Method for measuring damping per unit length of inhaul cable

Abstract

The invention provides a method for measuring the damping per unit length of an inhaul cable, and belongs to the technical field of inhaul cable damping measurement, and the method comprises the steps: measuring the mass per unit length of the inhaul cable, and arranging a laser displacement meter in the vibration direction of the inhaul cable; initial displacement is applied to the inhaul cable and released, and the inhaul cable is excited to vibrate; measuring a vibration displacement time-history curve, a speed time-history curve or an acceleration time-history curve in any point surface of the inhaul cable in the vibration state through a laser displacement meter, and carrying out filtering processing on the vibration displacement time-history curve, the speed time-history curve or the acceleration time-history curve; extracting peak values of the displacement time-history curve, the speed time-history curve or the acceleration time-history curve after filtering processing and moments corresponding to the peak values; and based on the peak value of the displacement time travel curve, the speed time travel curve or the acceleration time travel curve after filtering processing, the moment corresponding to the peak value and the mass per unit length of the inhaul cable, obtaining the damping per unit length of the inhaul cable.

Description

Technical Field

[0001] The present invention relates to the technical field of cable damping measurement, and in particular to a method for measuring the damping per unit length of a cable. Background Art

[0002] The cable damping ratio is the ratio of damping to critical damping, and reflects the attenuation between adjacent vibration peaks. However, the damping ratio of a cable structure is affected by parameters such as cable length, cable tension, cable diameter, cable density, damping level, and vibration frequency. For example, two cables with identical material parameters will have completely different damping ratios under different cable tensions, resulting in poor applicability. This shows that the damping ratio is not a fundamental parameter for evaluating cable vibration attenuation. In contrast, cable damping is a relatively basic natural property, primarily influenced by the cable material properties, and therefore offers greater applicability. However, there is currently a lack of research on the relationship between damping and vibration attenuation, and even less of a method for measuring the damping per unit length of a cable. Summary of the Invention

[0003] To solve the above problems, the present invention provides a method for measuring the damping per unit length of a cable, which can measure the damping of an actual bridge's inclined cable or an experimental cable, specifically comprising:

[0004] A method for measuring the damping per unit length of a cable, comprising:

[0005] S1. Measure the mass per unit length of the cable and arrange a laser displacement meter in the vibration direction of the cable;

[0006] S2, applying an initial displacement to the cable and releasing it to stimulate cable vibration;

[0007] S3, measuring the vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point in the surface of the cable in the vibrating state by a laser displacement meter;

[0008] S4. Filtering the measured vibration displacement time-history curve, velocity time-history curve, or acceleration time-history curve to obtain a filtered displacement time-history curve, velocity time-history curve, or acceleration time-history curve, wherein the filtered displacement time-history curve, velocity time-history curve, and acceleration time-history curve include a displacement time-history curve, velocity time-history curve, or acceleration time-history curve under any single mode;

[0009] S5. extracting the peak value and the time corresponding to the peak value of the displacement time history curve, velocity time history curve or acceleration time history curve after filtering;

[0010] S6. Obtain the cable damping per unit length based on the peak value of the displacement time history curve, the velocity time history curve, or the acceleration time history curve after filtering, the time corresponding to the peak value, and the cable mass per unit length.

[0011] Optionally, the calculation formula for the unit length damping of the cable of S6 is formula (1):

[0012] ; (1)

[0013] Where c is the cable damping per unit length;

[0014] m is the mass per unit length of the cable; t i is the time corresponding to the first peak, t i+1 is the moment corresponding to the second peak;

[0015] δ is a process parameter in the c calculation process, where δ satisfies formula (2):

[0016] ; (2)

[0017] Among them, v n (x, t i ) is the displacement of point x on the cable at the i-th moment under the n-order vibration condition; v n (x, t i+1 ) is the displacement of point x on the cable at the i+1th moment under the nth order vibration condition.

[0018] Optionally, v n (x, t i ) satisfies formula (3), v n (x, t i+1 ) satisfies formula (4):

[0019] ; (3)

[0020] Where n is the vibration order of the cable, l is the length of the cable, and x is the distance from any point to the anchor point;

[0021] ; (4).

[0022] Optionally, applying an initial displacement to the cable and releasing it in S2 to excite the cable to vibrate includes:

[0023] Tie the weight to the cable with a line;

[0024] Cutting the rope causes the weight to fall naturally, and the cable is excited to vibrate.

[0025] Optionally, the cable is a steel cable, a CFRP cable or a BFRP cable;

[0026] The structure of the pull rope is a parallel rope or a twisted rope.

[0027] Optionally, the cables may be arranged horizontally or inclined:

[0028] Among them, the cable only bears the tension force.

[0029] Optionally, the anchoring points of the cables are supported by lubricating oil or free-rotating bearings.

[0030] Optionally, the ratio of the sag of the cable to the span of the cable is less than 1:8.

[0031] Compared with the prior art, the above technical solution has at least the following beneficial effects:

[0032] The present invention considers the relationship between damping and vibration attenuation and measures the damping per unit length of the cable. Therefore, the present invention proposes a cable damping measurement method, which can measure the damping size of the inclined cable of an actual bridge or an experimental cable, thereby making up for the shortcomings of the existing technology.

[0033] In practical engineering, the damping ratio is often used to predict the rate of cable attenuation. However, the damping ratio of a cable structure is affected by parameters such as cable length, cable tension, cable diameter, cable density, damping level, and vibration frequency, making the damping ratio extremely dependent on actual measurements. Unlike the damping ratio, damping is a material-dependent parameter. Once the damping of a cable made of a certain material is determined, it can be further generalized to cables made of the same material. However, there is currently a lack of methods for measuring cable damping. This patent addresses this shortcoming. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 This is the experimental arrangement diagram for measuring the damping of the cable;

[0036] Figure 2 The mid-span displacement time history curve is obtained from the actual measurement experiment of the cable's damping;

[0037] Figure 3 The mid-span displacement time history curve of 1000m CFRP cable;

[0038] Figure 4 The mid-span displacement time history curve of 1500m CFRP cable;

[0039] Figure 5 The time history curve of mid-span displacement of 2000m CFRP cable;

[0040] The following is a description of the components in the accompanying drawings:

[0041] 1. Test cable, 2. Laser displacement meter, 3. Nylon rope. DETAILED DESCRIPTION

[0042] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meaning understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one", "an" or "the" do not indicate a quantity limitation, but rather indicate the presence of at least one. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0044] It should be noted that the terms "up", "down", "left", "right", "front" and "back" used in the present invention are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0045] Currently, there is a lack of research on the relationship between damping and vibration attenuation, and even less of a method for measuring the damping per unit length of cables. Therefore, this paper proposes a cable damping measurement method that can measure the damping of actual bridge cables or experimental cables. The details are as follows:

[0046] A method for measuring the damping per unit length of a cable, comprising:

[0047] S1. Measure the mass per unit length of the cable and arrange a laser displacement meter in the vibration direction of the cable;

[0048] Displacement meters, velocity meters or accelerometers can be arranged to prepare for subsequent tests.

[0049] The cables are made of steel, CFRP, or BFRP; they are either parallel or stranded. They can be arranged horizontally or tilted, and they only bear tension forces. This means they can be inclined cables used in actual engineering projects, or horizontal or tilted test cables used in laboratories. They only bear tension forces and no other loads.

[0050] The anchoring point of the cable is supported by lubricating oil or free-rotating bearings to reduce the influence of friction at the anchoring point on the damping test results.

[0051] The ratio of the sag of the cable to the span of the cable is less than 1:8.

[0052] S2, applying an initial displacement to the cable and releasing it to stimulate cable vibration;

[0053] Tie the weight to the cable with a line;

[0054] Cutting the rope causes the weight to fall naturally, and the cable is excited to vibrate.

[0055] S3, measuring the vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point in the surface of the cable in the vibrating state by a laser displacement meter;

[0056] S4. Filtering the measured vibration displacement time-history curve, velocity time-history curve, or acceleration time-history curve to obtain a filtered displacement time-history curve, velocity time-history curve, or acceleration time-history curve, wherein the filtered displacement time-history curve, velocity time-history curve, and acceleration time-history curve include a displacement time-history curve, velocity time-history curve, or acceleration time-history curve under any single mode;

[0057] S5. extracting the peak value and the time corresponding to the peak value of the displacement time history curve, velocity time history curve or acceleration time history curve after filtering;

[0058] In this step, peak values ​​spaced farther apart are used to reduce the discreteness of the test damping.

[0059] S6. Obtain the cable damping per unit length based on the peak value of the displacement time history curve, the velocity time history curve, or the acceleration time history curve after filtering, the time corresponding to the peak value, and the cable mass per unit length.

[0060] The calculation formula of the cable unit length damping is formula (1):

[0061] ; (1)

[0062] Where c is the cable damping per unit length;

[0063] m is the mass per unit length of the cable; ti is the time corresponding to the first peak, t i+1 is the moment corresponding to the second peak;

[0064] δ is a process parameter in the c calculation process, where δ satisfies formula (2):

[0065] ; (2)

[0066] Among them, v n (x, t i ) is the displacement of point x on the cable at the i-th moment under the n-order vibration condition; v n (x, t i+1 ) is the displacement of point x on the cable at the i+1th moment under the nth order vibration condition.

[0067] Among them, v n (x, t i ) satisfies formula (3), v n (x, t i+1 ) satisfies formula (4):

[0068] ; (3)

[0069] Where n is the vibration order of the cable, l is the length of the cable, and x is the distance from any point to the anchor point;

[0070] ; (4).

[0071] In addition, it supports multiple repeated executions of S1-S6 to verify the reliability of the results.

[0072] The present invention is mainly based on the cable vibration theory and energy attenuation law based on damping, and further proposes a cable damping measurement method.

[0073] For any cable microelement (this application is for cables), its total energy E is determined by the potential energy E in a very short time. S and kinetic energy E D Composition, where the potential energy E S Satisfies formula (5):

[0074] ; (5)

[0075] Where, H is the equal component of the cable force; h is the horizontal component of the additional cable force;

[0076] A1 is the initial amplitude corresponding to the first-order mode, l is the length of the cable; t is the vibration time; φ1 is the phase difference corresponding to the first-order mode;

[0077] Kinetic Energy E D Satisfies formula (6):

[0078] ; (6)

[0079] The potential energy E S and kinetic energy E D The total energy E of the cable element at any moment can be obtained by adding them up:

[0080] ; (7)

[0081] Based on formula (7), it can be concluded that the magnitude of the pre-tension does not affect the energy attenuation of the cable, but only affects the potential energy E S and kinetic energy E D That is, for the same cable, under different tensions, the position of the displacement peak point will be different, but the peak points all show the same exponential decay. When the cable amplitude is between adjacent peaks t i and t i+1 When the kinetic energy E D is zero, and the energy in the cable system is expressed as potential energy E S According to this principle, it can be deduced that the cable amplitude is between adjacent peak values ​​t i and t i+1 The amplitude formula (3) and formula (4) are used when . Substituting formula (3) and formula (4) into formula (2), we can get formula (1) by simplifying. Formula (1) can be used for damping measurement.

[0082] In a specific embodiment, this example also provides finite element simulation data for CFRP cables at three lengths: 1000m, 1500m, and 2000m, to verify the accuracy of the cable damping test method. Specific cable material parameters are shown in Table 1.

[0083] Table 1 CFRP cable material parameters

[0084]

[0085] A sine function excitation with an amplitude of 5 m was applied to the 1000m, 1500m, and 2000m cables, respectively. The corresponding excitation functions are: 5sin(πx / 576), 3sin(πx / 576), and sin(πx / 576). After release, the mid-span displacement time history data of the CFRP cables were extracted, as shown in the following table. Figure 3 、 4 , 5. The first and second vibration peaks and the corresponding times are extracted and substituted into formulas (1) and (2) to obtain the test cable damping c, and the corresponding error analysis results are shown in Table 2. It can be seen that this damping measurement method has a high test progress.

[0086] Table 2 Analysis of measurement damping error

[0087]

[0088] The present invention considers the relationship between damping and vibration attenuation and measures the damping per unit length of the cable. Therefore, the present invention proposes a cable damping measurement method, which can measure the damping size of the inclined cable of an actual bridge or an experimental cable, thereby making up for the shortcomings of the existing technology.

[0089] The following points need to be explained:

[0090] (1) The drawings of the embodiments of the present invention only relate to the structures related to the embodiments of the present invention. Other structures may refer to conventional designs.

[0091] (2) For the sake of clarity, the thickness of layers or regions in the drawings used to describe the embodiments of the present invention are exaggerated or reduced, that is, these drawings are not drawn to scale. It is understood that when an element such as a layer, film, region, or substrate is referred to as being "on" or "under" another element, the element may be "directly on" or "under" the other element or intervening elements may be present.

[0092] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to form new embodiments.

[0093] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for measuring the damping per unit length of a cable, characterized in that: include: S1. Measure the mass per unit length of the cable and arrange a laser displacement meter in the vibration direction of the cable; S2, applying an initial displacement to the cable and releasing it to stimulate cable vibration; S3, measuring the vibration displacement time history curve, velocity time history curve or acceleration time history curve of any point in the surface of the cable in the vibrating state by a laser displacement meter; S4. Filtering the measured vibration displacement time-history curve, velocity time-history curve, or acceleration time-history curve to obtain a filtered displacement time-history curve, velocity time-history curve, or acceleration time-history curve, wherein the filtered displacement time-history curve, velocity time-history curve, and acceleration time-history curve include a displacement time-history curve, velocity time-history curve, or acceleration time-history curve under any single mode; S5. extracting the peak value and the time corresponding to the peak value of the displacement time history curve, velocity time history curve or acceleration time history curve after filtering; S6. Obtain the cable damping per unit length based on the peak value of the displacement time history curve, the velocity time history curve, or the acceleration time history curve after filtering, the time corresponding to the peak value, and the cable mass per unit length.

2. The method for measuring the damping per unit length of a cable according to claim 1, characterized in that: The calculation formula of the unit length damping of the S6 cable is formula (1): ；（1） Where c is the cable damping per unit length; m is the mass per unit length of the cable; t i is the time corresponding to the first peak, t i+1 is the moment corresponding to the second peak; δ is a process parameter in the c calculation process, where δ satisfies formula (2): ；（2） Among them, v n (x, t i ) is the displacement of point x on the cable at the i-th moment under the n-order vibration condition; v n (x, t i+1 ) is the displacement of point x on the cable at the i+1th moment under the nth order vibration condition.

3. The method for measuring the damping per unit length of a cable according to claim 2, characterized in that: v n (x, t i ) satisfies formula (3), v n (x, t i+1 ) satisfies formula (4): ；（3） Where n is the vibration order of the cable, l is the length of the cable, and x is the distance from any point to the anchor point; ；（4）。 4. The method for measuring the damping per unit length of a cable according to claim 1, characterized in that: The step S2 of applying an initial displacement to the cable and releasing the initial displacement to excite the cable to vibrate comprises: Tie the weight to the cable with a nylon rope; Cutting the nylon rope causes the weight to fall naturally, and the cable is stimulated to vibrate.

5. The method for measuring the damping per unit length of a cable according to claim 1, characterized in that: The cable is a steel cable, a CFRP cable or a BFRP cable; The structure of the pull rope is a parallel rope or a twisted rope.

6. The method for measuring the damping per unit length of a cable according to claim 1, characterized in that: The cable arrangement can be horizontal or inclined: Among them, the cable only bears the tension force.

7. The method for measuring the damping per unit length of a cable according to claim 5, characterized in that: The anchoring points of the cables are supported by lubricating oil or free-rotating bearings.

8. The method for measuring the damping per unit length of a cable according to claim 6, characterized in that: The ratio of the sag of the cable to the span of the cable is less than 1:8.

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