CN110497088B - Flexible conformal antenna laser processing error control method based on curved surface mapping - Google Patents
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Abstract
The invention discloses a flexible conformal antenna laser processing error control method based on curved surface mapping, belongs to the technical field of flexible conformal antenna laser processing, and relates to a flexible conformal antenna laser processing error control method based on curved surface mapping. The method is characterized in that a transformation matrix between a measuring head-workpiece-machine tool coordinate system is established by measuring the coordinates of a clamping state curved surface. The curved surface characteristics of the flexible conformal antenna under different states are clarified through the triangular gridding processing of the curved surface measuring points and the mapping points thereof in the clamping state. And solving the mapping relation between the mesh vertex and the inner point of the clamping state curved surface and the theoretical curved surface, and establishing the mapping relation between the clamping state curved surface and the theoretical curved surface of the flexible conformal antenna. And generating an ideal processing track by the theoretical curved surface model, and solving the actual laser processing track of the flexible conformal antenna based on the mapping relation. The method can reduce the processing error caused by the deformation of the flexible conformal antenna, and has important practical application value for improving the performance of the flexible conformal antenna.
Description
Technical Field
The invention belongs to the technical field of flexible conformal antenna laser processing, and relates to a flexible conformal antenna laser processing error control method based on curved surface mapping.
Background
The flexible conformal antenna is used as an important part for transmitting and receiving electromagnetic waves in an aircraft, and is widely applied to the fields of aerospace and the like. The part can conform to the surface of the carrier, can be adjusted and adapted along with the change of the appearance of the carrier, and has better adaptability to the vibration of an aircraft caused by pneumatics and the like compared with a planar array antenna. However, in order to meet the weight reduction requirement of the aircraft, the flexible conformal antenna mostly adopts a plating type thin-wall curved surface structure, has low rigidity and high flexibility, and is easy to generate irregular deformation in a clamping state during processing, so that the deviation between an actually processed curved surface and an ideal curved surface is generated. The conventional processing method is mainly used for processing according to an ideal curved surface, so that the problems that a laser beam is out of focus, the strip line of a conformal antenna is under-ablated, the position of an antenna array is deviated, the array distribution does not conform to the original design and the like are easily caused, the precision requirement is difficult to guarantee, and the electrical performance of the conformal antenna is seriously influenced. In view of the unclear mapping relation between the clamping state curved surface and the ideal curved surface facing the laser high-precision machining, a flexible conformal antenna laser machining error control method based on curved surface mapping is urgently needed to be researched, the mapping relation between the clamping state curved surface and the theoretical curved surface is solved, and the actual laser machining track of the antenna is planned, so that the machining precision of the strip line of the flexible conformal antenna is improved.
Prior art documents "An error control adaptation to tool path adaptation control to the transformation of a thin-walled workpiece", Xiao-Jin Wan et al, International Journal of Machine Tools & Manual, 2011, 51: 221-229, which establishes a workpiece-holder-tool elastic deformation system, corrects the deviation of the position and direction of the tool relative to the workpiece in the thin-wall workpiece processing by predicting the elastic deformation of the workpiece, however, the method is mainly oriented to milling processing and is difficult to be directly applied to conformal antenna laser processing with extremely high precision requirements. Patent "a flexible circuit board processing fixing device is used in antenna plate processing" of single jinlin et al, patent publication No. CN 108601230A, this patent carries out the clamping location to the flexible antenna board through four groups of lugs and the mode of four groups of regulating plates of recess cooperation and fixed plates. However, the device is only suitable for a plane antenna plate, cannot analyze and control processing errors caused by clamping deformation in the laser processing process of the flexible antenna, and has certain limitation.
Disclosure of Invention
Aiming at the defects of the prior art, the invention discloses a flexible conformal antenna laser processing error control method based on curved surface mapping. Firstly, measuring a curved surface coordinate in a clamping state, and establishing a transformation matrix between a measuring head-workpiece-machine tool coordinate system; then triangularizing the clamped state curved surface and the theoretical curved surface mesh, and solving a mapping relation between the clamped state curved surface and the theoretical curved surface mesh vertex and a mapping relation between mesh internal points to realize mapping of the clamped state curved surface and the theoretical curved surface; and finally, according to the mapping relation, solving the actual laser processing track by the antenna ideal processing track generated by the theoretical curved surface. The method accurately describes the curved surface characteristics of the flexible conformal antenna in the clamping state, realizes the accurate solution of the strip line laser processing track of the flexible conformal antenna in the actual processing process, can effectively ensure the laser processing precision of the flexible conformal antenna, and has important practical application value for improving the performance of the flexible conformal antenna.
The invention adopts the technical scheme that the method is a flexible conformal antenna laser processing error control method based on curved surface mapping, and is characterized in that firstly, the method measures the coordinates of a clamping state curved surface and establishes a transformation matrix between a measuring head-workpiece-machine tool coordinate system; then triangularizing the clamped state curved surface and the theoretical curved surface mesh, and clarifying the curved surface characteristics of the flexible conformal antenna under different states; finally, solving a mapping relation between the clamping state curved surface and the theoretical curved surface of the flexible conformal antenna, and solving an actual laser processing track based on an antenna ideal processing track generated by the theoretical curved surface; the method comprises the following specific steps:
and (3) clamping and fixing a workpiece on the workbench, and fixing the dial indicator on one side of a laser shaft on the laser machine tool through the magnetic gauge stand to enable the axis where the measuring head of the dial indicator is located to be parallel to the laser shaft. Let the workpiece coordinate system be O1Xyz, machine coordinate system O2-x ' y ' z ', the probe coordinate system being O3-x "y" z ". In order to determine a measuring head coordinate system, the highest point of intersection of a fixture tray fixed on a workbench and the axis of the z axis of a machine tool is set as a reference point B, a dial indicator is moved to the position above the reference point by using a numerical control machine, the dial indicator is controlled to be in contact with the reference point, and the coordinate value displayed by the numerical control machine at the moment is recorded as the coordinate value of the reference point under the measuring head coordinate system. The coordinate value displayed by the numerical control machine tool when measuring a certain measuring point is (x)3,y3,z3) The number of the dial indicator is z3If the coordinate value of the point in the coordinate system of the measuring head is vi”(x3,y3,z3+z3') and the coordinate value of the measuring point in the workpiece coordinate system is recorded as vi(x1,y1,z1) The coordinate value under the machine coordinate system is vi'(x2,y2,z2)。
The coordinate transformation among the coordinate system of the measuring head, the coordinate system of the workpiece and the coordinate system of the machine tool is a combination of translation and rotation transformation of a space coordinate system. The spatial coordinate system is translated to the x-axis direction by Δ x, to the y-axis direction by Δ y, and to the z-axis direction by Δ z, so that the translation transformation matrix of the spatial coordinate system is formula (1), and the spatial coordinate system is rotated around the x-axis by θ, around the y-axis by θ, and around the z-axis by θ, so that the rotation transformation matrix is formula (2).
The machine tool coordinate system is translated by delta y from the workpiece coordinate system to the y-axis direction1Is translated in the z-axis direction by Δ z1Then rotated by theta along the z-axis1The angle is obtained, then the workpiece coordinate system O1-xyz machine coordinate system O2The transformation matrix of-x ' y ' z ' can be expressed as
The measuring head coordinate system can be translated by deltax from the machine tool coordinate system to the x-axis direction2Is translated in the y-axis direction by Δ y2Is translated in the z-axis direction by Δ z2Obtaining, then, a machine tool coordinate system O2-x ' y ' z ' direction gauge head coordinate system O3The transformation matrix of-x "y" z "can be expressed as
In summary, the transformation matrix of the workpiece coordinate system to the machine coordinate system can be expressed as
The transformation matrix from the machine coordinate system to the workpiece coordinate system can be expressed as
Machine tool coordinate system direction measuring head seatThe transformation matrix of the object system can be expressed as
The transformation matrix from the coordinate system of the measuring head to the coordinate system of the machine tool can be expressed as
The transformation matrix from the workpiece coordinate system to the stylus coordinate system can be expressed as
The transformation matrix from the coordinate system of the measuring head to the coordinate system of the workpiece can be expressed as
Represented by formula (3).
and selecting a region with a rectangular projection pattern on the clamping state curved surface, so that the region comprises processing strip lines, and uniformly distributing square gridding measuring points on the region. And (3) controlling by using a multi-axis linkage system of the numerical control machine tool, and measuring the coordinate data of the regular points on the surface of the curved surface in the clamping state by using a magnetic dial indicator. And dividing each minimum square grid unit in the measurement point grid along a diagonal line to realize the triangularization of the clamped-state curved surface grid, wherein each triangular patch in the grid comprises the serial numbers of three vertexes, and the coordinate value of the point can be searched according to the serial number value. The measured data points have unique mapping points in the theoretical surface, and the mapping points are triangulated by the same subdivision principle, so that the triangulation of the theoretical surface mesh is realized.
1) mapping of mesh vertices
Firstly, solving the mapping relation between the clamped state curved surface and the mesh vertex of the theoretical curved surface, namely solving the mapping point of the actual clamped state curved surface measurement point in the theoretical curved surface.According to the transformation matrix of the measuring head coordinate system and the workpiece coordinate system established in the step 1, the coordinate value v of the measuring point under the measuring head coordinate systemi”(x3,y3,z3+z3') to coordinate values v in the workpiece coordinate systemi(x1,y1,z1). The flexible conformal antenna is mainly a revolution surface, clamping deformation is mainly along the normal vector direction, and displacement along the y-axis direction is approximately zero. Let the measuring point vi(x1,y1,z1) The circle center of the cross section of the revolution surface is O, and the mapping point of the measuring point in the theoretical curved surface is wi(m1,n1,k1) Then point viAnd point wiThe following mapping relationship exists:
the mapping point coordinates of any measuring point in the theoretical curved surface can be obtained by calculation according to the formulas (4) to (6), and the mapping relation between the clamped curved surface and the mesh vertex in the theoretical curved surface triangular mesh is obtained.
2) Mapping of points within a mesh
And according to the triangular affine transformation theory, solving the mapping relation between the clamped state curved surface and the internal points of the theoretical curved surface triangular mesh. An affine transformation relation exists between any triangular surface patch and the mapping triangular surface patch in the flexible conformal antenna mesh curved surface, the mapping relation of any point on any triangle before and after the workpiece deformation is solved according to the invariance of the gravity center coordinate of the triangle affine transformation, and the complex three-dimensional graph mapping problem is converted into the mapping problem between two three-dimensional mesh sets.
Let the measuring point v1，v2，v3In a clamped curved surface triangular meshCoordinates of three vertexes of a triangular patch under a workpiece coordinate system, wherein a point V is delta V1v2v3One point inside, with barycentric coordinates of V (lambda)1,λ2,λ3) Then point V satisfies equation (7) and λ1+λ2+λ3＝1。
(λ1+λ2+λ3)V＝λ1v1+λ2v2+λ3v3(7)
At Δ v1v2v3For example, the formula for calculating the area of the triangle is:
points V and Δ V1v2v3Each vertex will be Δ v1v2v3Divided into Δ v1v2V，Δv2v3V，Δv1v3V, each area of
From the properties of the coordinates of the centroid of the triangle:
make triangle patch Deltav in the curved surface mesh of the clamping state1v2v3The mapping triangle in the theoretical surface is Δ w1w2w3From the affine transformation relation, Δ v can be found1v2v3Inner arbitrary point ViMapping to Δ w1w2w3Inner WiThe coordinates of the points are:
Wi＝λ1w1+λ2w3+λ3w3(10)
and 4, solving the actual laser processing track of the antenna based on the mapping relation:
and carrying out three-dimensional modeling on the theoretical curved surface, and planning a theoretical processing track according to the flexible conformal antenna processing strip line design. And calculating a theoretical curved surface triangular mesh unit where the theoretical machining cutter point is located, and determining the barycentric coordinates of the theoretical machining cutter point in the triangular mesh unit. And (3) mapping the flexible conformal antenna machining tool position point generated by the theoretical curved surface to the clamping state curved surface according to the mapping relation between the mesh top point and the internal point of the clamping state curved surface and the theoretical curved surface established in the step (3), and solving to obtain the actual machining tool position point data. And finally, converting the coordinates of the actual machining tool location point in the workpiece coordinate system into the coordinates of the tool location point in the machine tool coordinate system, and generating a machining program which can be identified by the machine tool, namely the actual laser machining track of the flexible conformal antenna strip line.
The method has the advantages that the method calculates the actual laser processing track of the antenna strip line by solving the mapping relation between the clamping state curved surface and the theoretical curved surface of the flexible conformal antenna, solves the problems of defocusing of laser beams, under ablation of the strip line of the conformal antenna and the like caused by clamping deformation in the laser processing process of the clamping state flexible conformal antenna, and can reduce the processing error caused by the deformation of the flexible conformal antenna.
Drawings
FIG. 1-flowchart of the overall process.
Fig. 2-theoretical surface plot.
Figure 3-a clamped state surface view.
FIG. 4-machining trajectory map; wherein, 1 represents a clamping state curved surface, 2 represents an actual processing track adjusted according to the clamping state curved surface, 3 represents a theoretical curved surface, and 4 represents a theoretical processing track.
FIG. 5-flexible conformal antenna surface strip ablation depth mapped without a machined trace; where 1 represents the theoretical ablation depth curve and 2 represents the actual ablation depth curve for an ideal trajectory.
FIG. 6-Flexible conformal antenna surface strip ablation depth mapped by the processing track; wherein, I represents a theoretical ablation depth curve, and II represents an actual ablation depth curve under the machining track adjusted according to the curved surface in the clamping state.
Detailed Description
The detailed description of the embodiments of the invention is provided with reference to the accompanying drawings.
The flexible conformal antenna generates irregular deformation in a clamping state, and a conventional processing method processes the antenna according to an ideal antenna line shape, so that processing errors are easy to generate. Aiming at the limitation of the prior art, the invention provides a flexible conformal antenna laser processing error control method based on curved surface mapping, and the whole process is shown in the attached figure 1.
The implementation of the present invention will be described in detail by taking as an example the flexible conformal antenna processing with the specification size of 98 × 1 × 200 (outer diameter × wall thickness × length, unit mm) and the copper plating layer.
Firstly, determining a measuring head coordinate system and determining a transformation relation between the measuring head-workpiece-machine tool coordinate system in the step 1. And uniformly distributing square gridding measuring points on the curved surface, controlling by using a multi-axis linkage system of the numerical control machine tool, and measuring coordinate data of regular points on the surface of the flexible conformal antenna in a clamping state under a measuring head coordinate system by using a magnetic dial indicator.
And then, under a workpiece coordinate system, sequencing the measuring points and then carrying out triangular gridding treatment to construct a triangular grid with a certain topological relation. And 3, calculating mapping point coordinates of the measuring points in the theoretical model according to the formulas (4) to (6), establishing a mapping relation between the clamped state curved surface and the vertex of the theoretical curved surface triangular mesh, and establishing a mapping relation between the clamped state curved surface and the internal points of the theoretical curved surface triangular mesh according to the formulas (8) to (10). And determining the triangular mesh mapping relation between the clamping state curved surface and the theoretical curved surface according to the mapping relation between the clamping state curved surface and the theoretical curved surface mesh vertex and the mapping relation between the mesh internal points.
And finally, performing three-dimensional modeling on the theoretical flexible conformal antenna model by step 4, and planning a theoretical processing track according to the design of the processing strip line. And converting the theoretical machining tool location point coordinate value in the machine tool coordinate system obtained by post-processing into a coordinate value in the workpiece coordinate system. And under a workpiece coordinate system, calculating the coordinate value of the actual machining tool location point of the clamping state curved surface according to the grid mapping model between the clamping state curved surface and the theoretical curved surface. The theoretical curved surface and the clamping state curved surface are respectively shown in the attached drawings 2 and 3; the processing track map is shown in fig. 4, in which 1 is a clamping state curved surface, 2 is an actual processing track adjusted according to the clamping state curved surface, 3 is a theoretical curved surface, and 4 is a theoretical processing track. And finally, converting the tool location point data into a processing program which can be identified by a machine tool, and realizing the laser precision processing of the antenna strip line.
And (3) carrying out a flexible conformal antenna strip line processing experiment, respectively processing by using a processing track generated by a theoretical curved surface and a processing track adjusted according to a clamping state curved surface, and measuring the ablation depth change of the strip line pattern by using a three-dimensional appearance to judge the processing precision. In the processing, a laser with a wavelength of 532nm is used, the spot radius is 40 μm, the feed speed is 800mm/min, the laser current is 34A, the pulse repetition frequency is 30kHz, and the theoretical depth of laser ablation of the copper layer is 21 μm under the parameters.
The experimental result shows that the processing track generated by the theoretical model is processed, the linear pattern is under-ablated, the average value of the ablation depth is 7.003 μm and is far less than the theoretical ablation depth 21 μm, as shown in figure 5, 1 is a theoretical ablation depth curve, and 2 is an actual ablation depth curve under an ideal track; the processing track adjusted according to the clamping state curved surface is used for processing, the linear ablation depth of the flexible conformal antenna fluctuates within the theoretical ablation depth range, the average value of the ablation depth is 20.905 mu m, as shown in figure 6, I is a theoretical ablation depth curve, and II is an actual ablation depth curve under the processing track adjusted according to the clamping state curved surface.
The experimental result shows that the flexible conformal antenna laser processing error control method based on the curved surface mapping achieves the purpose of improving the laser processing precision of the strip line of the flexible conformal antenna, and has guiding significance for the laser processing of the flexible conformal antenna.
Claims (1)
1. A flexible conformal antenna laser processing error control method based on curved surface mapping is characterized in that firstly, coordinates of a clamping state curved surface are measured, and a transformation matrix between a measuring head-workpiece-machine tool coordinate system is established; then triangularizing the clamped state curved surface and the theoretical curved surface mesh, and clarifying the curved surface characteristics of the flexible conformal antenna under different states; finally, solving a mapping relation between the clamping state curved surface and the theoretical curved surface of the flexible conformal antenna, and solving an actual laser processing track based on an antenna ideal processing track generated by the theoretical curved surface; the method comprises the following specific steps:
step 1, establishing a transformation matrix among a measuring head-workpiece-machine tool coordinate system:
clamping a workpiece and then fixing the workpiece on a workbench, and fixing a dial indicator on one side of a laser shaft on a laser machine tool through a magnetic gauge stand to enable the axis of a measuring head of the dial indicator to be parallel to the laser shaft; let the workpiece coordinate system be O1Xyz, machine coordinate system O2-x ' y ' z ', the probe coordinate system being O3-x "y" z "; in order to determine a measuring head coordinate system, setting the highest point of intersection of a fixture tray fixed on a workbench and the axis of the z axis of a machine tool as a reference point B, moving a dial indicator to the upper part of the reference point by using a numerical control machine, controlling the dial indicator to be in contact with the reference point, and recording the coordinate value displayed by the numerical control machine at the moment as the coordinate value of the reference point under the measuring head coordinate system; the coordinate value displayed by the numerical control machine tool when measuring a certain measuring point is (x)3,y3,z3) The number of the dial indicator is z3If the coordinate value of the point in the coordinate system of the measuring head is vi”(x3,y3,z3+z3') and the coordinate value of the measuring point in the workpiece coordinate system is recorded as vi(x1,y1,z1) The coordinate value under the machine coordinate system is vi'(x2,y2,z2)；
The coordinate transformation among the measuring head coordinate system, the workpiece coordinate system and the machine tool coordinate system is a combination of translation and rotation transformation of a space coordinate system; translating the space coordinate system by delta x in the direction of an x axis, by delta y in the direction of a y axis and by delta z in the direction of a z axis, wherein the translation transformation matrix of the space coordinate system is expressed by formula (1), and rotating the space coordinate system by theta angle around the x axis, theta angle around the y axis and theta angle around the z axis respectively, and the rotation transformation matrix is expressed by formula (2);
the machine tool coordinate system can be translated by delta y towards the y-axis direction from the workpiece coordinate system1Is translated in the z-axis direction by Δ z1Then rotated by theta along the z-axis1The angle is obtained, then the workpiece coordinate system O1-xyz machine coordinate system O2The transformation matrix of-x ' y ' z ' is represented as
The coordinate system of the measuring head is translated to the direction of the x axis by delta x from the coordinate system of the machine tool2Is translated in the y-axis direction by Δ y2Is translated in the z-axis direction by Δ z2Obtaining, then, a machine tool coordinate system O2-x ' y ' z ' direction gauge head coordinate system O3The transformation matrix of-x "y" z "is represented as
In summary, the transformation matrix of the workpiece coordinate system to the machine coordinate system can be expressed as
The transformation matrix from the machine coordinate system to the workpiece coordinate system can be expressed as
The transformation matrix from the machine coordinate system to the measuring head coordinate system can be expressed as
The transformation matrix from the coordinate system of the measuring head to the coordinate system of the machine tool can be expressed as
The transformation matrix from the workpiece coordinate system to the stylus coordinate system can be expressed as
The transformation matrix from the coordinate system of the measuring head to the coordinate system of the workpiece can be expressed as
Represented by formula (3);
step 2, triangularization of the clamped state curved surface and the theoretical curved surface mesh:
selecting a region with a rectangular projection graph on the clamping state curved surface, enabling the region to contain a processing strip line, and uniformly distributing square gridding measuring points on the region; the multi-axis linkage system of the numerical control machine tool is used for controlling, and a magnetic dial gauge is used for measuring coordinate data of regular points on the surface of the curved surface in the clamping state; each minimum square grid unit is subdivided along a diagonal line in a measurement point grid to realize the triangularization of a clamped-state curved surface grid, each triangular patch in the grid comprises the serial numbers of three vertexes, and the coordinate value of the point can be searched according to the serial number value; measuring data points with unique mapping points in a theoretical surface, and performing triangulation on the mapping points by using the same triangulation principle to realize triangulation of the theoretical surface mesh;
step 3, triangular mesh mapping between the clamping state curved surface and the theoretical curved surface:
1) mapping of mesh vertices
Firstly, solving a mapping relation between a clamped state curved surface and a theoretical curved surface mesh vertex, namely solving a mapping point of an actual clamped state curved surface measurement point in a theoretical curved surface; according to the transformation matrix of the measuring head coordinate system and the workpiece coordinate system established in the step 1, the coordinate value v of the measuring point under the measuring head coordinate systemi”(x3,y3,z3+z3') to coordinate values v in the workpiece coordinate systemi(x1,y1,z1) (ii) a The processing curved surface of the flexible conformal antenna is mostly a revolution surface, the clamping deformation is mainly along the normal vector direction, and the displacement along the y-axis direction is approximately zero; let the measuring point vi(x1,y1,z1) The circle center of the cross section of the revolution surface is O, and the mapping point of the measuring point in the theoretical curved surface is wi(m1,n1,k1) Then point viAnd point wiThe following mapping relationship exists:
the mapping point coordinates of any measuring point in the theoretical curved surface can be obtained through calculation according to the formulas (4) to (6), and the mapping relation between the clamped state curved surface and the mesh vertex in the theoretical curved surface triangular mesh is obtained;
2) mapping of points within a mesh
According to the affine transformation theory of the triangle, solving the mapping relation between the clamped state curved surface and the internal points of the theoretical curved surface triangular mesh; an affine transformation relation exists between any triangular surface patch and a mapping triangular surface patch of the triangular surface patch in the flexible conformal antenna mesh curved surface, the mapping relation of any point on any triangle before and after the deformation of a workpiece is solved according to the invariance of the gravity center coordinate of the triangular affine transformation, and the complex three-dimensional graph mapping problem is converted into the mapping problem between two three-dimensional mesh sets;
let the measuring point v1，v2，v3Is the coordinate of three vertexes of a triangular patch in a curved surface triangular mesh in a clamping state under a workpiece coordinate system, and the point V is delta V1v2v3One point inside, with barycentric coordinates of V (lambda)1,λ2,λ3) Then point V satisfies equation (7) and λ1+λ2+λ3＝1；
(λ1+λ2+λ3)V＝λ1v1+λ2v2+λ3v3(7)
At Δ v1v2v3For example, the formula for calculating the area of the triangle is:
points V and Δ V1v2v3Each vertex will be Δ v1v2v3Divided into Δ v1v2V，Δv2v3V，Δv1v3V, each area of
From the properties of the coordinates of the centroid of the triangle:
make triangle patch Deltav in the curved surface mesh of the clamping state1v2v3The mapping triangle in the theoretical surface is Δ w1w2w3From the affine transformation relation, Δ v can be found1v2v3Inner arbitrary point ViMapping to Δ w1w2w3Inner WiThe coordinates of the points are:
Wi＝λ1w1+λ2w3+λ3w3(10)
and 4, solving the actual laser processing track of the antenna based on the mapping relation:
performing three-dimensional modeling on a theoretical curved surface, and planning a theoretical processing track according to the flexible conformal antenna processing strip line design; calculating a theoretical curved surface triangular mesh unit where the theoretical machining cutter point is located, and determining the gravity center coordinate of the theoretical machining cutter point in the triangular mesh unit; mapping the flexible conformal antenna machining tool location point generated by the theoretical curved surface to the clamping state curved surface according to the mapping relation between the grid top points and the internal points of the clamping state curved surface and the theoretical curved surface established in the step 3, and solving to obtain actual machining tool location point data; and finally, converting the coordinates of the actual machining tool location point in the workpiece coordinate system into the coordinates of the tool location point in the machine tool coordinate system, and generating a machining program which can be identified by the machine tool, namely the actual laser machining track of the flexible conformal antenna strip line.
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| JP4714444B2 (en) * | 2004-08-31 | 2011-06-29 | 国立大学法人北海道大学 | Tetrahedral mesh generation method and program |
| JP5090121B2 (en) * | 2007-10-01 | 2012-12-05 | オリンパス株式会社 | Adjustment device, laser processing device, adjustment method, and adjustment program |
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| EP3255611A1 (en) * | 2016-06-08 | 2017-12-13 | Technische Universität München | Method and system for generating a mesh |
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