Cargo Pendulation Reduction of Ship-Mounted Cranes

Ship-mounted cranes are used to transfer cargo from large container ships to smaller lighters when deep-water ports are not available. The wave-induced motion of the crane ship can produce large pendulations of the cargo being hoisted and cause operations to be suspended. In this work, we show that it is possible to reduce these pendulations significantly by controlling the slew and luff angles of the boom. Such a control can be achieved with the heavy equipment that is already part of the crane so that retrofitting existing cranes would require a small effort. Moreover, the control is superimposed on the commands of the operator transparently. The successful control strategy is based on delayed feedback of the angles of the cargo-hoisting cable in and out of the plane of the boom and crane tower. Its effectiveness is demonstrated in a fully nonlinear three-dimensional computer simulation and in an experiment with a 1/24th-scale model of a T-ACS (The Auxiliary Crane Ship) crane mounted on a platform moving with three degrees of freedom. The results demonstrate that the pendulations can be significantly reduced, and therefore the range of sea conditions in which cargo-transfer operations can take place can be greatly expanded.     

Modeling of system dynamics of a slewing flexible beam with moving payload pendulum

When a tower crane is handling payload via rotation and moving the carriage simultaneously the jib structure and the payload can be modeled as a system consisting of a slewing flexible clamed-free beam with the spherical payload pendulum that moves along the beam. The present work completes the dynamic modeling of the system mentioned above. The clamed-free beam attached to a rotating hub is modeled by Euler–Bernoulli beam theory. The payload is modeled as a sphere pendulum of point mass attached to via massless inextensible cable the carriage moving on the rotating beam. Non-linear coupled equations of motion of the in- and out-of-plane of the beam and the payload pendulum are derived by means of the Hamilton principle. Some remarks are made on the equations of motion.     

Free vibration of a sagged cable with attached discrete elements

An algorithm is presented to analyze the free vibration in a system composed of a cable with discrete elements, e.g., a concentrated mass, a translational spring, and a harmonic oscillator. The vibrations in the cable are modeled and analyzed with the Lagrange multiplier formalism. Some fragments of the investigated structure are modeled with continuously distributed parameters, while the other fragments of the structure are modeled with discrete elements. In this case, the linear model of a cable with a small sag serves as a continuous model, while the elements, e.g., a translational spring, a concentrated mass, and a harmonic oscillator, serve as the discrete elements. The method is based on the analytical solutions in relation to the constituent elements, which, when once derived, can be used to formulate the equations describing various complex systems compatible with an actual structure. The numerical analysis shows that, the method proposed in this paper can be successfully used to select the optimal parameters of a system composed of a cable with discrete elements, e.g., to detune the frequency resonance of some structures.     

Dynamic analysis of beam-cable coupled systems using Chebyshev spectral element method

The dynamic characteristics of a beam–cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections,numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finiteelement method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam–cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.     

Parameters for Modeling Stranded Cables as Structural Beams

This paper presents a method for determining the effective homogenous beam parameters for stranded cables made up of non-homogenous wires, as well as characterization of the attachment method commonly used for cable harnesses on space structures. There is not yet a predictive model for quantifying the structural impact of cable harnesses on space flight structures, and towards this goal, the authors aim to predict cable resonance behavior from basic cable measurements. Cables can be modeled as shear beams, but the shear beam model assumes a homogenous, isotropic material, which a stranded cable is not. Thus, the cable-beam model requires both knowledge of the cable constraints and calculation of effectively homogenous properties, including density, area, bending stiffness, and modulus of rigidity to predict the natural frequencies of the cable. Through a combination of measurement and correction factors, upper and lower bounds for effective cable properties and attachment stiffness are calculated and shown to be effective in a cable-beam model for natural frequency prediction. Although the cables investigated are spaceflight cables, the method can be applied to any stranded cable for which the constituent material properties can be determined.     

Development of flexible telescopic boom model using absolute nodal coordinate formulation sliding joint constraints with LuGre friction

In this investigation, a modeling procedure of a telescopic boom of cranes is developed using the absolute nodal coordinate formulation together with the sliding joint constraints. Since telescopic booms are extracted and retracted under various operating conditions, the overall length of the boom changes dynamically, leading to the time-variant vibration characteristics. For modeling the telescopic structure of booms, a special care needs to be exercised since the location of the sliding contact point moves along the deformable axis of the flexible boom and the solution to a moving boundary problem is required. This issue indeed makes the modeling of the telescopic boom difficult, despite the significant needs for the analysis. It is, therefore, the objective of this investigation to develop a modeling procedure for the flexible telescopic boom by considering the sliding contact condition with the dynamic frictional effect. To this end, the sliding joint constraint developed for the absolute nodal coordinate formulation is employed for describing relative sliding motion between flexible booms, while flexible booms are modeled using the beam element of the absolute nodal coordinate formulation, which allows for modeling the large rotation and deformation of the structure.     

Mechanics of cable shovel-formation interactions in surface mining excavations

The cable shovel excavator is used for primary production in many surface mining operations. A major problem in excavation is the variability of material diggability, resulting in varying mechanical energy input and stress loading of shovel dipper-and-tooth assembly across the working bench. This variability impacts the shovel dipper and tooth assembly in hard formations. In addition, the geometrical constraints within the working environment impose production limitations resulting in low production efficiency and high operating costs. A potential solution to the above problems is the deployment of an intelligent shovel excavation (ISE) technology, with real-time formation identification, recording and knowledge transmission capabilities. This paper advances the ISE technology by developing dynamic models of the cable shovel using the Newton-Euler techniques. The models include the main factors that influence shovel performance including the effect of both linear and angular motions of dipper handle and dipper. A path trajectory is modeled to demonstrate the dynamic velocity and acceleration profiles. Numerical examples show that the critical performance variables include geometrical and physical properties of the dipper and dipper handle, digging strategies and formation properties. The kinematic results show that the critical phase occurs between 1.5 and 2.0 s of a 3-s excavation cycle with occurrence of maximum kinematic effects. The dynamic results also show a similar trend with maximum dynamic effects between 1.5 and 2.0 s. The results also show that the maximum resistive force occurs at 1.625 s within the excavation cycle. At this point the maximum breakout force of the equipment is reached and any increase in the resistive load will require further fragmentation. The results provide appropriate information for excavation planning and execution. These models form the basis for developing dynamic shovel simulators for the ISE technology.     

Noise influenced elastic cantilever dynamics with nonlinear tip interaction forces

In this work, the authors study the influence of noise on the dynamics of base-excited elastic cantilever structures at the macroscale and microscale by using experimental, numerical, and analytical means. The macroscale system is a base excited cantilever structure whose tip experiences nonlinear interaction forces. These interaction forces are constructed to be similar in form to tip interaction forces in tapping mode atomic force microscopy (AFM). The macroscale system is used to study nonlinear phenomena and apply the associated findings to the chosen AFM application. In the macroscale experiments, the tip of the cantilever structure experiences long-range attractive and short-range repulsive forces. There is a small magnet attached to the tip, and this magnet is attracted by another one mounted to a high-resolution translatory stage. The magnet fixed to the stage is covered by a compliant material that is periodically impacted by the cantilever’s tip. Building on their earlier work, wherein the authors showed that period-doubling bifurcations associated with near-grazing impacts occur during off-resonance base excitations of macroscale and microscale cantilevers, in the present work, the authors focus on studying the influence of Gaussian white noise when it is included as an addition to a deterministic base excitation input. The repulsive forces are modeled as Derjaguin–Muller–Toporov (DMT) contact forces in both the macroscale and microscale systems, and the attractive forces are modeled as van der Waals attractive forces in the microscale system and magnetic attractive forces in the macroscale system. A reduced-order model, based on a single mode approximation is used to numerically study the response for a combined deterministic and random base excitation. It is experimentally and numerically found that the addition of white Gaussian noise to a harmonic base excitation facilitates contact between the tip and the sample, when there was previously no contact with only the harmonic input, and results in a response that is nominally close to a period-doubled orbit. The qualitative change observed with the addition of noise is associated with near-grazing impacts between the tip and the sample. The numerical and experimental results further motivate the formulation of a general analytical framework, in which the Fokker–Planck equation is derived for the cantilever-impactor system. After making a set of approximations, the moment evolution equations are derived from the Fokker–Planck equation and numerically solved. The resulting findings support the experimental results and demonstrate that noise can be added to the input to facilitate contact between the cantilever’s tip and the surface, when there was previously no contact with only a harmonic input. The effects of Gaussian white noise are numerically studied for a tapping mode AFM application, and it is shown that contact between the tip and the sample can be realized by adding noise of an appropriate level to a harmonic excitation.     

Vibration control for a flexible-link robot arm with deflection feedback

The use of flexible links in a robot inevitably causes the elastic deflection and vibration of the endpoint of the robot during high-speed operations. The deflection and vibration will tend to degrade the positioning performance of the robot. In this paper, an optical sensing system consisting of a laser diode and a position sensitive detector is introduced for the real-time measurement of the dynamic deflection. Utilising a non-linear, coupled and measurement-based dynamic system model, a Lyapunov-type controller based on the deflection feedback is then proposed to damp out the tip oscillations and regulate the endpoint of the flexible robot. Experimental tests are conducted for a flexible one-link robot arm with a payload mass at the tip. The results demonstrate the effectiveness of the proposed measuring and control schemes.     

Effect of hoisting cable elasticity on anti-sway controllers of quay-side container cranes

Oscillation frequency of crane payloads is the main and most important factor in crane anti-sway control systems design. In the summer of 2005, a Smart Sway Control system (SSC) was installed on a 65-ton quay-side container crane at Jeddah Port. During the calibration phase of the installation, it was observed that heavy payloads combined with the dynamic stretch of the hoist cables had a significant impact on the configuration of the hoisting mechanism and the pattern of oscillation. This introduced considerable change in the oscillation frequency of the payload, which resulted in a significant impact on the performance of the anti-sway control system. Empirical formulas had to be used to compensate for the change in the frequency approximation used in the controller algorithm. In this work, an analytic approximation of the oscillation frequency of the hoisting mechanism of a quay-side container crane is developed, which takes into consideration the elasticity of the hoisting cables. A parametric study is performed to investigate the extent of the effect of the hoisting cables stretch on the system behavior for a typical range of payload masses and cable lengths. The performance of the delayed feedback control system used in the SSC controller is simulated on an elastic cables model using both the elastic and rigid cable frequency approximations.     

Exact post-buckling configurations of cantilevered column subjected to forces produced by a tensioned cable

This study deals with the post-buckling behavior of an inextensible elastic prismatic cantilevered column of length L which is loaded by a cable attached at the tip of the cantilever and at mid-length and terminate at the fixed support. The post-buckling behavior of the column–cable system is solved analytically in terms of elliptic integrals using the principle of elastic similarity.It was shown that for a given prescribed angle of inclination for the lower segment of the cable, four equilibrium configurations exist with two of these are of symmetrical type. Moreover, in order to generalize the present study for n-segment column, the case of the three-segment column has been investigated. For such case, the results showed that eight post-buckling equilibrium configurations existed with four of these configurations as a symmetrical type. This study has several interesting engineering applications in ultra-lightweight aerospace engineering such as in solar sails technology, flexible robotics arms, biomedical instrumentation and it can be used as a flexible fixing rod in space technology.     

基于动力松弛法的松弛索杆体系找形分析

索杆张力结构施工成形分析需要解决一个松弛态索杆系统的平衡形态求解问题,该问题可归结为一个给定构件原长的受荷索杆机构系统的找形问题。文中利用动力松弛法进行该类松弛索杆体系的找形分析。由于不建立刚度矩阵,避免了体系几何不稳定性所引起的刚度矩阵奇异问题。该方法采用悬链线索单元模型,可以考虑索大垂度效应。文中还推导了反映索原长和内力之间关系的悬链线索单元协调方程。通过一个正交松弛索网算例分析,考察了该找形方法的计算精度和收敛性。最后还模拟了一个索穹顶的施工成形过程,表明了该找形方法用于索杆张力结构施工成形分析的有效性。     

Vibration control of a transversely excited cantilever beam with tip mass

The problem of controlling the vibration of a transversely excited cantilever beam with tip mass is analyzed within the framework of the Euler–Bernoulli beam theory. A sinusoidally varying transverse excitation is applied at the left end of the cantilever beam, while a payload is attached to the free end of the beam. An active control of the transverse vibration based on cubic velocity is studied. Here, cubic velocity feedback law is proposed as a devise to suppress the vibration of the system subjected to primary and subharmonic resonance conditions. Method of multiple scales as one of the perturbation technique is used to reduce the second-order temporal equation into a set of two first-order differential equations that govern the time variation of the amplitude and phase of the response. Then the stability and bifurcation of the system is investigated. Frequency–response curves are obtained numerically for primary and subharmonic resonance conditions for different values of controller gain. The numerical results portrayed that a significant amount of vibration reduction can be obtained actively by using a suitable value of controller gain. The response obtained using method of multiple scales is compared with those obtained by numerically solving the temporal equation of motion and are found to be in good agreement. Numerical simulation for amplitude is also obtained by integrating the equation of motion in the frequency range between 1 and 3. The developed results can be extensively used to suppress the vibration of a transversely excited cantilever beam with tip mass or similar systems actively.     

Sway Reduction on Container Cranes Using Delayed Feedback Controller

Traditionally, container cranes are modeled as a simple pendulum, witheither a flexible or a rigid hoisting cable, and a lumped mass at theend of that cable. In the case of large container cranes, the actualconfiguration of the hoisting mechanism is significantly different. Itconsists typically of an arrangement of four hoisting cables, which arehoisted from four different points on the trolley and attached on theload side to four points on a spreader bar used to lift containers.Thus, the dynamics of the actual container-crane hoisting assembly isdifferent from that of a simple pendulum. A controller design based onthe actual model is more likely to result in an improved response. Inthis work, a mathematical model of the actual container crane isdeveloped. Then, a simplified version of this model is used to calculatethe gain and delay for the delay controller developed earlier. Numericalsimulations are performed by applying the delay controller to the fullnonlinear model of the container crane.     

Three-Dimensional Large Deformation Analysis of the Multibody Pantograph/Catenary Systems

To accurately model the nonlinear behavior of the pantograph/catenary systems, it is necessary to take into consideration the effect of the large deformation of the catenary and its interaction with the nonlinear pantograph system dynamics. The large deformation of the catenary is modeled in this investigation using the three-dimensional finite element absolute nodal coordinate formulation. To model the interaction between the pantograph and the catenary, a sliding joint that allows for the motion of the pan-head on the catenary cable is formulated. To this end, a non-generalized arc-length parameter is introduced in order to be able to accurately predict the location of the point of contact between the pan-head and the catenary. The resulting system of differential and algebraic equations formulated in terms of reference coordinates, finite element absolute nodal coordinates, and non-generalized arc-length and contact surface parameters are solved using computational multibody system algorithms. A detailed three-dimensional multibody railroad vehicle model is developed to demonstrate the use of the formulation presented in this paper. In this model, the interaction between the wheel and the rail is considered. For future research, a method is proposed to deal with the problem of the loss of contact between the pan-head and the catenary cable.     

Dynamic response of tower crane induced by the pendulum motion of the payload

Dynamic response of tower cranes coupled with the pendulum motions of the payload is studied in this paper. A simple perturbation scheme and the assumption of small pendulum angle are applied to simplify the governing equation. The tower crane is modeled by the finite element method, while the pendulum motion is represented as rigid-body kinetics. Integrated governing equations for the coupled dynamics problem are derived based on Lagrange’s equations including the dissipation function. Dynamics of a real luffing crane model with the spherical and planar pendulum motions is analyzed using the proposed formulations and computational method. It is found that the dynamic responses of the tower crane are dominated by both the first few natural frequencies of crane structure and the pendulum motion of the payload. The dynamic amplification factors generally increase with the increase of the initial pendulum angle and the changes are just slightly nonlinear for the planar pendulum motion.     

COMPUTATIONAL METHOD FOR DYNAMICS SIMULATION OF PAYLOAD SEPARATION FROM SATELLITE WITH RAIL CLEARANCE

传统在轨分离载荷动力学分析未考虑实际导轨的实时接触,无法准确分析分离时刻载荷的速度和角速度。针对半圆形双导轨,研究了空间导轨与定向器接触的特点及形式,基于分离装置的几何构型提出了一种确定发生相对轴向运动时导轨与定向器潜在接触对的方法,所提方法考虑了载荷轴线与导轨轴线的空间夹角,保证了分离后期接触检测的准确性,并可推广至多导轨接触计算。基于Lankarani与Nikravesh的连续接触力模型计算法向碰撞力,采用修正的Coulomb模型计算切向摩擦力。最后对飘浮基挠性航天器在轨分离载荷模型进行数值分析,验证了方法的有效性。结果表明导轨间隙增大了接触碰撞力,且随间隙的增大垂直于载荷分离方向的速度和角速度增大,导轨间隙使基座的转动与挠性附件强烈耦合,对航天器的稳定性造成影响。     

An aeroelastic model for composite rotor blades with straight and swept tips. Part I: Aeroelastic stability in hover

An analytical model for predicting the aeroelastic behavior of composite rotor blades with straight and swept tips is presented. The blade is modeled by beam type finite elements along the elastic axis. A single finite element is used to model the swept tip. The non-linear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. It is shown that composite ply orientation has a substantial effect on blade stability. At low thrust conditions, certain ply orientations can cause instability in the lag mode. The flap-torsion coupling associated with tip sweep can also induce aeroelastic instability in the blade. This instability can be removed by appropriate ply orientation in the composite construction.     

Reduction of the sonic boom level by heating the flow in front of the body

A numerical study of the possibility of reducing the sonic boom level in the case of local heat release to a supersonic gas flow at Mach number equal to 2 ahead of a body is described. The computations are performed for a spherical heat supply zone located on the flight trajectory ahead of the tip of an axisymmetric thin body. For the numerical study the combined method of “phantom bodies” is used. Different magnitudes of heat supply to the incoming flow are tested. These calculations are performed with allowance for interaction of shock waves emanating from the heated gas region and from the body in the far field. The computational results show that the local heat supply to a supersonic gas flow ahead of a body can reduce the sonic boom level by more than 20 %. The reduction of the sonic boom level is ensured by changing the free-stream parameters ahead of the body and by preventing the coalescence of shock waves from the heat supply zone and from the body in the far field.     

Stability of motion of two rigid bodies connected by a cable in the atmosphere

The spatial motion of two rigid bodies connected by a weightless inextensible cable in the atmosphere is considered. They are assumed to be bodies of revolution with static and dynamic symmetry. The condition of static stability of the system angular motion with respect to the direction of the incident airflow velocity vector is written out and analyzed. The influence of gyroscopic terms and damping moments on the stability condition is studied. An example of analysis of motion in the atmosphere of two connected bodies that are cones with a spherical tip is given. It is shown that the stable motion in the atmosphere can always be ensured by an appropriate matched choice of the parameters of the entire system on the basis of the obtained stability conditions. A numerical example of estimating the cable tension forces arising as the system descends on a ballistic trajectory in the atmosphere is presented.