Motion analysis of a linear vibratory feeder: Dynamic modeling and experimental verification

The mathematical model for evaluating the dynamic behavior of linear vibratory feeders is presented and discussed. The model is based on the Eksergian's equation of motion, with the aim at taking into account the effects of the main design parameters without unnecessarily increasing the complexity of the model. Deep emphasis is given to the procedure for the estimation of the external excitations applied to the driveline by proposing two procedures. The first one gives birth to a transcendent equation system, while the second procedure, based on more restrictive hypotheses regarding the geometry of the feeder, leads to a linear system. A dedicated experimental campaign for characterizing the dynamic behavior of a real machine is conducted under different operational conditions. Measured data are compared with simulated results obtained by applying both models; the experimental validation highlights the satisfactory quality of the model estimation, both in terms of torsional oscillations of the driveline and the global frame vibrations.