CN111967166B - Core lattice deformation evaluation method in honeycomb core bending process - Google Patents

Core lattice deformation evaluation method in honeycomb core bending process Download PDF

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CN111967166B
CN111967166B CN202010891274.XA CN202010891274A CN111967166B CN 111967166 B CN111967166 B CN 111967166B CN 202010891274 A CN202010891274 A CN 202010891274A CN 111967166 B CN111967166 B CN 111967166B
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lattice
core lattice
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CN111967166A (en
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赵志勇
李玉军
刘闯
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Northwestern Polytechnical University
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Abstract

The invention provides a core lattice deformation evaluation method in a honeycomb core bending process for a sandwich structure, which comprises the steps of extracting the core lattice outline on the surface of a deformed honeycomb core, identifying the vertex of the core lattice, assuming each core lattice as an m-edge unit consisting of m end points, and determining the displacement of each node by comparing the positions of the nodes before and after the deformation of the m-edge unit; constructing an m-edge unit shape function, and solving a coefficient corresponding to the unit shape function by node displacement so as to determine a deformation gradient corresponding to a unit; and calculating the strain tensor corresponding to the unit, and comprehensively evaluating the deformation of the core lattice by using the main strain and the unit area corresponding to the unit, thereby realizing the judgment of the integrity of the core lattice in the manufacturing process of the sandwich structure with the appearance of the complex free-form surface.

Description

Core lattice deformation evaluation method in honeycomb core bending process
Technical Field
The invention relates to a core lattice deformation evaluation method in a honeycomb core bending process, and belongs to the field of composite material sandwich structure manufacturing.
Background
The honeycomb sandwich structure consists of two high-strength upper and lower panels and a honeycomb core sandwich layer which is thick and light in the middle, has the excellent characteristics of light weight, high specific strength, high specific stiffness, high energy absorption efficiency and the like, and is widely applied to the fields of aerospace and the like, such as wing leading edge U-shaped pieces, flaps, ailerons, spoiler rudders, elevators, vertical and horizontal tail wall plates, engine nacelles, fairings and other structures.
Because the honeycomb is simple to manufacture, has light weight and simultaneously has good toughness and impact resistance, the application ratio of the honeycomb in an aviation sandwich structure is the largest. However, most composite material members adopting the honeycomb sandwich layer have complex free-form surface shapes, and in the process of attaching the honeycomb core to the molded surface, the core lattices generate serious stretching and extrusion deformation due to bending, so that the core lattices collapse, and the mechanical properties of the honeycomb core are seriously influenced. How to rapidly and accurately carry out quantitative evaluation on the deformation degree of the bent honeycomb core grids is a premise for ensuring the integrity of the honeycomb core grids and the excellent mechanical property of the sandwich structure.
Disclosure of Invention
In order to solve the problems in the prior art and realize the judgment of the integrity of a core lattice in the manufacturing process of a sandwich structure with a complex free-form surface appearance, the invention provides a core lattice deformation evaluation method in the bending process of a honeycomb core, which has the following basic principle: extracting the core grid outline of the non-mold-sticking surface of the bent honeycomb core test piece to obtain a deformed two-dimensional outline drawing of the honeycomb core grid, traversing the outline of a single core grid, extracting m end point coordinates of the core grid, comparing the positions of the end points before and after the deformation of the core grid, and calculating the displacement corresponding to each end point of the core grid; constructing a plane m-edge unit by using m end points of the core grid and constructing a quadratic polynomial function for describing a displacement field of the m-edge unit; and calculating a deformation gradient according to the unit displacement field and the coordinate relation of the nodes before and after unit deformation to obtain a strain tensor corresponding to the unit, and comprehensively evaluating the core lattice degeneration by using the main strain and the unit area corresponding to the unit.
The technical scheme of the invention is as follows:
the method for evaluating the deformation of the core lattice in the bending process of the honeycomb core comprises the following steps:
step 1: extracting the outline of the bent honeycomb core lattice to obtain a two-dimensional outline drawing after the core lattice is deformed; processing the two-dimensional profile graph after the core lattice deformation to extract the boundary line l of the core lattice profileiI is 1,2,3, …, n, n is the number of core grids;
run through core contour liObtaining m end points of the core grid with m boundary lines intersected in pairs, extracting the corresponding coordinates (x) of each end point under the preset global Cartesian coordinate systemi,j,yi,j)，j＝1,2,3,…,m；
Setting the honeycomb core lattice as standard regular m-shape before deformation, establishing local Cartesian coordinate system with the end point of the core lattice labeled as 1 as the original point, and setting the end point coordinate of the core lattice before deformation as (X) in the local coordinate systemi,j,Yi,j) J is 1,2,3, …, m, and the coordinate of the endpoint after deformation is (x'i,j,y′i,j) By coordinate transformation
Figure BDA0002657079660000021
Obtaining;
calculating each point coordinate of the core grid before and after deformation according to the local coordinate systemRelative displacement of each end point
Figure BDA0002657079660000022
Wherein u isi,jIs the relative displacement of the ith core grid end point j in the x-axis direction of the local coordinate system, vi,jThe relative displacement of the endpoint j in the ith core grid in the y-axis direction is taken as the relative displacement value of the endpoint as the origin point, and the relative displacement value is 0;
step 2: by using a catalyst comprising [ 1X Y X2 XY]Quadratic incomplete polynomial representation of the term core lattice plane m-edge displacement field [ u v]＝C[a b]Wherein u and v are relative displacement fields of the core lattice in x and y directions respectively, a and b are quadratic polynomial coefficient matrixes corresponding to the displacement fields in x and y directions respectively, and C is a core lattice endpoint coordinate matrix:
Figure BDA0002657079660000023
respectively obtaining a quadratic polynomial coefficient matrix a which corresponds to the displacement fields in the x direction and the y direction-1u，b＝C-1v；
And step 3: for a certain core lattice of the honeycomb core, the coordinates of each deformed position
Figure BDA0002657079660000024
Is coordinate before deformation
Figure BDA0002657079660000031
The coordinate relationship of (a) X ═ X + D, where
Figure BDA0002657079660000032
According to
Figure BDA0002657079660000033
Obtaining a deformation gradient F;
further obtaining values of a Green strain tensor E in a bending curvature direction and a vertical bending curvature direction according to the deformation gradient F, and obtaining a third invariant I representing unit area change in the Cauchy-Green strain tensor3To carry out comprehensive evaluation on the core lattice variant; wherein Green strain tensor
Figure BDA0002657079660000034
I is unit tensor, C ═ FTF is Cauchy-Green strain tensor, I3＝det(C)。
Further, the process of processing the two-dimensional profile map after the core lattice is deformed in the step 1 is as follows: denoising, enhancing and binarization processing.
Further, the m end points of the core grid in the step 1 are ordered according to a certain time order.
Advantageous effects
According to the core lattice deformation evaluation method in the bending process of the honeycomb core, the core lattice outline on the surface of the deformed honeycomb core is extracted, the core lattice vertex is identified, each core lattice is assumed to be an m-shaped unit consisting of m end points, and the displacement of each node is determined by comparing the positions of the nodes before and after the deformation of the m-shaped unit; constructing an m-edge unit shape function, and solving a coefficient corresponding to the unit shape function by node displacement so as to determine a deformation gradient corresponding to a unit; calculating the strain tensor corresponding to the unit, and comprehensively evaluating the deformation of the core lattice by using the main strain corresponding to the unit and the unit area; the method can quickly and accurately carry out quantitative evaluation on the deformation degree of the bent honeycomb core grids, and provides a premise for ensuring the integrity of the honeycomb core grids and the excellent mechanical property of the sandwich structure.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
figure 1 honeycomb core test piece after bending
FIG. 2 core lattice surface shape after extraction
FIG. 3 shows the extraction process of the end points of the deformed core grids
FIG. 4 is a schematic view of a core grid under a local coordinate system
FIG. 5 is a schematic diagram of core grids before and after deformation in a relative coordinate system
Figure 6 schematic diagram of honeycomb core cell area change after deformation
FIG. 7 is a statistical graph of cell strain of a deformed honeycomb core
Detailed Description
The following detailed description of embodiments of the invention is intended to be illustrative, and not to be construed as limiting the invention.
In this embodiment, a specific process of a core lattice deformation evaluation method in a honeycomb core bending process is described by taking a profile of a core lattice shape of a surface after bending a hexagonal honeycomb core (where m is 6, and therefore, the number of boundaries and end points of the core lattice is 6) shown in fig. 2 as an example, and referring to the accompanying drawings.
Step 1: carrying out mathematical morphology processing on the core lattice shape profile graph of the bent honeycomb core to realize the denoising and enhancement of an image, and converting the image into a binary image with only 0/1 pixel values; extracting the core grid contour line according to the adjacency relation of the honeycomb core grid boundary pixels to obtain a core grid contour line liAnd i is 1,2,3, …, and n is the number of the core grids.
Run through core contour liAll pixel points obtain coordinates (x) corresponding to 6 end points of the core grid according to the geometric relationship that the end points of the core grid are intersected pairwise by the boundary lines of the 6 edges of the core gridi,j,yi,j) (j ═ 1,2,3, …,6), the local honeycomb core grid end point coordinate extraction flow is shown in fig. 3.
With the lowest end of the core grid (y being the smallest value, i.e. min (y)i,j) Corresponding end points) as a first point and ordering the 6 end points of the core grid in a clockwise order, and establishing a local cartesian coordinate system o 'x' y 'with the first point as an origin, as shown in fig. 4, under which global coordinates (x') corresponding to the 6 end points of the core grid are seti,j,yi,j) Push button
Figure BDA0002657079660000041
Carrying out coordinate transformation to obtain local coordinates (x ') corresponding to 6 end points in the local coordinate system'i,j,y′i,j) (j ═ 1,2,3, …,6), where the local coordinate of endpoint 1 is(0,0)。
Assuming that the honeycomb core lattice before deformation is a standard regular hexagon, comparing the shapes of the core lattice before and after deformation (the shape of the core lattice before deformation is 123456, and the shape of the core lattice after deformation is 1 '2' 3 '4' 5 '6') under the local coordinate system, as shown in FIG. 5, the local coordinate of the endpoint before deformation of the core lattice is (X is)i,j,Yi,j) (j ═ 1,2,3, …, 6). According to the coordinates of the front and rear end points of the deformed core grids in the local coordinate system, the corresponding relative displacement of each end point of the deformed core grids is calculated
Figure BDA0002657079660000051
(Zhou)i,jIs the relative displacement of the ith core grid end point j in the x-axis direction of the local coordinate system, vi,jThe relative displacement of the endpoint j in the ith core grid in the y-axis direction is taken as the relative displacement value of the endpoint as the origin point, and the relative displacement value is 0; ) Wherein
Figure BDA0002657079660000052
Step 2: constructing a planar hexagonal unit by taking 6 end points of the honeycomb core grids as nodes, representing the deformation of the core grids by the deformation of the constructed planar hexagonal unit, wherein the displacement of the 6 nodes of the deformed planar hexagonal unit is the displacement corresponding to the 6 end points of the core grids in the step 1
Figure BDA0002657079660000053
Where the displacement value of node 1 is constant at 0.
By using a catalyst comprising [ 1X Y X2 XY]Quadratic incomplete polynomial representation of terms planar hexagonal displacement field [ u v]＝C[a b]U and v are relative displacement fields of the core grids in the x direction and the y direction respectively, a and b are quadratic polynomial coefficient matrixes corresponding to the displacement fields in the x direction and the y direction respectively, C is a core grid end point coordinate matrix, and the coefficient matrixes are solved by core grid unit end point displacement and end point coordinates, so that the displacement fields of any position of the planar hexagonal unit correspond to the position coordinates one by one.
The solving process of the x and y direction displacement field coefficient matrix is as follows: displacement u of j-th end point of i-th core lattice unit in x and y directionsi,j、vi,jWith the deformed front end pointLabel (X)i,j,Yi,j) The relationship is
Figure BDA0002657079660000054
The displacement fields in the x and y directions of the whole cell are respectively
Figure BDA0002657079660000055
While
Figure BDA0002657079660000061
Respectively obtaining a quadratic polynomial coefficient matrix a which corresponds to the displacement fields in the x direction and the y direction-1u，b＝C-1v。
And step 3: for a certain core lattice of the honeycomb core, the coordinates of each position of the deformed core lattice
Figure BDA0002657079660000062
Can be regarded as coordinates before deformation
Figure BDA0002657079660000063
The coordinate relationship of (a) X ═ X + D, where
Figure BDA0002657079660000064
A deformation gradient F is defined which is,
Figure BDA0002657079660000065
(the component form is:
Figure BDA0002657079660000066
the method is used for describing deformation and motion of the adjacent domain of the unit particle X. The deformation gradient of any position of the ith core grid unit is formed by the position coordinate before deformation of the position
Figure BDA0002657079660000067
And calculating displacement fields of the core grid cells in the x and y directionsObtaining:
Figure BDA0002657079660000068
as the deformation gradient not only contains the deformation information of the object, but also contains the rigid body motion of the object, the Green strain tensor E is adopted to describe the unit deformation,
Figure BDA0002657079660000069
FTfor transposing the deformation gradient F, C ═ FTF is Cauchy-Green strain tensor, and I is unit tensor. Thus, the third invariant I of the Cauchy-Green strain tensor of the planar cell may be used3(I3Det (c) characterisation of cell area change) and Green strain tensor E strain in the characteristic direction of honeycomb core L, W (as shown in fig. 4)
Figure BDA00026570796600000610
(pL、pWUnit vectors of corresponding directions in an o ' x ' y ' coordinate system for characteristic directions of the honeycomb core L, W) were comprehensively evaluated for core cell degeneration.
The calculation result of the area change of the core lattice of the bent honeycomb core test piece is shown in fig. 6, and the calculation result of the strain of the core lattice in two characteristic directions (in this embodiment, an o ' x ' y ' coordinate system is established in the characteristic direction of the core lattice L, W, and therefore, the two characteristic directions are the directions of coordinates x ' y ') is shown in fig. 7.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (3)

1. A core lattice deformation evaluation method in a honeycomb core bending process is characterized by comprising the following steps:
step 1: extracting the outline of the core grid of the bent honeycomb core to obtain the coreTwo-dimensional contour map after lattice deformation; processing the two-dimensional profile graph after the core lattice deformation to extract the boundary line l of the core lattice profileiI is 1,2,3, …, n, n is the number of core grids;
run through core grid outline liObtaining m end points of the core grid with m boundary lines intersected in pairs, extracting the corresponding coordinates (x) of each end point under the preset global Cartesian coordinate systemi,j,yi,j)，j＝1,2,3,…,m；
Setting the standard regular m-shape before deformation of the honeycomb core lattice, establishing a local Cartesian coordinate system with the end point of the core lattice marked as 1 as the origin, and setting the end point coordinate of the core lattice before deformation as (X) under the local coordinate systemi,j,Yi,j) J is 1,2,3, …, m, and the coordinate of the endpoint after deformation is (x'i,j,y′i,j) By coordinate transformation
Figure FDA0003513281700000011
Obtaining;
calculating the relative displacement corresponding to each end point according to the coordinates of the end points of the core grids before and after deformation under the local coordinate system
Figure FDA0003513281700000012
Wherein u isi,jIs the relative displacement of the ith core grid end point j in the x-axis direction of the local coordinate system, vi,jThe relative displacement of the endpoint j in the ith core grid in the y-axis direction is taken as the relative displacement value of the endpoint as the origin point, and the relative displacement value is 0;
step 2: by using a catalyst comprising [ 1X Y X2 XY]Quadratic incomplete polynomial representation of the term core lattice plane m-edge displacement field [ u v]＝C[a b]Wherein u and v are relative displacement fields of the core lattice in x and y directions respectively, a and b are quadratic polynomial coefficient matrixes corresponding to the displacement fields in x and y directions respectively, and C is a core lattice endpoint coordinate matrix:
Figure FDA0003513281700000013
Figure FDA0003513281700000014
obtaining a matrix of coefficients of a quadratic polynomial a ═ C corresponding to the displacement fields in the x and y directions, respectively-1u，b＝C-1v；
And step 3: for a certain core lattice of the honeycomb core, the coordinates of each deformed position
Figure FDA0003513281700000021
Is coordinate before deformation
Figure FDA0003513281700000022
The coordinate relationship of (a) X ═ X + D, where
Figure FDA0003513281700000023
According to
Figure FDA0003513281700000024
Obtaining a deformation gradient F;
obtaining values of a Green strain tensor E in a bending curvature direction and a vertical bending curvature direction according to the deformation gradient F, and obtaining a third invariant I representing unit area change in the Cauchy-Green strain tensor3To carry out comprehensive evaluation on the core lattice variant; wherein Green strain tensor
Figure FDA0003513281700000025
I is unit tensor, CG ═ FTF is Cauchy-Green strain tensor, I3＝det(CG)。
2. The method for evaluating deformation of a core lattice during bending of a honeycomb core according to claim 1, comprising the steps of: the process of processing the two-dimensional profile map after the core grid is deformed in the step 1 is as follows: denoising, enhancing and binarization processing.
3. The method for evaluating deformation of a core lattice during bending of a honeycomb core according to claim 1, comprising the steps of: in the step 1, the m end points of the core grids are sequenced according to a certain time sequence.
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