Crane Paper

7/31/2019 Crane Paper

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Simulation of Dynamic Behaviour of a FPSO Crane

by

Ivar Langen and Thuong Kim Than, Stavanger University College, N-4091 Stavanger

Oddvar Birkeland, Hydralift ASA, N-4604 KristiansandTerje Rlvg, Fedem Technology AS, N-4030 Trondheim

Abstract

Lifting operation on a FPSO (Floating Production, Storage and Offloading vessel) is muchmore demanding for the crane and the crane driver than similar operations on a fixed offshoreplatform. Due to the motion of the FPSO in heavy sea and strong wind, the crane is subjectedto additional dynamic forces as well as swinging loads.

The present paper deals with numerical simulation of the dynamic behaviour of the Norneoffshore crane during lifting operation. The simulations are performed by FEDEM a generalnonlinear dynamic analysis program for flexible multibody systems. The pedestal, king andboom are flexible links modelled by shell finite elements and connected together by different

joints. The hoisting rope and the hydraulic cylinders are modelled by linear and nonlinearspring and damper elements. A control system is implemented in the model making it possibleto control the movement of the boom and the winch to compensate for the relative motionbetween the ship and the supply vessel and keep the load in rest relative to the vessel.Examples are shown of calculated natural frequencies and mode shapes as function ofhoisting rope length and boom angle. Furthermore, maximum dynamic stresses in different

sections/details are presented as function of how the crane is operated.

Besides giving necessary stress data for design verification against overload and fatigue, thepresented model can be used to optimise the operation procedure, determine the maximumallowable load for various sea states and to calculate necessary power to control the motion ofthe load.

Introduction.

During the last decade, the focus in the North Sea offshore activities has changed from bottomsupported platforms to permanent located vessels and floating installations, for exampleFPSOs. With regard to offshore crane operations, this complicates the situation both forinternal load handling within the installation, and sealifts from or to a supply vessel. Thereason for this is, of course, that the installation on which the crane is located, experienceswave induced motions.

The motions of a floating vessel can be completely described by six motion components, threetranslational and three rotational motions. These are called the degrees of freedom for thevessel, see Figure1.

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z

y

x

G

x

y

Figur. 1 Vessel motions

The oscillating motion for the respective degrees of freedom are defined as:

x = surge , i.e. longitudinal translation

y = sway , i.e. transverse translation

z = heave , i.e. vertical translation

= roll , i.e. rotation about longitudinal axis

= pitch , i.e. rotation about transverse axis

= yaw , i.e. rotation about vertical axis

It is obvious that a crane on a vessel and especially the boom tip of the crane will have waveinduced motion components in both horizontal and vertical direction. The magnitude of thesemotions are very much depending on the seastate, heading of the waves and the position ofthe boom tip which again is dependent on the crane position relative to the centre of gravity

and on actual working radius R, and slew angle of the boom see Figure 2.

XC

XO

YC

YO

R

Figure 2 Horizontal position of boom tip

There has been a discussion about the fitness for purpose of various crane types on thesefloating installation, but a serious discussion of performances and comparison has not been

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possible, due to the variation in the crane specifications in various projects. Even if cranes ofdifferent type are located on the same installation, the localisation on board the vessel will bevery decisive for the dynamic loads on the crane and the pendulum effect of the lifted object.It seems that the best way to make some objective comparisons and statements for variouscrane types is to make realistic behaviour simulation studies.

Traditionally the analysis of large mechanical appliances with considerable functionalmotions, has been divided into three categories:

Structural analysis (for instance Finite Element programs) that can calculate stresses anddeformations in a structure consisting of members, elements, joints and links, under theassumption that the undeformed geometry of the structure remains constant during theanalysis.

Mechanism analysis that can calculate the positions, velocities, accelerations and forces ofvarious linkages and mechanisms for prescribed time-functions of motions or drivingforces, under the assumption that elastic deformations of the members are negligible in the

analysis. This analysis is often very simplified for cranes.

Hydraulic simulation programs, where the properties of the hydraulic systems and thecrane control system are modelled in a state space or a block diagram form, where massesand flexibilities are lumped or neglected. This model is used to perform a numerical time-simulation of the system response due to the many non-linearities in hydrauliccomponents.

In order to achieve a result with some required degree of accuracy, we will often have toexchange data and model properties between the various programs in an iteration sequence.And even if we do so, we may lose important properties of the total system, especially withregard to natural frequencies and mode shapes.

So the ideal analysis program for an offshore crane is a program that merges the capabilitiesof all three analysis categories, and this is exactly what FEDEM does.

The FEDEM modelling and simulation capabilities

FEDEM [1] represents the next generation crane simulation tools based on a non-linear finiteelement formulation and new object orientated techniques for effective modeling, simulationand visualization of Finite Element (FE) assemblies and control systems.

Fedem supports Multidisciplinary Mechanical Analysis e.g. powerful and integrated modelingand simulation capabilities within the traditionally separated design disciplines:

Finite Element Analysis (FEM) of components or assemblies

Multi Body System (MBS) analysis of mechanisms

Control / Hydraulic system analysis

Some of the FEDEM features/capabilities are:

Structural crane parts are represented by finite element models (superelements) created in

pre-processors like I-DEAS, PRO/Engineer, PATRAN etc. Superelement mass and stiffness matrices are calculated and reduced using static or

component mode synthesis reduction (CMS)

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Each superelement is imported, positioned and used as a link in the FEDEM mechanismassembly

A co-rotated frame is associated with each link (superelement) and the elasticdisplacements and stress results are calculated relative to this frame

Large rotations and displacements of the links are included but the elastic displacementsof each link is assumed to be small.

The crane parts are connected together with various joint types (revolute, ball, cam etc.) All joint types are based on master and slave techniques that are very numerical robust

Lumped masses and inertias can be applied directly on the mechanism model

Strain gages can be distributed on the crane parts to calculate strain variations for life timepredictions

Hot spots with respect to fatigue life can be calculated and visualized

Wave and wind induced motions can be applied directly or via transfer functions on thecrane models

Non-linear loads, dampers and springs can be attached between the crane parts

Control and hydraulic systems are created in a 2D environment and coupled together with

the 3D mechanism model The solvers are based on various numerical methods like Newton-Raphson and Newmark

integration schemes

All structural and control system variables are solved simultaneously

Simultaneous simulation and visualisation are supported

The modes can be calculated and animated at specified crane configurations and stressstates

The stresses can be solved at specified mechanism configurations

Direct interfaces to I-DEAS, NASTRAN, PATRAN and HYPERMESH are supported.

The crane motion can be animated with superimposed elastic deflections and stressdistribution

All modelling and simulation tasks are controlled by a uniform graphical user interface

With all these integrated capabilities FEDEM supports multidisciplinary modelling andsimulation features that enables design engineers to model and test the performance of cranesoperating in offshore environments.

Modelling of the crane

The actual crane for analysis in this paper is a box boom crane on the Norne FPSO. Thecrane is shown in Figure 3 and the main dimensions and weights are given i Tables 1.

Table 1. Main dimensions and weights

Dimensions Weight

Total length 47.037 m Boom 39.500 tonsLength of boom 45.382 m King with adapter 41.400 tonsHeight from slew ring 48.240 Hydraulic cylinders 9.400 tons

Hook 1.000 ton

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W i n ch

K i n g

S l e w R i n g

C y l i n d e r s B o o m P e d e s t a l A d a p t e r H o o k

Figure 3. The Norne crane

The lifting capacity depends on the boom angle . With a radius of 45 m the capacity is 15tons while it is 45 tons for a radius of 17 m.

The pedestal, king and boom are modelled in I-DEAS [2]

as separate components or links.Finite element models of the components are created using triangular and quadrilateral shellelements. The total number of elements and the degrees of freedom of the components areshown in Table 2.

Table 2 Number of elements

Link Elements

Pedestal 1674King 1006Boom 3791

The number of elements is chosen to model the stiffness and geometry with reasonableaccuracy for deformation and stress analysis. The FEM model of the links are shown inFigure 4. The links are then transferred to FEDEM where they are reduced to so-calledsuperelements using a component mode synthesis technique [3,4] and connected via joints,springs and dampers to a mechanism model. Only nodes referred to in the mechanism modelfor joints, springs, dampers and control input are retained for dynamic analysis.

The pedestal adapter and the king are connected at one central point by a revolute jointmodelling the slew ring. The king and the boom are connected by two ball joints placed on ahorizontal line and by two hydraulic cylinders. The hydraulic cylinders are in this analysismodelled by non-linear springs and dampers. The non-linear characteristics of the springswhen the boom are 5 degrees above horisontal shown in Figure 6 . The horizontal andvertical part of the hoisting rope are modelled by one equivalent spring and damper with

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Figure 4. FEM models of the links

Cylinder Stiffness vs Stroke

0.0E+00

1.0E+08

2.0E+08

3.0E+08

4.0E+08

5.0E+08

6.0E+08

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

Stroke [m]

Stiffnes

s[N/m]

Figure 5 Cylinder stiffness vs. stroke

Ekvivalent Stiffness of Rope

4.0E+05

4.5E+05

5.0E+05

5.5E+05

6.0E+05

6.5E+05

7.0E+05

7.5E+05

8.0E+05

8.5E+05

9.0E+05

10 20 30 40 50 60

Vertical length of rope [m]

Stiffnessofrope[N/m]

Figure 5 Equivalent spring stiffness vs. Vertical rope length

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varying stiffness corresponding to the varying length of the vertical rope, see Figure 5. Figure6 shows the final crane model.

Figure 7 Assembled crane model

There are little available data on damping. However, experience indicates that three distinctvibration amplitudes are visible in free vibration. The damping used for the, hydraulic

cylinders and rope are based on simulated free vibration tests using this observation giving adamping ratio of 12 %. For the boom the damping ratio is set to 2 % and the pedestal and king1.5%

Natural frequencies and mode shapes

The stiffness and dynamic properties of the crane are dependant of the instant geometry ofthe system meaning that the natural frequencies and mode shapes are changing during e.g alifting operation. Table 3 shows the 9 first natural frequencies of the crane for differentboom angles 25, 45, and 75 degrees and with a load of 5 ton hanging at sea level, 42.65m,55.29m and 67 metres below the boom tip, respectively.

Table 3. Natural frequencies in Hz for boom angles 25, 45, 75 degreesModes/angle 1 2 3 4 5 6 7 8 9

25 deg. 0.0761 0.0762 0.7374 0.9772 0.9222 2.770 3.016 4.871 5.299

45 deg. 0.0664 0.0665 0.6302 0.9561 1.689 2.775 3.014 5.048 5.110

75 deg. 0.0605 0.0607 0.4437 0.9433 1.463 2.782 3.045 4.996 5.483

The mode shapes for boom angle 25 degrees are shown in Figure 8. The first two frequenciesare pendulum modes of the load transversal and in line the boom, respectively. The small

difference between the two values is due to the difference in axial and transversal boomstiffness. . The value corresponds to the single pendulum value meaning that the boom doesnot participate significantly.

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The 3rd mode is the first vertical deflection of the boom with the load partly following andwith deflection of the hydraulic cylinders. The 5th, 7th and 9th mode are second order verticaldeflection of the boom with different degree of participation from the load, cylinders andpedestal. In the 5th and 7th the boom tip and load are 180 degree out of phase while in the 9ththe load is in rest. The 7th shows large bending of the pedestal while the 9th has large

deflection of the cylinders.

The 4th mode is the first horizontal deflection of the boom with the load resting and sometorsion of the pedestal. The 6th and the 8th mode are second order horizontal deflection of theboom with considerable bending and torsion of the pedestal, respectively. It is seen the modeswith significant pendulum movement or vertical movement of the boom are most dependentof the boom angle.

The natural frequencies and the mode shapes give good insight into the dynamic behaviour ofthe crane and how we can avoid dynamic problems during operations. Especially it is seenthat the frequency of pendulum movement of the loads is close to roll and pitch frequencies

in the sea states analysed below (about 5m Hs ).

Figure 8 Mode shapes for boom angle 25 degrees

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Figure 8 Mode shapes for boom angle 25 degrees (continued)

Dynamic analysis of the crane during operation

The dynamic response in terms of stresses/forces and displacements due to ship motion andcrane operation are calculated using Newmarks time integration method [3,4] with the

parameter = . Newton-Raphson iteration [3,4] is used within each time step to obtainequilibrium.

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The ship movements are introduced to the crane in terms of time series for the displacementsand rotations of the pedestal foundation. In the present analysis heave and roll motionmeasured at the living quarter and transformed to the crane location have been used.

Crane operation is simulated by specifying time functions, also called engines, for differentquantities. Engines are used for rotation of the king relatively to the pedestal, for the length

and the stiffness of the hydraulic cylinder spring to rise and lower the boom and for the lengthof the vertical hoisting rope to simulate winch operation.

The program and the model can now be used to simulate the crane behaviour in differentoperation modes and under different weather conditions. Especially, the program can be usedduring design to verify if the concept meets the design specifications and in operation toestablish operation guidelines.

In the following two operations will be simulated to demonstrate some capabilities of themodel and the program. These are a lift operation using the boom and using the winch and aswing operation, all during ship motion.

To compensate for the ship movement and control the movement of the lifted object, a controlsystem is implemented in the model. In this way we can study the effect and feasibility ofsuch systems to improve the performance.

Control System Design

A general block diagram representation of a feedback control system is shown in Figure 9.

Reference + Controller Process/ OutputInput Plant

_

Sensor

Figure 9. General feedback control system.

In FEDEM the above feedback control system can be represented as Figure 10 with a timedelay and a conversion factor block.

ReferenceInput +

Fedem

b PID Mechanism Time ActuatorModel Delay (Cylinders)

_Sensor Conversioninput Factor

Figure 10. Control system for vertical motion of load as defined in FEDEM.

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The conversion factor block is the relation between the cylinder deflection and the verticaldisplacement of the load. This relationship is the slope of the curve shown in Figure 3.

Cylinder Stroke vs Load Displacement

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

Cylinder stroke [m]

LoadDisplacement[m]

Figure 11. Load displacement vs. cylinder stroke

The process or plant is the mechanism model of the crane defined in FEDEM by finite

element links and joints, and the actuators in this feedback control system are thespring/damper system representing the double acting cylinders. A sensor is placed at the hookto measure the vertical displacement of the load.

When all the necessary connections between the blocks are made and all the functions withinFEDEM are defined, the most difficult part of the controller design process is to find theappropriate parameters in the PID controller. This is accomplished by using the Ziegler-Nichols [5] tuning rule for a closed-loop system. By increasing the gain in FEDEM, we canfind the ultimate gain, Ku, and the ultimate period, Pu, for the marginally stable system. Thesetwo values are then used to calculate the PID parameters according to Ziegler-Nichols rulesfor tuning the regulator. For this crane, the ultimate gain and period are 0.198 and 0.923respectively. The calculated parameters according to Ziegler-Nichols rules will not guaranty astable system, so a further tuning is necessary to make the system stable. With a time delay of0.2 second due to valve dynamics, the PID parameters that stabilise the load in verticaldirection are P = 0.8, Ti = 0.15, and Td = 0.08.

The feedback control system for the pendulum motion in transversal direction can berepresented in FEDEM exactly the same as the feedback control system for vertical motion ofthe load. The differences are the conversion block and the type of sensor used for feedbackpurposes. In this feedback loop, the sensor measures the motion of the load in transversal

direction relative to the tip of the boom and the conversion block convert this displacement toan angle in radians. In this case the actuator is the slew gear motor. As in the vertical motioncontrol system, the process of calculating the PID parameters in this control system isidentical to the previous case. But since the rope is not stiff, it is much more challenging totune the PID regulator to stabilise the pendulum motion of the load.

Lift operation

The first simulation example is a lift operation performed by the hydraulic cylinders assumingthe load is totally transmitted to the crane from the supply vessel. In this operation the craneafter 5 seconds lifts a load of 2 tons 15 metres in 25 seconds. The reference ramp input

displacement to the cylinders is shown in Figure 4. During this simulation, the crane isexposed to heave as well as pitch and roll motions of the ship. These ship motions as shown inFigure 6 are measured on the Norne FPSO in a sea state of Hs = 5 m and Tp = 10.5 s.

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Figure 12. Reference input (dotted line) vs sensor input (solid line)

Figure 13. Motion of the ship

The lift operation using the cylinders is simulated for two cases. One of the simulations iswith the vertical motion controller and one without the vertical motion controller. Thepurpose of these simulations is to see the changes in pressure in the cylinders as well as thedisplacement of the load.

a) With controller b) Without controller

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Figure 14. Load displacement compared with vertical motion of ship with and withoutcontroller.

Figure 5a shows the vertical load displacement with control. The displacement fluctuatesheavily around the reference value of zero due to the weight of the load and the boom the first

5 seconds. After 5 seconds, the cylinders start to extend and lift the load from the referencelevel of zero meter. During the lift interval (5s-30s), the load track the reference input verywell as can be seen from Figure 4, where the reference and the sensor input are coincident.After 30 seconds, the controller has some problem with compensating for the vertical motionof the load. This fluctuation is mainly due to the amplification of the pendulum motion alongthe length of the boom. This pendulum motion is not possible to control since there is noactuator to do the job.

Figure 5b shows the result of the lift operation without a control system. In this case, the loadwill just track the wave motion and the vertical motion of the load is of the same magnitude asthe amplitude of the wave.

Due to the roll motion of the crane, the load hanging on the tip of the boom is subjected topendulum motion. Figure 8 shows the horizontal displacement of the load in transversaldirection with and without controller.


Figure 15. Displacement of the load in horizontal transversal direction with and withoutcontroller.

As can be seen the pendulum amplitude is reduced from approximately 3 meters to 0.3 meter.

To simulate how much force is required for the cylinder to compensate for the vertical motionof the load, we have used a load of 2 tons and the cylinders as our actuator. The force requiredfor the cylinders to compensate for the vertical motion of the load is shown in Figure x below.

Force in Cylinder

0

500000

1000000

1500000

2000000

2500000

3000000

0 10 20 30 40 50 60

Time [s]

Force[N]

Force in Cylinder

0

500000

1000000

1500000

2000000

2500000

3000000

0 10 20 30 40 50 60

Time [s]

Force[N]

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Figure 16. Force in cylinder with and without vertical motion control system

From the above figures, we can see that the maximum force in one of the cylinders withvertical control system is 2659212 N when the load is 2 tons. This force is equivalent to a

pressure of 276 bars. With a working pressure of 300 bars, the force required to compensatefor the heave motion of the load is below the working pressure of the cylinders. This meansthat the crane can theoretically use to compensate for vertical motion with a load of 2 tons atsea state of Hs = 5m and Tp = 10.5s.

Without a heave motion controller, the load is now 2763650 N in the cylinders. If thecylinders are used to lift a load of 2 tons, the compression force in the cylinder is now 287bars. The crane is therefore able to lift a load of 2 tons using the cylinders when the boom is 5degrees above the horizontal position.

Lift Operation Using the Winch

One way to represent the winch in FEDEM, is to use the spring/damper system to hoist orlower the load by changing the length of the spring. To use the spring/damper system thisway, the spring is allowed to have stiffness in both compression and tension. In thissimulation the stiffness of the spring changes as the length of the changes. For a rope of initiallength of 23.58 metres from the tip of the boom to the load, the change in spring stiffness ofthe rope is given by Figure 17.

Rope Stiffnes vs Spring Deflection

5.5E+05

6.0E+05

6.5E+05

7.0E+05

7.5E+05

8.0E+05

8.5E+059.0E+05

-15 -10 -5 0 5 10

Deflection [m]

Ropestiffness[N/m^

2]

Figure 17. Rope stiffness vs rope deflection

A control system is then designed for hoisting of the load. In this case, the controller system isexactly like the control system for vertical motion, accept that there is no conversion block. Asensor is now used to measure the length of the rope and feedback directly to compare withthe reference input. The effect of using a control system to compensate for the vertical motionand not using a control system is shown in figures below.

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Figure 18. Hoisting of the load with and without controller.

Figures above are identical to the case of using the cylinders as the actuators. The heavyvibrations in Figure xa from 40-60s is due to the fact that the rope is getting shorter, but theconversion factor is a constant. Therefore, the sensor input is not exact. This error contributesto the amplification of the pendulum motion of the load.

Force Required for the Winch

Figures below shows the force sensed by the rope during the lift operation. The heavyvibrations of the rope are due to the disturbance of the sea on the system. This disturbance isthen introduced into the hydraulic system, the crane links and the rope.


Figure 19. Force in the winch during hoisting with and without controller

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Swing of crane boom

In this operation the revolute joint (rotation about one axis) is attached between the king andthe pedestal. The rotation of the king relative to the pedestal is obtained by specifying theangle in radians as the input to the joint. In this operation, an open loop control system is used

to control the transversal displacement of the load due to difficulties of co-ordinatetransformation and time limitations of this paper. Two simulations are simulated for the caseof slow and high acceleration during the swing of the boom. The input velocities for the twocases are shown in Figure 20 below.

a) With slow acceleration b) With high acceleration

Figure 20. Velocity input during the swing of the boom

The forces in the joint between the boom and the king in the slew joint are shown in Figure 21for the two cases mentioned above.

a) With high acceleration b) Without slow acceleration

Figure 21. Swing of crane with slow and high acceleration.

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Load Displacement

-5

0

5

10

15

20

25

30

35

40

45

50

-5 0 5 10 15 20 25 30 35 40 45 50

Position in x-direction [m]

Positioniny-dire

ction[m]

Figure 22. Position of load during a swing of the boom 90 degrees.

Concluding remarks

The present paper has dealt with simulation of the dynamic behaviour of cranes on a FPSO

vessel. The power of an integrated program system such as FEDEM featuring

- non-linear dynamic structural analysis

- multibody system analysis of flexible mechanism and

- control system modelling

for analysis of offshore cranes and crane operations is demonstrated. Such simulations are

important in design to assure that the crane is fit for purpose and fulfil the design

requirements. Furthermore, it can be used to optimise the mechanical design and the operationof the crane and to design an automatic control system for the crane.

The paper describes an analysis initiated internally at Stavanger University College as a

student thesis project to demonstrate the feasibility. A similar study of a FPSO crane with

truss work boom is under way. We believe that the tool and the analysis possibilities

presented represent great benefits to the industry. Therefore, to improve the model and

analysis capabilities and to study different and more realistic operational situations an

industry sponsored project will be proposed.

References

[1] FEDEM Reference Manual Release 2, Fedem Technology, 1998 1999.

[2] I-DEAS , Master Series 7, Student Guide, Structural Dynamics Research Corporation,

Milford ,Ohio,

[3] Langen, I. and Sigbjnsson, R.: Dynamisk analyse av konstruksjoner, Tapir,

Trondheim 1979

[4] Gradin, M. and Rixen, D: Mechanical vibrations : theory and application to

structural dynamics. - 2nd ed., Wiley, Chichester ,1997

[5] Franklin, G., Powell, J. and Emani-Naeini, A.: Feedback Control of Dynamic Systems.

Third ed. Addison Wesley, 1994

[6] Haugen, F.: Regulering av dynamiske systemer I, Tapir, Trondheim, 1994

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