Nonlinear, parametrically excited dynamics of two-stage spur gear trains with mesh stiffness fluctuation

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Volumn 226, Issue 8, 2012, Pages 1939-1957

  Liu, Gang ^a   Parker, Robert G ^b,c  

^a GE ENERGY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

^c SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

mesh interaction; mesh phasing; nonlinear dynamics; perturbation; Two stage counter shaft gear

Indexed keywords

CLOSED FORM SOLUTIONS; CONTACT LOSS; CONTACT RATIO; DESIGN PARAMETERS; GEAR TRAIN; HARMONIC BALANCE METHOD; MESH INTERACTION; MESH PHASING; MESH STIFFNESS; METHOD OF MULTIPLE SCALE; NUMERICAL INTEGRATIONS; PARAMETRIC EXCITATIONS; PERTURBATION; PERTURBATION ANALYSIS; SEMI-ANALYTICAL; SEPARATION FUNCTIONS; STEADY STATE SOLUTION; SUBHARMONIC RESONANCES; TIME-VARYING MESH STIFFNESS; WORK STUDY;

DYNAMICS; EXCITED STATES; SPUR GEARS;

STIFFNESS;

EID: 84870309652     PISSN: 09544062     EISSN: 20412983     Source Type: Journal    
DOI: 10.1177/0954406212447509     Document Type: Article

References (33)

1. Blankenship GW, Singh RA. Comparative study of selected gear mesh force interface dynamic models. ASME 6th Power Transmission and Gearing Conference ; 1992 Phoenix ; 1992..
2. Ozguven HN, Houser DR. Mathematical-models used in gear dynamics-a review. J Sound Vib. 1988 ; 121 (3). 383-411 (Pubitemid 18603605)
3. Velex P, Maatar M. A mathematical-model for analyzing the influence of shape deviations and mounting errors on gear dynamic behavior. J Sound Vib. 1996 ; 191 (5). 629-660 (Pubitemid 126368450)
4. Liu G, Parker RG. Dynamic modeling and analysis of tooth profile modification for multi-mesh gear vibration. ASME J Mech Des. 2008 ; 130: 121402-1
5. Liu G, Parker RG. Nonlinear dynamics of idler gear systems. Nonlin Dyn. 2008 ; 53: 345-367
6. Lin J, Parker RG. Mesh stiffness variation instabilities in two-stage gear systems. J Vib Acoust. 2002 ; 124 (1). 68-76 (Pubitemid 35202709)
7. Umezawa K, Ajima T, Houjoh H. Vibration of three axes gear system. Bull JSME. 1986 ; 29: 950-957 (Pubitemid 16546012)
8. Vinayak H, Singh R, Padmanabhan C. Linear dynamic analysis of multi-mesh transmissions containing external rigid gears. J Sound Vib. 1995 ; 185 (1). 1-32
9. Kahraman A. Dynamic analysis of a multi-mesh helical gear train. ASME J Mech Des. 1994 ; 116 (3). 706-712
10. Parker RG, Agashe V, Vijayakar SM. Dynamic response of a planetary gear system using a finite element/contact mechanics model. J Mech Des. 2000 ; 122: 305-311
11. Parker RG, Vijayakar SM, Imajo T. Nonlinear dynamic response of a spur gear pair: modeling and experimental comparisons. J Sound Vib. 2000 ; 237(3): 435-455
12. Vijayakar SM, Houser DR. Contact analysis of gears using a combined finite element and surface integral method. Gear Technology. 1993 ; July/August: 26-33 (Pubitemid 23695504)
13. Ambarisha VK, Parker RG. Nonlinear dynamics of planetary gears using analytical and finite element models. J Sound Vib. 2007 ; 302 (3). 577-595
14. Kubur M, Kahraman A. Dynamic analysis of a multi-shaft helical gear transmission by finite elements: model and experiment. J Vib Acoust. 2004 ; 126: 398-416
15. Raclot JP, Velex P. Analysis of dynamic couplings in two-stage geared systems. Proceedings of the 1999 ASME Design Engineers Technical Conferences ; 1999 Las Vegas, Nevada ; 1999. 1.
16. Iwatsubo T, Arii S, Kawai R. The coupled lateral torsional vibration of a geared rotor system. Institution of Mechanical Engineers Conference Publications ; 1984 ; 1984. 59.
17. Lida H, Tamura A, Oonishi M. Coupled dynamic characteristics of a counter shaft in a gear train system. Bull Jpn Soc Mech Eng. 1985 ; 28: 2694-2698
18. 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. 2005 ; 279: 417-451
19. Walha L, Fakhfakh F, Haddar M. Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash. Mech Mach Theory. 2009 ; 44: 1058-1069
20. Wang Q, Zhang Y. Coupled dynamic response of two-stage helical gear driving system. Electron Mech Eng Inform Technol. 2011 ; 7: 3333-3336
21. Tordion GV, Gauvin R. Dynamic stability of a two-stage gear train under the influence of variable meshing stiffnesses. ASME Journal of Engineering Industry. 1977 ; 99: 785-791
22. Bahk C, Parker RG. Analytical solution for the nonlinear dynamics of planetary gears. J Comput Nonlin Dyn. 2011 ; 6: 021007-1
23. Padmanabhan C, Singh R. Dynamics of a piecewise non-linear system subject to dual harmonic excitation using parametric continuation. J Sound Vib. 1995 ; 184: 767-799
24. Vijayakar SM. Calyx Users Manual, http://ansol.us/Manuals/CalyxManual.pdf (accessed on September 2004).
25. Vijayakar SM. A combined surface integral and finite element solution for a three-dimensional contact problem. Int J Numer Meth Eng. 1991 ; 31: 524-546
26. Kahraman A, Blankenship GW. Effect of involute contact ratio of spur gear dynamics. J Mech Des. 1999 ; 121: 112-128
27. Parker RG, Lin J. Mesh phasing relationships in planetary and epicyclic gears. ASME J Mech Des. 2004 ; 126: 365-370
28. Blankenship GW, Kahraman A. Gear dynamics experiments, part-I: characterization of forced response. ASME Power Transmission and Gearing Conference ; 1996 San Diego ; 1996..
29. Gregory RW, Harris SL, Munro RG. Dynamic behaviour of spur gears. Proc Inst Mech Eng. 1963 ; 178: 207-226
30. Raclot JP, Velex P. Simulation of the dynamic behaviour of single and multi-stage geared systems with shape deviations and mounting errors by using a spectral method. J Sound Vib. 1999 ; 220: 861-903 (Pubitemid 129605823)
31. Kahraman A, Singh R. Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. J Sound Vib. 1991 ; 146: 135-156 (Pubitemid 21653992)
32. Kahraman A, Blankenship GW. Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters. J Appl Mech. 1997 ; 64: 217-226 (Pubitemid 127754604)
33. Nayfeh AH, Mook DT Nonlinear oscillations. New York: John Wiley ; 1979 :