Nonlinear dynamics of idler gear systems

Abstract

This work examines the nonlinear, parametrically excited dynamics of idler gearsets. The two gear tooth meshes provide two interacting parametric excitation sources and two possible tooth separations. The periodic steady state solutions are obtained using analytical and numerical approaches. Asymptotic perturbation analysis gives the solution branches and their stabilities near primary, secondary, and subharmonic resonances. The ratio of mesh stiffness variation to its mean value is the small parameter. The time of tooth separation is assumed to be a small fraction of the mesh period. With these stipulations, the nonsmooth separation function that determines contact loss and the variable mesh stiffness are reformulated into a form suitable for perturbation. Perturbation yields closed-form expressions that expose the impact of key parameters on the nonlinear response. The asymptotic analysis for this strongly nonlinear system compares well to separate harmonic balance/arclength continuation and numerical integration solutions. The expressions in terms of fundamental design quantities have natural practical application.

Frictional effects on the dynamic responses of gear systems and the diagnostics of tooth breakages

“…In general, the theoretical friction coefficient is derived from elasto-hydrodynamic lubrication and tribology theory, however several experimental works show that a constant friction coefficient is acceptable for dynamic analysis as indicated in (Liu, 2007;Rebbechi, Oswald, & Townsend, 1996;Velex & Cahouet, 2000). Benedict and Kelley's empirical equation shows that the coefficient of friction can vary between 0.03 and 0.1 (He, Gunda, & Singh, 2007).…”

“…Benedict and Kelley's empirical equation shows that the coefficient of friction can vary between 0.03 and 0.1 (He, Gunda, & Singh, 2007). Furthermore the value of 0.1 or even values as high as 0.2 are commonly used in several gear dynamic models as explained by (Liu, 2007). To get meaningful values of μ o , the variation from 0.0 to 0.2 have been used in this study to simulate the Coulomb friction effect.…”

Analysis of frictional effects on the dynamic response of gear systems and the implications for diagnostics

“…They are not general and often represent certain lubricants, operating temperatures, speed and load ranges, and surface roughness conditions of roller specimens that might differ from those of the actual gear pair of interest [33]. In general, the theoretical friction coefficient is derived from elasto-hydrodynamic lubrication and tribology theory, however several experimental works show that, a constant friction coefficient is acceptable for dynamic analysis as indicated in [34][35][36]. Benedict and Kelley's empirical equation shows that, the coefficient of friction varies between 0.03 to 0.1 [37], furthermore the value of 0.1 or even values as high as 0.2 are commonly used in several gear dynamic models as explained in [36].…”

“…In general, the theoretical friction coefficient is derived from elasto-hydrodynamic lubrication and tribology theory, however several experimental works show that, a constant friction coefficient is acceptable for dynamic analysis as indicated in [34][35][36]. Benedict and Kelley's empirical equation shows that, the coefficient of friction varies between 0.03 to 0.1 [37], furthermore the value of 0.1 or even values as high as 0.2 are commonly used in several gear dynamic models as explained in [36]. To get meaningful values of μ o , the variation from 0.0 to 0.2 have been used in this study to simulate the Coulomb friction effect.…”

A Study on the Dynamic Behaviour of Lightweight Gears

“…Bonori et al [6] used this formulation to optimize design parameters while Liu and Parker [7] proved its usefulness performing dynamic simulation of more complex systems. Recently, a dynamic simulation model based on a lumped-parameter formulation was developed by Zhang et al to analyse the vibration modes of two-stage helical planetary gears used in cranes [8], while Dong et al coupled lumped mass modelling and theoretical models for loaded and unloaded tooth contact analysis with the aim of investigating the vibration characteristics of power-split transmissions [9].…”