The finite element analysis of an antenna framework structure was carried out in ANSYS by using parametric load variable.The precise equation of the reflecting surface was fitted applying the nodes of the reflecting surface to fitting nodes.The nonlinear curved face objective function was pseudo-linearized.The nonlinear parameters of the reflecting surface were solved numerically based on the least square method.This method is easy to program and available for antenna framework structure design.
Taking the hydraulic cylinder for the miter gate in Dateng Gorges Water Conservancy Project as the object, a large slenderness ratio test hydraulic cylinder was designed based on the similarity theory. The buckling analysis of the test hydraulic cylinder was carried out by the finite element method, considering the friction at the supports, the misalignments between piston rod and cylinder tube, and gravity. The results indicate that the stability safety factor is 10.55. A buckling experimental system was established, and the buckling stability of the test hydraulic cylinder was tested for the sliding bearing support and the rolling bearing support at the piston-rod end, respectively. The stability safety factor is over 9.01 and 6.82 relevantly. The similarities and differences among the results of the finite element method, experimental method, NB/T 35020-2013, and two-sections pressure bar method were analyzed. Experimental and analytical results clearly show that the friction at the supports is a key factor in determining the magnitude of the stability safety for large slenderness ratio horizontal hydraulic hoist and utilizing the sliding bearing can effectively improve the stability safety factor.
By building the finite element model of TC2400 tower belts with ANSYS software, this paper analyzes the whole structure's stiffness and strength under two operation modes and four different running conditions and discusses how to simplify complicated structure, how to build mixed element model and how to do contact analysis. It would be a better guide to structure analysis.
Pitch stability of the high-lift wire rope hoist vertical shiplift under dynamic hydraulic levelling has always been an issue of concern. It not only affects working efficiency but also brings significant challenges to operational safety. A new mechanical-hydraulic-structural-fluid (MHSF) coupling dynamics model and a developed semi-analytical method are presented for stable property analysis. The models of the hydraulic levelling subsystem, shallow water sloshing subsystem, the main hoist mechanical subsystem, and the shiplift chamber structure subsystem are built using a closed-loop transfer function, multi-modal theory, and an second-type Lagrangian equation, respectively. Then, a core twenty-one order state matrix of the MHSF coupling system is established using the state-space method. Subsequently, the Lyapunov motion stability theory and Eigen-analysis method are used in combination to judge the pitch stability and analyse the characteristics of the subsystems. Taking four typical high-lift hoist vertical shiplifts as examples, the rationality of the proposed model and method is validated. The results indicate that although the pitch stability safety factor under hydraulic dynamic levelling is reduced by about 15 % to 44 % with respect to hydraulic static levelling, hydraulic dynamic levelling still can meet stability requirements. Furthermore, for the designed 200 m level hoist vertical shiplift, the preliminary design parameters can ensure the pitch stability safety factor under dynamic hydraulic levelling of not less than 1.1. The element most prone to instability is the shallow water sloshing subsystem; increasing the synchronous shaft stiffness or the water boundary layer damping ratio can effectively enhance the pitch stability.
A theoretical formulation based on the linearized potential theory, the Descartes\' rule and the extremum optimization method is presented to calculate the critical distance of lifting points of the fully balanced hoist vertical ship lift, and to study pitching stability of the ship lift. The overturning torque of the ship chamber is proposed based on the Housner theory. A seven-free-degree dynamic model of the ship lift based on the Lagrange equation of the second kind is then established, including the ship chamber, the wire rope, the gravity counterweights and the liquid in the ship chamber. Subsequently, an eigenvalue equation is obtained with the coefficient matrix of the dynamic equations, and a key coefficient is analyzed by innovative use of the minimum optimization method for a stability criterion. Also, an extensive influence of the structural parameters contains the gravity counterweight wire rope stiffness, synchronous shaft stiffness, lifting height and hoists radius on the critical distance of lifting points is numerically analyzed. With the Runge-Kutta method, the four primary dynamical responses of the ship lift are investigated to demonstrate the accuracy/reliability of the result from the theoretical formulation. It is revealed that the critical distance of lifting points decreases with increasing the synchronous shaft stiffness, while increases with rising the other three structural parameters. Moreover, the theoretical formulation is more applicable than the previous criterions to design the layout of the fully balanced hoist vertical ship lift for the ensuring of the stability.
Pitch stability under shallow water sloshing–structure interaction has always been the most concerned issue in the design of the high-lift wire rope hoist vertical shiplift, which brings great challenges to the operational safety. A semi-analytical method including the developed modal system and the new coupled dynamics model is presented for pitch stability analysis. Based on the linear modal theory, the modal system is developed to describe the shallow water sloshing in the shiplift chamber, and the hydrodynamic moment associated with infinite set of modal functions is reasonably simplified by only retaining the lowest mode. Then a new 9-DOF coupled dynamics model of the complete main hoist system, shiplift chamber motion, and shallow water sloshing is established as dynamic equations by using the Lagrange equation of the second kind. Subsequently, the coefficient matrix of the dynamic equations and the Lyapunov motion stability theory are used in combination to numerically obtain the critical distance of suspension points. Taking four typical high-lift wire rope hoist shiplifts as an example, the results indicate that the proposed scheme improves the computational accuracy by 7.0–20.8% with respect to previous methods. Furthermore, for the being designed 200 m level wire rope hoist vertical shiplift, the preliminary design parameters can ensure the pitch stability safety factor not less than 1.3, increasing the wire rope stiffness or the synchronous shaft stiffness can effectively enhance the pitch stability.
An improved two sections pressure bar method (ITSPBM) was presented to analyze the stability of the large slenderness ratio horizontal hydraulic cylinder. The friction moments, the bearing reactions at the two hinge joints as well as the clearances between the piston and the inner wall of the cylinder were taken into consideration. The result shows that the stability safety factor is 6.20. Meanwhile, in the finite element model of the horizontal hydraulic cylinder, the nonlinear friction force and clearances were involved. The result reveals that the stability safety factor is 9.24. Through comparing the results of the ITSPBM, the traditional two sections pressure bar method (TTSPBM), the finite element method (FEM) and the method in NB/T 35020-2013, it suggests that the stability of the large slenderness ratio horizontal hydraulic cylinder meet the actual engineering requirements and the friction moments at the two hinge joints can extremely enhance the stability.
The existing critical buckling load calculation methods of horizontal hydraulic cylinder failed to fully reflect the initial boundary conditions and some critical influence factors, resulting in an unjustified critical buckling load. A new method to analyze the buckling behavior of the horizontal hydraulic cylinder articulated at both supports is developed on basis of large deflection theory and Timoshenko beam theory. Friction at supports, self-weight and initial misalignment by clearances are taken into account. Friction moments of supports are built according to Hertz contact theory. Bending stiffness of cylinder-rod junction is figured out in terms of elastic deformation theory. Runge–Kutta and Newton–Raphson method are used in numerical calculation for the critical buckling load. Practical calculation and stability test are carried out to verify the necessity of considering large deflection and shear effect in the proposed method. Experimental work shows the critical buckling load by the proposed method can well match to that by stability test with 0.55% deviation. Moreover, the numerical calculation results demonstrate that the friction moment of the support at piston rod end is crucial for the buckling behavior. The critical buckling load rises increasingly as the friction coefficient [Formula: see text] rises. As the friction coefficients [Formula: see text] increases from 0 to 0.020, the rise rate of critical buckling load increases from 1.782% to 8.055% per 0.001. And the clearance at cylinder-rod junction is a minor factor on the critical buckling load. As the clearances increase by 10 times, the critical buckling load decreases by 3.542%.
As the core structure of the shiplift, the ship chamber is a typical rectangular container with filling water depth less than 0.1. Even small pitching excitation could produce large liquid sloshing and significant capsizing moment, and lead to a catastrophic overturning accident. As a basis of dynamical modeling and simulation of the shiplift, a fluid dynamic model is presented to predict the capsizing moments based on the Housner theory. Assuming a time-harmonic pitching excitation, the potential solution reflecting dynamic characteristics between pitching excitation and the fluid free surface oscillation angle is expanded analytically. A series of engineering formulas for the capsizing moments, including impulsive and convective parts, are then imposed. Comprehensive numerical analysis further extends the applicability of formulations to the cases for most of ship chambers or other rectangular tanks with similar filling water depth. The validation of proposed scheme is extensively demonstrated through comparison with other theoretical method and experimental results, and the interaction between the forcing frequency, the capsizing moments and fluid natural frequency has been qualitatively descripted. The results exhibited that the present model has accurate description under the conditions of small pitching angles and only considering the capsizing moments coming from the convective pressures can ensure high accuracy in engineering design.
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