CN115688462A - Planning and designing method for forming trajectory of wire laying of orthogonal frame of normal Gaussian curved surface - Google Patents
Planning and designing method for forming trajectory of wire laying of orthogonal frame of normal Gaussian curved surface Download PDFInfo
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Abstract
The invention provides a planning and designing method for a silk laying forming track of a normal Gaussian curved surface orthogonal frame, which is used for automatically laying a silk on a composite material. The method comprises the following steps: reading a mould data model for laying, and determining parameter information of the mould surface and the laying layer; selecting a fiber laying reference coordinate axis and an initial boundary position; generating a laying track with a fixed angle of each layer of laying based on a differential geometric curved surface orthogonal frame principle; determining a fiber variable-width laying range with good track laying performance according to the curvature distribution of the surface of the mold; and generating a robot control language for the laying track, and operating the robot to carry out laying work. The method can obtain the optimal track optimization scheme before production and manufacturing, avoids laying and processing problems such as warping deformation and the like as much as possible, ensures the accuracy of automatic fiber laying, can convert the track into a robot code to command processing operation, and meets the requirements of carrying out track planning and design on fiber tows of various specifications and laying heads of different specifications.
Description
Technical Field
The invention relates to the technical field of automatic filament laying of composite materials, relates to path planning in an automatic filament laying forming process, and particularly relates to a path planning and designing method for a normal Gaussian curved surface orthogonal frame track of a carbon fiber composite material.
Background
The automatic filament laying technology is a molding manufacturing method proposed according to the manufacturing requirements of the United states solid rocket engine and is widely commercialized. The fiber laying technology adopts a plurality of fiber bundles with smaller width, and can complete the manufacture of the composite material structural member with more complex curved surfaces. The technology provides technical support for low-cost and rapid manufacturing of a high-performance composite material light structure, so that a complex light structure is manufactured, the structure of the light structure is expanded, and the application range of the composite material light structure is further expanded.
In the automatic silk laying process, according to the laying material, the laying path and the direction designed by a core mold, a plurality of pre-impregnated silks are collected into silk ribbons by a compression roller and laid on the surface of the core mold, the pre-impregnated silk ribbons are heated and softened in the laying process and compacted and shaped, and the whole process is controlled and coordinated by a computer. The automatic fiber laying technology can lay both expandable curved surfaces and revolving curved surfaces, can also lay complex double-curvature components, has the functions of cutting tows and increasing the tows when laying layers, and can meet the requirements of cutting the laying layers to adapt to local thickening, descending of the laying layers and opening laying layers. The laying planning of the automatic silk laying technology is combined with a silk laying path planning design scheme, and the path planning is to design a track algorithm for controlling the trend of a silk laying head in the processing process. The fiber laying path of the whole component is planned and designed according to the geometric shape, the stress condition, the strength requirement and the like of the curved surface component during the generation of the fiber laying path. Generally, a path design is laid first, referred to as the initial path, also referred to as the fiducial path or reference path, and then the remaining paths are densified with reference thereto to form a ply.
At present, the automatic fiber laying path planning algorithm is mostly used for approximately solving specific structures such as a revolving body and the like or a free-form surface is subdivided into a plurality of planes. The wire laying path planning algorithm of the revolving body is influenced by the surface complex geometric characteristics of an actual component mould and is difficult to apply to actual engineering. By adopting an algorithm for solving the plane approximate curved surface, the accumulation of a plurality of plane errors in the process of the plane approximate curved surface easily causes the condition of laying quality reduction or product failure in the latter half of the fiber laying path. In order to counteract the problem of curved surface errors, the existing laying scheme usually adopts the laying along the zero-curvature geodesic direction, and the zero-curvature direction of the curved surface is often inconsistent with the laying process design direction, so that the laying design direction is difficult to realize laying processing or more gaps exist in the laying processing process, and the product performance cannot meet the design requirement. Therefore, a design scheme capable of popularizing the ply and a track planning technology for robot placeability processing are needed.
Disclosure of Invention
In order to solve the problems, the invention provides a planning and designing method for a wire laying forming track of a normal Gaussian curved surface orthogonal frame, and develops a planning and designing software for a curved surface track of a wire laying robot based on the method. The method of the invention can realize the track planning scheme and code generation of the free-form surface of the current digital model.
The invention discloses a planning and designing method for a wire laying forming track of a normal Gaussian curved surface orthogonal frame, which comprises the following steps of:
s1, reading a data model of a mould actually used for laying, and determining parameter information of the surface of the laying mould and the laying layer;
determining parameter information of the composite material layering according to the designed layering scheme, wherein the parameter information comprises layering design sequence and fixed angle information of each layer of layering;
s2, selecting a fiber laying reference coordinate axis and an initial boundary position;
determining a curved surface boundary of an actual laying area according to the surface of a mold, and randomly selecting a point on the boundary as a starting point of an initial laying path;
s3, generating a laying track of the layer of the laying layer based on a differential geometric curved surface orthogonal frame principle;
firstly, a normal vector of a curved surface based on a starting point and a direction vector r selected by a ply angle v Establishing an orthogonal curved surface frame of the free curved surface, and setting the normal vector and the direction vector r of the curved surface of the initial point v Form aThe section of the curve is taken as an initial track; secondly, taking the initial track as a reference, moving the width of the filament bundle to lay the next track in parallel until the whole curved surface is fully paved;
s4, determining a fiber variable-width laying range with good track laying performance according to the curvature distribution condition of the surface of the mold;
a mathematical model between the trajectory radius of curvature R and the fiber tow width W is established as follows:
wherein k is g K is gaussian curvature for geodesic curvature;
calculating the curvature radius of the laying track at different curved surface positions on the surface of the mould, determining the limitation of the width W of the fiber tows based on the mathematical model, and performing the area division of widening laying and the width selection of the fiber tows;
and S5, generating a robot control language for the laying track, and using the robot control language to operate and control the robot to carry out laying work.
And (4) generating laying track and fiber prepreg tow material data of each layer according to the steps 2-4, correspondingly generating robot control language, and operating and controlling the robot to carry out laying work.
Compared with the prior art, the method has the advantages and positive effects that:
(1) The method generates the laying track of the laying layer through the differential geometric expression of the free-form surface, breaks through the problem that the traditional rotator wire laying path planning is limited by shape, and can realize the wire laying path planning of various curved surface structures.
(2) The method of the invention is based on the curved surface differential geometry principle, realizes the problem of obtaining the track on the free curved surface, has arbitrariness in the setting of the starting point, and effectively improves the efficiency and the convenience of track planning.
(3) The method correspondingly realizes the curved surface track planning design software of the fiber laying robot, can identify various actually used fiber laying head equipment parameters and fiber material attribute data based on the adopted fiber laying machine equipment and the parameter data of the laid fiber bundles, can be suitable for most industrial scenes to be used in actual laying work, and effectively improves the applicability.
(4) The method of the invention correspondingly realizes the wire-laying robot curved surface track planning and designing software, combines the computer language of the track planning and designing program with the robot track mechanical language data, can realize the basic wire-laying track planning and designing, and is easy to further upgrade and program optimization.
Drawings
FIG. 1 is a schematic flow chart of a planning and designing method for a wire laying forming track of a normal Gaussian curved surface orthogonal frame according to the present invention;
FIG. 2 is a diagram illustrating an example of a digital geometric model established for an placement mold according to an embodiment of the present invention;
FIG. 3 is a schematic view of an operation interface of the trajectory planning design software of the present invention;
FIG. 4 is a schematic diagram of the principle of the wire-laying reference trajectory solution of the present invention;
FIG. 5 is a schematic diagram of the present invention for densifying and laying an entire curved track;
FIG. 6 is a schematic diagram illustrating the principle of the present invention for verifying the spreadability of a laydown track;
FIG. 7 is a schematic diagram of the design principle of variable-bandwidth laying of the laying wire of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following drawings and examples, and the following embodiments of the surface model are only used for illustrating the process of the present invention and are not intended to limit the scope of the present invention.
According to the planning and design method for the normal Gaussian curved surface orthogonal frame laying wire forming track of the carbon fiber composite material, provided by the invention, the basic parameter information of laying layer design is identified and analyzed according to a mould digital model actually applied to the laying process, the laying track of each layer of fixed-angle laying layers is generated by using the curved surface orthogonal frame principle, and in combination with the laying analysis principle, the optimal optimization scheme can be obtained before production and manufacturing, so that the laying processing problems such as warping deformation and the like are avoided as far as possible, and the track can be converted into a robot code to command the processing operation. The implementation of the present invention is illustrated in five steps as shown in fig. 1.
S1: and reading a data model of the mould actually used for laying, and determining the parameter information of the surface of the laying mould and the laying layer.
In the embodiment of the invention, the method is realized as the curved surface track planning and designing software of the fiber-laying robot by using a computer language, and the software is called track planning and designing software in the following.
Firstly, establishing a simulation model according to geometric data of a laying mold, then storing the mold simulation model as a standard form commonly used by CAD files, importing the model into track planning design software, and determining the surface accuracy of a curved surface according to an adopted file storage mode. In the embodiment of the invention, CATIA modeling software is used for establishing an example of a geometric model of a die for laying, as shown in FIG. 2, the established model is stored in STP format, and is imported into the curved surface track planning and designing software of the filament laying robot written based on the method of the invention for model processing. The open-source Opencascade module function is embedded in the track planning design software, and the module function can be used for recognizing and storing the geometric information of the digital model of the mould.
And then, determining the curved surface of the laying mold for automatic filament laying of the robot according to the mold geometric model data information of the CAD file. And determining the layering information of each layer of composite material according to the designed layering scheme, and importing the adopted data information of the prepreg tow material. Wherein, the ply information data comprises ply design sequence and fixed angle information of each ply. The tow material data comprises data information such as tow width, tow thickness and the like.
The operation interface of the trajectory planning and designing software developed by the invention is shown in fig. 3, the software can perform imaging generation processing on the read mold digital model, and each angle view of the digital model can be observed in an image generation area, and the software has operation methods such as translation, rotation and the like. And by using the surface pickup function, the selected curved surface data can be further read, the curved surface is activated and highlighted, and meanwhile, the activated curved surface is considered to be the curved surface for laying the mold in contact with the press roller in the laying process.
In order to ensure the adaptability to various fiber laying devices and fiber bundle materials, an input port for setting fiber bundle parameter data exists in a track planning design software interface, the input port is used for adapting to the fiber bundle materials with various widths, track planning design of various fiber bundles with variable bandwidths can be carried out, and therefore the track planning curved surface condition with complex track can be adapted. In order to realize the trajectory planning of the curved surface according to the selected angle, a parameter curve network of the curved surface is established based on a differential geometry principle to carry out parametric expression and trajectory generation.
S2: and selecting a fiber laying reference coordinate axis and an initial boundary position.
Based on the following theorem in differential geometry:
tangent vector parallel theorem: on a regular parametric surface S: s = S (u, v) has two continuously differentiable tangent vector fields a, b, u, v which are linearly independent everywhere and are curved surface parameters, so that for each point p epsilon S, a neighborhood of the point p must be present
And new parameters on U
Such that in the parameter system
Are parallel to a and b, respectively.
Orthogonal parameter curve net existence theorem: regular parametric surface S: s = S (u, v) each point p e S must have a neighborhood of points p
And new parameters on U
So that in the parameter system
Lower curveThe tangent-line vectors being orthogonal to each other, i.e.
The parameter system is an orthogonal parameter system of the curved surface S on U.
Based on the tangent vector parallel theorem, the vector field in any parameter system direction can be selected at any point of the curved surface, only the modulus difference exists, and based on the existence theorem of the orthogonal parameter curve network, the parameter system selected at any point of the curved surface can be simultaneously the orthogonal parameter system. Namely, at any point of the curved surface, selecting a direction vector field of a parameter system according to the design angle of the laying layer, then constructing an orthogonal parameter system according to the existence theorem of an orthogonal parameter curve network, and establishing an orthogonal frame field and an orthogonal parameter curve network of the curved surface. The trajectory planning and designing software of the invention gives the option of selecting the angle of laying and laying according to the laying design, thereby determining the planning direction of the curved trajectory, and defaulting the fixed angle to be 0 degree, plus or minus 45 degrees and 90 degrees. The above principles are not limited to the generally default 0 °, ± 45 °,90 ° angles, but can also be applied to other ply angles.
Firstly, selecting a coordinate system of a curved surface model, secondly, determining the boundary of an actual laying area on the curved surface according to the laying curved surface of the selection mould, and then, randomly selecting a point on the laying boundary as a starting point of an initial laying path.
An operation interface for picking up coordinate axes is given in the track planning design program, a coordinate system of a part can be constructed by picking up an original point and two coordinate axis directions, and an original model reference system can be used according to read data; according to the mode of establishing the curved surface orthogonal parameter system in the step 2, the intersection curve of the curved surface boundary and the orthogonal parameter curve network is calculated, an initial default laying area is generated, the u and v parameter ranges of the laying area boundary in the orthogonal parameter system under the condition are given, and the further scaling modification of the position of the laying area boundary is realized by modifying the parameter ranges, so that the function of freely modifying the laying range is realized, the flexible drawing of the laying area is ensured according to the area size condition of each layer of laying in the laying design, and the track planning performance of the layered variable-area laying is further improved.
S3: and generating a laying track of the layer of the paving layer based on a differential geometric curved surface orthogonal frame principle.
The trajectory generation task in the deposition area is mainly divided into two phases: a first stage generates a first reference track; and in the second stage, the initial tracks are parallelly and densely paved on the whole curved surface structure.
In the first stage, based on the direction vector in the process of forming the curved surface orthogonal frame has the random characteristic, the invention establishes the orthogonal curved surface frame of the free curved surface based on the direction vector and the initial point normal vector selected by the curved surface in the step S2. And determining an initial track of the laying track according to the selected laying angle and the boundary starting point. And taking a curve obtained by intercepting a section and a curved surface based on the starting point and the vector containing the angle direction of the layering as an initial track. In the second stage, on the free curved surface based on the orthogonal curved surface frame system, the width of the tows is moved in parallel to generate the next track on the basis of the initial path until the track generates a curved surface boundary which is paved on the whole paving layer. And in the second stage, based on the adopted parameter information of the filament-laying head equipment, the laying performance of the laying path on the curved surface is preliminarily analyzed, and error reporting processing is carried out on the non-laying area.
As shown in fig. 4, to realize the generation of the initial trajectory, according to the general principle of reference trajectory selection, the embodiment of the present invention takes the center position of the curved surface of the mold laying surface, and selects any point p in the region 0 Then, taking the point as a starting point, respectively generating tracks towards the boundaries of the two ends, and determining the direction of the generated tracks according to the angle direction of the layer of the pavement; according to the normal vector n of the curved surface of the point and the selected direction vector r u The only curved surface frame forming the curved surface in the angle direction of the paving layer can be determined, and in the frame, another orthogonal base direction can be determined as r v ＝n×r u . According to the normal vector n in the frame and the parameter curve net, the number r u The cross section of the parametric curve formed by the substrate and the intersection line of the curved surface form a laying reference track. The starting point in the present invention is the one set according to step S2.
In order to realize the scheme of track densely paving the whole paving layer, the next track can be obtained by moving the width w of the tows in parallel on the basis of the reference track generated in the steps, but the normal vector n is changed along with the change of the curvatures of the free-open curved surface at different positions, and the parallel directions of all the positions are not identical. As shown in FIG. 5, to realize parallel movement with equal distance, a plurality of position points are selected on the track, a curved surface frame is established at each position point according to the normal vector of the point and the direction of the reference track, and r in the frame is arranged v The width distance of the tows is parallelly moved as the next position point, and a plurality of points are respectively arranged at r v The mapping curve is subjected to the parallel movement to form track points of the subsequent track, and the track points are connected to obtain the subsequent track until the track reaches the boundary of the laying area in the dense laying and extending process.
The verification of the spreadability shows that whether the compression roller can realize contact with the die or not in the width range of the tows at the laying position of the track, the compression roller is in a compaction process, the contact area with the curved surface is similar to a rectangle, namely the length of the rectangle is ensured to be larger than the width of the tows, and the compression roller can be considered to successfully compact the tows. As shown in FIG. 6, the projection of the axis of the contact part of the press roll and the curved surface is C, the length of the press roll is H, and a coordinate system is established at the contact center point P of the press roll and the curved surface, wherein e 1 Is a unit vector of the laying direction, e 2 The unit vector of the axial direction of the compression roller is shown, n is the normal vector direction of the point P, and the rectangular length of the contact surface of the compression roller is ensured to be larger than the width of the tows, namely the deformation of the compression roller is larger than the height h from a die to the tangent plane of the compression roller in the figure. In the neighborhood of point P, the height h of the mold from the nip plane can be calculated using an arc as an approximation, according to the euler formula:
wherein k is the normal curvature in the laying direction at point P, k 1 And k 2 Respectively a maximum principal curvature and a minimum principal curvature at P,
denotes the lay down direction and k 1 Angle of included angle of direction, v 1 Is corresponding to k 1 The principal curvature direction unit vector of (2). Thereby calculating the maximum value w of the width w of the filament bundle which can be compacted by the compression roller max ：
And D is the maximum deformation of the press roll and is determined according to the geometric parameters and materials of the spreading head press roll.
The height h from the compression roller to the surface of the mold is obtained according to the method, the height h is compared with the maximum deformation D of the compression roller, and when h is smaller than D, the compression roller can ensure that the whole curved surface can be compacted in the compaction process; and comparing the obtained tow width range with the selected tow width to judge whether all tows can be compacted in the laying process, and verifying the laying performance.
S4: according to the curvature distribution condition of the surface of the mold, the fiber widening laying range with good laying performance and no defect on the track is determined.
Aiming at a free curved surface with positive Gaussian curvature, the process of determining the spreadability of the track is mainly divided into two processes, the curvature of the corresponding position of the curved surface is solved in the first stage by combining the parameters of the track, and the curvature data on the track is determined; and in the second stage, based on the curvature calculation of the curved surface, the width limitation of the prepreg fiber bundles without defects during actual laying can be compared with the width-widened prepreg fiber bundle material parameters, and the prepreg fiber width suitable for the track is determined.
And evaluating the laying performance based on the curvature radius of each point on the trajectory line in the laying process, and determining the maximum curvature position of the defects such as fiber buckling as the condition for dividing the variable-width laying region according to the common defect form of curved surface laying. According to the stress distribution characteristics of the prepreg fiber yarn structure, the curvature radius formula of a certain point on a trajectory line is determined, and a mathematical model between the curvature radius and the fiber width is established, wherein in the mathematical model, except the fiber width and the curvature radius, other characteristic parameters are related to inherent material parameters of the prepreg fiber bundle and curved surface curvature parameters of the surface of a mold, and can be obtained through measurement or material test. And based on the obtained mathematical model, carrying out regional treatment on the laying region of the surface of the die, laying the region with small curvature of the curved surface by using the wide prepreg fiber bundle, and laying the region with large curvature by using the wide-width filament laying head equipment by using the thin prepreg fiber bundle.
As shown in fig. 7, for the laying track designed in step S3, a curved frame describing a curved laying track is established by defining the direction along the curve of the laying track as the u direction and defining the direction along the width of the fiber as the v direction, and if the laying length of the center line of the track is defined as L and the width of the fiber is defined as w in the regular parametric curved surface S (u, v) determined by the frame, a relation of the differential track length ds can be obtained for a segment of the differential geodesic coordinates of the track curve:
the lay-down length L in the varying width direction for the entire lay-down trajectory C From the integration, one can obtain:
wherein, when u =0, L C I.e., the centerline length L, when u approaches 0, it is assumed that there is any sufficiently small amount ε that satisfies 0<ε<u, according to Taylor's expansion, surface expression
Can be expressed as:
based on the differential geometry principle, part of the above formula can be replaced by:
wherein k is gu＝0 (v) Is the geodesic curvature of point P (0, v) and K (ε, v) is the Gaussian curvature of point (ε, v), which can be approximated to the Gaussian curvature of point P in the differential range. The above equation is taken into the deposit trajectory integral to obtain:
memory k g For geodesic curvature, K is Gaussian curvature, and the difference of the shift terms can obtain a distance deviation value between the laying track on the curved surface and the actual laying as a laying variation limit value for describing the fibers. Defining theta as the ultimate sliding degree of the laid fiber edge and the fiber center, namely the degree of the occurrence of defects such as folds and the like, and calculating as follows:
in the certain determined fiber laying process, theta is controlled by laying equipment, fiber material parameters, laying process parameters and the like, and aiming at the specific laying process, the laying equipment and process parameter control scheme is determined environmental parameters, the parameters are not changed along with the width change of the variable-width fibers, and L C Maximum value of (2) is w/2 at the fiber boundaryWhere u = w/2, the maximum value of θ max Can be expressed as a relation only with respect to the variables w, L as follows:
in the actual placement process, the variation of the fiber boundary length from the center length is affected by the fiber placement length L, the fiber width w, and the radius of curvature R of the trajectory, with the actual slippage being:
namely, the following conditions are satisfied:
further, the following can be obtained:
based on the curvature of the laying track points and the curvature radius of the actual laying track, the limitation of the fiber width w can be determined, and then the area division and the fiber width selection of variable-width laying are carried out according to the width limitation condition.
According to the method, a threshold value of the curvature radius is set based on material characteristics, when the calculated curvature radius of the laying track on the curved surface is smaller than the threshold value, the curvature of the curved surface is smaller, and the wide prepreg fiber bundles are used for laying the curved surface area; otherwise, the curve surface has larger curvature, and the area with larger curvature is paved by the thin pre-impregnated fiber bundle by adopting the wide-width fiber head paving equipment.
S5: and generating a robot control language for the laying track, and using the robot control language for operating and controlling the robot to carry out laying work.
Generating track data of each layer and fiber prepreg tow material data according to the steps, converting algebraic data information obtained by analyzing the curved surface of the track into a mechanical language G code and the like, generating a control language which can be recognized by a robot, and controlling the fiber laying robot to finish the fiber laying work. In the embodiment of the invention, the robot control language adopts G code storage, and one or more stored document files are generated based on the upper limit of the size of the file read by the robot.
The method comprises the steps of carrying out curved line mesh processing on a curved surface, using two curve equations as a substrate to describe each position information on the curved surface, and constructing two sets of composite mapping relations by using the curve equations and direction vectors of points to directly describe the curved surface, thereby avoiding errors in the process of projecting the curved surface on the plane and avoiding the defect of laying caused by error accumulation in the process of calculating a series of points. The invention provides a planning and designing method for a silk laying forming track of a normal Gaussian curved surface orthogonal frame, which is characterized in that a track is directly generated on a curved surface based on a curve mapping equation relation of the curved surface orthogonal frame; based on the change condition of the curvature distribution of the positive Gaussian curved surface, the width limit of the track design is determined, specific width limit data caused by curvature change can be determined for the limited region which cannot be laid, and the width limit is based on which the tow is laid in a widening mode to densely lay the whole curved surface.
In conclusion, the invention provides a novel method for planning and designing the track of the curved orthogonal frame in the aspect of planning the track of the automatic carbon fiber laying robot, breaks through the structural limitation of the traditional track planning, ensures the accuracy of automatic fiber laying, and can meet the requirements of planning and designing the track of fiber tows of various specifications and laying heads of different specifications. In order to improve the accuracy of the trajectory planning result, the invention also determines the spreadability of the filament spreading process through the deformation of the compression roller in the compaction process. The software program for the wire-laying robot curved surface track planning algorithm provided by the invention can realize the generation of the path data of the curved surface track planning, further convert the path data into the output scheme of the mechanical language, and simultaneously carry out the planning design of the robot curved surface wire-laying track under the conditions of different tow widths, different thicknesses and different wire-laying head models, thereby providing technical guidance for the actual robot laying optimization scheme.
In addition to the technical features described in the specification, the technology is known to those skilled in the art. Descriptions of well-known components and techniques are omitted so as to not unnecessarily obscure the present invention. The embodiments described in the above embodiments do not represent all embodiments consistent with the present application, and various modifications or variations which may be made by those skilled in the art without inventive efforts based on the technical solution of the present invention are still within the protective scope of the present invention.
Claims (7)
1. A planning and designing method for a wire laying forming track of a normal Gaussian curved surface orthogonal frame is characterized by comprising the following steps:
step 1, reading a digital model of a mould actually used for laying, and determining the information of the surface of the laying mould and the parameters of laying;
step 2, selecting a fiber laying reference coordinate axis and an initial boundary position;
determining a curved surface boundary of an actual laying area according to a laying surface of a mold, and randomly selecting a point on the boundary as a starting point of an initial laying path;
step 3, generating a laying track of the current laying layer based on a differential geometric curved surface orthogonal frame principle;
firstly, a normal vector of a curved surface based on a starting point and a direction vector r selected by a ply angle v Establishing an orthogonal curved surface frame of the free curved surface, and setting the normal vector and the direction vector r of the curved surface of the initial point v Taking the section and the curve intercepted by the curved surface as an initial track; secondly, taking the initial track as a reference, moving the width of the fiber tows in parallel to lay the next track until the whole curved surface is fully paved;
step 4, determining the width-widening laying range of the fiber according to the curvature distribution condition of the surface of the mold, so that the track has good laying performance;
a mathematical model between the trajectory radius of curvature R and the fiber tow width w is established as follows:
wherein k is g In order to measure the curvature of the earth, K is Gaussian curvature;
calculating the curvature radius of the laying track at different curved surface positions on the surface of the mould, determining the limitation of the width W of the fiber tows based on the mathematical model, and performing region division of width-widening laying and width selection of the fiber tows;
and 5, generating a robot control language according to the laying track generated in the steps 2-4 and the data of the fiber prepreg tow material, and operating the robot to carry out laying work.
2. The method of claim 1, wherein in step 1, according to the designed ply scheme, parameter information of the composite material plies is determined, wherein the parameter information comprises a ply design sequence and a fixed angle of each ply; the fiber prepreg tow material data used, including fiber tow width and thickness, were determined.
3. The method according to claim 1 or 2, wherein said step 2 comprises:
(1) Selecting a direction vector field of a parameter system at any point of a laying curved surface of the mould according to the angle of the designed laying, then constructing an orthogonal parameter system, and establishing an orthogonal frame field and an orthogonal parameter curve network of the curved surface;
(2) And calculating an intersection curve of the curved surface boundary and the orthogonal parameter curve net to generate an initial default laying area, simultaneously giving a curved surface parameter range of the current laying area boundary in the orthogonal parameter system, and zooming the position of the laying area boundary by modifying the curved surface parameter range.
4. The method according to claim 1, wherein in step 3, when laying down the next track, a plurality of position points are selected on the current track, and each position point is determined according to the normal vector of the curved surface of the point and the square of the initial trackTo the curved frame at the point of construction, along the direction vector r in the curved frame v The width distance of the fiber tows is moved in parallel in the direction of (1) to serve as a next position point, and all the next position points obtained from all the current position points are connected to obtain a subsequent track.
5. The method according to claim 1 or 4, wherein in the step 3, the spreadability is detected during the laying track, and whether the press roll can contact with the mould within the width range of the fiber tows at the track laying position is detected; specifically, the height h of the press roll to the die surface and the fiber tow width range are calculated as follows:
wherein H is the length of the compression roller, k is the normal curvature of the laying direction at the laying position point, and k is 1 And k 2 Respectively a maximum principal curvature and a minimum principal curvature at the laying location point,
denotes the lay down direction and k 1 Angle of included angle of direction, v 1 Is corresponding to k 1 Principal curvature direction unit vector of (e) 1 Is a unit vector of the laying direction;
when h is smaller than D, the spreadability is represented, otherwise, the spreadability is not represented;
and simultaneously judging whether the width w of the currently used fiber tows meets the following conditions:
if not, no spreadability is indicated.
6. A method according to claim 1 or 4, characterized in that in the step 4, the laying area of the mould surface is processed in a zoning mode according to the curvature radius of the laying track, a curvature radius threshold value is set in advance based on the material characteristics, when the calculated curvature radius of the curved surface is smaller than the threshold value, the curved surface curvature is in a smaller area, otherwise, the curved surface curvature is in a larger area, and the width of the fiber tows is adjusted to different areas for track laying.
7. The method according to claim 1 or 4, wherein in the step 4, the position of the maximum curvature limit of the fiber defect is determined, so as to further obtain the area division of the variable fiber tow width laying, and the fiber tow width is set, and the method comprises the following steps:
for the laying track designed in the step 3, defining the direction along the curve of the laying track as the u direction, defining the direction along the width of the fiber tows as the v direction, establishing a curved surface frame for describing the curved surface laying track, defining the laying length of the track central line as L in a regular parameter curved surface S (u, v) determined by the frame, and obtaining a relation formula of a section of differential track length ds as follows:
the laying length L in the width direction of the fiber tow varies for the entire laying trajectory C From the integration, we get:
wherein, when u =0, L C For the centerline length L, when u approaches 0, let e be present in any sufficiently small amount to satisfy 0<ε<u, according to Taylor's expansion, surface expression
Expressed as:
based on the differential geometry principle, the terms in the formula are replaced as follows:
wherein k is gu＝0 (v) Geodesic curvature, which is point P (0, v); k (epsilon, v) is the Gaussian curvature of the point (epsilon, v), and is approximate to the Gaussian curvature of the point P in the differentiation range;
further obtaining:
defining θ as the ultimate degree of slippage of the edge of the deposited fiber from the center of the fiber, indicating the degree of occurrence of the defect, is calculated as follows:
wherein k is g In order to measure the curvature of the earth, K is Gaussian curvature;
in the process of determining the laying of the fibers, the laying equipment and the laying process parameter control scheme are determined environment parameters which do not change along with the change of the width of the fibers, and L C Is at w/2 of the fiber boundary, i.e. u = w/2, so the maximum value of θ, θ max Is expressed as a relation only with respect to the variables w, L, as follows:
in the actual laying process, the fiber boundary length and centerThe change in length is affected by the fiber placement length L, the fiber tow width w, and the radius of curvature R of the trajectory, with the actual slippage being:
therefore, it is necessary to satisfy
Further obtaining:
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| CN117172399B (en) * | 2023-11-02 | 2024-03-15 | 成都飞机工业（集团）有限责任公司 | Automatic wire laying track planning method based on heuristic algorithm |
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