Mathematical Modeling of Torsional and Longitudinal Oscillations in a Mine Winding Plant as a Multimass System

Abstract

The purpose of the study is to determine the dynamic loads in the mechanical system of a mine winding plant. A 6-mass equivalent dynamic design model is constructed by reducing the number of discrete masses in the original 12-mass system by a special method. Spectra of natural oscillation frequencies of the initial and design systems are obtained. Differential equations that describe oscillations in the shaft line and ropes are drafted. Oscillation curves of the moments in the elastic coupling of the design system are obtained using numerical integration of the equations. The dynamic response factors are calculated. It was confirmed that the conversion of a 12-mass system into a 6-mass system almost does not affect the accuracy of determining the dynamic loads in the transmission line of the hoist in a given frequency range. The proposed methodology for constructing a mathematical model can be used not only for mine hoists, but also for other machines with multiple moving masses.