Simulation of Dynamic Behaviour of a FPSO Crane

Transcription

1 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 Kristiansand Terje Rølvåg, Fedem Technology AS, N-4030 Trondheim Abstract Lifting operation on a FPSO (Floating Production, Storage and Offloading vessel) is much more demanding for the crane and the crane driver than similar operations on a fixed offshore platform. Due to the motion of the FPSO in heavy sea and strong wind, the crane is subjected to additional dynamic forces as well as swinging loads. The present paper deals with numerical simulation of the dynamic behaviour of the Norne offshore crane during lifting operation. The simulations are performed by FEDEM a general nonlinear dynamic analysis program for flexible multibody systems. The pedestal, king and boom 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 nonlinear spring and damper elements. A control system is implemented in the model making it possible to control the movement of the boom and the winch to compensate for the relative motion between 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 of hoisting 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, the presented model can be used to optimise the operation procedure, determine the maximum allowable load for various sea states and to calculate necessary power to control the motion of the load. Introduction. During the last decade, the focus in the North Sea offshore activities has changed from bottom supported platforms to permanent located vessels and floating installations, for example FPSO s. With regard to offshore crane operations, this complicates the situation both for internal load handling within the installation, and sealifts from or to a supply vessel. The reason for this is, of course, that the installation on which the crane is located, experiences wave induced motions. The motions of a floating vessel can be completely described by six motion components, three translational and three rotational motions. These are called the degrees of freedom for the vessel, see Figure 1. 1

2 z η ψ η z x y ηθ η x η φ η y G Figur. 1 Vessel motions The oscillating motion for the respective degrees of freedom are defined as: η x = surge, i.e. longitudinal translation η y = sway, i.e. transverse translation η z = heave, i.e. vertical translation η φ = roll, i.e. rotation about longitudinal axis η θ = pitch, i.e. rotation about transverse axis η ψ = 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 wave induced motion components in both horizontal and vertical direction. The magnitude of these motions are very much depending on the seastate, heading of the waves and the position of the 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 β of the boom see Figure 2. R Y C β Y O X O X C Figure 2 Horizontal position of boom tip There has been a discussion about the fitness for purpose of various crane types on these floating installation, but a serious discussion of performances and comparison has not been 2

3 possible, due to the variation in the crane specifications in various projects. Even if cranes of different type are located on the same installation, the localisation on board the vessel will be very 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 various crane types is to make realistic behaviour simulation studies. Traditionally the analysis of large mechanical appliances with considerable functional motions, has been divided into three categories: Structural analysis (for instance Finite Element programs) that can calculate stresses and deformations in a structure consisting of members, elements, joints and links, under the assumption that the undeformed geometry of the structure remains constant during the analysis. Mechanism analysis that can calculate the positions, velocities, accelerations and forces of various linkages and mechanisms for prescribed time-functions of motions or driving forces, 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 the crane control system are modelled in a state space or a block diagram form, where masses and flexibilities are lumped or neglected. This model is used to perform a numerical timesimulation of the system response due to the many non-linearities in hydraulic components. In order to achieve a result with some required degree of accuracy, we will often have to exchange 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 with regard to natural frequencies and mode shapes. So the ideal analysis program for an offshore crane is a program that merges the capabilities of 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 finite element formulation and new object orientated techniques for effective modeling, simulation and visualization of Finite Element (FE) assemblies and control systems. Fedem supports Multidisciplinary Mechanical Analysis e.g. powerful and integrated modeling and 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) 3

4 Each superelement is imported, positioned and used as a link in the FEDEM mechanism assembly A co-rotated frame is associated with each link (superelement) and the elastic displacements and stress results are calculated relative to this frame Large rotations and displacements of the links are included but the elastic displacements of 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 time predictions 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 the crane 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 stress states 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 stress distribution All modelling and simulation tasks are controlled by a uniform graphical user interface With all these integrated capabilities FEDEM supports multidisciplinary modelling and simulation features that enables design engineers to model and test the performance of cranes operating in offshore environments. Modelling of the crane The actual crane for analysis in this paper is a box boom crane on the Norne FPSO. The crane 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 m Boom tons Length of boom m King with adapter tons Height from slew ring Hydraulic cylinders tons Hook ton 4

5 Winch King Slew R in g Pedestal A dapter C ylinders Boom Hook Figure 3. The Norne crane The lifting capacity depends on the boom angle. With a radius of 45 m the capacity is 15 tons 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 shell elements. The total number of elements and the degrees of freedom of the components are shown in Table 2. Table 2 Number of elements Link Elements Pedestal 1674 King 1006 Boom 3791 The number of elements is chosen to model the stiffness and geometry with reasonable accuracy for deformation and stress analysis. The FEM model of the links are shown in Figure 4. The links are then transferred to FEDEM where they are reduced to so-called superelements 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 model for 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 joint modelling the slew ring. The king and the boom are connected by two ball joints placed on a horizontal line and by two hydraulic cylinders. The hydraulic cylinders are in this analysis modelled by non-linear springs and dampers. The non-linear characteristics of the springs when the boom are 5 degrees above horisontal shown in Figure 6. The horizontal and vertical part of the hoisting rope are modelled by one equivalent spring and damper with 5

6 Figure 4. FEM models of the links Cylinder Stiffness vs Stroke 6.0E+08 Stiffness [N/m] 5.0E E E E E E Stroke [m] Figure 5 Cylinder stiffness vs. stroke Stiffness of rope [N/m] Ekvivalent Stiffness of Rope 9.0E E E E E E E E E E E Vertical length of rope [m] Figure 5 Equivalent spring stiffness vs. Vertical rope length 6

7 varying stiffness corresponding to the varying length of the vertical rope, see Figure 5. Figure 6 shows the final crane model. Figure 7 Assembled crane model There are little available data on damping. However, experience indicates that three distinct vibration 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 a damping ratio of 12 %. For the boom the damping ratio is set to 2 % and the pedestal and king 1.5% Natural frequencies and mode shapes The stiffness and dynamic properties of the crane are dependant of the instant geometry of the system meaning that the natural frequencies and mode shapes are changing during e.g a lifting operation. Table 3 shows the 9 first natural frequencies of the crane for different boom 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 degrees Modes/angle deg deg deg The mode shapes for boom angle 25 degrees are shown in Figure 8. The first two frequencies are 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 boom stiffness.. The value corresponds to the single pendulum value meaning that the boom does not participate significantly. 7

8 The 3 rd mode is the first vertical deflection of the boom with the load partly following and with deflection of the hydraulic cylinders. The 5 th, 7 th and 9 th mode are second order vertical deflection of the boom with different degree of participation from the load, cylinders and pedestal. In the 5 th and 7 th the boom tip and load are 180 degree out of phase while in the 9 th the load is in rest. The 7 th shows large bending of the pedestal while the 9 th has large deflection of the cylinders. The 4 th mode is the first horizontal deflection of the boom with the load resting and some torsion of the pedestal. The 6 th and the 8 th mode are second order horizontal deflection of the boom with considerable bending and torsion of the pedestal, respectively. It is seen the modes with significant pendulum movement or vertical movement of the boom are most dependent of the boom angle. The natural frequencies and the mode shapes give good insight into the dynamic behaviour of the crane and how we can avoid dynamic problems during operations. Especially it is seen that 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 8

9 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 and crane operation are calculated using Newmarks time integration method [3,4] with the parameter β = ¼. Newton-Raphson iteration [3,4] is used within each time step to obtain equilibrium. 9

10 The ship movements are introduced to the crane in terms of time series for the displacements and rotations of the pedestal foundation. In the present analysis heave and roll motion measured 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 different quantities. 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 length of the vertical hoisting rope to simulate winch operation. The program and the model can now be used to simulate the crane behaviour in different operation modes and under different weather conditions. Especially, the program can be used during design to verify if the concept meets the design specifications and in operation to establish operation guidelines. In the following two operations will be simulated to demonstrate some capabilities of the model and the program. These are a lift operation using the boom and using the winch and a swing operation, all during ship motion. To compensate for the ship movement and control the movement of the lifted object, a control system is implemented in the model. In this way we can study the effect and feasibility of such 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/ Output Input Plant _ Sensor Figure 9. General feedback control system. In FEDEM the above feedback control system can be represented as Figure 10 with a time delay and a conversion factor block. Reference Input + Fedem Σb PID Mechanism Time Actuator Model Delay (Cylinders) _ Sensor Conversion input Factor Figure 10. Control system for vertical motion of load as defined in FEDEM. 10

11 The conversion factor block is the relation between the cylinder deflection and the vertical displacement of the load. This relationship is the slope of the curve shown in Figure 3. Cylinder Stroke vs Load Displacement 35 Load Displacement [m] Cylinder stroke [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 the spring/damper system representing the double acting cylinders. A sensor is placed at the hook to measure the vertical displacement of the load. When all the necessary connections between the blocks are made and all the functions within FEDEM are defined, the most difficult part of the controller design process is to find the appropriate 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 can find the ultimate gain, K u, and the ultimate period, P u, for the marginally stable system. These two values are then used to calculate the PID parameters according to Ziegler-Nichols rules for tuning the regulator. For this crane, the ultimate gain and period are and respectively. The calculated parameters according to Ziegler-Nichols rules will not guaranty a stable system, so a further tuning is necessary to make the system stable. With a time delay of 0.2 second due to valve dynamics, the PID parameters that stabilise the load in vertical direction are P = 0.8, T i = 0.15, and T d = The feedback control system for the pendulum motion in transversal direction can be represented in FEDEM exactly the same as the feedback control system for vertical motion of the load. The differences are the conversion block and the type of sensor used for feedback purposes. 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 to an angle in radians. In this case the actuator is the slew gear motor. As in the vertical motion control system, the process of calculating the PID parameters in this control system is identical to the previous case. But since the rope is not stiff, it is much more challenging to tune 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 assuming the load is totally transmitted to the crane from the supply vessel. In this operation the crane after 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 is exposed to heave as well as pitch and roll motions of the ship. These ship motions as shown in Figure 6 are measured on the Norne FPSO in a sea state of Hs = 5 m and Tp = 10.5 s. 11

12 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 is with the vertical motion controller and one without the vertical motion controller. The purpose of these simulations is to see the changes in pressure in the cylinders as well as the displacement of the load. a) With controller b) Without controller 12

13 Figure 14. Load displacement compared with vertical motion of ship with and without controller. Figure 5a shows the vertical load displacement with control. The displacement fluctuates heavily 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 reference level of zero meter. During the lift interval (5s-30s), the load track the reference input very well 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 motion of the load. This fluctuation is mainly due to the amplification of the pendulum motion along the length of the boom. This pendulum motion is not possible to control since there is no actuator to do the job. Figure 5b shows the result of the lift operation without a control system. In this case, the load will just track the wave motion and the vertical motion of the load is of the same magnitude as the amplitude of the wave. Due to the roll motion of the crane, the load hanging on the tip of the boom is subjected to pendulum motion. Figure 8 shows the horizontal displacement of the load in transversal direction with and without controller. a) With controller b) Without controller Figure 15. Displacement of the load in horizontal transversal direction with and without controller. 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 motion of the load, we have used a load of 2 tons and the cylinders as our actuator. The force required for the cylinders to compensate for the vertical motion of the load is shown in Figure x below. Force [N] Force in Cylinder Time [s] Force [N] Force in Cylinder Time [s] 13

14 a) With controller b) Without controller 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 with vertical control system is 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 compensate for the heave motion of the load is below the working pressure of the cylinders. This means that the crane can theoretically use to compensate for vertical motion with a load of 2 tons at sea state of H s = 5m and T p = 10.5s. Without a heave motion controller, the load is now N in the cylinders. If the cylinders are used to lift a load of 2 tons, the compression force in the cylinder is now 287 bars. The crane is therefore able to lift a load of 2 tons using the cylinders when the boom is 5 degrees 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 or lower the load by changing the length of the spring. To use the spring/damper system this way, the spring is allowed to have stiffness in both compression and tension. In this simulation the stiffness of the spring changes as the length of the changes. For a rope of initial length of metres from the tip of the boom to the load, the change in spring stiffness of the rope is given by Figure 17. Rope Stiffnes vs Spring Deflection Rope stiffness [N/m^2] 9.0E E E E E E E E Deflection [m] Figure 17. Rope stiffness vs rope deflection A control system is then designed for hoisting of the load. In this case, the controller system is exactly like the control system for vertical motion, accept that there is no conversion block. A sensor is now used to measure the length of the rope and feedback directly to compare with the reference input. The effect of using a control system to compensate for the vertical motion and not using a control system is shown in figures below. 14

15 a) With controller b) Without controller 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 heavy vibrations in Figure xa from 40-60s is due to the fact that the rope is getting shorter, but the conversion factor is a constant. Therefore, the sensor input is not exact. This error contributes to 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 heavy vibrations of the rope are due to the disturbance of the sea on the system. This disturbance is then introduced into the hydraulic system, the crane links and the rope. a) With controller b) Without controller Figure 19. Force in the winch during hoisting with and without controller 15

16 Swing of crane boom In this operation the revolute joint (rotation about one axis) is attached between the king and the pedestal. The rotation of the king relative to the pedestal is obtained by specifying the angle 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-ordinate transformation and time limitations of this paper. Two simulations are simulated for the case of slow and high acceleration during the swing of the boom. The input velocities for the two cases 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 21 for the two cases mentioned above. a) With high acceleration b) Without slow acceleration Figure 21. Swing of crane with slow and high acceleration. 16

17 Position in y-direction [m] Load Displacement Position in x-direction [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 operation of 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, [2] I-DEAS, Master Series 7, Student Guide, Structural Dynamics Research Corporation, Milford,Ohio, [3] Langen, I. and Sigbjönsson, R.: Dynamisk analyse av konstruksjoner, Tapir, Trondheim 1979 [4] Géradin, 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,