Theoretical analysis and verification of particles moving along the arc-shaped surface in vibration machinery

Vibration machinery with an arc-shaped surface as the main working surface widely exists. The experimental phenomenon shows that the bulk material particles exhibit regular sliding motion and throwing motion along the arc-shaped surface under the alternating load of the exciting system. It is essential to systematically investigate the motion theory of particles considering the interactions between the vibration body and the particles. In this paper, firstly, the interaction mechanism between the vibration body and the particles under different motion states is analyzed, and the particle's kinematics equation is established based on the nonlinear force analysis of sliding motion and throwing motion. After that, the differential equation of the vibration body movement considering the interaction forces is given. Then, the discrete element method (DEM) is used to verify the feasibility of using a small number of particles to study the whole motion law of particle flow. Meanwhile, the correctness of the mechanical model established in this paper and the numerical solution of the vibration system solved by the Newmark-beta method are also verified by DEM. Finally, the particle's motion state intervals are given, and the Sommerfeld effect's influence on the system's motion stability is further discussed. In addition, the effects of the nonlinear force, particle mass, friction coefficient, exciting force, and installation angle on the system's frequency-domain response, conveying efficiency, and throwing index are discussed emphatically. The theoretical basis and experimental method in designing this kind of mechanical equipment are provided for reference.

Automated summary

This paper investigates the motion theory of particles in vibration machinery with an arc-shaped surface. The interaction mechanism between the vibration body and the particles is analyzed, and the kinematics equation of particles and the differential equation of vibration body movement are established. The feasibility of studying the whole motion law of particle flow using a small number of particles is verified using the discrete element method. The correctness of the mechanical model and numerical solution of the vibration system are also confirmed. The study provides a theoretical basis and experimental method for designing this type of mechanical equipment.