Misalignment error of gear pair will affect the load distribution along the tooth-width and have a great effect on dynamic characteristics. For the planetary gear set, it is complicated to model the misalignment error of carrier as, when this error is present, the planets and the carrier are tilted and contacts between sun–planet and ring–planet along tooth width are skewed. In this paper, a new lumped parameter model is set up to quasi-statically and dynamic analyze the planetary gear set with the position-dependent line of action due to the misalignment of the carrier. In the analytical model, each potential line of contact on the gear mesh is discretized into finite independent time-varying stiffness. External and internal gear stiffness is obtained through the potential energy method. The dynamic responses, load distribution along the tooth width, load sharing between planets, trajectories of sun gear are simulated and analyzed with carrier misalignment error in planetary gear set.
SennbaM. Gear errors and strength, Tokyo, Japan: The Nikkan Kogyo Shimbun Press, 1974, pp. 70–148. (in Japanese).
2.
RademacherJ. Ermittlung von Lastverteilungsfaktoren für Stirnradgetrieben. Ind Anz1967; 89: 331–337.
3.
OpitzHTimmersJBoschM. Möglichkeiten zur Verbesserung des Geräuschverhaltens von Zahnradgetrieben. Forschungsberichte des Landes Nordrhein-Westfalen1976; 5: 1867–1873.
4.
ConryTFSeiregA. A mathematical programming method for design of elastic bodies in contact. Trans ASME J Appl Mech1971; 6: 387–392.
5.
ConryTFSeiregA. A mathematical programming technique for the evaluation of load distribution and optimal modifications for gear systems. J Eng Ind Trans Am Soc Mech Eng1973; 95: 1115–1122.
6.
LiS. Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears. Mech Mach Theory2007; 42(6): 698–726.
7.
LiS. Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications. Mech Mach Theory2007; 42(1): 88–114.
8.
VelexPMaatarM. A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behaviour. J Sound Vib1996; 191(5): 629–660.
9.
StewardJH. The compliance of solid, wide-faced spur gears. J Mech Des1990; 112: 590–595.
10.
JaramilloTJ. Deflections and moments due to a concentrated load on a cantilever plate of infinite length. J Appl Mech1950; 17: 67–72.
11.
WellauerEJSeiregA. Bending strength of gear teeth by cantilever-plate theory. J Eng Ind1960; 82(3): 213–221.
12.
AjmiMVelexP. A model for simulating the quasi-static and dynamic behaviour of solid wide-faced spur and helical gears. Mech MachTheory2005; 40: 173–190.
BodasAKahramanA. Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets. JSME Int J Ser C2004; 47: 908–915.
15.
LigataHKahramanASinghA. An experimental study of the influence of manufacturing errors on planetary gear stresses and load sharing. J Mech Des2008; 130: 04170–04171.
16.
SinghA. Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation. Mech Mach Theory2010; 45: 511–530.
17.
VecchiatoD. Tooth contact analysis of a misaligned isostatic planetary gear train. Mech Mach Theory2006; 41: 617–631.
18.
WeberC. The deformation of loaded gears and the effect on their load carrying capacity. Report 3, DSIR Sponsored Research, London, 1949.
19.
SainsotPVelexP. Contribution of gear body to tooth deflections—A new bidimensional analytical formula. J Mech Des2004; 126: 748–752.
20.
YangDCHLinJY. Hertzian damping, tooth friction and bending elasticity in gear impact dynamics. J Mech Des1987; 109(2): 189–196.
21.
YangDCHSuZS. A rotary model for spur gear dynamics. ASME J Mech Trans Aut Des1985; 107: 529–535.
22.
LiangXZuoMJPandeyM. Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set. Mech Mach Theory. 2014; 76: 20–38.
23.
LiangXZuoMJPatelTH. Evaluating time-varying mesh stiffness of a planetary gear set using the potential energy method. Proc IMechE, Part C: J Mechanical Engineering Science. 2014; 228: 535–547.
24.
LinJParkerRG. Analytical characterization of the unique properties of planetary gear free vibration. Trans ASME J Vib Acoust1999; 121: 316–321.
25.
AmbarishaVKParkerRG. Nonlinear dynamic planetary gear using analytical and finite element models. J Sound Vib2007; 302(3): 577–595.
26.
ChenZShaoY. Dynamic features of a planetary gear system with tooth crack under different sizes and inclination angles. J Vib Acoust2013; 135(3): 031004.
27.
GuXVelexP. A dynamic model to study the influence of planet position errors in planetary gears. J Sound Vib2012; 331: 4554–4574.
28.
ParkerRG. Mesh phasing relationships in planetary and epicyclic gears. J Mech Des2004; 126: 365–370.
