Mesh stiffness calculation of cycloid-pin gear pair with tooth profile modification and eccentricity error

Abstract

Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis (TCA) and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.

Keywords

cycloid speed reducer / mesh stiffness / tooth contact analysis / load distribution / modification

References

[1] LiS T. Design and strength analysis methods of the trochoidal gear reducers [J]. Mechanism and Machine Theory, 2014, 81: 140-154

[2] ChenB, ZhongH, LiuJ, LiC, FangTing. Generation and investigation of a new cycloid drive with double contact [J]. Mechanism and Machine Theory, 2012, 49: 270-283

[3] TranT L, PhamA D, AhnH J. Lost motion analysis of one stage cycloid reducer considering tolerances [J]. International Journal of Precision Engineering and Manufacturing, 2016, 17: 1009-1016

[4] KumarN, KosseV, OloyedeA. A new method to estimate effective elastic torsional compliance of single-stage cycloidal drives [J]. Mechanism and Machine Theory, 2016, 105: 185-198

[5] ChenZ, ShaoYi. Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack [J]. Mechanism and Machine Theory, 2013, 62: 63-74

[6] ChenB-K, FangT, LiC-Y, WangShu. Gear geometry of cycloid drives [J]. Science in China Series E: Technological Sciences, 2008, 51: 598-610

[7] BlagojevicM, MarjanovicN, DjordjevicZ, StojanovicB, DisicA. A new design of a two-stage cycloidal speed reducer [J]. Journal of Mechanical Design, 2011, 133: 085001

[8] ShinJ H, KwonS M. On the lobe profile design in a cycloid reducer using instant velocity center [J]. Mechanism and Machine Theory, 2006, 41596-616

[9] LiX, LiC, WangY, ChenB, LimT C. Analysis of a cycloid speed reducer considering tooth profile modification and clearance-fit output mechanism [J]. Journal of Mechanical Design, 2017, 139: 033303

[10] BlancheJ G, YangD C H. Cycloid drives with machining tolerances [J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 111337-344

[11] IvanovićL, DevedžićG, ĆukovićS, MirićN. Modeling of the meshing of trochoidal profiles with clearances [J]. Journal of Mechanical Design, 2012, 134: 041003

[12] SensingerJ W. Unified approach to cycloid drive profile, stress, and efficiency optimization [J]. Journal of Mechanical Design, 2010, 132024503

[13] ZhuC, SunZ, LiuH, SongC, GuZong. Effect of tooth profile modification on lubrication performance of a cycloid drive [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2015, 229785-794

[14] MihailidisA, AthanasopoulosE, AgouridasK. EHL film thickness and load dependent power loss of cycloid reducers [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2015, 230: 1303-1317

[15] WeiB, WangJ, ZhouG, YangR, ZhouH, HeTao. Mixed lubrication analysis of modified cycloidal gear used in the RV reducer [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2015, 230: 121-134

[16] XuL, YangYu. Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing [J]. Mechanism and Machine Theory, 2016, 104: 327-349

[17] HsiehC F. Dynamics analysis of cycloidal speed reducers with pinwheel and nonpinwheel designs [J]. Journal of Mechanical Design, 2014, 136: 091008

[18] KimK H, LeeC S, AhnH JTorsional rigidity of a cycloid drive considering finite bearing and hertz contact stiffness [C]//Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2009, San Diego, American Society of Mechanical Engineers: 125-130

[19] ZhangD, WangG, HuangTian. Dynamic formulation of RV reducer and analysis of structural parameters [J]. Journal of Mechanical Engineering, 2001, 37: 69-74

[20] LiuJ, MatsumuraS, ChenB, HoujohHTorsional stiffness calculation of double-enveloping cycloid drive [J], 2012, 6: 2-14

[21] HeW, LiL, LiXin. New optimized tooth-profile of cycloidal gear of high precision rv reducer used in robot [J]. Journal of Mechanical Engineering, 2000, 36: 51-55

[22] GorlaC, DavoliP, RosaF, LongoniC, ChiozziF, SamaraniA. Theoretical and experimental analysis of a cycloidal speed reducer [J]. Journal of Mechanical Design, 2008, 130: 112604

[23] LinW S, ShihY P, LeeJ J. Design of a two-stage cycloidal gear reducer with tooth modifications [J]. Mechanism and Machine Theory, 2014, 79184-197

[24] LitvinF L, FuentesAGear geometry and applied theory (second edition) [M], 2004, New York, Cambridge University Press

[25] LitvinF L, FengP H. Computerized design and generation of cycloidal gearings [J]. Mechanism and Machine Theory, 1996, 31: 891-911

[26] DemenegoA, VecchiatoD, LitvinF L, NervegnaN, MancóS. Design and simulation of meshing of a cycloidal pump [J]. Mechanism and Machine Theory, 2002, 37: 311-332

[27] JohnsonK LContact mechanics [M], 1987, Cambridge, Cambridge University Press: 84104