CN110032783B - Distributed optical fiber monitoring method for surface expansion deformation of flexible buffer air bag - Google Patents

Distributed optical fiber monitoring method for surface expansion deformation of flexible buffer air bag Download PDF

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CN110032783B
CN110032783B CN201910255187.2A CN201910255187A CN110032783B CN 110032783 B CN110032783 B CN 110032783B CN 201910255187 A CN201910255187 A CN 201910255187A CN 110032783 B CN110032783 B CN 110032783B
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deformation
point
section
air bag
points
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CN110032783A (en
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曾捷
何弯弯
于惠勇
顾欣
胡锡涛
张益昕
吴心怡
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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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
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
    • G01B11/165—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge by means of a grating deformed by the object
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Abstract

The invention relates to a distributed optical fiber monitoring method for surface expansion deformation of a flexible buffer air bag, which mainly comprises the following steps: the method comprises the following steps: selecting a typical expansion section S to establish a coordinate system and arranging a fiber grating sensing network; step two: establishing a key discrete point X-direction deformation calculation model on the axial section S; step three: acquiring a deformation value of a key discrete point X direction on a section SS after the section S is subjected to expansion deformation under different internal air pressures; step four: acquiring an X-direction deformation value of any position on the section SS; step five: and (5) repeating the steps from (2-2) to (IV) to obtain the Y-direction deformation value of any position on the section SS. Step six: and acquiring two-dimensional coordinates of any position on the section SS. According to the method, the expansion deformation of the typical expansion section S on the surface of the flexible buffer air bag can be rapidly calculated by acquiring the response strain signals of the fiber bragg gratings of a small number of discrete points and by finite element simulation and formula derivation.

Description

Distributed optical fiber monitoring method for surface expansion deformation of flexible buffer air bag
Technical Field
The invention belongs to the field of structural health monitoring, and particularly provides a distributed optical fiber monitoring method for surface expansion deformation of a flexible buffer air bag.
Background
The flexible buffer airbag is a landing buffer device, belongs to a novel flexible inflatable structure, has the characteristics of foldable expansion, light weight, low cost, good extensibility and the like, and is widely used in the fields of aerospace recycling engineering, air drop protection of material equipment, emergency protection of personnel and the like as an energy attenuation system.
The stability, accuracy and reliability of the flexible buffer airbag structure in the service process directly relate to the service safety, efficiency and observation accuracy of the aerospace structure. The expansion deformation of the flexible buffering air bag structure under the action of different internal air pressures is obtained in real time, so that an important basis can be provided for form control and health condition evaluation of the flexible buffering air bag structure in the working process, and the method has important significance for bearing tolerance characteristic research and performance improvement of the buffering air bag. Therefore, the deformation condition of the key area of the flexible buffer air bag structure under the action of different internal air pressures needs to be calculated.
At present, structural deformation monitoring is widely concerned in the aerospace field. In the future, the spatial structure will be developed more towards multi-functionalization and multitasking, which will certainly put higher requirements on structural shape sensing. Foss and Haugse first proposed a modal transformation algorithm for structural deformation calculation. On the basis, P.B.Boert et al further studied the mode conversion method based on the strain test, and provided the finite element analysis steps of the method. A reverse finite element method is provided for wing deformation calculation, Tessler and the like, and a transfer function between a structural strain field and a displacement field is obtained by solving based on a least square variational equation. The algorithm mainly focuses on analyzing deformation characteristics of rigid structures such as plates and wings, and does not relate to real-time monitoring and calculation of deformation states of the flexible inflatable structure in the service process. In addition, the surface of the flexible buffering air bag is of an irregular arc structure, the expansion deformation of the surface of the bag body is nonlinear under different internal pressures, the deformation is small, and the expansion change of the surface of the bag body is difficult to accurately capture by adopting a non-contact measurement method. Aiming at the problems, the invention provides a method for monitoring the expansion deformation of a balloon by acquiring the strain information of discrete points on the surface of a flexible buffer airbag.
The fiber grating sensing technology has the advantages of small volume, light weight, low cost, easy instrumentation, distributed measurement, strong corrosion resistance and the like, and is receiving more and more extensive attention. Based on the analysis, the invention provides a method for monitoring the strain information of the key nodes on the surface of the flexible buffer airbag by adopting a distributed fiber bragg grating sensor and deducing and calculating the surface expansion deformation condition of the flexible buffer airbag.
Disclosure of Invention
The invention aims to provide a method for quickly calculating the surface axial section expansion deformation fiber bragg grating of a flexible buffer air bag structure. The method comprises the steps of collecting strain response signals of a fiber grating sensor with a small number of discrete points, and providing a calculation model of expansion deformation of an axial section of a flexible buffer air bag structure through finite element simulation results.
In order to solve the technical problems, the method for quickly calculating the surface expansion deformation of the key area on the surface of the flexible buffer air bag structure based on the distributed fiber bragg grating does not need a large number of data sample points, and the process is simple. Comprises the following steps:
the method comprises the following steps: numerical simulation is carried out on the balloon surface expansion deformation characteristics of the flexible buffer airbag structure under different internal pressures by adopting a finite element simulation method, and the balloon deformation characteristics and strain distribution characteristics under different internal pressures are obtained. Selecting a surface reinforcing band D of the flexible buffer air bag1And a reinforcing band D2And the axial section with the largest relative deformation in the middle area is used as a typical expansion section S to establish a coordinate system and arrange a fiber grating sensing network, and the transverse expansion deformation direction of the air bag under different internal air pressures is defined as the X direction, and the axial deformation direction of the air bag under different internal air pressures is defined as the Y direction.
8 reinforcing bands are uniformly distributed on the surface of the flexible buffer air bag structure, and the areas between any two reinforcing bands are the same, so that the reinforcing band D is selected1And D2The deformation characteristics of the interregion expansion area are analyzed. The finite element simulation result shows that the surface of the bag body is reinforced by the belt D1And D2The axial section of the central axis of the middle area is a relatively large deformation area. This axial section is taken as a typical expansion section and is marked as section S.
(1-1) first, an expansion section coordinate system is established. The center of a circle of the bottom surface of the flexible buffering air bag structure is used as an original point, an x axis is established along the diameter direction of the bottom surface and the direction passing through the section, and a y axis is established along the direction perpendicular to the diameter direction of the bottom surface and the direction passing through the section. Assuming that the axial height of the flexible buffer air bag is L, the coordinates of the top point of the surface of the bag body are (0, L). The coordinate of the corresponding y axis on the axial section S corresponding to the initial state is
Figure GDA0003425906040000021
Is denoted as A and the coordinates are denoted as
Figure GDA0003425906040000022
Corresponding to a height of
Figure GDA0003425906040000023
The point is marked as B and the coordinates are marked as
Figure GDA0003425906040000024
Corresponding to a height of
Figure GDA0003425906040000025
The point of (A) is marked as C, and the coordinates are marked as
Figure GDA0003425906040000026
And (1-2) arranging a fiber grating sensing network. The fiber grating sensors FBG1, FBG2 and FBG3 are respectively pasted at the point A, B, C, the three fiber grating sensors are all pasted along the circumferential direction of the balloon surface, and the pasting direction is perpendicular to the y axis. The three fiber bragg grating sensors are connected in series by adopting fiber jumper wires to form a fiber bragg grating sensing network;
step two: and establishing an X-direction deformation calculation model corresponding to the key discrete points on the axial section S according to the finite element calculation result.
(2-1) obtaining the strain change characteristics of the positions of three points A, B, C on the axial section S under different internal air pressures by using a finite element numerical simulation method. Simulation calculation results show that the internal air pressure of the flexible buffer airbag is approximately monotonous with the strain of the position of the A, B, C, and the internal air pressure and the strain of the position of the A, B, C correspond to a fitting relation model, which has the following expression:
p＝aε+b
wherein p is internal air pressure, a and b are relational coefficients of air pressure and strain of each point obtained by adopting a linear fitting method, and epsilon is strain.
Then, according to the finite element simulation result, the corresponding relation expression of the internal air pressure and the position strain of the point A can be obtained: p is a radical ofA＝aAεA+bAAnd the corresponding relation expression of the internal air pressure and the position strain of the point B is as follows: p is a radical ofB＝aBεB+bBAnd the corresponding relation expression of the internal air pressure and the strain of the position of the point C is as follows: p is a radical ofC＝aCεC+bCWherein, epsilonA、εB、εCRespectively, indicating the strain at point A, B, C.
To reduce the error, p is addedA、pB、pCThe average value of the pressure difference is used as the measured value of the air pressure in the air bag, and the measured value of the air pressure in the flexible buffer air bag
Figure GDA0003425906040000031
Can be calculated using the following formula:
Figure GDA0003425906040000032
(2-2) calculating to obtain the deformation value of each point on the section S in the X direction under different internal air pressures by a finite element simulation analysis method, obtaining the deformation trend of the section S in the X direction, and drawing a corresponding curve between the deformation amount in the X direction and the y-axis coordinate. The troughs appearing on the curve are marked in turn
Figure GDA0003425906040000033
The peak points are marked in turn
Figure GDA0003425906040000034
Figure GDA0003425906040000035
Wherein l1、l3…l2n+1Represents the y-axis coordinate, l, corresponding to the position of the valley point on the deformation curve2、l4…l2nThe y-axis coordinate corresponding to the position of the peak point on the deformation curve is represented, and l is more than or equal to 01＜l2＜l3＜...＜ln< L. Selecting discrete points on the characteristic curve of deformation of the balloon
Figure GDA0003425906040000036
Calculating key discrete points as the expansion deformation of the axial section S of the flexible buffer air bag.
And taking the X-direction deformation value of the position of each key discrete point, and establishing the corresponding relation between the X-direction deformation corresponding to each key discrete point and the internal air pressure. According to the finite element calculation result, key discrete points
Figure GDA0003425906040000037
The X-direction deformation value of the position is in linear relation with the internal air pressure. Key discrete point
Figure GDA0003425906040000038
The corresponding relation model of the deformation value of the position and the internal air pressure of the flexible buffer air bag can be expressed as follows:
Δlj＝mjp+nj，
Figure GDA0003425906040000039
wherein,. DELTA.ljFor the X-direction deformation value, m, of each pointj、njThe coefficient of the relation between deformation and air pressure is obtained by adopting a linear fitting method. Therefore, an expression matrix corresponding to the X-direction deformation value and the internal air pressure of the position of the key discrete point can be obtained.
Will be provided with
Figure GDA0003425906040000041
Substituting the corresponding relation model between the X-direction deformation value and the internal pressure of each discrete point to obtain the key discrete point on the axial section S of the balloon
Figure GDA0003425906040000042
The X-direction deformation value at the position corresponds to the strain of three points A, B, C on the axial section S of the balloon surface:
Δlj＝kj∑εi+qj，
Figure GDA0003425906040000043
in the above formula, j is a subscript and represents the mark name of a key discrete point on the axial section S of the flexible buffer air bag, and k and q are corresponding relation model expression coefficients，εiRepresents the strain at A, B, C at the position of three points, where i ═ a, B, and C.
According to the function model matrix, a relation model between the X-direction deformation values of the positions of the discrete points on the axial section S of the flexible buffer airbag and the strain of the position of the three points A, B, C on the surface of the airbag is established, namely the strain of the positions of the three points A, B, C on the surface of the airbag under different internal air pressures is established, and the X-direction deformation values of the key discrete points on the axial section S of the airbag under different internal air pressures can be obtained.
Step three: and monitoring the surface strain change of the flexible buffer airbag structure under the action of different internal air pressures by using the fiber grating sensor, bringing the strain measured by the fiber grating sensor into a deformation calculation inversion model, and obtaining a deformation value of a key discrete point X direction on the section S.
Step four: according to an X-direction deformation change curve on a section S of the surface of the flexible buffer air bag under different internal air pressures, extracting a key discrete point deformation value in the curve, establishing an X-direction deformation value calculation model at any position on the section S, and obtaining an X-direction deformation value at any position on a section SS after the section S is subjected to expansion deformation under different internal air pressures.
Finite element calculation results show that the change curve of the deformation value in the X direction at the position between the adjacent wave trough and the wave peak point on the deformation trend curve on the axial section S of the surface of the flexible buffer air bag is approximately in a linear relation. Assuming that the relational expression between the deformation value of any point between two adjacent wave troughs and the wave peak point and the initial y-axis coordinate corresponding to the point is as follows:
Δx＝wy+h
and delta X is the X-direction deformation value of any point between adjacent wave troughs and wave crests, and y is the initial y-axis coordinate corresponding to any point between the wave troughs and the wave crests.
Assuming adjacent valley points
Figure GDA0003425906040000044
And peak point
Figure GDA0003425906040000045
Corresponding deformation value and initial y-axisThe coordinates are respectively (Δ x)2n-1,y2n-1)、(Δx2n,y2n) Then, the coefficient of the deformation value calculation expression of any point between the adjacent trough point and the crest point can be calculated as:
Figure GDA0003425906040000051
Figure GDA0003425906040000052
according to the values of w and h and two adjacent valley points on the section S of the flexible buffer air bag
Figure GDA0003425906040000053
And peak point
Figure GDA0003425906040000054
The initial y-axis coordinate of any point between the two points can be used for calculating the X-direction deformation value of any point on the expanded axial section SS of the balloon under the action of different internal air pressures.
Step five: and (5) repeating the steps from (2-2) to (IV), establishing a Y-direction deformation calculation model of any position on the section S on the surface of the flexible buffer air bag, and obtaining a Y-direction deformation value of any position on the section SS after the section S is expanded and deformed under different internal air pressures.
(5-1) calculating to obtain the deformation value of each point on the section S in the Y direction under different internal air pressures by a finite element simulation analysis method, obtaining the deformation trend of the section S in the Y direction, and drawing a corresponding curve between the deformation amount in the Y direction and the Y-axis coordinate. The troughs appearing on the curve are marked in turn
Figure GDA0003425906040000055
The peak points are marked in turn
Figure GDA0003425906040000056
Wherein l1、l3…l2n+1Showing the valley point on the deformation curveY-axis coordinate corresponding to position, l2、l4…l2nThe y-axis coordinate corresponding to the position of the peak point on the deformation curve is represented, and l is more than or equal to 01＜l2＜l3＜...＜ln< L. Selecting discrete points on the characteristic curve of deformation of the balloon
Figure GDA0003425906040000057
Calculating key discrete points as the expansion deformation of the axial section S of the flexible buffer air bag.
And taking the Y-direction deformation value of the position of each key discrete point, and establishing the corresponding relation between the Y-direction deformation corresponding to each key discrete point and the internal air pressure. According to the finite element calculation result, key discrete points
Figure GDA0003425906040000058
The Y-direction deformation value of the position is in linear relation with the internal air pressure. Key discrete point
Figure GDA0003425906040000059
The corresponding relation model of the deformation value of the position and the internal air pressure of the flexible buffer air bag can be expressed as follows:
Figure GDA00034259060400000510
wherein,. DELTA.lkFor the value of the Y-direction deformation of each point, ek、gkThe coefficient of the relation between deformation and air pressure is obtained by adopting a linear fitting method. Therefore, an expression matrix corresponding to the Y-direction deformation value and the internal air pressure of the position of the key discrete point can be obtained.
Relational expression for corresponding air pressure in air bag and three-point strain A, B, C on surface of bag body
Figure GDA0003425906040000061
Substituting the corresponding relation model of the deformation value of each discrete point in the Y direction and the internal pressure to obtain the key discrete point on the axial section S of the balloon
Figure GDA0003425906040000062
The deformation value in the Y direction at the position corresponds to the strain of three points A, B, C on the axial section S of the balloon surface:
Figure GDA0003425906040000063
in the above formula, k is subscript and represents the mark name of discrete key point on the axial section S of the flexible buffer air bag, r and t are corresponding relation model expression coefficients, epsiloniRepresents the strain at A, B, C at the position of three points, where i ═ a, B, and C.
According to the function model matrix, a relation model between the Y-direction deformation values of the positions of the discrete points on the axial section S of the flexible buffer airbag and the strain of the position of the three points A, B, C on the surface of the airbag is established, namely the strain of the positions of the three points A, B, C on the surface of the airbag under different internal air pressures is established, and the Y-direction deformation values of the critical discrete points on the axial section S of the airbag under different internal air pressures can be obtained.
And (5-2) monitoring the surface strain change of the flexible buffer airbag structure under the action of different internal air pressures by using the fiber grating sensor, bringing the strain measured by the fiber grating sensor into a deformation calculation inversion model, and obtaining a deformation value of a key discrete point Y direction on the section S.
(5-3) according to an X-direction deformation change curve on the surface section S of the flexible buffer air bag under different internal air pressures, extracting a key discrete point deformation value in the curve, establishing a Y-direction deformation value calculation model at any position on the section S, and obtaining a Y-direction deformation value at any position on the section SS after the section S is subjected to expansion deformation under different internal air pressures;
finite element calculation results show that Y-direction deformation value change curves of positions between adjacent wave troughs and wave peak points on a deformation trend curve on the axial section S of the surface of the flexible buffer air bag are approximately in a linear relation. Assuming that the relational expression between the deformation value of any point between two adjacent wave troughs and the wave peak point and the initial y-axis coordinate corresponding to the point is as follows:
Δy＝vy+z
and Y is an initial Y-axis coordinate corresponding to any point between the wave troughs and the wave crests.
Assuming adjacent valley points
Figure GDA0003425906040000064
And peak point
Figure GDA0003425906040000065
The corresponding deformation value and the initial y-axis coordinate are respectively (delta y)2n-1,y2n-1)、(Δy2n,y2n) Then, the coefficient of the deformation value calculation expression of any point between the adjacent trough point and the crest point can be calculated as:
Figure GDA0003425906040000071
Figure GDA0003425906040000072
according to the values of z and y and two adjacent valley points on the section S of the flexible buffer air bag
Figure GDA0003425906040000073
And peak point
Figure GDA0003425906040000074
And the initial Y-axis coordinate of any point between the two points can be used for calculating the Y-direction deformation value of any point on the expanded axial section SS of the balloon under the action of different internal air pressures.
Step six: and D, acquiring two-dimensional coordinates of any position on the section SS according to the deformation information of any position in the X direction and the deformation information in the Y direction on the section SS, which is obtained by the expansion deformation of the section S under different internal air pressures in the step four and the step five.
Assume that the initial coordinate of any point on the cross section S in the initial state is (x)0,y0) The expanded section SS according to the section S obtained in the fourth step and the fifth stepThe intentional point coordinates may be represented as (xx, yy). Wherein: xx ═ x0+Δx，yy＝y0+ Δ y will Δ x ═ wy0+h，Δy＝vy0Substituting + z into the above formula to obtain
Figure GDA0003425906040000075
Figure GDA0003425906040000076
2. The method for calculating the expansion deformation of the axial section S of the flexible buffer air bag based on the fiber bragg grating sensor as claimed in claim 1, wherein the method comprises the following steps: the flexible buffer air bag structure is a symmetrical similar-circular structure, so that the representative axial section expansion deformation of the surface of the air bag can be obtained according to the method, and the whole expansion deformation of the flexible buffer air bag structure can be approximately obtained according to the same principle of the deformation of the symmetrical structure.
Drawings
FIG. 1 is a schematic diagram of a finite element simulation model of a flexible buffer airbag structure;
FIG. 2 is a schematic diagram of the cross-section S coordinate system setup;
FIG. 3 is a graph showing the deformation-y-axis coordinate correspondence on the surface section S of the flexible buffer airbag under different internal air pressures;
detailed description of the preferred embodiments
The technical scheme of the invention is explained in detail in the following with the accompanying drawings: aiming at the expansion deformation of the flexible buffer air bag, a calculation method for realizing the expansion deformation of the surface of the bag body by adopting a distributed fiber bragg grating sensing network under the action of different internal air pressures in the flexible air bag structure is provided.
The method comprises the following steps: numerical simulation is carried out on the balloon surface expansion deformation characteristics of the flexible buffer airbag structure under different internal pressures by adopting a finite element simulation method, and the balloon deformation characteristics and strain distribution characteristics under different internal pressures are obtained. Selecting a surface reinforcing band D of the flexible buffer air bag1And a reinforcing band D2The axial section with the largest relative deformation in the middle area is taken as a modelThe type expansion section S establishes a coordinate system and is distributed with a fiber grating sensing network, the transverse expansion deformation direction of the air bag under different internal air pressures is defined as the X direction, and the axial deformation direction of the air bag under different internal air pressures is defined as the Y direction.
8 reinforcing bands are uniformly distributed on the surface of the flexible buffer air bag structure, and the areas between any two reinforcing bands are the same, so that the reinforcing band D is selected1And D2The deformation characteristics of the interregion expansion area are analyzed. The finite element simulation result shows that the surface of the bag body is reinforced by the belt D1And D2The axial section of the central axis of the middle area is a relatively large deformation area. This axial section is taken as a typical expansion section and is marked as section S.
(1-1) first, an expansion section coordinate system is established. The center of a circle of the bottom surface of the flexible buffering air bag structure is used as an original point, an x axis is established along the diameter direction of the bottom surface and the direction passing through the section, and a y axis is established along the direction perpendicular to the diameter direction of the bottom surface and the direction passing through the section. Assuming that the axial height of the flexible buffer air bag is L, the coordinates of the top point of the surface of the bag body are (0, L). The coordinate of the corresponding y axis on the axial section S corresponding to the initial state is
Figure GDA0003425906040000081
Is denoted by A and the coordinates are denoted by
Figure GDA0003425906040000082
Corresponding to a height of
Figure GDA0003425906040000083
The point is marked as B and the coordinates are marked as
Figure GDA0003425906040000084
Corresponding to a height of
Figure GDA0003425906040000085
The point of (A) is marked as C, and the coordinates are marked as
Figure GDA0003425906040000086
And (1-2) arranging a fiber grating sensing network. The fiber grating sensors FBG1, FBG2 and FBG3 are respectively pasted at the point A, B, C, the three fiber grating sensors are all pasted along the circumferential direction of the balloon surface, and the pasting direction is perpendicular to the y axis. The three fiber bragg grating sensors are connected in series by adopting fiber jumper wires to form a fiber bragg grating sensing network;
step two: and establishing an X-direction deformation calculation model corresponding to the key discrete points on the axial section S according to the finite element calculation result.
(2-1) obtaining the strain change characteristics of the positions of the A, B, C points on the axial section S under different internal air pressures by using a finite element numerical simulation method. Simulation calculation results show that the internal air pressure of the flexible buffer airbag is approximately monotonous with the strain of the position of the A, B, C, and the internal air pressure and the strain of the position of the A, B, C correspond to a fitting relation model, which has the following expression:
p＝aε+b
wherein p is internal air pressure, a and b are relational coefficients of air pressure and strain of each point obtained by adopting a linear fitting method, and epsilon is strain.
Then, according to the finite element simulation result, the corresponding relation expression of the internal air pressure and the position strain of the point A can be obtained: p is a radical ofA＝aAεA+bAAnd the corresponding relation expression of the internal air pressure and the position strain of the point B is as follows: p is a radical of formulaB＝aBεB+bBAnd the corresponding relation expression of the internal air pressure and the position strain of the point C is as follows: p is a radical ofC＝aCεC+bCWherein, epsilonA、εB、εCRespectively, indicating the strain at point A, B, C.
To reduce the error, p is addedA、pB、pCThe average value of the pressure difference is used as the measured value of the air pressure in the air bag, and the measured value of the air pressure in the flexible buffer air bag
Figure GDA0003425906040000091
Can be calculated using the following formula:
Figure GDA0003425906040000092
(2-2) calculating to obtain the deformation value of each point on the section S in the X direction under different internal air pressures by a finite element simulation analysis method, obtaining the deformation trend of the section S in the X direction, and drawing a corresponding curve between the deformation amount in the X direction and the y-axis coordinate. The troughs appearing on the curve are marked in turn
Figure GDA0003425906040000093
The peak points are marked in turn
Figure GDA0003425906040000094
Figure GDA0003425906040000095
Wherein l1、l3…l2n+1Represents the y-axis coordinate, l, corresponding to the position of the valley point on the deformation curve2、l4…l2nThe y-axis coordinate corresponding to the position of the peak point on the deformation curve is represented, and l is more than or equal to 01＜l2＜l3＜...＜ln< L. Selecting discrete points on the characteristic curve of deformation of the balloon
Figure GDA0003425906040000096
Calculating key discrete points as the expansion deformation of the axial section S of the flexible buffer air bag.
And taking the X-direction deformation value of the position of each key discrete point, and establishing the corresponding relation between the X-direction deformation corresponding to each key discrete point and the internal air pressure. According to the finite element calculation result, key discrete points
Figure GDA0003425906040000097
The X-direction deformation value of the position is in a linear relation with the internal air pressure. Key discrete point
Figure GDA0003425906040000098
The corresponding relation model of the deformation value of the position and the internal air pressure of the flexible buffer air bag can be expressed as follows:
Figure GDA0003425906040000099
wherein,. DELTA.ljFor the X-direction deformation value, m, of each pointj、njThe coefficient of the relation between deformation and air pressure is obtained by adopting a linear fitting method. Therefore, an expression matrix corresponding to the X-direction deformation value and the internal air pressure of the position of the key discrete point can be obtained.
Will be provided with
Figure GDA0003425906040000101
Substituting the corresponding relation model between the X-direction deformation value and the internal pressure of each discrete point to obtain the key discrete point on the axial section S of the balloon
Figure GDA0003425906040000102
The X-direction deformation value at the position corresponds to the strain of three points A, B, C on the axial section S of the balloon surface:
Figure GDA0003425906040000103
in the above formula, j is a subscript and represents the mark name of a discrete point of a key on the axial section S of the flexible buffer air bag, k and q are corresponding relation model expression coefficients, epsiloniRepresents the strain at A, B, C at the position of three points, where i ═ a, B, and C.
According to the function model matrix, a relation model between the X-direction deformation values of the positions of the discrete points on the axial section S of the flexible buffer airbag and the strain of the position of the three points A, B, C on the surface of the airbag is established, namely the strain of the positions of the three points A, B, C on the surface of the airbag under different internal air pressures is established, and the X-direction deformation values of the key discrete points on the axial section S of the airbag under different internal air pressures can be obtained.
Step three: and monitoring the surface strain change of the flexible buffer airbag structure under the action of different internal air pressures by using the fiber grating sensor, bringing the strain measured by the fiber grating sensor into a deformation calculation inversion model, and obtaining a deformation value of a key discrete point X direction on the section S.
Step four: according to an X-direction deformation change curve on a section S of the surface of the flexible buffer air bag under different internal air pressures, extracting a key discrete point deformation value in the curve, establishing an X-direction deformation value calculation model at any position on the section S, and obtaining an X-direction deformation value at any position on a section SS after the section S is subjected to expansion deformation under different internal air pressures.
Finite element calculation results show that the change curve of the deformation value in the X direction at the position between the adjacent wave trough and the wave peak point on the deformation trend curve on the axial section S of the surface of the flexible buffer air bag is approximately in a linear relation. Assuming that the relational expression between the deformation value of any point between two adjacent wave troughs and the wave peak point and the initial y-axis coordinate corresponding to the point is as follows:
Δx＝wy+h
and delta X is the X-direction deformation value of any point between adjacent wave troughs and wave crests, and y is the initial y-axis coordinate corresponding to any point between the wave troughs and the wave crests.
Assuming adjacent valley points
Figure GDA0003425906040000104
And peak point
Figure GDA0003425906040000105
The corresponding deformation value and the initial y-axis coordinate are respectively (delta x)2n-1,y2n-1)、(Δx2n,y2n) Then, the coefficient of the deformation value calculation expression of any point between the adjacent trough point and the crest point can be calculated as:
Figure GDA0003425906040000111
Figure GDA0003425906040000112
according to the values of w and h and two adjacent valley points on the section S of the flexible buffer air bag
Figure GDA0003425906040000113
And peak point
Figure GDA0003425906040000114
The initial y-axis coordinate of any point between the two points can be used for calculating the X-direction deformation value of any point on the expanded axial section SS of the balloon under the action of different internal air pressures.
Step five: and (5) repeating the steps from (2-2) to (IV), establishing a Y-direction deformation calculation model of any position on the surface section S of the flexible buffer air bag, and obtaining a Y-direction deformation value of any position on the section SS after the section S is expanded and deformed under different internal air pressures.
(5-1) calculating to obtain the deformation value of each point on the section S in the Y direction under different internal air pressures by a finite element simulation analysis method, obtaining the deformation trend of the section S in the Y direction, and drawing a corresponding curve between the deformation amount in the Y direction and the Y-axis coordinate. The troughs appearing on the curve are marked in sequence
Figure GDA0003425906040000115
The peak points are marked in turn
Figure GDA0003425906040000116
Wherein l1、l3…l2n+1Represents the y-axis coordinate, l, corresponding to the position of the valley point on the deformation curve2、l4…l2nThe y-axis coordinate corresponding to the position of the peak point on the deformation curve is represented, and l is more than or equal to 01＜l2＜l3＜...＜lnIs less than L. Selecting discrete points on the characteristic curve of deformation of the balloon
Figure GDA0003425906040000117
Calculating key discrete points as the expansion deformation of the axial section S of the flexible buffer air bag.
And taking the Y-direction deformation value of the position of each key discrete point, and establishing the corresponding relation between the Y-direction deformation corresponding to each key discrete point and the internal air pressure. According to the finite element calculation result, key discrete points
Figure GDA0003425906040000118
The Y-direction deformation value of the position is in linear relation with the internal air pressure. Key discrete point
Figure GDA0003425906040000119
The corresponding relation model of the deformation value of the position and the internal air pressure of the flexible buffer air bag can be expressed as follows:
Figure GDA00034259060400001110
wherein,. DELTA.lkFor the value of the Y-direction deformation of each point, ek、gkThe coefficient of the relation between deformation and air pressure is obtained by adopting a linear fitting method. Therefore, an expression matrix corresponding to the Y-direction deformation value and the internal air pressure of the position of the key discrete point can be obtained.
Corresponding relation between air pressure in the air bag and three-point strain of the surface A, B, C of the bag body
Figure GDA0003425906040000121
Substituting the corresponding relation model of the deformation value of each discrete point in the Y direction and the internal pressure to obtain the key discrete point on the axial section S of the balloon
Figure GDA0003425906040000122
The deformation value in the Y direction at the position corresponds to the strain of three points A, B, C on the axial section S of the balloon surface:
Figure GDA0003425906040000123
in the above formula, k is subscript and represents the mark name of discrete key point on the axial section S of the flexible buffer air bag, r and t are corresponding relation model expression coefficients, epsiloniRepresents the strain at A, B, C at the position of three points, where i ═ a, B, and C.
According to the function model matrix, a relation model between the Y-direction deformation values of the positions of the discrete points on the axial section S of the flexible buffer airbag and the strain of the position of the three points A, B, C on the surface of the airbag is established, namely the strain of the positions of the three points A, B, C on the surface of the airbag under different internal air pressures is established, and the Y-direction deformation values of the critical discrete points on the axial section S of the airbag under different internal air pressures can be obtained.
And (5-2) monitoring the surface strain change of the flexible buffer airbag structure under the action of different internal air pressures by using the fiber grating sensor, bringing the strain measured by the fiber grating sensor into a deformation calculation inversion model, and obtaining a deformation value of a key discrete point Y direction on the section S.
(5-3) according to an X-direction deformation change curve on the surface section S of the flexible buffer air bag under different internal air pressures, extracting a key discrete point deformation value in the curve, establishing a Y-direction deformation value calculation model at any position on the section S, and obtaining a Y-direction deformation value at any position on the section SS after the section S is subjected to expansion deformation under different internal air pressures;
finite element calculation results show that Y-direction deformation value change curves of positions between adjacent wave troughs and wave peak points on a deformation trend curve on the axial section S of the surface of the flexible buffer air bag are approximately in a linear relation. Assuming that the relational expression between the deformation value of any point between two adjacent wave troughs and the wave peak point and the initial y-axis coordinate corresponding to the point is as follows:
Δy＝vy+z
and Y is an initial Y-axis coordinate corresponding to any point between the wave troughs and the wave crests.
Assuming adjacent valley points
Figure GDA0003425906040000124
And peak point
Figure GDA0003425906040000125
The corresponding deformation value and the initial y-axis coordinate are respectively (delta y)2n-1,y2n-1)、(Δy2n,y2n) Then, the coefficient of the deformation value calculation expression of any point between the adjacent trough point and the crest point can be calculated as:
Figure GDA0003425906040000131
Figure GDA0003425906040000132
according to the values of z and y and two adjacent valley points on the section S of the flexible buffer air bag
Figure GDA0003425906040000133
And peak point
Figure GDA0003425906040000134
And the initial Y-axis coordinate of any point between the two points can be used for calculating the Y-direction deformation value of any point on the expanded axial section SS of the balloon under the action of different internal air pressures.
Step six: and D, acquiring two-dimensional coordinates of any position on the section SS according to the deformation information of any position in the X direction and the deformation information in the Y direction on the section SS, which is obtained by the expansion deformation of the section S under different internal air pressures in the step four and the step five.
Assume that the initial coordinate of any point on the cross section S in the initial state is (x)0,y0) The coordinates of an arbitrary point on the expanded section SS of the section S obtained according to the fourth and fifth steps may be represented as (xx, yy). Wherein: xx ═ x0+Δx，yy＝y0+ Δ y will Δ x ═ wy0+h，Δy＝vy0+ z is substituted into the above formula to obtain
Figure GDA0003425906040000135
Figure GDA0003425906040000136
The flexible buffering air bag structure is a symmetrical similar-circular structure, the representative axial section of the surface of the air bag can be subjected to expansion deformation according to the method, and the whole expansion deformation of the flexible buffering air bag structure is approximately obtained according to the same principle of the deformation of the symmetrical structure.

Claims (2)

1. A distributed optical fiber monitoring method for the surface expansion deformation of a flexible buffer air bag is characterized in that 8 reinforcing bands are uniformly distributed on the surface of the structure of the flexible buffer air bag, the regions between any two reinforcing bands are the same, and a reinforcing band D is selected1And D2The deformation characteristics of the expansion region are analyzed, and the method is characterized by comprising the following steps of:
the method comprises the following steps: numerical simulation is carried out on the expansion deformation characteristics of the surface of the capsule body of the flexible buffering air bag structure under different internal pressures by adopting a finite element simulation method, so that the deformation characteristics and the strain distribution characteristics of the capsule body under different internal pressures are obtained; selecting a surface reinforcing band D of the flexible buffer air bag1And a reinforcing band D2The axial section with the largest relative deformation in the middle area is used as a typical expansion section S to establish a coordinate system and arrange a fiber grating sensing network, the transverse expansion deformation direction of the air bag under different internal air pressures is defined as the deformation in the X direction, and the axial deformation direction of the air bag under different internal air pressures is defined as the deformation in the Y direction;
the finite element simulation result shows that the surface of the bag body is reinforced by the belt D1And D2The axial section of the central axis of the middle area is a relatively large deformation area; this axial section is taken as a typical expansion section and is marked as section S;
(1-1) firstly establishing an expansion section coordinate system; taking the circle center of the bottom surface of the flexible buffering air bag structure as an origin, establishing an x-axis along the diameter direction of the bottom surface and the direction passing through the section, and establishing a y-axis along the direction perpendicular to the diameter direction of the bottom surface and the direction passing through the section; assuming that the axial height of the flexible buffer air bag is L, the vertex coordinates of the surface of the bag body are (0, L); the coordinate of the corresponding y axis on the axial section S corresponding to the initial state is
Figure FDA0003554417440000011
Is denoted as A and the coordinates are denoted as
Figure FDA0003554417440000012
Corresponding to a height of
Figure FDA0003554417440000013
The point of is marked as B and the coordinates are marked as
Figure FDA0003554417440000014
Corresponding to a height of
Figure FDA0003554417440000015
The point of (A) is marked as C, and the coordinates are marked as
Figure FDA0003554417440000016
(1-2) arranging a fiber grating sensing network; adhering fiber grating sensors FBG1, FBG2 and FBG3 at a point A, B, C respectively, wherein the three fiber grating sensors are adhered along the circumferential direction of the surface of the balloon, and the adhering direction is vertical to the y axis; the three fiber bragg grating sensors are connected in series by adopting fiber jumper wires to form a fiber bragg grating sensing network;
step two: establishing an X-direction deformation calculation model corresponding to the key discrete point on the axial section S according to the finite element calculation result;
(2-1) obtaining the strain change characteristics of the positions of three points A, B, C on the axial section S under different internal air pressures by using a finite element numerical simulation method; simulation calculation results show that the internal air pressure of the flexible buffer airbag is approximately monotonous with the strain of the position of the A, B, C, and the internal air pressure and the strain of the position of the A, B, C correspond to a fitting relation model, which has the following expression:
p＝aε+b
wherein, p is internal air pressure, a and b are relational coefficients of air pressure and strain of each point obtained by adopting a linear fitting method, and epsilon is strain;
obtaining the corresponding relation expression of the internal air pressure and the position strain of the point A according to the finite element simulation result:
pA＝aAεA+bAand the corresponding relation expression of the internal air pressure and the position strain of the point B is as follows: p is a radical ofB＝aBεB+bBAnd the corresponding relation expression of the internal air pressure and the strain of the position of the point C is as follows: p is a radical ofC＝aCεC+bCWherein, epsilonA、εB、εCRespectively representing the position strain of point A, B, C;
to reduce the error, p is addedA、pB、pCThe average value of the pressure difference is used as the measured value of the air pressure in the air bag, and the measured value of the air pressure in the flexible buffer air bag
Figure FDA0003554417440000021
Calculated using the formula:
Figure FDA0003554417440000022
(2-2) calculating to obtain deformation values of all points in the X direction on the section S under different internal air pressures by using a finite element simulation analysis method, obtaining the deformation trend of the section S in the X direction, and drawing a corresponding curve between the deformation in the X direction and the y-axis coordinate; the troughs appearing on the curve are marked in turn
Figure FDA0003554417440000023
The peak points are marked in turn
Figure FDA0003554417440000024
Figure FDA0003554417440000025
Wherein l1、l3…l2n+1Represents the y-axis coordinate, l, corresponding to the position of the valley point on the deformation curve2、l4…l2nThe y-axis coordinate corresponding to the position of the peak point on the deformation curve is represented, and l is more than or equal to 01＜l2＜l3＜...＜ln< L; selecting discrete points on the characteristic curve of the deformation of the capsule
Figure FDA0003554417440000026
Calculating key discrete points as the expansion deformation of the axial section S of the flexible buffer air bag;
taking the X-direction deformation value of the position of each key discrete point, and establishing the corresponding relation between the X-direction deformation corresponding to each key discrete point and the internal air pressure; according to the finite element calculation result, key discrete points
Figure FDA0003554417440000027
The X-direction deformation value of the position corresponds to the internal air pressure in a linear relation; key discrete point
Figure FDA0003554417440000028
The corresponding relation model of the deformation value of the position and the internal air pressure of the flexible buffer air bag is expressed as follows:
Figure FDA0003554417440000029
wherein, Δ ljFor X-direction deformation values, m, of each key discrete pointj、njThe coefficient of the relation between deformation and air pressure is obtained by adopting a linear fitting method; thus obtaining an expression matrix corresponding to the X-direction deformation values and the internal air pressure of the positions of the key discrete points;
will be provided with
Figure FDA0003554417440000031
Substituting the corresponding relation model of the X-direction deformation value and the internal pressure of each discrete point to obtain the key discrete point on the axial section S of the capsule body
Figure FDA0003554417440000032
The X-direction deformation value at the position corresponds to the strain of three points A, B, C on the axial section S of the balloon surface:
Figure FDA0003554417440000033
in the above formula, j is a subscript and represents the mark name of a discrete point of a key on the axial section S of the flexible buffer air bag, k and q are corresponding relation model expression coefficients, epsiloniRepresents the strain at the position of A, B, C, where i ═ a, B, C;
according to the function model matrix, a relation model between X-direction deformation values of positions of a plurality of discrete points on the axial section S of the flexible buffer air bag and strain of the position of three points A, B, C on the surface of the air bag is established, namely the strain of the positions of three points A, B, C on the surface of the air bag under different internal air pressures is obtained, and the X-direction deformation values of the key discrete points on the axial section S of the air bag under different internal air pressures are obtained;
step three: monitoring the surface strain change of the flexible buffer airbag structure under the action of different internal air pressures by using an optical fiber grating sensor, bringing the strain measured by the optical fiber grating sensor into a deformation calculation inversion model, and obtaining a deformation value in the X direction of a key discrete point on the section S;
step four: according to an X-direction deformation change curve on a section S of the surface of the flexible buffer air bag under different internal air pressures, extracting a key discrete point deformation value in the curve, establishing an X-direction deformation value calculation model at any position on the section S, and obtaining an X-direction deformation value at any position on a section SS after the section S is subjected to expansion deformation under different internal air pressures;
the finite element calculation result shows that the X-direction deformation value change curve of the position between the adjacent wave trough and the wave peak point on the deformation trend curve on the axial section S of the surface of the flexible buffer air bag is approximately in a linear relation; assuming that the relational expression between the deformation value of any point between two adjacent wave troughs and the wave peak point and the initial y-axis coordinate corresponding to the point is as follows:
Δx＝wy+h
wherein, Δ X is the X-direction deformation value of any point between adjacent wave troughs and wave crests, and y is the initial y-axis coordinate corresponding to any point between the wave troughs and the wave crests;
assuming adjacent valley points
Figure FDA0003554417440000034
And peak point
Figure FDA0003554417440000035
The corresponding deformation values and the initial y-axis coordinate are respectively corresponding to (delta x)2n-1,y2n-1)、(Δx2n,y2n) Then, the coefficient of the deformation value calculation expression of any point between the adjacent trough point and the crest point can be calculated as follows:
Figure FDA0003554417440000041
Figure FDA0003554417440000042
according to the values of w and h and two adjacent valley points on the section S of the flexible buffer air bag
Figure FDA0003554417440000043
And peak point
Figure FDA0003554417440000044
The initial y-axis coordinate of any point between the two points can calculate the X-direction deformation value of any point on the expanded axial section SS of the balloon under the action of different internal air pressures;
step five: repeating the steps from (2-2) to (IV), establishing a Y-direction deformation calculation model at any position on the section S on the surface of the flexible buffer air bag, and obtaining a Y-direction deformation value at any position on the section SS after the section S is expanded and deformed under different internal air pressures;
(5-1) calculating to obtain Y-direction deformation values of all points on the section S under different internal air pressures by a finite element simulation analysis method, obtaining the deformation trend of the section S in the Y direction, and drawing a corresponding curve between the Y-direction deformation and the Y-axis coordinate; the troughs appearing on the curve are marked in turn
Figure FDA0003554417440000045
The peak points are marked in turn
Figure FDA0003554417440000046
Figure FDA0003554417440000047
Selecting discrete points on the characteristic curve of deformation of the balloon
Figure FDA0003554417440000048
Calculating key discrete points as the expansion deformation of the axial section S of the flexible buffer air bag;
taking a Y-direction deformation value of the position of each key discrete point, and establishing a corresponding relation between Y-direction deformation corresponding to each key discrete point and internal air pressure; according to the finite element calculation result, key discrete points
Figure FDA0003554417440000049
The Y-direction deformation value of the position is in a linear relation with the internal air pressure; key discrete point
Figure FDA00035544174400000410
The corresponding relation model of the deformation value of the position and the internal air pressure of the flexible buffer air bag is expressed as follows:
Figure FDA00035544174400000411
wherein,. DELTA.lkFor the value of the Y-direction deformation of each point, ek、gkThe coefficient of the relation between deformation and air pressure is obtained by adopting a linear fitting method; thus obtaining an expression matrix corresponding to the Y-direction deformation values and the internal air pressure of the positions of the key discrete points;
relational expression for corresponding air pressure in air bag and three-point strain A, B, C on surface of bag body
Figure FDA00035544174400000412
Y direction change into each discrete pointObtaining key discrete points on the axial section S of the capsule body by using a model of the corresponding relation between the shape value and the internal pressure
Figure FDA00035544174400000413
The deformation value in the Y direction at the position corresponds to the strain of three points A, B, C on the axial section S of the balloon surface:
Figure FDA0003554417440000051
in the above formula, k is subscript and represents the mark name of discrete key point on the axial section S of the flexible buffer air bag, r and t are corresponding relation model expression coefficients, epsiloniRepresents the strain at the position of A, B, C, where i ═ a, B, C;
according to the function model matrix, a relation model between Y-direction deformation values of positions of a plurality of discrete points on the axial section S of the flexible buffer air bag and strain of the position of three points A, B, C on the surface of the air bag is established, namely the strain of the positions of three points A, B, C on the surface of the air bag under different internal air pressures is obtained, and the Y-direction deformation values of the key discrete points on the axial section S of the air bag under different internal air pressures are obtained;
(5-2) monitoring the surface strain change of the flexible buffer airbag structure under the action of different internal air pressures by using the fiber bragg grating sensor, bringing the strain measured by the fiber bragg grating sensor into a deformation calculation inversion model, and obtaining a deformation value of a key discrete point in the Y direction on the section S;
(5-3) according to an X-direction deformation change curve on the surface section S of the flexible buffer air bag under different internal air pressures, extracting a key discrete point deformation value in the curve, establishing a Y-direction deformation value calculation model at any position on the section S, and obtaining a Y-direction deformation value at any position on the section SS after the section S is subjected to expansion deformation under different internal air pressures;
finite element calculation results show that Y-direction deformation change curves of positions between adjacent wave troughs and wave peak points on a deformation trend curve on the axial section S of the surface of the flexible buffer air bag are approximately in a linear relation; assuming that the relational expression between the deformation value of any point between two adjacent wave troughs and the wave peak point and the initial y-axis coordinate corresponding to the point is as follows:
Δy＝vy+z
the Y-direction deformation value of any point between adjacent wave troughs and wave crests is the Y-direction deformation value, and the Y-direction deformation value is the initial Y-axis coordinate corresponding to any point between the wave troughs and the wave crests;
assuming adjacent valley points
Figure FDA0003554417440000052
And peak point
Figure FDA0003554417440000053
The corresponding deformation value and the initial y-axis coordinate are respectively (delta y)2n-1,y2n-1)、(Δy2n,y2n) Then, the coefficient of the deformation value calculation expression of any point between the adjacent trough point and the crest point can be calculated as follows:
Figure FDA0003554417440000054
Figure FDA0003554417440000055
according to the values of z and y and two adjacent valley points on the section S of the flexible buffer air bag
Figure FDA0003554417440000061
And peak point
Figure FDA0003554417440000062
The initial Y-axis coordinate of any point between the two points can calculate the Y-direction deformation value of any point on the expanded axial section SS of the balloon under the action of different internal air pressures;
step six: acquiring two-dimensional coordinates of any position on the section SS according to deformation information of any position in the X direction and the Y direction on the section SS, which is obtained by the expansion deformation of the section S under different internal air pressures in the fourth step and the fifth step;
assume that the initial coordinate of any point on the cross section S in the initial state is (x)0,y0) Then the coordinates of any point on the expanded section SS obtained from the section S obtained in the fourth and fifth steps are expressed as (xx, yy); wherein: xx ═ x0+Δx，yy＝y0+ Δ y will Δ x ═ wy0+h，Δy＝vy0+ z is substituted into the above formula to obtain
Figure FDA0003554417440000063
Figure FDA0003554417440000064
2. The distributed optical fiber monitoring method for the surface expansion deformation of the flexible buffer airbag according to claim 1, characterized in that: the flexible buffer air bag structure is a symmetrical similar-circular structure, so that the representative axial section expansion deformation of the air bag surface can be obtained according to the method, and the whole expansion deformation of the flexible buffer air bag structure can be approximately obtained according to the same principle of the deformation of the symmetrical structure.
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