Tether Tension Research Articles

Dynamic analysis of offshore triceratops supporting wind turbine: Preliminary studies

Offshore triceratops, the recent innovation in deep water compliant platforms, is primarily designed to withstand lateral forces through its geometric shape. The uniqueness of the platform is the presence of the ball joints between the legs and deck, which partially restrain the transfer of rotations from the legs to the deck and vice-versa. However, displacements such as surge, sway, and heave motions are transferred, ensuring a rigid connection between the legs and the deck. Efficient operations of offshore wind turbines are more dependent on the support systems on which they are mounted. Increased stability and reduction in stress concentration in rigid connections are desirable. Nonlinear dynamic response analysis is carried out in FAST by coupling the frequency response of the platform obtained in ANSYS AQWA with that of the HydroDyn module of FAST. The current study investigates a fully coupled three-dimensional hydro-aerodynamic model of triceratops mounted with a horizontal axis wind turbine. Unsteady Blade Element Momentum theory (BEM) is used to estimate the aerodynamic loads, which encompasses the effect of wind shear using a power law and spatially coherent turbulence. In contrast, Morison equations are used to estimate the hydrodynamic loads on the platform. After the preliminary proportioning of the platform, Response Amplitude Operator (RAO) plots are drawn to illustrate the partial motion transfer between the deck and the buoyant legs. Based on the preliminary studies, it is seen that the environmental loads do not impose instability, reinforcing the dynamic stability of the platform. Frequency responses for operating and parked conditions illustrate the coupling between the degrees of freedom and the influence of the rotor motion of the wind turbine on the platform deck. Tether tension variation is assessed in all three legs for the operational sea states to check the safety standards for a compliant system to avoid tether pull-out. The presented study is prima facie to encourage the suitability of triceratops as floaters to support the wind turbine under moderate sea states. Highlights This study is focused on new-generation offshore triceratops as support system for wind turbine Prelimiary dynamic anlaysis of coupled action of the supprting system and wind turbine are presented Use of ball joints help partial isolation of the deck and restrain transfer of moment from the turbine shaft to the supporting system, which is a novelty Infleunce of rotor motion of the triceratops is illustarted to highlight the advantage of complinacy of trirceratops This study disucsses only the performance assessment and not the design perspectives

Wednesday, September 26, 2018 7:35 AM–9:00 AM ePosters: P13. Changes in spinous process tether looping method significantly alters segmental biomechanics for proximal junctional kyphosis prophylaxis

BACKGROUND CONTEXT Spinous process (SP) tethering is gaining interest as a prophylactic technique to alleviate load concentrations and reinforce the posterior ligament complex (PLC) at the uppermost instrumented vertebra (UIV) to reduce the risk of developing proximal junctional kyphosis (PJK) in adult spinal deformity (ASD) surgeries. Consensus has yet to be established on appropriate technique and there is a lack of biomechanical data to provide initial guidance. While multiple SP looping methods have recently been proposed, no study has evaluated the effect of tether looping method on segmental biomechanics. PURPOSE We sought to evaluate the effects of four tether looping methods on segmental biomechanics at UIV, UIV+1, and UIV+2. We hypothesized that the different looping methods would result in significant differences in flexion range-of-motion (ROM), intervertebral disc (IVD) pressures, and peak tether loop tensions. STUDY DESIGN/SETTING Biomechanical study. OUTCOME MEASURES Flexion ROM, IVD pressure, peak tether tension. METHODS Nine T1–T4 cadaveric motion segments were tested in flexion–extension bending to 5 Nm using a pure-moment testing machine. UIV was located at T3 using standard pedicle screws and rods. A rod crosslink (CL) was placed inferior to the pedicle screws. Motion of UIV, UIV+1, and UIV+2 was recorded using a motion capture system. IVD pressure was measured at UIV/UIV+1 and UIV+1/UIV+2 using custom pressure probes. A 5 mm braided polyester suture was used for tethering. The tether was looped under the CL at UIV, and through holes drilled at the base of UIV+1 and UIV+2 SPs. Tether tension was measured using custom in-line tension sensors for each independent loop. An untethered test was used for baseline values. Tethered tests included one single level (SL) and three double level (DL) tests: (1) SL, a single tether from CL at UIV to UIV+1 SP, (2) DL Common (CM), a tether from CL at UIV to UIV+1 SP and another tether from CL at UIV to UIV+2 SP, (3) DL Chained (CH), a tether from CL at UIV to UIV+1 SP and another tether from UIV+1 SP to UIV+2 SP, and (4) DL Figure-Eight (F8), a single tether from CL at UIV to UIV+1 SP and UIV+2 SP in a woven figure-eight loop. Loops were pretensioned to 22N before each test. RESULTS The SL method resulted in significant reductions in flexion ROM at UIV/UIV+1 (p=.001) but not at UIV+1/UIV+2 (p=.052). SL also yielded significant reductions in IVD pressure at both UIV/UIV+1 (p=.007) and UIV+1/UIV+2 (0.002). The choice of DL method had a significant univariate effect on flexion ROM reduction at UIV/UIV+1 (p=.004) but not at UIV+1/UIV+2 (0.14). The choice of DL method also had a significant univariate effect on IVD pressure reduction at UIV/UIV+1 (p CONCLUSIONS The use of different tether looping methods significantly alters the tether's effect on segmental biomechanics. double level techniques provide greater reductions in flexion ROM and IVD pressures; however, they yield greater tether tensions at the uppermost tethered level compared to SL. CM produced the best results for improved segmental stability. The transfer of peak SP loading to superjacent levels may provide benefits in protecting the UIV+1 SP and the PLC. New understanding in the effect of looping methods may provide improved ability to reduce PJK caused by ligamentous laxity.

224 - Effect of Spinous Process Tether Tension for Prophylactic Treatment of Proximal Junctional Kyphosis in Adult Spinal Deformity Surgery

224 - Effect of Spinous Process Tether Tension for Prophylactic Treatment of Proximal Junctional Kyphosis in Adult Spinal Deformity Surgery

Tether tension control law design during orbital transfer via small-gain theorem

Issues of controller design via small gain theorem for tethered satellite system (TSS) during orbit maneuvering under transversal thrust are considered. First, dynamic equations of tethered satellite system in orbital maneuvering are established based on a dumbbell model. It is proved that the in-plane system is weak minimum phase by selecting a proper Lyapunov candidate function, and there are some difficulties for controller designing based on nonlinear model directly. Next, a controller is designed by utilizing Small-gain Theorem based on a control oriented model. An input-to-state stable (ISS) based tether rate control law is derived as the reference signal for the tether length system. A tether tension control law is proposed such that the uncertainties caused by linearization will be suppressed by properly selected control parameters and the closed loop system will be forced to a small neighborhood of origin as time approaches infinity. Finally, numerical simulation results demonstrate the validity of the proposed algorithm.

Nonlinear control of sway in a tethered satellite system via attitude control of the main satellite

In this study a new nonlinear control approach is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether. To achieve this goal, the main satellite attitude control actuators are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit. Governing dynamic equations of motion are derived using extended Lagrange method. Controllability of the system about equilibrium state is studied and a nonlinear controller is designed using feedback linearization method to regulate libration of the system. By studying the conditions of feedback linearization method, stability of the controller is also proved. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as the feedback to the controller. By implementing the controller and observer on the system, simulations demonstrate that the controller lead to reduction of the tether libration from large amplitudes.

Stability of TLP tether using a stochastic averaging technique

Tension Leg Platforms (TLPs) are popular deep water platforms for extracting oil and gas. TLPs are connected to the sea bed by pretensioned tethers. If fluctuating tension in tethers is sizable compared to the pretension, many dynamic stability problems may arise which also affects the platform motion. In this paper, stochastic stability of TLP tethers in transverse oscillations is investigated using stochastic averaging technique and the probability flow of the reduced Fokker–Plank equation. Stochastic averaging is used to obtain drift and diffusion coefficients independent of time. Onset of such transverse oscillations may be caused due to regular or random vortex shedding. The tension fluctuation of the tether due to random vertical wave forces on the platform induces multiplicative random excitation in the tether because of the presence of nonlinear drag. As a consequence, dynamic instability may become a significant problem. The tether is modeled as a simply supported uniform beam under initial tension assuming transverse oscillation to take place only in its fundamental natural mode. Thus, the problem is reduced to a single degree of freedom system. Fluid resistance is calculated by Morison's equation consisting of drag and inertia forces. A semi-analytical procedure combined with stochastic averaging technique is employed to obtain the drift and diffusion coefficients of the response in closed form. By examining the probability flow in terms of drift and diffusion coefficients at the two boundaries, the stability of the system is investigated. Stability of tethers of a TLP in 300m water depth, for different pretensions, is studied for sea states of 21m, 16m and 8m significant wave heights represented by PM spectrum. It is shown that for low values of pretension, stochastic stability of tether in transverse direction may take place for large wave heights.

First experimental results on enhancing hovering performance of unmanned helicopters by using a tethered setup

The hovering capabilities of helicopters can be seriously affected by wind. This could be even more significant in the small-size platforms used for developing unmanned aerial vehicles. One possible solution for improving performance under such circumstances is the use of a tethered setup. This approach takes advantage of the tension exerted on the cable linking the helicopter to the ground. This paper analyzes the mechanical model of this augmented setup to show its benefits in stabilizing translational dynamics. Control guidelines to exploit these potentialities are also highlighted. The latter allows the definition of a model-based control strategy consisting of a combination of classical PID laws together with model inversion blocks. Tether tension feed-forward is also included to take into account the side effects of tether tension in rotational dynamics. Experiments performed with the real platform confirm the validity of the proposed approach.

Anti-sway control of tethered satellite systems using attitude control of the main satellite

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite׳s actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether׳s motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

Tethers tension force effect in the response of a squared tension leg platform subjected to ocean waves

The tension leg platform (TLP) is one of the compliant structures which are generally used for deep water oil exploration. With respect to the horizontal degrees of freedom, it behaves like a floating structure moored by vertical tethers which are pretension due to the excess buoyancy of the platform, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. In the current study, a numerical study for square TLP using modified Morison equation was carried out in the time domain with water particle kinematics using Airy\'s linear wave theory to investigate the effect of changing the tether tension force on the stiffness matrix of TLP\'s, the dynamic behavior of TLP\'s; and on the fatigue stresses in the cables. The effect was investigated for different parameters of the hydrodynamic forces such as wave periods, and wave heights. The numerical study takes into consideration the effect of coupling between various degrees of freedom. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables. Nonlinear equation was solved using Newmar\'s beta integration method. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e., 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether tension force, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations that is significantly dependent on wave height, and that special attention should be given to tethers fatigue because of their high tensile static and dynamic stress.

Tether Tension Performance Utilizing Various Materials for a Coplanar and Non-Coplanar Model of a Flexible Tethered Satellite System

This paper presents a numerical model for a flexible tethered satellite system in both planar and co-planar environment. This tethered satellite system consists of three rigid bodies with two flexible tethers, each connecting two rigid bodies with one located in the center serving as the mothership. The dynamics of the system include tether deformations, rotational dynamics and orbital mechanics. Five different materials that are commonly used will be tested accordingly in order to observe its performance based on the tension of the tether. It is found that, based on all of the materials simulated, diamond has the best tension performance.

Effect of Tethers Tension Force on the Behavior of Triangular Tension Leg Platform

Compliant structures like triangular tension leg platforms (TLPs) are proven to be highly cost effective in deep waters. The estimation of hydraulic forces due to waves on structural member of TLP is vital for its economic and safe design. In the current study, a numerical study for a triangular TLP using modified Morison equation was carried out in the time domain with water particle kinematics using Airy’s linear wave theory to investigate the effect of changing the tether tension force on the stiffness matrix of TLP's, the dynamic behavior of TLP's; and on the fatigue stresses in the cables. The effect was investigated for different parameters of the hydrodynamic forces such as wave periods, and wave heights. The numerical study takes into consideration the effect of coupling between various degrees of freedom. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables. Nonlinear equation was solved using Newmark’s beta integration method. Only uni-directional waves in the surge direction was considered in the analysis.

Prediction of Extreme Tether Tension for a TLP by the AUR and ACER Methods

The paper presents a study of the extreme value statistics related to measurements on a scale model of a large tension leg platform (TLP) subjected to random waves in a wave basin. Extensive model tests were carried out in three irregular sea states. Time series of the motion responses and tether tension were recorded for a total of 18 three hour tests (full scale). In this paper we discuss the statistics of the measured tether tension. The focus is on a comparison of two alternative methods for the prediction of extreme tether tension from finite time series records. One method is based on expressing the extreme value distribution in terms of the average upcrossing rate (AUR). The other is a novel method that can account for statistical dependence in the recorded time series by utilizing a cascade of conditioning approximations obtained by defining the average conditional exceedance rates (ACER). Both methods rely on introducing a specific parametric form for the tail part of the extreme value distribution. This is combined with an optimization procedure to determine the parameters involved, which allows prediction of various extreme response levels.

Periodical Motion of a Tethered Satellite System around Collinear Libration Points

This paper studies the motion of a rotational tethered satellite system flying around collinear Lagrangian points of the Earth-Moon system. Equations of spatial motion of the mass center and the tether libration are deduced, but only the planar motion with constant rotation rate is discussed. First, the equation of the mass center is simplified and solved analytically for the scenario where the system is moving in the neighborhood of the libration point. The analytical solution indicates that both a bounded solution and periodical solution exist. A fully nonlinear dynamics analysis is then performed. A numerical method combining continuation and piecewise differential corrections is applied to obtain the periodical solution. Tether tension is also investigated. Simulation results validate the effectiveness of the proposed numerical method and the existence of the periodical orbits. The influence of parameters, such as spin rate, mass ratio of end satellites, and tether length are analyzed.

Offshore triangular tension leg platform earthquake motion analysis under distinctly high sea waves

TLPs are compliant structures designed to withstand moderate loads without damage and severe loads without seriously endangering the occupants. Dynamic behavior of TLPs under distinctly high sea waves in the presence of both horizontal and vertical seismic excitations is examined and method of analysis is discussed. Seismic forces imposed at tether bottom make tether tension unbalanced when the hull is under offset condition. Tether tension varies nonlinearly under vertical seismic excitations generated using Kanai-Tajimi ground acceleration spectrum. Analytical studies conducted on triangular TLPs show that this tension variation is much higher than the regulation values indicating the necessity for examining them for seismic safety. Clearly, the peaks seen in the response of all active degrees-of-freedom occurring near to the average sum frequencies of waves and input ground motion is a significant influence of seismic excitations on TLP tethers under high sea waves. The numerical results obtained also verify/establish the fact that TLPs built in deeper sea locations show significantly lesser response to the combined wave and earthquake loading.

238 柔軟な大型太陽電池板の振動制御(宇宙システム, OS-2 運動と振動のモデリングと制御(2))

238 柔軟な大型太陽電池板の振動制御(宇宙システム, OS-2 運動と振動のモデリングと制御(2))

1P1-A05 テザー拘束を受ける宇宙ロボットの動的干渉について

本研究では, 軌道上の母衛星からテザーにより吊り下げられた宇宙ロボットの挙動について調べる。宇宙空間に浮遊している宇宙ロボットの挙動については多くの研究がなされているが, 拘束を受ける宇宙ロボットの挙動についての研究は行われていない。そこで, 浮遊状態/(剛体としての)テザー拘束下/(柔軟)テザー拘束下での宇宙ロボットとテザー・母衛星との動的干渉を調べる。特に, 宇宙ロボットの手先軌道に注目し, 干渉の大きさを比較する。

Influence of a Small End Mass on Tether-Mediated Orbital Injection

The tether-assisted slingshot injection allows raising the apogee up to about 14 tether lengths, depending on the angular speed, whereas the perigee only rises by one tether length. With a two-cut procedure, the tether departs with the satellite at the e rst cut and is discarded close to the apogee, so that the momentum transferred by the tether provides an additional raising of the perigee. This results in a longer lifetime. The disadvantages are that typical tethers are light and can transfer little momentum at the second cut and that libration with a free end is highly unstable. With zero tension at the tip, perturbations easily propagate and the rectilinear shape is lost. A modie cation is proposed that improves on both counts, leaving a mass attached to the free end of the tether. It can be part of the deployer assembly, so that no additional weight is needed. This increases themomentum transferred at the second cut, thus raising drag-sensitive perigee. Even small masses appreciably increase in lifetime. Tether tension is higher, so that libration is more stable and the rectilinear shape is preserved for a longer time. The new mass distribution changes the frequencies of the tether oscillations and can be used to avoid resonances. Nomenclature a = semimajor axis of the orbit of G, km as = semimajor axis of the e nal orbit of S, km as1 = order one term of the expansion of as B = tether end opposite to S E.?/ = time evolution of out-of-plane oscillations e = eccentricity of the orbit of G es = eccentricity of the e nal orbit of S es1 = order one term of the expansion of es

Stress concentration factors at circumferential welds in tubulars

In this paper analytical expressions for stress concentration factors due to fabrication tolerances are derived for a number of design cases based on classical shell theory. These cases include butt welds in tubulars, welds at ring stiffeners and bulkheads in shell structures, welds at conical transitions without and with ring stiffeners and tubulars with colinearity subjected to axial tension in risers and tethers of tension leg platforms.

Stochastic TLP response under long crested random sea

The coupled response of a tension leg platform (TLP) for random waves characterized by a long crested sea spectrum is investigated. The response analysis is based on simulation technique which duly considers various nonlinear effects such as relative velocity squared drag force, variable added mass due to variable submergence and nonlinearity due to large excursion. It also accounts for variable tension in tethers due to variable submergence, variable buoyancy and vertical wave forces. Variable tether tension tends to produce sub-harmonic resonance which is critically examined. Also, the phenomenon of super-harmonic resonance which is introduced by variable submergence effect is investigated. The responses are obtained by employing a time integration scheme in which iterations are required at each time station due to nonlinear coupling of all six degrees of freedom. A detailed parametric study is reported that includes maximum, minimum, mean and standard deviation of responses in all six degrees of freedom. Some typical power spectral density functions of responses are shown to illustrate the effects of sub-harmonic and super-harmonic resonances in the system.

Probabilistic Design of the Tethers of a Tension Leg Platform

Probabilistic design of the tethers of a tension leg platform is described. It is used to determine the maximum and minimum tension in tethers for the intact condition. The reliability of the tethers for maximum and minimum tension when one tether is missing has been calculated. Also, the reliability of maximum and minimum tension in the tethers as a function of flooding of a corner column has been calculated.