CN108106586B - The test method of umbilical cables maximum deflection curvature in fatigue test - Google Patents
The test method of umbilical cables maximum deflection curvature in fatigue test Download PDFInfo
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- 238000009661 fatigue test Methods 0.000 title claims abstract description 20
- 238000010998 test method Methods 0.000 title claims abstract description 12
- 238000005452 bending Methods 0.000 claims abstract description 29
- 238000000034 method Methods 0.000 claims abstract description 14
- 238000009795 derivation Methods 0.000 claims description 4
- 238000006467 substitution reaction Methods 0.000 claims description 3
- 238000012360 testing method Methods 0.000 description 8
- 238000004088 simulation Methods 0.000 description 6
- 210000003954 umbilical cord Anatomy 0.000 description 6
- 238000002474 experimental method Methods 0.000 description 4
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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Abstract
The invention discloses a kind of test methods of umbilical cables maximum deflection curvature in fatigue test, advantage is using the error very little between this method umbilical cables bending deformation curve being fitted and actual flexion deformation curve, it can be used as actual flexion deformation curve of the umbilical cables in fatigue test to be analyzed, and the position of obtained maximum deflection curvature is the position that umbilical cables are easy to happen fracture or breakage in fatigue test；In addition, entire test method is relatively simple.
Description
Technical field
The maximum deflection in fatigue test the present invention relates to the performance test methods of umbilical cables more particularly to a kind of umbilical cables
The test method of curvature.
Background technique
Oceanic umbilical cord cable (abbreviation umbilical cables) is one of most important equipment in deep-sea oil gas resource development and production system.Its
It is mainly made of cable, optical cable, armouring wire, sheath, steel pipe and filler, umbilical cables are as marine equipment and underwater production system
Unique media between system plays a part of transmitting electric power, signal and the chemical mediator that may be needed.But the complexity of its structure
Property is but also the nonlinear degree of umbilical cables bending stiffness increased.Umbilical cables are under actual condition or try in fatigue loading
When testing middle Tensile, bending load effect, the bending stiffness of umbilical cables itself also shows apparent nonlinear characteristic, this is just needed
The actual curve shape that rear cable is deformed to it is analyzed.
The fatigue test of umbilical cables is a process complexity, test with high costs.Umbilical cables fatigue tester needs energy
It is enough to be loaded by simulating actual condition, and monitor, record the loading condition in each dangerous tired region of umbilical cables.Such as
During test, need to detect the integrality of the electrical connection of the continuity and umbilical cables of spread fiber signal in umbilical cables,
Sometimes it also needs that the dynamic tensile stress and bending stress that each element is born in umbilical cables is monitored and controlled.The umbilical cord of complete set
Cable fatigue test, which generally requires, lasts completion in 3~7 months, and power consumption may be more than 100,000 dollars.Just because of its at
This is high, test lasts the features such as longer, technological difficulties are more, so that the research to such technology and few in the world.And
The most key in umbilical cables fatigue test is a little exactly to detect umbilical cables generated bending deformation when doing fatigue test to be
The no subject that reaches requires.But due to the nonlinear influence by this body structure of umbilical cables, so that test umbilical cables are tried in fatigue
There is certain difficulties for the actual flexion deformation curve for testing under operating condition.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of test method is simple, and error is small, umbilical cord with high accuracy
The test method of cable maximum deflection curvature in fatigue test.
The technical scheme of the invention to solve the technical problem is: umbilical cables maximum deflection in fatigue test is bent
The test method of rate, comprising the following specific steps
(1), apply bending force in one end of umbilical cables, so that it is generated bending, while applying in the other end of umbilical cables and drawing
Stretch；
(2), at the 1/3 of the curved end of umbilical cables to its length, every half meter of setting, one obliquity sensor, in umbilical cord
The 1/3 of cable length is to end is stretched, every one meter of setting, one obliquity sensor；
(3), assume the curvilinear equation after umbilical cables occur bending and deformation are as follows: y=f (x) a≤x≤b, in formula, section [a,
B] it is the domain of curvilinear equation y=f (x), and the stretching end of umbilical cables is set as the origin in plane coordinate system, from umbilical cord
To curved end, the tangent line of the branch where each obliquity sensor and the angle of horizontal plane are θ at the stretching end of cable1, θ2..., θn,
Bending angle measured by i.e. each obliquity sensor, and set the tangent line of branch and x-axis forward direction angle is positive, with x-axis negative sense
Angle is negative, and from the stretching end of umbilical cables to curved end, the length of curve between each adjacent branch is followed successively by S1,S2,…,
Sn；
(4), the coordinate of i-th of branch in umbilical cables is denoted as (xi,yi), the coordinate of i+1 branch is denoted as (xi+1,
yi+1), center of curvature coordinate corresponding to i-th section of curve is denoted as (Ci,di), it sets between i-th of branch and i+1 branch
It is R that i-th section of curve, which is equivalent arc radius,i, the center of curvature be (Ci,di) circular curve, corresponding arc angle be ψi=|
θi-θi+1|, it can obtain:
And it can be obtained according to circular curve characteristic:
And formula progress trigonometric substitution can be obtained:
(5), the branch coordinate where the stretching end of umbilical cables is (xi,yi)=(0,0), umbilical cables are acquired by iterative method
Actual coordinate (the x of upper each branchi,yi) approximation；
(6), branch data point discrete in umbilical cables is fitted by least square method, ifFor the continuous function of section [a, b] upper one group of linear independence, enableIn formula, S (x) is the fitting function of actual curve, α0,α1…αnFor
The real coefficient of fitting function remembers error are as follows:
δi=S (xi)-yi, i=0,1,2 ..., n, in formula, S (xi)、yiRespectively fitting function and actual function is in xiPlace
Functional value；
(7), with error deltaiWeighted quadratic on the basis of, it may be assumed thatFormula
In, I is error deltaiWeighted quadratic,ω(xi) be i-th of obliquity sensor weight function, and ω (xi) >=0, to reach error
To minimum, the necessary condition of the extreme value of above formula is taken are as follows:And real system is obtained by the formula
Number α0,α1…αnUnique solutionTo obtain the bending deformation matched curve of umbilical cables are as follows:
(8), to the bending deformation matched curve derivation of umbilical cables, curvature equation is obtained are as follows:
, in formula, C is curvature when umbilical cables are bent, S*' it is S*(x) first derivative, S*It " is S*(x) second dervative,
Maximum value of the curvature equation in domain is maximum deflection curvature of the umbilical cables in fatigue test.
Compared with prior art, it is an advantage of the invention that the umbilical cables bending deformation curve being fitted using this method with
Error very little between actual flexion deformation curve can be used as actual flexion deformation curve of the umbilical cables in fatigue test and carry out
Analysis, and the position of obtained maximum deflection curvature is the position that umbilical cables are easy to happen fracture or breakage in fatigue test
It sets；In addition, entire test method is relatively simple.
Detailed description of the invention
Fig. 1 is the branch schematic diagram of umbilical cables buckling curve of the invention；
Fig. 2 is simulation umbilical cables actual flexion curve and cubic fit curve comparison figure in emulation experiment of the invention；
Error Graph when Fig. 3 is umbilical cables curve cubic fit in emulation experiment of the invention；
Fig. 4 is simulation umbilical cables actual flexion curve and twice fitting curve comparison figure in emulation experiment of the invention；
Error Graph when Fig. 5 is umbilical cables curve twice fitting in emulation experiment of the invention.
Specific embodiment
The present invention will be described in further detail below with reference to the embodiments of the drawings.
As shown, the test method of umbilical cables maximum deflection curvature in fatigue test, comprising the following specific steps
(1), apply bending force in one end of umbilical cables, so that it is generated bending, while applying in the other end of umbilical cables and drawing
Stretch；
(2), in the curved end A of umbilical cables to its length 1/3 at, every half meter of setting, one obliquity sensor, in navel
With cable length 1/3 to stretch end B, every one meter of setting, one obliquity sensor；
(3), assume the curvilinear equation after umbilical cables occur bending and deformation are as follows:
Y=f (x) a≤x≤b (1)
In formula, section [a, b] is the domain of curvilinear equation y=f (x), and the stretching end B of umbilical cables is set as plane
Origin in coordinate system, from the stretching end B to curved end A of umbilical cables, the tangent line and water of the branch where each obliquity sensor
The angle of plane is θ1, θ2..., θn, i.e., bending angle measured by each obliquity sensor, and set the tangent line and x of branch
Axis forward direction angle is positive, and is negative with x-axis negative sense angle, and from the stretching end B to curved end A of umbilical cables, each adjacent branch it
Between length of curve be followed successively by S1,S2,…,Sn；
(4), the coordinate of i-th of branch in umbilical cables is denoted as (xi,yi), the coordinate of i+1 branch is denoted as (xi+1,
yi+1), center of curvature coordinate corresponding to i-th section of curve is denoted as (Ci,di), it sets between i-th of branch and i+1 branch
It is R that i-th section of curve, which is equivalent arc radius,i, the center of curvature be (Ci,di) circular curve, corresponding arc angle be ψi=|
θi-θi+1|, it can obtain:
And it can be obtained according to circular curve characteristic:
And the progress trigonometric substitution of (3) formula can be obtained:
(5), the branch coordinate where the stretching end of umbilical cables is (xi,yi)=(0,0), umbilical cables are acquired by iterative method
Actual coordinate (the x of upper each branchi,yi) approximation；
(6), branch data point discrete in umbilical cables is fitted by least square method, ifFor the continuous function of section [a, b] upper one group of linear independence, enable
In formula, S (x) is the fitting function of actual curve, α0,α1…αnFor the real coefficient of fitting function, error is remembered are as follows:
δi=S (xi)-yi, i=0,1,2 ..., n (6)
In formula, S (xi)、yiRespectively fitting function and actual function is in xiThe functional value at place；
(7), with error deltaiWeighted quadratic on the basis of, it may be assumed that
In formula, I is error deltaiWeighted quadratic, ω (xi) be i-th of obliquity sensor weight function, and ω (xi) >=0,
To make error reach minimum, the necessary condition of the extreme value of (7) formula is taken are as follows:
And real coefficient α is obtained by (8) formula0,α1…αnUnique solutionTo obtain umbilical cord
The bending deformation matched curve of cable are as follows:
(8), to the bending deformation matched curve derivation of umbilical cables, curvature equation is obtained are as follows:
In formula, C is curvature when umbilical cables are bent, S*' it is S*(x) first derivative, S*" it is S*(x) second dervative,
Maximum value of the curvature equation in domain is maximum deflection curvature of the umbilical cables in fatigue test.
Simulation results show
It in above-described embodiment, for the precision for examining the test method, avoids the problem that being likely to occur in Practical Project, use
MATLAB emulates the fitting of a polynomial effect of the umbilical cables curve after bending in engineering.Assuming that umbilical cables are after bending
Curvilinear equation is y=0.027x2+ 0.27x (- 12≤x≤0) will obtain 13 Along ents after 12 equal part of horizontal axis section, each etc.
The inclination angle of branch is turned left from the right side is successively denoted as θ1,θ2,…,θ13, sensed with this to simulate apply in actual condition 13 inclination angles
The data obtained measured by device.The precision of the obliquity sensor as used in test is 0.1 degree, so according to actual condition,
Corresponding noise is added in MATLAB simulation process, it is adjacent according to inclination angle measured by each obliquity sensor and every two
Length of curve (can be acquired by derivation, integral in l-G simulation test) between obliquity sensor, is calculated by formula (2), (3), (4)
The equivalent coordinate position of 13 obliquity sensor layout points.The inclination angle of each obliquity sensor layout points, radian, practical horizontal seat
Mark, equivalent abscissa, equivalent ordinate are shown in Table 1.
1 obliquity sensor layout points parameter of table
It can be obtained from table 1, the coordinate and actual coordinate of 13 Along ents calculated according to equivalent circular arc algorithm are very nearly the same,
Its error precision is within 0.1%, and in practical engineering applications, error can be ignored completely.
Since the weight of each obliquity sensor is consistent, weighting function ω (x)=1 is taken.It to guarantee fitting precision, and is anti-
Only due to the imperial lattice phenomenon that may occur when fitting order is too high, the curve of simulation umbilical cables is carried out three times with orthogonal polynomial
Fitting.It is calculated horizontal, ordinate data are simulated in table 1, the cubic fit approximation to function of the curve are as follows:
Y1=0.0026x3+0.0737x2+0.4898x+0.1725, -12≤x≤0
As shown in Fig. 2, after the data point that equivalent algorithm is obtained carries out quadratic fit with orthogonal polynomial, matched curve with
Primitive curve difference is bigger, and the error between matched curve left end lengthwise position and physical location is more than 10%.In order to become apparent from
The error between matched curve and actual curve is found out on ground, definition cubic fit error be ε=| y-y1 |.In curve definitions domain
Interior, the variation relation of cubic fit error ε and x are as shown in Figure 3.
As shown in figure 3, the value of cubic fit error ε fluctuates between 0-0.2 within the scope of domain.And work as x=-12
Or when x=0, the value of ε is more than 0.15m, and the error of relatively primitive curve ordinate is more than 20%, this will be to umbilical cables fatigue test
The normal operation of machine can produce a very large impact.So fitting scheme is changed to quadratic fit, horizontal, ordinate number will be simulated in table 1
According to being calculated, the quadratic fit approximation to function of curve after umbilical cables bending is simulated are as follows:
Y2=0.0269x2+0.3688x+0.0009, -12≤x≤0
The schematic diagram of curve and quadratic fit curve is as shown in figure 4, matched curve and virgin curve after simulating umbilical cables bending
It is almost overlapped, shows match value largely close to true value.Definition quadratic fit error is q=| y-y2 |,
In curve definitions domain, the variation relation of quadratic fit error q and x are as shown in Figure 5.Fig. 5 shows the song being fitted by this method
Line and the actual curve value of quadratic fit error q in domain are not above 0.005m.That is, matched curve and reality
The error of curve is maintained within 0.1%, and error small so does not influence the normal operation of umbilical cables fatigue tester,
It also indicates that the precision for the sensor coordinates position algorithm and curve fitting algorithm that this method proposes is very high, and then carries out curvature
When calculating, the maximum curvature of original equation is 0.054, and equation maximum curvature is 0.0538 after fitting, and error is less than 0.1%, completely
Requirement when meeting fatigue tester work to precision.
Claims (1)
1. the test method of umbilical cables maximum deflection curvature in fatigue test, it is characterised in that comprising the following specific steps
(1), apply bending force in one end of umbilical cables, so that it is generated bending, while applying drawing force in the other end of umbilical cables；
(2), long in umbilical cables every half meter of setting, one obliquity sensor at the 1/3 of the curved end of umbilical cables to its length
The 1/3 of degree is to end is stretched, every one meter of setting, one obliquity sensor；
(3), assume the curvilinear equation after umbilical cables occur bending and deformation are as follows: y=f (x) a≤x≤b, in formula, section [a, b] is
The domain of curvilinear equation y=f (x), and the stretching end of umbilical cables is set as the origin in plane coordinate system, from umbilical cables
End is stretched to curved end, the tangent line of the branch where each obliquity sensor and the angle of horizontal plane are θ1, θ2..., θn, i.e., respectively
Bending angle measured by a obliquity sensor, and set the tangent line of branch and x-axis forward direction angle is positive, with x-axis negative sense angle
It is negative, and from the stretching end of umbilical cables to curved end, the length of curve between each adjacent branch is followed successively by S1,S2,…,Sn；
(4), the coordinate of i-th of branch in umbilical cables is denoted as (xi,yi), the coordinate of i+1 branch is denoted as (xi+1, yi+1),
Center of curvature coordinate corresponding to i-th section of curve is denoted as (Ci,di), set i-th section between i-th of branch and i+1 branch
Curve is that equivalent arc radius is Ri, the center of curvature be (Ci,di) circular curve, corresponding arc angle be ψi=| θi-θi+1
|, it can obtain:
And it can be obtained according to circular curve characteristic:
And formula progress trigonometric substitution can be obtained:
(5), the branch coordinate where the stretching end of umbilical cables is (xi,yi)=(0,0), it is acquired by iterative method each in umbilical cables
Actual coordinate (the x of a branchi,yi) approximation；
(6), branch data point discrete in umbilical cables is fitted by least square method, ifFor the continuous function of section [a, b] upper one group of linear independence, enableIn formula, S (x) is the fitting function of actual curve, α0,α1…αnFor
The real coefficient of fitting function remembers error are as follows: δi=S (xi)-yi, i=0,1,2 ..., n, in formula, S (xi)、yiRespectively it is fitted letter
Several and actual function is in xiThe functional value at place；
(7), with error deltaiWeighted quadratic on the basis of, it may be assumed thatIn formula, I
For error deltaiWeighted quadratic, ω (xi) be i-th of obliquity sensor weight function, and ω (xi) >=0, to make error reach pole
Small value takes the necessary condition of the extreme value of above formula are as follows:And real coefficient is obtained by the formula
α0,α1…αnUnique solutionTo obtain the bending deformation matched curve of umbilical cables are as follows:
(8), to the bending deformation matched curve derivation of umbilical cables, curvature equation is obtained are as follows:, formula
In, C is curvature when umbilical cables are bent, S*' it is S*(x) first derivative, S*" it is S*(x) second dervative, curvature equation exist
Maximum value in domain is maximum deflection curvature of the umbilical cables in fatigue test.
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Application publication date: 20180601 Assignee: NINGBO FANYE MARINE TECHNOLOGY Co.,Ltd. Assignor: NINGBO ORIENT WIRES & CABLES Co.,Ltd. Contract record no.: X2023330000917 Denomination of invention: Test method for maximum bending curvature of umbilical cables in fatigue testing Granted publication date: 20191101 License type: Common License Record date: 20231213 |
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Denomination of invention: Test method for maximum bending curvature of umbilical cables in fatigue testing Granted publication date: 20191101 Pledgee: Agricultural Bank of China Limited Ningbo Beilun branch Pledgor: NINGBO ORIENT WIRES & CABLES Co.,Ltd. Registration number: Y2024980001110 |
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