Electromechanical coupling dynamics modeling of a bolted piezoelectric vibrating feeder

• A semi-analytical dynamic model is developed for a piezoelectric vibrating feeder. • Frictional contact is modeled using an iterative correction coefficient. • The model greatly improves efficiency while maintaining comparable accuracy. • Experiments confirm accuracy in predicting modal behavior of key structural parts. The piezoelectric vibrating feeders (PVFs) play a crucial role as automated transport systems. Developing an accurate and efficient dynamic model for the PVFs is essential for optimizing its vibration characteristics and transportation performance. Conventional analytical models provide natural frequency information but fail to capture flexible dynamic response of individual components. Numerical models based the finite element method (FEM) or discrete element method are computationally intensive and inefficient for PVFs. To address these limitations, an electromechanical coupling dynamics model for PVF was developed using the semi-analytical transfer matrix method (TMM). First, the structure of the PVF is simplified and discretized into fundamental elements. Subsequently, transfer matrix equations of the elements are given. By integrating these equations through transfer conditions, a comprehensive electromechanical coupling dynamics model is developed. The effect of bolts on the structure is considered, and frictional contact instead of rigid connection is added. An iterative frictional contact correction coefficient is proposed and analyzed, and then introduced into the model to develop a corrected electromechanical coupling dynamic model. Finally, the validity of the developed model is confirmed through experiments and FEM simulations. Compared to FEM models, the developed model achieves over 40 times the computational efficiency while maintaining comparable accuracy. The results demonstrate that the developed model efficiently and accurately predicts the modal shapes of both the top plate and spring plate of the PVF. These findings verify the accuracy and effectiveness of the model, highlighting its potential for improving the design and performance analysis of the PVFs.