Effect of Hoisting Cable Elasticity on the Period of Oscillation of Quay-Side Container Cranes

Abstract

Oscillation frequency of crane payloads is the main and most important factor in crane anti-sway control systems design. In the summer of 2005, a Smart Sway Control system (SSC) was developed and installed on a 65-ton quay-side container crane at Jeddah Port. During the calibration phase, it was observed that heavy payloads combined with the dynamic stretch of the hoist cables had a signiflcant impact on the conflguration of the hoisting mechanism and the pattern of oscillation. This introduced considerable change in the oscillation frequency of the payload, which resulted in a signiflcant impact on the performance of the anti-sway control system. Empirical formulas were used to compensate for the change in the frequency approximation used in the controller algorithm. In this work, an analytic approximation of the oscillation frequency of the hoisting mechanism of a quay-side container crane is developed, which takes into consideration the elasticity of the hoisting cables. A parametric study is performed to investigate the extent of the efiect of the hoisting cables stretch on the system behavior for a typical range of payload masses and cable lengths. I. Introduction Since the introduction of Super-Post-Panamax container ships, demand on larger and faster quay-side container cranes became an essential requirement. A Super-Post-Panamax ship has a capacity of up to 12,000 containers and up to 22 containers across the width of the ship. The large span of quay-side containers cranes that handle such ships necessitates higher trolley speeds and accelerations, flgure 1. Operating such cranes demands special skills and long experience. Accidents during the operations of these cranes are usually severe and costly. These accidents may result is a severe damage to the ship, its payload, and sometimes to the crane itself. Consequently, more stringent motion suppression requirements are the norm rather than the exception. The last four decades have seen mounting research interest in the modeling and control of cranes. 1 Container cranes are traditionally modeled as a two-dimensional simple pendulum with a lumped mass at the end of a rigid inextensible massless link. However, the hoisting mechanism of a quay-side container crane is signiflcantly difierent. The actual hoisting mechanism of a quay-side container crane consists typically of a multi-cable hoisting arrangement. The cables are hoisted using a number of hoisting cables dropping from four pulleys on a trolley to four pulleys on a spreader bar used to lift containers. An anti-sway controller design based on the actual model of a quay-side container crane is most likely to result in a performance superior to those based a simple pendulum model. Input-shaping is one of the most widely used open-loop control strategies for quay-side container cranes. Controllers using various forms of input-shaping are incorporated into cranes currently used in ports. 2 Apart from command flltering, these techniques are used to move the trolley of the crane a preset distance along a preset path. These controllers have also been used for inching maneuvers in tight work spaces and near target points. The acceleration proflle of the trolley is designed to induce minimum payload oscillation during travel and to deliver the payload at the target point free of residual oscillations. However, input-shaping techniques are limited by the fact that they are sensitive to variations in the parameter values about the nominal values, and to changes in the initial conditions and external disturbances, and that they require \highly accurate values of the system parameters to achieve satisfactory system performance. 3{5 Singhose et al. 6 developed four input-shaping controllers. Simulations of their best controller