Research on bifurcation and chaos characteristics of planet gear transmission system with mixed elastohydrodynamic lubrication (EHL) friction

In order to study the influence of friction on the nonlinear dynamic characteristics of a planetary gear system, the dynamic model of a planet gear transmission system considering mixed elastohydrodynamic lubrication (EHL) friction, time-varying meshing stiffness, backlash and comprehensive meshing error is established. The Runge–Kutta method is used to solve the dynamic differential equations, and the bifurcation and chaos characteristics of the system are analysed through the bifurcation diagram, largest lyapunov exponent (LLE), Poincaré map, phase diagram, time history curve diagram and fast fourier transform (FFT)spectrum. The results of numerical simulation show that the planetary gear system with mixed EHL friction exhibits rich bifurcation characteristics, and the system experiences short-periodic motion, long-periodic motion, quasi-periodic motion and chaotic motion. The effect of tooth surface friction on the bifurcation characteristics of the planetary gear system is more obvious at high frequency than that at low frequency. Tooth surface friction causes the system to enter chaotic motion in advance.

A discussion of Arana, A., Larrañaga, J., & Ulacia, I. (2019). Partial EHL friction coefficient model to predict power losses in cylindrical gears. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, Vol. 233(2) 303–316

There is presently a heated debate within the field of elastohydrodynamic lubrication (EHL). Some have attributed this to a controversy regarding the shear dependence of viscosity. However, the real nature of the debate is, as it has been for more than 40 years, whether or not to correctly describe the piezoviscous effect. If real pressure dependence of viscosity were to be employed in all EHL analyses, then the true nature of shear dependence would become apparent and the debate would end.

Partial EHL friction coefficient model to predict power losses in cylindrical gears

The accurate prediction of friction coefficient and power losses in the gear mesh is a key subject to several gear-related fields of study. However, there is still not a unified method for large ranges of operating conditions, different gear geometries and lubricant types. The current paper meets this demand by modelling partial EHL friction with an asperity-fluid load sharing approach where fluid traction is calculated with the Ree-Eyring equation and the reference stress behaviour is predicted from piezoviscosity coefficient. It will be shown that only an accurate description of the lubricant’s viscosity behaviour is required to compute friction in gears. Finally, mesh power losses are predicted considering thermal effects and numerical predictions are compared to experimental results showing good agreement.