Abstract
A new analytical model of a spur gear system with sliding friction is presented. Unlike previous models, the excitation consists of two parts: the rotational driving speed of the pinion and the drag torque acting on the gear. The proposed model was validated with the finite element model. Using numerical method, the steady state resolutions was obtained to mainly demonstrate the nonlinear characteristics under both constant and variable excitations. The results obtained illustrate that sliding friction could introduce additional vibration. Moreover, the sliding friction even could decrease the dynamic transmission errors under proper operation condition. Further, the bifurcation diagram was plotted to show the influence of the rotational driving speed of the pinion on the dynamical characteristic of the gear system. Finally, the fluctuated excitation was used to exhibit their different effects on the gear system, which should form the basis of further analytical and experimental work in the gear dynamic area.
Similar content being viewed by others
References
R. Singh, H. Xie and R. Comparin, Analysis of automotive neutral grear rattle, J. Sound. Vib., 131 (2) (1989) 177–196.
A. Kahraman and R. Singh, Non-linear dynamics of a spur gear pair, J. Sound. Vib., 142 (1) (1990) 49–75.
G. Bonori and F. Pellicano, Non-smooth dynamics of spur gears with manufacturing errors, J. Sound. Vib., 306 (1) (2007) 271–283.
A. Al-Shyyab and A. Kahraman, Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: period-one motions, J. Sound. Vib., 284 (1) (2005) 151–172.
A. Farshidianfar and A. Saghafi, Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems, Nonlinear Dynam., 75 (4) (2014) 783–806.
C. Gill-Jeong, Analysis of the nonlinear behavior of gear pairs considering hydrodynamic lubrication and sliding friction, J. Mech. Sci. Tech., 23 (8) (2009) 2125–2137.
T. Lin, H. Ou and R. Li, A finite element method for 3D static and dynamic contact/impact analysis of gear drives, Comput. Method. Appl. M, 196 (9) (2007) 1716–1728.
M. Amabili and A. Rivola, Dynamic analysis of spur gear pairs: steady-state response and stability of the sdof model with timevarying meshing damping, Mech. Syst. Signal Pr., 11 (3) (1997) 375–390.
V. Atanasiu et al., Nonlinear dynamics of steel/plastic gears of servomechanism structures, Mater. Plast., 48 (1) (2011) 98–103.
Y. Shen, S. Yang and X. Liu, Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method, Int. J. Mech. Sci., 48 (11) (2006) 1256–1263.
L. Walha, T. Fakhfakh and M. Haddar, Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash, Mech. Mach. Theory., 44 (5) (2009) 1058–1069.
H. Jiang et al., The influence of mesh misalignment on the dynamic characteristics of helical gears including sliding friction, J. of Mechanical Science and Technology, 29 (11) (2015) 4563–4573.
Z. Chen, Y. Shao and T. Lim, Non-linear dynamic simulation of gear response under the idling condition, Int. J. of Auto. Tech., 13 (4) (2012) 541–552.
I. Howard, S. Jia and J. Wang, The dynamic modelling of a spur gear in mesh including friction and a crack, Mech. Syst. Signal Pr., 15 (5) (2001) 831–853.
G. Liu and R. G. Parker, Impact of tooth friction and its bending effect on gear dynamics, J. Sound. Vib., 320 (4) (2009) 1039–1063.
S. He, R. Gunda and R. Singh, Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness, J. Sound. Vib., 301 (3) (2007) 927–949.
P. Velex and V. Cahouet, Experimental and numerical investigations on the influence of tooth friction in spur and helical gear dynamics, J. Mech. Design., 122 (2000) 515.
S. Baud and P. Velex, Static and dynamic tooth loading in spur and helical geared systems-experiments and model validation, J. Mech. Design., 124 (2) (2002) 334–346.
M. Khabou et al., Study of a spur gear dynamic behavior in transient regime, Mech. Syst. Signal Pr., 25 (2011) 3089–3101.
S. Wu, M. J. Zuo and A. Parey, Simulation of spur gear dynamics and estimation of fault growth, J. Sound. Vib., 317 (3) (2008) 608–624.
S. He, S. Cho and R. Singh, Prediction of dynamic friction forces in spur gears using alternate sliding friction formulations, J. Sound. Vib., 309 (3) (2008) 843–851.
F. Liu et al., Analytical characterization of damping in gear teeth dynamics under hydrodynamic conditions, Mech. Mach. Theory., 94 (2015) 141–147.
M. De la Cruz, S. Theodossiades and H. Rahnejat, An investigation of manual transmission drive rattle, P. I. Mech. Eng, K-J. Mul., 224 (2) (2010) 167–181.
S. Theodossiades, O. Tangasawi and H. Rahnejat, Gear teeth impacts in hydrodynamic conjunctions promoting idle gear rattle, J. Sound. Vib., 303 (3) (2007) 632–658.
R. Parker, S. Vijayakar and T. Imajo, Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons, J. Sound. Vib., 237 (3) (2000) 435–455.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editor Yeon June Kang
Fuhao Liu received his Ph.D. from Tianjin University, China in 2012. He spent two years as a Visiting Scholar at The Ohio State University and University of Illinois at Urbana-Champaign to conduct research in vibration and noise. His research interests include dynamics and nonlinear vibration.
Rights and permissions
About this article
Cite this article
Liu, F., Jiang, H., Liu, S. et al. Dynamic behavior analysis of spur gears with constant & variable excitations considering sliding friction influence. J Mech Sci Technol 30, 5363–5370 (2016). https://doi.org/10.1007/s12206-016-1103-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-016-1103-8