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Verification of Experimental Component Mode Synthesis in the Sierra Analysis Framework Read chapter Read first chapter

2016 | OriginalPaper | Chapter

30. Nonlinear Time-Varying Dynamic Analysis of a Multi-Mesh Spur Gear Train

Authors : Siar Deniz Yavuz, Zihni Burcay Saribay, Ender Cigeroglu

Published in: Dynamics of Coupled Structures, Volume 4

Publisher: Springer International Publishing

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Abstract

The nonlinear dynamics of a multi-mesh spur gear train is considered in this study. The gear train consists of three spur gears, with one of the gears in mesh with the other two. Dynamic model includes gear backlash in the form of clearance-type displacement functions and time variation of gear mesh stiffness. The system is reduced to a two-degree-of-freedom definite model by using the relative gear mesh displacements as the coordinates. The equations of motion are solved for periodic steady-state response by using Harmonic Balance Method (HBM). The accuracy of the HBM solutions is demonstrated by comparing them to direct numerical integration solutions. Floquet theory is applied to determine the stability of the steady-state solutions. Two different loading conditions, where the system is driven by the middle gear and driven by one of the end gears, are considered. Phase difference between the two gear meshes is determined under each loading condition and natural modes are predicted for each loading condition. The forced response due to the combination of parametric excitation and static transmission error excitation is obtained and effects of loading conditions and asymmetric positioning on the response are explored.

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Literature
1.
Kahraman, A., Singh, R.: Non-linear dynamics of a spur gear pair. J. Sound Vib. 142(1), 49–75 (1990)CrossRef
2.
Kahraman, A., Singh, R.: Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. J. Sound Vib. 146(1), 135–156 (1991)CrossRef
3.
Kahraman, A., Blankenship, G.W.: Steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity. J. Sound Vib. 185(5), 743–765 (1995)CrossRefMATH
4.
Kahraman, A., Blankenship, G.W.: Interactions between commensurate parametric and forcing excitations in a system with clearance. J. Sound Vib. 194(3), 317–336 (1996)CrossRef
5.
Kahraman, A., Lim, J., Ding, H.: A dynamic model of a spur gear pair with friction. In: Proceesdings of 12th IFToMM World Congress, Besançon (2007)
6.
Shen, Y., Yang, S., Liu, X.: Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method. Int. J. Mech. Sci. 48, 1256–1263 (2006)CrossRefMATH
7.
Kahraman, A., Blankenship, G.W.: Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters. J. Appl. Mech. 64, 217–226 (1997)CrossRef
8.
Kahraman, A., Singh, R.: Non-linear dynamics of a geared rotor-bearing system with multiple clearances. J. Sound Vib. 144(3), 469–506 (1991)CrossRef
9.
Özgüven, H.N.: A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics. J. Sound Vib. 145(2), 239–260 (1991)CrossRef
10.
Maliha, R., Doruer, C.U., Ozguven, H.N.: Nonlinear dynamic modeling of gear-shaft-disk-bearing systems using finite elements and describing functions. J. Mech. Des. 126, 534–541 (2004)CrossRef
11.
Gürkan, N.E., Ozguven, H.N.: Interactions Between backlash and bearing clearance nonlinearity in geared flexible rotors. In: Proceedings of IDETC/PTG 2007 ASME 2007 International Design Engineering Technical Conferences and ASME International Power Transmission and Gearing Conference, Las Vegas, pp. 1–10 (2007)
12.
Kahraman, A.: Effect of axial vibrations on the dynamics of a helical gear pair. J. Vib. Acoust. 115, 33–39 (1993)CrossRef
13.
Kahraman, A.: Dynamic analysis of a multi-mesh helical gear train. J. Mech. Des. 116, 706–712 (1994)CrossRef
14.
Kubur, M., Kahraman, A., Zini, D.M., Kienzle, K.: Dynamic analysis of a multi-shaft helical gear transmission by finite elements: model and experiment. J. Vib. Acoust. 126(3), 398–406 (2004)CrossRef
15.
Al-shyyab, A., Kahraman, A.: Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: period-one motions. J. Sound Vib. 284, 151–172 (2005)CrossRef
16.
Al-shyyab, A., Kahraman, A.: Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions. J. Sound Vib. 279, 417–451 (2005)CrossRef
17.
Al-shyyab, A., Kahraman, A.: A nonlinear torsional dynamic model of multi-mesh gear trains having flexible shafts. Jordan J. Mech. Ind. Eng. 1(1), 31–41 (2007)
18.
Liu, G., Parker, R.G.: Nonlinear dynamics of idler gear systems. Nonlinear Dyn. 53(4), 345–367 (2008)CrossRefMATH
19.
Liu, G., Parker, R.G.: Nonlinear, parametrically excited dynamics of two-stage spur gear trains with mesh stiffness fluctuation. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 226(8), 1939–1957 (2012)CrossRef
20.
Al-shyyab, A., Kahraman, A.: A non-linear dynamic model for planetary gear sets. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 221(4), 567–576 (2007)
21.
Sondkar, P., Kahraman, A.: A dynamic model of a double-helical planetary gear set. Mech. Mach. Theory 70, 157–174 (2013)CrossRef
22.
Cigeroglu, E., Samandari, H.: Nonlinear free vibration of double walled carbon nanotubes by using describing function method with multiple trial functions. Phys. E Low-dimensional Syst. Nanostructures 46, 160–173 (2012)CrossRef
23.
Yümer, M.E., Ciğeroglu, E., Özgüven, H.N.: Non-linear forced response analysis of mistuned bladed disk assemblies. In: Proceedings of ASME Turbo Expo 2010: Power for Land, Sea and Air, Glascow (2010)
24.
Von Groll, G., Ewins, D.J.: The harmonic balance method with arc-length continuation in rotor/stator contact problems. J. Sound Vib. 241(2), 223–233 (2001)CrossRef
25.
Cardona, A., Lerusse, A., and Geradin, M.: Fast Fourier nonlinear vibration analysis. Comput. Mech. 22, 128--142 (1998)
Metadata
Title
Nonlinear Time-Varying Dynamic Analysis of a Multi-Mesh Spur Gear Train
Authors
Siar Deniz Yavuz
Zihni Burcay Saribay
Ender Cigeroglu
Copyright Year
2016
Book
Dynamics of Coupled Structures, Volume 4

Print ISBN: 978-3-319-29762-0

Electronic ISBN: 978-3-319-29763-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-29763-7_30

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