Method for measuring maximum tension in laying of submarine cable and method for controlling bottom touch tension

Abstract

This invention discloses a method for measuring maximum tension and a method for controlling bottoming tension during submarine cable laying, belonging to the field of submarine cable construction. The method for measuring maximum tension includes: establishing a shape equation for the suspended section of the submarine cable on the deck, considering the bending stiffness of the cable; and setting L=L... a , ω=ω a And when x=0, y=D a H=T adown Substitute this into the formula of step S1; use the Newton-Raphson method to iteratively solve for the tension T at the point where the submarine cable touches the deck. adown , will T adown +ω a D a As the maximum tension during submarine cable laying, this invention incorporates the influence of cable bending stiffness on the suspended deck section, while employing classical catenary theory for the underwater catenary section. This invention can more accurately simulate the influence of bending stiffness on submarine cable tension under different aspect ratios, offering advantages such as higher computational efficiency, more accurate results, and avoidance of cable damage, thus improving the quality and efficiency of submarine cable laying.

Description

Technical Field

[0001] This invention relates to a method for measuring maximum tension and a method for controlling bottoming tension during submarine cable laying, belonging to the field of submarine cable construction. Background Technology

[0002] Tension control during submarine cable construction is generally achieved by monitoring the entry angle into the water. The bottom tension of the cable is obtained through the relationship between the entry angle and the bottom tension using the catenary equation. However, in actual offshore operations, the cable-laying vessel experiences significant rolling due to wind and waves, making it difficult to measure the entry angle and ensuring accuracy. There is a one-to-one correspondence between the cable profile on deck and the bottom tension of the catenary after entry into the water. Furthermore, the horizontal projected length of the cable on deck can be easily measured using pressure sensors. Therefore, the bottom tension can be controlled by monitoring the horizontal projected length of the cable on deck.

[0003] The classic catenary model simplifies submarine cables into ideally flexible cables with no bending stiffness, subjected only to axial force. When the length-to-diameter ratio of the cable is large (such as deep-sea entry cables), the influence of bending stiffness is negligible, making the classic catenary theory suitable. However, the length between the cable exiting the cable-laying machine and the contact deck of deck-mounted cables is relatively small. Ignoring the influence of bending stiffness can introduce certain errors in controlling the cable's bottoming tension. Summary of the Invention

[0004] To address the aforementioned problems in existing technologies for monitoring tension during submarine cable construction, this invention proposes a method for measuring the maximum tension during submarine cable laying and a method for controlling the bottoming tension. The method considers the influence of the cable's bending stiffness when calculating the maximum tension during submarine cable laying, and adopts the classic catenary equation when establishing the catenary equation for the submarine cable in water, thereby making the results more accurate and enabling precise control of the bottoming tension during submarine cable laying.

[0005] To solve the above technical problems, the present invention includes the following technical solutions: A method for measuring maximum tension during submarine cable laying, using a cable-laying vessel equipped with a cable-laying machine, wherein the submarine cable, after being output from the cable-laying machine, sequentially forms a deck-suspended section, a horizontal contact section, an arc-shaped contact section, and a catenary section in the water, before touching the bottom, the measurement method includes the following steps: Step S1. Establish the shape equation of the deck suspension section of the submarine cable considering the bending stiffness of the cable: ;in, ; In the formula, ω is the vertical load per unit length of the submarine cable, L is the horizontal length of the cable's suspended deck section, H is the horizontal component of the cable tension, EI is the bending stiffness of the cable, and T... adown Tension at the point where the submarine cable touches the deck; Step S2: Measure the projected length L of the suspended section of the submarine cable on the deck in real time.a , ω=ω a And when x=0, y=D a H=T adown Substituting this into the formula in step S1, we get: ; In the formula, D a ω is the vertical distance between the location of the cable delivery machine and the top of the deck roller. a T represents the vertical load per unit length of the submarine cable in the air. adown Tension at the point of contact between the submarine cable and the deck; Step S3: Solve the formula in step S2 iteratively using the Newton-Raphson method to obtain the tension T at the point where the submarine cable touches the deck. adown Considering the weight of the submarine cable in the suspended section of the deck, T adown +ω a D a As the maximum tension during submarine cable laying.

[0006] This embodiment also provides a method for controlling the bottom tension during submarine cable laying, including the following steps: Step P1. Establish the catenary equation for the underwater catenary segment of the submarine cable and solve for the tension T at the bottom of the cable. wdown The apex of the catenary is the suspension point of the submarine cable's entry into the water, and the horizontal tension at the apex of the catenary is T. wtop T wtop Equal to the solved T adown ; Step P2. Calculate the difference ΔT between the bottoming tension and the minimum allowable tension; Step P3. Control the cable laying speed of the cable laying machine according to ΔT, so that ΔT approaches 0, and T wdown With T R match.

[0007] Furthermore, setting the origin of the coordinate system at the lowest point of the catenary, with the X-axis horizontal and the Y-axis vertically downward, the equation of the catenary segment of the submarine cable in the water is expressed as: T wdown =T adown -ω w D; In the formula, ω w denoted as , where is the vertical load per unit length of the submarine cable in the water, and is a known value; D is the depth from the suspension point of the submarine cable entry section to the seabed, and is a real-time measured value.

[0008] Furthermore, the minimum permissible tension is T. R Located at the bottom of the submarine cable, it satisfies: ; In the formula: R RLet be the minimum permissible radius of curvature for the submarine cable, which is a known value.

[0009] Furthermore, step P3 specifically involves: When ΔT > m, increase the cable laying speed of the cable laying machine to reduce the tension T of the submarine cable touching the bottom. wdown ; When ΔT < 0, reduce the cable laying speed of the cable laying machine to increase the submarine cable's bottom tension T. wdown ; When 0≤△T≤m, the cable laying speed remains constant.

[0010] This invention, by employing the above technical solutions, offers the following advantages and positive effects compared to existing technologies: It distinguishes between the deck-suspended section and the underwater catenary section of the submarine cable. For the deck-suspended section, it incorporates the influence of the cable's bending stiffness, calculates the tension at the cable's contact plate, and thus accurately calculates the maximum tension of the cable, effectively preventing damage due to excessive tension. For the underwater catenary section, it uses classical catenary theory, calculating the cable's bottom tension based on the already calculated tension at the cable's contact plate. This allows for a more accurate simulation of the influence of bending stiffness on cable tension under different length-to-diameter ratios, thereby precisely controlling the bottom tension of the cable to approach the minimum allowable tension. Compared to existing technologies, this invention offers higher computational efficiency, more accurate results, and avoids damage to the cable, improving the quality and efficiency of submarine cable laying. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of submarine cable laying in one embodiment of the present invention;

[0012] Figure 2 This is a schematic diagram of the force on a submarine cable micro-element in one embodiment of the present invention.

[0013] The numbers in the diagram are as follows: 1-Cable laying vessel; 2-Submarine cable; 3-Cable laying machine; 4-Deck suspended section; 5-Horizontal contact section; 6-Arc-shaped contact section; 7-Cableway section in water; 8-Inlet bridge; 9-Roller; 10-Pressure sensor; 11-Sea level; 12-Seabed. Detailed Implementation

[0014] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, further illustrates the method for controlling the bottom tension of submarine cables based on bending stiffness provided by the present invention. The advantages and features of the present invention will become clearer from the following description. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0015] Example 1

[0016] like Figure 1As shown, a cable-laying vessel 1 is used to lay the submarine cable 2. The cable-laying vessel 2 is equipped with a cable-laying machine 3 and a water-entry bridge 8 at the stern. After being output from the cable-laying machine 3, the submarine cable 2 sequentially forms a deck-suspended section 4, a horizontal contact section 5, an arc-shaped contact section 6, and a catenary section 7 in the water, before finally touching the seabed 12. The cable-laying machine 3 controls the cable-laying speed v of the submarine cable 2; as v increases, the horizontal projection length L of the deck-suspended section of the submarine cable increases. a The tension of cable 2 is reduced. The entry bridge 8 guides the cable during its descent and ensures the bending radius meets requirements, preventing damage. The cable in the water, under its own weight, pulls the cable above it, causing tension at the arc-shaped contact section 6, the horizontal contact section 5, and the deck-suspended section 4, with the maximum tension occurring at the cable exiting the cable laying machine. Several tightly connected circular roller pressure sensors 10 are arranged on the deck along the cable 2 path. When the cable falls on a pressure sensor 10, the sensor generates pressure. Therefore, the pressure sensor 10 with the closest monitored reading to the cable laying machine is identified, and the distance between this pressure sensor 10 and the cable laying machine's output end is taken as the horizontal projected length L of the deck-suspended section 4 of the cable. a To reduce friction on the submarine cable, rollers 9 are installed on the curved surface of the inlet bridge.

[0017] The core of this invention lies in distinguishing between the suspended section of a submarine cable deck and the catenary section in the water. The catenary section in the sea utilizes classical catenary theory, while the suspended section on the deck needs to consider the influence of the cable's bending stiffness. This allows for a more accurate simulation of the effect of bending stiffness on cable tension under different length-to-diameter ratios, thereby controlling the horizontal length projection L of the suspended section. a Precisely control the tension of the submarine cable when it touches the bottom.

[0018] The method for monitoring maximum tension during submarine cable laying provided in this embodiment includes the following steps: Step S1. Establish the shape equation of the deck suspension section of the submarine cable considering the bending stiffness of the cable: ; in, ; In the formula, ω is the vertical load per unit length of the submarine cable, L is the horizontal length of the cable's suspended deck section, H is the horizontal component of the cable tension, EI is the bending stiffness of the cable, and T... adown The tension at the cable contact point on the deck is given. The origin of the coordinate system is the intersection of the horizontal line at the highest point of the suspended section of the cable deck and the vertical line at the lowest point. The positive direction of the y-axis is vertically downward, and the positive direction of the x-axis is towards the cable laying machine.

[0019] Step S2. Measure the projected length L of the suspended section of the submarine cable on the deck in real time. a , ω=ω a And when x=0, y=Da H=T adown Substituting this into the formula in step S1, we get: ; in, In the formula, D a ω is the vertical distance from the cable delivery machine position to the top of the deck roller. a T represents the vertical load per unit length of the submarine cable in the air. adown Tension at the point where the submarine cable touches the deck.

[0020] Step S3. Solve the formula in step S2 iteratively using the Newton-Raphson method to obtain the tension T at the point where the submarine cable touches the deck. adown Considering the weight of the submarine cable in the suspended section of the deck, T adown +ω a D a As the maximum tension during submarine cable laying, precise calculation of the maximum tension of the submarine cable can effectively prevent damage caused by excessive tension.

[0021] The following is a further explanation of the shape equation of the deck suspension section of the submarine cable considering the bending stiffness of the submarine cable in step S1.

[0022] like Figure 2 The diagram shows a submarine cable segment. In the diagram, H represents the horizontal component of tension, V represents the vertical shear force, M represents the bending moment, ds represents the arc length of the segment, ωds represents the vertical force on the segment, and ω represents the vertical load per unit length.

[0023] Depend on The equilibrium equations in the vertical direction are as follows: (1); Taking the moment balance at the left end of the micro segment: (2); The above equation omits higher-order terms. and to After differentiation, we get: (3); From the relationship between bending moment M and curvature k ,available: (4); In the formula: EI is the bending stiffness. Substituting equation (4) into equation (3) and using equation (1), we can obtain: (5); Equation (5) is the static equilibrium equation for a submarine cable subjected only to a uniform vertical load, considering bending stiffness and large deformation. For deck submarine cables, the cable exit height of the cable laying machine is 1-2 meters, while L... aThe value is much greater than 2 meters, and the submarine cable has a relatively flat shape. Therefore, higher-order nonlinear terms can be ignored, resulting in the following static equilibrium equations: (6); The static equilibrium equation (6) is a non-homogeneous differential equation, and the corresponding homogeneous equation is: (7); make The general solution of the homogeneous equation (7) is: (8); Suppose that a particular solution to the nonhomogeneous equation (6) is a quadratic polynomial: (9); Substituting (9) into equation (6) yields .

[0024] Solution of equation (6) The sum of the general solution (8) of the homogeneous equation and the particular solution (9) of the non-homogeneous equation is given by setting the constant... , Each of these is incorporated into equation (8). , : (10); The origin of the coordinate axis is set at the intersection of the horizontal line at the highest point of the suspended section of the cable deck and the vertical line at the lowest point. The positive direction of the y-axis is vertically downward, and the positive direction of the x-axis is towards the cable-laying machine. The coordinates of the cable output point of the cable-laying machine are: L represents the horizontal projection length of the submarine cable on the deck. A complete submarine cable alignment satisfies... Therefore, the constant in the formula , Fixed support, , The equation for the shape of the deck cable can be obtained by solving for: (11).

[0025] like Figure 1 As shown, the vertical distance from the cable-laying machine position to the top of the deck roller is a fixed value, which can be measured in advance and recorded as D. a The horizontal projection length L of the suspended section of the submarine cable on the deck was measured in real time. a The vertical load per unit length of a submarine cable in the air is denoted as ω. a For a deck cable, when x=0, y=D a H=T adown Substitute into equation (11) to solve for the tension T at the contact point of the submarine cable. adown : (12); In the formula: .

[0026] The following section discusses step S3, specifically the calculation of the tension T at the cable contact point. adown Further explanation is needed.

[0027] The Newton-Raphson method is used to iteratively solve equation (12), and the function is defined as follows: (13); (14); Choose the catenary solution as the initial value. The formula for the (n+1)th iteration of the Newton-Raphson method is: (15); In the formula: for The derivative; , They are respectively The values ​​in the nth and n+1th iterations. When Stop iterating when the tension T at the point where the submarine cable touches the deck is obtained. adown = Thus, the maximum tension T of the submarine cable is obtained. adown +ω a D a .

[0028] Example 2 During submarine cable laying, the maximum tension of the submarine cable must not exceed its maximum allowable tension value, which is specified at the factory. However, there are also requirements for the minimum tension of the submarine cable, which occurs at the point where the cable touches the bottom. Therefore, it is necessary to control the tension at the bottom of the cable.

[0029] This embodiment provides a method for controlling the bottoming tension during submarine cable laying, including the following steps: Step P1. Establish the equation of the catenary for the underwater catenary segment of the submarine cable. The vertex of the catenary is point F, and the horizontal tension of the submarine cable at point F is T. wtop T wtop Equal to T obtained in Example 1 adown Solve for the tension T at the bottom of the submarine cable. wdown .

[0030] A pressure sensor with a circular roller is installed on the deck below the horizontal contact section of the submarine cable, and rollers are installed on the water entry bridge of the arc-shaped contact section. By neglecting the friction of the submarine cable, the tension T at the water entry suspension point of the submarine cable can be obtained. wtop ,Right now: Twtop =T adown (16).

[0031] Since the position of the suspension point F of the cable entering the water does not change significantly, and the distance between the suspension point and the sea level is small, the difference between the vertical load per unit length of the cable between point F and the sea level and the vertical load per unit length of the cable in the water can be ignored. The vertical load per unit length of the cable below point F can be considered as ω = ω w ω w This represents the vertical load per unit length of the submarine cable in the water. Measure the depth D from the suspension point F of the cable entry section to the seabed, where D is the distance between sea level 11 and seabed 12 plus the distance from the suspension point F of the cable entry section to the sea level.

[0032] With the origin of the coordinate axis set at the lowest point of the catenary, the X-axis horizontal and the Y-axis vertically downward, the expression for the classic catenary tension T is as follows: (17); When y = -D is substituted, T = T wtop The tension T at the bottom of the catenary in water can be obtained. wdown (Equal to the horizontal tension H of the catenary in water): (18).

[0033] Step P2. Calculate the difference ΔT between the bottoming tension and the minimum allowable tension.

[0034] According to classical catenary theory, the minimum radius of curvature is located at the lowest point of the catenary, and the minimum allowable tension T is... R Located at the bottom: (19); In the formula: R R Let be the minimum permissible radius of curvature for the submarine cable, which is a known value.

[0035] Find the tension T at the bottom. wdown With minimum allowable tension T R Difference △T: (20); Step P3. Control the cable laying speed of the cable laying machine according to ΔT, so that ΔT approaches 0, and T wdown With T R Matching. Specifically: when At the same time, increase the cable laying speed of the cable laying machine to reduce the tension T of the submarine cable when it touches the bottom. wdown ; when At the same time, reduce the cable laying speed of the cable laying machine to increase the tension of the submarine cable when it touches the bottom. ; when At the same time, maintain a constant cable laying speed.

[0036] Of course, setting the control point to ΔT=0 will cause the cable laying speed of the cable laying machine to be adjusted frequently. In order to reduce the frequency of adjustment, ΔT can be controlled to be within the interval [0, m], where m is a set positive number close to 0. Specifically: When ΔT > m, increase the cable laying speed of the cable laying machine to reduce the tension T of the submarine cable touching the bottom. wdown ; When ΔT < 0, reduce the cable laying speed of the cable laying machine to increase the submarine cable's bottom tension T. wdown ; When 0≤△T≤m, the cable laying speed remains constant.

[0037] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0038] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for measuring the maximum tension during submarine cable laying, comprising using a cable-laying vessel equipped with a cable-laying machine, wherein the submarine cable, after being output from the cable-laying machine, sequentially forms a deck-suspended section, a horizontal contact section, an arc-shaped contact section, and a catenary section in the water, before touching the bottom, characterized in that... The measurement method includes the following steps: Step S1. Establish the shape equation of the deck suspension section of the submarine cable considering the bending stiffness of the cable: ;in, ; In the formula, ω is the vertical load per unit length of the submarine cable, L is the horizontal length of the cable's suspended deck section, H is the horizontal component of the cable tension, EI is the bending stiffness of the cable, and T... adown Tension at the point where the submarine cable touches the deck; Step S2: Measure the projected length L of the suspended section of the submarine cable on the deck in real time. a , L=L a , ω=ω a And when x=0, y=D a H=T adown Substituting this into the formula in step S1, we get: ； In the formula, D a ω is the vertical distance between the location of the cable delivery machine and the top of the deck roller. a T represents the vertical load per unit length of the submarine cable in the air. adown Tension at the point of contact between the submarine cable and the deck; Step S3: Solve the formula in step S2 iteratively using the Newton-Raphson method to obtain the tension T at the point where the submarine cable touches the deck. adown Considering the weight of the submarine cable in the suspended section of the deck, T adown +ω a D a As the maximum tension during submarine cable laying.

2. A method for controlling bottom tension during submarine cable laying, characterized in that, Includes the following steps: Step P1. Establish the catenary equation for the underwater catenary segment of the submarine cable and solve for the tension T at the bottom of the cable. wdown The apex of the catenary is the suspension point of the submarine cable's entry into the water, and the horizontal tension at the apex of the catenary is T. wtop T wtop Equal to T obtained by solving in claim 1 adown ; Step P2. Calculate the difference ΔT between the bottoming tension and the minimum allowable tension; Step P3. Control the cable laying speed of the cable laying machine according to ΔT, so that ΔT approaches 0, and T wdown With T R match.

3. The method for controlling bottom tension during submarine cable laying as described in claim 2, characterized in that, In step P1, the origin of the coordinate system is set at the lowest point of the catenary, the X-axis is horizontal, and the Y-axis is vertically downward. The equation of the catenary segment of the submarine cable in the water is expressed as: T wdown =T adown -ω w D; In the formula, ω w denoted as , where is the vertical load per unit length of the submarine cable in the water, and is a known value; D is the depth from the suspension point of the submarine cable entry section to the seabed, and is a real-time measured value.

4. The method for controlling bottom tension during submarine cable laying as described in claim 3, characterized in that, The minimum allowable tension is T R Located at the bottom of the submarine cable, it satisfies: ； In the formula: R R Let be the minimum permissible radius of curvature for the submarine cable, which is a known value.

5. The method for controlling bottom tension during submarine cable laying as described in claim 4, characterized in that, Step P3 specifically involves: When ΔT > m, increase the cable laying speed of the cable laying machine to reduce the tension T of the submarine cable touching the bottom. wdown ; When ΔT < 0, reduce the cable laying speed of the cable laying machine to increase the submarine cable's bottom tension T. wdown ; When 0≤△T≤m, the cable laying speed remains constant.

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