A rigid-flexible coupled dynamic modeling method for multi-cable vertical hoisting systems is proposed, as the current models cannot accurately handle the complex spatial geometric constraints between flexible cables and rigid lifting unit (i.e., elevator car and mine cage). By modeling boundary constraint equations for the cables and lifting unit, based on Lagrange’s equations and introducing the multiplier method to handle system constraints, the constraint conditions are coupled to the dynamics equations in algebraic form. Taking a four-cable mine hoisting system as an example, a coupled dynamic model of cables, cage, and guide rollers is established, and the generalized α method is used for numerical solution. The simulation results are compared with the experimental data of the mine hoist under lowering conditions, and the results are highly consistent in both the time and frequency-domain, effectively verifying the accuracy of the model. The study shows that when only transverse excitation is applied to the guide rollers, the cage will generate indirect longitudinal-transverse coupled vibrations of the same frequency.
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