Abstract
An elastohydrodynamic lubrication line contact-vibration model is proposed to study the stiffness and damping of the oil film existed in the EHL contact region. An initial mutual approach between interacting surfaces, which deviates from the steady-state balanced position, is assumed under the free contact-vibration to predict the response of the mutual approach. An inertia term, which represents the acceleration of the gap motion, is added to the classical force balance equation to form the equation of motion of the mutual approach. Response of the mutual approach is solved based upon the solving of the contact-dynamic model. The oil stiffness is calculated according to the natural frequency of the response under damped and non-damped conditions, the latter of which represents dry contact conditions. The oil film damping is calculated in terms of the principle of the energy conservation which utilizes the whole history of response compared with the log decrement method. Effect of the normal load, the rolling speed and the amplitude of the regular sinusoidal surface waviness on the oil film stiffness, the contact stiffness and the oil film damping are studied. The study provides an insight on the oil film dynamic characteristics of lubricated contact-vibration problems which appear in gears, bearings, etc. The results show that the oil film damping factor decreases with the increasing normal load as well as the increasing rolling speed. The oil film stiffness increases with the normal load and decreases with the rolling speed. Also, compared to the contact stiffness, the oil film stiffness makes less contribution to the total stiffness. The surface waviness amplitude has little effect on the oil film stiffness and the oil film damping.
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P. Velex and M. Maatar, A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behaviour, J. of Sound and Vibration, 191 (18) (1996) 629–660.
P. Velex and M. Ajmi, Dynamic tooth loads and quasi-static transmission errors in helical gears — Approximate dynamic factor formulae, Mechanism and Machine Theory, 42 (2007) 1512–1526.
G. Liu and R. G. Parker, Dynamic modeling and analysis of tooth profile modification for multimesh gear vibration, J. of Mechanical Design, 130 (2008).
T. C. Lim and R. Singh, Vibration transmission through rolling element bearings, part I: Bearing stiffness formulation, J. of Sound and Vibration, 139 (1990) 179–199.
Y. H. Wijnant, C. H. Venner, R. Larsson and P. Eriksson, Effects of structural vibrations on the film thickness in an EHL circular contact, J. of Tribology-Transactions of the Asme, 121 (1999) 259–264.
Y. H. Wijnant, J. A. Wensing and G. C. Nijen, The influence of lubrication on the dynamic behavior of ball bearings, J. of Sound and Vibration, 222 (1999) 579–596.
M. Ankouni, A. A. Lubrecht and P. Velex, Numerical simulation of damping in EHL line contacts, International Gear Conference 2014, Lyon (2014) 1020–1028.
H. Moes, Optimum similarity analysis with applications to elastohydrodynamic lubrication, Wear, 159 (1992) 57–66.
K. J. Huang, M. R. Wu and J. T. Tseng, Dynamic analyses of gear pairs incorporating the effect of time-varying lubrication damping, J. of Vibration and Control, 17 (2011) 355–363.
M. Barbieri and F. Pellicano, Energy dissipation in EHL film in gear lubrication (2011).
S. Li and A. Kahraman, A spur gear mesh interface damping model based on elastohydrodynamic contact behaviour, International J. of Powertrains, 1 (2011) 4–21.
F. Nonato and K. L. Cavalca, On the non-linear dynamic behavior of elastohydrodynamic lubricated point contact, J. of Sound and Vibration, 329 (2010) 4656–4671.
F. Nonato and K. L. Cavalca, An approach for including the stiffness and damping of elastohydrodynamic point contacts in deep groove ball bearing equilibrium models, J. of Sound and Vibration, 333 (10) (2014) 6960–6978.
H. Liu, K. Mao, C. Zhu, X. Xu and M. Liu, Parametric studies of spur gear lubrication performance considering dynamic loads, Proc. Inst. Mech. Eng. Part J: J. Engineering Tribology (2012).
S. Li and A. Kahraman, A tribo-dynamic model of a spur gear pair, J. of Sound and Vibration, 332 (2013) 4963–4978.
Y. H. Wijnant, Contact dynamics in the field of elastohydrodynamic lubrication, Ph.D. Thesis, Universiteit Twente, The Netherland (1998).
C. J. A. Roelands, Correlation aspects of viscositytemperature-pressure relationship of lubricating oils, Ph.D. Thesis, Delft University of Technology, Netherlands (1966).
D. Dowson and G. Higginson, Elastohydrodynamic lubrication, Oxford: Pergamon Press (1966).
H. Liu, C. Zhu, Z. Sun and C. Song, Starved lubrication of a spur gear pair, Tribology International (2015).
S. Liu, Q. Wang and G. Liu, A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses, Wear, 243 (2000) 101–111.
C. H. Venner and A. Lubrecht, Multilevel method in lubrication, Elsevier (2000).
D. Yang and Z. Sun, A rotary model of spur gear dynamics, J. of Mechanisms, Transmissions, and Automation in Design, 107 (1985) 529–535.
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Recommended by Associate Editor Cheolung Cheong
Huaiju Liu received Ph.D. from the University of Warwick, UK in 2013. His research fields include gear tribology and gear dynamics.
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Zhang, Y., Liu, H., Zhu, C. et al. Oil film stiffness and damping in an elastohydrodynamic lubrication line contact-vibration. J Mech Sci Technol 30, 3031–3039 (2016). https://doi.org/10.1007/s12206-016-0611-x
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DOI: https://doi.org/10.1007/s12206-016-0611-x