This article investigates the multiphysics coupling mechanism among Dynamic Thermal Elastohydrodynamic Lubrication (DTEHL), Load Tooth Contact Analysis (LTCA), and system dynamics in a Closed Differential Herringbone Gear Transmission System (CDHGTS). Based on gear meshing theory, ring gear flexibility, and rough surface contact, a dynamic contact lubrication model is developed using thermoelastic fluid dynamic lubrication theory. A gear heat transfer model integrating heat transfer and flexible deformation is established to capture dynamic thermal variations at each ring gear node. By coupling the DTEHL model, heat transfer model, and LTCA model, a nonlinear dynamic model incorporating flexible-tribo coupling is constructed. The nonlinear dynamic response of the CDHGTS under DTEHL conditions is analyzed, focusing on the influence of ring gear flexibility on system vibration. Furthermore, nonlinear dynamic behavior induced by ring gear flexibility, friction coefficient, and damping coefficient is examined. The proposed model is validated through bench vibration experiments. The study refines dynamic modeling and analysis methods for herringbone gears, offering theoretical guidance for evaluating the impact of coupled engineering factors on gear dynamics.
WangHZhouCLeiY, et al. An adhesive wear model for helical gears in line-contact mixed elastohydrodynamic lubrication. Wear2019; 426-427: 896–909. https://doi.org/10.1016/j.wear.2019.01.104
2.
WangHTangLZhouC, et al. Wear life prediction method of crowned double helical gear drive in point contact mixed elastohydrodynamic lubrication. Wear2021; 484-485: 204041. https://doi.org/10.1016/j.wear.2021.204041
3.
WangZPuWHeT, et al. Numerical simulation of transient mixed elastohydrodynamic lubrication for spiral bevel gears. Tribol Int2019; 139: 67–77. https://doi.org/10.1016/j.triboint.2019.06.032
4.
MoSZhangYChenK, et al. Dynamics analysis of helical gear considering de-meshing and reverse impact with EHL lubrication condition. Chaos2024; 34(2): 023103. https://doi.org/10.1063/5.0186433
5.
GuZZhuCLiuH, et al. Subsurface stress-field analysis of generating ground helical gear based on finite line-contact mixed elastohydrodynamic lubrication. P I Mech Eng J-J Eng2021; 235(1): 3–17. https://doi.org/10.1177/1350650120925574
6.
LiSKahramanA.A transient mixed elastohydrodynamic lubrication model for spur gear pairs. J Tribol2010; 132: 011501. https://doi.org/10.1115/1.4000270
7.
XuHKahramanAAndersonNE, et al. Prediction of mechanical efficiency of parallel-axis gear pairs. J Mech Des2007; 129(1): 58–68. https://doi.org/10.1115/1.2359478
ZhuCLiuMLiuH, et al. A thermal finite line contact EHL model of a helical gear pair. P I Mech Eng J-J Eng2013; 227(4): 299–309. https://doi.org/10.1177/1350650112462324
10.
DongHLHuJBLiXY.Temperature analysis of involute gear based on mixed elastohydrodynamic lubrication theory considering tribo-dynamic behaviors. J Tribol2014; 136(2): 021504. https://doi.org/10.1115/1.4026347
11.
BeilickeRBobachLBartelD.Transient thermal elastohydrodynamic simulation of a DLC coated helical gear pair considering limiting shear stress behavior of the lubricant. Tribol Int2016; 97: 136–150. https://doi.org/10.1016/j.triboint.2015.12.046
12.
ZhouCPanLXuJ, et al. Non-Newtonian thermal elastohydrodynamic lubrication in point contact for a crowned herringbone gear drive. Tribol Int2017; 116: 470–481. https://doi.org/10.1016/j.triboint.2017.08.007
13.
DobiášJHrubýJKordíkJ, et al. Frictional study of a high-speed helical gear pair using computational and experimental thermo-elastic analyses. J Tribol2020; 142(5): 051602. https://doi.org/10.1115/1.4046013
14.
YinZFanZWangM.Thermal elastohydrodynamic lubrication characteristics of double involute gears at the graded position of tooth waist. Tribol Int2020; 144: 106028. https://doi.org/10.1016/j.triboint.2019.106028
15.
ChimanpureASKahramanATalbotD.A transient mixed elastohydrodynamic lubrication model for helical gear contacts. J Tribol2021; 143(6): 061601. https://doi.org/10.1115/1.4048499
16.
FarrenkopfFSchwarzALohnerT, et al. Analysis of a low-loss gear geometry using a thermal elastohydrodynamic simulation including mixed lubrication. Lubricants2022; 10(9): 200. https://doi.org/10.3390/lubricants10090200
17.
LuRTangWHuangQ, et al. An improved load distribution model for gear transmission in thermal elastohydrodynamic lubrication. Lubricants2023; 11(4): 177. https://doi.org/10.3390/lubricants11040177
18.
ZhangYWangYLuB.Thermal elastohydrodynamic lubrication of herringbone gear considering the effect of oil gas mixture. J Therm Sci Eng Appl2023; 15(6): 061003. https://doi.org/10.1115/1.4062126
19.
ZhengZYanHWuJ, et al. Tribo-dynamic modelling and analysis for a high-speed helical gear system with time-varying backlash and friction under elastohydrodynamic lubrication condition. Meccanica2024; 59(7): 1019–1036. https://doi.org/10.1007/s11012-024-01793-3
20.
YinJMengXChengS, et al. Tribo-dynamics modeling and analysis of planetary gear bearing systems in wind turbines considering sun-planetary-ring helical gear mesh and elastic deformation effects. Tribol Int2024; 200: 110059. https://doi.org/10.1016/j.triboint.2024.110059
21.
ChapronMVelexPBruyèreJ, et al. Optimization of profile modifications with regard to dynamic tooth loads in single and double-helical planetary gears with flexible ring-gears. J Mech Des2016; 138(2): 023301. https://doi.org/10.1115/1.4031939
22.
LiuWShuaiZGuoY, et al. Modal properties of a two-stage planetary gear system with sliding friction and elastic continuum ring gear. Mech Mach Theory2019; 135: 251–270. https://doi.org/10.1016/j.mechmachtheory.2019.01.026
FanZZhuCSongC.Dynamic analysis of planetary gear transmission system considering the flexibility of internal ring gear. IJST-T Mech Eng2020; 44(3): 695–706. https://doi.org/10.1007/s40997-019-00290-3
XieCShuX.A new mesh stiffness model for modified spur gears with coupling tooth and body flexibility effects. Appl Math Model2021; 91: 1194–1210. https://doi.org/10.1016/j.apm.2020.11.003
27.
WangCZhangXZhouJ, et al. Calculation method of dynamic stress of flexible ring gear and dynamic characteristics analysis of thin-walled ring gear of planetary gear train. J Vib Eng Technol2021; 9(5): 751–766. https://doi.org/10.1007/s42417-020-00259-6
28.
CaoZRaoM.Coupling effects of manufacturing error and flexible ring gear rim on dynamic features of planetary gear. P I Mech Eng C-J Mec2021; 235(21): 5234–5246. https://doi.org/10.1177/0954406220983365
29.
ZhaoZHanHWangP, et al. An improved model for meshing characteristics analysis of spur gears considering fractal surface contact and friction. Mech Mach Theory2021; 158: 104219. https://doi.org/10.1016/j.mechmachtheory.2020.104219
30.
GeHShenYZhuY, et al. Simulation and experimental test of load-sharing behavior of planetary gear train with flexible ring gear. J Mech Sci Technol2021; 35(11): 4875–4888. https://doi.org/10.1007/s12206-021-1006-1
31.
LiuCYangCZhaoY, et al. Dynamic modeling and analysis of high-speed flexible planetary gear transmission systems. Alex Eng J2023; 80: 444–464. https://doi.org/10.1016/j.aej.2023.08.079
32.
KongXHuZTangJ, et al. Effects of gear flexibility on the dynamic characteristics of spur and helical gear system. Mech Syst Signal Process2023; 184: 109691. https://doi.org/10.1016/j.ymssp.2022.109691
33.
YangXLeiYLiuH, et al. Rigid-flexible coupled modeling of compound multistage gear system considering flexibility of shaft and gear elastic deformation. Mech Syst Signal Process2023; 200: 110632. https://doi.org/10.1016/j.ymssp.2023.110632
34.
WuSZhouYZhaoC, et al. Study on the method of analyzing the time-variant internal mesh stiffness of helical gears considering the flexibility of the gear ring. J Adv Mech Des Syst2023; 17(6): JAMDSM0076. https://doi.org/10.1299/jamdsm.2023jamdsm0076
35.
TianHMaHPengZ, et al. Study on rigid-flexible coupling modeling of planetary gear systems: incorporation of the pass effect and random excitations. Mech Mach Theory2024; 201: 105745. https://doi.org/10.1016/j.mechmachtheory.2024.105745
36.
ConryTFSeiregA.A mathematical programming technique for the evaluation of load distribution and optimal modifications for gear systems. J Eng Ind1973; 95(4): 1115–1122. https://doi.org/10.1115/1.3438259
