Summary
Delft University of Technology - 3ME (2009)
Dynamic coefficient of offshore cranes
4Summary
This project has been carried out in order to gain a better insight of the dynamics of offshore crane lift operations and to optimize crane design. The purpose of this assignment was to construct and to solve a mathematical model of a crane on a fixed platform which hoists a load from a supply boat. The model should provide guidelines for several crane configurations. The mathematical model has to describe the dynamic behaviour of cranes, the effect of the dynamic forces on different (components) parts.
The crane has been subdivided into two models: 1. The crane model
2. The main hoist model.
First each system has been represented as a dynamic model and a mathematical analysis of the model has been carried out. Then the equation of motion of the models has been found.
In applying the principles of mechanics, the models have been formulated by incorporating appropriate physical assumptions and mathematical approximations. Each model is represented as a mass-spring-damper combination.
The crane model has been represented by three masses: the main load, the mass center of the boom and the mass center of the gantry. The main hoist mechanism, which is composed of upper and lower sheave block assembly, has been modelled in more detail by taking the inertia and efficiency of each sheave into account. The two models, the crane and the main hoist mechanism, have been developed separately and after that integrated as one model.
Then the equation of motion for each mass-spring-damper system has been found. Because of the physical relation between the mass-spring-damper systems, the equations are all related to each other. Afterwards, the equations of motion are solved by Matlab.
Some of the geometrical and mechanical data of the crane are already known. However, an analytical excel sheet has been developed in order to calculate the unknown input variables for the Simulink model. Basic design data will be converted by the analytical excel sheet into input data for the Simulink model.
The difference between the dynamic factor on the hook and other parts of the crane has been investigated with the model by simulating the dynamic behaviour of the 500 t Bard crane. The influence of many other different variables can also be investigated with the Simulink model as damping ratio and spring constant of the main hoist and boom hoist wire ropes. Also the sheave efficiency and inertia, contact force between supply boat and main load, motor moment, boom angle, winch inertia and the weight of the main load are crucial variables.
According to the results the dynamic factors on the heel point and the slewing point are considerably lower than the dynamic factor on the hook (the main hoist). However, the dynamic factor on the gantry top is as high as the dynamic factor on the hook or even higher. This is because the dynamic peak force in the boom hoist is affected by the main hoist force as well as motion of the boom.
The damping of the main hoist wire ropes, sheave efficiency and sheave inertia have a small impact on the dynamic forces. From this can be concluded that damping of the main hoist wire ropes as well as sheave efficiency and inertia in the upper and lower sheave blocks are almost negligible in determination of the dynamic factor in the main hoist compound tackle.
The smaller the boom angle, the higher the dynamic peak factors. This is because the dynamic peak forces in the boom hoist will decrease by increasing boom angle, while other forces as gravity remain the same. The dynamic factor of the crane is most sensitive for the contact force between the main load and the supply boat deck. This means in order to get the greatest possible degree of realistic outcomes, the contact force has to be determined as accurate as possible.
This thesis can serve as the starting point for future research about calculation of the dynamic factors on a crane according to a dynamic model, instead of simple and very conservative calculation rules provided by standards, which is a way to reduce material use and costs. For this purpose the model have to be enlarged to a more complex model by taking the crane ship movements into account and calculating the interaction between the main load and the deck.
