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Triggers of coupled singularities and homoclinic orbits in the dynamics of the planetary gear trains
Rade Knežević Stanoje Cvetković
Analytic and numerical analysis of the non-linear system dynamics and phase space based on the planetary gear train with three teeth satellite has been treated in this paper. Phase portraits for different kinetic parameters with deviation properties of eccentric masses distribution have been composed. Furthermore, the disappearance of coupled singularities triggers and eight-shaped homoclinic orbits in the phase plane were analysed along with the characteristics in the planetary gear train dynamics. Based on the analytical solutions and numerical results, the nonlinear phenomena have been graphically presented by means of the surface of total system energy, portraits of constant energy curves and phase trajectories for different system parameters.
Key words: planetary gear train, nonlinear dynamics, surface of total system energy, constant energy curve, homoclinic point, phase trajectory, phase portrait. |