Rigid-Flexible Coupling Dynamic Modeling Of A Tower Crane With Long Flexible Boom

Currently most studies about dynamic modeling of tower cranes are based on treating them as rigid-bodies. Usually a five-degree dynamic model is used to apply control strategies to the tower crane system. Whereas treating the tower crane as rigid-bodies system means that the impact of the deformations of its flexible structures such as the boom and the body will be neglected. With the increasing working velocity of the tower crane and the higher requirement for the accuracy of the moving payload’s location, an enhanced mathematical model is much more needed to investigate the boom’s dynamic deformation and how the payload swings as well as to lay a foundation for the development of a tower crane simulator.So this paper focuses on researching a rigid-flexible coupling dynamic model of a tower crane with long flexible boom, in which the flexibility of the boom and system’s motions are considered. The main work are as follow:Firstly, the boom is modeled as an Euler-Bernoulli boom, and the tie bars are treated as linear springs, and the boom’s gravity and structural damping are also included in this model. Then the Lagaragian method is used to formulate the rigid-flexible coupling model which could fully describe the typical motions of a tower crane, including its luffing, rotating and lifting motions. By using the assumed mode method, a simplified motion equation is also presented in the form of matrix.Secondly, the governing equation of the traditional spherical pendulum of the payload and that of the spherical pendulum which takes the vertical deformation of the boom into account are compared in three cases numerically solved by Maple software.Thirdly, in order to verify this mathematical model, a simplified dynamic simulation model of a tower crane was built in ADAMS software. After that the dynamic response of both the boom and the payload got from simulation and that got from numerical computing are analyzed respectively. The reason of the differences existing was explained.Finally, to research the effects of equivalent parameters and further demonstrate this model, another numerical case is designed and this time both the vertical and horizontal deformations are considered.Results show that this model could explain the effects of the boom’s deformations to the system so that would be very useful for investigating the dynamic response of tower cranes with long flexible boom.