A mooring line damage assessment method based on internal friction driven damage propagation

Abstract

The application provides a mooring cable damage evaluation method based on internal friction driving damage expansion, which comprises the following steps: 1) obtaining the basic mechanical properties and geometric parameters of the polyester cable; 2) performing conversion on the polyester cable sub-cable, strand and yarn performance, and calculating the breaking strength, elongation and stiffness curve of the components; 3) discretizing the yarn in the strand into several layers of axis coincident cylindrical shells, and calculating the extrusion force and fiber tension in the adjacent fibers and adjacent cylindrical shells in the cylindrical shells; 4) calculating the tension of each layer of yarn to determine the friction form of the yarn and the friction force between different layers of yarn; 5) calculating the area damage of each layer of cylindrical shell after a single cycle or several cycles of combined calculation according to the friction force between different layers of yarn; 6) calculating the influence of micro-damage on the performance of the yarn and cyclically executing steps 4) to 6) until damage. The application can reveal the damage expansion law and realize the method of component-level real-time evaluation, and provides support for the safety of deep-sea mooring systems.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, and specifically to a method for assessing damage to mooring cables based on damage propagation driven by internal friction. Background Technology

[0002] As global marine resource development extends into deep-sea areas, large floating structures such as Floating Production Storage and Offloading (FPSO) units and semi-submersible platforms are widely used in deep-sea oil and gas extraction and offshore wind power. The mooring system, as the key to maintaining the floating structure and its subsea foundation, bears the core functions of restraining displacement and resisting wind, wave, and current loads; its safety directly determines the service life and reliability of offshore engineering projects. The mooring cable, as the core load-bearing component of the mooring system, endures long-term combined loads such as alternating tension, bending, and torsion in the complex marine environment, and also faces the effects of seawater corrosion, marine organism attachment, and erosion. With extended service life, damage such as internal polyester fiber wear and thinning, filament breakage, and localized plastic deformation can easily occur, leading not only to a decrease in load-bearing capacity but also potentially altering the structural dynamics and threatening the safety of the mooring system. Current damage assessment techniques for polyester mooring cables have significant limitations: traditional time-cumulative damage methods (such as the TN curve fatigue assessment method) only focus on fatigue damage and cannot reflect the specific damage of hierarchical structures such as sub-rods, strands, and yarns, nor can they reveal the impact of internal damage on macroscopic performance; in engineering, manual inspection and sampling tests are costly and difficult to achieve real-time monitoring and dynamic assessment during service, making it impossible to provide timely warnings of safety risks.

[0003] In the field of fracture mechanics, although mature damage analysis theories have been established—Griffith proposed the foundations of solid fracture mechanics, Ewing first correlated fatigue cracks in metals with microstructural changes, Paris established an empirical formula for crack propagation rate and stress intensity factor amplitude, Walker proposed a stress ratio correction model, and Dowling applied it to steel to verify its accuracy; in steel cable evaluation, Adewole analyzed the impact of microcracks on the fracture performance of armored steel wires, and Erena constructed multiaxial fatigue life prediction curves—none of these methods have been applied to polyester mooring cables, as they cannot be adapted to their material properties, hierarchical helical structure, and damage mechanism dominated by internal friction.

[0004] Current research on the fatigue performance of polyester cables still has shortcomings: Milty clarified the linear superposition of yarn failure mechanisms and damage; Lyons studied the effects of temperature, stroke, and frequency on cyclic fatigue of polyester fibers; Seo compared the wear fatigue of nylon and polyester cables; MANDELL proposed a low-load, high-cycle wear failure model (without considering uneven wear of strands); Casey studied the stiffness variation law of polyester ropes; Banfield compared the performance of steel cables and polyester cables and found that the main failure mode of polyester cables is internal wear; Flory verified the neutral buoyancy and corrosion resistance advantages of polyester cables in deep-water mooring; Ayers proposed the 20-Hurricane test method to assess strength loss; Liu derived the dynamic stiffness criterion for damaged ropes; and Feng revealed the time effect of the logarithmic decrease in stiffness with loading cycles. However, these studies mostly rely on direct regression of experimental data or artificial cutting to simulate damage, without considering structural reconstruction effects, and cannot simulate the accumulation of small damage and in-situ continuous performance changes.

[0005] In the field of damage prediction and detection: BSEE experiments confirmed that 10% cross-sectional area damage caused a strength loss of over 10% in polyester cables; MA analysis examined the impact of overall cable breakage on mooring (without detailing internal damage); Ward obtained the nonlinear relationship between residual strength and damage; Beltran solved damage localization through multi-scale modeling; Moretti achieved deep-water mooring fault detection through buoy design; Chung fused deep neural networks with physical simulation to detect damage; Khatri used image recognition algorithms for real-time detection (limited by water turbidity); and Jebari used a two-step artificial neural network to achieve FPSO mooring fault detection. However, existing technologies cannot achieve real-time damage assessment at the component level such as sub-lines and strands, nor can they reveal the damage propagation mechanism driven by internal friction, making it difficult to meet the safety assurance requirements of mooring systems.

[0006] In summary, existing technologies cannot adapt to the hierarchical structure and internal friction damage mechanism of polyester mooring cables. They have shortcomings such as difficulty in reflecting internal damage, inability to conduct real-time component-level assessment, and neglect of damage transmission. There is an urgent need for a method that can reveal the damage propagation law and achieve real-time component-level assessment to make up for the deficiencies of existing technologies and provide support for the safety of deep-sea mooring systems. Summary of the Invention

[0007] To address the technical problems existing in the background art, this invention proposes a mooring cable damage assessment method based on internal friction-driven damage propagation. The method is well-conceived and can reveal the damage propagation law and realize real-time component-level assessment, thereby making up for the deficiencies of existing technologies, providing support for the safety of deep-sea mooring systems, and effectively solving the defects such as difficulty in reflecting internal damage, inability to conduct real-time component-level assessment, and neglect of damage transmission.

[0008] To address the aforementioned technical problems, this invention provides a method for assessing mooring cable damage based on internal friction-driven damage propagation, comprising the following steps:

[0009] 1) Obtain the basic mechanical properties and geometric parameters of the polyester cable from the cable manufacturer or through experiments;

[0010] 2) Based on the geometric relationship of the polyester cable and its layered structure, the properties of the polyester cable sub-ropes, strands and yarns are calculated, and the breaking strength, elongation and stiffness curves of its components are calculated.

[0011] 3) Discretize the yarn in the rope strand into several layers of cylindrical shells with overlapping axes, and calculate the extrusion pressure and fiber tension of adjacent fibers inside the cylindrical shells and adjacent cylindrical shells.

[0012] 4) Calculate the tension of each layer of yarn based on the pressure and stiffness between the yarn strands and adjacent yarn strands to determine the friction mode of the yarn and calculate the friction force between different layers of yarn.

[0013] 5) Calculate the area damage of each layer of the column shell after a single cycle or after several cycles based on the frictional force between different layers of yarn;

[0014] 6) Calculate the impact of microscopic damage on yarn performance and return to step 4), continue to cycle through steps 5) to 6) until damage occurs or the expected number of cycles is reached.

[0015] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein: in step 1), the basic mechanical properties of the polyester cable include the dynamic stiffness curve of the polyester cable, the actual breaking strength (ABS) of the polyester cable, and wear test data; and information on the number of sub-rods in the polyester cable, the number of strands in the sub-rods, the number of yarns in the strands, and the helix angle of the spatial helix are obtained.

[0016] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein: in step 2), the performance of internal components of the polyester cable, such as sub-rods and strands, is calculated based on the overall performance of the polyester cable provided by the manufacturer: the tension and deformation relationship of the polyester cable is converted into the characteristics of the polyester cable sub-rods and strands, and the conversion method of tension and elongation of the polyester cable sub-rods is as shown in formula (1):

[0017] (1);

[0018] In the above formula (1), For the overall tension of the polyester cable; This refers to the elongation of the polyester cable; The angle of the sub-rope is 0 for parallel sub-ropes. This refers to the number of neutron cords in the polyester cable;

[0019] The method for calculating the number of strands is then obtained, as shown in formula (2):

[0020] (2);

[0021] The tension of the polyester cable is derived from the equilibrium equation. The breaking tension of the sub-rope at that time:

[0022] (3);

[0023] Further derivation of the maximum load that a single strand can withstand results in the breaking strength of the polyester cable. axial friction coefficient and the helix angle of the sub-rope under tension Number of ropes This is represented as shown in formula (4):

[0024] (4).

[0025] The mooring cable damage assessment method based on internal friction-driven damage propagation includes the following step: In step 3), the yarn properties are calculated, and by extrapolation, the tension and deformation of the yarn can be assessed. Firstly, it is necessary to obtain the tension and elongation of all the core shells in the polyester cable strands under undamaged conditions. Assuming there are a total of... Layer from the inside out The layer tension is as shown in formula (5), and the elongation is the same as the strand elongation:

[0026] (5);

[0027] In the above formula, For the tension of the polyester cable rope; The number of core shell layers in the rope strand; The number of layers from the inside out is the number of cylindrical shells pointing from the center of the axis to the surface. The innermost single fiber is 0, the adjacent outermost layer is 1, and so on.

[0028] Since both the cylindrical shell and the polyester cable sub-rod are single-layer structures, by analogy, after obtaining the tension of the cylindrical shell, the tension and deformation of the yarn can be obtained by referring to the conversion relationship between the sub-rod and the strand; the number of yarns in the strand is shown in formula (6), and the tension and elongation of the yarn are calculated as shown in formula (7):

[0029] (6);

[0030] (7);

[0031] In the above formula, The diameter of the polyester cable yarn; The diameter of the outer ring of the polyester cable post shell; The number of columnar shell layers from the inside out; For the first The number of yarns in each layer; The helix angle of the polyester cable fiber filament; This refers to the elongation of the cylindrical shell, i.e., the polyester cable rope. For yarn tension, This refers to the yarn elongation. For yarn shell tension. This refers to the number of yarns inside the cylindrical shell. is the axial friction coefficient.

[0032] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein: in step 3), the rope strands are discretized into multiple layers of cylindrical shells, and the sub-ropes of the same color come from the same layer of cylindrical shells. Except for the innermost yarn and the outermost yarn, there are three types of contact friction: friction between the yarns within the same cylindrical shell, friction with the yarns of the inner cylindrical shell, and friction with the yarns of the outer cylindrical shell; the innermost fiber only has friction with the fibers of the outer cylindrical shell, and the outermost fiber is similar to ordinary fiber, but the friction with the yarns of the outer cylindrical shell becomes friction between different rope strands.

[0033] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein in step 3), the extrusion pressure inside and between the polyester cable strands is calculated. In the cross-section, the contact positions within the same strand are approximated as follows: assuming the extrusion direction points to the yarn center, due to symmetry, the three outer contact loads are equivalent to the radial load of one strand. Based on the fact that the net external force is 0 at any position of the i-th layer fiber perpendicular to the axis, the relationship between the interstrand pressure of the i-th layer and the inner and outer extrusion pressures can be calculated, i≥1, as shown in formula (8):

[0034] (8);

[0035] In the above formula, i represents the number of polyester cable post shell layers, calculated from the inside out, with the innermost single fiber defined as the 0th post shell layer. The extrusion force of adjacent yarns within the i-th layer of the cylindrical shell; The diameter of the yarn; Let be the outer diameter of the i-th cylindrical shell; For the pressure on the outer cylindrical shell; The pressure on the inner cylindrical shell is given by equation (9):

[0036] (9);

[0037] For the analysis of the innermost two cylindrical shells, the outer pressure is equivalent to six equal radial pressures. Then, the equilibrium equations and deformation compatibility conditions are used to calculate... and As shown in formula (10):

[0038] (10);

[0039] Once the pressure of the outermost layer is known, the pressure of any cylindrical shell can be calculated recursively layer by layer.

[0040] Since the wear of the outermost yarn of the rope strand is related to the inter-strand pressure, it is necessary to analyze the inter-strand pressure. When the radial direction of the sub-rope is a compacted structure, its pressure is approximately equal to the compaction pressure. When there is no compaction pressure in the radial direction, due to the helical structure of the polyester cable strand, the axial pressure can be solved through the equilibrium equation. The axial pressure per unit length of non-compacted strand is shown in formula (11):

[0041] (11);

[0042] In the above formula (11), Let the radius of the sub-rope be . The diameter of the rope strands For the tension of the rope strands, It is a stranded spiral.

[0043] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein: in step 4), the calculation of the frictional force between different layers of yarn mainly considers the axial slippage between the contacting yarns of adjacent cylindrical shells, and the frictional force generated between the relative contact surfaces of the components, causing each component to generate shear force or distributed torque along the structural radius direction; if The diameter of the component is determined by the component's strain. and component orientation from initial attitude Become The resulting slip As shown in formula (12), its frictional force is approximately calculated according to Coulomb's law of friction:

[0044] (12).

[0045] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein step 5) comprises the following specific steps:

[0046] Step 5.1) Calculate the wear and damage of the innermost yarn.

[0047] The central fiber only has one friction condition, that is, the central yarn is rubbed by the adjacent cylindrical shell yarn on its outer side; when the damage is not transmitted to the central yarn and its adjacent cylindrical shell, the different damage to the central yarn and its adjacent cylindrical shell causes the critical relaxation length and elongation of the inner yarn and the adjacent cylindrical shell to change, thus losing the geometric retention structure, and axial slippage occurs during the stretching process. The wear damage generated during the slippage process realizes the quantitative analysis of wear damage. Based on the Archard wear model, by constructing the quantitative relationship between wear volume and load, sliding distance and material hardness, it provides a basic theoretical support for engineering wear prediction. Its formula is shown in formula (13):

[0048] (13);

[0049] In the above formula, For wear volume, The pressure on the vertical surface, The sliding distance, The hardness of a softer material, The wear coefficient is dimensionless and depends on material properties, surface condition, and operating conditions. Based on the internal friction characteristics of polyester cable fibers and referring to the Archard method, assuming friction is parallel to the polyester cable axis and perpendicular to the cable axis, the cross-sectional damage area can be approximately calculated using the following formula:

[0050] (14);

[0051] In the above formula, denoted as the cross-sectional area loss of the polyester cable fiber; k is the linear abrasion coefficient, which is determined by both the abrasion coefficient and the friction coefficient, and is calculated based on macroscopic abrasion tests or cycle-to-failure tests of polyester cables. The ratio of wear distance to polyester cable length can be determined based on the geometric deformation of the polyester cable during the stretching process. For ease of analysis of the polyester cable fibers, a dimensionless quantity can be used, and the relative slip distance per unit cross-section between yarns is approximated as follows:

[0052] Quasi-static analysis is adopted, that is, the relative displacement at the instantaneous peak and trough values ​​is analyzed. The peak and trough tensions are substituted into the industry-standard deformation coordination conditions and the equilibrium equation with zero net external force. Then, the relative slip difference between the outer and inner layers at the instantaneous peak and trough values ​​is calculated and evenly distributed to the elongation length. After that, the peak and trough tensions are substituted into the strand tension, and the difference between the two states is calculated to obtain the wear slip. The friction force is calculated as if the net external force of the fiber at any position is zero. Since the relative values ​​of the two are usually not much different under small cycles, the average value is used as the friction force at this stage. The cross-sectional area of ​​the wear loss is shown in formula (15).

[0053] (15);

[0054] In the above formula, This represents the initial length of the polyester cable. This represents the critical relaxation length of adjacent cylindrical shells. and The elongation lengths at two instantaneous states; and The frictional forces at two instants are obtained by solving the equilibrium equation of static friction or Coulomb's law of friction for kinetic friction; k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient.

[0055] Step 5.2) Calculate the wear and damage of the most common yarn strand.

[0056] Besides the innermost and outermost layers, the other yarns exhibit three types of wear: friction within the same yarn housing, friction with the yarn housing on the inner side, and friction with the yarn housing on the outer side. Among these, the friction within the same yarn housing is a fixed value, related only to its inherent properties, independent of its position, and unaffected by damage propagation. The friction on the outer and inner sides is the key factor leading to different wear patterns at different locations.

[0057] According to the friction form, it is divided into three types: A, B and C: wear area A corresponding to friction with the outer cylindrical shell yarn, wear area B corresponding to friction with the yarn inside the same cylindrical shell, and wear area C corresponding to friction with the outer cylindrical shell yarn.

[0058] The wear damage in wear region B is calculated by geometric relationship to determine its relative displacement and by equilibrium equation to calculate the friction force. The formula for the wear loss area in the cross section is shown in formula (16). The friction force at two instants is used. and Average value analysis of wear:

[0059] (16);

[0060] In the above formula, k is the linear wear coefficient, which is determined by friction experiments or obtained by material-level experiments; The diameter of the polyester cable post shell; The elongation of the column shell; and The helix angle representing the peak and trough values ​​of yarn tension within the cylindrical shell; and The length of the fiber at two moments is calculated based on the lengths corresponding to the peak and trough elongation rates in the tension-elongation curve. and The frictional forces at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction.

[0061] When there is no damage, the effect of shear friction in wear regions A and C can be ignored. When the damage extends to the point where the column shell begins to be damaged, the area of ​​wear loss in its cross section is calculated according to formula (17):

[0062] (17);

[0063] In the above formula, n is the number of contact surfaces with the layer, wear area A is 1, and wear area C is 3; k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient. This is the critical relaxation length of the yarn in this layer; The critical relaxation length of the friction yarn; and The analysis focuses on the elongation length at the peak and trough of tension. and The frictional forces at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction.

[0064] Step 5.3) Calculate the wear and damage of the outermost yarn.

[0065] There are three types of wear on the inner and outer strands: friction between the yarn within the same cylindrical shell, friction with the yarn within the inner cylindrical shell, and friction with the adjacent outer strand. The friction of the yarn within the same cylindrical shell is a fixed value, which is only related to its inherent properties and is independent of its position, and is not affected by the spread of damage. The inner pattern is related to the wear degree of the yarn itself, and the wear of adjacent strands is solved by the geometric structure and the equilibrium equation.

[0066] The aforementioned three types of wear are classified according to the form of friction as follows: wear area A corresponding to friction with adjacent strands, wear area B corresponding to friction with yarns within the same cylindrical shell, and wear area C corresponding to friction with yarns in the outer cylindrical shell; the wear damage in wear areas B and C is the same as that in ordinary yarns within the strands.

[0067] The wear pattern in wear area A is mainly friction between the strands, and the main type of friction is axial slippage between the strands. The calculation method for its loss area is shown in formula (18):

[0068] (18);

[0069] In the above formula, k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient; d is the diameter of the rope strands. For the strain of the rope strands; and The helix angle of the strand; and The elongation length of the rope strands under the two states being analyzed; and The frictional forces of the rope strands at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction.

[0070] The mooring cable damage assessment method based on internal friction-driven damage propagation, wherein step 6), calculates the impact of micro-damage on yarn properties, considering the impact on yarn properties, stiffness changes, and tension distribution between yarns, is detailed as follows:

[0071] Step 6.1) Calculate the change in yarn properties

[0072] Referring to the macroscopic loss mechanism of polyester cables, and considering the structural similarity between the cylindrical shell structure of polyester cable yarns and the sub-rod structure of polyester cable strands, the following assumptions are made regarding the damaged yarns after wear:

[0073] First, it is assumed that the wear on the cylindrical shell is uniformly distributed on the friction surface, and the wear degree of the rope strands in the same cylindrical shell is the same; second, it is assumed that the friction between the strands occurs uniformly on the surface of the rope strands; third, it is assumed that the radial pressure of the fiber rope strands and yarns remains unchanged during the wear process; finally, it is assumed that the yarns in each cylindrical shell break at the same time, and the influence of the broken and detached fibers on the unbroken yarns is ignored.

[0074] When the fibers inside the polyester cable post shell are damaged, its structure will undergo geometric reconstruction; after the damaged fibers become thinner, the helix angle and critical relaxation length of the sub-rod will change accordingly, leading to changes in mechanical properties; among them, the critical relaxation length of the post shell after wear damage is calculated by formula (19):

[0075] (19);

[0076] In addition, the helix angle of the yarn will also change, as shown in formula (20):

[0077] (20);

[0078] In the above equations (19)-(20), denoted as the helix angle of the yarn inside the i-th layer of the cylindrical shell; a is the cross-sectional area of ​​the polyester cable yarn. This represents the area of ​​wear loss within the cross-section; This is the critical relaxation length of the polyester cable strand;

[0079] When the polyester cable yarn suffers wear damage resulting in a loss of its cross-sectional area, the tension after wear is calculated based on the previously obtained yarn properties, keeping the strain the same, as shown in formula (21):

[0080] (twenty one);

[0081] Subsequently, based on the relationship between the polyester cable strand structure and the geometric rearrangement process, the tension and elongation of the damaged cylindrical shell can be obtained, as shown in formula (22):

[0082] (twenty two);

[0083] Therefore, the properties of the rope strands can be calculated based on the properties of the cylindrical shell.

[0084] Step 6.2) Determine the tension distribution based on the performance of the damaged column shell. First, determine the tension relationship, then establish the equilibrium equation, and then establish the equilibrium compatibility equation based on the equal length relationship. Solving the equilibrium equation and the deformation compatibility equation simultaneously can solve for the tension distribution of the column shell layer by layer. Then, calculate its elongation according to different tension levels:

[0085] (twenty three);

[0086] In the above formula, For polyester cable, i represents the layer number of the polyester cable strand shell. This refers to the number of strands in the polyester cable. The tension after damage to the i-th layer of cylindrical shell. For the i-th layer cylindrical shell of the polyester cable Elongation under tension This refers to the elongation of the polyester cable strands. Let be the maximum relaxation length after damage to the i-th layer of cylindrical shell. L represents the maximum relaxation length of the polyester cable post shell after damage, where L is the length of the polyester cable strand.

[0087] This allows us to obtain the tension-elongation curve and residual strength after damage.

[0088] By adopting the above technical solution, the present invention has the following beneficial effects:

[0089] This invention presents a well-conceived method for assessing mooring cable damage based on internal friction-driven damage propagation. It focuses on a comprehensive innovation in the analysis of polyester mooring cable damage assessment, and for the first time constructs a complete technical system encompassing "hierarchical deconstruction, multi-friction mode coupling, quantitative calculation, and real-time tracking." Drawing on the analytical logic of crack propagation in fracture mechanics, it breaks through the limitations of traditional methods' "holistic assessment" of polyester cables, innovatively deconstructing the polyester cable into a four-level hierarchical structure: sub-rope, strands, yarn, and shell. This achieves a refined deconstruction from macro to micro, laying a structural foundation for tracking damage transmission paths. The system incorporates four internal friction modes: axial slip, in-plane torsional friction, shear friction, and sawing friction, comprehensively covering the internal mechanical behavior of polyester cables under alternating tension. This addresses the shortcomings of existing research that only focuses on a single friction type or ignores friction transmission effects, making damage analysis more closely aligned with actual service conditions. Furthermore, by integrating the Archard wear model with the structural characteristics of polyester cables, it derives… A quantitative formula for cross-sectional loss applicable to the fiber level is developed. By selecting the instantaneous state of the cyclic peak and trough values ​​through quasi-static analysis, the complex integral is replaced by the product of the average friction force and the slippage. This simplifies the calculation while ensuring accuracy, enabling quantitative calculation of wear damage, rather than traditional qualitative descriptions or manual cutting simulations. A layer-by-layer performance conversion method from macro to micro is proposed. Through a series of mechanical formulas, the overall performance of polyester cables provided by manufacturers (such as tension-elongation curves) is accurately converted to the sub-rod, strand, yarn, and shell layers. This solves the industry pain point of difficulty in obtaining the mechanical parameters of internal components and clarifies the force distribution law of each layer (such as the shell tension decreasing from the inside to the outside in a specific proportion). A closed-loop theory of "geometrically maintained structure failure → relative slippage → damage propagation inward" is constructed, revealing for the first time the core mechanism of damage propagation from the outside to the inside, clarifying the boundary law between high-damage and low-damage zones, and filling the gap in existing research on the lack of clear understanding of damage propagation paths.

[0090] Compared with the prior art, the present invention has the following significant advantages:

[0091] (1) The physical mechanism is clearer. Existing technologies such as the TN curve method and direct regression method cannot reflect the internal structural damage and transmission effect. However, this invention fully restores the whole process of "micro-damage accumulation - structural reconstruction - damage transmission" through hierarchical analysis and multi-friction mode coupling, making the evaluation results more in line with reality.

[0092] (2) The evaluation accuracy is higher. Through experimental verification, the relative error between the model and the experimental data is less than 3%, which is far better than the rough estimation of traditional methods, and avoids the defect that manual cutting experiments cannot simulate the accumulation of micro-damage.

[0093] (3) It is more practical for engineering. By combining real-time tension monitoring and factory performance testing, it can realize real-time damage assessment at the component level, breaking through the bottleneck of traditional methods such as "offline detection, high cost and inability to provide real-time feedback". It does not require expensive equipment such as underwater image recognition, which greatly reduces the cost of engineering applications.

[0094] (4) It has better scalability and is applicable to any fiber structure made of spiral yarn. It can further incorporate marine environmental factors such as seawater corrosion and marine organism attachment, and has the potential to be extended to complex multi-factor coupling scenarios.

[0095] This invention successfully solves a series of key technical problems: traditional evaluation methods cannot reflect the internal structural damage of polyester cables and its impact on overall performance. By hierarchical disassembly and performance conversion, the invention achieves accurate capture of internal component damage; existing methods suffer from difficulties in real-time monitoring and high detection costs. Through a combination of "tension monitoring + theoretical conversion," a low-cost, real-time damage assessment is achieved; existing research lacks a clear understanding of damage transmission paths and inter-level frictional coupling effects. By coupling closed-loop theory with multiple friction modes, the invention clarifies the damage expansion law from the outside to the inside and the key influencing factors; and the invention addresses the lack of quantitative analysis of the relationship between key design parameters and damage. Through parameter analysis, the invention clarifies the influence of parameters such as average tension, tension cycle amplitude, and yarn helix angle on damage, providing a direct basis for the optimized design of polyester cables.

[0096] The technical effects brought about by this invention are significant and groundbreaking: it not only accurately reveals the laws governing the expansion of polyester cable damage from the outside to the inside and the boundary between high-damage and low-damage zones, providing theoretical support for cable design and selection, but also provides early warning of risks, avoids sudden failures, and extends the service life of polyester cables by more than 15%; by quantifying the impact of key parameters, it clarifies optimization directions such as "increasing average tension can reduce wear" and "damage decreases linearly when the helix angle approaches perpendicularity," guiding the selection of cable strength at least three times the amplitude of the main operating cycle in engineering projects, significantly improving the safety of mooring systems; the quantification of damage assessment simplifies calculations, providing engineers with an operable analytical tool and promoting the transformation of polyester cable damage assessment from "experience-based judgment" to "precise calculation"; it discovers that the damage rate of the middle column shell exhibits a "first increases and then decreases" broken line pattern, with the outer layer peak appearing earlier, providing a basis for developing differentiated maintenance strategies and further improving the operation and maintenance efficiency of mooring systems. Attached Figure Description

[0097] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0098] Figure 1 This is a schematic diagram of the rope strand discrete into a multi-layered cylindrical shell according to the present invention;

[0099] Figure 2 This is a schematic diagram of the axial sliding involved in the present invention;

[0100] Figure 3 This is a schematic diagram of the wear zone of the ordinary ply yarn involved in the present invention;

[0101] Figure 4 This is a schematic diagram of the wear zone of the outermost yarn involved in the present invention;

[0102] Figure 5 This invention relates to a tension-elongation curve of the rope strands after conversion.

[0103] Figure 6 This is a tension-elongation curve of the yarn after conversion according to the present invention;

[0104] Figure 7 This is a diagram showing the tension distribution of the cylindrical shell in its intact state, as per the present invention.

[0105] Figure 8 This is a diagram showing the elongation of the cylindrical shell in its intact state, as per the present invention.

[0106] Figure 9 This invention relates to a diagram showing the wear amount in a single cycle under non-destructive conditions.

[0107] Figure 10 This invention relates to a diagram showing the wear amount per cycle after 48 million cycles.

[0108] Figure 11 This invention relates to a diagram showing the yarn loss area and remaining area after 48 million cycles;

[0109] Figure 12 This is a diagram showing the elongation of the layer-by-layer cylindrical shell after 48 million cycles, as per the present invention.

[0110] Figure 13 This is a tension distribution diagram of the layer-by-layer cylindrical shell after 48 million cycles, as per the present invention.

[0111] Figure 14 This is a tension-elongation curve after 48 million cycles, as per the present invention.

[0112] Figure 15 This is a flowchart of the mooring cable damage assessment method based on internal friction-driven damage propagation according to the present invention. Detailed Implementation

[0113] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0114] The present invention will be further explained below with reference to specific embodiments.

[0115] like Figure 15 As shown in the figure, this embodiment provides a method for assessing mooring cable damage based on internal friction-driven damage propagation, which includes the following steps:

[0116] Step 1: Obtain the basic mechanical properties (such as breaking strength, abrasion resistance and dynamic stiffness curve) and geometric parameters (such as number of sub-rods, number of strands, helix angle and yarn diameter) of the polyester cable from the cable manufacturer or through experiments.

[0117] Step 2: Based on the geometric relationship of the polyester cable and its layered structure, calculate the properties of the polyester cable rope, strands and yarn, and calculate the breaking strength, elongation and stiffness curves of its components.

[0118] Step 3: Discretize the yarn in the rope strand into several layers of cylindrical shells with overlapping axes, and calculate the extrusion pressure and fiber tension of adjacent fibers inside the cylindrical shells and adjacent cylindrical shells.

[0119] Step 4: Calculate the tension of each layer of yarn based on the pressure and stiffness between the yarns within the strand and between adjacent strands to determine the friction mode of the yarn and calculate the friction force between different layers of yarn.

[0120] Step 5: Calculate the area damage of each layer of the cylindrical shell after a single cycle or after several cycles based on the frictional force between different layers of yarn;

[0121] Step 6: Calculate the impact of microscopic damage on yarn performance and return to step 4. Continue to cycle through steps 4, 5, and 6 until damage occurs or the expected number of cycles is reached.

[0122] Furthermore, in step 1, the basic mechanical properties of the polyester cable include the dynamic stiffness curve of the polyester cable, the actual breaking strength (ABS) of the polyester cable (which can be approximated by the minimum breaking strength (MBL) in engineering), and wear test data (used to determine the linear wear coefficient k). Information on the number of sub-ropes in the polyester cable, the number of strands in the sub-ropes, and the number of yarns in the strands (or calculated based on the layer-by-layer structural dimensions of the polyester cable) and the helix angle of the spatial helix are also obtained. In particular, in commonly used parallel sub-rope polyester cables, since there is no friction between the sub-ropes, the analysis can begin directly from the sub-ropes.

[0123] Further, in step 2, the performance of internal components of the polyester cable, such as sub-rods and strands, is calculated based on the overall performance of the polyester cable provided by the manufacturer: the tension and deformation relationship of the polyester cable is converted into the characteristics of the polyester cable sub-rods and strands. The conversion method of tension and elongation of the polyester cable sub-rods is shown in formula (1):

[0124] (1);

[0125] in, For the overall tension of the polyester cable, This refers to the elongation of the polyester cable. The angle is the helix angle of the sub-rope; for parallel sub-ropes, it is 0. This represents the number of neutron ropes in the polyester cable.

[0126] Similarly, the method for calculating the number of strands can also be obtained, as shown in formula (2):

[0127] (2);

[0128] The tension of the polyester cable can be derived from the equilibrium equation. The breaking tension of the sub-rope at that time:

[0129] (3);

[0130] Further derivation of the maximum load that a single strand can withstand: the breaking strength of the polyester cable axial friction coefficient and the helix angle of the sub-rope under tension Number of ropes This is represented as shown in formula (4):

[0131] (4);

[0132] Further, in step 3, the yarn properties are calculated, and extrapolation can be used to evaluate the yarn tension and deformation. However, since different layers have different deformation characteristics, it is first necessary to obtain the tension and elongation of all the cylindrical shells in the polyester cable strands under undamaged conditions. Assuming there are a total of Layer from the inside out The layer tension is as shown in formula (5), and the elongation is the same as the strand elongation:

[0133] (5);

[0134] In the above formula, For the tension of the polyester cable rope, This represents the number of columnar shell layers in the rope strand. The number of layers from the inside out; The number of layers from the inside out is the number of cylindrical shells pointing from the center of the axis to the surface. The innermost single fiber is 0, the adjacent outermost layer is 1, and so on.

[0135] Since both the cylindrical shell and the polyester cable sub-rod are single-layer structures, by analogy, after obtaining the tension of the cylindrical shell, the tension and deformation of the yarn can be obtained by referring to the conversion relationship between the sub-rod and the strand; the number of yarns in the strand is shown in formula (6), and the calculation method for the tension and elongation of the yarn is shown in formula (7):

[0136] (6);

[0137] (7);

[0138] In the above formula, The diameter of the polyester cable yarn. The diameter of the outer ring of the polyester cable post shell. The diameter of the polyester cable yarn. The number of columnar shell layers from the inside out. For the first Number of yarns in the layers The helix angle of the polyester cable fiber filaments. This refers to the elongation of the cylindrical shell, i.e., the polyester cable rope. For yarn tension, This refers to the yarn elongation. For yarn shell tension. This refers to the number of yarns inside the cylindrical shell. is the axial friction coefficient.

[0139] Furthermore, in step 3, the rope strands are discretized into multiple layers of cylindrical shells, such as... Figure 1 As shown in the diagram, the sub-cords of the same color come from the same cylindrical shell. Except for the innermost and outermost yarns, there are three types of contact friction (wear): friction between yarns within the same cylindrical shell, friction with yarns on the inner cylindrical shell, and friction with yarns on the outer cylindrical shell. The innermost fiber only experiences friction with the outermost cylindrical shell fiber. The outermost fiber is similar to ordinary fibers, but the friction with the outermost cylindrical shell yarn changes to friction between different strands.

[0140] Further, in step 3, the extrusion pressure inside and between the polyester cable strands is calculated. Within the cross-section, the contact positions within the same strand are approximated as follows: Assuming the extrusion direction points towards the center of the yarn, due to symmetry, the three outer contact loads are equivalent to the radial load of one strand. Based on the fact that the net external force is 0 at any position of the i-th layer of fiber perpendicular to the axis, the relationship between the interstrand pressure of the i-th layer and the extrusion pressure between the inner and outer sides can be calculated, i≥1, as shown in formula (8):

[0141] (8);

[0142] In the above formula, i represents the number of polyester cable post shell layers, calculated from the inside out, with the innermost single fiber defined as the 0th post shell layer. The compression force of adjacent yarns within the i-th layer of the cylindrical shell. The diameter of the yarn. Let be the outer diameter of the i-th cylindrical shell; For the pressure of the outer cylindrical shell, The pressure on the inner cylindrical shell is given by equation (9):

[0143] (9);

[0144] Specifically, for the analysis of the innermost two cylindrical shells, the outer pressure is equivalent to six equal radial pressures. Then, the solution can be obtained by calculating using the equilibrium equations and deformation compatibility conditions. and As shown in formula (10):

[0145] (10);

[0146] Once the pressure of the outermost layer is known, the pressure of any cylindrical shell can be calculated recursively layer by layer.

[0147] In particular, since the wear of the outermost yarn of the rope strand is related to the inter-strand pressure, it is necessary to analyze the inter-strand pressure. When the radial direction of the sub-rope is a compacted structure, its pressure is approximately equal to the compaction pressure. When there is no compaction pressure in the radial direction, the axial pressure can be solved by the equilibrium equation because of the helical structure of the polyester cable strand. The axial pressure per unit length of non-compacted strand is shown in formula (11):

[0148] (11);

[0149] In the above formula, Let the radius of the sub-rope be . The diameter of the rope strands For the tension of the rope strands, It is a stranded spiral.

[0150] Further, in step 4, the calculation of friction between different layers of yarn mainly considers the axial slippage between the contacting yarns of adjacent cylindrical shells. The friction generated between the relative contact surfaces of the components causes each component to generate shear force or distributed moment along the structural radius. This is due to the tensile and / or torsional structure. The structural changes are shown in the unfolded diagram, along with the two adjacent / contacting components marked. These components have a certain diameter, and it is precisely because of this radius that the slippage is not zero; if the structure is stretched without torsion, then the relative distance between the corresponding positions on the contacting components at zero deformation will change, as illustrated in the diagram. Figure 2 As shown. If Let be the diameter of the component, then due to the strain of the component... and component orientation from initial attitude Become The resulting slip As shown in formula (12), its frictional force can be approximately calculated according to Coulomb's law of friction:

[0151] (12);

[0152] Furthermore, in step 5, different methods need to be used for calculations of different types of yarn. The specific detailed steps are as follows:

[0153] Step 501: Calculate the wear and damage of the innermost yarn.

[0154] The central fiber only has one friction condition, that is, the central yarn is rubbed by the adjacent cylindrical shell yarn on its outer side; when the damage does not reach the central yarn and its adjacent cylindrical shell, due to the geometric retention structure, there is only shear friction caused by the change of the contact point angle. This friction form has a negligible effect because the contact slip is very small and the friction force is also small. When the damage does not reach the central yarn and its adjacent cylindrical shell, the different damage to the central yarn and its adjacent cylindrical shell causes the critical relaxation length and elongation of the inner yarn and the adjacent cylindrical shell to change, thereby losing the geometric retention structure and generating axial slip during the stretching process, which is the dominant factor of wear. The wear damage generated during the slip process realizes the quantitative analysis of wear damage. Based on the Archard wear model, by constructing the quantitative relationship between wear volume and load, sliding distance and material hardness, it provides a basic theoretical support for engineering wear prediction. Its formula is shown in formula (13):

[0155] (13);

[0156] In the above formula, For wear volume, The pressure on the vertical surface, The sliding distance, The hardness of a softer material, The wear coefficient is dimensionless and depends on material properties, surface condition, and operating conditions. Based on the internal friction characteristics of polyester cable fibers and referring to the Archard method, assuming friction is parallel to the polyester cable axis and perpendicular to the cable axis, the cross-sectional damage area can be approximately calculated using the following formula:

[0157] (14);

[0158] In the above formula, denoted as the cross-sectional area loss of the polyester cable fiber; k is the linear abrasion coefficient, which is determined by both the abrasion coefficient and the friction coefficient, and is calculated based on macroscopic abrasion tests or cycle-to-failure tests of polyester cables. The ratio of wear distance to polyester cable length can be determined based on the geometric deformation of the polyester cable during the stretching process. For ease of analysis of the polyester cable fibers, a dimensionless quantity can be used, and the relative slip distance per unit cross-section between yarns is approximated as follows:

[0159] Quasi-static analysis is adopted, that is, the relative displacement at the instantaneous peak and trough values ​​is analyzed. The peak and trough tensions are substituted into the industry-standard deformation coordination conditions and the equilibrium equation with zero net external force. Then, the relative slip difference between the outer and inner layers at the instantaneous peak and trough values ​​is calculated and evenly distributed to the elongation length. After that, the peak and trough tensions are substituted into the strand tension, and the difference between the two states is calculated to obtain the wear slip. The friction force is calculated as if the net external force of the fiber at any position is zero. Since the relative values ​​of the two are usually not much different under small cycles, the average value is used as the friction force at this stage. The cross-sectional area of ​​the wear loss is shown in formula (15).

[0160] (15);

[0161] In the above formula, This represents the initial length of the polyester cable. This represents the critical relaxation length of adjacent cylindrical shells. and The elongation lengths at two instantaneous states; and The frictional forces at two instants are obtained from the equilibrium equation of static friction or Coulomb's law of friction for kinetic friction; k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient.

[0162] Step 502: Calculate the wear and damage of the most common yarn strand.

[0163] Besides the innermost and outermost layers, the other yarns exhibit three types of wear: friction within the same yarn housing, friction with yarns in the innermost yarn housing, and friction with yarns in the outermost yarn housing. Friction within the same yarn housing is a fixed value, related only to its inherent properties and independent of location, and is almost unaffected by damage propagation. Friction on the outer and inner sides is the key factor leading to different wear patterns at different locations. A schematic diagram of the wear patterns and wear zones is shown below. Figure 3 As shown.

[0164] The diagram is divided into three types according to the form of friction: A, B, and C. The wear area corresponding to friction with the outer cylindrical shell yarn is A; the wear area corresponding to friction with the yarn inside the same cylindrical shell is B; and the wear area corresponding to friction with the outer cylindrical shell yarn is C.

[0165] The wear damage in wear region B is calculated by geometric relationship to determine its relative displacement and by equilibrium equation to determine the friction force. The formula for the wear loss area in the cross section is shown in formula (16). Since the friction force changes little, the friction force at two instantaneous moments is still used. and Average value analysis of wear:

[0166] (16);

[0167] In the above formula (16), k is the linear wear coefficient, which is determined by friction experiments or obtained by material-level experiments; The diameter of the polyester cable post shell. The elongation of the column shell is denoted as . and The helix angle representing the peak and trough values ​​of yarn tension within the cylindrical shell; and The length of the fiber at two moments is calculated based on the lengths corresponding to the peak and trough elongation rates in the tension-elongation curve. and The frictional forces at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction.

[0168] When there is no damage, the effect of shear friction in wear regions A and C can be ignored. When the damage extends to the point where the column shell begins to be damaged, the area of ​​wear loss in its cross section is calculated according to formula (17):

[0169] (17);

[0170] In the above formula (17), n is the number of contact surfaces with the layer, wear area A is 1, and wear area C is 3; k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient. This is the critical relaxation length of the yarn in this layer. The critical relaxation length of the friction yarn; and The analysis focuses on the elongation length at the peak and trough of tension. and The frictional forces at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction.

[0171] Step 503: Calculate the wear and damage of the outermost yarn.

[0172] There are three types of wear on the inner and outer yarns, such as... Figure 4 As shown, this represents the friction of yarns within the same cylindrical shell, friction with yarns in the inner cylindrical shell, and friction with adjacent strands on the outer side. The friction of yarns within the same cylindrical shell is a fixed value, related only to inherent properties and independent of position, and is almost unaffected by damage propagation. The inner pattern is related to the wear degree of the yarn itself, while the wear of adjacent strands can be solved using geometric structure and equilibrium equations.

[0173] Similar to ordinary yarn within a strand, the wear area shown in the diagram can be categorized into three types based on friction patterns: A (wear area corresponding to friction with adjacent strands), B (wear area corresponding to friction with yarn within the same cylindrical shell), and C (wear area corresponding to friction with yarn within the outer cylindrical shell). The wear damage in areas B and C is the same as that in ordinary yarn within a strand, and will not be elaborated upon here.

[0174] The wear pattern in wear area A is mainly friction between the strands, and the main type of friction is axial slippage between the strands. The calculation method for its loss area is shown in formula (18):

[0175] (18);

[0176] In the above formula (18), k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient; d is the diameter of the rope strand; For the strain of the rope strands; and The helix angle of the strand; and The elongation length of the rope strands under the two states being analyzed; and The frictional force of the rope strands at two instants can be solved from the equilibrium equation of static friction or Coulomb's law of friction for kinetic friction.

[0177] Furthermore, in step 6, calculating the impact of micro-damage on yarn properties requires considering the effects on yarn properties, stiffness changes, and tension distribution between yarns. The detailed steps are as follows:

[0178] Step 601: Calculate the change in yarn properties

[0179] Referring to the macroscopic loss mechanism of polyester cables, and considering the structural similarity between the cylindrical shell structure of polyester cable yarns and the sub-rod structure of polyester cable strands, the following assumptions are made regarding the damaged yarns after wear:

[0180] First, it is assumed that the wear on the cylindrical shell is uniformly distributed on the friction surface, and the wear degree of the rope strands within the same cylindrical shell is the same. Second, it is assumed that the friction between the strands occurs uniformly on the surface of the rope strands. Third, it is assumed that the radial pressure of the fiber rope strands and yarns remains unchanged during the wear process. Although in actual engineering, wear will cause the polyester rope strands or yarns to become thinner, resulting in a decrease in their radial clamping force, the overall impact can be ignored because the wear pits are small. Finally, it is assumed that the yarns within each cylindrical shell break simultaneously, and the impact of the broken fibers on the unbroken yarns is ignored.

[0181] When the fibers inside the polyester cable post shell are damaged, its structure will undergo geometric reconstruction; after the damaged fibers become thinner, the helix angle and critical relaxation length of the sub-rod will change accordingly, leading to changes in mechanical properties; among them, the critical relaxation length of the post shell after wear damage can be calculated by formula (19):

[0182] (19);

[0183] In addition, the helix angle of the yarn will also change, as shown in formula (20):

[0184] (20);

[0185] In the above equations (19)-(20), denoted as the helix angle of the yarn inside the i-th layer of the cylindrical shell, and α is the cross-sectional area of ​​the polyester cable yarn. This represents the area of ​​wear loss within the cross-section; This is the critical relaxation length of the polyester cable strand.

[0186] When the polyester cable yarn suffers wear damage resulting in a loss of its cross-sectional area, the tension after wear is calculated based on the previously obtained yarn properties, keeping the strain the same, as shown in formula (21):

[0187] (twenty one);

[0188] Subsequently, based on the relationship between the polyester cable strand structure and the geometric rearrangement process, the tension and elongation of the damaged cylindrical shell can be obtained (based on the length before damage), as shown in formula (22):

[0189] (twenty two);

[0190] Therefore, the properties of the rope strands can be calculated based on the properties of the cylindrical shell.

[0191] Step 602: Determine the tension distribution based on the performance of the damaged column shell. First, determine the tension relationship, then establish the equilibrium equation, and then establish the equilibrium compatibility equation based on the equal length relationship. Solving the equilibrium equation and the deformation compatibility equation simultaneously can solve for the tension distribution of the column shell layer by layer. Then, calculate its elongation according to different tension levels:

[0192] (twenty three);

[0193] In the above formula, For polyester cable, i represents the layer number of the polyester cable strand shell. This refers to the number of strands in the polyester cable. The tension after damage to the i-th layer of cylindrical shell. For the i-th layer cylindrical shell of the polyester cable Elongation under tension This refers to the elongation of the polyester cable strands. Let be the maximum relaxation length after damage to the i-th layer of cylindrical shell. L represents the maximum relaxation length of the polyester cable post shell after damage, where L is the length of the polyester cable strand.

[0194] This allows us to obtain the tension-elongation curve and residual strength after damage.

[0195] The present invention will be further described below with reference to specific embodiments:

[0196] This embodiment takes a polyester cable with a nominal breaking strength of 6 tons and an average actual breaking strength (expected value) of 61.94 kN as an example to evaluate the damage under tension cycling, including the following steps:

[0197] Step 1: Obtain the basic mechanical properties (such as breaking strength, abrasion resistance and dynamic stiffness curve) and geometric parameters (such as number of sub-ropes, number of strands, helix angle and yarn diameter) of 6t polyester sub-rope with a helix angle of 77 degrees from the cable manufacturer or through experiments.

[0198] The component performance in this case is shown in Table 1:

[0199]

[0200] Step 2: Based on geometric relationships, the performance of the polyester cable components (including sub-rods, strands, and yarns) is recalculated, and the breaking strength, elongation, and stiffness curves of the components are calculated. Since this case does not involve macroscopic breaking, only the tension-elongation is calculated, and the results are as follows: The tension-elongation curves of the sub-rods and yarns after recalculation are shown below. Figure 5 and Figure 6 As shown

[0201] Step 3: Discretize the yarn within the strand into several layers of cylindrical shells with overlapping axes, and calculate the extrusion pressure and fiber tension within adjacent fibers and adjacent cylindrical shells:

[0202] Taking a 6t sub-rope as the intact condition, the sub-rope consists of three strands, each strand containing 11 layers of cylindrical shells (the innermost single yarn). The calculated average tension is 20% ABS (12.4kN), and the tension cycle is one cycle of 20% ABS (12.4kN), that is, the yarn loss area during the process of tension being loaded from 10% ABS (6.2kN) to 30% ABS (18.6kN) and then unloaded back to 10% ABS (6.2kN). The wear forms of polyester cable yarn have been described above, and now they are classified into two categories: internal friction of the cylindrical shell and external friction of the cylindrical shell. To analyze the intact sub-rope, it is necessary to first determine the two static elongation fractions and axial loads based on the tension-elongation curve of the sub-rope, and convert them into the performance of each stage of the structure. The stress results of each stage of the structure are shown in Table 2:

[0203]

[0204] Further analysis of yarns located in different cylindrical shells yielded the following results regarding tension and elongation: Figure 7 and Figure 8 As shown:

[0205] Step 4: Calculate the tension of each layer of yarn based on the pressure and stiffness between the yarns to determine the friction mode of the yarn and calculate the friction force between different layers of yarn.

[0206] When the rope strands are in a brand new state, except for the innermost shell (actually just one yarn), which has slightly less elongation and tension than other fibers due to the lack of a helix angle, the other shells bear almost the same load and provide equal strength. Since the elongation of different shells is the same, their friction is mainly shear friction between adjacent yarns inside the shell. However, since the included angle changes very little and the shear friction force is very small, its influence can be ignored.

[0207] When the rope strands have worn down to a certain extent, the wear can be divided into two areas: the low-damage area and the high-damage area. In the low-damage area, the adjacent yarns between the shaft shells experience static friction, while in the high-damage area, the adjacent yarns between the shaft shells experience dynamic friction.

[0208] Step 5: Calculate the area damage of each column shell after a single cycle or after a combination of several cycles based on the friction force;

[0209] Step 501: Calculate the wear condition of the innermost yarn.

[0210] Step 502: Calculate the wear of the ordinary yarn within the strand.

[0211] Step 503: Calculate the wear condition of the outermost yarn.

[0212] Steps 501-503, the wear of the sub-rope under undamaged conditions is as follows: Figure 9 As shown, the damage per cycle after 48 million cycles is as follows: Figure 10 As shown:

[0213] Step 6: Calculating the impact of micro-damage on yarn properties requires considering the effects on yarn properties, changes in stiffness, and tension distribution between yarns.

[0214] Step 601: Taking one sub-rod of a polyester cable with a nominal breaking strength of 6 tons and an average actual breaking strength (expected value) of 61.94 kN as an example, calculate and evaluate its damage under 48 million cycles with 20% average load and 20% tension cycles. The fiber loss area and remaining area in the layered shell of the sub-rod are as follows: Figure 11 As shown.

[0215] Step 602: Calculate the elongation (based on the length before damage) and tension of different shells of the polyester cable under 10% and 30% tension after 48 million cycles. The results of the elongation and tension of each shell layer are as follows: Figure 12 and Figure 13 As shown; subsequently, the tension-elongation curve is calculated based on the equilibrium equation and the deformation compatibility equation, as shown. Figure 14 As shown.

[0216] Taking one sub-rod of a polyester cable with a nominal breaking strength of 6 tons and an average actual breaking strength (expected value) of 61.94 kN as an example, the damage was assessed by calculating 48 million cycles under 20% average load and 20% tension cycles. The residual strength of the yarn after damage was used as the verification result, as shown in Table 3.

[0217] .

[0218] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for assessing mooring cable damage based on internal friction-driven damage propagation, characterized in that, Includes the following steps: 1) Obtain the basic mechanical properties and geometric parameters of the polyester cable from the cable manufacturer or through experiments; 2) Based on the geometric relationship of the polyester cable and its layered structure, the properties of the polyester cable sub-ropes, strands and yarns are calculated, and the breaking strength, elongation and stiffness curves of its components are calculated. 3) Discretize the yarn in the rope strand into several layers of cylindrical shells with overlapping axes, and calculate the extrusion pressure and fiber tension of adjacent fibers inside the cylindrical shells and adjacent cylindrical shells. 4) Calculate the tension of each layer of yarn based on the pressure and stiffness between the yarn strands and adjacent yarn strands to determine the friction mode of the yarn and calculate the friction force between different layers of yarn. 5) Calculate the area damage of each layer of the column shell after a single cycle or after several cycles based on the frictional force between different layers of yarn; 6) Calculate the impact of microscopic damage on yarn performance and return to step 4), continue to cycle through steps 5) to 6) until damage occurs or the expected number of cycles is reached.

2. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that: In step 1), the basic mechanical properties of the polyester cable include the dynamic stiffness curve of the polyester cable, the actual breaking strength (ABS) of the polyester cable, and wear test data; and obtain information on the number of sub-rods in the polyester cable, the number of strands in the sub-rods, the number of yarns in the strands, and the helix angle of the spatial helix.

3. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 2, characterized in that: In step 2), the performance of internal components of the polyester cable, such as sub-rods and strands, is calculated based on the overall performance of the polyester cable provided by the manufacturer: the tension and deformation relationship of the polyester cable is converted into the characteristics of the polyester cable sub-rods and strands. The conversion method of tension and elongation of the polyester cable sub-rods is shown in formula (1): （1）； In the above formula (1), For the overall tension of the polyester cable; This refers to the elongation of the polyester cable; The angle of the sub-rope is 0 for parallel sub-ropes. This refers to the number of neutron cords in the polyester cable; The method for calculating the number of strands is then obtained, as shown in formula (2): （2）； The tension of the polyester cable is derived from the equilibrium equation. The breaking tension of the sub-rope at that time: （3）； Further derivation of the maximum load that a single strand can withstand results in the breaking strength of the polyester cable. axial friction coefficient and the helix angle of the sub-rope under tension Number of ropes This is represented as shown in formula (4): （4）。 4. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that: In step 3), the yarn properties are calculated, and by extrapolation, the tension and deformation of the yarn can be evaluated. Firstly, it is necessary to obtain the tension and elongation of all the cylindrical shells in the polyester cable strands under undamaged conditions. Assuming there are a total of... Layer from the inside out The layer tension is as shown in formula (5), and the elongation is the same as the strand elongation: （5）； In the above formula, For the tension of the polyester cable rope; The number of core shell layers in the rope strand; The number of layers from the inside out is the number of cylindrical shells pointing from the center of the axis to the surface. The innermost single fiber is 0, the adjacent outermost layer is 1, and so on. Since both the cylindrical shell and the polyester cable sub-rod are single-layer structures, by analogy, after obtaining the tension of the cylindrical shell, the tension and deformation of the yarn can be obtained by referring to the conversion relationship between the sub-rod and the strand; the number of yarns in the strand is shown in formula (6), and the tension and elongation of the yarn are calculated as shown in formula (7): （6）； （7）； In the above formula, The diameter of the polyester cable yarn; The diameter of the outer ring of the polyester cable post shell; The number of columnar shell layers from the inside out; For the first The number of yarns in each layer; The helix angle of the polyester cable fiber filament; This refers to the elongation of the cylindrical shell, i.e., the polyester cable rope. For yarn tension, This refers to the yarn elongation. For yarn shell tension. This refers to the number of yarns inside the cylindrical shell. is the axial friction coefficient.

5. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that, In step 3), the rope strands are discretized into multiple layers of cylindrical shells. Sub-ropes of the same color come from the same layer of cylindrical shells. Except for the innermost yarn and the outermost yarn, there are three types of contact friction: friction between yarns within the same cylindrical shell, friction with yarns in the inner cylindrical shell, and friction with yarns in the outer cylindrical shell. The innermost fiber only has friction with the outer cylindrical shell fiber. The outermost fiber is similar to ordinary fiber, but the friction with the outer cylindrical shell yarn becomes friction between different rope strands.

6. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that, In step 3), the extrusion pressure inside and between the polyester cable strands is calculated. Within the cross-section, the contact positions within the same strand are approximated as follows: Assuming the extrusion direction points to the center of the yarn, due to symmetry, the three outer contact loads are equivalent to the radial load of one strand. Based on the fact that the net external force is 0 at any position of the i-th layer of fiber perpendicular to the axis, the relationship between the interstrand pressure of the i-th layer and the extrusion pressure between the inner and outer sides can be calculated, i≥1, as shown in formula (8): （8）； In the above formula, i represents the number of polyester cable post shell layers, calculated from the inside out, with the innermost single fiber defined as the 0th post shell layer. The extrusion force of adjacent yarns within the i-th layer of the cylindrical shell; The diameter of the yarn; Let be the outer diameter of the i-th cylindrical shell; For the pressure on the outer cylindrical shell; The pressure on the inner cylindrical shell is given by equation (9): （9）； For the analysis of the innermost two cylindrical shells, the outer pressure is equivalent to six equal radial pressures. Then, the equilibrium equations and deformation compatibility conditions are used to calculate... and As shown in formula (10): （10）； Once the pressure of the outermost layer is known, the pressure of any cylindrical shell can be calculated recursively layer by layer. Since the wear of the outermost yarn of the rope strand is related to the inter-strand pressure, it is necessary to analyze the inter-strand pressure. When the radial direction of the sub-rope is a compacted structure, its pressure is approximately equal to the compaction pressure. When there is no compaction pressure in the radial direction, due to the helical structure of the polyester cable strand, the axial pressure can be solved through the equilibrium equation. The axial pressure per unit length of non-compacted strand is shown in formula (11): （11）； In the above formula (11), Let the radius of the sub-rope be . The diameter of the rope strands For the tension of the rope strands, It is a stranded spiral.

7. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that: In step 4), the calculation of friction between different layers of yarn mainly considers the axial slippage between the contacting yarns of adjacent cylindrical shells, and the friction generated between the relative contact surfaces of the components, causing each component to generate shear force or distributed torque along the structural radius; if The diameter of the component is determined by the component's strain. and component orientation from initial attitude Become The resulting slip As shown in formula (12), its frictional force is approximately calculated according to Coulomb's law of friction: （12）。 8. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that, The specific steps of step 5) are as follows: Step 5.1) Calculate the wear and damage of the innermost yarn. The central fiber only has one friction condition, that is, the central yarn is rubbed by the adjacent cylindrical shell yarn on its outer side; when the damage is not transmitted to the central yarn and its adjacent cylindrical shell, the different damage to the central yarn and its adjacent cylindrical shell causes the critical relaxation length and elongation of the inner yarn and the adjacent cylindrical shell to change, thus losing the geometric retention structure, and axial slippage occurs during the stretching process. The wear damage generated during the slippage process realizes the quantitative analysis of wear damage. Based on the Archard wear model, by constructing the quantitative relationship between wear volume and load, sliding distance and material hardness, it provides a basic theoretical support for engineering wear prediction. Its formula is shown in formula (13): （13）； In the above formula, For wear volume, The pressure on the vertical surface, The sliding distance, The hardness of a softer material, The wear coefficient is dimensionless and depends on material properties, surface condition, and operating conditions. Based on the internal friction characteristics of polyester cable fibers and referring to the Archard method, assuming friction is parallel to the polyester cable axis and perpendicular to the cable axis, the cross-sectional damage area can be approximately calculated using the following formula: （14）； In the above formula, denoted as the cross-sectional area loss of the polyester cable fiber; k is the linear abrasion coefficient, which is determined by both the abrasion coefficient and the friction coefficient, and is calculated based on macroscopic abrasion tests or cycle-to-failure tests of polyester cables. The ratio of wear distance to polyester cable length can be determined based on the geometric deformation of the polyester cable during the stretching process. For ease of analysis of the polyester cable fibers, a dimensionless quantity can be used, and the relative slip distance per unit cross-section between yarns is approximated as follows: Quasi-static analysis is adopted, that is, the relative displacement at the instantaneous peak and trough values ​​is analyzed. The peak and trough tensions are substituted into the industry-standard deformation coordination conditions and the equilibrium equation with zero net external force. Then, the relative slip difference between the outer and inner layers at the instantaneous peak and trough values ​​is calculated and evenly distributed to the elongation length. After that, the peak and trough tensions are substituted into the strand tension, and the difference between the two states is calculated to obtain the wear slip. The friction force is calculated as if the net external force of the fiber at any position is zero. Since the relative values ​​of the two are usually not much different under small cycles, the average value is used as the friction force at this stage. The cross-sectional area of ​​the wear loss is shown in formula (15). （15）； In the above formula, This represents the initial length of the polyester cable. This represents the critical relaxation length of adjacent cylindrical shells. and The elongation lengths at two instantaneous states; and The frictional forces at two instants are obtained by solving the equilibrium equation of static friction or Coulomb's law of friction for kinetic friction; k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient. Step 5.2) Calculate the wear and damage of the most common yarn strand. Besides the innermost and outermost layers, the other yarns exhibit three types of wear: friction within the same yarn housing, friction with the yarn housing on the inner side, and friction with the yarn housing on the outer side. Among these, the friction within the same yarn housing is a fixed value, related only to its inherent properties, independent of its position, and unaffected by damage propagation. The friction on the outer and inner sides is the key factor leading to different wear patterns at different locations. According to the friction form, it is divided into three types: A, B and C: wear area A corresponding to friction with the outer cylindrical shell yarn, wear area B corresponding to friction with the yarn inside the same cylindrical shell, and wear area C corresponding to friction with the outer cylindrical shell yarn. The wear damage in wear region B is calculated by geometric relationship to determine its relative displacement and by equilibrium equation to calculate the friction force. The formula for the wear loss area in the cross section is shown in formula (16). The friction force at two instants is used. and Average value analysis of wear: （16）； In the above formula, k is the linear wear coefficient, which is determined by friction experiments or obtained by material-level experiments; The diameter of the polyester cable post shell; The elongation of the column shell; and The helix angle representing the peak and trough values ​​of yarn tension within the cylindrical shell; and The length of the fiber at two moments is calculated based on the lengths corresponding to the peak and trough elongation rates in the tension-elongation curve. and The frictional forces at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction. When there is no damage, the effect of shear friction in wear regions A and C can be ignored. When the damage extends to the point where the column shell begins to be damaged, the area of ​​wear loss in its cross section is calculated according to formula (17): （17）； In the above formula, n is the number of contact surfaces with the layer, wear area A is 1, and wear area C is 3; k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient. This is the critical relaxation length of the yarn in this layer; The critical relaxation length of the friction yarn; and The analysis focuses on the elongation length at the peak and trough of tension. and The frictional forces at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction. Step 5.3) Calculate the wear and damage of the outermost yarn. There are three types of wear on the inner and outer strands: friction between the yarn within the same cylindrical shell, friction with the yarn within the inner cylindrical shell, and friction with the adjacent outer strand. The friction of the yarn within the same cylindrical shell is a fixed value, which is only related to its inherent properties and is independent of its position, and is not affected by the spread of damage. The inner pattern is related to the wear degree of the yarn itself, and the wear of adjacent strands is solved by the geometric structure and the equilibrium equation. The aforementioned three types of wear are classified according to the form of friction as follows: wear area A corresponding to friction with adjacent strands, wear area B corresponding to friction with yarns within the same cylindrical shell, and wear area C corresponding to friction with yarns in the outer cylindrical shell; the wear damage in wear areas B and C is the same as that in ordinary yarns within the strands. The wear pattern in wear area A is mainly friction between the strands, and the main type of friction is axial slippage between the strands. The calculation method for its loss area is shown in formula (18): （18）； In the above formula, k is the linear wear coefficient, which is determined by the wear coefficient and the friction coefficient; d is the diameter of the rope strands. For the strain of the rope strands; and The helix angle of the strand; and The elongation length of the rope strands under the two states being analyzed; and The frictional forces of the rope strands at two instants can be solved using the equilibrium equations for static friction or Coulomb's law of friction for kinetic friction.

9. The mooring cable damage assessment method based on internal friction-driven damage propagation as described in claim 1, characterized in that, In step 6), calculating the impact of micro-damage on yarn properties requires considering the effects on yarn properties, changes in stiffness, and tension distribution between yarns. The detailed steps are as follows: Step 6.1) Calculate the change in yarn properties Referring to the macroscopic loss mechanism of polyester cables, and considering the structural similarity between the cylindrical shell structure of polyester cable yarns and the sub-rod structure of polyester cable strands, the following assumptions are made regarding the damaged yarns after wear: First, it is assumed that the wear on the cylindrical shell is uniformly distributed on the friction surface, and the wear degree of the rope strands in the same cylindrical shell is the same; second, it is assumed that the friction between the strands occurs uniformly on the surface of the rope strands; third, it is assumed that the radial pressure of the fiber rope strands and yarns remains unchanged during the wear process; finally, it is assumed that the yarns in each cylindrical shell break at the same time, and the influence of the broken and detached fibers on the unbroken yarns is ignored. When the fibers inside the polyester cable post shell are damaged, its structure will undergo geometric reconstruction; after the damaged fibers become thinner, the helix angle and critical relaxation length of the sub-rod will change accordingly, leading to changes in mechanical properties; among them, the critical relaxation length of the post shell after wear damage is calculated by formula (19): （19）； In addition, the helix angle of the yarn will also change, as shown in formula (20): （20）； In the above equations (19)-(20), denoted as the helix angle of the yarn inside the i-th layer of the cylindrical shell; a is the cross-sectional area of ​​the polyester cable yarn. This represents the area of ​​wear loss within the cross-section; This is the critical relaxation length of the polyester cable strand; When the polyester cable yarn suffers wear damage resulting in a loss of its cross-sectional area, the tension after wear is calculated based on the previously obtained yarn properties, keeping the strain the same, as shown in formula (21): （21）； Subsequently, based on the relationship between the polyester cable strand structure and the geometric rearrangement process, the tension and elongation of the damaged cylindrical shell can be obtained, as shown in formula (22): （22）； Therefore, the properties of the rope strands can be calculated based on the properties of the cylindrical shell. Step 6.2) Determine the tension distribution based on the performance of the damaged column shell. First, determine the tension relationship, then establish the equilibrium equation, and then establish the equilibrium compatibility equation based on the equal length relationship. Solving the equilibrium equation and the deformation compatibility equation simultaneously can solve for the tension distribution of the column shell layer by layer. Then, calculate its elongation according to different tension levels: （23）； In the above formula, For polyester cable, i represents the layer number of the polyester cable strand shell. This refers to the number of strands in the polyester cable. The tension after damage to the i-th layer of cylindrical shell. For the i-th layer cylindrical shell of the polyester cable Elongation under tension This refers to the elongation of the polyester cable strands. Let be the maximum relaxation length after damage to the i-th layer of cylindrical shell. L represents the maximum relaxation length of the polyester cable post shell after damage, where L is the length of the polyester cable strand. This allows us to obtain the tension-elongation curve and residual strength after damage.

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