0
Research Papers

Study of Dynamic Model of Helical/Herringbone Planetary Gear System With Friction Excitation

[+] Author and Article Information
Shaoshuai Hou

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: hou_shaoshuai@163.com

Jing Wei

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: weijing_slmt@163.com

Aiqiang Zhang

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: zaq_sklmt@163.com

Teik C. Lim

Office of The Provost,
University of Texas Arlington,
701 South Nedderman Drive Davis Hall,
Suite 321,
Arlington, TX 19118
e-mail: teik.lim@uta.edu

Chunpeng Zhang

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: zhangchunpeng92@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 16, 2018; final manuscript received October 9, 2018; published online October 31, 2018. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 13(12), 121007 (Oct 31, 2018) (14 pages) Paper No: CND-18-1313; doi: 10.1115/1.4041774 History: Received July 16, 2018; Revised October 09, 2018

Tooth friction is unavoidable and changes periodically in gear engagement. Friction excitation is an important excitation source of a gear transmission system. They are different than the friction coefficients of any two points on the same contact line of a helical/herringbone gear. In order to obtain the influence of the friction excitation on the dynamic response of a helical/herringbone planetary gear system, a method that uses piecewise solution and then summing them to analyze the friction force and frictional torque of tooth surfaces is proposed. Then, the friction coefficient is obtained based on the mixed elastohydrodynamic lubrication (EHL) theory. A dynamic model of a herringbone planetary gear system is established considering the friction, mesh stiffness, and meshing error excitation by the node finite element method. The influence of friction excitation on the dynamic response of the herringbone planetary gear is studied under different working conditions. The results show that friction excitation has a great influence on the vibration acceleration of the sun and planetary gear. However, the effect on the radial and tangential vibration acceleration of a planetary gear is the opposite. In addition, the friction excitation has a slight effect on the meshing force.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lin, J. , and Parker, R. G. , 1999, “ Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration,” ASME J. Vib. Acoust., 121(3), pp. 316–321. [CrossRef]
Parker, R. G. , Agashe, V. , and Vijayakar, S. M. , 2000, “ Dynamic Response of a Planetary Gear System Using a Finite Element Contact Mechanics Model,” ASME J. Mech. Des., 304(3), pp. 304–310. [CrossRef]
Bahk, C. , and Parker, R. G. , 2011, “ Analytical Solution for the Nonlinear Dynamics of Planetary Gear,” ASME J. Comput. Nonlinear Dyn., 6(2), p. 021007. [CrossRef]
Guo, Y. , and Parker, R. G. , 2012, “ Dynamic Analysis of Planetary Gears With Bearing Clearance,” ASME J. Comput. Nonlinear Dyn., 7(4), p. 041002. [CrossRef]
Kahraman, A. , 1994, “ Planetary Gear System Dynamics,” ASME J. Mech. Des., 116(3), pp. 713–720. [CrossRef]
Wei, J. , Zhang, A. Q. , Qin, D. T. , Lim, T. C. , Shu, R. Z. , Lin, X. Y. , and Meng, F. M. , 2017, “ A Coupling Dynamics Analysis Method for a Multistage Planetary Gear System,” Mech. Mach. Theory, 110, pp. 27–49. [CrossRef]
Yang, F. C. , Shi, Z. X. , and Meng, J. F. , 2013, “ Nonlinear Dynamics and Load Sharing of Double-Mesh Helical Gear System,” J. Eng. Sci. Technol. Rev., 6(2), pp. 29–34. [CrossRef]
Sondkar, P. , and Kahraman, A. , 2013, “ A Dynamic Model of a Double-Helical Planetary Gear Set,” Mech. Mach. Theory, 70, pp. 157–174. [CrossRef]
Wu, Y. J. , Wang, J. J. , and Han, Q. K. , 2012, “ Contact Finite Element Method for Dynamic Meshing Characteristics Analysis of Continuous Engaged Gear Drives,” J. Mech. Sci. Technol., 26(6), pp. 1671–1685. [CrossRef]
Howard, I. , Jia, S. X. , and Wang, J. D. , 2001, “ The Dynamic Modeling of a Spur Gear in Mesh Including Friction and a Crack,” Mech. Syst. Signal Process., 15(5), pp. 831–853. [CrossRef]
Vedmar, L. , and Andersson, A. , 2003, “ A Method to Determine Dynamic Loads on Spur Gear Teeth and on Bearings,” J. Sound Vib., 267(5), pp. 1065–1084. [CrossRef]
Vaishya, M. , and Singh, R. , 2003, “ Strategies for Modeling Friction in Gear Dynamics,” ASME J. Mech. Des., 125(2), pp. 383–393. [CrossRef]
Liu, G. , and Parker, R. G. , 2009, “ Impact of Tooth Friction and Its Bending Effect on Gear Dynamics,” J. Sound Vib., 320(4–5), pp. 1039–1063. [CrossRef]
He, S. , Gunda, R. , and Singh, R. , 2007, “ Effect of Sliding Friction on the Dynamics of Spur Gear Pair With Realistic Time-Varying Stiffness,” J. Sound Vib., 301(3–5), pp. 927–949. [CrossRef]
He, S. , Cho, S. , and Singh, R. , 2008, “ Prediction of Dynamic Friction Forces in Spur Gears Using Alternate Sliding Friction Formulations,” J. Sound Vib., 309(3–5), pp. 843–851. [CrossRef]
Kar, C. , and Mohanty, A. R. , 2007, “ An Algorithm for Determination of Time-Varying Frictional Force and Torque in a Helical Gear System,” Mech. Mach. Theory, 42(4), pp. 482–496. [CrossRef]
He, S. , and Singh, R. , 2008, “ Dynamic Transmission Error Prediction of Helical Gear Pair Under Sliding Friction Using Floquet Theory,” ASME J. Mech. Des., 130(5), pp. 680–682. [CrossRef]
He, S. , Gunda, R. , and Singh, R. , 2007, “ Inclusion of Sliding Friction in Contact Dynamics Model for Helical Gears,” ASME J. Mech. Des., 129(1), pp. 48–57. [CrossRef]
Velex, P. , and Cahouet, V. , 2000, “ Experimental and Numerical Investigations on the Influence of Tooth Friction in Spur and Helical Gear Dynamics,” ASME J. Mech. Des., 122(4), pp. 515–522. [CrossRef]
Xu, H. , Kahraman, A. , Anderson, N. E. , and Maddock, D. G. , 2007, “ Prediction of Mechanical Efficiency of Parallel-Axis Gear Pairs,” ASME J. Mech. Des., 129(1), pp. 58–68. [CrossRef]
Castro, J. , and Seabra, J. , 2007, “ Coefficient of Friction in Mixed Film Lubrication: Gears Versus Twin-Discs,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 221(3), pp. 399–411. [CrossRef]
Zhu, D. , and Hu, Y. Z. , 2001, “ A Computer Program Package for the Prediction of EHL and Mixed Lubrication Characteristics, Friction, Subsurface Stresses and Flash Temperatures Based on Measured 3D Surface Roughness,” Tribol. Trans., 44(3), pp. 383–390. [CrossRef]
Zhang, A. Q. , Wei, J. , Qin, D. T. , Hou, S. S. , and Lim, T. C. , 2018, “ Coupled Dynamic Characteristics of Wind Turbine Gearbox Driven by Ring Gear Considering Gravity,” ASME J. Dyn. Syst. Meas. Control, 140 (9), p. 091009. [CrossRef]
Ma, H. , Song, R. Z. , Pang, X. , and Wen, B. C. , 2014, “ Time-Varying Mesh Stiffness Calculation of Cracked Spur Gears,” Eng. Failure Anal., 44(6), pp. 179–194. [CrossRef]
Parker, R. G. , and Lin, J. , 2004, “ Mesh Phasing Relationships in Planetary and Epicyclic Gears,” ASME J. Mech. Des., 126(2), pp. 365–374. [CrossRef]
Wei, J. , Bai, P. X. , Qin, D. T. , Lim, T. C. , Yang, P. W. , and Zhang, H. , 2018, “ Study on the Vibration Characteristics of the Fan Shaft of the Geared Turbofan Engine With Sudden Unbalance Caused by Blade Off,” ASME J. Vib. Acoust., 140(4), p. 041010. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Sketch of meshing pair of herringbone gear with tooth friction

Grahic Jump Location
Fig. 2

Position of contact line

Grahic Jump Location
Fig. 3

Relationship between height of cone platform and length of contact line

Grahic Jump Location
Fig. 4

Herringbone planetary gear system with (a) three-dimensional model and (b) transmission principle

Grahic Jump Location
Fig. 5

Meshing model of planetary gear system

Grahic Jump Location
Fig. 6

Coupling dynamic model of herringbone planetary gear system

Grahic Jump Location
Fig. 7

Varying mesh stiffness of (a) external meshing and (b) internal meshing

Grahic Jump Location
Fig. 8

Vibration acceleration of each gear under different loading in (a) radial direction and (b) tangential direction

Grahic Jump Location
Fig. 9

Change rate of vibration acceleration of each gear with or without friction excitation under different loading in (a) radial direction and (b) tangential direction

Grahic Jump Location
Fig. 10

Meshing force and effect of friction excitation on meshing force under different loading: (a) external meshing gear, (b) internal meshing gear, and (c) change rate

Grahic Jump Location
Fig. 11

Vibration displacement of each gear in radial direction at different input speeds: (a) sun gear, (b) planetary gear, and (c) ring gear

Grahic Jump Location
Fig. 12

Effect of friction excitation on vibration displacement of each gear in (a) radial direction and (b) tangential direction

Grahic Jump Location
Fig. 13

Vibration acceleration of each gear in radial direction at different input speeds: (a) sun gear, (b) planetary gear, and (c) ring gear

Grahic Jump Location
Fig. 14

Effect of friction excitation on vibration acceleration of each gear in (a) radial direction and (b) tangential direction

Grahic Jump Location
Fig. 15

Meshing force and effect of friction excitation on meshing force at different input speeds: (a) external meshing gear, (b) internal meshing gear, and (c) change rate

Grahic Jump Location
Fig. 16

Frequency domain response of vibration displacement of ring gear at different input speeds (a) with friction excitation, (b) without friction excitation, and (c) change rate with/without friction excitation

Grahic Jump Location
Fig. 17

Frequency domain response of vibration acceleration of ring gear at different input speeds (a) with friction excitation, (b) without friction excitation, and (c) change rate with/without friction excitation

Grahic Jump Location
Fig. 18

Frequency domain response of mesh force at different input speeds (a) with friction excitation, (b) without friction excitation, and (c) change rate with/without friction excitation

Grahic Jump Location
Fig. 19

Vibration acceleration of every gear under different supporting stiffness in (a) radial direction and (b) tangential direction

Grahic Jump Location
Fig. 20

Change rate of vibration acceleration of each gear with or without friction excitation under different supporting stiffness in (a) radial direction and (b) tangential direction

Grahic Jump Location
Fig. 21

Meshing force and effect of friction excitation on meshing force under different supporting stiffness: (a) external meshing gear, (b) internal meshing gear, and (c) change rate

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In