Mathematical model of dynamic processes

Abstract

Purpose. Research of dynamic processes in the system "main rope –lifting vessel" in the transient modes of operation of the car-cage inclined lift. Establishing and substantiating the influence of external disturbances of the system on the dynamic parameters of the interaction between the links of the transport chain. Detection of resonance phenomena during the movement of the vessel along the track, which occur at certain ratios of the operating parameters of heavy-duty and high-speed elevators. Justification of the rational parameters of the movement of the vessel along the track, which will ensure the safe operation of the lift. The methods ofresearch consists in the development of a mathematical description of the dynamics of the "main rope –lifting vessel" system under conditions of external disturbances of the system. Conducting numerical experiments to investigate resonance phenomena that occur during the movement of a lifting vessel along the track of an inclined lift. Development of recommendations for determination of rational parameters that will ensure safe movement of the vessel in conditions of resonant loads. Findings. The mathematical model was built to describe the behavior of the system during the movement when the top rope is drilled periodically. The occurrence of periodic exciting stresses is substantiated and rational parameters are determined. The originality. New dependencies and regularities of kinematic and power characteristics of the oscillation process of the "main rope –lifting vessel" system during lifting and lowering of cargo along the track of an inclined car-cage lift have been established. Practical significance. The research results make it possible to develop recommendations to ensure stable and trouble-free operation of the lifting installation under the actual parameters of external disturbances. The proposed method makes it possible to determine the kinematic and power parameters of dynamic processes in the "main rope –lifting vessel" system during the lifting and lowering of the load, both for the main and for demultiplicative resonances, which can be realized in the branches of the installation with certain ratios between their parameters of the hoist.