Dynamic behavior and energy distribution in a crank-excited three-mass vibratory separator

Abstract

This study presents the development and dynamic analysis of a mechanical model representing a multi-component vibratory system consisting of a feeder, a vibratory transporter, and a conveyor-separator. The main goal is to simulate the oscillatory response of a three-mass separator excited by a crank-slider mechanism and analyse its efficiency, focusing on the working body responsible for material separation. The vibratory system is modeled using a set of second-order linear differential equations derived via Lagrange’s second kind formulation. Masses are connected by spring-damper elements, capturing the elastic and dissipative interactions. The excitation is modeled as a kinematically imposed harmonic displacement of the third mass, simulating the crank mechanism’s motion. Frequency-domain and time-domain simulations were conducted in MATLAB to determine displacements, velocities, accelerations, and damping-induced energy losses under harmonic excitation. The model enables the identification of key dynamic characteristics, including resonance frequencies, peak amplitudes, and phase shifts, and the evaluation of amplitude control under industrial constraints. Simulation results show that the system achieves a stable working regime at 15.2 Hz, where the working body reaches the target amplitude of ~4.8 mm, suitable for effective material separation. The energy analysis reveals that more than 90 % of the input energy is dissipated through damping. This confirms the dissipative nature of the design, which is advantageous for controlling excess oscillations and achieving stable motion. The model aligns well with industrial reference data and provides a foundation for future optimization of full-process vibratory systems, from feeding to separation. The proposed model demonstrates good agreement with experimental values and industrial references. It provides a solid foundation for further optimization and design of industrial vibratory separators and feeders. Future work may incorporate nonlinear damping effects and control strategies to further enhance system performance under variable loading and operating conditions.