Periodic and Chaotic Dynamic Responses of Face Gear Transmission System

Abstract:

The periodic and chaotic dynamic responses of face gear transmission system considering time-varying mesh stiffness and backlash nonlinearity are studied. Firstly, a nonlinear time-varying dynamic model of face gear pair is developed and the motion equations are presented, the real accurate mesh stiffness is obtained by applying Finite element approach. Then, the dynamic equations are solved using Runge-Kutta numerical integral method and bifurcation diagrams are presented and analyzed. The stability properties of steady state responses are illustrated with Floquet multipliers and Lyapunov exponents. The results show that a process of periodic-chaotic-periodic motion exists with the dimensionless pinion rotational frequency as control parameters. The analysis can be a reference to avoid the chaotic motion and unstable periodic motion through choosing suitable rotational frequency.

• Periodical: Advanced Materials Research (Volumes 834-836)
• Pages: 1273-1280
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.834-836.1273
• Online since: October 2013
• Authors: Ze Hua Hu, Jin Yuan Tang, Si Yu Chen
• Keywords: Chaotic Motion, Face Gear, Periodic Motion, Stability Property

References

[1] F.L. Litvin, J. Wang, R.B. Bossler, Y.D. Chen, and G. Heath, Face-Gear Drives: Design, Analysis, and Testing for Helicopter Transmission Applications, United States, 1992, pp. 16p.

[2] D.A. Binney, H. Vinayak, Y. Gmirya, L.M. Zunski, D.R. Houser, and E.C. Ames, Face Gear Transmission Development Program at Sikorsky Aircraft. ASME Conference Proceedings 2003 (2003): 307-313.

DOI: 10.1115/detc2003/ptg-48039

[3] F.L. Litvin, A. Egelja, J. Tan, D.Y.D. Chen, and G. Heath, Handbook on Face Gear Drives with a Spur Involute Pinion, United States, 2000, pp. 107p.

[4] A. Kahraman, and R. Singh, Non-linear dynamics of a spur gear pair. Journal of Sound and Vibration 142 (1990): 49-75.

DOI: 10.1016/0022-460x(90)90582-k

[5] G. Blankenship, and A. Kahraman, Steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity. Journal of Sound and Vibration 185 (1995): 743-765.

DOI: 10.1006/jsvi.1995.0416

[6] K. Sato, and S. Yamamoto, Bifurcation sets and chaotic states of a gear system subjected to harmonic excitation. Computational Mechanics 7 (1991): 173-182.

DOI: 10.1007/bf00369977

[7] A. Raghothama, and S. Narayanan, Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method. Journal of Sound and Vibration 226 (1999): 469-492.

DOI: 10.1006/jsvi.1999.2264

[8] S. Theodossiades, and S. Natsiavas, Non-linear dynamics of gear-pair systems with periodic stiffness and backlash. Journal of Sound and Vibration 229 (2000): 287-310.

DOI: 10.1006/jsvi.1999.2490

[9] S. Theodossiades, and S. Natsiavas, Periodic and chaotic dynamics of motor-driven gear-pair systems with backlash. Chaos, Solitons & Fractals 12 (2001): 2427-2440.

DOI: 10.1016/s0960-0779(00)00210-1

[10] C. -W. Chang-Jian, and C. -K. Chen, Bifurcation analysis of flexible rotor supported by couple-stress fluid film bearings with non-linear suspension systems. Tribology International 41 (2008): 367-386.

DOI: 10.1016/j.triboint.2007.09.007

[11] C. -W. Chang-Jian, and C. o. -K. Chen, Chaos of rub–impact rotor supported by bearings with nonlinear suspension. Tribology International 42 (2009): 426-439.

DOI: 10.1016/j.triboint.2008.08.002

[12] C. -W. Chang-Jian, Strong nonlinearity analysis for gear-bearing system under nonlinear suspension—bifurcation and chaos. Nonlinear Analysis: Real World Applications 11 (2010): 1760-1774.

DOI: 10.1016/j.nonrwa.2009.03.027

[13] C. -W. Chang-Jian, and S. -M. Chang, Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension. Nonlinear Analysis: Real World Applications 12 (2011): 979-989.

DOI: 10.1016/j.nonrwa.2010.08.021

[14] G. Tordion, and R. Gauvin, Dynamic stability of a two-stage gear train under the influence of variable meshing stiffnesses. Journal of Engineering for Industry 99 (1977): 785.

DOI: 10.1115/1.3439314

[15] C. -S. Chen, S. Natsiavas, and H. Nelson, Stability analysis and complex dynamics of a gear-pair system supported by a squeeze film damper. Journal of Vibration and Acoustics 119 (1997): 85-88.

DOI: 10.1115/1.2889691

[16] T. Shiau, J. Chang, and S. Choi, Stability analysis of a gear pair system supported by squeeze-film dampers. International Journal of Rotating Machinery 7 (2001): 143-151.

DOI: 10.1155/s1023621x01000124

[17] H. Wolf, Z. Terze, and A. Sušić, Dynamical stability of the response of oscillators with discontinuous or steep first derivative of restoring characteristic. European Journal of Mechanics - A/Solids 23 (2004): 1041-1050.

DOI: 10.1016/j.euromechsol.2004.08.001

[18] M. Wang, and F. Su, Numerical Research on Stochastic Duffing System. Procedia Engineering 29 (2012): 1979-(1983).

DOI: 10.1016/j.proeng.2012.01.247