Design of an experimental model for a semi-active vibration damping system on a jack-up platform

Transcription

1 Design of an experimental model for a semi-active vibration damping system on a jack-up platform Delft Center for Systems and Control

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3 Design of an experimental model for a semi-active vibration damping system on a jack-up platform For the degree of Master of Science in Mechanical Engineering at Delft University of Technology April 1, 2015 Faculty of Mechanical, Maritime and Materials Engineering (3mE) Delft University of Technology

4 The work in this thesis was supported by Siemens. Their cooperation is hereby gratefully acknowledged. Copyright c Delft Center for Systems and Control (DCSC) All rights reserved.

5 Abstract Jack-up platforms are off-shore structure which are more often placed in deeper water and harsher weather conditions. The consequence is that the natural frequency of the platform coincides with the wave frequency and starts to resonate in its natural frequency. The problem becomes more complicated, due to the fact that the natural frequency of the platform is not constant and varies in time due to structural properties, variable deck loading and environmental conditions. These vibrations are undesired and have to be damped. The aim of this thesis is to design an experimental model for a damping system on a jack up platform, which can optimally damp the motion of the primary structure when it is excited in the time varying natural frequency. This problem is tackled by comparing passive, semi-active and active Tuned Mass Damper (TMD) systems, regarding feasibility and robustness for installation on a jack-up platform. Hereafter the optimal tuning frequency and damping ratio are obtained by studying the work of Tsai and Lin [21], Connor [4] and Den Hartog [6]. These tuning laws are then combined with a Self-Tuning Regulator (STR), which makes it possible to continuously tune the semi-active damping system to its optimal parameters by estimating the unknown structural parameter using a Recursive Least Square Estimator (RLSE). The designed experimental model is a two degree of freedom model and incorporates crucial characteristics such as mass distribution, damping ratio and natural frequency. The semiactive TMD system is able to adapt its stiffness and damping coefficient, such that is it always optimally tuned when the structural parameters of the experimental model changes. This thesis concludes that a semi-active TMD system is the most appropriate type of damping system for a jack-up platform, regarding feasibility and robustness. A semi-active TMD system in combination with optimal tuning laws and a STR is able to optimally damp the vibrations of a jack-up platform, when it is excited in time varying natural frequency. This model can be used to test and validate the performance of the damping system and controller.

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7 Table of Contents Preface v 1 Introduction The jack-up platform Requirements for the damping system Assumptions made in this thesis Problem statement Outline Selection of the type damping system for a jack-up platform Passive TMD systems Semi-active TMD systems Active TMD systems Conclusion TMD system Introduction to TMD systems General procedure to obtain the optimal TMD parameters for a damped primary structure Summary of procedure Design example for a TMD system on a GustoMSC CJ-46 jack-up platform Conclusion Adaptive Control Introduction to adaptive control The control scheme Self-Tuning Regulator Model structure

8 iv Table of Contents Input signal Recursive Least Square Estimation Parameter validation Optimal tuning laws Control adaptive stiffness and damping coefficient Conclusion and Discussion Design of the experimental model Design constraints Primary structure design Adaptive stiffness mechanism Additional structural damping Modal exciter Semi-active TMD system design Adaptive stiffness mechanism Adaptive damping mechanism Addition of mass on the primary system Stepper motor and controller Sensors and additional required components Position sensor Acceleration sensor Load cell Additional components Complete design Conclusion Conclusion Further research A Specifications GustoMSC CJ-46 jack-up platform 75 B Specifications of sensors, actuators and additional components 79 Bibliography 99 Glossary 101 List of Acronyms List of Symbols

9 Preface During my visit at the career fair in Amsterdam RAI I came in contact with Siemens NV. This company inspired me by their diversity of products and their international involvement in projects. This convinced me to do my graduation project at Siemens. After applying for a graduation project, they gave me this challenging opportunity to design a damping system which can optimally damp the oscillations of the jack-up structure when it is excited in its resonance frequency. I would like to thank my supervisors prof.dr.ir.j.hellendoorn and ir.r.van der Groep for their assistance during the writing of this thesis. Further I would like to thank Kees Slinkman and Will van Geest for their time, advice and assistance during the design of the model and last but not least I want to thank Jos van Driel from the Meetshop for helping me with the choice of the sensors. Delft, University of Technology April 1, 2015

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11 Those who contemplate the beauty of the earth find resources of strength that will endure as long as life lasts. Rachel Carson

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13 Chapter 1 Introduction Jack-up units have been a part of the offshore oil industry exploration fleet since They are used for several applications such as exploration drilling, tender assisted drilling, production, accommodation and work/maintenance platforms. A jack-up platform is a self elevating unit which consists of a hull and legs with a jacking system in between. One of the most used jack-up structure is the CJ-46, which is designed by GustoMSC. This structure is designed to be installed in a water depth of 350 ft. The largest jack-up structure that is in use, is the CJ-70 which can be installed in a water depth of 450 ft and even a larger jack-up system is under construction (CJ-80). This jack-up structure is capable to stand in 575 ft of water. Since the demand for jack-up platforms to perform in deeper sea water level and harsher environmental conditions is increasing, the jack-up will be exposed to higher environmental loads. Due to these loads the jack-up will vibrate in its natural frequency. When the amplitude of these vibrations become too large some processes, such as drilling, have to be stopped. The consequence is that more time will be required to perform the task and therefore reduces the efficiency of the platform. Some projects have a limited amount of time in which e.g. a drilling task has to be performed and efficiency then becomes of crucial importance. Safety and discomfort of employees also limit the efficiency of the platform. Sensitive people notice accelerations of 0.05 g and long term exposure to an acceleration between 0.1 g and 0.25 g leads to nausea [10]. Large dynamic loading on the platform eventually result in long term structural fatigue, which increases the maintenance or reconstruction costs. To prevent the consequences of large deflections a solution is required to damp the obtained oscillations. Siemens delivers a broad variety of products for the offshore industry, such as power generators, compressors, control systems, jacking motors and much more. One of the aims of Siemens is to invest in innovating solutions. Therefore, Siemens is interested to solve this problem.

14 2 Introduction Figure 1-1: The main elements of a jack-up structure 1-1 The jack-up platform The jack-up platform can be roughly divided into four parts, namely the hull, legs, footings and the jacking system. All these parts have influence on the stiffness and damping coefficient of the total structure, which are important parameters for the design of an effective damping system. Figure 1-1 shows an example of a jack-up structure, where the hull and legs are indicated. The footings are placed at the end of each leg and the jacking system forms the connection between the leg and the hull. In the sequel of this section these parts and the relationship with the jack-up structure will be explained in more detail. The hull is a watertight structure, which provides space to house equipment and employees. An important fact is that a large hull translates into large weight and a large outer surface. The platform is therefore subjected to more wind, wave and current loads. This makes the platform more sensitive to these forces and the magnitude of the oscillations at the natural frequency will therefore be larger. For this reason a damping system is required to damp the amplitude of the oscillation at the natural frequency. The type, length and the number of legs of the structure combined with the water depth in which the structure is standing in, influences the stiffness and damping of the total structure. The stiffness determines the natural period for lightly damped structures and the amount of damping influences the magnitude of the oscillation at the natural frequency. The way the footings are penetrated into the soil and the type of footing that is used, influences the natural period of the structure. The connection between the soil and the legs

15 1-2 Requirements for the damping system 3 is partly responsible for the non-linear behaviour of the structure. It is difficult to obtain in which way the footing is connected with the soil. Therefore the influence of these nonlinearities on the stiffness and damping coefficient of the total structure is difficult to calculate beforehand [16]. The jacking system forms the connection between the leg and hull and is used to jack the hull to a higher or lower level. This connection causes a complex non-linear behaviour to the response of the jack-up structure and has significant influence on the stiffness of the total structure [8, 16]. Therefore the natural period of the jack-up platform is difficult to estimate and is dependent of these non-linearities. 1-2 Requirements for the damping system To be able to damp the response of a jack-up structure when it is excited in its resonance frequency, the stiffness, damping coefficient and mass of the primary structure has to be estimated. Since these parameters vary during the lifetime of a jack-up structure, an advanced damping system is required. This is illustrated by a simple example below. In this example below, I made a rough design of a Tuned Mass Damper (TMD) system for a widely used platform around the world, namely the GustoMSC CJ-46. The specifications of this platform can be found in Specifications GustoMSC CJ-46 jack-up platform. The mass on this platform changes significantly over time. The design procedure to obtain the optimal parameters of the TMD system is discussed in detail in Chapter 3 and will not be substantiated in this example. The jack-up platform is excited by a sinusoidal wave force and the stiffness and damping ratio of the platform is assumed to remain constant. Example 1 The GustoMSC CJ-46 is a three legged jack-up unit and is used in a maximum water depth of 375 ft. This platform has a rack and pinion jacking system and uses 18 motors on each leg to jack the platform to a higher level. From the previous it can be concluded that the whole platform has 54 pinions. When the jack-up hull is effectively jacked to a higher level, each pinion carries kg. It can be concluded that the total mass of the jack-up platform m 1 is roughly kg. According to the specifications the variable load in normal conditions of this platform is kg, which leads to an increase between 0 and approximately 30 % of the initial mass. The performance of an optimal designed TMD system on a jack-up platform with zero variable load is shown in Figure 1-2. In this example it is assumed that the damping ratio is 0.05 and the TMD mass is 3% of the primary mass. It can be concluded that the amplitude of the jack-up is approximately 47% of the case when no TMD is used. When the maximum amount of variable load is added to this weight and the TMD system is not adapted, the amplitude of the optimal response increases with 21%. This is shown in Figure 1-3. From this example it is concluded that significant performance degradation occurs when the TMD system is off-tuned due to the change in mass. In practice, the stiffness of the structure and the damping coefficient also variate during the lifetime of the platform. These parameters also contribute to off-tuning.

16 4 Introduction Figure 1-2: Optimal tuned TMD system for effective weight GustoMSC CJ-46

17 1-2 Requirements for the damping system 5 Figure 1-3: Off tuned TMD system for effective and maximum variable weight GustoMSC CJ-46

18 6 Introduction For lightly damped structures the natural frequency is close to the resonance frequency of the structure and is derived from the stiffness, damping coefficient and the mass of the primary structure. The following statements hold for the natural period of a jack-up structure [7]. The larger the water depth/airgap 1 /penetration, the larger the natural period. The larger the elevated weight, the larger the natural period. The larger the rotational soil resistance (fixity), the lower the natural period. The larger the legs (chord cross-sectional area and spacing), the lower the natural period. From these facts and the given example it can be concluded that the stiffness, damping coefficient and mass are not constant and therefore an advanced damping system is required to damp the oscillations of a jack-up structure when it is excited in its natural frequency. To optimally damp the vibrations of a jack-up platform these parameters of the structure have to be estimated. The estimation of these parameters is influenced by the non-linearities in the soil/leg connection and leg/hull connection and the exerted external loads on the jackup platform. A way to obtain representative values of these parameters is by performing a system identification on that specific platform on the location where it is installed. These parameters, however, change when e.g. the height or mass of the platform changes. Moreover load eccentricities also influence these parameters. During the life time of a jack-up platform the stiffness and damping coefficient of the structure changes. This can be caused by changed environmental conditions, degradation of material properties, mass changes, load changes, modification of construction etcetera. The behaviour of the platform will not act linear, due to all the non linearities in the structure. Therefore, the natural frequency of the platform is not fixed during its life time. Since the performance of a damping system deteriorates when it is off-tuned, the best performance can be achieved when the damping system can act to these variation of parameters. 1-3 Assumptions made in this thesis I assume that the jack-up structure can be modelled as a single degree of freedom structure. This assumption is valid due to the fact that most of the mass is concentrated on the top of the structure and the leg/top mass ratio is small. In the sequel of this thesis, this system will be called the primary system. The damping system is also modelled as a single degree of freedom system and consists of a mass, damper and a spring. The combination of the primary structure and the TMD system forms a two degree of freedom system, shown in Figure 2-2. The jack-up platform is exposed to wind, wave and current loads. Cassidy states that the influence of the wave load dominates the response of the platform and therefore it is allowed to neglect the wind and current loads [14]. In this thesis the waves are assumed to be sinusoidal forces. Their only aim is to excite the jack-up platform in the first natural frequency. This frequency is most likely to get excited 1 The distance between the bottom of the hull and the mean sea level.

19 1-4 Problem statement 7 Figure 1-4: A single degree of freedom model of a jack-up platform by wave forces and has the largest amplitude [12]. Other natural frequencies occur at higher frequencies and are neglected because the amplitude is smaller and the possibility that these frequencies are excited by waves are negligible. An example of the single degree of freedom jack-up platform is shown in Figure 1-4. In this figure the k v and c v represent the varying stiffness and damping coefficient. The mass of the platform is shown as m 1 and the exerted sinusoidal wave force on this mass is represented as p. The relative movement of the mass with respect to the ground is defined as x Problem statement The market trend toward heavier jack-ups being built to cope with deeper and harsher seas of operation, resulting in higher waves acting upon the structure. Therefore the problem can be stated as following. The response of a jack-up structure increases when it is excited in its resonance frequency due to the wave loads. The workability and the safety on the platform therefore decreases. The resonance frequency is dependent on varying environmental conditions and structural properties and therefore not constant over time. Siemens is interested in an advanced damping system to optimally damp this motion. The solution for this problem should be compact, robust and feasible to implement on a jack-up structure without large structural modifications. The aim of this thesis is to design an experimental TMD model which is able to control the stiffness and damping coefficient of the damping system, such that the motion of the primary system is optimally damped when it is excited in the natural frequency. This frequency is not constant and varies in time due to changes in mass, stiffness and damping coefficient of the primary system. The designed experimental model can be used to test and validate the damping performance of the damping system on the platform. 1-5 Outline This thesis is divided in two parts, namely the proof of concept and the design of an experimental model. In Chapter 2 the passive, semi-active and active TMD systems are discussed

20 8 Introduction and the appropriate damping system for a jack-up platform will be chosen. In Chapter 3 an introduction is given about the working principle of a TMD system and the general procedure to obtain the optimal parameters for the TMD system is shown, followed by an example of a TMD design for a GustoMSC CJ-46 jack-up platform. Chapter 4 presents the required control procedure which is needed to control the stiffness and damping coefficient of the semi-active TMD to their optimal values to damp the motion of the primary structure. In Chapter 5 of part 2 the design constraints and assumptions in the experimental model are discussed. These constraints and assumptions are then used in Chapter 6 to obtain the final design of the experimental model. At last in Chapter 7 an overall conclusion is drawn and proposals for further research will be given.

21 Chapter 2 Selection of the type damping system for a jack-up platform A damping system is used to damp the vibrations of a structure when it is excited in its natural frequency. There are various types of damping systems, such as Tuned Liquid Damper (TLD), Tuned Mass Damper (TMD) or Tuned Rotor Damper (TRD) systems. The working principle of all these dampers is the same. They absorb the energy of the primary system and then dissipate the energy eventually into heat. The choice of which damping system can be used is purely dependent on the physical constraints of the primary structure on which the damping system will be installed in. In this thesis I will use a TMD system. This system represents the damping procedure in the most fundamental way. The difference in the above mentioned damping systems is the way the damping can be controlled. The most simple and conventional TMD system is the passive configuration. A more advanced way to control a damping system is by using a semi-active TMD system. When total control of the damping system is required, an active TMD system can be used. These damping systems will be discussed in more detail in the sequel of this chapter [9]. 2-1 Passive TMD systems A passive TMD system is a damping system in its most primitive form. It consists of a spring, damper and mass with fixed properties and does not require an external power supply to function as damping system. The damping system is only tuned for one frequency of the primary system and can only perform optimally when a reliable estimate of the design loading and an accurate numerical model of the physical system is available. A passive control scheme often results in an over conservative design, which makes the damping system not as effective as desired when it is used in practice. The advantage of a passive TMD system is that it is simple, robust and relatively inexpensive compared to their more advanced variants. The disadvantage is that, when the tuning is not done properly, the performance of the TMD system decreases significantly. A way to solve this problem and to increase the performance,

22 10 Selection of the type damping system for a jack-up platform Figure 2-1: Performance increase by adding 11% extra mass in off tuned conditions is by using a larger mass. If I take the same example as shown in Chapter 1, the mass of the TMD system has to be increased with 11% to obtain the same performance in off-tuned conditions and damp the main structure below an amplitude of 0.5 m. This is illustrated in Figure 2-1. It is obvious that a larger mass on a jack-up structure is not desirable. In general the mass ratio of a passive damping system is larger than the mass of the semi-active and active TMD variants [17]. When self-weight is an important design constraint, it is not afforded to be over conservative. Therefore a semi-active and active TMD system provide a better solution to damp the response of the structure. An example of a passive TMD system is shown in Figure 2-2, when it is installed on a single degree of freedom system. Robustness A passive TMD is completely mechanically regulated. The damping system does not require any sensors, actuators or external power supply. It is tuned mechanically to the required frequency and is therefore robust. Since a passive TMD system can only generate a resisting force, it can only dissipate energy and can not add energy to the system. This makes the system always stable and unable to destabilize a stable primary structure. For these reasons the passive TMD system is the most robust solution, but has poor performance when it is not optimally tuned.

23 2-2 Semi-active TMD systems 11 Figure 2-2: An example of a passive TMD system Feasibility to scale the passive TMD system for a jack-up structure A passive TMD can be scaled to a real platform and does not require as much maintenance as the more advanced damping systems. As shown in the above mentioned example, the TMD mass has to be large enough, such that the damping system is also able to damp the primary system in off-tuned conditions. As mentioned in Chapter 1, the natural frequency of the jack-up platform changes, which increases the probability of an off-tuned damping system. Solving this problem by using a large TMD mass to satisfy the constraints is not desirable on a jack-up structure. Overview of required components are listed below. The main components to realize a passive TMD system TMD Mass Spring Damper It can be stated that this type of damping system require minimal amount of components. 2-2 Semi-active TMD systems The semi-active TMD system is a passive damping system which is able to change the stiffness and damping coefficient. These properties make the damping system therefore able to tune the parameters to their optimal values so that the response of the primary structure in the resonance frequency is optimally reduced. Adapting the stiffness and damping coefficient of the semi-active TMD system is done by using actuators to change these values mechanically. The required energy for the actuator is relatively small compared with the amount of energy

24 12 Selection of the type damping system for a jack-up platform Figure 2-3: An example of a semi-active TMD system the semi-active TMD is able to dissipate. This makes the semi-active TMD able to tune its parameters to their optimal values by using minimal external energy. The required energy to tune the damping system can be reduced more by only turning the actuators on, when the amplitude of the oscillation of the primary structure exceeds a certain threshold. After tuning the semi-active TMD to the optimal values, it will function as a passive TMD system. An example of this configuration on a single degree of freedom system is shown in Figure 2-3. Robustness The semi-active TMD only needs one position sensor to measure the horizontal displacement of the jack-up platform and relative small actuators to change the stiffness and damping coefficient. The energy requirement is therefore also minimal compared with the more advanced active damping system. Since a semi-active damping system is actually a tunable passive damping system, it also has the property that it can only deliver a resistive force. The semi-active damping system is therefore always stable and not able to destabilize a stable primary system. Due to the low energy demand of an semi-active damping system, it can also perform with energy from a battery. In case of a power failure, it can still perform on battery power. Even if the battery fails, it will function as a passive damping system. The previous mentioned facts make the damping system robust and safe. Feasibility to scale the semi-active TMD system for a jack-up structure A semi-active system requires an advanced variable stiffness mechanism and damping mechanism with actuators to change these values. These actuators require a minimal amount of energy to vary these values by e.g. opening valves. Therefore the most actuators are off-shelf products and do not need requirements. Since semi-active damping systems can adapt their parameters in off-tuned conditions, a smaller TMD mass is required than when a passive damping system has to achieve a similar

25 2-2 Semi-active TMD systems 13 Figure 2-4: An example of a variable orifice damper performance. An example of a variable damping mechanism and variable stiffness mechanism, which are used on full scale applications is shown below. Variable damping mechanism Variable orifice dampers. This type of damping system uses a controlled electromechanical valve to vary the resistance of the flow in the orifice of a conventional hydraulic fluid damper. An example of this device is shown in Figure 2-4. The required power to control this damper is typically 50 W and is capable of delivering large resisting force, e.g. 1 to 2 MN. These dampers can handle a large variation of damping coefficient cmax /c min = 200 and is widely used in large buildings and bridges to damp wind and earthquake vibrations. Controllable-Fluid dampers. The variable orifice dampers, have components which are mechanically connected to each other and can be a problem in terms of reliability and maintenance. Controllable fluid dampers, however, have the advantage that they do not contain moving parts except the dampers piston. The fluid used for this damper is Magnetorheological (MR) fluid and has the property to electronically change the viscosity of the fluid in milliseconds of time. These dampers withmr fluid have been shown to be tractable for large engineering structures. An example of such a damper is shown in Figure 2-5. This fluid can operate between -40 and 150 degrees Celsius and can be readily controlled with less than 50 W. The required voltage and current to control this system requires only a voltage of V and a current 1-2 A, approximately. Such power levels can easily be realized by batteries. Variable stiffness mechanism Active Variable Stiffness (AVS) An example of an AVS system is shown in Figure 2-6. This mechanism is also used as a variable orifice dampers, but has also the property to use it as a variable stiffness damper in combination with an on-off mode controller. A very high stiffness can be achieved

26 14 Selection of the type damping system for a jack-up platform Figure 2-5: An example of a damper with MR technology when the valve is closed, due to the compressibility of hydraulic fluid (primarily due to entrapped air) and has no stiffness when the valve opens. The disadvantage of this system is that it can not vary the stiffness continuously, between different states. Semi-Active Independent Variable Stiffness (SAIVS) An example of a SAIVS device is shown in Figure 2-7, [15, 19]. This device consists of four springs with constant stiffness (k e ) in a rhombus configuration. In this configuration (Θ) represents the angle between the springs and the horizontal x-axis. The SAIVS device is able to continuously and smoothly vary the stiffness of the system by changing this angle and thereby the aspect ratio of the rhombus. When the angle is equal to 0, the stiffness of the system is maximal and when the angle is equal to 90 degrees, the stiffness becomes minimal. The changing of the configuration is done by a linear actuator at joint 1, with relative low energy consumption. This variable stiffness mechanism is scalable and can be used with real time control on large TMD systems. The effectiveness of the SAIVS mechanism is comparable with the performance of an active TMD system. Overview of required components system are listed below: The main components to realize a semi-active TMD TMD Mass Variable spring stiffness mechanism Variable damping constant mechanism Two actuators with position feedback to control the variable spring and damper mechanisms Position sensor to measure the motion of a jack-up platform

27 2-2 Semi-active TMD systems 15 Figure 2-6: An example of a semi-active TMD system Figure 2-7: The working principle of a SAIVS device

28 16 Selection of the type damping system for a jack-up platform Computer This type of damping system requires more components than a passive damping system. The key difference is the use of an advanced variable damping coefficient and stiffness mechanism. 2-3 Active TMD systems An active TMD system is able to measure or estimate the present state of the structure and compare it with a desired state. When the estimated or measured state differs from the desired state, it can use a control force to minimize this difference. Offshore structures generally require large control forces in the order of a mega newton. The advantage of an active TMD is that it is able to outperform the passive and the semiactive TMD when the disturbance is perfectly estimated and when the actuator is strong enough to deliver the required power. An active TMD system can be used in three configurations, namely stand alone, in combination with a passive damping system or in combination with a semi-active damping system. The standalone configuration needs the largest power supply, but optimal control of the damping system and primary system is possible. To decrease the amount of energy supply, a force actuator can be combined with a passive TMD system. The actuator can correct the desired motion of the TMD system such that the desired motion is accomplished. The third configuration uses a force actuator in combination with the semi-active TMD system. This configuration has the advantage that the parameters of the stiffness and damping system are tuned to their optimal values and the force of the force actuator can be used to compensate any shortcomings of the semi-active systems to achieve a specific performance. The passive and semi-active TMD systems are only able to damp out the steady state response of a primary structure when they are excited by forced excitations. The control force of a semi-active damping system becomes larger when the velocity of the TMD system becomes larger. So when the velocity is small, the control force will also be small and the damping performance too. The only way to solve this problem is by adding an actuator to increase the velocity in the required direction, such that the desired performance is achieved. For this reason an active active TMD system can also damp the transient response of the primary structure and non-harmonic excitations. A active TMD system uses linear feedback to change the fundamental frequency and damping ratio of the primary system. The damping ratio is increased by velocity feedback and decreased by displacement feedback. For this reason velocity feedback is required when the aim is to decrease the structural response, when using active control. An example of the second configuration is shown in Figure 2-8. Robustness The disadvantage of an active TMD is that it is not as robust as the passive and semi-active TMD systems. This is caused by the fact that an active TMD system requires more sensors to estimate the current state. Since a jack-up structure is an offshore structure and is subjected to harsh weather conditions, not all sensors are able to function properly in these conditions.

29 2-3 Active TMD systems 17 Figure 2-8: An example of an active TMD system An active TMD system also requires a larger power supply, which results in large power generators and safety systems. These equipments require more space. It has to be also noted that an active damping system is able to make the primary system unstable as opposed to passive and semi-active damping systems. This is possible because energy is added to the primary system via an external power supply. An defect active TMD system can therefore magnify the jack-up response in stead of damping it. The disadvantage of an active TMD system is that it is relatively more expensive, complex and less robust compared to their passive variants. Feasibility to scale the active TMD system To control the motion of the primary structure, large linear force actuators are required. The widely available and extensively used force actuators can be divided into three groups based on the force generation mechanisms. In the sequel these groups will be discussed with their advantages and disadvantages [18, 4, 5, 3]. Hydraulic linear force actuators These systems have the highest force capacity of the linear actuator group in the order of mega newtons. Precise control of the movement and force can be achieved. However, the disadvantage of this type of system are the requirements for fluid storage system, complex valves and pumps to regulate the flow and pressure, seals and continuous maintenance. Durability of seals and the potential for fluid spills are critical issues. Hydraulic actuators are composed of many parts which are mechanically connected to each other and are therefore subjected to wear and breakdown. Electromechanical linear force actuators The motion of the electromechanical motor generates the force by moving the piston with a gear mechanism that is driven by a

30 18 Selection of the type damping system for a jack-up platform linear motor. The motion and force is controlled by the power input to the motor. These devices are often compact in size, environmentally safe and economical. The disadvantage is that they are composed of many parts which are mechanically connected to each other and are therefore also subjected to wear and breakdown. Electromagnetic linear force actuators These linear force actuators are driven by magnetic forces and are not subject to wear and are therefore theoretically more reliable. Other advantages are that they are compact, require low voltage and amperage and have fast response time. The disadvantage is that they are not yet capable of generating forces in order of mega newtons. Civil and offshore structures generally require large control forces in the order of a mega Newton. The hydraulic and electromechanical force generation mechanism require large energy supply, which eventually requires large amount of space and are therefore not suited for offshore use. Also the electromagnetic linear actuators are not suitable for offshore use, due to the fact that they can not produce the required force. Overview of required components listed below: The main components to realize an active TMD system TMD Mass Large force actuator Large power supply for force actuator Additional (variable) damper system Additional (variable) spring system Position sensor to measure the motion of jack-up platform Velocity sensor for control feedback Safety requirements (back-up power supply, brakes, sensors for safety) Computer It can be concluded that the amount of parts are more than for passive and semi-active TMD systems. This can in general be translated to more required space and less robustness. Figure 2-9 gives an overview of the different control strategies for damping systems. 2-4 Conclusion A jack-up structure is a part of the offshore industry where robustness, safety and space are of crucial importance. There are three levels of control which can be applied to damp the motion of a jack-up structure. A passive TMD system is the most robust solution and requires minimal components. Due to varying environmental conditions and structural properties, this way of damping is too conservative and results in large TMD mass to effectively damp the structures response in off-tuned conditions. These facts limit the use of a passive TMD damping system and therefore a more advanced and more optimal damping solution is required.

31 2-4 Conclusion 19 Figure 2-9: Various configurations to control a TMD systems (Con: controller, a: actuator, S:sensor) The active TMD system is able to maximally damp the response of the jack-up structure when the external forces and the model are estimated perfectly and the actuators of the TMD system are strong enough to deliver the required power. An active TMD system is not only able to damp forced excitations but also to damp the transient response. However, due to the fact that more components are required to obtain an active TMD system, which in general can be translated to more space requirements, and the fact that it is able to destabilize a jack-up platform, an active TMD system is not robust and safe and requires more space compared to its alternatives. A semi-active TMD system always absorbs energy from the primary system and is not able to destabilize the system. It requires slightly more components than an passive damping system but is able to tune its parameters such that it optimally damps the response of a jack-up structure. The required TMD mass is therefore small. By considering the above mentioned facts, it becomes clear that the semi-active TMD system is the most feasible, robust and compact solution to damp the oscillation of a jack-up structure, when it is excited in its resonance frequency.

32 20 Selection of the type damping system for a jack-up platform

33 Chapter 3 Tuned Mass Damper (TMD) system The first section of this chapter gives an introduction to the TMD system. This is followed by a general procedure to obtain the optimal parameters for a TMD system when in it is installed on a lightly damped primary structure. In the third section an overview of this procedure is given with an example of the design of a TMD system for a GustoMSC CJ-46 jack-up structure at the end. 3-1 Introduction to TMD systems A TMD system is used to damp the excitation of the primary system by dissipating its energy. In 1911, Frahm used the TMD principle to damp the rolling motion of ships and ship hull vibrations. Due to its great success, this theory was further explained by Ormondroyd and Den Hartog. Obtaining the optimal parameters for the damping system were further discussed by Den Hartog in 1940 in his book Mechanical Vibrations [6]. The initial theory was designed to find the optimal parameters for undamped primary structures which are excited by a sinusoidal excitation force. This theory is used by Tsai and Lin to find the optimal parameters for lightly damped structures [21] and is used to write this chapter. A jack-up platform has its mass primarily distributed on the top of the structure. Therefore a representative estimation of the behaviour of the jack-up platform can be obtained by modelling the structure as a single degree of freedom structure with a TMD system installed on top of the structure. The TMD system is most effective when it is installed at the position where the displacement of the primary system is the largest. For this reason the TMD should be placed at the top of the jack-up structure. An example of this system is given in Figure 3-1. The design of an optimal tuned TMD system requires three parameters of the primary structure, namely the stiffness coefficient (k 1 ), damping coefficient (c 1 ) and the mass (m 1 ). These parameters in combination with the external excitation force (p) on the primary structure determines the optimal parameters of the TMD system, which are the stiffness coefficient (k 2 ), damping coefficient (c 2 ) and mass (m 2 ).

34 22 TMD system Figure 3-1: An example of a passive TMD system To have a better understanding of the problem and to find the optimal parameters of the TMD system, these parameters are rewritten into new notations. These notations are defined in the sequel. Mass ratio The mass ratio is defined as the ratio of the TMD mass (m 2 ) and the primary mass (m 1 ) as shown in (3-1). In practice the mass of the TMD varies between 1% up to 10 % of the primary mass. m = m 2 m 1 (3-1) Natural frequency The natural frequency is the frequency in which the system will oscillate when no damping or driving force is involved. This means that when the system starts to oscillate it is not able to damp out and will oscillate infinitely in time, due to the absence of damping. This is only theoretically possible. The equation for the natural frequency is presented in (3-2), where ω n is expressed in rad s. ω n(j) = kj m j for j = 1,2 (3-2) Damped natural frequency In practice damping is always present. Therefore the natural frequency has to be adapted such that damping is included. The equation for the damped natural frequency is presented in (3-3), where ω dn is expressed in rad s.

35 3-1 Introduction to TMD systems 23 ω dn(j) = ω n(j) 1 ζ 2 j for j = 1,2 (3-3) Resonance frequency When a system is excited in the resonance frequency the system stores vibrational energy and is able to magnify the amplitude of the oscillation. The damping coefficient of the primary structure (ζ 1 ) determines the dynamic amplification factor of the static response. The dynamic amplification factor is shown earlier in Figure 3-3. The equation for the resonance frequency is shown in (3-4), where ω res is expressed in rad s. ω res(j) = ω n(j) 1 2ζ 2 j for j = 1,2 (3-4) A jack-up platform is a lightly damped structure, which means that these systems have a damping ratio between approximately 0.05 and 0.1, [7]. For example, when the natural frequency is equal to 1 Hz, the damped natural frequency for a system with ζ 1 equal to 0.1 is Hz and for the resonance frequency it is equal to 0.99 Hz. From these three equations it can be concluded that they are almost equal for lightly damped systems. Therefore in practice often the natural frequency is calculated in stead of the resonance frequency for these lightly damped systems. Damping ratio The damping ratio of the primary structure and the TMD are described in (3-5). There are three cases which can be distinguished for the damping ratio. The first case is when the damping ratio is smaller than 1, then the system is underdamped and the structural vibration will oscillate around the equilibrium position and eventually damp out. The second case is when the damping ratio is equal to 1, the system is then critically damped and will move towards the equilibrium position as fast as possible without any oscillation. The last case is when the damping ratio is larger than 1, then the system is over damped and the structure will move slowly to the initial condition without oscillation. An example of all three cases for a normalized transient response of a single degree of freedom system is shown in Figure 3-2. The x-axis represents the time and the y-axis shows the normalized response of the system. ζ j = c j 2 k j m j for j = 1,2 (3-5) When the damping ratio of the primary system and the TMD system is known, the equivalent damping ratio of the total system is described by (3-21). ζ eq = m ( 2ζ1 m + 1 ) 2 (3-6) 2ζ 2 The damping ratio of the TMD (ζ 2 ) system is an important tuning parameter to optimally damp the primary structure. Obtaining the optimal value of this parameter is discussed in the next section.

36 24 TMD system Figure 3-2: Effect of different damping ratio s on a normalized transient response Excitation force The force which is exerted on the primary mass is described by p and has a magnitude of ˆp with an excitation frequency of Ω. The force equation is shown in (3-7). p = ˆpe iωt (3-7) Excitation frequency ratio The ratio between the excitation frequency and the natural frequency of the primary mass is described by (3-8). When the ratio is equal to 1, the primary system is excited in its natural frequency and resonance occurs. This holds for an undamped primary system. When the structure is lightly damped the theoretical value of the excitation frequency will be slightly less than 1, due to the fact that the resonance frequency is lower than the natural frequency of the primary system. The magnitude of the response at resonance depends on the damping ratio of the primary system and is larger for lightly damped structures than for significantly damped structures. ρ = Ω ω 1 = Ω k1 m1 (3-8) Tuning frequency ratio The ratio of the natural frequency of the damping system and the primary system is noted as the tuning frequency ratio. The equation of this ratio is shown in (3-9). To optimally damp the primary structure, the tuning frequency has to be chosen properly. This will be discussed in the next section. f = ω 2 ω 1 (3-9)

37 3-2 General procedure to obtain the optimal TMD parameters for a damped primary structure 25 Optimal TMD parameters The aim of the damping system is to absorb the maximal amount of energy from the primary system and dissipate this energy via the damper. The excitation frequency of a TMD system should be tuned to a particular frequency so that when this frequency is excited, the damping system will resonate out of phase with the primary structure. Maximal energy dissipation is obtained when the TMD has a phase shift of 90 degrees with respect to the displacement of the primary structure at the resonance frequency. The optimal tuning frequency ratio (f) and damping ratio (ζ 2 ) is found by properly choosing the mass (m 2 ), stiffness (k 2 ) and damping coefficient (c 2 ) of the TMD. These values depend on m 1, k 1 and c 1 of the primary structure. It has to be noted that these values for the parameters are optimal when the primary system is a lightly damped structure, excited by a sinusoidal excitation force and the values for k 1, c 1 and m 1 are estimated correctly. This procedure will be discussed in the next section. 3-2 General procedure to obtain the optimal TMD parameters for a damped primary structure In this section the general procedure to obtain optimal tuning parameters for a TMD will be explained by using the theory of Connor, Tsai and Lin [4, 21]. The equations of motion of this system are defined in (3-10) and (3-11), where x 1 is defined as the relative displacement of m 1 with respect to the ground and x 2 is defined as the relative displacement of mass 2 with respect to mass 1. m 1 ẍ 1 + c 1 ẋ 1 + k 1 x 1 c 2 ẋ 2 k 2 x 2 = p (3-10) m 2 ẍ 2 + c 2 ẋ 2 + k 2 x 2 + m 2 ẍ 1 = 0 (3-11) The response of the primary structure and the TMD when it is excited by the wave force (p) can be described by equations in the form of (3-12). x j = x j e iωt for i = 1,2 (3-12) In these expressions x j describes the maximum response amplitude and can be found by substituting (3-12) into (3-10) and (3-11) and cancelling for e iωt. The equations which are obtained are complex and can be rewritten into polar form. By using the earlier described notations in Section 3-1 the equations for x j are represented in (3-13). x j = ˆp k 1 H j e iδj for i = 1,2 (3-13)

38 26 TMD system From this equation it can be noted that ˆp k 1 represents the static response of m j and the terms H j is defined as the dynamic amplification factor. In resonance the dynamic amplification factor is responsible for amplifying the static response of the corresponding system. The last term (e iδj ) represents the delay caused by the presence of the dampers. These dynamic amplification factors are described in more detail in (3-14) and (3-15). H 1 = [f 2 ρ 2 ] 2 + [2ζ 2 ρf] 2 D (3-14) H 2 = ρ2 D (3-15) D = {[ f 2 ρ 2 m+(1 ρ 2 )(f 2 ρ 2 ) 4ζ 1 ζ 2 fρ 2 ] 2 +4[ζ 1 ρ(f 2 ρ 2 )+ζ 2 fρ(1 ρ 2 (1+ m)) 2 ]} (3-16) δ 1 = α 1 δ 2 (3-17) ( ) 2ζ2 ρf α 1 = arctan f 2 ρ 2 ( ζ 1 ρ(f 2 ρ 2 ) + ζ 2 fρ(1 ρ 2 ) (1 + m)) δ 2 = arctan 2 f 2 ρ 2 m + (1 ρ 2 )(f 2 ρ 2 ) 4ζ 1 ζ 2 fρ 2 (3-18) (3-19) From the previous equation it can be stated that the dynamic amplification factors are functions of m, f, ρ, ζ 1 and ζ 2. Numerical simulations can be applied to evaluate H 1 and H 2 for a range of ρ given the values of m, ζ 1, zeta 2 and f. Starting with specific values for m and ζ 1, plots of H 1 versus ρ can be generated for a range of f and ζ 2. Each H 1 ρ plot has a peak value of H 1. The particular combination of f and ζ 2 that corresponds to the lowest peak value of H 1 is taken as the optimal state. Repeating this process for different values of m and ζ 1 produces behavioural data needed to design the damper system. Figure 3-3 shows the variation of the maximum value of H 1 for the optimal state. The corresponding response of the damper is plotted in Figure 3-4. The dynamic amplification factor for the primary system decreases when the mass ratio increases. This also holds for the dynamic amplification factor of the TMD system. From these figures it can be concluded that adding damping to the primary system has an appreciable effect for small m. By taking the ratio of the dynamic amplification factor of the primary system and the TMD, equation (3-20) is obtained. A plot of the dynamic amplification ratio by using (3-14) and (3-15) for different m and ζ 1 is shown in Figure 3-5. It is clear that a small mass ratio corresponds with large displacements of the TMD system and that the damping ratio of the primary system does not influence the dynamic amplification ratio, which is also verified by (3-20). H 2 H 1 = ρ 2 [f 2 ρ 2 ] 2 + [2ζ 2 ρf] 2 (3-20)

39 3-2 General procedure to obtain the optimal TMD parameters for a damped primary structure 27 Figure 3-3: Maximum dynamic amplification factor for single degree of freedom system Figure 3-4: Maximum dynamic amplification factor for TMD

40 28 TMD system Figure 3-5: Ratio of maximum TMD amplitude to maximum system amplitude When the damping coefficient of the primary structure is known and the optimal damping coefficient of the TMD is set, the equivalent total damping of the system is described by (3-21). This function is plotted in Figure 3-6 against the mass ratio for different damping ratios of the primary structure. It can be concluded that the use of a TMD increases the equivalent damping ratio effectively when the primary structure is lightly damped. ζ eq = 1 2H 1 opt (3-21) Tsai and Lin obtained equations for the optimal tuning frequency f opt and ζ opt determined by curve fitting of data from numerical simulations [21]. These equations (3-22) and (3-23), respectively, are only verified for ζ 1 between 0 and 0.1 and for m between 0 and 0.1. A plot of f opt and ζ opt against the mass ratios for different damping ratios of the primary structure is shown in Figure 3-7 and Figure 3-8. From Figure 3-7 it can be concluded that the optimal tuning frequency decreases when the mass ratio increases and that the optimal tuning frequency is strongly influenced by the damping ratio of the primary structure. By analysing the plot of the optimal damping ratio, it can be obtained that this parameter is less sensitive to the damping ratio of the primary structure and that it increases when the mass ratio increases.

41 3-3 Summary of procedure 29 Figure 3-6: Equivalent damping ratio for optimally tuned TMD m f opt = ( 1 + m + 1 2ζ1 2 1) ( (3-22) m m)ζ 1 m ( m m)ζ 1 2 m 3 m ζ opt = 8(1 + m)(1 0.5 m) + (0.151ζ ζ1) 2 + (0.163ζ ζ1) 2 m (3-23) The calculation of the required stiffness and damping coefficient is shown in (3-24) and (3-25). k 2 = mf 2 optk 1 (3-24) c 2 = ζ opt 2 k 2 m 2 (3-25) 3-3 Summary of procedure In this section a summary is given to design a TMD system for a lightly damped structure 1. This procedure requires an estimation of damping ratio of the primary structure and of the 1 Only verified for ζ 1 between 0 and 0.1 and m between 0 and 0.1

42 30 TMD system Figure 3-7: Optimum tuning frequency ratio for TMD Figure 3-8: Optimal damping ratio for TMD

43 3-4 Design example for a TMD system on a GustoMSC CJ-46 jack-up platform 31 maximum external force exerted on the structure and results in the required stiffness k 2 and damping coefficient c 2 to optimally damp the primary structure. 1. Step 1: Determine the damping ratio (ζ 1 ) of the primary mass. To obtain the damping ratio, an estimation of the mass, stiffness and damping coefficient is required. The required equation is shown in (3-5). 2. Step 2: Determine the static response of the system. The static response is calculated by dividing the maximum expected wave load (ˆp) by the estimated stiffness (k 1 ), as mentioned in Section Step 3: Determine the allowed maximal dynamic amplification factor of structures static response and the maximal dynamic amplification factor of the TMD system response and choose the appropriate TMD mass. The static response (step 2) is multiplied by the dynamic amplification factor when the structure is excited in the natural frequency. Calculate what the maximal dynamic amplification factor can be for your application. The required minimal TMD mass can then be derived from Figure 3-3. The corresponding dynamic amplification factor of the TMD systems static response is shown in Figure 3-4. When the displacement of the TMD system forms the constraint in your application, determine the required minimal TMD mass from Figure 3-4 to satisfy this constraint. The corresponding dynamic amplification factor of the primary structure static response is then shown in Figure 3-3. The use of the dynamic amplification ratio of the TMD system and primary structure shown in Figure 3-5 can ease this step. 4. Step 4: Find the optimal tuning frequency (f opt ) for the TMD. The required parameters for this step are the damping ratio (step 1) of the primary structure and the mass ratio (step 3). By using (3-22), the optimal tuning frequency ratio can be calculated. 5. Step 5: Find the optimal damping ratio (ζ opt ) for the TMD. The required parameters for this step are the damping ratio (step 1) of the primary structure and the mass ratio (step 3). By using (3-23) the optimal damping ratio can be calculated. 6. Step 6: Calculate the stiffness (k 2 ) and damping coefficient (c 2 ) of the TMD. By using (3-24) and (3-25) the required stiffness and damping coefficient of the TMD system can be calculated, such that the optimal tuning frequency ratio and damping ratio are met. 3-4 Design example for a TMD system on a GustoMSC CJ-46 jack-up platform In this example I will make a rough design of a TMD system for a widely used platform around the world, namely the GustoMSC CJ-46. The specifications of this platform can be

44 32 TMD system Dimensions (mm) Hull Dimension Length m Breadth 62 m Depth 8.0 m Table 3-1: Hull dimensions found in appendix A. Properties GustoMSC CJ-46 This jack-up platform is equipped with a drilling unit and is used in a maximum water depth of 375 ft. This platform has a rack and pinion jacking system and uses 18 motors on each leg to jack the platform to a higher level. From the previous it can be concluded that the whole platform has 54 pinions. When the jack-up hull is effectively jacked to a higher level, each pinion carries 215 tons. From this I conclude that the total mass of the jack-up platform M 1 is roughly kg. The natural period of a jack-up platform is between 6 to 11 seconds and the damping ratio is between 0.05 and 0.1 [7]. In the sequel I assume that the GustoMSC CJ-46 has a natural period of 10 seconds and a damping ratio of 0.05 %. The natural frequency is then equal to 0.1 Hz or rad s. Available space on the jack-up platform for the TMD system The hull dimensions of the jack-up structure are shown in Table 3-1. The deck shape can be simplified to a perfect triangle. The surface area then becomes equal to m 2. I assume that 5% of this space is available for the TMD system, which is approximately 100 m 2. Since the TMD system is moving in one direction, I assume that a reasonable breadth of the system is not more than 5 m, which result in a corresponding maximum length of 20 m. Procedure The design constraint for the TMD system is that the jack-up platform should not be able to have a displacement larger than 1 meter and that the total surface area of the TMD system should not exceed 100 m Step 1: Determine the damping ratio (ζ 1 ) of the primary mass. As previously mentioned, the damping ratio of the platform is 0.5 %. 2. Step 2: Determine the static response of the system. By using (3-2), the stiffness of the primary structure is approximately 4583 kn/m. Assuming that the maximal external wave load on the jack-up structure is 460 kn, results in a static response of the jack up structure of approximately 0.10 m. Assuming that the deformation of the jack-up legs are linear. 3. Step 3: Determine the allowed maximal dynamic amplification factor of the primary structure and the TMD system and choose the appropriate TMD mass.

45 3-4 Design example for a TMD system on a GustoMSC CJ-46 jack-up platform 33 I constraint the maximum amplitude of the hull displacement to 0.50 meter, which limits the dynamic amplification factor to 5. By using Figure 3-3 it can be concluded that a minimal mass ratio ( m) of 0.03 is required. The dynamic amplification factor of the TMD system becomes approximately 20. This means that the TMD system has to make a stroke of 2.0 m. 4. Step 4: Find the optimal tuning frequency (f opt ) for the TMD. The optimal tuning frequency ratio becomes 0.94 by using (3-22). 5. Step 5: Find the optimal damping ratio (ζ opt ) for the TMD. The optimal damping ratio becomes 0.11 by using (3-23). 6. Step 6: Calculate the stiffness (k 2 ) and damping coefficient (c 2 ) of the TMD. The required stiffness and damping coefficient of the TMD system is kn m, using (3-24) and (3-25) respectively. kns m and 46.6 Figure 3-9 concludes that the displacement of the jack-up platform is reduced more than 50 % by only using 3% of the primary mass. The displacement of the primary mass does not exceed the constraint of 1 m and the TMD mass is only moving approximately 4 m. However from Figure 3-5 the movement of the TMD should be approximately 20 times the static deformation of 0.2 m, which corresponds to a displacement of 2.0 m. The reason for this difference is explained by the fact that the optimal damping ratio and optimal tuning frequency ratio is obtained from curve fitting. The actual values can therefore differ slightly from the fitted value. The required TMD mass is kg. To have an indication of the size of this mass, it corresponds with a solid stainless steel block with a breadth of 5 m, a height of 2 m and a length of 4.42 m. The magnitude of this weight and volume is in the same or lower order of other equipment on board. A few examples are given below. Main deck pipe rack has a weight of kg. Cantilever pipe rack has a weight of kg. Fuel oil storage tank has a volume of 800 m 3. Drill water storage tank has a volume of 2000 m 3. Liquid mud storage tank has a volume of 740 m 3. Fuel oil storage tank has a volume of 800 m 3. Variable load in normal conditions on the CJ-46 is kg. These values are obtained from appendix A.

46 34 TMD system Figure 3-9: Damping performance of CJ-46 jack-up structure with a m of 0.03 and ζ 1 of 0.05

47 3-5 Conclusion Conclusion This chapter discusses the design of an optimal TMD system with a design procedure and an example at the end. By observing equivalent damping ratio in Figure 3-6 two important conclusions can be drawn about the use of a TMD system to damp the motion of the primary structure. 1. A TMD system is most effective for lightly damped structures. The lower the damping ratio of the primary system (ζ 1 ), the better the performance of the TMD. 2. The effectiveness of a TMD system decreases when the TMD mass increases. The slope of the equivalent damping ratio is the largest at a low mass ratio less and decreases until approximately 4 %. This slope remains constant for larger mass ratios. The design example showed that a realistic TMD system in terms of space and mass can be designed for a GustoMSC CJ-46 jack-up platform. The displacement of the jack-up platform (ζ 1 = 0.05) is decreased more than 50 % by only using a mass ratio of 3%.

48 36 TMD system

49 Chapter 4 Adaptive Control 4-1 Introduction to adaptive control A jack-up platform is a lightly damped structure and deals with varying mass, stiffness and damping coefficient over time. These changing parameter conditions has the consequence that the resonance frequency of the primary structure also becomes time varying, which is important to optimally damp the vibrations at this frequency. The variation of mass is primarily caused by storage of materials and fluids, which can increase the total nett mass of the platform by 30 %. The stiffness of the platform is primarily influenced by the installation height of the platform. Also stiffness degradation over time, eccentric load distribution (P ) effect and structure modifications causes variation of the platform stiffness in the sway movement. The damping coefficient is influenced by the water depth, leg-soil fixation, soil-hull connection and can be influenced by change in soil fixation and installation. It can be concluded from Chapter 2 that a semi-active Tuned Mass Damper (TMD) is most appropriate damping method for a jack-up platform. Chapter 3 presents the optimal tuning laws to optimally damp the primary structure when it is excited by harmonic excitations. By considering the above mentioned facts, it can be concluded that an adaptive type of controller has to be used, [22, 20]. These controllers can be divided in two categories, namely direct and indirect control methods. The direct method uses adjustment rules which tell directly how the controller parameters should be updated, [13]. This method requires direct measurements of the unknown parameters, which in our case are the mass, stiffness and damping coefficient. All these parameters can be measured by using appropriate sensors e.g. load cells, strain gauges and position sensors, respectively. However, the use of sensors are not desired, since they are vulnerable and need maintenance and modification of the legs for installation. Offshore structures require solutions which are robust and contain as less possible sensor elements. The more sensors a system uses, the higher the risk for malfunctioning.

50 38 Adaptive Control Therefore the preference goes to indirect control method. This method uses an adaptive control scheme based on recursive parameter estimation to estimate the unknown and slowly varying parameters of the system continuously. The specific type of adaptive control that will be used in this chapter is a Self-Tuning Regulator (STR), [2]. This control scheme is able to recursively estimate the unknown and slow varying parameters and use these information to optimally control the semi-active TMD system. This chapter uses a qualitative approach to design a control scheme which is able to optimally control the experimental model. The sequel of this chapter discusses the used control scheme. This is followed by defining an extensive description of a STR scheme with all the important elements. 4-2 The control scheme Considering the facts mentioned in Section 4-1, a control scheme is designed as shown in Figure 4-1. This control scheme is based on the STR principle. The plant represents the jackup platform with the semi-active TMD system. The input of the plant are the wave forces, which are the dominant excitation forces, compared with forces generated by currents and wind. The output of the plant represents the position and velocity of the primary structure and the TMD mass. These input and output data are send to the most important block of this control scheme, namely the Recursive Least Square Estimator (RLSE). This recursive estimator estimates the value for the stiffness and damping coefficient of the primary structure. These values and the mass of the primary structure, which can be obtained from platform measurements, are send to the optimal control law block. These laws are obtained in Chapter 3 and are used to calculate the required stiffness and damping coefficient for the semi-active TMD to optimally damp the platform. These optimal parameter are send to the controllers of the Adaptive Stiffness Mechanism (ASM) and Adaptive Damping Mechanism (ADM) blocks, which uses gain scheduling to regulate the adapting stiffness and damping coefficient. The STR part is indicated by the dotted line in Figure 4-1. This partitioning contains three indispensable elements for a STR, namely the estimator, control adjustment mechanism and the controller. This partitioning represents an adaptive controller scheme, which adjust the controller of the semi-active TMD system, when the structural parameters of the platform changes. This partitioning is also convenient due to the fact that the parameter estimator, control adjusting mechanism and controller are time shared. The STR can therefore perform in continuous adaptive control or batch adaptive control. Continuous adaptive control Since the structural parameters of a jack-up platform do not change instantaneously and are relative slow varying parameters a recursive continuous estimation process is preferred above batch estimation. The estimation is then based on more data samples and therefore results in a more accurate estimation. The time required to obtain correct estimates depends on the quality of the input signal and the amount of samples. The disadvantage of continuous estimation and tuning of the semi-active TMD system is that scattering can occur, if slight changes in optimal parameters arise. This problem can

51 4-2 The control scheme 39 Figure 4-1: Overview of used adaptive control scheme

52 40 Adaptive Control be solved by introducing a minimal required variation (minimum threshold) before tuning the parameters to the optimal values. Also the inverse can occur, large control action due to incorrect parameter estimates of the primary structure. Also these control actions can be limited by setting maximal variations (maximum threshold). Assumptions made in control design control scheme as shown in Figure 4-1. The following assumptions are made in using the It is assumed that the wave forces which act on a real platform and the corresponding response of the structure can be accurately measured. It is assumed that the jack-up platform is only excited by wave forces. It is assumed that the structural parameters of the platform vary relative slowly in time compared with the state variables. The waves are assumed to be periodic and persistently exciting. In the sequel of this chapter each of the blocks in Figure 4-1 are explained in more detail. 4-3 Self-Tuning Regulator A STR is composed by three main parts, namely a recursive parameter estimator, a controller and a controller adjustment block. There are different combinations possible to estimate the parameters and calculate the regulation parameters. In this thesis I combine a RLSE with gain scheduling in the controller of the ASM and ADM. The estimated parameters are treated as if they are true in designing the controller, known as the certainty equivalence principle. The choice of model structure and its parametrization are important aspects for a STR to obtain accurate estimations of the primary structure parameters. Also the input signal (waves) are of significant importance. A STR controller can only be used when a proper input signal, model structure and estimation algorithm is used. These topics are discussed in detail in the sequel of this section [11] Model structure The jack up platform including the TMD system can be simplified to a two degree of freedom structure and can be modelled by using first principle modelling. The simplified model and the corresponding equation of motion are presented in Chapter 3 and are, for convenience, repeated below. m 1 ẍ 1 + c 1 ẋ 1 + k 1 x 1 c 2 ẋ 2 k 2 x 2 = p (4-1) m 2 ẍ 2 + c 2 ẋ 2 + k 2 x 2 + m 2 ẍ 1 = 0 (4-2)

53 4-3 Self-Tuning Regulator 41 Figure 4-2: Simplification in a two degree of freedom model These equations contains six structural parameter, namely k 1, c 1, m 1, k 2, c 2 and m 2, which are the stiffness, damping coefficient and mass for respectively the primary structure and TMD system. The values of the parameters k 2 and c 2 are known from the gain schedule used in the semiactive TMD system. More details about the gain schedule will be explained in detail in the sequel of this chapter. The mass m 2 is a known predefined quantity and does not vary. The value of m 1 can be measured from load sensors, which are already installed in jackup structures. The force p are the excitation forces to excite the primary structure in the resonance frequency. The two unknown values that have to be recursively estimated by the estimator are the stiffness (k 1 ) and damping coefficient (c 1 ) of the primary structure. It is important for the Least Square Estimator (LSE) that a proper model structure is chosen Input signal It is obvious that parameter estimation can not take place if the primary structure is not excited. The input signal has to satisfy the condition that it is persistently exciting of order n and contains a signal which is larger that the order of the to be identified model. The definition of persistence excitation is as follows: An input signal u is persistently exciting or order n if the limits in (4-4) exist and the matrix C n is positive definite. 1 C n = lim t t c(0) c(1) c(n 1) t φ(k)φ T c(1) c(0) c(n 2) (k) =. k= c(n 1) c(n 2) c(0) Where c(k) are the covariances of the input as expressed in (4-4). 1 c(k) = lim t t (4-3) t u(i)u(i k) (4-4) i=1

54 42 Adaptive Control The input excitations has to be persistently exciting of order 6 to estimate all parameters. This correspond with a minimum input signal of 3 sinusoids. Each sinusoid is persistently exciting of order 2. However, since the amount of unknown variables is reduced to 2 parameters. A single sinusoid should theoretically be enough to estimate these values Recursive Least Square Estimation A RLSE is a real-time estimator and forms a key element in the STR scheme. In general an adaptive controller deals with continuously varying process parameters, so it becomes necessary to have an estimation method that updates the parameters recursively. An important criteria that has to be satisfied for using a LSE, is that the model has to be linear in the parameters. The transfer function from the input to the output can be rewritten into discrete time as (4-5). y(t) = a 1 y(t 1) a 2 y(t 1) a n y(t n) + b 0 u(t d 0 ) + + b m u(t d 0 m) (4-5) As can be seen from this equation, the model is linear in the parameters and can therefore be written into regression form (4-9), by using the definitions for θ T and φ T as shown in (4-6) and (4-7) in which d 0 is equal to n m. In these equations φ contains the regression variables and θ contains the parameters. θ T = [a 1 a 2... a n b 0 b 1... b m ] (4-6) φ T = [ y(t 1)... y(t n) u(t d 0 )... u(t d 0 m)] (4-7) ( t 1 P (t) = φ(i)φ (i)) T (4-8) i=1 y(t) = φ T θ (4-9) The cost function which has to be minimized is shown in (4-10), where y(i) presents the observed values and ŷ(i) presents the estimated values. The parameters in θ should be chosen in such a way that this function is minimized. V (θ, t) = 1 t (y(i) ŷ(i)) 2 = 1 t (y(i) φ T (i)θ) 2 (4-10) 2 2 i=1 i=1 The RLSE estimates of the unknown parameter values are based on earlier measurement in time. The estimation method which is used in this thesis is the so called, exponential forgetting factor method. This method is ideal for slowly time-varying parameters relative to the structures behaviour. Equation (4-10) can then be rewritten to (4-11).

55 4-3 Self-Tuning Regulator 43 V (θ, t) = 1 t λ t 1 (y(i) ŷ(i)) 2 = 1 t λ t 1 (y(i) φ T (i)θ) 2 (4-11) 2 2 i=1 i=1 The parameter λ in this equation has a value between 0 and 1. The most recent data is given a weight equal to 1 and data which is n time units old is weighted by λ n. The memory (N) on which the estimation is based is expressed in (4-12). N = 2 1 λ (4-12) When this process is used recursively, the following equations have to be used to estimate the unknown parameters ˆθ(t) recursively, based on the forgetting factor method. ˆ θ(t) = ˆθ(t 1) + K(t)(y(t) φ T (t)ˆθ(t 1)) (4-13) K(t) = P (t)φ(t) = P (t 1)φ(t)(λ + φ ( T )(t)p (t 1)Φ(t))) 1 (4-14) P (t) = 1 λ (I K(t))φT (t)p (t 1) (4-15) Parameter validation To conclude whether the parameters are well estimated, a first observation can be made by looking at the percentage error as expressed by equation (4-16). When these values are small, it indicates that the parameters are well estimated. ɛ = y(i) φt (i)θ y(i) (4-16) A second validation can be obtained by looking at the covariance matrix P (t). The values on the diagonal of this matrix represent the variance of the estimated parameters. When these variances are relatively small compared with the estimated value, it means that the parameter is a good estimate of the actual parameter. However, it has to be noted that this conclusion is based on one-step-ahead predictor. When the error or the variance is large, it indicates that the chosen model structure is not rich enough to estimate the plant or that the input signal is not sufficiently exciting the system Optimal tuning laws The estimated values for the stiffness (k 1 ) and damping coefficient (c 1 ) and the measured mass (m 1 ) are used to obtain the optimal tuning frequency ratio using (3-22) and the optimal damping ratio (3-23) as shown in Chapter 3. The optimal stiffness and damping coefficient values of the TMD can easily be derived as shown in (3-24) and (3-25).

56 44 Adaptive Control Figure 4-3: ASM control scheme Figure 4-4: ADM control scheme Control adaptive stiffness and damping coefficient The required stiffness and damping coefficient are realized by the controllers of the ASM and ADM, respectively. These two systems are shown in Figure 4-1 as ASM and ADM. The control procedure of both blocks are shown in more detail in Figure 4-3 and Figure 4-4. Gain scheduling The used ASM and ADM for the experimental model is explained in detail in the next chapter. Both systems can adapt the stiffness and damping coefficient by simply controlling the motor shaft. The rotation angle of the motor shaft is denoted as Θ. The stiffness and damping coefficient of the ASM and ADM can not be measured during the process and is therefore not able to perform as a control parameter. To control the stiffness and damping coefficient of both mechanisms during the damping process, the non-linear transfer functions of stiffness and damping coefficient has to be translated to a measurable and controllable value (Θ) by performing gain scheduling. This scheduling can be regarded as a mapping from process parameters to controller parameters, e.g. a certain stiffness or damping coefficient is then related to a certain measurable angular position (Θ) of the motor shaft. The control of the ASM and ADM then becomes a reference tracking process and can easily be performed by using PID controller. The PID controller minimizes the error between the reference angle (Θ ref ) and measured angle (Θ m. Also certain thresholds can be set, to avoid scattering (minimum threshold) or large control forces (maximum threshold). The obtained angle (Θ) can then be transformed to a stiffness or damping coefficient value by using the non-linear inverse relationship of the gain scheduling. These values k 2 and c 2 are used for further recursive estimations of parameter k 1 and c 1.

57 4-4 Conclusion and Discussion 45 The gain schedule for the required stiffness and damping coefficient of the adaptive semiactive TMD to the control variable (Θ) can be obtained by performing experiments in all the expected operation conditions. This results in a gain schedule with a specific angle Θ for a specific stiffness k 2 or damping coefficient c 2. The advantage of using gain scheduling is that fast control can be achieved for non-linear systems, since all values are predefined. However, the disadvantageous is that making a gain schedule is a time consuming task. The values have to be obtained and verified by experiments and simulations. 4-4 Conclusion and Discussion This chapter discusses the use of an indirect adaptive controller in combination with a semiactive TMD system and the optimal control laws. The control scheme that has been used is a STR, which estimates the unknown and slow varying parameters by using the RLSE principle. The obtained estimations are then used to find the optimal TMD parameters, by using the optimal tuning laws, to optimally damp the response of the primary structure. By gain scheduling the non-linear stiffness and damping functions of the ASM and ADM, a simple PID controller becomes sufficient to control the stiffness and damping mechanism. This control procedure will always optimally damp the response of the primary structure when it is excited in the natural frequency, even if the structural properties of the primary structure changes. It has to be mentioned that this control approach does not account for non-linear behaviour of the primary structure. The consequence of this behaviour are incorrect recursive estimates of the primary structure parameters. However, the platform is inherently stable, which means that incorrect estimations can not destabilize the platform in all cases and has the only consequence of less semi-active TMD performance.

58 46 Adaptive Control

59 Chapter 5 Design of the experimental model In this chapter of my thesis a quantitative experimental model will be designed, discussed and presented in SolidWorks. The aim of building this model is to test and validate the performance of the semi-active Tuned Mass Damper (TMD) system on a jack-up platform model. The test considers the variation of stiffness and mass of the primary structure. The damping ratio is constrained to be between 0.05 and 0.1, such that the primary system satisfies the conditions for a lightly damped structure. The experimental model is not a scale model of an actual jack-up platform. It simulates the dynamical behaviour of a lightly damped structure with a similar mass distribution as an actual platform. This chapter starts with specifying the design constraints. These constraints are then used as guidelines for the final experimental model. This chapter divides the experimental model into two subsystems, namely an experimental model for the jack-up platform and the semi-active TMD damping system installed on top of it. The calculations of the design specifications and the expected response of these subsystems are followed by choosing the appropriate sensors, actuators and the required additional components to complete the test set-up. The final design is obtained by performing several design iterations, such that the dimensions, weight and specifications of each subsystem are scaled to each other and form an entity. The final model is extensively illustrated at the end of this chapter. The full specifications of the main components and their manufacturers are attached in appendix B. The actual building of the experimental model falls beyond the scope of this thesis. This chapter includes the design and calculation of a quantitative model, a part list of all the required components and their manufacturers and a visualisation of the final design in SolidWorks. 5-1 Design constraints The total system is designed as a two degree of freedom system and built to optimally damp the vibrations of the primary structure in the resonance frequency. The dominant force, responsible for these excitations, is the wave force acting on the primary structure. The

60 48 Design of the experimental model design of the experimental model is bounded by constraints. These are listed by mentioning the most important constrain as first and the less important constrain as last. Time The available time to design the experimental model in my graduation thesis is 3 months. This period includes the following deliverables. Design and calculation of the quantitative model Part list of the required components and their manufacturers Visualization of the final design in SolidWorks Damping ratio The experimental model should be a lightly damped structure. Jack-up structures which are widely used around the world have a damping ratio between 0.05 and 0.1. Standard components Due to the short time constraint and due to the fact that this is a prototype model, my preference goes out to use standard off shelf products. Custom made products have a long delivery time, are often several times more expensive than standard components and last but not least require more time before it actually satisfies the required specifications. Considering these points, it is important to think in using standard components to test and validate the performance of a semi-active TMD system on a jack-up platform. The second step is to adapt the prototype model by using more custom made products, if necessary, such that a more accurate model is achieved. Dimensions The experimental model is not a scale model. The aim is to design the model as small as possible, while satisfying the constrain to use standard components. This forms the lower bound for the dimension constrain. The model will eventually be placed in an office or on demonstration stands. Therefore I have constrained the upper bound such that it does not exceed a volume of approximately 0.5 m 3. Weight The weight of the model is an important aspect. The mass should be large enough such that non-linearities, stiction and undesired friction in components do not dominate the response of the system. In general the friction coefficient and non-linear behaviour play a larger roll in small models than in large models. The mass of the semi-active TMD is a constant and the aim is to use 5 % of the primary mass. Higher mass ratios are undesired for implementation in jack-up structures and lower mass ratios result in not realizable displacements of the TMD mass, see Section 3-2. Resonance frequency of the primary structure The natural period of a jack up platform is low and for a modal platform it varies between 6 and 11 seconds. This corresponds with a resonance frequency between 0.17 Hz and 0.09 Hz. From this fact, it can be concluded that the resonance frequency of a jack-up platform is very low. Therefore the resonance frequency of the experimental model should be chosen as low as possible, but high enough such that the primary system contains enough energy such that the TMD system is able to absorb this energy and damp the motion. If the resonance frequency is too low, friction (in particular

61 5-2 Primary structure design 49 stiction) will dominate the behaviour of the system. The experimental model will not be able to demonstrate the performance of the semi-active damping system. An initial guess, based on simple experiments, is that a system which has a resonance frequency at 1 Hz should contain enough energy to demonstrate the performance of the semi-active damping system. Maximum displacement of the primary structure The use of standard components has a high priority, resulting in a minimal size of the model. The critical parts, e.g. dampers with variable damping coefficient, are not small and therefore form the lower bound for the size of the experimental model. The maximum displacement of the primary structure should be in proportion with the size of the model. Since I have indicated that the maximum size of the model should be smaller than 0.5 m 3, the aim is to design the primary structure such that the total stroke of the structure is approximately 25 mm, when it is excited in its resonance frequency. It is important that the excitation amplitude should stay within the linear elastic behaviour of the primary system. As shown in the previous part, the semi-active TMD system should be able to damp this motion to approximately 47 % of the initial amplitude of 5 cm for a lightly damped structure with ζ 1 = 0.05 and m = The experimental model will be designed in the sequel of this chapter by considering the above mentioned design constraints. 5-2 Primary structure design This model is only interested in damping the motion of the lightly damped jack-up structure in one direction, namely the sway movement. All other movements are constrained. The model also includes the mass distribution of an actual platform in which the mass is primarily concentrated at the top of the structure. Next to these requirements the model should also be able to simulate the variation of mass and stiffness of the primary structure and have a damping ratio between 0.05 and 0.1. This section is divided in four subsections, namely the adaptive stiffness mechanism, adaptive damping mechanism, additional of mass on the primary system and the modal exciter Adaptive stiffness mechanism A jack-up structure is a tall structure with the mass concentrated at the top. Since the behaviour of the jack-up structure in one direction is of interest in this thesis, this system can be simplified to a structure as shown in Figure 5-1. In this figure m 1 represents mass of the primary system, E is the elasticity modulus of the used material, I is the moment of inertia of each slab, p is the external force acting on the system and x 1 represents the lateral displacement of the primary mass with respect to the equilibrium point. The legs of this structure are assumed to be rigidly clamped connected to the primary mass and the ground. Also the mass at the top is assumed to have infinite amount of stiffness and is therefore not able to bend. Section 3-1 shows that the difference between the natural, damped natural and resonance frequency for lightly damped structure is negligible. The aim is to design the primary structure, such that it has a natural frequency at 1 Hz (6.28 rad /s).

62 50 Design of the experimental model Figure 5-1: Simplification of a jack-up structure Dimensions (mm) Nominal length (L) 733 Thickness (h) 2 Width (b) 100 Table 5-1: Dimension legs of experimental model The material that will be used for the legs is stainless spring steel (RVS 301). This type of material has the property to store energy for relative large deformations and does not rust. The E-modulus of this steel type is 195 MP a. The equation to calculate the total stiffness k s of the structure is shown in (5-1). k s = 24EI L 3 (5-1) The moment of inertia is calculated in (5-2), where h is thickness, b is width, L is length. I = 1 12 bh3 (5-2) The mass of the primary structure (m 1 ) is constrained to 20 kg. The corresponding total stiffness of the structure to obtain a natural frequency ((3-2)) of 1 Hz, becomes 802 N /m. By using (5-1) and (5-2) the parameters h, b, L can be chosen such that the required stiffness of the structure is achieved. By considering the dimensions of the installed parts on the primary system and common size steel thickness s, the final leg dimensions, as shown in Table 5-1, satisfy the required stiffness. By observing equation (5-1), the most effective parameter to adapt the stiffness is the length of the legs. The variation of the natural frequency is shown in Figure 5-2 for a range of effective lengths. It can be concluded that the relation between the natural frequency and the effective length of the legs can be assumed linear for this small range. The nominal length corresponding to a frequency of 1 Hz is approximately 733 mm. A natural frequency of 1.1 Hz

63 5-2 Primary structure design 51 Figure 5-2: Influence of effective leg length on natural frequency of structure corresponds with an effective length of 688 mm and a frequency of 0.9 Hz corresponds with an effective length of 787 mm. These values can be used to test and validate the performance of the semi-active TMD system against variation of stiffness of the primary structure. The mechanism to change the stiffness of the primary structure is shown in Figure 5-3. A modified jack is used to clamp the legs of the primary structure at a certain position such that the effective length of the legs can be changed. The jack is powered by a Nanotec SC4118 stepper motor with an integrated encoder for position feedback. More details about the stepper motor, encoder and control device are discussed in the fifth section. Buckling load Since the total mass of the system rests on two legs, a simple calculation can verify if the legs are strong enough to hold the total mass without buckling due to the static load. The equation to calculate the load when a single steel slab buckles when it is rigidly clamped at both sides is presented in (5-3). F buckling = ( 4π 2 ) EI L 2 (5-3) This equation states that the maximum static load both slabs can carry is approximately 1926 N, before buckling. A mass of 21 kg (m 1 and m 2 ) corresponds with a gravitational load

64 52 Design of the experimental model Figure 5-3: Adaptable stiffness mechanism for the primary structure of approximately 206 N. Since the maximum static load is more than 9 times larger than the actual static load, it can be assumed that the slaps will not buckle during the process Additional structural damping A jack-up platform is a lightly damped structure, which has a damping ratio between 0.05 and 0.1 [7]. The total damping coefficient of the primary structure can be expressed as (5-4). c tot = c s + c add (5-4) In this equation c s presents the structural damping coefficient and forms an uncontrollable amount of damping. Structural damping is caused by the following energy dissipating factors. Drag force of air. Friction between components. Material damping. Since the structural damping coefficient of the experimental model is unknown and can be best approximated by experiments, a variable viscous dash-pot damper (c add ) is added to the structure at a height of the primary mass (m 1 ). By manually adapting the valve on the dash-pot damper the damping coefficient of the total structure can be increased, such that a damping ratio between 0.05 and 0.1 is guaranteed. Dampers with the ability to adapt the damping coefficient are used for industrial use and have a large initial damping coefficient, which makes it not useful for relative small experimental models. Most of these dampers, can only adapt its damping coefficient at static conditions and

65 5-2 Primary structure design 53 Figure 5-4: Adaptable damping mechanism for the primary structure thus not continuously during the process. However, a company called Airpot makes precision dash-pot dampers which are able to mechanically adapt the damping coefficient by manually controlling a valve. The size of these dampers constrain the design of the experimental model, because these dampers are the only dampers to use for relative small systems. Apart from the fact that these dampers are rare, they operate with superior accuracy and have little to no friction between moving the moving parts. These dampers use air as damping medium to damp the vibrations. The used damper for this purpose is an Airpot 2K95 damper. The main properties of the damper is that it can add a damping coefficient between approximately 0 Ns /m and 350 Ns /m and has almost no stiction. It also has a 15 degree of rotational freedom to compensate for miss alignment and can be delivered with a customized stroke of 50 mm and an initial length of 70 mm. The used damper can deliver a damping force for pull and push damping up to 4.45 N. The location at which the damper is installed is shown in Figure Modal exciter To simulate the waves, which are primarily responsible for exciting the platform in the resonance frequency, a modal exciter can be used. This device delivers a certain amount of force at a specified frequency and is responsible for the maximal force (ˆp ) for the static displacement ˆp /k, as discussed in Chapter 3. By exciting the system in the resonance frequency, the

66 54 Design of the experimental model Figure 5-5: Definitions static displacements of leg by modal exciter static displacement ˆp /k is multiplied by the corresponding dynamic amplification factor (H 1 ). The modal exciter should be placed as low as possible, since the aim is to damp the primary system and not the modal exciter. This exciter is then able to amplify the static displacement of the structure, without being a mechanically constrain to the amplitude of the response. Equation (5-5) describes the relation between the required maximum force (ˆp) exerted by the modal exciter to obtain a static displacement of x ex at a height L ex. x m = ˆpL3 ex 24EI (5-5) By using Figure 3-3 it is shown that when using a mass ratio of 5 % and a damping ratio of 0.05, the dynamic amplification factor (H 1 ) is maximally 5 and becomes smaller for higher damping ratios and is almost constant for all mass ratios larger than By assuming a linear deformation between L ex = 146mm and L m1 = 730mm, as shown in Figure 5-5, a static displacement of 0.5 mm at point L ex is required such that the static response at L m1 becomes 2.5 mm and the dynamic response at point L m1 is approximately 12.5 mm. The total stroke of the primary mass m 1 then becomes 25 mm. The modal exciter should therefore be able to produce a force of 50 N with a peak to peak stroke of 1 mm at a frequency of 1 Hz, using equation (5-1). These requirements are satisfied by a TMS 2025E modal exciter and will be placed as shown in Figure 5-6 at a height of 146 mm from the jack surface. The modal exciter is placed on the jack such that the distance between the exciter and the jack is always constant (L ex ). The required force becomes independent

67 5-3 Semi-active TMD system design 55 Figure 5-6: Placement of the model exciter, stinger, load cell and stepper motor of jack of the jack height. This would not be the case if the jack and the model exciter were placed independently. To support the stinger during variation of jack height, a guiding mechanism is used as shown in Figure 5-7. This mechanism restricts the stinger to bend in vertical direction, during variation of jack height and allows to excite in horizontal direction. Stinger A stinger is a thin and flexible rod and is used by the modal exciter to transmit the force in the stiff axial direction and flexes laterally to reduce input side loads to the structure. The stinger also isolates the undesired dynamic behaviour of the model exciter. This uniaxial force therefore increases the accuracy of the measurement. The stinger is also shown in Figure Semi-active TMD system design The resonance frequency of the primary structure depends on the mass, stiffness and damping coefficient. The semi-active TMD should therefore be able to sense these changes and have a mechanism to adapt its own stiffness and damping coefficient, such that it always optimally damps the vibrations of the primary structure, when the structure is excited in the resonance frequency. The design of the adaptive stiffness mechanism and adaptive damping mechanism is discussed in the sequel.

68 56 Design of the experimental model Figure 5-7: Support of stinger during jack height variations Figure 5-8: Parameter definition coil spring Adaptive stiffness mechanism A method to build an adaptive stiffness mechanism is by adapting the active amount of coils of a spring [1]. This system requires a linear coil spring and a mechanism to change the amount of active coils. The equation to calculate the stiffness is shown in (5-6). In this equation n represents the number of active coils, r is the radius of the spring, d is the diameter of the spring wire and G is the shear modulus. These parameters are shown in Figure 5-8. k 2 = 64nr3 d 4 G (5-6) An example of the adaptable stiffness regime by varying the amount of active coils is shown in Figure 5-9. This spring has a minimal stiffness 40 N /m of and a maximal stiffness of 150 N/m, by varying approximately 190 coils. This spring has a wire diameter of 0.8 mm, a radius of 4 mm and is made from stainless spring steel (RVS302) with a shear modulus of 69 GP a.

69 5-3 Semi-active TMD system design 57 Figure 5-9: Example of stiffness range of a spring by adapting the amount of coils By calculating the required maximum and minimum amount of stiffness and the available space for the amount of coils, a spring can be made by selecting the radius of the spring and the diameter of the spring wire such that the spring is able to cover the required stiffness regime. It is important to note that a minimal amount of coils is required, to guarantee a linear spring stiffness characteristic for a constrained extension of 50 mm, see Section The most simple way is by gauging the spring characteristics for an extension of 50 mm and find the minimal amount of active coils to obtain a linear characterized force-extension curve for this amount of extension, without plastic deformation. In the sequel it is assumed that a coil spring is able to minimally extend a length equal to the length of the spring in rest, without plastic deformation. This assumption is based on a simple experiment with a random coil spring. The implementation of the described adaptive spring stiffness mechanism in the semi-active TMD system, without extending the spring, forms a complicated task. When an ordinary mechanism is used to change the amount of active coils is, it results in an extension of the spring. This is caused by the fact that the coil selector and motor is fixed on the fixed surrounding and rotating the coil selector then results in an extension of the spring by x n. This is simply illustrated in Figure The undesired extension causes an initial undesired

70 58 Design of the experimental model Figure 5-10: Ordinary mechanism to adapt the amount of coils force F 0 = k 2 x n on the TMD mass. required. To avoid this, a more complicated mechanism is To explain the working principle of this mechanism in detail, the parts are indicated by the numbers (1 to 7) and distances in letters (A to E) as shown in Figure 5-11, Figure 5-12 and Figure Distance (A) represents the minimal length of the spring, this length should guarantee the linear behaviour of the spring characteristics. Distance (B) represents the space to adapt the stiffness. Shaft (5) is a threaded shaft and can move freely through the spring. This shaft is only horizontally fixated at point (4) by a rotational sliding contact with the spring and by threads in block (1). By rotation shaft (5), through component (1), the effective length of the spring can be selected. A minimal stiffness configuration is obtained when point (4) is positioned at a distance (A+B) and a maximum stiffness is obtained when point (4) is positioned at a distance (A). The thread in part (1) in which shaft (5) rotates, should have the same thread as the used spring. Distance (D) is required to move the shaft through the spring and block (1). This distance is equal to distance (B). This will result in adapting the stiffness of the spring without extending the spring. Finally shaft (5) is rotated by a smaller shaft (2) by using a key-way and component (6). This mechanism makes it possible to rotate shaft (5) through the thread in block (1), while shaft (2) slides into shaft (5). This mechanism is shown in Figure The configurations of shafts (2) and (5) at minimal and maximal stiffness configuration, are shown in Figure 5-14 and Figure 5-15, respectively. Shaft (2) is driven by a stepper motor, which is fixed to the platform. This construction has the advantage of adapting the amount of coils, without the need to extend/compress the spring or enabling the actuator to move along the axis. To control the rotation of shaft (2) and thus (5) a stepper motor, including a position encoder and motor controller, is used. These parts are explained in the fifth section Adaptive damping mechanism A semi-active TMD requires an adaptive damping mechanism to optimally dissipate the energy of the primary system. The used damper is an Airpot precision dash-pot damper. The adaptability of the damping coefficient can be controlled by using a stepper motor with a stepper motor controller. These components are discussed in detail in the sequel. Continuously adaptable dampers An Airpot damper uses air as damping medium and can therefore deliver small damping forces, which is ideal for small scale models. The used damper

71 5-3 Semi-active TMD system design 59 Figure 5-11: Adaptive stiffness mechanism for semi-active TMD Figure 5-12: Definition of distances and components of the adaptive stiffness mechanism

72 60 Design of the experimental model Figure 5-13: Mechanism to adapt the stiffness without extending the spring Figure 5-14: Position shaft (2) and (5) in the minimal stiffness configuration

73 5-3 Semi-active TMD system design 61 Figure 5-15: Position shaft (2) and (5) in the maximal stiffness configuration to dissipate the energy from the primary system is an Airpot 2K95 damper and is able to adapt its damping coefficient between approximately 0 and 350 Ns /m. The Airpot 2K95 stock damper has a maximum stroke of 50 mm and forms the most important constrain in the design of the semi-active TMD system for the experimental model, due to its rareness. Airpot delivers push, pull and push & pull dampers. The damping characteristics of push damping and pull damping are different, due to the fact that air is a compressible medium. Push damping compresses the air before it leaves the cylinder, while pull damping only sucks the air into the cylinder. To avoid individual complicated control for push and pull damping, only pull damping is used for each direction. This results in a damping mechanism as shown in Figure Each damper has a screw at one side of the damper to adapt the damping coefficient. By connecting a stepper motor to this screw, the damping coefficient becomes controllable. In Figure 5-17 it can be seen that the semi-active damping mechanism is used twice, but in opposite directions. To solve the problem of using continuous pull damping in both directions and at the same time maintaining a compact design, an additional mechanism is required. The total length of the green wire, shown in Figure 5-26, is constant and runs all the way from one side of the TMD mass through plate A and B back to the other side of the TMD mass. By adding a restriction on the wire on the right side of plate A and on the left side of plate B, the TMD mass always exhibits continuous pull damping, during the excitation of the semi-active TMD system. I assume that plates A and B have negligible rotation during the damping process at 1 Hz.

74 62 Design of the experimental model Figure 5-16: Adaptive damping mechanism for semi-active TMD Figure 5-17: Guarantee continuous pull damping in both directions

75 5-4 Addition of mass on the primary system 63 Figure 5-18: Mounting pins for additional mass slabs 5-4 Addition of mass on the primary system The addition of mass can easily be performed by adding solid mass slabs on both sides of the primary structure. These slabs can be mounted on the pins, as shown in Figure The maximal variable load of an actual jack-up platform is approximately 30 % of the nett jack-up mass. The primary mass of the experimental model is 20 kg, which means that the variable added load should be 3 kg at each side of the platform. 5-5 Stepper motor and controller The adaptive stiffness and damping mechanism is controlled by using stepper motors in combination with a stepper motor controller. Stepper motors are widely used in accurate positioning control in servo configuration. This type of motor is characterized by the large torque delivered at static conditions. A stepper motor is controlled by providing the number of steps it has to perform. The disadvantage is that a stepper motor is able to skip steps without noticing it. By adding an encoder to the system, a servo configuration is obtained. The stepper motor can then perform in closed loop configuration and will not be able to skip steps. It has to be noted that this only holds for the case when the stepper motor is powerful enough to deliver the required amount of torque. An important selection criteria therefore becomes the required amount of torque the stepper motor can deliver at a certain speed and the number of steps per revolution. By measuring the amount of torque required to adapt the valve of the Airpot damper and the adaptive stiffness mechanism, it can be concluded that a torque of 0,5 Nm easily satisfy the minimal required torque. A stepper motor which satisfies the requirement is the Nanotech SC4118 stepper motor. The torque curve is shown in Figure This stepper motor can deliver a torque of 0.5 Nm at a speed of approximately 100 RP M (0.6 RP S) and can even hold this torque to 400 RP M, when it is connected to a 48 V source. Since the fine thread of the Airpot damper valve limits the speed of the valve to 100 RP M, the stepper motor satisfies the required amount of torque on a 24 V source. The stepper motor is mechanically able to make full steps of 1.8 degrees, which corresponds to 200 steps per revolution. The amount of steps can be increased by selecting an appropriate stepper motor controller.

76 64 Design of the experimental model Figure 5-19: Nanotec SC4118 torque curve The Nanotech SMCI33 controller is able to translate the desired motion into corresponding amount of steps and is also able to increase the resolution of the stepper motor to steps per revolution when more precise control is required. The controller is also able to reduce the resonance which occurs when high resolution motor control is used. 5-6 Sensors and additional required components This section discusses the selection of the required sensors to measure the position and acceleration of the primary structure and the TMD mass. Also a load cell is specified to measure the load exerted by the modal exciter. At the end of this section, the required additional required components are discussed to perform these measurements. The placement of all the sensors are shown in Figure 5-20, 5-21 and Position sensor The experimental model requires two position sensors, namely one to measure the response of the primary structure and the second one to measure the response of the TMD mass. The position of the primary system will be measured at the point where the largest displacement take place. In my case it will be at the top of the structure. As mentioned in the previous section, the maximum amplitude at this point will be a total stroke of 25 mm. The

77 5-6 Sensors and additional required components 65 TMD mass is moving along a straight line and is constrained to make a total stroke of 100 mm. The position sensors should satisfy the mentioned measurement ranges and the following conditions: Able to measure the structural response when it is excited at 1 Hz Have an accuracy less than 0.1 mm The measuring rate should be at least 100 Hz (100 times the highest measured frequency) No physical contact with the measured object Negligible influence of sensor cable on the measurement of the object The conditions are satisfied by using a Micro-Epsilon 1302 sensor. This device uses the triangular measurement method to estimate the position of the object. The dynamic measurement rate of this sensor is 750 Hz. The used sensor for the primary structure is the Micro-Epsilon sensor, which has a measurement range of 50 mm and an accuracy of 25 µm. The measurement starts at a distance of 45 mm. The sensor is optimally placed at a distance of 70 mm from the primary structure, such that the full measurement range is used. The sensor choice to measure the position of the TMD mass is in particular limited by the last two conditions. The TMD mass should only be damped by the semi-active damping system and the unavoidable friction that goes along with realising this system. Since the TMD mass is only 1 kg and the behaviour of the mass is sensitive to small forces, the position sensor should therefore not be installed on the TMD system (e.g. linear magnetic position encoder), due to the influence of additional damping forces caused by the sensor cable. Considering this fact, only a triangular laser measurement sensor fulfils all the required conditions. The sensor used for this purpose is a Micro-Epsilon sensor, which has a measurement range of 200 mm. This sensor has an accuracy of 100 µm and starts measuring from 60 mm. By placing the sensor at one end of the platform, as shown in Figure 5-20, it will be able to measure the full TMD stroke of 100 mm Acceleration sensor To measure the acceleration of the primary system and the TMD mass, an accelerometer is required. Widely used accelerometer uses semi conductive strain gauges to measure the acceleration. Since this system is excited at a low frequency, special sensors are required to measure these low frequencies. The primary structure is excited at 1 Hz and has an amplitude of 12.5 mm to each side. This corresponds with a maximum acceleration of 0.05 g. The TMD mass is excited by the primary structure with a frequency slightly less than 1 Hz and has an amplitude of 50 mm to each side. This corresponds with an maximum acceleration of 0.2 g. An accelerometer which satisfies both conditions is the MTN7200-1G sensor from AE Sensors with a 4 ma to 20 ma output. This sensor uses piëzo-resistive components and is able to measure low-frequency vibrations from approximately 0 Hz and small acceleration from a threshold of m /s 2. The acceleration sensor is, in contrary to the position sensor, wired

78 66 Design of the experimental model Figure 5-20: Placement of all sensors (top view) Figure 5-21: Placement of all sensors (side view) and could therefore add damping to the TMD mass. These sensors have to be mounted on the moving object, since the acceleration is measured by strain gauges in the sensor Load cell The load cell is used to measure the applied load by the modal exciter. This sensor measures the load by using strain gauges. From the previous section it is calculated that the theoretical exerted force by the modal exciter is approximately 50 N. A sensor which is able to measure tensile and compressive forces and forces up to 100 N, is the KD24S load cell from MEsysteme. This sensor is S-shaped and ideal to measure forces exerted on one axis and has a high accuracy, due to the fact that they are insensitive to transverse forces and moments Additional components The sensors used to measure the response of the primary structure and the TMD mass and the load cell to measure the force exerted by the modal exciter are on purpose chosen to have an analogue output, such that the sensitivity of these sensors can be optimized by using appropriate resistors. Besides that, the accelerometer and load cell contain strain gauges and therefore require a strain gauge conditioner. Eventually, the analogue voltage outputs of all sensors are converted from analogue to digital signals by Analogue Digital Converter (ADC) converter. The above mentioned components are discussed in more detail in the sequel.

79 5-7 Complete design 67 Strain gauge conditioner Acceleration and load sensor measures the acceleration and load by using strain gauges implemented in the sensors. These devices require a strain gauge conditioner to translate and condition the deformation of the strain gauges inside the sensor to useful output values. Each acceleration sensor and load cell requires an own strain gauge conditioner. A widely used strain gauge conditioner, which is recommended to use with the mentioned accelerometer and load cell is the Scaime CPJ. This device produces a voltage output, which is required by the ADC device. Resistors The acceleration and position sensors are chosen such that the output of the sensors produce an analogue 5 ma to 20 ma current output to express the full measuring range of the sensor. By adding a resistor, a higher digital resolution can be obtained in combination with a 12 bits ADC. A smaller analogue output range can then be sampled with the ADC, which means that smaller sensor output changes are eventually digitally measurable. Data acquisition device All the sensors are on purpose chosen to have an analogue output. The signal can then be converted to a digital signal by using only one ADC, instead of purchasing an ADC for each sensor. After adapting the sensitivity of the sensors by using resistors and converting the current output to voltage output, these signals are then digitalized by the ADC and send to the computer. The used data acquisition device is the NI USB-6008 from National Instruments. This device has 8 single-ended or 4 differential analogue voltage inputs. The disadvantage of single-ended use of the ADC is shown below. A difference in ground voltage level exists between transmitting and receiving circuits. Signal wires are sensitive to noise, caused by electromagnetic activity in surroundings. Since the accelerometer and load cell use strain gauges and produce small signals, these sensors become susceptible to noise. For this reason it is preferable to use the differential use of the ADC device. The ADC uses the difference in the signal, since both signal wires are subjected to the same amount of noise, it does not influence the measurement signal. The input resolution of this ADC is 12 bits, which is a sufficient input resolution for the chosen sensors and for their applications. A higher resolution results in sampling noise, which has no added value. The ADC is able to sample the analogue input signal with a maximal rate of 10 ks/s. The Nyquist-Shannon sampling theorem states that the sampling frequency should be at least two times the highest frequency (Nyquist frequency) contained in the original analogue input signal. Since the experimental modal is excited by the modal exciter with only 1 Hz, the maximal sampling frequency of the NI USB-6008 is far above the required sampling frequency and therefore should easily satisfy the Nyquist-Shannon sampling theorem to obtain a correct discrete signal without aliasing. 5-7 Complete design The final design of the experimental model, including the sensors and actuators, is shown in detail in the figures below.

80 68 Design of the experimental model Figure 5-22: Front view experimental model

81 5-7 Complete design 69 Figure 5-23: Right corner view experimental model

82 70 Design of the experimental model Figure 5-24: Left corner view experimental model

83 5-7 Complete design 71 Figure 5-25: Bottom view semi-active TMD Figure 5-26: Front view semi-active TMD system Figure 5-27: Back view semi-active TMD system

84 72 Design of the experimental model 5-8 Conclusion This chapter discusses the design of an experimental model of a jack-up platform with a semiactive TMD system in detail. A jack-up platform is modelled as a single degree of freedom system with the possibility to adapt the mass, stiffness and damping coefficient. This system is then excited by a modal exciter in its resonance frequency. The semi-active TMD system possesses sensors to measure the response of the platform and is able to adapt its own stiffness and damping coefficient, such that the primary structure is always optimally damped. The response of the primary system and the force exerted by the modal exciter are also measured. This model can be used to test and validate the performance of the semi-active TMD system. This chapter contains all the required calculations and the required components. Therefore this model is ready for the next step, which is building the model.

85 Chapter 6 Conclusion This thesis discusses the vibration problem when a jack-up platform is excited in its natural frequency due to wave loads. The workability and the safety on the platform therefore decreases. This problem becomes more complicated, due to the fact that the natural frequency is dependent on varying environmental conditions and structural properties and is therefore not constant over time. Siemens is interested in an advanced damping system to optimally damp this motion. The solution for this problem should be compact, robust and feasible to implement on a jack-up structure without large structural modifications. Damping the excitations in the natural frequency can easily be performed by a Tuned Mass Damper (TMD) system and will have a significant performance because a jack-up structure is a lightly damped structure. It can be concluded that a semi-active TMD system is by far the best damping system for a jack-up platform. It is robust, safe and requires a minimal amount of space compared with its passive and active TMD alternatives. Since the structural properties of a jack-up structure is slowly varying in time, an adaptive control approach is required to optimally tune the semi-active TMD system. These structural parameters can not be measured directly and have to be estimated. Therefore an indirect Self-Tuning Regulator (STR) control scheme is required. By combining the optimal tuning laws for TMD systems and a Recursive Least Square Estimator (RLSE) it becomes possible to tune the semiactive TMD in real-time to their optimal values. This damping system solves the problem for damping the jack-up structure when it is excited in a time varying natural frequency. This means that the damping system becomes able to adapt its stiffness and damping coefficient to the optimal values in real-time, when the jack-up structure becomes heavier or stiffer by lowering the deck. This thesis extensively discusses the design of an experimental model of a jack-up structure and the damping system, supported by a model in SolidWorks. The obtained model is not a scale model, but incorporates fundamental characteristics of the jack-up structure, such as damping ratio, mass distribution and natural frequency. The experimental model is able to vary the stiffness, damping coefficient and mass in time, to simulate structural property changes. These properties make it possible to test and validate this control scheme and semi-active damping system.

86 74 Conclusion 6-1 Further research The obtained experimental model is designed to test and validate the performance of the controller, when the stiffness, mass and damping coefficient of the primary structure vary slowly in time. I expect that when this model is built, it will contain small amount of nonlinearities and the STR will be able to optimally damp this structure. To improve this experimental model and thereby simulating the dynamics of a jack-up platform more accurately, it also has to account for the non-linearities of an actual platform in the soil-leg and leg-hull connections. These non-linearities increase the difficulty to obtain an appropriate model. The designed STR with a RLSE will then not be sufficient to optimally control the platform, due to the fact that the RLSE principle uses a linear model structure and does not account for these non-linearities. In this thesis, I was not able to obtain data from an actual platform to perform parameter estimations. Therefore I recommend to obtain real data which contains information about the wave forces and the displacement of the platform. If a proper fit is not realizable, a passive or active TMD system has to be considered in combination with a robust control scheme.

87 Appendix A Specifications GustoMSC CJ-46 jack-up platform

88 CJ46-X100-D This product sheet describes the basic design of a three legged cantilever type jack-up drilling unit GustoMSC CJ46-X100-D. The CJ46-X100-D is intended for use in water depths up to m (375 ft). Special features are: The GustoMSC X-Y large reach (70 ft) high load (1,500 kips) cantilever High capacity drilling equipment Unit can be fully customized to owner s requirements Platform particulars Hul Length hull m (214 ft) Breadth hull m (203 ft) Leg centres Transverse 46 m (151 ft) Longitudinal 40 m (131 ft) Depth hull 8.0 m (26.2 ft) Design draft 4.5 m (15 ft) Fixation systems Number 18 Make GustoMSC Type 5000 Drive AC electric Jacking systems Number Make Effective jacking Pre-load jacking Jacking speed (hull lifting) Jacking speed (leg lifting) Drive 3 x 18 pinions GustoMSC 215 t per pinion (475 kips) 296 t per pinion (650 kips) 0.45 m/min 0.68 m/min AC electric, variable speed Legs Number 3 Type triangular open truss X-braced Size 10 m chord center to center Overall length m (483.5 ft) Max leg length 154 m (505 ft) Footing reaction 7,900 tf (17,350 kips) Footing area 150 m 2 (1,615 sqft) Preload 10,500 m 3 (66,000 bbls) Raw water 150 m 3 (840 bbls) Liquid mud 740 m 3 (4,650 bbls) Mud treatment 40 m 3 (250 bbls) Brine 200 m 3 (1,250 bbls) Base oil 200 m 3 (1,250 bbls) Bulk mud/cement 425 m 3 (15,000 cuft) Sacks 5,000 Main deck pipe rack 500 ton (1,100 kips) Cantilever pipe rack 360 ton (800 kips) Design temperatures For steel: design temperature For AC and ventilation systems: Max ambient temperature Min ambient temperature Accommodation Fully air conditioned for persons -10 C +45 C -10 C Storage capacities Fuel oil Potable water Drill water 800 m 3 (5,000 bbls) 450 m 3 (2,800 bbls) 2,000 m 3 (12,600 bbls) Productsheet R2 GustoMSC Page 1 of 3 The Netherlands Karel Doormanweg 25, 3115 JD, Schiedam Telephone +31 (0) P.O. Box 687, 3100 AR Schiedam Telefax +31 (0)

89 Classification, regulations Det Norske Veritas or ABS Self-elevating drilling unit MODU code 1989/ 1991 SNAME T&R 5-5A Power plant Main power Emergency power Drilling equipment Drilling depth Mud pumps Rotary table Draw works Derrick BOP s Diverter Choke and Kill Manifold Iron rough neck 5 diesels driving 1,720 KW generators 1 diesel driving 1,720 KW generator 9,144 m (30,000 ft) 3 x 2,200 HP 49.5 inch, hydraulic-driven 3 x 1,000 HP 170 ft, 35 x 35 ft base 18 3/4 inch, 15,000 psi 49.5 inch, 500 psi 15,000 psi Units built to CJ46 design Noble Ronald Hoope Noble Lynda Bossler Noble Piet van Ede Naga 2 Perro Negro 6 COSL 936 COSL 937 Perro Negro 8 Naga 3 Units under construction TS Amber & TS Pearl (2014) TBN 1 & 2 (2014) TBN 1 & 2 (2015) TBN 1 & 2 (2015) Deck equipment Mooring winches Cranes Helideck Helicopter Dimensions Cantilever Type Reach: Longitudinal Transverse 2 single drum winches 35 t pull 65 t brake load 700 m of 38 mm wire 3.5 t HHP anchors 3 diesel driven pedestal 41.1 m boom 50 t at 9.1 m 10 t at 41.1 m S61N 22.2 x 22.2 m GustoMSC X-Y m (70 ft) 6.1 m (20 ft) Combined load: 680 t (1,500 kips) over full envelope of 70 by 40 ft 1,135 t (2,500 kips) up to 50 ft reach First generation CJ46 (1980 s) Productsheet R2 GustoMSC Page 2 of 3

90 Design conditions CJ46-X100-D Elevated conditions The unit is designed to withstand the external loadings in the elevated position according to the following typical combinations of conditions. Survival conditions 300 ft, 100 kn wind 350 ft, 100 kn wind 375 ft, 100 kn wind leg length m (483.5 ft) m (483.5 ft) 154 m (505 ft) waterdepth 91.4 m (300 ft) m (350 ft) m (375 ft) air gap m (50 ft) m (50 ft) m (50 ft) wave height m (60 ft) m (50 ft) m (45 ft) wave period 15.6 s 15.0 s 15.0 s surface current 0.51 m/s (1 knots) 0.51 m/s (1 knots) 0.51 m/s (1 knot) wind velocity (1 min sust.) 51.4 m/s (100 knots) 51.4 m/s (100 knots) 51.4 m/s (100 knots) leg penetration 5.79 m (19 ft) 5.79 m (19 ft) 4.57 m (15 ft) variable load 2,500 t (5,495 kips) 2,500 t (5,495 kips) 2,500 t (5,495 kips) cantilever load 300 tf (661 kips) 300 tf (661 kips) 300 tf (661 kips) at reach aft from stern m (70 ft) m (70 ft) m (70 ft) at either side of CL 6.0 m (20 ft) 6.0 m (20 ft) 6.0 m (20 ft) Operational conditions 300 ft 350 ft 375 ft leg length m (483.5 ft) m (483.5 ft) 154 m (505 ft) waterdepth 91.4 m (300 ft) m (350 ft) m (375 ft) air gap m (50 ft) m (50 ft) m (50 ft) wave height 13.0 m (43 ft) 10.0 m (33 ft) 9.0 m (30 ft) wave period 12.0 s 11.0 s 11.0 s surface current 0.51 m/sec (1 knots) 0.51 m/sec (1 knot) 0.51 m/sec (1 knot) wind velocity (1 min sust.) 35.6 m/sec (70 knots) 35.6 m/sec (70 knots) 35.6 m/sec (70 knots) leg penetration 5.79 m (19 ft) 5.79 m (19 ft) 4.57 m (15 ft) variable load 3,500 t (7,692 kips) 3,500 t (7,692 kips) 3,500 t (7,692 kips) cantilever load 680 tf (1500 kips) 680 tf (1500 kips) 680 tf (1500 kips) at reach aft from stern m (70 ft) m (70 ft) m (70 ft) at either side of CL 6.0 m (20 ft) 6.0 m (20 ft) 6.0 m (20 ft) Transit conditions The unit is designed to withstand the external loadings in the transit conditions according to the following main criteria: location move dry ocean transport variable load 2,500 t (5,495 kips) 1,000 t (2,200 kips) displacement 13,600 t (29,890 kips) 12,100 t (26,600 kips) draft hull approx 4.5 m - max roll or pitch motion each side 10 deg/ 10 s - Data presented in this product sheet is for information only and subject to change without notice. Productsheet R2 GustoMSC Page 3 of 3

91 Appendix B Specifications of sensors, actuators and additional components

92 CUSTOM DASHPOT Model 2K95 Call (800) Fax (203) Airpot Specifications Bore:.366" (9.30 mm) PERFORMANCE 1. Damping Coefficient 0 2 lb/(in/s) adjustable N/(mm/s) 2. Force Guidelines Pull Damping: 1.4 lb max (6.23 N) Push Damping: 1.0 lb max (4.45 N) 3. Friction Coefficient: 0.2 Force without side load: < 1 g 4. Operating Temperature Range -55 C to +150 C If operating at temperatures above +70 C, please advise factory. MOUNTING DATA 5. Mounting Hole Rectangular:.312" x.375" or 8 mm x 10 mm Round:.375" or 10 mm 6. Suggested Mounting Bracket Thickness.060".125" ( mm) 7. Mounting Nut Torque Head: 4 8 in-lb ( Nm) Rod End: 2 5 in-lb ( Nm) 8. Stroke Full stroke is obtained with customer held mounting tolerance of +.015" (0.38 mm). FULL SCALE All dimensions in inches unless otherwise specified Stock Part Description click the Custom Part Description Fill in the blank boxes at the right button with located choices at from the top the of the list browser below. window, Example: to generate Model 2K your 95 model A 1.5 number. N F 2.00 K DAMPING DIRECTION TWO-WAY DAMPING DASHPOT... A PULL DAMPING DASHPOT... B PUSH DAMPING DASHPOT... C STROKE MIN =.125 inch Specify increments of inch ROD TYPE.058 DIA. S.S. STANDARD... N N ROD END BALL UNIVERSAL 4-40 THD... F LOOP WITH.156 ID RULON BUSHING... Y PLAIN...W MODEL 2K95 Choose One Choose One RETRACTED MOUNTING LENGTH MINIMUMS BY ROD END TYPE Specify to x.xxx F Y W OTHER OPTIONS EPDM PROTECTIVE CASE... K ADJUSTMENT KNOB... M SIDE PORT (include location i.e. Rx.xxx)... R Choose All Needed 13.3 Airpot is a registered trademark of Airpot Corporation. Pyrex is a registered trademark of Corning Glass Works. APC-01G

93 R17 Front view and mounting Side view Rear view ± A ± ± ±0.25 A Ø54 Ø M3 DEEP Ø ± A 7 10 JST B6B-EH-A ENCODER: NOE2-24-K14, 4000 Incr./Rev.

94 2-phase stepper motors g Type SC4118 stepper motor with encoder - Nema 17 Speed/torque curves Option SC4118L1804 Order identifier SC4118L1804-ENO05K (5-V encoder) SC4118L1804-ENO24K (24-V encoder) A 24V 1.8A 48V fs = start/stop frequency Dimension image (in mm) SC4118L1804-EN Front view and mounting Side view Rear view Drehmoment / Torque / Couple / Par [Nm] fs Drehzahl / Speed / Vitesse / Velocidad [min-1] Type Current per winding A/winding Available versions (others on request) Holding torque Ncm Resistance per winding ohm/winding Inductance per winding mh/winding Rotor inertia torque g cm 2 SC4118L1804-ENO05K 1,8 50 1,75 3,3 66,5 0,34 47,5 SC4118L1804-ENO24K 1,8 50 1,75 3,3 66,5 0,34 47,5 Weight kg Length "A" mm 36 37

95 g Closed loop motor controller with encoder input, SMCI33 Inputs/outputs (X1) Pin Function 1 Input1 2 Input2 3 Input3 4 Input4 5 Input5 6 Input6 7 Com 8 Output 1 9 Output 2 10 Output 3 11 Analog In 12 GND Technical data Operating voltage: 12 to 48 V DC Phase current: Nominal value 2 A, can be set up to a max. 3 A / phase Interface: RS485 or USB Operating type: Position, speed, flag position, cycle direction, analog, joystick Operating mode: 1/1, 1/2, 1/4, 1/5, 1/8, 1/10, 1/32, 1/64, adaptive (1/128) Step frequency: 0 to 50 khz in cycle/direction mode, 0 to 25 khz in all other modes Inputs: 6 opto-coupler inputs (5 to 24 V) Outputs: 3 open collectors, 30 V / 30 ma max. Position monitoring: Automatic error correction up to 0.9 Current reduction: can be set 0 to 100% Protective circuit: Overvoltage, undervoltage and heat sink temperature > 80 C Temperature range: 0 to +40 C * Phoenix connectors are included in the delivery. Encoder (X2) Pin Function 1 +5 V 2 CH-B 3 CH-A 4 INDEX 5 GND Motor connection (X3) Pin Function 1 Motor coil A 2 Motor coil A\ 3 Motor coil B\ 4 Motor coil B g! Caution: Always use a back-up capacitor for the operating voltage of the control system. This is to be placed as close as possible to the control system. Control systems up to 4 A require a 4700μF capacitor, and control systems up to 10 A require a 10,000μF capacitor. Otherwise there is a danger of destruction of the control system. Outline drawing (mm) Input circuits Optocoupler Supply (X4) Pin Function 1 UB24-48V 2 GND SMCI33-2: RS485 (X5) Pin Function 1 NC 2 RX V 4 TX+ 5 N.C. 6 N.C. 7 RX- 8 GND 9 TX- SMCI33-1: USB (X5) USB standard Order identifier X1-X4: Phönix plug type MICRO COMBICON X5: Mini USB type B (SMCI33-1) Sub-D 9-pin (SMCI33-2) SMCI33-1= USB 2= RS

96 MTN/7200 Series Accelerometer with DC Response and 4-20mA Output Applications: Research & Development Structural Monitoring Slow Rotating Machines Test Rigs MTN/7210 MTN/7200 Ø21mm 25mm 25mm MTN/7220 TECHNICAL DATA Data Sheet DS0012 Iss 7 Page 1 of 3 Red +ve Supply Blue -ve Supply Yellow +ve Output Green -ve Output Screen (Not connected) 28mm Ø33mm 34mm Red Blue Yellow Green Screen 33mm Ø25mm Red Blue Yellow Green Screen Technical Specification: Sensitivity 4 20mA (dependent on range). Calibration data supplied Frequency Response Dependant on dynamic range (±5%) ±1g DC to 250 Hz, ±10g DC to 500 Hz ±2g DC to 250 Hz, ±20g DC to 700 Hz ±5g DC to 300 Hz, ±50g DC to 1 khz Resonant Frequency Isolation Operation Temp. Storage Temp. DC Supply Acceleration Limits Case Material Weight Cable (Standard) Electrical Noise 10µg Sealing ±1g 700 Hz, ±10g 850 Hz ±2g 700 Hz, ±20g 1200 Hz ±5g 800 Hz, ±50g 1800 Hz Base Isolated -20 C to +85 C (extend range available up to 125 C) -40ºC to +125ºC Volts x 20 any direction Stainless steel 40g nominal 5m of 4 Core stainless steel overbraided PVC IP65 ORDER CODE PART No MTN/7100 MTN/7110 MTN/7120 MTN/7120F MTN/7120Q MOUNTING SMALL FOUR POINT LARGE FOUR POINT ¼ UNF SINGLE POINT 10-32UNF SINGLE POINT QUICK FIT SINGLE POINT REQUIRES 4 x M3 BOLTS SEE OVER PAGE FOR BASE ADAPTERS Monitran Ltd Monitor House 33 Hazlemere Road Penn Bucks HP10 8AD UK Tel: +44 (0) info@monitran.com Registered in England No Fax: +44 (0) Web: Vat No. GB

97 8 Low cost sensors with analogue outputs optoncdt Hz 375Hz 1000Hz Analog Digital Trigger TeachIn Four models with measuring ranges from 20mm to 200mm Ideal for OEM applications Measuring rate up to 750Hz Analogue (U/I) and digital output Trigger input and teach-in High flex cables for dragchain or robot use The miniaturised optoncdt 1302 is a lowcost laser sensor for common measuring tasks. The extremely small design facilitates its integration even in areas with limited space. Despite the small dimensions, the 1302 series provides precise measurement results and is suitable for machine integration and automation technology Start of measuring range (SMR) Measuring range (MR) 12 optoncdt 1302 connection, rotatable M12x mounting holes ø4.3/5.8 A 5 B ø 6 MR SMR α ϕ ε A B laser beam 80 ε ϕ α 16 4 (Dimensions in mm, not to scale)

98 9 Model ILD ILD ILD ILD Measuring range 20mm 50mm 100mm 200mm Start of measuring range SMR 30mm 45mm 50mm 60mm Midrange MR 40mm 70mm 100mm 160mm End of measuring range EMR 50mm 95mm 150mm 260mm Linearity Resolution Measuring rate Light source averaged with averaging factor 64 dynamic 750Hz 40µm 100µm 200µm 400µm ±0.2 % FSO 4µm 10µm 20µm 40µm 0.02 % FSO 10µm 25µm 50µm 100µm 0.05 % FSO 750Hz semiconductor laser <1mW, 670nm (red) Laser safety class class 2 IEC : SMR 210µm 1100µm 1400µm 2300µm Spot diameter MR 530µm 110µm 130µm 2200µm EMR 830µm 1100µm 1400µm 2100µm Protection class IP 67 Vibration 15g / 10Hz 1kHz Shock 15g / 6ms (IEC ) Weight (without cable) approx. 83g Temperature stability 0.03 % FSO/ C 0.08 % FSO/ C Operating temperature Storage temperature Output Control I/O Power supply Controller C C analogue mA (1...5V with cable PC /U) digital RS422 1x open collector output (switching output, switch, error); 1x input (teach in, trigger); 1x laser on/off VDC, 24VDC / 50mA integrated signal processor Electromagnetic compatibility (EMC) FSO = Full scale output All specifications apply for a diffusely reflecting matt white ceramic target SMR = Start of measuring range; MR = Midrange; EMR = End of measuring range Connector axial Ø EN :2006 / EN Class B (Interface emission) EN :2006 / EN : A1: A2:2001 (Interference resistance) 12-pin-connector (view on solder termination side of male inserts) Pin Description colour PC1402-x/I 3 RS422 Rx+ serial input green 4 RS422 Rx- serial input yellow 5 RS422 Tx+ serial output grey 6 RS422 Tx- serial output pink 7 +U B 11-30VDC type 24V red 8 Laser off switch input black 9 Teach in switch input violet 10 Error switch output brown 11 I OUT mA white 12 GND supply and signal ground blue 1/2 n.c The cable screen is connected with the sensor housing. The interface and power supply cable are robot rated and UL certfied. At one end there is a 12pin M12 connector, the other end is open.

99 Technical Sales (866) Requirements and Compatibility Ordering Information Detailed Specifications For user manuals and dimensional drawings, visit the product page resources tab on ni.com. Last Revised: :14:12.0 Low-Cost, Bus-Powered Multifunction DAQ for USB 12- or 14-Bit, Up to 48 ks/s, 8 Analog Inputs 8 analog inputs at 12 or 14 bits, up to 48 ks/s 2 analog outputs at 12 bits, software-timed 12 TTL/CMOS digital I/O lines One 32-bit, 5 MHz counter Digital triggering Bus-powered 1-year warranty Overview With recent bandwidth improvements and new innovations from National Instruments, USB has evolved into a core bus of choice for measurement applications. The NI USB-6008 and USB-6009 are low-cost DAQ devices with easy screw connectivity and a small form factor. With plug-and-play USB connectivity, these devices are simple enough for quick measurements but versatile enough for more complex measurement applications. Back to Top Requirements and Compatibility OS Information Mac OS X Windows 2000/XP Windows 7 Windows CE Windows Mobile Windows Vista 32-bit Windows Vista 64-bit Driver Information NI-DAQmx NI-DAQmx Base Software Compatibility ANSI C/C++ LabVIEW LabWindows/CVI Measurement Studio SignalExpress Visual Basic.NET Visual C# Back to Top Comparison Tables Product Analog Inputs Input Resolution Max Sampling Rate (ks/s) Analog Outputs Output Resolution Output Rate (Hz) Digital I/O Lines 32-Bit Counter Triggering USB single-ended/4 differential USB single-ended/4 differential Digital Digital Back to Top 1/7

100 NI offers options for extending the standard product warranty to meet the life-cycle requirements of your project. In addition, because NI understands that your requirements may change, the extended warranty is flexible in length and easily renewed. For more information, visit ni.com/warranty. OEM NI offers design-in consulting and product integration assistance if you need NI products for OEM applications. For information about special pricing and services for OEM customers, visit ni.com/oem. Alliance Our Professional Services Team is comprised of NI applications engineers, NI Consulting Services, and a worldwide National Instruments Alliance Partner program of more than 700 independent consultants and integrators. Services range from start-up assistance to turnkey system integration. Visit ni.com/alliance. Back to Top Detailed Specifications FThe following specifications are typical at 25 C, unless otherwise noted. Analog Input Converter type Successive approximation Analog inputs 8 single-ended, 4 differential, software selectable Input resolution NI USB bits differential, 11 bits single-ended NI USB bits differential, 13 bits single-ended Max sampling rate (aggregate) 1 NI USB ks/s NI USB ks/s AI FIFO 512 bytes Timing resolution ns (24 MHz timebase) Timing accuracy 100 ppm of actual sample rate Input range Single-ended ±10 V Differential 2 ±20 V, ±10 V, ±5 V, ±4 V, ±2.5 V, ±2 V, ±1.25 V, ±1 V Working voltage ±10 V Input impedance 144 kω Overvoltage protection ±35 Trigger source Software or external digital trigger System noise 3 Single-ended ±10 V range 5 mvrms Differential ± 20 V range 5 mvrms ±1 V range 0.5 mvrms Absolute accuracy at full scale, single-ended Range Typical at 25 C (mv) Maximum over Temperature (mv) ± Absolute accuracy at full scale, differential 4 Range Typical at 25 C (mv) Maximum over Temperature (mv) ± ± /7

101 Absolute accuracy at full scale, differential 4 Range Typical at 25 C (mv) Maximum over Temperature (mv) ± ± ± ± ± ± Analog Output Analog outputs 2 Output resolution 12 bits Maximum update rate 150 Hz, software-timed Output range 0 to +5 V Output impedance 50 Ω Output current drive 5 ma Power-on state 0 V Slew rate 1 V/μs Short circuit current 50 ma Absolute accuracy (no load) 7 mv typical, 36.4 mv maximum at full scale Digital I/O Digital I/O P0.<0..7> 8 lines P1.<0..3> 4 lines Direction control Each channel individually programmable as input or output Output driver type NI USB-6008 Open collector (open-drain) NI USB-6009 Compatibility TTL, LVTTL, CMOS Absolute maximum voltage range 0.5 to 5.8 V with respect to GND Pull-up resistor 4.7 kω to 5 V Power-on state Input Each channel individually programmable as active drive (push-pull) or open collector (open-drain) Digital logic levels Level Min Max Units Input low voltage V Input high voltage V Input leakage current 50 μa Output low voltage (I = 8.5 ma) 0.8 V Output high voltage Active drive (push-pull), I = 8.5 ma V Open collector (open-drain), I = 0.6 ma, nominal V Open collector (open-drain), I = 8.5 ma, with external pull-up resistor 2.0 V External Voltage 5/7

102 +5 V output (200 ma maximum) +5 V typical, V minimum +2.5 V output (1 ma maximum) +2.5 V typical +2.5 V accuracy 0.25% max Reference temperature drift 50 ppm/ C max Counter Number of counters 1 Resolution 32 bits Counter measurements Edge counting (falling-edge) Counter direction Count up Pull-up resistor 4.7 kω to 5 V Maximum input frequency 5 MHz Minimum high pulse width 100 ns Minimum low pulse width 100 ns Input high voltage 2.0 V Input low voltage 0.8 V Power Requirements USB 4.10 to 5.25 VDC 80 ma typical, 500 ma max USB suspend 300 μa typical, 500 μa max Physical Characteristics Dimensions Without connectors With connectors 6.35 cm 8.51 cm 2.31 cm (2.50 in in in.) 8.18 cm 8.51 cm 2.31 cm (3.22 in in in.) I/O connectors USB series B receptacle, (2) 16 position terminal block plug headers Weight With connectors 84 g (3 oz) Without connectors 54 g (1.9 oz) Screw-terminal wiring 16 to 28 AWG Torque for screw terminals N m ( lb in.) Safety If you need to clean the module, wipe it with a dry towel. Safety Voltages Connect only voltages that are within these limits. Channel-to-GND ±30 V max, Measurement Category I Measurement Category I is for measurements performed on circuits not directly connected to the electrical distribution system referred to as MAINS voltage. MAINS is a hazardous live electrical supply system that powers equipment. This category is for measurements of voltages from specially protected secondary circuits. Such voltage measurements include signal levels, special equipment, limited-energy parts of equipment, circuits powered by regulated low-voltage sources, and electronics. Caution Do not use this module for connection to signals or for measurements within Measurement Categories II, III, or IV. Safety Standards This product is designed to meet the requirements of the following standards of safety for electrical equipment for measurement, control, and laboratory use: IEC , EN UL , CSA Note For UL and other safety certifications, refer to the product label or visit ni.com/certification, search by model number or product line, and click the appropriate link in the Certification column. Hazardous Locations The NI USB-6008/6009 device is not certified for use in hazardous locations. 6/7

103 Conditionneur de signal analogique Analog signal conditioner CPJ / CPJ2S ±10 V/0-10 V / 4-20 ma Conditionne jusqu à 4 capteurs à jauges de contrainte (350 Ω) Capteur 4 ou 6 fils Sortie tension (±10 Vdc ou 0-10 Vdc) et sortie courant (4-20 ma) Signal d étalonnage par shunt 2 seuils sur relais en option (CPJ2S) The CPJ is able to run up to 4 strain gauge load cells (350 Ω) 4 or 6 wire load cell Voltage output (±10 Vdc or 0-10 Vdc) and current ouput (4-20 ma) Shunt calibration signal 2 set points on relays optional version CPJ2S Version Rail DIN DIN Rail Version Version Carte Board Version Version Boîtier Housing Version CPJ - CPJ2S Version Rail Din Din Rail Version POWER CPJ ANALOG TRANSMITTER SP1 SP2 OPTION CPJ2S : carte option 2 seuils 2 set points optional card Toutes dimensions en mm - All dimensions in mm

104 CPJ/CPJ2S Conditionneur de signal analogique Analog signal conditioner Caractéristiques CPJ - CPJ Specifications Alimentation Nominal input voltage 24 ±4 Vdc Classe de précision Accuracy class 0.05 % Effet température sur le zéro Temperature effect on zero %F.S.*/ C Effet température sur le gain Temperature effect on span 0.02 %/ C Plage de température de fonctionnement Operating temperature range C Alimentation capteur (commutable par cavalier) Load cell input voltage (engaged with jumper) 3, 5, 10 Vdc Impédance min. capteur : alimentation capteur 3/5 V alimentation 10 V Min. load cell impedance: excitation 3/5 V excitation 10 V Réglage du gain Span adjustment mv/v Consommation max. CPJ / CPJ2S Max supply current CPJ / CPJ2S 120 / 170 ma Sortie tension Voltage output ±10, 0-10 V Sortie courant Current output 4-20 ma Impédance de charge en sortie tension Load impedance for voltage output 2000 Ω Impédance de charge en sortie courant Load impedance for current output 500 Ω Charge capacitive en sortie Capacitive load on the output 1 nf Filtre (commutable par cavalier) passe bas (-3 db) Filtering (engaged with jumper) low pass (-3dB) 10 Hz Bande passante Bandwidth 20 KHz Caractéristiques points de consignes CPJ2S - CPJ2S Set points specifications GÉNÉRALES GENERAL Nombre de points de consigne Number of set points 2 Réglage Adjustment 2 potentiomètres 2 potentiometers Sens de fonctionnement Functionning direction Sélectionnable Selectable Hystérésis Hysteresis 1.1 / 0.2 % F.S.* Temps de maintien Holding time 5 / 600 ms Fonction vérouillage relais Latch function Sélectionnable Selectable Temps de réponse Response time 7 ms RELAIS Options - Options Entrée potentiomètre Input for potentiometer Filtre personnalisé Customized fi ltering Hz BP501 - F Annemasse Cedex Tél. : (+33) Fax : (+33) E.mail : info@scaime.com RELAY Type Technology Statiques opto-isolés Photorelays Courant max. à 40 C On-state current max. at 40 C 0.4 A Tension max. à l état ouvert Off-state voltage 55 V Résistance à l état passant On-state resistance 2 Ω Tension d isolement Isolation voltage Vrms * F.S. : Pleine échelle - Full scale Téléchargez tous nos documents sur : Download all our documents from : Agent Ω Ω FT-CPJ-CPJ2S-FE SCAIME - SIREN R.C.S. THONON LES BAINS - SIRET SCAIME se réserve le droit d apporter toutes modifications sans avis préalable - SCAIME reserves the right to bring any modification without prior notice.

105 Kraftsensor KD24s Nennkraftbereiche: ±2N, ±10N, ±20N, ±50N, ±100N, ±200N, ±500N/VA, ±1kN/VA Der Kraftsensor KD24S ist der kleinste Kraftsensor in S-Form. Er eignet sich hervorragend für Prüfaufgaben in der Qualitätssicherung sowie in der Werkstoffprüfung. Krafteinleitung und Kraftausleitung sind zentrisch angeordnet. Die Krafteinleitungsbügel werden bei Belastung parallel verschoben. Der Kraftsensor KD24S ist wie der Sensor KD40s als Mehrbereichssensor ausgeführt. Die Genauigkeit von 0,1% wird bereits bei einem Kennwert von 0,5 mv/v erreicht. Die Sensoren von 2 bis 20N können mit dem 4fachen und von 50 bis 200N mit dem doppelten ihres Nennkraftbereichs betrieben werden. Bis 200N werden die Sensoren aus Aluminium gefertigt, ab 500N ist der Sensor aus hochfestem Edelstahl gefertigt. Es wird empfohlen, den Sensor so zu montieren, das die Kabelseite (im Bild unten) an der unbeweglichen Seite, der Krafteinleitung, befestig wird. Abmessungen ±500N, ±1kN ME-Meßsysteme GmbH, Neuendorfstr. 18a, DE Hennigsdorf Tel +49 (0) , Fax +49 (0) , info@me-systeme.de, 1