Research Papers

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

[+] Author and Article Information
Zehua Hu

e-mail: huzehua0414@163.com

Jinyuan Tang

e-mail: jytangcsu@yahoo.com.cn

Siyu Chen

e-mail: csyd5053@yahoo.com.cn

Duncai Lei

e-mail: leiduncai2006@163.com
State Key Laboratory of High Performance
Complex Manufacturing,
Central South University,
Changsha, Hunan 410083, China

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received July 22, 2012; final manuscript received April 15, 2013; published online xx xx, xxxx. Assoc. Editor: Avinash Singh.

J. Mech. Des 135(7), 071005 (May 24, 2013) (7 pages) Paper No: MD-12-1371; doi: 10.1115/1.4024369 History: Received July 22, 2012; Revised April 15, 2013; Accepted April 29, 2013

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

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Litvin, F. L., Wang, J. C., Bossler, J. R. B., Chen, Y. J. D., Heath, G., and Lewicki, D. G., 1994, “Application of Face-Gear Drives in Helicopter Transmissions,” ASME J. Mech. Des., 116(3), pp. 672–676. [CrossRef]
Binney, D. A., Vinayak, H., Gmirya, Y., Zunski, L. M., Houser, D. R., and Ames, E. C., 2003, “Face Gear Transmission Development Program at Sikorsky Aircraft,” Proceedings of DETC03, Sept. 2–6, Paper no. PTG-48039.
Litvin, F. L., Fuentes, A., Zanzi, C., and Pontiggia, M., 2002, “Design, Generation, and Stress Analysis of Two Versions of Geometry of Face-Gear Drives,” Mech. Mach. Theory, 37(10), pp. 1179–1211. [CrossRef]
Litvin, F. L., and Fuentes, A., 2004, Gear Geometry and Applied Theory, Cambridge University Press, Cambridge.
Zanzi, C., and Pedrero, J. I., 2005, “Application of Modified Geometry of Face Gear Drive,” Comput. Methods Appl. Mech. Eng., 194(27-29), pp. 3047–3066. [CrossRef]
Litvin, F. L., Egelja, A., Tan, J., Chen, D. Y. D., and Heath, G., 2000, “Handbook on Face Gear Drives With a Spur Involute Pinion,” Technical Report No. CR-2000-209909. Available at: http://www.dtic.mil/dtic/tr/fulltext/u2/a380815.pdf
Litvin, F. L., Egelja, A., Tan, J., and Heath, G., 1998, “Computerized Design, Generation and Simulation of Meshing of Orthogonal Offset Face-Gear Drive With a Spur Involute Pinion With Localized Bearing Contact,” Mech. Mach. Theory, 33(1-2), pp. 87–102. [CrossRef]
Litvin, F. L., Fuentes, A., and Howkins, M., 2001, “Design, Generation and TCA of New Type of Asymmetric Face-Gear Drives,” Comput. Methods Appl. Mech. Eng., 190(43-44), pp. 5837–5865. [CrossRef]
Litvin, F. L., Fuentes, A., Zanzi, C., Pontiggia, M., and Handschuh, R. F., 2002, “Face-Gear Drive With Spur Involute Pinion: Geometry, Generation by a Worm, Stress Analysis,” Comput. Methods Appl. Mech. Eng., 191(25-26), pp. 2785–2813. [CrossRef]
Litvin, F. L., Gonzalez-Perez, I., Fuentes, A., Hayasaka, K., and Yukishima, K., 2005, “Topology of Modified Surfaces of Involute Helical Gears With Line Contact Developed for Improvement of Bearing Contact, Reduction of Transmission Errors, and Stress Analysis,” Math. Comput. Modell., 42(9-10), pp. 1063–1078. [CrossRef]
Litvin, F. L., Gonzalez-Perez, I., Fuentes, A., Vecchiato, D., Hansen, B. D., and Binney, D., 2005, “Design, Generation and Stress Analysis of Face-Gear Drive With Helical Pinion,” Comput. Methods Appl. Mech. Eng., 194(36-38), pp. 3870–3901. [CrossRef]
Guingand, M., De Vaujany, J.-P., and Jacquin, C.-Y., 2005, “Quasi-Static Analysis of a Face Gear Under Torque,” Comput. Methods Appl. Mech. Eng., 194(39-41), pp. 4301–4318. [CrossRef]
Chen, G.-Y., Chen, G.-D., Li, Y.-X., and Zhao, N., 2009, “Dynamic Response Analysis of Gear Drive With Face-Gears,” Hangkong Dongli Xuebao/J. Aerosp. Power, 24(10), pp. 2391–2396.
Lim, T. C., and Singh, R., 1990, “Vibration Transmission Through Rolling Element Bearings, Part II: System Studies,” J. Sound Vib., 139(2), pp. 201–225. [CrossRef]
Chen, S. Y., Tang, J. Y., Luo, C. W., Wang, Q. B., 2011, “Nonlinear Dynamic Characteristics of Geared Rotor Bearing Systems With Dynamic Backlash and Friction,” Mech. Mach. Theory, 46(4), pp. 466–478. [CrossRef]
Jin, G., Zhu, R., and Bao, H., 2010, “Nonlinear Dynamical Characteristics of Face Gear Transmission System,” J. Central South Univ. (Sci. Technol.), 41(5), pp. 1807–1813 (in Chinese).
Peng, M., Desmidt, H., Saribay, Z. B., and Smith, E. C., 2011, Parametric Instability of Face-Gear Drives With a Spur Pinion, Vol. 4, American Helicopter Society, Virginia Beach, VA, pp. 2478–2488.
Wang, J., and Lim, T. C., 2009, “Effect of Tooth Mesh Stiffness Asymmetric Nonlinearity for Drive and Coast Sides on Hypoid Gear Dynamics,” J. Sound Vib., 319(3-5), pp. 885–903. [CrossRef]
Chowdhury, I., and Dasgupta, S. P., 1998, “Computation of Rayleigh Damping Coefficients for Large Systems,” Department of Civil Engineering, India Institute of Technology, India.
Cheon, G.-J., 2007, “Nonlinear Behavior Analysis of Spur Gear Pairs With a One-Way Clutch,” J. Sound Vib., 304(1–2), pp. 18–30. [CrossRef]
Kahraman, A., and Blankenship, G. W., 1999, “Effect of Involute Contact Ratio on Spur Gear Dynamics,” ASME J. Mech. Des., 121(1), pp. 112–118. [CrossRef]
Kuang, J., and Yang, Y., 1992, “An Estimate of Mesh Stiffness and Load Sharing Ratio of a Spur Gear Pair,” Advancing Power Transmission into the 21st Century, pp. 1–9.
Chang-Jian, C.-W., 2010, “Nonlinear Analysis for Gear Pair System Supported by Long Journal Bearings Under Nonlinear Suspension,” Mech. Mach. Theory, 45(4), pp. 569–583. [CrossRef]
zgüven, H. N., and Houser, D. R., 1988, “Dynamic Analysis of High Speed Gears by Using Loaded Static Transmission Error,” J. Sound Vib., 125(1), pp. 71–83. [CrossRef]


Grahic Jump Location
Fig. 2

Model of 6DOF face gear transmission system

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Fig. 1

Illustration of face gear transmission system: (a) Two-dimensional schematic figure and (b) three-dimensional schematic figure

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Fig. 3

Bifurcation diagram of face gear drive system (a) rotational speed 0–10,000 rpm; (b) rotational speed 2500–3500 rpm; and (c) rotational speed 5500–7500 rpm

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Fig. 4

Response curves of NLTV system

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Fig. 5

Phase plane of chaotic response at the rotational speed (6000 rpm)

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Fig. 6

Dynamic factor of face gear drive system

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Fig. 7

Dynamic mesh force of NLTV system and NLTI system

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Fig. 8

Frequency spectrum of velocity on line of action of NLTV system (a) and NLTI system (b)




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