The paper presents a tribo-dynamic model for planetary gear sets of hybrid-electric-vehicle configurations. The model comprises a six degree-of-freedom torsional multi-body dynamic system, as well as a tribological contact model in order to evaluate the lubricant film thickness, friction and efficiency of the meshing gear teeth contacts. The tribological model takes into account the non-Newtonian, thermal-mixed elastohydrodynamic regime of lubrication. Analysis is performed for a hybrid electric C-segment vehicle. The simulated conditions correspond to cases of power supplied by either the engine or the electric motor. The results illustrate that in the electric motor drive mode, improved noise, vibration and harshness refinement would be expected, whereas better transmission efficiency is achieved in the internal combustion engine drive mode.
Won S, Ashish K and Sungwook H. 6 speed automatic transmission vibration magnitude prediction and whine noise improvement through transmission system modelling. SAE Technical Paper 2011-01-153, 2011.
SunTHuHH. Nonlinear dynamics of a planetary gear system with multiple clearances. Mech Mach Theory2003; 38: 1371–1390.
4.
Eisele G, Wolff K and Alt N. Application of vehicle interior noise simulation for NVH analysis of a passenger car. SAE Technical Paper 2005-01-2514, 2005.
5.
Hwang SJ, Stout JL and Ling CC. Modelling and analysis of powertrain torsional response. SAE Technical Paper 980276, 1998.
6.
SyedFUKuangMLYingH. Active damping wheel-torque control system to reduce driveline oscillations in a power-split hybrid electric vehicle. IEEE Trans Veh Technol2009; 58: 4769–4785.
7.
KahramanAVijayakarS. Effect of internal gear flexibility on the quasi-static behavior of a planetary gear set. Trans ASME J Mech Des2001; 123: 408–415.
8.
MohammadpourMTheodossiadesSRahnejatH. Transient mixed non-Newtonian thermo-elastohydrodynamics of vehicle differential hypoid gears with starved partial counter-flow inlet boundary. Proc IMechE, Part J: J Engineering Tribology2014; 228: 1158–1173.
9.
VelexPCahouetV. Experimental and numerical investigations on the influence of tooth friction in spur and helical gear dynamics. Trans ASME J Mech Des2000; 122: 515–522.
10.
De la CruzMTheodossiadesSRahnejatH. An investigation of manual transmission drive rattle. Proc IMechE, Part K: J Multi-body Dynamics2010; 224: 167–181.
11.
KoroniasGTheodossiadesSRahnejatH. Axle whine phenomenon in light trucks: A combined numerical and experimental investigation. Proc IMechE, Part D: J Automobile Engineering2011; 225: 885–894.
12.
DietlPWensingJVan NijenGC. Rolling bearing damping for dynamic analysis of multi-body systems-experimental and theoretical results. Proc IMechE, Part K: J Multi-body Dynamics2000; 214: 33–43.
13.
MohammadpourMTheodossiadesSRahnejatH. Multi-physics investigations on the dynamics of differential hypoid gears. Trans ASME J Vib Acoust2014; 136: 041007–041007.
14.
Mohammadpour M, Theodossiades S and Rahnejat H. Tribodynamics of differential hypoid gears. In: International gear conference, Lyon, France, 2014.
15.
MohammadpourMTheodossiadesSRahnejatH. Transmission efficiency and noise, vibration and harshness refinement of differential hypoid gear pairs. Proc IMechE, Part K: J Multi-body Dynamics2014; 228: 19–33.
16.
InalpolatMKahramanA. Dynamic modelling of planetary gears of automatic transmissions. Proc IMechE, Part K: J Multi-body Dynamics2008; 222: 229–242.
17.
AmbarishaVKParkerR. Suppression of planet mode response in planetary gear dynamics through mesh phasing. Trans ASME J Vib Acoust2006; 128: 133–142.
18.
GreenwoodJATrippJH. The contact of two nominally flat rough surfaces. Proc Instn Mech Engrs1970–1971; 185: 625–633.
19.
GoharRRahnejatH. Fundamentals of tribology, London: Imperial College Press, 2008.
20.
JohnsonKLCameronR. Shear behaviour of elastohydrodynamic oil films at high rolling contact pressures. Proc Instn Mech Engrs1967; 182: 307–330.
21.
MohammadpourMTheodossiadesSRahnejatH. Non-Newtonian mixed elastohydrodynamics of differential hypoid gears at high loads. Meccanica2014; 49: 1115–1138.
22.
EvansCRJohnsonKL. Regimes of traction in elastohydrodynamic lubrication. Proc IMechE, Part C: J Mechanical Engineering Science1986; 200: 313–324.
ZhangJTangXYuH. Multi-body dynamics and noise analysis for the torsional vibration of a power-split hybrid driveline. Proc IMechE, Part K: J Multi-body Dynamics2014. DOI: 1464419314540152.
25.
KaragiannisITheodossiadesSRahnejatH. On the dynamics of lubricated hypoid gears. Mech Mach Theory2012; 48: 94–120.
26.
RahnejatH. Multi-body dynamics: Vehicles, machines and mechanisms, Bury St Edmunds, UK: Professional Engineering Publishing, 1998.
