Floating wind turbine hmpe mooring line dynamic stiffness calculation method

Abstract

The application provides a floating wind turbine HMPE mooring cable dynamic stiffness calculation method, and relates to the technical field of offshore photovoltaic clean renewable energy development. The method comprises the following steps: establishing a lumped mass dynamic analysis model of the mooring cable, discretizing the cable and numbering each node and unit, and determining the physical parameters of each unit; based on the dynamic analysis model, the top tension of the mooring system in the initial equilibrium state is calculated; the initial elastic modulus is set, the static stiffness is iteratively updated, and the static stiffness is obtained; the static stiffness is taken as the initial dynamic stiffness, the top end of the mooring cable is given a simple harmonic motion time history, and dynamic analysis is performed; the strain rate is introduced as a nonlinear adjustment factor, the dynamic stiffness is iteratively updated, and the final dynamic stiffness is obtained; the dynamic stiffness calculation precision is improved, the adaptability and reliability of deep sea engineering application are enhanced, the accuracy of in-situ motion simulation, offset prediction and fatigue life evaluation of the floating wind turbine is improved through the introduction of the strain rate correction term.

Description

Technical Field

[0001] This invention relates to the field of offshore photovoltaic clean and renewable energy development technology, and in particular to a method for calculating the dynamic stiffness of the mooring cable of a floating wind turbine HMPE. Background Technology

[0002] With the continued growth of global demand for renewable energy, offshore wind power has developed rapidly as an important form of clean energy, with floating wind turbines in deep-sea areas becoming the core direction for developing deep-sea wind energy resources. Unlike traditional fixed offshore wind turbines, floating wind turbines rely on mooring systems to maintain their stable operation in specific locations. As a core component of the mooring system, the mechanical properties of the mooring cables directly affect the safe positioning and dynamic response of the wind turbine.

[0003] In the selection of mooring line materials, HMPE (ultra-high molecular weight polyethylene) fiber ropes are gradually replacing traditional steel cables and other materials due to their significant advantages. Compared to steel chains or cables, HMPE ropes have higher strength and stiffness, while being lighter and having a smaller diameter. This significantly reduces the weight and volume of mooring systems, simplifying construction and maintenance, and offering particularly prominent advantages for transportation and installation in open seas or harsh sea conditions.

[0004] However, as a synthetic fiber material, HMPE cables exhibit complex nonlinear mechanical properties. In the complex and ever-changing marine environment, under the dynamic loads of waves, currents, and sea winds, the stiffness of HMPE cables changes dynamically over time, rather than remaining constant. Accurately predicting its dynamic stiffness is crucial for ensuring the dynamic response analysis and structural safety assessment of floating wind turbines. While some studies have proposed empirical formulas for iterative calculations of HMPE cable dynamic stiffness, these methods generally neglect the nonlinear influence of strain rate on dynamic stiffness. Under complex conditions such as high-frequency response in deep-sea environments and extreme environmental loads, existing methods cannot accurately reflect the stiffness evolution under actual service conditions, resulting in insufficient simulation accuracy and failing to meet the scientific requirements for structural safety assessment in engineering design.

[0005] Similarly, in applications involving other synthetic fiber cables (such as polyester cables and nylon ropes), material nonlinearity also presents challenges in stiffness calculation. Existing methods for calculating the dynamic stiffness of polyester or nylon cables, while considering factors such as average tension and tension amplitude and employing lumped mass models for dynamic analysis, fail to incorporate strain rate—a crucial dynamic factor—into the dynamic stiffness correction model. This makes them unsuitable for accurate calculations under high dynamic loads, further highlighting the necessity of considering dynamic nonlinear factors in the dynamic stiffness calculation of synthetic fiber cables. Summary of the Invention

[0006] The main objective of this invention is to provide a method for calculating the dynamic stiffness of the mooring cable of a floating wind turbine (HMPE), thereby solving at least one technical problem involved in the prior art.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for calculating the dynamic stiffness of the mooring cable of a floating wind turbine (HMPE), comprising the following steps: S1: Establish a lumped mass dynamic analysis model for the mooring cable, discretize the cable into N elements and N+1 nodes, number each node and element, and determine the physical parameters of each element; S2: Based on the dynamic analysis model, calculate the top tension of the mooring system in the initial equilibrium state, and use it as the average tension Lm; S3: Perform static stiffness iterative calculation: Set the initial elastic modulus Based on the formula Iteratively update the static stiffness until convergence, and obtain the static stiffness. ; S4: Perform dynamic stiffness iterative calculation: using the static stiffness... As the initial dynamic stiffness, the time history of the simple harmonic motion of the mooring cable tip is given and dynamic analysis is performed. A dynamic load is applied, and the dynamic tension amplitude is extracted. With strain rate Based on the modified dynamic stiffness formula: ; In the formula, 、 、 These are all parameters related to the rope material and structure. This is the strain rate correction factor; Iteratively update the dynamic stiffness until the convergence condition is met, and output the final dynamic stiffness.

[0008] In the preferred embodiment, the lumped mass dynamic analysis model in step S1 includes: Anchoring node number 1, any node i The position is determined by the vector definition, Includes Position coordinates in three directions; cable unit In unstretched length l equivalent diameter d ,density ρ Young's modulus E and internal damping coefficient ; The lumped mass dynamic analysis model includes the following mechanical components: Axial tension inside the mooring cable: using time-varying elastic modulus Participate in calculation; Damping force: based on damping coefficient And strain rate calculation; Gravity, buoyancy, hydrodynamics based on the Morison equation, and seabed contact friction.

[0009] In the preferred embodiment, the cable unit The weight and buoyancy are calculated together, and the net buoyancy is used. To represent, therefore, cable unit The net buoyancy is: (1); In the formula, Indicates the density of seawater. The acceleration due to gravity; the net buoyancy at node i is distributed in vector form; Since the net buoyancy of the cable element is evenly distributed between adjacent nodes, the nodes are given in vector form. i The net buoyancy at point is: (2); In the above formula, yes z The unit vector along the positive axis.

[0010] In the preferred scheme, the calculation of the axial tension inside the mooring cable includes the cable unit. The axial tensile force is based on the elastic modulus. Iterative calculation, specifically: Cable unit The magnitude of the axial tensile force is: (3); At this point, a cable unit in vector form is given. The axial tensile force is: (4); Axial tension By node i Pointing to node i +1 indicates that the force is applied to the node. i Meanwhile, the force in the opposite direction acts on the node. i +1; And it satisfies the condition for the existence of tension: tension exists only when the cable unit is stretched; otherwise, the tension is zero. (5).

[0011] In the preferred embodiment, the damping force is calculated in vector form as follows: (6); In the formula, The internal damping coefficient is related to the elastic modulus of the cable; strain rate of cable unit Calculated by the following formula: (7); In the formula, Let i represent the three directional positions of any node i. Let be the velocities in the three directions of any node i.

[0012] In the preferred scheme, the hydrodynamic calculations apply resistance and additional body forces. First, the relative flow velocity and acceleration at the nodes are decomposed into normal and tangential components. i The tangent direction at a given point is approximately through two adjacent nodes. i +1 and i The direction of the straight line between -1: (8); Among them, the normal direction is used It is represented as perpendicular to In still water, cable nodes i The relative water flow velocity is Then the tangential component of the relative water flow velocity is Then the normal component of the relative water flow velocity is Treating the cable as a slender cylindrical structure, the normal hydrodynamic load on the cable is calculated using the Morison equation. Based on the above components, the load is applied to the nodes. i The tangential and normal resistances are respectively: (9); (10); In the formula, The normal drag coefficient, This is the tangential drag coefficient; Apply to node i The tangential and normal additional mass forces are respectively: (11); (12); In the formula, Added mass coefficient to the normal direction. Add a mass matrix to the normal direction; For tangential additional mass coefficient, Add a tangential mass matrix; Let be the acceleration of any node i.

[0013] In the preferred embodiment, the seabed contact friction is simulated using a linear spring damper. When the node contacts the seabed, i.e. There is an interaction force between the mooring cable and the seabed, and the nodes in contact with the seabed... i Interaction forces I i for: (13); In the formula, This represents the vertical displacement of the seabed. This is the stiffness coefficient. The damping coefficient is... Let be the vertical displacement of node i. Vertical velocity, It is a unit vector along the positive z-axis.

[0014] In the preferred embodiment, strain rate is introduced in step S4. η As a nonlinear adjustment factor, it participates in subsequent stiffness iterations. The calculation of the strain rate η includes: extracting the strain change rate per unit length of the cable, and defining the strain rate as... : ; In the formula, For strain rate, The change in strain This represents the change in the effective length of the cable. This corresponds to the time step.

[0015] In the preferred scheme, in step S3, the initial elastic modulus during static stiffness iteration... The initial Young's modulus of the cable material; In step S4, the time history of the simple harmonic motion of the dynamic analysis is matched with the actual motion state of the upper floating wind turbine at the equilibrium position.

[0016] In a preferred embodiment, the mooring rope is an ultra-high molecular weight polyethylene (HMPE) fiber rope; The parameters 、 、 The strain rate correction factor was determined through cable material performance testing. δ Calibration based on dynamic mechanical tests of cables under different strain rates.

[0017] This invention provides a method for calculating the dynamic stiffness of mooring cables in a floating wind turbine (HMPE). The method includes establishing a lumped-mass dynamic analysis model of the mooring cable, discretizing the cable into N elements and N+1 nodes, numbering each node and element, and determining the physical parameters of each element; based on the dynamic analysis model, calculating the top tension of the mooring system in its initial equilibrium state as the average tension; performing iterative static stiffness calculation: setting an initial elastic modulus, iteratively updating the static stiffness until convergence to obtain the static stiffness; performing iterative dynamic stiffness calculation: using the static stiffness as the initial dynamic stiffness, giving the time history of the simple harmonic motion at the top of the mooring cable and performing dynamic analysis, applying a dynamic load, extracting the dynamic tension amplitude and strain rate, introducing the strain rate as a nonlinear adjustment factor to participate in subsequent stiffness iterations; iteratively updating the dynamic stiffness until the convergence condition is met, and outputting the final dynamic stiffness. This invention accurately reflects the stiffness evolution of fiber optic cables under extreme sea conditions in deep and far ocean, improving the accuracy of dynamic stiffness calculation and enhancing the adaptability and reliability of deep and far ocean engineering applications. By introducing a strain rate correction term, it can accurately capture the mechanical evolution characteristics of the cable under dynamic multi-condition conditions, effectively improving the modeling accuracy of dynamic responses such as wind turbine platform offset and sway, significantly improving the accuracy of in-situ motion simulation, offset prediction, and fatigue life assessment of floating wind turbines, enhancing the overall system's design safety and operational reliability, and improving the scientific rigor and engineering practical value of numerical simulation. By introducing the cable strain rate as a key variable into the dynamic stiffness calculation model, the equivalent stiffness level of the HMPE cable under different loading rates can be dynamically adjusted, solving the problem of inaccurate prediction by traditional static empirical formulas under rapidly changing wind and wave conditions. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the dynamic stiffness calculation method of the present invention; Figure 2 This is a schematic diagram of the floating wind turbine mooring of the present invention; Figure 3 This is a schematic diagram of the force analysis of the concentrated mass spring model of the present invention; Figure 4 This is a schematic diagram of the iterative process for the stiffness of synthetic fiber cables based on strain rate correction in this invention. Detailed Implementation

[0019] Example 1 like Figure 1-4 As shown, a method for calculating the dynamic stiffness of the mooring cable of a floating wind turbine HMPE includes the following steps: S1: Establish a lumped mass dynamic analysis model for the mooring cable, discretize the cable into N elements and N+1 nodes, number each node and element, and determine the physical parameters of each element.

[0020] S2: Based on the dynamic analysis model, calculate the top tension of the mooring system in the initial equilibrium state, and use it as the average tension Lm.

[0021] S3: Perform static stiffness iterative calculation: Set the initial elastic modulus Based on the formula Iteratively update the static stiffness until convergence, and obtain the static stiffness. .

[0022] S4: Perform dynamic stiffness iterative calculation: using the static stiffness... As the initial dynamic stiffness, the time history of the simple harmonic motion of the mooring cable tip is given and dynamic analysis is performed. A dynamic load is applied, and the dynamic tension amplitude is extracted. With strain rate The strain rate η is introduced as a nonlinear adjustment factor to participate in subsequent stiffness iterations; the dynamic stiffness is iteratively updated until the convergence condition is met, and the final dynamic stiffness is output.

[0023] This embodiment establishes a lumped mass dynamic analysis model of the mooring cable, determines the physical parameters of each unit, calculates the top tension of the mooring system in the initial equilibrium state, and uses strain rate correction for iterative calculation of static and dynamic stiffness. This significantly improves the accuracy of dynamic stiffness calculation, enhances the adaptability and reliability of deep-sea engineering applications, and enables the dynamic stiffness model to adapt to different loading rates and load conditions through dynamic adjustment of the strain rate term. This solves the problem of large prediction deviations in traditional static or quasi-static models under rapidly changing wind and wave conditions, significantly improves the accuracy of in-situ motion simulation, offset prediction, and fatigue life assessment of floating wind turbines, enhances the design safety and operational reliability of the overall system, and improves the scientific rigor and engineering practical value of numerical simulation.

[0024] This embodiment employs a lumped-mass mooring cable dynamic analysis model to refine the mechanical properties of the mooring cable. Before iterating the dynamic stiffness of the mooring cable using HMPE, the mooring cable is first divided into elements and numbered. For example... Figure 3 As shown, based on the lumped mass mooring cable dynamic analysis model, the mooring cable is divided into N cable units of equal size, which are connected by N+1 nodes.

[0025] In the preferred embodiment, the lumped mass dynamic analysis model in step S1 includes: Anchoring node number 1, any node i The position is determined by the vector definition, Includes Position coordinates in three directions.

[0026] Each node is actually a short straight rod, representing two half-segment cable units on either side of the node. The two end nodes (node ​​1 and N+1) each have only one half-segment cable unit on their adjacent side, so the two end nodes represent only one half-segment cable unit.

[0027] Any mooring cable unit In the unstretched length ( l ), equivalent diameter ( d ),density( ρ Young's modulus ( E and internal damping coefficient .

[0028] The lumped-mass mooring cable dynamic analysis model combines the axial tension, damping force, gravity, buoyancy, hydrodynamic forces calculated using the Morison equation, and frictional forces generated during contact with the seabed within the mooring cable. (Cable unit) Axial tension in T i+1 / 2 and damping force C i+1 / 2 Using AND and AND respectively, in the node i The concentrated weight of the cable and the buoyancy it experiences are used for W i and B i This is represented as follows. For the hydrodynamic load at the node, the hydrodynamic force at the midpoint of the cable element is calculated and then distributed to the node. The equivalent element in the tangential direction at each node is approximately the average value of two adjacent cable elements in the tangential direction, such as... Figure 3 The dashed element is shown. This tangential equivalent element is essential for calculating hydrodynamics, i.e., normal resistance. D pi The normal added mass is calculated using the Morison equation, and the tangential drag is calculated. D qi The calculation of tangential additional mass is similar.

[0029] In the preferred embodiment, the cable unit The weight and buoyancy are calculated together, and the net buoyancy is used. To represent, therefore, cable unit The net buoyancy is: (1); In the formula, Indicates the density of seawater. is the acceleration due to gravity; the net buoyancy at node i is distributed in vector form.

[0030] Since the net buoyancy of the cable element is evenly distributed between adjacent nodes, the nodes are given in vector form. i The net buoyancy at point is: (2); In the formula, yes z The unit vector along the positive axis.

[0031] Due to the complex nonlinear properties of synthetic fibers, the tether stiffness changes dynamically with load time, i.e., the HMPE cable elastic modulus. E Nonlinear changes, therefore the cable element in this iterative design analysis The elastic modulus is adopted Participating in iterative calculations, specifically: Cable unit The magnitude of the axial tensile force is: (3); At this point, a cable unit in vector form is given. The axial tensile force is: (4); Axial tension By node i Pointing to node i +1 indicates that the force is applied to the node. i Meanwhile, the force in the opposite direction acts on the node. i +1.

[0032] Note: This mooring cable dynamic analysis model is designed for flexible cables such as HMPE cables and does not consider cable compression. Therefore, the above formula requires the following condition to exist for tension to exist; otherwise, the tension is zero: (5).

[0033] In this embodiment, due to the complex nonlinear characteristics of the HMPE fiber cable, the cable stiffness dynamically changes with load time. That is, the elastic modulus E changes nonlinearly. Therefore, the cable unit... The elastic modulus of the axial tensile force is adopted Participate in iterative calculations.

[0034] Damping force has a significant impact on the stability of numerical modeling.

[0035] In the preferred scheme, the damping force is calculated in vector form as follows: (6); In the above formula, It is the internal damping coefficient related to the elastic modulus of the cable, with units of N·s / m. Additionally, the strain rate of the cable element... Calculated by the following formula: (7); In the formula, Let i represent the three directional positions of any node i. Let be the velocities in the three directions of any node i.

[0036] In the fluid dynamics analysis, the influence of wave motion was ignored, and only the forces generated by the cable element moving in still water were modeled.

[0037] In the preferred scheme, the hydrodynamic calculations apply resistance and additional body forces. First, the relative flow velocity and acceleration at the nodes are decomposed into normal and tangential components. i The tangent direction at a given point is approximately through two adjacent nodes. i +1 and i The direction of the straight line between -1: (8); Normal direction It is represented as perpendicular to In still water, cable knots i The relative water flow velocity is Then the tangential component of the relative water flow velocity is It is easy to see that the normal component of the relative water flow velocity is Treating the cable as a slender cylindrical structure, the normal hydrodynamic load on the cable is calculated using the Morison equation. Based on the velocity components given above, the load is applied to the nodes. i The tangential and normal resistances are respectively: (9); (10); In the formula, The normal drag coefficient, This is the tangential drag coefficient; Apply to node i The tangential and normal additional mass forces are respectively: (11); (12); In the formula, Added mass coefficient to the normal direction. Add a mass matrix to the normal direction; For tangential additional mass coefficient, Add a tangential mass matrix; Let be the acceleration of any node i.

[0038] This embodiment ignores wave motion and therefore does not model the Froude-Krylov force. To handle the interaction between the mooring cable and the seabed, a linear spring damper is used to simulate the vertical reaction force generated when the mooring cable node contacts the seabed. That is, the seabed is smooth and flat enough that the horizontal reaction force is ignored.

[0039] In the preferred scheme, the seabed contact force is simulated using a linear spring damper. When the node contacts the seabed, i.e. There is an interaction force between the mooring cable and the seabed, and the nodes in contact with the seabed... i Interaction forces I i for: (13); In the formula, This represents the vertical displacement of the seabed. This is the stiffness coefficient. The damping coefficient is... Let be the vertical displacement of node i. Vertical velocity, for z The unit vector along the positive axis.

[0040] This embodiment introduces a dynamic stiffness calculation method based on strain rate. First, the material parameters, structural dimensions, and tension-time duration curve of the cable are obtained, and the average tension and tension amplitude are extracted.

[0041] In the preferred embodiment, strain rate is introduced in step S4. η As a nonlinear adjustment factor, it participates in subsequent stiffness iterations. The calculation of the strain rate η includes: extracting the strain change rate per unit length of the cable, and defining the strain rate as... : ; In the formula, The change in strain This represents the change in the effective length of the cable. This is the initial length of the cable. This corresponds to the time step.

[0042] Then perform the corrected dynamic stiffness model calculation: Introducing strain rate η As a nonlinear adjustment factor, it participates in subsequent stiffness iterations to correct dynamic stiffness. Kr d The calculation formula is as follows: ; In the formula, 0 represents the strain rate under static loading. 、 、 These are all parameters related to the rope material and structure. This is the strain rate correction factor.

[0043] In this embodiment, the strain rate is extracted directly from the cable's geometric deformation (length change) and time dimension. The calculation logic is simple and fits the engineering measurement scenario, avoiding strain rate errors caused by empirical estimation.

[0044] By clearly defining strain rate as a "nonlinear adjustment factor" participating in dynamic stiffness iteration, this provides a precise dynamic correction parameter for revising the dynamic stiffness formula, quantifies the stiffness change trend of the cable under different loading rates, and solves the core problem that traditional methods cannot capture the influence of strain rate on dynamic stiffness.

[0045] In the preferred scheme, the initial elastic modulus in the static stiffness iteration in step S3 is... The initial Young's modulus of the cable material; in step S4, the time history of the simple harmonic motion of the dynamic analysis is matched with the actual motion state of the upper floating wind turbine at the equilibrium position.

[0046] In the preferred embodiment, the mooring rope is an ultra-high molecular weight polyethylene (HMPE) fiber rope.

[0047] parameter 、 、 The strain rate correction factor was determined through cable material performance testing. δ Calibration based on dynamic mechanical tests of cables under different strain rates.

[0048] like Figure 4 As shown, the specific iterative process mainly includes three parts: equilibrium position calculation, static stiffness iteration, and dynamic stiffness iteration.

[0049] Step (1): Calculation of equilibrium position Calculate the mooring tension at the guide hole when the upper floating wind turbine is in its initial equilibrium position; this tension is the initial preload at the top of the mooring cable. Then, when the upper floating wind turbine undergoes simple harmonic motion in its equilibrium position, this initial preload will be used as the average load at the top of the mooring cable. And participate in subsequent iterative calculations.

[0050] Step (2): Static stiffness iteration Solve for the static stiffness of the mooring cable at its initial equilibrium position (at which point the load amplitude is...). ): Pre-set the initial iterative stiffness of the mooring cable Based on this initial value, the top tension of the mooring cable at the initial equilibrium position is calculated. Then, using the formula Calculate the stiffness of the mooring cable and recalculate the top tension of the mooring cable at the initial equilibrium position. Repeat the iterative calculation. n Repeat until satisfied. Stop iteration ( λ (for a pre-defined tolerance), and the iterative convergence As the static stiffness of the mooring cable.

[0051] Step (3): Dynamic stiffness iteration Solve for the dynamic stiffness of the mooring cable when it undergoes simple harmonic motion around its equilibrium position (at this time) (The fixed value obtained in step (1) is used as the initial iterative stiffness of the mooring cable.) Next, given the time history of the simple harmonic motion at the tip of the mooring cable, a dynamic analysis is performed. Subsequently, the amplitude of the dynamic load on the mooring cable is calculated. and And according to the formula: The stiffness of the mooring cable was calculated. After re-performing the dynamic analysis, the change in the dynamic tension amplitude of the mooring cable was calculated. Repeated iterative calculation n Repeat until satisfied. Stop the iteration when it converges, and then... As the dynamic stiffness of the mooring cable.

[0052] This embodiment introduces a strain rate factor based on the traditional empirical formula for dynamic stiffness, overcoming the limitation of existing methods that ignore the influence of strain rate changes on dynamic stiffness, thus improving modeling accuracy. Through a model with lumped mass discretization and full mechanical component coverage, it fully restores the actual stress and deformation state of HMPE cables in deep-sea environments, solving the problem of mechanical property distortion caused by the simplification of traditional models. It fully considers the nonlinear mechanical response law of mooring cables under extreme sea conditions in deep-sea areas, improving the accuracy and adaptability of dynamic stiffness calculation. It is particularly suitable for the engineering design and dynamic analysis of floating wind turbines under high dynamic load conditions, providing a more reliable data foundation for dynamic response simulation and fatigue life prediction, and has good engineering practical value and innovative significance.

[0053] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for calculating the dynamic stiffness of mooring cables for a floating wind turbine (HMPE), characterized in that, Includes the following steps: S1: Establish a lumped mass dynamic analysis model for the mooring cable, discretize the cable into N elements and N+1 nodes, number each node and element, and determine the physical parameters of each element; S2: Based on the dynamic analysis model, calculate the top tension of the mooring system in the initial equilibrium state, and use it as the average tension Lm; S3: Perform static stiffness iterative calculation: Set the initial elastic modulus Based on the formula Iteratively update the static stiffness until convergence, and obtain the static stiffness. ; S4: Perform dynamic stiffness iterative calculation: using the static stiffness... As the initial dynamic stiffness, the time history of the simple harmonic motion of the mooring cable tip is given and dynamic analysis is performed. A dynamic load is applied, and the dynamic tension amplitude is extracted. With strain rate Based on the modified dynamic stiffness formula: ； In the formula, 、 、 These are all parameters related to the rope material and structure. This is the strain rate correction factor; 0 represents the strain rate under static loading; Iteratively update the dynamic stiffness until the convergence condition is met, and output the final dynamic stiffness; The lumped mass dynamic analysis model mentioned in step S1 includes: Anchoring node number 1, any node i The position is determined by the vector definition, Includes Position coordinates in three directions; cable unit In unstretched length l equivalent diameter d ,density ρ Young's modulus E and internal damping coefficient ; The lumped mass dynamic analysis model includes the following mechanical components: Axial tension inside the mooring cable: using time-varying elastic modulus Participate in calculation; Damping force: based on damping coefficient And strain rate calculation; Gravity, buoyancy, hydrodynamics based on the Morison equation, and seabed contact friction; The damping force is calculated in vector form as follows: （6）； In the formula, The internal damping coefficient is related to the elastic modulus of the cable; strain rate of cable unit Calculated by the following formula: （7）； In the formula, Let i represent the three directional positions of any node i. Let be the velocities in the three directions of any node i; In step S4, strain rate is introduced. η As a nonlinear adjustment factor, it participates in subsequent stiffness iterations. The calculation of the strain rate η includes: extracting the strain change rate per unit length of the cable, and defining the strain rate as... : ； In the formula, For strain rate, The change in strain This represents the change in the effective length of the cable. This corresponds to the time step.

2. The method for calculating the dynamic stiffness of the HMPE mooring cable of a floating wind turbine according to claim 1, characterized in that, cable unit The weight and buoyancy are calculated together, and the net buoyancy is used. To represent, therefore, cable unit The net buoyancy is: （1）； In the formula, Indicates the density of seawater. Let be the acceleration due to gravity; the net buoyancy at node i is distributed in vector form; since the net buoyancy of the cable element is uniformly distributed between adjacent nodes, the nodes are given in vector form. i The net buoyancy at point is: （2）； In the above formula, yes z The unit vector along the positive axis.

3. The method for calculating the dynamic stiffness of the HMPE mooring cable of a floating wind turbine according to claim 1, characterized in that, In the calculation of axial tension inside the mooring cable, the cable unit The axial tensile force is based on the elastic modulus. Iterative calculation, specifically: Cable unit The magnitude of the axial tensile force is: （3）； At this point, a cable unit in vector form is given. The axial tensile force is: （4）； Axial tension By node i Pointing to node i +1 indicates that the force is applied to the node. i Meanwhile, the force in the opposite direction acts on the node. i +1; And it satisfies the condition for the existence of tension: tension exists only when the cable unit is stretched; otherwise, the tension is zero. （5）。 4. The method for calculating the dynamic stiffness of the HMPE mooring cable of a floating wind turbine according to claim 2, characterized in that, In hydrodynamic calculations, by applying resistance and additional body forces, the relative flow velocity and acceleration at the nodes are first decomposed into normal and tangential components. i The tangent direction at a given point is approximately through two adjacent nodes. i +1 and i The direction of the straight line between -1: （8）； Among them, the normal direction is used It is represented as perpendicular to In still water, cable nodes i The relative water flow velocity is Then the tangential component of the relative water flow velocity is Then the normal component of the relative water flow velocity is Treating the cable as a slender cylindrical structure, the normal hydrodynamic load on the cable is calculated using the Morison equation. Based on the above components, the load is applied to the nodes. i The tangential and normal resistances are respectively: （9）； （10）； In the formula, This is the normal drag coefficient. This is the tangential drag coefficient; Apply to node i The tangential and normal additional mass forces are respectively: （11）； （12）； In the formula, Added mass coefficient to the normal direction. Add a mass matrix to the normal direction; For tangential additional mass coefficient, Add a tangential mass matrix; Let be the acceleration of any node i.

5. The method for calculating the dynamic stiffness of the HMPE mooring cable of a floating wind turbine according to claim 1, characterized in that, The seabed contact friction force is simulated using a linear spring damper. When the node contacts the seabed, i.e. There is an interaction force between the mooring cable and the seabed, and the nodes in contact with the seabed... i Interaction forces I i for: （13）； In the formula, This represents the vertical displacement of the seabed. This is the stiffness coefficient. The damping coefficient is... Let be the vertical displacement of node i. Vertical velocity, It is a unit vector along the positive z-axis.

6. The method for calculating the dynamic stiffness of the mooring cable of a floating wind turbine HMPE according to claim 1, characterized in that, In step S3, the initial elastic modulus in the static stiffness iteration The initial Young's modulus of the cable material; In step S4, the time history of the simple harmonic motion of the dynamic analysis is matched with the actual motion state of the upper floating wind turbine at the equilibrium position.

7. The method for calculating the dynamic stiffness of the mooring cable of a floating wind turbine HMPE according to claim 1, characterized in that, The mooring cable is an ultra-high molecular weight polyethylene fiber cable. The parameters 、 、 The strain rate correction factor was determined through cable material performance testing. δ Calibration based on dynamic mechanical tests of cables under different strain rates.

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