Abstract
Gear manufacturing errors are key parameters in planetary gear trains and have effects on load sharing, tooth stress, and so on. Accurate estimation of manufacturing errors can help monitor the conditions of planetary gear systems. This study investigates the dynamic response sensitivity to model parameters for a nonlinear single-stage planetary gear set with coupled lateral and torsional motions. Power flow theory is introduced to assess the gear vibration and the parameter sensitivity. The response sensitivity equations are deduced with the direct method (DM). The influence of the rotating speed is considered in the sensitivity analysis. Then, the identifiability of the parameter estimation is investigated based on the sensitivity results. The Gauss-Newton method is applied to estimate the manufacturing errors. Gear meshing is a primary factor in gear vibration, so the sensitivities of its vibration power to the parameters are analyzed in this paper. The estimated results are accurate when the collected data contain a lower noise signal. The sensitivity and parameter estimation make it possible to provide support for the design and diagnosis of a planetary gear set.
Issue Section:
Research Papers
References
1.
Hu
, Y.
, Talbot
, D.
, and Kahraman
, A.
, 2019
, “A Gear Load Distribution Model for a Planetary Gear Set With a Flexible Ring Gear Having External Splines
,” ASME J. Mech. Des.
, 141
(5
), p. 053301. 2.
Chaari
, F.
, Fakhfakh
, T.
, Hbaieb
, R.
, Louati
, J.
, and Haddar
, M.
, 2006
, “Influence of Manufacturing Errors on the Dynamic Behavior of Planetary Gears
,” Int. J. Adv. Manuf. Technol.
, 27
(7
), pp. 738
–746
. 3.
Litvin
, F.
, Vecchiato
, D.
, Demenego
, A.
, Karedes
, E.
, Hansen
, B.
, and Handschuh
, R.
, 2002
, “Design of One Stage Planetary Gear Train With Improved Conditions of Load Distribution and Reduced Transmission Errors
,” ASME J. Mech. Des.
, 124
(4
), pp. 745
–752
. 4.
Bodas
, A.
, and Kahraman
, A.
, 2004
, “Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of Planetary Gear Sets
,” JSME Int. J. C-Mech. Syst. Mach. Elem. Manuf.
, 47
(3
), pp. 908
–915
. 5.
Cheon
, G.-J.
, and Parker
, R. G.
, 2004
, “Influence of Manufacturing Errors on the Dynamic Characteristics of Planetary Gear Systems
,” KSME Int. J.
, 18
(4
), pp. 606
–621
. 6.
Ligata
, H.
, Kahraman
, A.
, and Singh
, A.
, 2008
, “An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing
,” ASME J. Mech. Des.
, 130
(4
), p. 041701
. 7.
Hidaka
, T.
, and Terauchi
, Y.
, 1976
, “Dynamic Behavior of Planetary Gear: 1st Report Load Distribution in Planetary Gear
,” Bull. JSME
, 19
(132
), pp. 690
–698
. 8.
Cao
, Z.
, and Rao
, M.
, 2021
, “Coupling Effects of Manufacturing Error and Flexible Ring Gear Rim on Dynamic Features of Planetary Gear
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 235
(21
), pp. 5234
–5246
. 9.
Heng
, A.
, Zhang
, S.
, Tan
, A. C.
, and Mathew
, J.
, 2009
, “Rotating Machinery Prognostics: State of the Art, Challenges and Opportunities
,” Mech. Syst. Signal Process
, 23
(3
), pp. 724
–739
. 10.
Lee
, J.
, Wu
, F.
, Zhao
, W.
, Ghaffari
, M.
, Liao
, L.
, and Siegel
, D.
, 2014
, “Prognostics and Health Management Design for Rotary Machinery Systems—Reviews, Methodology and Applications
,” Mech. Syst. Signal Process
, 42
(1
), pp. 314
–334
. 11.
Hai
, Y.
, Tsui
, K.-L.
, and Zuo
, M. J.
, 2012
, “Gear Crack Level Classification Based on Multinomial Logit Model and Cumulative Link Model
,” Proceedings of the IEEE 2012 Prognostics and System Health Management Conference (PHM-2012 Beijing)
, pp. 1
–6
.12.
Li
, C. J.
, and Lee
, H.
, 2005
, “Gear Fatigue Crack Prognosis Using Embedded Model, Gear Dynamic Model and Fracture Mechanics
,” Mech. Syst. Signal Process
, 19
(4
), pp. 836
–846
. 13.
Zhang
, X.
, Kang
, J.
, Bechhoefer
, E.
, and Zhao
, J.
, 2014
, “A New Feature Extraction Method for Gear Fault Diagnosis and Prognosis
,” Eksploatacja i Niezawodność
, 16
(2
), pp. 295
–300
.14.
Kacprzynski
, G. J.
, Roemer
, M. J.
, Modgil
, G.
, Palladino
, A.
, and Maynard
, K.
, 2002
, “Enhancement of physics-of-failure prognostic models with system level features
,” Proceedings, IEEE Aerospace Conference
, Big Sky, MT
, Mar. 9–16
, vol. 6, p. 6
.15.
Tan
, C. K.
, 2005
, “An Investigation on the Diagnostics and Prognostic Capabilities of Acoustic Emission (ae) on a Spur Gearbox
,” Ph.D. thesis
, Cranfield University
.16.
Gašperin
, M.
, Juričić
, Đ.
, Boškoski,
P.
, and Vižintin
, J.
, 2011
, “Model-Based Prognostics of Gear Health Using Stochastic Dynamical Models
,” Mech. Syst. Signal Process
, 25
(2
), pp. 537
–548
. 17.
Beck
, J. V.
, and Arnold
, K. J.
, 1977
, Parameter Estimation in Engineering and Science
, Wiley
, New York
.18.
Guay
, M.
, and McLean
, D.
, 1995
, “Optimization and Sensitivity Analysis for Multiresponse Parameter Estimation in Systems of Ordinary Differential Equations
,” Comput. Chem. Eng.
, 19
(12
), pp. 1271
–1285
. 19.
Jiang
, R.
, Yu
, J.
, and Makis
, V.
, 2012
, “Optimal Bayesian Estimation and Control Scheme for Gear Shaft Fault Detection
,” Comput. Ind. Eng.
, 63
(4
), pp. 754
–762
. 20.
Koech
, W.
, Rotich
, T.
, Nyamwala
, F.
, and Rotich
, S.
, 2016
, “Parameter Estimation of a dc Motor-Gearalternator (MGA) System via Step Response Methodology
,” Am. J. Appl. Math.
, 4
(5
), p. 252
. 21.
Zhan
, Z.
, Liu
, H.
, Feeny
, B.
, Xiang
, C.
, and Han
, L.
, 2019
, “Response Sensitivity in a Nonlinear Planetary Gear Set
,” ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Anaheim, CA
, Aug. 18–21
, ASME Paper No. DETC2019-97366, pp. 1–6
.22.
Masoumi
, A.
, Pellicano
, F.
, Samani
, F. S.
, and Barbieri
, M.
, 2015
, “Symmetry Breaking and Chaos-Induced Imbalance in Planetary Gears
,” Nonlinear Dyn.
, 80
(1–2
), pp. 561
–582
. 23.
Zhai
, H.
, Zhu
, C.
, Song
, C.
, Liu
, H.
, Li
, G.
, and Ma
, F.
, 2015
, “Dynamic Modeling and Analysis for Transmission System of High-Power Wind Turbine Gearbox
,” J. Mech. Sci. Technol.
, 29
(10
), pp. 4073
–4082
. 24.
Saxena
, A.
, Parey
, A.
, and Chouksey
, M.
, 2016
, “Time Varying Mesh Stiffness Calculation of Spur Gear Pair Considering Sliding Friction and Spalling Defects
,” Eng. Fail. Anal.
, 70
, pp. 200
–211
. 25.
Wang
, C.
, Liu
, H.
, Du
, M.
, and Xiang
, C.
, 2017
, “A Gear Mesh Dynamic Model for Analyzing the Nonlinear Vibrations of Spur Gears Supported by Compliant Shafts
,” International Conference on Mechanical Design
, Springer
, pp. 97
–124
.26.
Xing
, J. T.
, 2015
, Energy Flow Theory of Nonlinear Dynamical Systems With Applications
, Springer
, Switzerland
.27.
Barten
, E.
, van der Seijs
, M. V.
, and de Klerk
, D.
, 2014
, “A Complex Power Approach to Characterise Joints in Experimental Dynamic Substructuring
,” Dynamics of Coupled Structures
, Vol. 1
, pp. 281
–296
. 28.
van der Seijs
, M. V.
, de Klerk
, D.
, and Rixen
, D. J.
, 2016
, “General Framework for Transfer Path Analysis: History, Theory and Classification of Techniques
,” Mech. Syst. Signal Process
, 68
, pp. 217
–244
. 29.
Dai
, X.
, Cooley
, C. G.
, and Parker
, R. G.
, 2016
, “Dynamic Tooth Root Strains and Experimental Correlations in Spur Gear Pairs
,” Mech. Mach. Theory
, 101
, pp. 60
–74
. 30.
Hamby
, D.
, 1994
, “A Review of Techniques for Parameter Sensitivity Analysis of Environmental Models
,” Environ. Monit. Assess.
, 32
(2
), pp. 135
–154
. 31.
Gembicki
, F.
, and Haimes
, Y.
, 1975
, “Approach to Performance and Sensitivity Multiobjective Optimization: The Goal Attainment Method
,” IEEE Trans. Automat. Contr.
, 20
(6
), pp. 769
–771
. 32.
Rituraj
, F.
, Vacca
, A.
, and Morselli
, M. A.
, 2019
, “Modeling of Manufacturing Errors in External Gear Machines and Experimental Validation
,” Mech. Mach. Theory
, 140
, pp. 457
–478
. 33.
Park
, Y.-J.
, Lee
, G.-H.
, Oh
, J.-S.
, Shin
, C.-S.
, and Nam
, J.-S.
, 2019
, “Effects of Non-Torque Loads and Carrier Pinhole Position Errors on Planet Load Sharing of Wind Turbine Gearbox
,” Int. J. Precis. Eng. Manuf. Green Technol.
, 6
(2
), pp. 281
–292
. 34.
Moradi
, H.
, and Salarieh
, H.
, 2012
, “Analysis of Nonlinear Oscillations in Spur Gear Pairs With Approximated Modelling of Backlash Nonlinearity
,” Mech. Mach. Theory
, 51
, pp. 14
–31
. 35.
Huang
, Y.
, 2015
, “Response Sensitivity of Nonlinear Vibration and Dynamic Modification of Vehicle Transmission System
,” Ph.D. dissertation, Beijing Institute of Technology, Beijing.36.
Inalpolat
, M.
, and Kahraman
, A.
, 2010
, “A Dynamic Model to Predict Modulation Sidebands of a Planetary Gear Set Having Manufacturing Errors
,” J. Sound Vib.
, 329
(4
), pp. 371
–393
. 37.
Liang
, X.
, Zuo
, M. J.
, and Hoseini
, M. R.
, 2015
, “Vibration Signal Modeling of a Planetary Gear Set for Tooth Crack Detection
,” Eng. Fail. Anal.
, 48
, pp. 185
–200
. 38.
Feng
, Z.
, and Zuo
, M. J.
, 2012
, “Vibration Signal Models for Fault Diagnosis of Planetary Gearboxes
,” J. Sound Vib.
, 331
(22
), pp. 4919
–4939
. 39.
Lee
, S.
, and White
, P.
, 1998
, “The Enhancement of Impulsive Noise and Vibration Signals for Fault Detection in Rotating and Reciprocating Machinery
,” J. Sound Vib.
, 217
(3
), pp. 485
– 505
. 40.
Bartelmus
, W.
, and Zimroz
, R.
, 2009
, “A New Feature for Monitoring the Condition of Gearboxes in Non-Stationary Operating Conditions
,” Mech. Syst. Signal Process
, 23
(5
), pp. 1528
–1534
. 41.
Feng
, K.
, Wang
, K.
, Ni
, Q.
, Zuo
, M. J.
, and Wei
, D.
, 2017
, “A Phase Angle Based Diagnostic Scheme to Planetary Gear Faults Diagnostics Under Non-Stationary Operational Conditions
,” J. Sound Vib.
, 408
, pp. 190
–209
. Copyright © 2022 by ASME
You do not currently have access to this content.
