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Modeling and Simulation of a Container Gantry

Crane Cabins Operation with Simulink

Juan Jose Gonzalez De la Rosa, J.A. Carmona Torres, A. Illana, Carlos G. Puntonet, J.M GorrizUniv. of Cadiz/Electronics-PAI-TIC-168, Algeciras, Spain, e-mail: [email protected]

Univ. of Granada, Granada, Spain, e-mail: [email protected]

Abstract This paper deals with the simulation of a ship-containers gantry crane cabin behavior, during an operationof load releasing. The goal consists of obtaining a reliablemodel of the cabin, with the aim of reducing the non-desiredcabin vibrations. We present the Simulink-based model andthe simulation results when the load is released by the cranein the containers ship. We conclude that the mass centerposition of the cabin affects dramatically to the vibrations

of the crane. A set of graphs are presented involvingdisplacements and rotations of the cabin to illustrate theeffect of the mass center positions bias.

Keywords Gantry crane, Mechanical Engineering, Sig-nal processing.

I. INTRODUCTION

The study of the vibrations in a gantry crane used in

a containers terminal is an issue related to the security

of the crane operator and to the durability of the design.

The vibrations take place mostly in the operator cabin.

The main problem is that a short amplitude vibration

in the trolley may produce high amplitude values in thecabin, which may affect the operators safety. Numerous

achievements have been made in the field of the control

for overhead crane systems, which have proven to be

an improvement in the position accuracy, safety and

stabilization control [1][5].

With the goal of adapting the developed control

schemes to portainers (container gantry cranes), the mod-

eling of the system has to be developed. In this paper we

present an innovative Simulink model of a real-life gantry

crane cabin, like one shown in Fig. 1, and its emulated

performance when a container is released into the ship.

The results show a new set of signals that may be used ina future vibration control scheme. The paper is structured

as follows. In Section II we present the Simulink model

of the portainer cabin; Section III comprises the set of

the simulation results which in fact are the guts of the

paper; finally conclusions are drawn in Section IV.

II. THE S IMULINKM ODEL

A. Model Equations

Fig. 2 shows an scheme of the complete crane structure

where we can see the cabin, whose dimensions are

detailed in Fig. 3.

The six degrees of freedom of the cabin are solvedusing the well-known Newton equations, applied to the

mass center of the cabin, three of them for forces and

Fig. 1. Container Gantry Cranes at Algeciras harbor.

other three for torques, from Eq. (1) to Eq. (6); where all

the variables and points are referred to Fig. 3.

i{5,6,7,8}

Fi,x= Mxmc

Fi,x= Ci,x(xi,r xi,b)Ci,xy(yi,r yi,b)

+Ki,x(xi,r xi,b)Ki,xy(yi,r yi,b)

(1)

i{5,6,7,8}

Fi,y =Mymc

Fi,y =Ci,y(yi,r yi,b)Ci,xy(xi,r xi,b)

+Ki,y(yi,r yi,b)Ki,xy(xi,r xi,b)

(2)

i{5,6,7,8}

Fi,z =Mzmc

Fi,z =Ci,z(zi,r zi,b) +Ki,z(zi,r zi,b)

(3)

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Fig. 2. Gantry crane model scheme.

Fig. 3. Gantry crane cabin dimensions. Units in meters. Note wherethe mass center is and where it should be. Points 5-8 play a special rolein the equations that model the dynamics.

i{5,6,7,8}

Mi,x= Ixwx,mc (Iy Iz)wy,mcwz,mc

i{5,6,7,8}

Mi,x=

(Fi,zdi,y+ Fi,ydi,ydi,z)(4)

i{5,6,7,8}

Mi,y =Iywy,mc (Iz Ix)wz,mcwx,mc

i{5,6,7,8}

Mi,y =

(Fi,zdi,x+ Fi,xdi,z)(5)

i{5,6,7,8}

Mi,z =Izwz,mc (Ix Iy)wx,mcwy,mc

i{5,6,7,8}

Mi,z =

(Fi,xdi,y+ Fi,ydi,x)(6)

Some remarks are to be made in this set of equations.

The refers to index i=5,8, respectively, the - sign

refers to i=6,7. Subindex mc refers to the mass center,

r refers to the trolley and b to the cabin. w are

angles, F forces, M torques, I inertias, K are for

springs, C are for dumpers; d symbolizes distances.

B. Simulink Scheme

Simulink model solves and plot displacements, veloc-ities and accelerations of each one of the six degrees of

freedom of the cabin. To do that, it must be inserted

the trolley movements and the system physical constants:

mass, inertias, spring and dumper values and mass center

position. Fig. 4 presents a detail of the Simulink model,

the forces and torques solver block.

Fig. 4. Detail of the Simulink model. Forces and torques solver block.

The model is mainly divided into four blocks. The

forces and torques solver block (Fig. 4), it receive all

the constants and positions of the system and solve every

force and torque.

The second block is the equations solver, it receives

forces, torques, mass, inertias and angles to solve every

acceleration of the mass center of the cabin. The third

block converts accelerations into velocities and positions

of the mass center, which are the outputs of the system.

Finally the fourth block calculates positions and velocities

of the four cabin-trolley connection points, using cabin

and trolley positions and velocities; finally it connectsthem to the first block, so the new forces and torques

may be calculated.

III. RESULTS

We present the set of results in the form of graphics

due to the interest related to the topic of the conference.

We have introduced, in the simulated model, a real-life

bias in the position of the mass center (A = 1 m, B = 1.35

m, C = 1 m), in order to asses the real cabin behavior. A

delay of 1 sec is introduced to enhance the visualization

of the graphs. The initial conditions are null for all the

variables involved in the differential equations.

A step-type input (5 cm amplitude) is chosen to as-sess the outputs of the system. This input emulates the

behavior of the sudden bump in the trolley when the

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load is released in the container ship. Fig. 5 shows the X

displacement of the mass center of the cabin. It can be

seen than the system is not able to dump it adequately.

This movement is produced by the horizontal bias; it has

the peculiarity that the vertical bias of the mass center

also affects this horizontal movement in a critical way.

But we have to point out that the unique presence of a

vertical bias is not enough to start this movement.

1 2 3 4 5 6 7 8 9 103

2

1

0

1

2

3x 10

3

Time instances,sec

xdisplacement,m

Fig. 5. Displacement in X axis of the mass center.

In Fig. 6 we can see another coupling effect produced

by the vertical input, this time in the Y axis. The high

frequency component of the signal is rapidly attenuated

while the low frequency component is not attenuated at

all and remains as a parasitic vibration in the system. Thisfact has also been shown in Fig. 5.

1 2 3 4 5 6 7 8 9 102.5

2

1.5

1

0.5

0

0.5

1

1.5

2

2.5x 10

3

Time instances, sec.

ydisplacement,m

Fig. 6. Displacement in Y axis of the mass center.

The displacement of the system in the Z-axis, shown

in Fig. 7, is the only one that behaves like a typical

response to a step-like input. We must point out than the

amplitude of the movement nearly doubles the input; so,

an immediate conclusion is that the systems behavior isfar from its original aim of isolate the cabin from the

trolley vibrations. in other words, this movement has the

peculiarity of not being fully dumped.

1 2 3 4 5 6 7 8 9 100

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1


zdisplacement,m

Fig. 7. Displacement in Z axis of the mass center.

Figs. , and , show the rotations of the cabin. It can

be seen that the movements are not attenuated. These

rotations affect to the X, Y, Z movements, and will not

be extinguished due to the geometric disposition of the

dumps.

1 2 3 4 5 6 7 8 9 104

2

0

2

4x 10

4


xangle,rad

Fig. 8. Rotation in X axis of the cabin.

IV. CONCLUSIONS

We conclude that the system is not able to dump the

cabin vibrations, as every real cabin mass center has a

bias. Even with very high values of dump constants, the

time needed to attenuate the vibrations is high.

Our direct real-life experience in those cabins shows

that they continually work in a transitory vibration state,

often leading the system to resonances.

A real cabin prototype is being built to adequate our

model to the reality, and solutions to the vibration matter

will be tested in it. The critical influence of the mass

center position showed in this paper lead us to think thatcabin-trolley connection points must be placed around

the real mass center position instead than on the top of

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1 2 3 4 5 6 7 8 9 101

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

1x 10

3


yangle,rad

Fig. 9. Rotation in Y axis of the cabin.

1 2 3 4 5 6 7 8 9 104

3

2

1

0

1

2

3x 10

5


zangle,rad

Fig. 10. Rotation in Z axis of the cabin.

the cabin, where the vertical distance to the mass center

makes the system to behave like a pendulum.

Apart from properly dumping the cabin, we think that

the entire crane model should be fully understood and

controlled so the operational movements and vibrations

will not add each other.

ACKNOWLEDGEMENT

We would like to acknowledge Mr. John Thonsem for

the trust shown in the research group PAI-TIC-168 from

the University of Cadiz, which works in the MAERSK

containers terminal in the Algeciras harbor.

REFERENCES

[1] F. Ju, Y. Choo, , and F. Cui, Dynamic response of tower craneinduced by the pendulum motion of the payload, International

Journal of Solids and Structures, no. 43, pp. 376389, 2006.

[2] Y. J. Hua and Y. K. Shine, Adaptive coupling control for overheadcrane systems, Mechatronics, no. -, p. in Press, 2007.

[3] D.-H. Lee, Z. Cao, and Q. Meng, Scheduling of two-transtainersystems for loading outbound containers in port container terminalswith simulated annealing algorithm, Int. J. Production Economics,no. -, p. in Press, 2007.

[4] A. Benhidjeb and G. Gissinger, Fuzzy control of an overheadcrane performance comparison with classic control, Proceedingsof Control Eng. Practice, no. 12, p. 168796, 1995.

[5] Y. Jianqiang, Y. Naoyoshi, and H. Kaoru, Anti-swing and position-ing control of overhead traveling crane, Inform Sci., no. 155, pp.1942, 2003.

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