Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function.
The homogenization of the energy functional of a sandwich plate, its minimization and its discretization by finite element methods and modeling the viscoelastic core behavior by an hysteretic structural damping lead to the homogenized dynamic equation of a sandwich plate. The vibratory analysis permits the determination of the elastic eigenmodes and the characterization of the modal damping which will serve to the establishment of dynamical responses if we used the modal dynamic recombination method. The numerical results obtained show that the eigenmodes are not orthogonal to the damping matrix but are only weakly coupled. Besides, the modal damping matrix coefficients vary according to the ratio of the core thickness and the total thickness of sandwich plate and follow a second-order polynomial function of this ratio.
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