Lateral response of cable-guided hoisting system with time-varying length: Theoretical model and dynamics simulation verification

The lateral response of the moving hoisting conveyance in cable-guided hoisting system is investigated in this paper. The equations of motion are derived by Hamilton's principle while the equivalent mass and stiffness of the guide cables are formulated. Galerkin method is employed to transform the governing equation into a set of ordinary differential equations. Subsequently, an ADAMS simulation model based on multi-degree of freedom is established to validate the theoretical model. Meanwhile, a high-efficiency simulation approach is proposed, in which the contact force is replaced with fixed joints and distance sensors. The numerical solution for equations set is obtained using Newmark- method and the convergence of the solution is discussed, then the presented theoretical model is compared with the previous models describing the rigid rail-guided hoisting system. The results indicate that the numerical simulations are in reasonably good agreement with the ADAMS simulations and this presented model includes the previous models. The influence of parameters on the lateral response is analyzed, which reveals the maximum lateral displacement is linearly proportional to the excitation amplitude. Also, the appropriate preload can be determined by the theoretical model, which is beneficial for vibration control.