Effects of Time-Varying Mesh Stiffness, and its Modifications, on Planetary Gear Dynamics
Abstract
Time-varying mesh stiffness in gears has been found to be the primary cause for vibration in gears. This parametric excitation opens up bands of unstable regions of frequency, rather than just isolated resonances. Despite its many advantages, planetary gears, by virtue of having more components, and therefore more degrees of freedom, add to the complexity in terms of vibrational response. This research is aimed at carrying out a numerical investigation on the effects of mesh stiffness. To establish this objective, a discretized model of a planetary gear assembly is set up using a lumped parameter approach. Subsequently, its natural frequencies are determined, and categorized based on the structured properties of modal response. A numerical algorithm using the Floquet theory is developed to trace the stability boundaries of a reduced order model. The boundaries for a Rayleigh-damped system are also traced, and compared with the instabilities of the undamped system. Qualitative dependence of the external gear mesh stiffness on tooth profile modification is discussed, and stability boundaries are re-computed for different kinds of modifications. Forced response plots for ‘relieved’ profiles show that while the peak amplitudes of super-harmonic resonances decrease dramatically, amplitudes for primary resonances increase, owing to an increased strength of the fundamental frequency component in a modified stiffness profile.
Degree
M.S.M.E.
Advisors
Krousgrill, Purdue University.
Subject Area
Mechanics|Mechanical engineering
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