Mathematical and computer modeling of gantry crane load-beam system oscillation

Abstract

Introduction. Gantry grappling cranes are the main equipment for cargo transportation in the technological processes of mining and enrichment of rocks. During the operation of the crane, undesirable effects such as the rocking of the payload occur, which in turn affects the dynamic state of the crane beam. Materials and methods. To solve this problem, methods of mathematical and computer modeling of a system with two degrees of freedom were used. To identify the influence of different combinations of the combination of payload mass and cable length on oscillation frequencies, a computational experiment was carried out and the response surface of the oscillation frequency function was constructed. The natural oscillation frequencies of the beam were determined by the finite element method in the NASTRAN program. Results. The results of mathematical modeling were graphs of changes in the angle of deviation of the cable from the vertical and the movement of the trolley, the response surface of the frequency of oscillation of the payload from the length of the cable and the weight of the cargo. Discussion. A comparison of the simulation results of cargo vibrations and crane beam vibrations showed the proximity of the values of the frequencies of the payload vibrations and the gantry crane design, which justifies the need for further analysis of the frequency response of the crane beam to the disturbance of the payload vibration force. Conclusion. The frequency of vibrations of the load significantly affects the static and vibration strength of the crane beam of the gantry crane Resume. The research results can be useful in the development of technical solutions for the engineering implementation of promising gantry crane designs.