Abstract
In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.
Issue Section:
Research Papers
References
1.
Kahraman
, A.
, 1994
, “Load Sharing Characteristics of Planetary Transmissions
,” Mech. Mach. Theory
, 29
(8
), pp. 1151
–1165
. 10.1016/0094-114X(94)90006-X2.
Saada
, A.
, and Velex
, P.
, 1995
, “An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains
,” J. Mech. Des.—Trans. ASME
, 117
(2
), pp. 241
–247
. 10.1115/1.28261293.
Jian
, L.
, and Parker
, R. G.
, 1999
, “Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration
,” J. Vib. Acoust.—Trans. ASME
, 121
(3
), pp. 316
–321
. 10.1115/1.28939824.
Farshidianfar
, A.
, and Saghafi
, A.
, 2014
, “Global Bifurcation and Chaos Analysis in Nonlinear Vibration of Spur Gear Systems
,” Nonlinear Dyn.
, 75
(4
), pp. 783
–806
. 10.1007/s11071-013-1104-45.
Gou
, X.
, Zhu
, L.
, and Chen
, D.
, 2015
, “Bifurcation and Chaos Analysis of Spur Gear Pair in Two-Parameter Plane
,” Nonlinear Dyn.
, 79
(3
), pp. 2225
–2235
. 10.1007/s11071-014-1807-16.
Li
, Z.
, and Peng
, Z.
, 2015
, “Nonlinear Dynamic Response of a Multi-Degree of Freedom Gear System Dynamic Model Coupled With Tooth Surface Characters: A Case Study on Coal Cutters
,” Nonlinear Dyn.
, 84
(1
), pp. 1
–16
. 10.1007/s11071-015-2475-57.
Wang
, J.
, He
, G.
, Zhang
, J.
, and Zhao
, Y.
, 2017
, “Nonlinear Dynamics Analysis of the Spur Gear System for Railway Locomotive
,” Mech. Syst. Sig. Process.
, 85
(2
), pp. 41
–55
. 10.1016/j.ymssp.2016.08.0048.
Xiang
, L.
, Zhang
, Y.
, Gao
, N.
, Hu
, A.
, and Xing
, J.
, 2018
, “Nonlinear Dynamics of a Multistage Gear Transmission System With Multi-Clearance
,” Int. J. Bifurcation Chaos
, 28
(3
), p. 1850034
. 10.1142/S02181274185003479.
Hou
, L.
, and Cao
, S.
, 2019
, “Nonlinear Dynamic Analysis on Planetary Gears-Rotor System in Geared Turbofan Engines
,” Int. J. Bifurcation Chaos
, 29
(6
), p. 1950076
. 10.1142/S021812741950076710.
Sheng
, L.
, Li
, W.
, Wang
, Y.
, Fan
, M.
, and Yang
, X.
, 2019
, “Nonlinear Dynamic Analysis and Chaos Control of Multi-Freedom Semi-Direct Gear Drive System in Coal Cutters
,” Mech. Syst. Sig. Process.
, 116
, pp. 62
–77
. 10.1016/j.ymssp.2018.06.04311.
Mao
, K.
, Li
, W.
, Hooke
, C. J.
, and Walton
, D.
, 2009
, “Friction and Wear Behaviour of Acetal and Nylon Gears
,” Wear
, 267
(1
), pp. 639
–645
. 10.1016/j.wear.2008.10.00512.
TunalioğLu
, MŞ
, and Tuç
, B.
, 2014
, “Theoretical and Experimental Investigation of Wear in Internal Gears
,” Wear
, 309
(1–2
), pp. 208
–215
. 10.1016/j.wear.2013.11.01613.
Wojnarowski
, J.
, and Onishchenko
, V.
, 2003
, “Tooth Wear Effects on Spur Gear Dynamics
,” Mech. Mach. Theory
, 38
(2
), pp. 161
–178
. 10.1016/S0094-114X(02)00091-514.
Kuang
, J. H.
, and Lin
, A.
, 2001
, “The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair
,” J. Vib. Acoust.—Trans. ASME
, 123
(3
), pp. 311
–317
. 10.1115/1.137937115.
Flodin
, A.
, and Andersson
, S.
, 1997
, “Simulation of Mild Wear in Spur Gears
,” Wear
, 207
(1–2
), pp. 16
–23
. 10.1016/S0043-1648(96)07467-416.
Flodin
, A.
, and Andersson
, S.
, 2000
, “Simulation of Mild Wear in Helical Gears
,” Wear
, 241
(2
), pp. 123
–128
. 10.1016/S0043-1648(00)00384-717.
Yuksel
, C.
, and Kahraman
, A.
, 2004
, “Dynamic Tooth Loads of Planetary Gear Sets Having Tooth Profile Wear
,” Mech. Mach. Theory
, 39
(7
), pp. 695
–715
. 10.1016/j.mechmachtheory.2004.03.00118.
Ding
, H.
, and Kahraman
, A.
, 2007
, “Interactions Between Nonlinear Spur Gear Dynamics and Surface Wear
,” J. Sound Vib.
, 307
(3–5
), pp. 662
–679
. 10.1016/j.jsv.2007.06.03019.
Kahraman
, A.
, and Ding
, H.
, 2010
, “A Methodology to Predict Surface Wear of Planetary Gears Under Dynamic Conditions
,” Mech. Based Des. Struct. Mach.
, 38
(4
), pp. 493
–515
. 10.1080/15397734.2010.50131220.
Zhang
, J.
, and Liu
, X.
, 2015
, “Effects of Misalignment on Surface Wear of Spur Gears
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 229
(9
), pp. 1145
–1158
. 10.1177/135065011557473221.
Liu
, X.
, Yang
, Y.
, and Zhang
, J.
, 2016
, “Investigation on Coupling Effects Between Surface Wear and Dynamics in a Spur Gear System
,” Tribol. Int.
, 101
, pp. 383
–394
. 10.1016/j.triboint.2016.05.00622.
Zhou
, C.
, and Wang
, H.
, 2018
, “An Adhesive Wear Prediction Method for Double Helical Gears Based on Enhanced Coordinate Transformation and Generalized Sliding Distance Model
,” Mech. Mach. Theory
, 128
, pp. 58
–83
. 10.1016/j.mechmachtheory.2018.05.01023.
Archard
, J. F.
, 1953
, “Contact and Rubbing of Flat Surfaces
,” J. Appl. Phys.
, 24
(8
), pp. 981
–988
. 10.1063/1.172144824.
Wei
, J.
, Zhang
, A.
, and Gao
, P.
, 2015
, “A Study of Spur Gear Pitting Under EHL Conditions: Theoretical Analysis and Experiments
,” Tribol. Int.
, 94
, pp. 146
–154
. 10.1016/j.triboint.2015.08.03725.
Johnson
, K. L.
, 1985
, Contact Mechanics
, Cambridge University Press
, Cambridge
.26.
Spitas
, C.
, and Spitas
, V.
, 2006
, “Calculation of Overloads Induced by Indexing Errors in Spur Gearboxes Using Multi-Degree-of-Freedom Dynamical Simulation
,” Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn.
, 220
(4
), pp. 273
–282
. 10.1243/1464419JMBD6727.
Spitas
, C.
, and Spitas
, V.
, 2016
, “Coupled Multi-DOF Dynamic Contact Analysis Model for the Simulation of Intermittent Gear Tooth Contacts, Impacts and Rattling Considering Backlash and Variable Torque
,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
, 230
(7–8
), pp. 1022
–1047
. 10.1177/095440621559669628.
Benatar
, M.
, Handschuh
, M.
, Kahraman
, A.
, and Talbot
, D.
, 2019
, “Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications
,” ASME J. Mech. Des.
, 141
(10
), p. 103301
. 10.1115/1.404358629.
Chen
, Z.
, and Shao
, Y.
, 2011
, “Dynamic Simulation of Spur Gear With Tooth Root Crack Propagating Along Tooth Width and Crack Depth
,” Eng. Failure Anal.
, 18
(8
), pp. 2149
–2164
. 10.1016/j.engfailanal.2011.07.00630.
Chen
, Z.
, and Shao
, Y.
, 2013
, “Mesh Stiffness Calculation of a Spur Gear Pair With Tooth Profile Modification and Tooth Root Crack
,” Mech. Mach. Theory
, 62
, pp. 63
–74
. 10.1016/j.mechmachtheory.2012.10.01231.
Chen
, Z.
, and Shao
, Y.
, 2015
, “Dynamic Features of Planetary Gear Train With Tooth Errors
,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
, 229
(10
), pp. 1769
–1781
. 10.1177/095440621454950332.
Wang
, Q.
, and Zhang
, Y.
, 2017
, “A Model for Analyzing Stiffness and Stress in a Helical Gear Pair With Tooth Profile Errors
,” J. Vib. Control
, 23
(2
), pp. 272
–289
. 10.1177/107754631557682833.
Liu
, G.
, Hong
, J.
, and Parker
, R. G.
, 2019
, “Influence of Simultaneous Time-Varying Bearing and Tooth Mesh Stiffness Fluctuations on Spur Gear Pair Vibration
,” Nonlinear Dyn.
, 97
(2
), pp. 1403
–1424
. 10.1007/s11071-019-05056-934.
Sakaridis
, E.
, Spitas
, V.
, and Spitas
, C.
, 2019
, “Non-Linear Modeling of Gear Drive Dynamics Incorporating Intermittent Tooth Contact Analysis and Tooth Eigenvibrations
,” Mech. Mach. Theory
, 136
, pp. 307
–333
. 10.1016/j.mechmachtheory.2019.03.01235.
Xiao
, Z.
, Zhou
, C.
, Chen
, S.
, and Li
, Z.
, 2019
, “Effects of Oil Film Stiffness and Damping on Spur Gear Dynamics
,” Nonlinear Dyn.
, 96
(1
), pp. 145
–159
. 10.1007/s11071-019-04780-636.
Chen
, Z.
, Zhou
, Z.
, Zhai
, W.
, and Wang
, K.
, 2020
, “Improved Analytical Calculation Model of Spur Gear Mesh Excitations With Tooth Profile Deviations
,” Mech. Mach. Theory
, 149
. 103838
.37.
Cao
, Z.
, Shao
, Y.
, Rao
, M.
, and Yu
, W.
, 2018
, “Effects of the Gear Eccentricities on the Dynamic Performance of a Planetary Gear Set
,” Nonlinear Dyn.
, 91
(1
), pp. 1
–15
. 10.1007/s11071-017-3738-038.
Chaari
, F.
, Fakhfakh
, T.
, and Haddar
, M.
, 2009
, “Analytical Modelling of Spur Gear Tooth Crack and Influence on Gearmesh Stiffness
,” Eur. J. Mech. A—Solid
, 28
(3
), pp. 461
–468
. 10.1016/j.euromechsol.2008.07.00739.
Siyu
, C.
, Jinyuan
, T.
, Caiwang
, L.
, and Qibo
, W.
, 2011
, “Nonlinear Dynamic Characteristics of Geared Rotor Bearing Systems With Dynamic Backlash and Friction
,” Mech. Mach. Theory
, 46
(4
), pp. 466
–478
. 10.1016/j.mechmachtheory.2010.11.016Copyright © 2020 by ASME
You do not currently have access to this content.
