# DEVELOPING A MATHEMATICAL MODEL FOR DESCRIBING THE MOTION OF A VIBRATORY TYPE SEPARATOR WITH SEQUENTIAL SCREENS

The developed mathematical model of a vibratory separator with sequential screen placement and spring suspension is nonlinear, unified, and parametric. It was derived based on the utilization of the second-order Lagrange equation and asymptotic methods of nonlinear mechanics. The model is intended for investigating the dynamics of the separator during its design and subsequent operation, particularly for selecting its optimal design parameters and determining the conditions of steady-state and transient operating modes. It is presented as a set of analytical dependencies representing the motion laws of arbitrary points of the separator's working body in terms of its geometric, mass-inertial, and kinematic parameters with the ability to cover a wide range of variations. The model can be integrated into systems for automated design and calculation of various vibratory separators, differing in the number of screens, arrangement, and complexity of the drive, suspension, working body, etc.

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