Method for determining the change in position of a load under the action of waves for a full-circle crane vessel

Abstract

The application discloses a method for determining the position change of a hoisted object under the action of waves of a full-circle crane ship, and comprises the following steps: step 1, determining the second-order wave force of the waves acting on the full-circle crane ship; step 2, determining the displacement of six degrees of freedom of the full-circle crane ship in an anchored state based on the second-order wave force; step 3, determining the end point coordinates of the top end of a hoisting arm of a crane for suspending the hoisted object on the full-circle crane ship; step 4, determining the movement vectors of the top end of the hoisting arm in the directions of three coordinate axes; and step 5, calculating the in-plane angle and the out-of-plane angle. The application considers the influence of the second-order wave force on the spatial position and movement of the hoisted object suspended by the crane of the full-circle crane ship in the anchored state, can quantitatively reflect the position of the hoisted object at each time node under the action of the waves through the in-plane angle and the out-of-plane angle, and provides a theoretical basis and guidance for the safety of subsequent hoisting operation nodes.

Description

Technical Field

[0001] This invention relates to the field of crane suspension and load position change technology, specifically a method for determining the load position change of a fully rotating crane vessel under wave action. Background Technology

[0002] Full-rotation crane vessels (hereinafter referred to as crane vessels) are widely used in port construction, shipbuilding, bridge construction, underwater salvage, and various marine engineering operations involving waterworks. Crane vessels are subject to the influence of wind and waves, which cause movement of the loads suspended on the vessel. Especially during operation, significant movement of the loads can severely impact the safety of crane vessel operations. Accurate analysis of the relative position and movement patterns of the loads suspended by the crane on the crane vessel during operation, particularly under wave conditions, is crucial for automating the lifting and unloading process, optimizing lifting procedures, and ensuring operational safety. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for determining the positional changes of a suspended load on a fully rotating crane vessel under wave action, which can solve the problems described in the background art.

[0004] The technical solution to achieve the objective of this invention is: a method for determining the position change of a suspended load on a fully rotating crane vessel under wave action, comprising the following steps:

[0005] Step 1: Determine the second-order wave force F acting on the azimuth crane vessel. 2nd ;

[0006] Step 2: Determine the displacements of the six degrees of freedom of the hull of the fully rotating crane vessel under the second-order wave force in the anchored state: roll μ1, pitch μ2, yaw μ3, roll μ4, pitch μ5, and heave μ6.

[0007] Step 3: Determine the coordinates (x, y) of the top end of the boom of the crane used to suspend the load on the full-rotation crane vessel. p ,y p ,z p );

[0008] Step 4: Determine the motion vector (s) of the top end of the boom in the x, y, and z coordinate axes according to formula ③. px ,s py ,s pz ):

[0009]

[0010] In the formula, (x p,y p ,z p () represents the coordinates of the endpoint of the boom.

[0011] And based on the motion vector (s) px ,s py ,s pz Further, determine the velocity vector at the top end of the boom. and acceleration vector

[0012] Step 5: Calculate the interior angle α and exterior angle β using formula ④:

[0013]

[0014] In the formula, g is the acceleration due to gravity, and l is the length of the suspension rope. and These are the second and first derivatives of the interior angle α, respectively. and These are the second and first derivatives of the in-plane angle β, respectively, and λ represents the combined coefficient of friction and air resistance of the suspended object.

[0015] Furthermore, in step 2, the displacements of the six degrees of freedom can be calculated using formula ①:

[0016]

[0017] In the formula, m jk It is the generalized mass matrix, A jk It is the additional quality coefficient, B jk It is the damping coefficient, C jk It is the generalized restoring force coefficient. It is the Froud-Kryloff force. It is diffraction force, μ k The displacements of the ship's hull in six degrees of freedom—roll, pitch, yaw, heave, and heave—can be obtained by solving formula ①. μ k The second derivative, μ k The first derivative.

[0018] Furthermore, the endpoint coordinates (x) of the top of the boom p ,y p ,z p The result is obtained by calculation using formula ②:

[0019]

[0020] In the formula, (x g ,y g ,zg ) represents the coordinates of the center of gravity of the slewing crane vessel, θ is the boom tilt angle, γ is the slewing angle, and l c It is the length of the top of the crane boom along the axis of the boom from the center of gravity of the ship. b It refers to the length of the boom.

[0021] Furthermore, in step 5, the interior angle α and exterior angle β of formula ④ are solved using a numerical solution method.

[0022] The beneficial effects of this invention are as follows: This invention considers the influence of second-order wave force on the spatial position and motion of the suspended object of a fully rotating crane vessel in an anchored state, especially considering the influence of the motion caused by the six degrees of freedom displacement of the second-order wave force on the motion of the suspended object. It can effectively reflect the position of the suspended object at each time node under the action of waves by using in-plane and out-of-plane angles, providing a theoretical basis and guidance for the safety of subsequent crane operation nodes. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the process of the present invention;

[0024] Figure 2 This is a schematic diagram showing the state of a crane suspending a load Q via its boom;

[0025] Figure 3 A schematic diagram of the time history curve of the in-plane angle α fluctuation of the suspended object;

[0026] Figure 4 This is a schematic diagram of the time-series curve of the in-plane angle β fluctuation of the suspended object;

[0027] Figure 5 It is a schematic diagram of the relative position of the suspended object on the crane arm and the ship hull from various viewing angles. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0029] like Figures 1-4 As shown, a method for determining the position change of a suspended load under wave action on a fully rotating crane vessel includes the following steps:

[0030] Step 1: Determine the second-order wave force F acting on the azimuth crane vessel. 2nd .

[0031] The motion of engineering vessels (including azimuth crane vessels) caused by waves can be categorized into first-order effects (corresponding to first-order motion) and second-order effects (corresponding to second-order motion). The first-order motion of an engineering vessel is linearly related to the wave height and has the same frequency as the wave. The second-order motion of an engineering vessel is proportional to the square of the wave height and includes the mean wave force (the average periodic value in regular waves) and the drift force (the sum and difference frequencies of waves in a wave group). For engineering vessels in an anchored state, the influence of the second-order wave force is very important, especially the drift force and moment, which cause significant resonance in the directions of sway, roll, and pitch. Therefore, this invention uses the second-order wave force to characterize the wave effect.

[0032] The second-order wave force can be determined using existing techniques such as the pressure integral method or the energy-momentum conservation method. For example, the second-order wave force F can be determined using the following formula. 2nd :

[0033]

[0034] In the formula, ρ is the density of water, g is the acceleration due to gravity, η is the wave height, and n represents the outward normal vector of the azimuth crane ship. wL dl represents the surface integral along the waterline, Ω (1) Let m represent the first-order component of the angular displacement vector of the object about its center of gravity, and m be the mass of the azimuth crane. X is the acceleration of the ship's center of gravity, φ is the velocity potential, and X is the velocity acceleration. (1) It is the first-order component of the displacement at any point on the object. ∫∫ is the first-order component of the displacement at the object's center of gravity, and r is the angular displacement vector of the object about its center of gravity. s dS represents the integral along the surface of the object.

[0035] Of course, other methods can also be used to calculate the second-order wave force p. 2nd .

[0036] Step 2: Determine the displacements of the six degrees of freedom of the hull of the fully rotating crane vessel under the second-order wave force in the anchored state: roll μ1, pitch μ2, yaw μ3, roll μ4, pitch μ5, and heave μ6.

[0037] The displacements of the above six degrees of freedom can be calculated using formula ①:

[0038]

[0039] In the formula, m jk It is the generalized mass matrix, A jk It is the additional quality coefficient, B jk It is the damping coefficient, C jk It is the generalized restoring force coefficient. It is the Froud-Kryloff force. It is diffraction force, μ k (k=1~6) represents the displacements of the ship's six degrees of freedom: roll, pitch, sway, roll, pitch, and heave. Therefore, the displacements of these six degrees of freedom can be obtained by solving equation ①. μ k The second derivative, μ k The first derivative.

[0040] Among them, in the above equation and It can be obtained through diffraction potential and radiation potential, which can be determined according to existing technology and will not be elaborated here.

[0041] Step 3: Determine the coordinates (x, y) of the top end of the boom of the crane used to suspend the load on the full-rotation crane vessel. p ,y p ,z p The top end of the boom is connected to one end of the hoisting rope, and the other end of the hoisting rope is connected to the object being hoisted, thus suspending the object through the hoisting rope.

[0042] refer to Figure 5 The diagram shows the relative position of the load suspended by the crane and the slewing crane vessel on which the crane is located. R in the diagram represents the angular displacement vector of the load about its center of gravity, which is r in formula ①.

[0043] During the operational phase, a full-rotation crane vessel typically involves several operations, including lifting cargo, moving cargo to other locations (such as to other vessels or docks) via slewing, and lowering cargo to a fixed position. Lifting operations are achieved by adjusting the boom angle, slewing point, and hoisting rope length.

[0044] The coordinates of the endpoint of the boom (x) p ,y p ,z p The result is obtained by calculation using formula ②:

[0045]

[0046] In the formula, (x g ,y g ,z g ) represents the coordinates of the center of gravity of the slewing crane vessel, θ is the boom tilt angle, γ is the slewing angle, and l c It is the length of the top of the crane boom along the axis of the boom from the center of gravity of the ship. b It refers to the length of the boom.

[0047] Step 4: Determine the motion vector (s) of the top end of the boom in the x, y, and z coordinate axes according to formula ③. px ,s py ,s pz ):

[0048]

[0049] The motion vectors of the top end of the boom in various directions can be determined using the formula. And based on the motion vector (s) px ,s py ,s pz The velocity vector at the top end of the boom can be further calculated. and acceleration vector That is, respectively, the motion vectors (s) px ,s py ,s pz The first and second derivatives of ).

[0050] Step 5: Calculate the interior angle α and exterior angle β using formula ④:

[0051]

[0052] In the formula, g is the acceleration due to gravity, and l is the length of the suspension rope. and These are the second and first derivatives of the interior angle α, respectively. and These are the second and first derivatives of the in-plane angle β, respectively, and λ represents the combined coefficient of friction and air resistance of the suspended object.

[0053] Among them, formula ④ can be solved numerically using the Runge-Kutta method to obtain numerical solutions for the interior angle α and the exterior angle β.

[0054] refer to Figure 2 , Figure 2 This is a schematic diagram showing the state of a crane suspending a load Q via its boom. In the diagram, Q represents the load, G represents the center of gravity of the slewing crane vessel, and P represents the endpoint of the boom. The coordinate systems x0y0z0 and xyz are Cartesian coordinate systems with different origins. The origin of coordinate system x0y0z0 is the center of gravity G, and the origin of coordinate system xyz is the endpoint P. The in-plane angle α is the angle between the swung load and the plane yPz, and the out-of-plane angle β is the angle between the projection of the swung load PM (i.e., the straight line PM) onto the plane yPz and the z-axis.

[0055] Taking a floating crane as the analysis object, the ship's oblique wave angle is 135°, the significant wave height is 2m, the spectral peak period is 8s, the coordinates of the top point of the boom are (x=67.8m, y=0, z=73.8m), the length of the lifting rope is taken as 41.6m, and the joint coefficient of friction and air resistance of the suspended load is taken as 0.01. The wave history curves of the in-plane angle α and out-of-plane angle β of the suspended load are obtained as follows: Figure 3 and Figure 4 As shown. Figure 3 It is the time-history curve of the in-plane angle α of the suspended object. Figure 4 These are the time-history curves of the out-of-plane angle β of the suspended object. From these two figures, we can obtain the swing angle at different time points under the action of waves. The swing angle reflects the position of the suspended object, and the swing angle at different time points reflects the position change of the suspended object.

[0056] This invention considers the influence of second-order wave forces on the spatial position and motion of a suspended load on a fully rotating crane vessel in an anchored state. In particular, it takes into account the influence of the motion caused by the six degrees of freedom displacement of the second-order wave forces on the motion of the suspended load. It can effectively reflect the position of the suspended load at each time point under the action of waves by using in-plane and out-of-plane angles, providing a theoretical basis and guidance for the safety of subsequent lifting operation nodes.

[0057] The embodiments disclosed in this specification are merely illustrative of one aspect of the invention, and the scope of protection of the invention is not limited to these embodiments. Any other functionally equivalent embodiments fall within the scope of protection of the invention. Those skilled in the art can make various other corresponding changes and modifications based on the technical solutions and concepts described above, and all such changes and modifications should fall within the scope of protection of the claims of this invention.

Claims

1. A method for determining the positional changes of a suspended load on a fully swivel crane vessel under wave action, characterized in that, Includes the following steps: Step 1: Determine the second-order wave force acting on the azimuth crane vessel. ; Step 2: Determine the roll of the hull of the crane vessel under anchorage conditions based on the second-order wave force acting on it. , unrestrained First lottery , sweeping , swaying Rise and fall Displacement with six degrees of freedom; Step 3: Determine the coordinates of the top end of the boom of the crane used to suspend the load on the full-rotation crane vessel. ; Step 4: Determine the motion vectors of the top end of the boom along the x, y, and z coordinate axes according to formula ③. : ------③ In the formula, Here are the coordinates of the endpoint at the top of the boom. And based on the motion vector Further calculate the velocity vector at the top end of the boom. and acceleration vector ; Step 5: Calculate the interior angles using formula ④ outer corners of dough : ------④ In the formula, g is the acceleration due to gravity. It is the length of the suspension rope. and They are the interior angles of the face. The second and first derivatives, and They are the exterior angles of the face. The second and first derivatives, The coefficient representing the combined friction and air resistance of the suspended load. internal angle The angle between the suspended object after swinging and the plane yPz is called the exterior angle. It refers to the angle between the projection PM of the suspended object in the plane yPz after swinging and the z-axis of the coordinate system. y represents the y-axis, P represents the origin, which is the endpoint of the boom used to suspend the suspended object, and z represents the z-axis.

2. The method for determining the position change of a suspended load under wave action by a fully rotating crane vessel according to claim 1, characterized in that, In step 2, the displacements of the six degrees of freedom can be calculated using formula ①: ------① In the formula, It is a generalized mass matrix. It is an additional quality coefficient. It is the damping coefficient. It is the generalized restoring force coefficient. It is the Froud-Kryloff force. It is diffraction force. The displacements of the ship's hull in six degrees of freedom—roll, pitch, yaw, heave, and heave—can be obtained by solving formula ①. express The second derivative, express The first derivative.

3. The method for determining the position change of a suspended load under wave action by a fully rotating crane vessel according to claim 2, characterized in that, Endpoint coordinates of the top of the boom Calculated using formula ②: ------② In the formula, The coordinates represent the position of the center of gravity of the azimuth crane vessel. It is the boom tilt angle. It is the rotation angle, It is the distance from the top of the crane boom along the axis of the boom to the center of gravity of the ship. It refers to the length of the boom.

4. The method for determining the position change of a suspended load under wave action by a fully rotating crane vessel according to claim 3, characterized in that, In step 5, the interior angles in formula ④ are solved using a numerical method. outer corners of dough .

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