CN114474741B - Multi-axis unsupported 3D printing curved surface slicing method, device and server - Google Patents

Multi-axis unsupported 3D printing curved surface slicing method, device and server Download PDF

Info

Publication number
CN114474741B
CN114474741B CN202210027787.5A CN202210027787A CN114474741B CN 114474741 B CN114474741 B CN 114474741B CN 202210027787 A CN202210027787 A CN 202210027787A CN 114474741 B CN114474741 B CN 114474741B
Authority
CN
China
Prior art keywords
printing
curved surface
angle
printing direction
control point
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210027787.5A
Other languages
Chinese (zh)
Other versions
CN114474741A (en
Inventor
李亚敏
朱继宏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Northwestern Polytechnical University
Original Assignee
Northwestern Polytechnical University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Northwestern Polytechnical University filed Critical Northwestern Polytechnical University
Priority to CN202210027787.5A priority Critical patent/CN114474741B/en
Publication of CN114474741A publication Critical patent/CN114474741A/en
Application granted granted Critical
Publication of CN114474741B publication Critical patent/CN114474741B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/30—Auxiliary operations or equipment
    • B29C64/386—Data acquisition or data processing for additive manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F10/00—Additive manufacturing of workpieces or articles from metallic powder
    • B22F10/80—Data acquisition or data processing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F10/00—Additive manufacturing of workpieces or articles from metallic powder
    • B22F10/80—Data acquisition or data processing
    • B22F10/85—Data acquisition or data processing for controlling or regulating additive manufacturing processes
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/30—Auxiliary operations or equipment
    • B29C64/386—Data acquisition or data processing for additive manufacturing
    • B29C64/393—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00—Data acquisition or data processing for additive manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00—Data acquisition or data processing for additive manufacturing
    • B33Y50/02—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P10/00—Technologies related to metal processing
    • Y02P10/25—Process efficiency

Landscapes

  • Chemical & Material Sciences (AREA)
  • Engineering & Computer Science (AREA)
  • Materials Engineering (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • Mechanical Engineering (AREA)
  • Optics & Photonics (AREA)

Abstract

The application discloses a multi-axis unsupported 3D printing curved surface slicing method, a device and a server, and belongs to the field of 3D printing. The curved surface slicing method comprises the steps of dividing a three-dimensional model to be printed into polyhedral grids with a plurality of polyhedral units; randomly selecting a plurality of vertexes in the polyhedral grid as control points; establishing an optimization model about the control points; averaging the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G of the polyhedral grid; iteratively solving the optimization model to obtain a control point prescription directional angle G which minimizes the overhanging angle evaluation function f (G) under the condition that the layered curved surface curvature constraint condition cond (G) is satisfied and an optimal printing direction vector field G distributed on the whole three-dimensional model to be printed corresponding to the control point prescription directional angle G 0 The method comprises the steps of carrying out a first treatment on the surface of the Obtaining vector field G along optimal printing direction 0 The monotonically increasing distance scalar field phi, and the equivalent surface fitted by the distance scalar field phi is the printing curved surface slice layer. The method is suitable for unsupported printing of complex parts.

Description

Multi-axis unsupported 3D printing curved surface slicing method, device and server
Technical Field
The application relates to the technical field of 3D printing, in particular to a multi-axis unsupported 3D printing curved surface slicing method, a device and a server.
Background
Additive manufacturing techniques such as fused deposition and direct energy deposition can extrude or spray materials such as plastics, composite materials, metal powder and the like from a nozzle by heating and melting, and manufacture workpieces with different shapes by stacking layer by layer. However, most of the existing 3D printing apparatuses are based on 2.5 axis systems and planar layering technologies, and when manufacturing structures with complex features such as cantilevers and multiple holes, a large number of support structures are required to prevent material collapse, which becomes a bottleneck that limits the processing efficiency, cost and precision thereof.
Multi-axis printing systems have received increasing attention in recent years. Compared with the traditional 2.5-axis system, the 5/6-axis system provides more degrees of freedom, and can enable the nozzle to continuously change direction relative to the workpiece in the printing process, so that extruded/ejected materials fall on the current workpiece as much as possible, thereby effectively reducing the volume of a supporting structure and even realizing completely unsupported printing, greatly improving the manufacturing efficiency of complex parts and saving the cost, and a reasonable slicing process planning method is a key for realizing the above-mentioned aim.
In recent years, a large number of students have proposed a new unsupported dicing process planning method based on a multi-axis printing system to achieve unsupported printing of complex components. The 3+2 axis printing mode is a flexible multi-axis printing process, which completes the manufacture of a complex model by changing the printing direction for several times in the printing process, and the printing process corresponding to each direction is still 2.5 axis printing. To achieve 3+2 axis printing, the model is typically first appropriately diced, then the corresponding print direction is planned for each section, and finally planar layering is performed along that direction. However, the current process planning method based on the 3+2 axis printing system does not fully utilize the degree of freedom and flexibility of the multi-axis printing system, and the 3+2 axis printing mode with multiple directions in blocks is generally suitable for tree structures, but has poor universality for some free-form parts with complex features.
Compared with 3+2-axis printing, the curved surface layering technology based on the continuous multi-axis printing mode can better utilize the degree of freedom and flexibility of a multi-axis printing system, so that the unsupported printing of complex parts can be realized. However, existing curved surface slicing methods, whether based on 3+2 axis equipment or multi-axis continuous printing equipment, do not fully guarantee unsupported printing for some complex structural parts, such as porous structural parts.
Disclosure of Invention
The embodiment of the application solves the problem that the existing curved surface slicing method cannot completely guarantee the unsupported printing of some complicated structural parts by providing the multi-axis unsupported 3D printing curved surface slicing method, the device and the server.
In a first aspect, an embodiment of the present invention provides a multi-axis unsupported 3D printing curved surface slicing method, including:
dividing a stereoscopic model to be printed into polyhedral grids with a plurality of polyhedral units;
randomly selecting a plurality of vertexes in the polyhedral grid as control points;
establishing an optimization model about the control points:
wherein,, to control the print direction angle at the point,the printing direction angle of the mth control point is the printing direction angle of the mth control point, and n is the number of the control points; cond (g) is a layered curved surface curvature constraint condition, and f (g) is an overhanging angle evaluation function;
averaging the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G;
iteratively solving the optimization model to obtain a control point prescription directional angle G which minimizes the overhanging angle evaluation function f (G) under the condition that the layered curved surface curvature constraint condition cond (G) is satisfied and an optimal printing direction vector field G distributed on the whole three-dimensional model to be printed corresponding to the control point prescription directional angle G 0 ；
Obtaining a vector field G along the optimal printing direction 0 And a monotonically increasing distance scalar field phi, wherein an isosurface fitted by the distance scalar field phi is the printed curved surface slice layer.
With reference to the first aspect, in one possible implementation manner, the step of averaging the printing direction angle G at the control point to the whole to-be-printed stereoscopic model to obtain a printing direction vector field G distributed in the polyhedral grid corresponding to G includes the specific steps of: and solving a Laplace equation DeltaG=0 by taking the printing direction angle G at the control point as a Dirichlet boundary condition so as to average the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G.
With reference to the first aspect, in one possible implementation manner, the overhanging angle evaluation function f (g) is expressed as:
wherein m is the total number of vertexes at the boundary of the three-dimensional model to be printed; x is x i Is the overhang angle factor at the ith vertex of the boundary; s is(s) max The maximum value of the smoothing factors in all vertexes in the current printing direction vector field G; s is(s) mean The average value of the smoothing factors of all vertexes in the current printing direction vector field G; alpha is penalty coefficient, alpha is [0,1 ]]。
With reference to the first aspect, in one possible implementation manner, the overhanging factor x at the ith vertex of the boundary i Expressed as:
wherein θ o For the angle of overhang at the currently calculated vertex, θ t Is a preset critical overhang angle.
With reference to the first aspect, in a possible implementation manner, one vertex v in the polyhedral grid i Is the smoothing factor s of (1) i Expressed as:
wherein N (i) represents vertex v i The polygon unit and vertex v i A set of other vertices of the same edge; v j Represents a vertex in N (i); w (w) ij A weight coefficient representing the edge ij; n is n i Representing vertex v i Is a vector of the direction of (2); n is n j Representing vertex v j Is a direction vector of (a).
With reference to the first aspect, in one possible implementation manner, the layered curved surface curvature constraint cond (g) is expressed as:
wherein H is the average curvature field of the layered curved surface, expressed asR is a preset minimum allowable radius of curvature.
With reference to the first aspect, in one possible implementation manner, the iteratively solving an optimization model includes: and adopting a genetic algorithm to iteratively solve the optimization model.
With reference to the first aspect, in a possible implementation manner, the obtaining a vector field G along the optimal printing direction 0 A monotonically increasing distance scalar field Φ comprising: the obtained optimal direction field G 0 Substituted Poisson equation L c Φ＝DivG 0 Solving to obtain a vector field G along the optimal printing direction 0 Monotonically increasing distance scalar field Φ.
In a second aspect, an embodiment of the present invention provides a multi-axis unsupported 3D printing curved surface slicing device, which is characterized by comprising:
the grid dividing module is used for dividing the stereoscopic model to be printed into polyhedral grids with a plurality of polyhedral units;
a selecting module, configured to randomly select a plurality of vertices in the polyhedral mesh as control points;
a model building module for building an optimization model for the control points:
wherein,, to control the print direction angle at the point,the printing direction angle of the mth control point is the printing direction angle of the mth control point, and n is the number of the control points; cond (g) is a layered curved surface curvature constraint condition, and f (g) is an overhanging angle evaluation function;
the averaging module is used for averaging the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G which is distributed on the polyhedral grid and corresponds to G;
the solving module is used for iteratively solving the optimization model to obtain the control point prescription direction angle G which minimizes the overhanging angle evaluation function f (G) under the condition of meeting the layered curved surface curvature constraint condition cond (G) and the optimal printing direction vector field G which is distributed on the whole three-dimensional model to be printed and corresponds to the control point prescription direction angle G 0 ；
A slicing module for obtaining vector field G along the optimal printing direction 0 And a monotonically increasing distance scalar field phi, wherein an isosurface fitted by the distance scalar field phi is the printed curved surface slice layer.
In a third aspect, an embodiment of the present invention provides a server, including: a memory and a processor;
the memory is used for storing program instructions;
the processor is configured to execute program instructions in a server, so that the server executes the multi-axis unsupported 3D printing curved surface slicing method described above.
In a fourth aspect, an embodiment of the present invention provides a computer readable storage medium, where executable instructions are stored, where the computer is capable of implementing the above-mentioned multi-axis supportless 3D printing curved surface slicing method when executing the executable instructions.
One or more technical solutions provided in the embodiments of the present invention at least have the following technical effects or advantages:
the embodiment of the invention provides a multi-axis unsupported 3D printing curved surface slicing method, which comprises the following steps: the stereoscopic model to be printed is divided into a polyhedral mesh having a plurality of polyhedral cells. A plurality of vertices in the polyhedral mesh are randomly selected as control points. Establishing a controlAnd (3) preparing an optimization model of the point:wherein (1)> To control the print direction angle at the point,the printing direction angle of the mth control point is n, the number of the control points is n, cond (g) is a curvature constraint condition of the layered curved surface, and f (g) is an overhanging angle evaluation function. And averaging the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G. Iteratively solving the optimization model to obtain a control point prescription directional angle G which minimizes the overhanging angle evaluation function f (G) under the condition that the layered curved surface curvature constraint condition cond (G) is satisfied and an optimal printing direction vector field G distributed on the whole three-dimensional model to be printed corresponding to the control point prescription directional angle G 0 . Obtaining vector field G along optimal printing direction 0 The monotonically increasing distance scalar field phi, and the equivalent surface fitted by the distance scalar field phi is the printing curved surface slice layer. The multi-axis unsupported 3D printing curved surface slicing method provided by the embodiment of the invention is suitable for multi-axis unsupported printing of complex parts, can quantitatively control the printing overhanging angle and the curvature of a layered curved surface, and is particularly suitable for printing complex characteristic parts with porous structures and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention and the technical solutions of the prior art, the drawings that are needed in the description of the embodiments of the present invention and the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a multi-axis unsupported 3D printing curved surface slicing method provided in an embodiment of the application;
FIG. 2 is a schematic diagram of control point selection for a porous structure according to an embodiment of the present application;
FIG. 3 is a schematic diagram of the current print direction vector field of the porous structure of FIG. 2;
FIG. 4 is a schematic diagram of the porous structure optimal printing direction vector field of FIG. 2;
FIG. 5 is a schematic illustration of an iso-surface derived from the optimal print direction vector field of FIG. 4;
FIG. 6 is a schematic structural view of a practical porous structure according to an embodiment of the present application;
FIG. 7 is a schematic diagram of the resulting optimal direction vector field for the actual porous structure of FIG. 6;
FIG. 8 is a schematic diagram of the division of an actual porous structure model into curved slice layers according to the optimal direction vector field of FIG. 7;
FIG. 9 is a schematic diagram of a prior art slicing method for dividing the actual porous structure of FIG. 6 into curved sliced layers;
FIG. 10 is a schematic diagram of a printed entity of the actual porous structure of FIG. 6 obtained by the curved surface slicing method provided in the embodiments of the present application;
FIG. 11 is a schematic structural view of another practical porous structure provided in an embodiment of the present application;
FIG. 12 is a schematic diagram of a curved surface slicing method according to an embodiment of the present application, dividing the actual porous structure of FIG. 11 into curved surface sliced layers;
FIG. 13 is a schematic diagram of a printed entity of the actual porous structure of FIG. 11 obtained by the curved surface slicing method provided in an embodiment of the present application;
FIG. 14 is a schematic view of a structure of yet another practical porous structure provided in an embodiment of the present application;
FIG. 15 is a schematic diagram of a curved surface slicing method according to an embodiment of the present application for dividing the actual porous structure of FIG. 14 into curved surface sliced layers;
FIG. 16 is a schematic diagram of a printed entity of the actual porous structure of FIG. 14 obtained using the curved surface slicing method provided by the embodiments of the present application;
fig. 17 is a schematic structural diagram of a tetrahedral unit according to an embodiment of the present application.
Icon: 1-a control point; 2-isosurface.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention provides a multi-axis unsupported 3D printing curved surface slicing method, which is shown in fig. 1 and comprises the following steps:
step 1: the stereoscopic model to be printed is divided into a polyhedral mesh having a plurality of polyhedral cells.
In practice, the stereoscopic model to be printed may be divided into tetrahedral meshes having a plurality of tetrahedral units, or may be divided into hexahedral meshes having a plurality of hexahedral units. Fig. 2 shows a schematic diagram of a structure of a tetrahedral mesh dividing a stereoscopic model to be printed into a plurality of tetrahedral cells, the tetrahedral mesh being represented by M (V, E, F, T), wherein V represents a set of vertices of the tetrahedral mesh, E represents a set of edges of the tetrahedral mesh, F represents a set of triangular faces of the tetrahedral mesh, and T represents a set of tetrahedral cells of the tetrahedral mesh. The tetrahedral grid has lower complexity, so that the calculation speed is higher, and the tetrahedral grid generation algorithm is adopted, so that the automation, the efficiency, the reliability and the geometric universality are better, and the calculation cost is lower.
Step 2: a plurality of vertices in the polyhedral mesh are randomly selected as control points 1.
Wherein the randomly selected control point 1 may be a vertex inside the polyhedral mesh or at a boundary. Preferably, as shown in fig. 2 to 5, the control points 1 are vertices on respective boundaries of a randomly selected polyhedral mesh. In the follow-up optimization model, when the optimization objective function is the overhanging angle, the overhanging angle is defined more closely with the boundary, so that the vertex on each boundary of the polyhedral grid is selected as the control point 1, and the optimization effect is better.
Step 3: establishing an optimization model about the control point 1:wherein (1)> For controlling the print direction angle at point 1 +.>The printing direction angle of the mth control point 1, and n is the number of the control points 1; cond (g) is a curvature constraint condition of the layered curved surface, and f (g) is an overhanging angle evaluation function.
The hierarchical surface curvature constraint cond (g) in the optimization model is expressed as:
wherein H is the average curvature field of the layered curved surface, expressed asThe dispersion form of the current printing direction vector field G can be expressed; r is a preset minimum allowable radius of curvature, and the value of R can be determined by the shape parameters of the nozzle.
Alternatively, the overhang angle evaluation function f (g) is expressed as:
wherein m is the total number of vertexes at the boundary of the three-dimensional model to be printed; x is x i Is the overhang angle factor at the ith vertex of the boundary; s is(s) max The maximum value of the smoothing factors in all vertexes in the current printing direction vector field G; s is(s) mean The average value of the smoothing factors of all vertexes in the current printing direction vector field G; alpha is penalty coefficient, alpha is [0,1 ]]。
Further, the overhang angle factor x at the ith vertex of the boundary i Expressed as:
wherein θ o The overhanging angle on the vertex calculated at present, namely the included angle between the normal vector at the vertex and the current printing direction vector of the vertex; θ t For the preset critical overhang angle, the preset critical overhang angle can be set according to actual requirements. θ o -θ t When < 0, x i =0, i.e. when the overhang angle θ o Is greater than a preset critical overhang angle theta t When this is the case, support is required.
Optionally, one vertex v in the polyhedral mesh i Is the smoothness factor s of (2) i Expressed as:
wherein N (i) represents vertex v i The polygon unit and vertex v i If the polyhedral unit is a tetrahedron unit, as shown in FIG. 17, N (i) represents a point v j 、v p And v q Is a collection of (3); v j Represents a vertex in N (i); w (w) ij A weight coefficient representing the edge ij; n is n i Representing vertex v i Is a vector of the direction of (2); n is n j Representing vertex v j Is a direction vector of (a). Wherein the smoothness factor s i Measure vertex v i The vector direction consistency at the vertices around the vertex is adopted to calculate the vertex v by adopting the method provided by the embodiment of the application i Is the smoothness factor s of (2) i The effect is measured more accurately.
Step 4: and averaging the printing direction angle G at the control point 1 to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G.
Further, the printing direction angle G at the control point 1 is used as a Dirichlet boundary condition to solve the Laplace equation DeltaG=0, so that the printing direction angle G at the control point 1 is averaged to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G. Specifically, for g in the printing direction angle g θ Andand respectively carrying out Laplace equation, solving two equations, and averaging the printing direction angle G at the control point 1 to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G.
Step 5: iteratively solving the optimization model to obtain the direction angle G at the control point 1 which minimizes the overhanging angle evaluation function f (G) under the condition of meeting the layered curved surface curvature constraint condition cond (G) and the optimal printing direction vector field G distributed on the whole three-dimensional model to be printed corresponding to the direction angle G 0 Namely, under the constraint condition cond (G) of curvature of the layered curved surface, a group of printing direction angle sets G are found at the randomly selected control points 1, so that the overhanging angle evaluation function f (G) is minimum, and vector fields G distributed on a polyhedral grid corresponding to the current G 0 Is the optimal print direction vector field. The optimal printing direction vector field obtained in this way has both unsupported and collision free factors. As shown in fig. 4, the optimal printing direction vector field G is obtained according to the control point 1 of fig. 2 0 Is a schematic diagram of (a).
Further, a genetic algorithm is adopted to iteratively solve the optimization model. The genetic algorithm takes the code of the decision variable as an operation object, can directly operate structural objects such as a set, a sequence, a matrix, a tree, a graph and the like, directly takes the objective function value as search information, measures the individual goodness by using the fitness function value, does not involve the process of deriving and differentiating the objective function value, and can solve a plurality of objective functions which are difficult to derive and even do not have derivatives in reality. The genetic algorithm has the characteristic of group searching, and the searching process is started by a group P (0) with a plurality of individuals, so that on one hand, the searching of some unnecessary points can be effectively avoided, and on the other hand, the traditional single-point searching method is easy to trap local certain unimodal extreme points when searching the multimodal distributed searching space, and the group searching characteristic of the genetic algorithm can avoid the problems, so that the parallelization and better global searching performance of the genetic algorithm can be embodied. The genetic algorithm is based on probability rules rather than deterministic rules, so that the search is more flexible, and the influence of parameters on the search effect is smaller.
Step 6: obtaining vector field G along optimal printing direction 0 The monotonically increasing distance scalar field phi, and the isosurface 2 fitted by the distance scalar field phi is the printing curved surface slice layer. Further, the obtained optimal direction field G 0 Substituted Poisson equation L c Φ＝DivG 0 Solving to obtain vector field G along the optimal printing direction 0 Monotonically increasing distance scalar field phi, as shown in fig. 5, the isosurface 2 fitted by the distance scalar field phi is the printed surface slice layer, and the isosurface 2 can be perpendicular to the optimal printing direction vector field G 0 The suspension angle condition of the unsupported printing and the curvature constraint condition of the collision-free curved surface are quantitatively considered. And step 5, namely the curved surface slicing method step.
The embodiment of the invention provides a printing example, and the actual porous structure shown in fig. 6 is subjected to unsupported printing curved slice. The tetrahedral mesh of the actual porous structure contains 2667 vertices and 9812 tetrahedrons. 40 vertexes are randomly selected on the surface of the tetrahedron grid as control points 1, a penalty coefficient alpha is set to be 0.5, and a critical overhang angle theta is preset t Set to 135 deg., the preset minimum allowable radius of curvature R is set to 2mm. FIG. 7 shows an optimal print direction vector field G obtained by solving an optimization model 0 . The obtained optimal direction field G 0 Substituted Poisson equation L c Φ＝DivG 0 Solving to obtain a distance scalar field phi, and naturally dividing the three-dimensional model to be printed into a plurality of curved surface slice layers by using an isosurface 2 of the scalar field phi shown in fig. 8. FIG. 9 shows a conventional slicing method for slicing a curved surface of a three-dimensional model to be printedSchematic of the post-sheet. Definition of support area ratio r=a s /a t Wherein a is s And a t The support area and the total surface area of the three-dimensional model to be printed, respectively. The supporting area rate of the curved surface slicing result of the method is 1.5%, which is far less than 8.9% of that of the traditional plane slicing method. Further, the maximum curvature of the sliced curved surface was 0.44mm -1 . Fig. 10 is a schematic diagram of a printed entity obtained by using the multi-axis unsupported 3D printing curved surface slicing method according to the embodiment of the application. Fig. 11 to 16 show curved surface slices of two other actual porous parts and the results of physical printing, which can realize unsupported printing.
The multi-axis unsupported 3D printing curved surface slicing method provided by the embodiment of the invention is suitable for multi-axis unsupported printing of complex parts, can quantitatively control the printing overhanging angle and the curvature of a layered curved surface, and is particularly suitable for printing complex characteristic parts with porous structures and the like.
Another embodiment of the present invention provides a multi-axis supportless 3D printing curved surface slicing device, comprising:
and the grid dividing module is used for dividing the stereoscopic model to be printed into polyhedral grids with a plurality of polyhedral units.
And the selection module is used for randomly selecting a plurality of vertexes in the polyhedral grid as control points.
The model building module is used for building an optimization model about the control points:
wherein,, to control the print direction angle at the point,the printing direction angle of the mth control point is the number of control points, and n is the number of control points; cond (g)And f (g) is an overhanging angle evaluation function for the curvature constraint condition of the layered curved surface.
Further, a model building module is used for building an optimization model about the control points:wherein (1)> For the printing direction angle at the control point +.>The printing direction angle of the mth control point is the number of control points, and n is the number of control points; cond (g) is a curvature constraint condition of the layered curved surface, and f (g) is an overhanging angle evaluation function expressed as:
wherein m is the total number of vertexes at the boundary of the three-dimensional model to be printed; x is x i Is the overhang angle factor at the ith vertex of the boundary; s is(s) max The maximum value of the smoothing factors in all vertexes in the current printing direction vector field G; s is(s) mean The average value of the smoothing factors of all vertexes in the current printing direction vector field G; alpha is penalty coefficient, alpha is [0,1 ]]。
Further, a model building module is used for building an optimization model about the control points:wherein (1)> For controlling the printing direction angle at the dot，/>The printing direction angle of the mth control point is the number of control points, and n is the number of control points; cond (g) is a curvature constraint condition of the layered curved surface, and f (g) is an overhanging angle evaluation function expressed as:
wherein m is the total number of vertexes at the boundary of the three-dimensional model to be printed; x is x i Is the overhanging angle factor at the ith vertex of the boundary, expressed as
Wherein θ o For the angle of overhang at the currently calculated vertex, θ t Is a preset critical overhang angle; s is(s) max The maximum value of the smoothing factors in all vertexes in the current printing direction vector field G; s is(s) mean The average value of the smoothing factors of all vertexes in the current printing direction vector field G; alpha is penalty coefficient, alpha is [0,1 ]]。
Further, a model building module is used for building an optimization model about the control points:wherein (1)> For the printing direction angle at the control point +.>The printing direction angle of the mth control point is the number of control points, and n is the number of control points; cond (g) is a curvature constraint condition of the layered curved surface, and f (g) is an overhanging angle evaluation function expressed as:
wherein m is the total number of vertexes at the boundary of the three-dimensional model to be printed; x is x i Is the overhang angle factor at the ith vertex of the boundary; s is(s) max The maximum value of the smoothing factors in all vertexes in the current printing direction vector field G; s is(s) mean The average value of the smoothing factors of all vertexes in the current printing direction vector field G; one vertex v in a polyhedral mesh i Is the smoothness factor s of (2) i Expressed as:
wherein N (i) represents vertex v i The polygon unit and vertex v i A set of another vertex of the same edge, v j Represents a vertex, w, in N (i) ij Weight coefficient representing edge ij, n i Representing vertex v i Direction vector n of (2) j Representing vertex v j Is a vector of the direction of (2); alpha is penalty coefficient, alpha is [0,1 ]]。
Further, the model building module is configured to build an optimization model regarding the control points:wherein (1)> For the printing direction angle at the control point +.>The printing direction angle of the mth control point is the number of control points, and n is the number of control points; cond (g) is a layered curved surface curvature constraint, expressed as:
wherein H is the average curvature field of the layered curved surface, expressed asR is a preset minimum allowable curvature radius; f (g) is the overhang angle evaluation function.
And the averaging module is used for averaging the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G which is distributed on the polyhedral grid and corresponds to the printing direction vector field G.
Further, the averaging module is configured to solve a laplace equation Δg=0 by using the print direction angle G at the control point as a Dirichlet boundary condition, so as to average the print direction angle G at the control point to the whole to-be-printed stereoscopic model to obtain a print direction vector field G distributed on the polyhedral grid corresponding to G.
The solving module is used for iteratively solving the optimization model to obtain the control point prescription direction angle G which minimizes the overhanging angle evaluation function f (G) under the condition of meeting the layered curved surface curvature constraint condition cond (G) and the optimal printing direction vector field G which is distributed on the whole three-dimensional model to be printed and corresponds to the control point prescription direction angle G 0 。
Further, the solving module is used for iteratively solving the optimization model by adopting a genetic algorithm to obtain a control point prescription direction angle G which enables the overhanging angle evaluation function f (G) to be minimum under the condition that the layered curved surface curvature constraint condition cond (G) is met and an optimal printing direction vector field G which is distributed on the whole three-dimensional model to be printed and corresponds to the control point prescription direction angle G 0 。
A slicing module for obtaining vector field G along the optimal printing direction 0 The monotonically increasing distance scalar field phi, and the isosurface 2 fitted by the distance scalar field phi is the printing curved surface slice layer.
Further, the slicing module is used for obtaining the optimal direction field G 0 Substituted Poisson equation L c Φ＝DivG 0 Solving to obtain vector field G along the optimal printing direction 0 The monotonically increasing distance scalar field phi, and the isosurface 2 fitted by the distance scalar field phi is the printing curved surface slice layer.
A further embodiment of the present invention provides a server including: memory and a processor.
The memory is used for storing program instructions.
The processor is configured to execute program instructions in the server, so that the server executes the multi-axis supportless 3D printing curved surface slicing method.
Still another embodiment of the present invention provides a computer readable storage medium, where executable instructions are stored, where the computer is capable of implementing the above-mentioned multi-axis supportless 3D printing curved surface slicing method when executing the executable instructions.
The storage medium includes, but is not limited to, a random access Memory (English: random Access Memory; RAM), a Read-Only Memory (ROM), a Cache Memory (English: cache), a Hard Disk (English: hard Disk Drive; HDD), or a Memory Card (English: memory Card). The memory may be used to store computer program instructions.
Although the present application provides method operational steps as an example or flowchart, more or fewer operational steps may be included based on conventional or non-inventive labor. The order of steps recited in the present embodiment is only one way of performing the steps in a plurality of steps, and does not represent a unique order of execution. When implemented by an actual device or client product, the method of the present embodiment or the accompanying drawings may be performed sequentially or in parallel (e.g., in a parallel processor or a multithreaded environment).
The apparatus or module set forth in the above embodiments may be implemented in particular by a computer chip or entity, or by a product having a certain function. For convenience of description, the above devices are described as being functionally divided into various modules, respectively. The functions of the various modules may be implemented in the same piece or pieces of software and/or hardware when implementing the present application. Of course, a module that implements a certain function may be implemented by a plurality of sub-modules or a combination of sub-units.
The methods, apparatus or modules of the present application may be implemented in computer readable program code means and in any suitable manner, for example, the controller may take the form of, for example, a microprocessor or processor and a computer readable medium storing computer readable program code (e.g., software or firmware) executable by the (micro) processor, logic gates, switches, application specific integrated circuits (english: application Specific Integrated Circuit; abbreviated: ASIC), programmable logic controllers and embedded microcontrollers, examples of which include, but are not limited to, the following microcontrollers: ARC 625D, atmel AT91SAM, microchip PIC18F26K20, and Silicone Labs C8051F320, the memory controller may also be implemented as part of the control logic of the memory. Those skilled in the art will also appreciate that, in addition to implementing the controller in a pure computer readable program code, it is well possible to implement the same functionality by logically programming the method steps such that the controller is in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc. Such a controller can be regarded as a hardware component, and means for implementing various functions included therein can also be regarded as a structure within the hardware component. Or even means for achieving the various functions may be regarded as either software modules implementing the methods or structures within hardware components.
Some of the modules of the present apparatus may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, classes, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
From the description of the embodiments above, it will be apparent to those skilled in the art that the present application may be implemented in software plus necessary hardware. Based on such understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art in the form of a software product, or may be embodied in the implementation of data migration. The computer software product may be stored on a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., comprising instructions for causing a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to perform the methods of the various embodiments or portions of the embodiments herein.
In this specification, each embodiment is described in a progressive manner, and the same or similar parts of each embodiment are referred to each other, and each embodiment is mainly described as a difference from other embodiments. All or portions of the present application can be used in a number of general purpose or special purpose computer system environments or configurations. For example: personal computers, server computers, hand-held or portable devices, tablet devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like.
The above embodiments are only for illustrating the technical solution of the present application, and not for limiting the present application; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced with equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions.

Claims (10)

1. A multi-axis unsupported 3D printed curved surface slicing method, comprising:
dividing a stereoscopic model to be printed into polyhedral grids with a plurality of polyhedral units;
randomly selecting a plurality of vertexes in the polyhedral grid as control points;
establishing an optimization model about the control points:
wherein,, to control the print direction angle at the point,the printing direction angle of the mth control point is the printing direction angle of the mth control point, and n is the number of the control points; cond (g) is a layered curved surface curvature constraint condition, and f (g) is an overhanging angle evaluation function;
solving a Laplace equation DeltaG=0 by taking the printing direction angle G at the control point as a Dirichlet boundary condition so as to average the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G;
iteratively solving the optimization model to obtain a control point prescription directional angle G which minimizes the overhanging angle evaluation function f (G) under the condition that the layered curved surface curvature constraint condition cond (G) is satisfied and an optimal printing direction vector field G distributed on the whole three-dimensional model to be printed corresponding to the control point prescription directional angle G 0 ；
Obtaining a vector field G along the optimal printing direction 0 And a monotonically increasing distance scalar field phi, wherein an isosurface fitted by the distance scalar field phi is the printed curved surface slice layer.
2. The multi-axis supportless 3D printing curved surface slicing method of claim 1, wherein the overhanging angle evaluation function f (g) is expressed as:
wherein m is to be beatenPrinting the total number of vertexes at the boundary of the three-dimensional model; x is x i Is the overhang angle factor at the ith vertex of the boundary; s is(s) max The maximum value of the smoothing factors in all vertexes in the current printing direction vector field G; s is(s) mean The average value of the smoothing factors of all vertexes in the current printing direction vector field G; alpha is penalty coefficient, alpha is [0,1 ]]。
3. The multi-axis supportless 3D printing surface slicing method of claim 2, wherein the overhanging angle factor x at the ith vertex of the boundary i Expressed as:
wherein θ o For the angle of overhang at the currently calculated vertex, θ t Is a preset critical overhang angle.
4. A multi-axis supportless 3D printing surface slicing method as in claim 2 or 3, wherein one vertex v in the polyhedral grid i Is the smoothing factor s of (1) i Expressed as:
wherein N (i) represents vertex v i The polygon unit and vertex v i A set of other vertices of the same edge; v j Represents a vertex in N (i); w (w) ij A weight coefficient representing the edge ij; n is n i Representing vertex v i Is a vector of the direction of (2); n is n j Representing vertex v j Is a direction vector of (a).
5. The multi-axis unsupported 3D printed curved surface slicing method of claim 1, wherein the layered curved surface curvature constraint cond (g) is expressed as:
wherein H is the average curvature field of the layered curved surface, expressed asR is a preset minimum allowable radius of curvature.
6. The multi-axis, unsupported, 3D printed curved surface slicing method of claim 1, wherein the iteratively solving an optimization model comprises: and adopting a genetic algorithm to iteratively solve the optimization model.
7. The multi-axis supportless 3D printing curved surface slicing method of claim 1, wherein said obtaining a vector field G along said optimal printing direction 0 A monotonically increasing distance scalar field Φ comprising: the obtained optimal direction field G 0 Substituted Poisson equation L c Φ＝DivG 0 Solving to obtain a vector field G along the optimal printing direction 0 Monotonically increasing distance scalar field Φ.
8. A multi-axis unsupported 3D printing curved surface slicing device, comprising:
the grid dividing module is used for dividing the stereoscopic model to be printed into polyhedral grids with a plurality of polyhedral units;
a selecting module, configured to randomly select a plurality of vertices in the polyhedral mesh as control points;
a model building module for building an optimization model for the control points:wherein (1)> For the printing direction angle at the control point +.>The printing direction angle of the mth control point is the printing direction angle of the mth control point, and n is the number of the control points; cond (g) is a layered curved surface curvature constraint condition, and f (g) is an overhanging angle evaluation function;
the average module is used for solving a Laplace equation DeltaG=0 by taking the printing direction angle G at the control point as a Dirichlet boundary condition so as to average the printing direction angle G at the control point to the whole three-dimensional model to be printed to obtain a printing direction vector field G distributed on the polyhedral grid corresponding to G;
the solving module is used for iteratively solving the optimization model to obtain the control point prescription direction angle G which minimizes the overhanging angle evaluation function f (G) under the condition of meeting the layered curved surface curvature constraint condition cond (G) and the optimal printing direction vector field G which is distributed on the whole three-dimensional model to be printed and corresponds to the control point prescription direction angle G 0 ；
A slicing module for obtaining vector field G along the optimal printing direction 0 And a monotonically increasing distance scalar field phi, wherein an isosurface fitted by the distance scalar field phi is the printed curved surface slice layer.
9. A server, comprising: a memory and a processor;
the memory is used for storing program instructions;
the processor is configured to execute program instructions in a server, causing the server to perform the multi-axis supportless 3D printing curved surface slicing method of any of claims 1-7.
10. A computer-readable storage medium storing executable instructions that when executed by a computer enable the multi-axis supportless 3D printing curved surface slicing method of any of claims 1-7.
CN202210027787.5A 2022-01-11 2022-01-11 Multi-axis unsupported 3D printing curved surface slicing method, device and server Active CN114474741B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210027787.5A CN114474741B (en) 2022-01-11 2022-01-11 Multi-axis unsupported 3D printing curved surface slicing method, device and server

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210027787.5A CN114474741B (en) 2022-01-11 2022-01-11 Multi-axis unsupported 3D printing curved surface slicing method, device and server

Publications (2)

Publication Number Publication Date
CN114474741A CN114474741A (en) 2022-05-13
CN114474741B true CN114474741B (en) 2023-07-21

Family

ID=81512568

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210027787.5A Active CN114474741B (en) 2022-01-11 2022-01-11 Multi-axis unsupported 3D printing curved surface slicing method, device and server

Country Status (1)

Country Link
CN (1) CN114474741B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115630412B (en) 2022-10-25 2023-04-28 浙江大学 Self-supporting structure optimal design and manufacturing method based on multi-axis 3D printing
CN117301527B (en) * 2023-10-30 2024-04-05 科路睿(天津)生物技术有限公司 Single-path slicing method and printing method for four-axis 3D printing sheet model

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110210122A (en) * 2019-05-30 2019-09-06 华南理工大学 A kind of boundary coloring width confining method of Cont of Color Slice layer

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9928663B2 (en) * 2015-07-27 2018-03-27 Technische Universiteit Delft Skeletal joint optimization for linear blend skinning deformations utilizing skeletal pose sampling
CN106079433B (en) * 2016-05-31 2018-04-17 西北工业大学 The soft stud 3D printing methods of turbo blade Tao Xin
EP3647973A1 (en) * 2018-11-04 2020-05-06 Dassault Systèmes Designing a mechanical part with topology optimization
US11016470B2 (en) * 2018-11-09 2021-05-25 Autodesk, Inc. Conversion of mesh geometry to watertight boundary representation
US10948237B2 (en) * 2019-03-14 2021-03-16 Raytheon Technologies Corporation Method of creating a component via transformation of representative volume elements
CN110765506B (en) * 2019-09-30 2023-03-31 杭州电子科技大学上虞科学与工程研究院有限公司 Multi-resolution equal-geometric topological optimization method of solid model
US11465361B2 (en) * 2020-03-27 2022-10-11 Wisconsin Alumni Research Foundation Systems, methods, and media for controlling support structures and build orientation in manufacturing
CN112132968B (en) * 2020-08-25 2023-08-08 山东大学 Two-scale periodic lattice self-adaptive filling and modeling method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110210122A (en) * 2019-05-30 2019-09-06 华南理工大学 A kind of boundary coloring width confining method of Cont of Color Slice layer

Also Published As

Publication number Publication date
CN114474741A (en) 2022-05-13

Similar Documents

Publication Publication Date Title
Xu et al. Curved layer based process planning for multi-axis volume printing of freeform parts
Wu et al. RoboFDM: A robotic system for support-free fabrication using FDM
CN114474741B (en) Multi-axis unsupported 3D printing curved surface slicing method, device and server
Dai et al. Support-free volume printing by multi-axis motion
CN110555285B (en) Full-automatic generation method for surface structure grid of complex aircraft
Taufik et al. Role of build orientation in layered manufacturing: a review
Canellidis et al. Genetic-algorithm-based multi-objective optimization of the build orientation in stereolithography
EP1804146B1 (en) Head assignment modeling and simulation for a Multiple Head Tape Lamination Machine.
Canellidis et al. Efficient parts nesting schemes for improving stereolithography utilization
CN106650147B (en) A kind of non-probability Topology Optimization Method of Continuum Structure based on uncertain but bounded
US7769481B2 (en) Head assignment system and method
CN104331933B (en) A kind of fabrication orientation self adaptation fast selecting method
US20220203621A1 (en) Method for the Lightweighting and/or Designing of an Additively Manufactured Article
Zhu et al. Design of lightweight tree-shaped internal support structures for 3D printed shell models
Lu et al. Smoothing rotary axes movements for ball-end milling based on the gradient-based differential evolution method
Feng et al. Curved-layered material extrusion modeling for thin-walled parts by a 5-axis machine
Zhou et al. A path planning method of lattice structural components for additive manufacturing
Gibson et al. Software for additive manufacturing
Zhang et al. A unit sphere discretization and search approach to optimize building direction with minimized volumetric error for rapid prototyping
Tang et al. A review of multi-axis additive manufacturing: potential, opportunity and challenge
Guo et al. Multi-orientation optimization of complex parts based on model segmentation in additive manufacturing
CN114407350B (en) Continuous fiber reinforced composite material 3D printing filling path planning method and device
S. Pande et al. A generative process planning system for parts produced by rapid prototyping
Luo et al. Optimal tool orientation generation and chip volume/cutting force predictions for 5-axis CNC machining of curved surfaces using flat-end mills
Chen et al. An automatic optimization method for minimizing supporting structures in additive manufacturing

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant