Simulation of load lifting with equalizers used in shipyards

Abstract

Abstract One of the most commonly used pieces of equipment for lifting a load is the equalizer of a crane in shipbuilding production. The equalizer distributes the tension in wire ropes between the load and equipment equally. While the equalizer is composed simply of several fixed and moving pulleys, the mechanism of an equalizer is not easy to adapt to physics-based simulations because only one wire rope is coiled around all of the pulleys. Thus, instead of the real mechanism of the equalizer, an alternative mechanism, such as stretching or shortening the initial lengths of the wire ropes, logically, has been used in previous simulations. In this study, a mass-less constraint-based wire rope is adopted to realize the real mechanism of the equalizer. The constant length constraint is used to realize one wire rope among the fixed and moving equalizer pulleys. We derive a discrete Euler–Lagrange (DEL) equation to represent the motion of a multibody system including the constraint wire ropes. The DEL equation is shown to be numerically stable for the case of linear holonomic constraints, such as the constant length constraint. We test several series of fixed and moving pulleys and model the equalizer based on the real mechanism. Finally, the equalizer based on the real mechanism is applied to two typical lifting cases in shipbuilding production. One is lifting a load using a Goliath crane with three equalizers and the other is to use a floating crane with one equalizer and two crawler cranes. As a result, the tensions in the wire ropes connected to the load are adjusted equally as the position of the moving pulleys and the orientation of the equalizer change.