: 102080.
25.
ZhuXDaiYMaF. On the estimation of the windage power losses of spiral bevel gears: an analytical model and CFD investigation. Simul Model Pract Th2021; 110: 102334.
26.
KyrkouMENikolakopoulosPG. Simulation of thermo-hydrodynamic behavior of journal bearings, lubricating with commercial oils of different performance. Simul Model Pract Th2020; 104: 102128.
27.
WeiCWuWHouX, et al.Research on flow pattern of low temperature lubrication flow field of rotating disk based on MPS method. Tribol Int2023; 180: 108221.
28.
ShaoSZhangKLYaoY, et al.Investigations on lubrication characteristics of high-speed electric multiple unit gearbox by oil volume adjusting device. J Zhejiang Univ-Sc A2022; 23: 1013–1026.
29.
KellerMCBraunSWiethL, et al.Numerical modeling of oil-jet lubrication for spur gears using smoothed particle hydrodynamics. In Proceedings of the 11th International SPHERIC Workshop, Munich, Germany, 2016 June, pp. 14–16.
30.
LiuHArfaouiGStanicM, et al.Numerical modelling of oil distribution and churning gear power losses of gearboxes by smoothed particle hydrodynamics. Proc IMechE, Part J: J Engineering Tribology2019; 233: 74–86.
31.
LegradyBTaeschMTschirschnitzG, et al.Prediction of churning losses in an industrial gear box with spiral bevel gears using the smoothed particle hydrodynamic method. Forsch Ingenieurwes2021; 86: 379–388.
32.
HuXLiPQuanC, et al.CFD investigation on oil injection lubrication of meshing spur gears via lattice Boltzmann method. Lubricants2022; 10: 184.
33.
GongRGongQCheH, et al.Numerical investigation on churning loss torque and oil distribution of reducer based on lattice Boltzmann method. Tribol T2021; 64: 968–979.
34.
JiangYXuBLuX, et al.Multiscale simulation of flow in gas-lubricated journal bearings: a comparative study between the Reynolds equation and lattice Boltzmann methods. Eng Appl Comp Fluid2021; 15: 1792–1810.
35.
LiuHJurkschatTLohnerT, et al.Determination of oil distribution and churning power loss of gearboxes by finite volume CFD method. Tribol Int2017; 109: 346–354.
36.
ConcliFGorlaC. Numerical modeling of the power losses in geared transmissions: windage, churning and cavitation simulations with a new integrated approach that drastically reduces the computational effort. Tribol Int2016; 103: 58–68.
37.
ConcliFGorlaC. Numerical modeling of the churning power losses in planetary gearboxes: an innovative partitioning based meshing methodology for the application of a computational effort reduction strategy to complex gearbox configurations. Lubr Sci2017; 29: 455–474.
38.
HuXJiangYLuoC, et al.Churning power losses of a gearbox with spiral bevel geared transmission. Tribol Int2019; 129: 398–406.
39.
HuXWangALiP, et al.Influence of dynamic attitudes on oil supply for bearings and churning power losses in a splash lubricated spiral bevel gearbox. Tribol Int2021; 159: 106951.
40.
LuFWangMBaoH, et al.Churning power loss of the intermediate gearbox in a helicopter under splash lubrication. Proc IMechE, Part J: J Engineering Tribology2022; 236: 49–58.
41.
HildebrandLDanglFSedlmairM, et al.CFD analysis on the oil flow of a gear stage with guide plate. Forsch Ingenieurwes2022; 86: 395–408.
42.
YakhotVSmithLM. The renormalization group, the ɛ-expansion and derivation of turbulence models. J Sci Comput1992; 7: 35–61.
43.
SuJZhouCChenH, et al.The physical and mechanical properties for flexible biomass particles using computer vision. Fuel2022; 315: 123278.
44.
ZhouCJiangXSuJ, et al.Injection lubrication for high-speed helical gears using the overset mesh method and experimental verification. Tribol Int2022; 173: 107642.
