CN115709567A - Three-dimensional printing path planning method and system based on free-form surface slicing - Google Patents
Three-dimensional printing path planning method and system based on free-form surface slicing Download PDFInfo
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Abstract
The invention discloses a three-dimensional printing path planning method and a system based on free-form surface slicing, wherein the method comprises the following steps: taking the ratio of the pressurizing deformation quantity of each layer of material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer as the gravity settling influence weight of each layer of material beam, taking the extrusion time of each layer of material beam to the material beam on the lower layer as the material beam hardening time weight of each layer of material beam, and dividing the three-dimensional printing model into a plurality of free-form surface sliced layers from the longitudinal direction according to the product of the gravity settling influence weight of each layer of material beam and the material beam hardening time weight; and carrying out curved surface discretization on each curved surface sliced layer to obtain a discrete point set of each free curved surface sliced layer, selecting discrete points in the discrete point set of each curved surface sliced layer by taking the shortest path as a target to form a printing path, and connecting the printing paths of all the free curved surface sliced layers to form a three-dimensional printing path. The printing precision of the curved surface component is ensured by reducing the influence of the step effect and the gravity on the model.
Description
Technical Field
The invention belongs to the field of additive manufacturing, and particularly relates to a three-dimensional printing path planning method and system based on free-form surface slicing.
Background
The 3D printing technology can be widely applied to various fields because the conversion from model design to finished product production can be quickly realized. The 3D printing technology is applied to the manufacture of complex models with structural characteristics such as free-form surfaces and the like, and for example, the 3D building printing technology has unique advantages in customized scenes such as landscape construction and ancient building restoration. However, in the 3D printing technology at the present stage, due to the influence of the hardening performance of the printing material and the gravity extrusion phenomenon, the problems of the step effect and the like limit the conversion of the personalized and artistic design into an actual product.
The principle of the existing curved surface component slicing and path planning technology is generally based on a horizontal layer-by-layer accumulation technology in traditional 3D printing, and the layer heights of different areas of each sliced layer are adjusted on the basis of horizontal layer-by-layer slicing and path planning, so that the similar curved surface slicing and path planning of a model are realized. However, this method cannot ensure the reasonability of slice design and the surface precision after machining.
The method mainly comprises two modes for the current curved surface path planning method, one mode is that the thickness of a sliced layer is changed by adjusting the flow of an extruded material beam on a horizontal plane substrate through a traditional slicing and path planning algorithm, and the printing work of the curved surface structure is realized. The other mode is that a mechanical arm is matched with a three-axis platform, one drives the extrusion material beam, and the other adjusts the horizontal plane substrate platform to rotate around an Euler angle, so that each time the nozzle prints, the nozzle prints are perpendicular to the tangential direction of the current path to be printed. However, in the case that the material beam is solidified slowly and thick, the method may cause the structure to deform obviously and even cause printing failure because the material beam is not solidified yet in the printing process.
Therefore, the technical problems that the curved surface model is deformed by gravity extrusion, the material beam is not solidified, the structure is obviously deformed, and the printing precision is low exist in the conventional curved surface path planning technology.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a three-dimensional printing path planning method and a three-dimensional printing path planning system based on free-form surface slicing, so that the technical problems that a curved surface model is extruded and deformed by gravity, a material beam is not solidified yet, the structure is obviously deformed, and the printing precision is low in the conventional curved surface path planning technology are solved.
To achieve the above object, according to an aspect of the present invention, there is provided a three-dimensional printing path planning method based on a free-form surface slice, including the steps of:
(1) Taking the ratio of the pressurizing deformation quantity of each layer of material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer as the gravity settling influence weight of each layer of material beam, taking the extrusion time of each layer of material beam to the material beam on the lower layer as the material beam hardening time weight of each layer of material beam, and dividing the three-dimensional printing model into a plurality of free-form surface sliced layers from the longitudinal direction according to the product of the gravity settling influence weight of each layer of material beam and the material beam hardening time weight;
(2) And carrying out curved surface discretization on each free-form surface sliced layer to obtain a discrete point set of each free-form surface sliced layer, selecting discrete points in the discrete point set of each free-form surface sliced layer by taking the shortest path as a target to form a printing path of each free-form surface sliced layer, and connecting the printing paths of all the free-form surface sliced layers to form a three-dimensional printing path.
Further, the step (1) includes:
dividing the three-dimensional printing model into a plurality of vertical analysis units in the longitudinal direction;
the method comprises the steps that a vertical analysis unit is pre-divided into a plurality of cuboids with equal intervals from bottom to top, for the first cuboid, the ratio of the compression deformation amount of a previous-layer material beam to the height direction of a lowest-layer material beam corresponding to the cuboid to the height of the lowest-layer material beam is used as the gravity settling influence weight of the previous-layer material beam, the extrusion time of the previous-layer material beam to the lowest-layer material beam is used as the material beam hardening time weight of the previous-layer material beam, and the height is sub-divided according to the integral of the gravity settling influence weight of the previous-layer material beam and the material beam hardening time weight;
the other parts of the first cuboid which is divided again are removed by the vertical analysis unit for re-pre-division, the ratio of the pressurizing deformation quantity of the layer of material beam corresponding to the cuboid in the height direction of all material beams at the lower layer of the cuboid to the height of all material beams at the lower layer of the cuboid is used as the gravity settling influence weight of the layer of material beam, the extrusion time of the layer of material beam to all material beams at the lower layer of the cuboid is used as the material beam hardening time weight of the layer of material beam, the vertical analysis unit is divided into a plurality of cuboids according to the integral distribution height of the gravity settling influence weight of the layer of material beam and the material beam hardening time weight, and the height of the vertical analysis unit is divided into a plurality of cuboids;
and splicing the central points of the cuboids in all the vertical analysis units from bottom to top to form a plurality of free-form surface sliced layers.
Further, the height of the subdivided cuboid is:
wherein k is the number of the re-divided cuboids above the re-divided cuboid, h D Height of subdivided cuboid,. DELTA.Hg i Is the gravity sedimentation influence weight, delta T, of the ith layer of the material bundle i And D is the diameter of the printing nozzle.
Further, the height of the pre-divided cuboid is as follows: the diameter of the printing nozzle is as follows: the ratio of the height of the vertical analysis unit to the diameter of the printing nozzle, and the height of the cuboid pre-divided again is as follows: printing the diameter of the spray head, wherein the number of the cuboid subjected to pre-segmentation again is as follows: the vertical analysis unit removes a ratio of a height of the other portion of the first rectangular parallelepiped to a diameter of the print head which is subdivided.
Further, the specific way of the curved surface discretization is as follows:
describing the free-form surface sliced layer as a curved surface constructed by a plurality of curves in the u and v directions;
the coordinates in the v direction on the curved surface are made to be the same, interpolation is carried out in the u direction to obtain a u-direction parameter line, the coordinates in the u direction on the curved surface are made to be the same, and interpolation is carried out in the v direction to obtain a v-direction parameter line;
all the intersection points of all the parameter lines in the u direction and the v direction form a discrete point set of the free-form surface sliced layer;
and performing curved surface discretization on the free curved surface sliced layers from bottom to top layer by layer to obtain discrete point sets of the free curved surface sliced layers.
Further, the interval during interpolation is the extrusion width l of the material beam D ，
Further, the printing paths of the free-form surface sliced layers corresponding to the upper top surface and the lower bottom surface in the three-dimensional printing model are formed in the following modes:
setting the current point as i and the last step as search direction
The search direction deflection angle θ of the next target point is:
θ＝arccosθ
multiplying the search direction deflection angle theta of the next target point by the weight coefficient omega, and calculating the distance D between the current point and the next target point after the search direction correction next ：
Wherein, d next Is the straight-line distance between the current point and the candidate target point,
searching direction for the next step;
selecting D in discrete point set of free-form surface sliced layer next The smallest point is taken as the next target point;
and sequentially connecting all target points from the discrete points of the free-form surface sliced layer to the starting point to the end point to form a printing path.
Further, the printing path of the free-form surface sliced layer corresponding to the middle layer of the three-dimensional printing model is composed in the following mode:
the shortest path is taken as a target, the rotation angle is limited to be 60-120 degrees, the length from the printing nozzle to the material beam section before the nozzle turns is limited to be more than 10 times of the diameter of the printing nozzle, discrete points are selected from the discrete points of the free-form surface slice layer in a concentrated mode, and the printing path of the free-form surface slice layer is formed.
Further, the step (2) further comprises:
detecting whether a cross point exists in the printing path in each free-form surface sliced layer, if so, exchanging the end point of the first section of path in two cross path sections corresponding to the cross point with the start point of the second section of path to generate a printing path for eliminating the local cross point, and if not, connecting the start point of the printing path of the free-form surface sliced layer i with the end point of the printing path of the free-form surface sliced layer i-1 to form a three-dimensional printing path, wherein i is more than or equal to 2.
According to another aspect of the present invention, there is provided a three-dimensional printing path planning system based on free-form surface slices, comprising:
the model slicing module is used for taking the ratio of the pressurizing deformation quantity of each layer of material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer as the gravity sedimentation influence weight of each layer of material beam, taking the extrusion time of each layer of material beam to the material beam on the lower layer as the material beam hardening time weight of each layer of material beam, and dividing the three-dimensional printing model into a plurality of free-form surface slicing layers from the longitudinal direction according to the product of the gravity sedimentation influence weight of each layer of material beam and the material beam hardening time weight;
the curved surface layer discrete module is used for performing curved surface discrete on the respective curved surface sliced layers to obtain discrete point sets of the free curved surface sliced layers;
and the path planning module is used for selecting discrete points in the discrete point set of each free-form surface sliced layer by taking the shortest path as a target, forming the printing paths of each free-form surface sliced layer and connecting the printing paths of all the free-form surface sliced layers to form a three-dimensional printing path.
In general, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:
(1) The method considers the influence of gravity action and curvature of the curved surface of the printing curved surface structure, the curved surface model is subjected to gravity extrusion deformation, the ratio of the pressurizing deformation amount of the material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer is used as the gravity settling influence weight of the material beam, the extrusion time of the material beam to the material beam on the lower layer is used as the material beam hardening time weight when the free curved surface is sliced, the gravity settling influence weight and the material beam hardening time weight are introduced, and the phenomenon that the model is subjected to gravity extrusion deformation and the material beam is not solidified to cause the obvious deformation of the structure during path planning can be avoided. The continuous, smooth and compact path planning on the free-form surface sliced layer is realized, the influence of the step effect and the gravity on a printed piece is reduced, and the printing precision of the curved surface component is ensured.
(2) The three-dimensional printing model is divided into a plurality of vertical analysis units in the longitudinal direction, each vertical analysis unit is pre-divided, in order to obtain the number of approximate material beams on the vertical analysis unit, then the weight of gravity sedimentation influence and the weight of material beam hardening time are introduced for segmentation, the interior of the model is subjected to gridding division treatment by combining material deformation and a gravity field, and the profile of each slice layer is formed from bottom to top according to grids, so that the inconsistency between the gravity sedimentation influence and the material beam hardening time of each position in a free-form surface slice layer is fully considered.
(3) Pre-dividing a vertical analysis unit, and for a first cuboid, performing re-division according to the integral distribution height of the gravity sedimentation influence weight and the material beam hardening time weight; and re-pre-dividing other parts of the vertical analysis unit except the first re-divided cuboid, and re-dividing the first re-pre-divided cuboid from bottom to top, wherein the slicing mode of layer by layer is that the diameter of a discharge port of the printing spray head is constant, and the thickness of a layer of slices which can be printed is constant, so that the slices are sliced layer by layer. Meanwhile, the reason for slicing the free-form surface from bottom to top in a layering manner is that due to the influence of gravity settling weight, the gravity settling effect is different at different positions of curvature in the free-form surface slicing, and the curvature can be changed after printing. The curvature of the current sliced layer and the curvature of the later sliced layer are changed, so that the curvature dispersion of the later sliced layer needs to be carried out again, the curved surface dispersion is carried out on the respective curved surface sliced layers from bottom to top layer by layer, the individualized analysis can be better carried out on the sliced layers, the model printing precision is higher, and the actual printing model is closer to a model file.
(4) The surface slicing layer, namely the upper surface layer and the lower surface layer, can be seen by naked eyes, the path planning of the surface layer is better to have stronger regularity and is more attractive from the viewpoint of attractiveness, and the path planning of the surface layer is ensured to be closer to the shape of the outer surface of the model from the viewpoint of printing precision, so that the existence of corners is reduced, and the filling density is increased. The inertial link search algorithm is adopted for path planning, so that the precision and the attractiveness of a surface layer can be guaranteed.
(5) The middle layer slicing layer is also the internal structure of the model, the partial structure mainly influences the structural strength of the model after printing, the structural strength in a certain direction is lower due to the fact that route planning with too strong regularity is carried out, a corner link searching algorithm is introduced, improvement is carried out on the basis of the traditional GASA algorithm, route searching is carried out according to the shortest route principle, due to the fact that searching is only carried out according to the shortest route principle, the situations that the corners of the route are too many, the situations that line segments are short are more, and smooth printing of printing equipment is not facilitated. Therefore, three constraints are introduced on the basis, namely the angle of the corner is limited (the angle range is preferably between 60 and 120 degrees), the limitation of the length factor of the path section is limited (namely when one printing path section sprays the material beam from the printing nozzle, the length of the material beam section before the corner appears in the printing path of the nozzle is preferably more than 10 times of the diameter of the nozzle, so that the stable forming of the material beam is facilitated), and the limitation of the number of the corners is that the number of the corners can be greatly reduced under the action of the angle of the corner and the length factor of the path section. Such an internal structure can increase its structural strength, guaranteeing the structural strength of the whole model.
Drawings
Fig. 1 is a flowchart of a three-dimensional printing path planning method based on a free-form surface slice according to an embodiment of the present invention;
FIG. 2 (a) is a schematic diagram of a free-form surface substrate physical model provided by an embodiment of the present invention;
fig. 2 (b) is a schematic diagram of three-dimensional reconstruction of a free-form surface substrate according to an embodiment of the present invention;
fig. 3 (a) is a schematic diagram of a slice world coordinate system construction provided by an embodiment of the present invention;
fig. 3 (b) is a schematic diagram of an actual slicing effect of the model provided by the embodiment of the present invention;
fig. 4 is a schematic diagram illustrating a principle of surface discretization of a free-form surface sliced layer according to an embodiment of the present invention;
fig. 5 (a) is a schematic diagram illustrating an example of curvature analysis of a sliced layer provided by an embodiment of the present invention;
fig. 5 (b) is a schematic diagram of a slice-level discrete point set provided by an embodiment of the present invention;
FIG. 6 is a schematic diagram of a path planning workflow of an inertial link search algorithm according to an embodiment of the present invention;
FIG. 7 (a) is a schematic diagram of a path planning simulation of an inertial link search algorithm according to an embodiment of the present invention;
FIG. 7 (b) is a schematic diagram of the effect of the inertial link search algorithm on 3D printing of the actual model according to the embodiment of the present invention;
fig. 8 (a) is a schematic diagram of a path planning simulation of a corner link search algorithm according to an embodiment of the present invention;
fig. 8 (b) is a schematic diagram of an effect of a 3D printing actual model by a corner link search algorithm according to an embodiment of the present invention;
fig. 9 is a schematic diagram of a 3D printed finished model according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a method for planning a three-dimensional printing path based on a free-form surface slice includes:
(1) Taking the ratio of the pressurizing deformation quantity of each layer of material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer as the gravity settling influence weight of each layer of material beam, taking the extrusion time of each layer of material beam to the material beam on the lower layer as the material beam hardening time weight of each layer of material beam, and dividing the three-dimensional printing model into a plurality of free-form surface sliced layers from the longitudinal direction according to the product of the gravity settling influence weight of each layer of material beam and the material beam hardening time weight;
(2) And carrying out curved surface discretization on each free-form surface sliced layer to obtain a discrete point set of each free-form surface sliced layer, selecting discrete points in the discrete point set of each free-form surface sliced layer by taking the shortest path as a target to form a printing path of each free-form surface sliced layer, and connecting the printing paths of all the free-form surface sliced layers to form a three-dimensional printing path.
Example 1
A three-dimensional printing path planning method based on free-form surface slices comprises the following steps:
fig. 2 (a) is a schematic diagram of a point cloud for three-dimensional reconstruction of a free-form surface substrate, and fig. 2 (b) is a schematic diagram of a point cloud for three-dimensional reconstruction of a free-form surface substrate.
And placing the model on a free-form surface substrate, and setting a point cloud model of the free-form surface substrate as a lower bottom boundary of the model to be printed to form a final actual printing model.
Gridding the actual printing model in the vertical direction, and introducing gravity settlement weight delta Hg i . As shown in fig. 3 (a), a coordinate system is established on the plane where the highest point of the model is located, and the positive direction of the z-axis is vertically and horizontally downward. According to different height differences delta h of the upper top surface and the lower bottom surface of different areas, each vertical analysis unit is divided into i grids, and the central points of the ith grids in each vertical direction are spliced from bottom to top to form i free-form surface slice layers. Fig. 3 (b) is a diagram showing the actual effect of the curved surface slice.
Specifically, the method comprises the following steps: establishing a world coordinate system at the highest point of the model, constructing a model bounding box, dividing the bounding box into n x n compact grids in the horizontal direction (n represents the number of unidirectional grids, and the value of n is determined by compactness), longitudinally cutting the compact grids, and dividing the printing model into n 2 A vertical analysis unit.
Introduction of gravity sedimentation weight DeltaHg i And a beam hardening time weight Δ T i . Gravity sedimentation weight Δ Hg i Namely the weight of the gravity settlement influence of the material beam of the ith layer above the current layer on the material beam of the current layer. Beam hardening time weight Δ T i I.e. the weight of the beam hardening time after the current beam printing.
And carrying out unequal height division on each vertical analysis unit of the model. The specific method comprises the following steps: the height difference between the upper top surface and the lower bottom surface in the vertical analysis unit is delta h, and all vertical directions are pre-divided into n cuboids from bottom to top by the diameter D of the printing spray head.
And (4) subdividing the height of the 1 st cuboid according to the gravity settling weight and the beam hardening time weight. The method comprises the following specific steps:
wherein h is D I.e. the height of the 1 st cuboid subdivision, l D To redistribute the extruded width of the strand. Delta Hg i And Δ T i The gravity settling weight and the strand hardening time weight of the ith cube on the 1 st cuboid. For the other cuboids except the first cuboid of the vertical analysis unit, the cuboid needs to be pre-divided again, and the height difference is changed from delta h to delta h' = delta h-h D ，
And then, re-segmenting the first cuboid from bottom to top after re-pre-segmentation to obtain the re-segmentation height. And by analogy, n + k cuboids after the subdivision in the vertical analysis unit are obtained, and k is the number of the cuboids increased after the repeated subdivision.
And after each vertical analysis unit is analyzed, splicing the ith cuboid central point in each vertical direction from bottom to top to form i free-form surface sliced layers. The upper top surface and the lower bottom surface are fixed slicing layers and cannot be changed, and the surface precision and integrity of the printed model are guaranteed.
The basis of the weight distribution of the beam hardening time is determined according to the material characteristics, and corresponding hardening time analysis needs to be carried out in advance for different printing materials used in different printing scenes. The gravity settling weight is based on the hardening time of the material beam and the printing time of the model, after the current material beam is sprayed out, the printing path of how many layers are planned, and before the current material beam is not completely hardened, the newly printed material beam layer on the current material beam layer can have the gravity extrusion effect on the layer.
These two parameters need to be weighted accordingly for different material run times. Such as concrete material for experimentThe material, which solidifies at a slow rate and requires 2 hours to close to solidification without deformation, is subjected to a gravity squeeze action on the layer of the bundle printed at its vertical height within two hours. The material of the concrete formula needs to be subjected to a gravity extrusion test in advance, a plurality of layers of material bundles are printed on one material bundle to obtain the compression deformation quantity delta x of the material bundles with different heights to the lowest fabric bundle in the height direction, and then the original height x is divided by the delta x to obtain the gravity settlement weight delta Hg of the material bundle layers with different heights to the lowest fabric bundle i . The weight Δ Ti of the beam hardening time in the slice refers to the extrusion time of the plurality of printed beams to the lowest beam, for example, from bottom to top, the lowest beam is a 1-layer beam and a 2-layer beam, the extrusion time of the 2-layer beam to the 1-layer beam is 1 hour and 50 minutes, and the extrusion time of the n-layer beam to the 1-layer beam is 20 minutes (namely, when the uppermost beam is printed, the lowest beam is close to solidification, so only a small time is available for extrusion of the beam), so the remaining time Δ T of the 1-layer beam from solidification when the n-layer beam is printed is obtained by dividing the Δ T by the total solidification time T (2 hours), and the weight Δ T of the n-layer beam to the 1-layer beam hardening time weight Δ T is obtained i . According to two weight parameters obtained by experiments, corresponding additional weight is carried out when the model is printed for the printing material, and the extrusion height of a material bundle on the material bundle becomes h D 。
And performing curved surface dispersion on the respective curved surface sliced layers, specifically:
and (2) performing mathematical expression of the free-form surface slice layer i by NURBS, wherein the free-form surface can be regarded as a result of multiple construction of a plurality of curves in u and v directions, and a control point network of the free-form surface slice layer i is composed of (m + 1) × (n + 1) points. And (3) setting the free-form surface sliced layer i as a curved surface with p × q times, and expressing the curved surface as a two-parameter segmentation rational vector function:
where i, j are weights, P i，j For two-dimensional control of point grids, N i，p (u) and N i，q (v) Two are the p-th and q-th basis functions, respectively.
Calculating the curvature radius of each point of the curved surface, wherein the formula of the curvature radius of a certain point is as follows:
where H and K represent the average curvature and gaussian curvature of the corresponding dots on the printed surface, which can be represented by E, F, G and L, M, N, respectively. E. F, G are three coefficients of the first basic form in the differential geometry in mathematics, and L, M, N are three coefficients of the second basic coefficient in the differential geometry.
The normal direction of each point on the curved surface can be calculated according to the curvature value of each point, and the value is the normal direction of the movement of the printing nozzle, so that the problem of interference between the nozzle and the curved surface caused by non-perpendicularity is avoided. Calculating the extrusion width l of the extruded material beam according to the weight of the hardening time of the material beam, the weight of gravity settlement and the diameter of a spray head of the printing equipment in the model slice D . Besides the point space coordinate parameters, each point on the curved surface is additionally provided with three parameter values of the normal direction of the nozzle printing, the extrusion width and the vertical height.
Dispersing the free-form surface slice layer by adopting an isoparametric method, and enabling v = v on the curved surface layer i (u, v) e And carrying out interpolation and densification in the u direction to obtain a unidirectional point set, grouping and connecting the nearest points in the point set to obtain a series of u-direction parameter lines, wherein the NURBS of the initial parameter line is expressed as S (u, 0), and the termination parameter line is S (u, 1). Let u = u again e And interpolating the v direction, obtaining a v-direction parameter line set after connecting lines, wherein NURBS of the initial parameter line is expressed as S (0, v), and the termination parameter line is expressed as S (1, v). Wherein the interpolated distance Deltax is the calculated final strand extrusion width l D The difference interval is influenced by gravity settling weight and material beam hardening time weight, and the diameter of the material beam sprayed by the spray head is changed by gravity extrusionStrand width, which is the differential spacing).
The number of the discrete point concentration points is determined according to the diameter of the printing nozzle (because the diameter after gravity extrusion is close to the diameter of the nozzle and cannot exceed the order of magnitude of one time), the influence factors such as the curvature, the weight and the like of a plurality of points around one point are basically the same, and therefore a plurality of points in a small range are replaced by one point through the discrete method. All the intersections of the parameter lines in the u-direction and the v-direction constitute a discrete point set of the curved layer.
Fig. 5 (a) is a diagram showing curvature analysis of each point of the entire free-form surface sliced layer i by mathematical expression of a curved surface. Fig. 5 (b) is a discrete point set of the free-form surface sliced layer i obtained by the isoparametric method according to the curvature analysis result.
The free-form surface sliced layers are divided into two categories: a surface layer and an intermediate layer.
The surface layer, namely the upper top surface and the lower bottom surface, adopts an inertial link search algorithm to plan the path, so that the planned path direction is clearer, and the precision and the attractiveness of the surface layer are ensured. As shown in fig. 6, specifically:
each neighboring point in the set of discrete points may be defined as: one of the u, v parameters of the two points is equal, while the other parameter difference is deltax, i.e. the final strand extrusion radius that each discrete point has. A search direction preference factor is introduced, i.e. an inertial search direction is set. Setting the current search to point i and the previous search direction as
The search direction bias angle theta can be calculated for the i +1 point.
θ＝arccosθ
Introducing the declination into the distance calculation with a weight ω:
wherein d is next Is the linear distance between the current point and the candidate target point, D next And the next target point distance after the search direction correction.
Iteratively searching adjacent points or directly traversing discrete point set and calculating to obtain the distance between each candidate point and the current point, and selecting the correction distance D next And the minimum point is used as the next target point, and the connection of all the points in the curved surface point set is finished by the analogy.
Fig. 7 (a) is a diagram illustrating a simulation effect of path planning for a free-form surface sliced layer i by using an inertial link search algorithm according to an embodiment of the present invention, and fig. 7 (b) is a diagram illustrating an actual 3D printing effect of a curved surface printing path planned by using an inertial link search algorithm according to an embodiment of the present invention.
The middle layer is other middle slice layers except the upper top surface and the lower bottom surface. And a corner link search algorithm is adopted to enhance the filling density and the structural strength of the middle layer. The method comprises the following specific steps:
on the basis of the restriction condition that the total path is shortest, a corner angle restriction, a corner number restriction and a path section length factor (the optimal path section length is 10 times of the path width) are introduced according to the current printing equipment condition, and a printing path with the path corner number being rapidly converged is generated. Fig. 8 (a) is a simulation effect diagram of path planning of the free-form surface sliced layer i by the corner link search algorithm, and fig. 8 (b) is an actual 3D printing effect diagram of a curved surface printing path planned according to the corner link search algorithm.
And for the free-form surface sliced layer i, a path planning path preliminarily generated by using an inertial link search algorithm and a corner link search algorithm is used for intersection point detection and intersection point solution, so that the influence of the superposition of material beams caused by the printing of intersection points in the 3D printing process on the printing precision is avoided.
Get path P to be judged 1 P 2 、Q 1 Q 2 And the following vector cross product results are calculated, respectively,
if the four normal vectors are all zero vectors, judging
And
the direction of the results of the two groups can prove that the cross point exists if the results of the two groups are homogeneous. If zero vectors are present, e.g.
Is 0, P can be proved 1 P 2 Q 1 Three points are collinear, at judgment Q 1 Whether it is located on path P 1 P 2 The above. If the two pairs of cross multiplication results are both zero vectors, P can be verified 1 P 2 Q 1 Q 2 If the four points are collinear, the starting positions of the paths at the two ends are needed to judge whether the overlapped part exists.
If the intersection exists, a method of exchanging the end point of the first section of path with the start point of the second section of path is adopted to generate a printing path { i, i + 1.. J.j +1} for eliminating local intersection. Since new intersection points may appear after local de-intersection, the combination of the detection path segments needs to be traversed again until no intersection situation exists in one complete detection traversal.
And performing path connection on the free-form surface slice layer i +1 and the free-form surface slice layer i. And for the free-form surface sliced layer i +1, the end point coordinate of the free-form surface sliced layer i is the starting point of the free-form surface sliced layer i +1, if the path planning cannot be normally realized on the free-form surface sliced layer i, the path planning is carried out on the free-form surface sliced layer i again, a new end point coordinate is generated to be used as the starting point of the free-form surface sliced layer i +1 until the path planning is realized on the free-form surface sliced layer i +1, and the free-form surface sliced layer i is completely connected with the free-form surface sliced layer i + 1. And repeating the steps until the path planning and the path connection of all the free-form surface sliced layers are finished, and generating a final complete path planning path of the whole model for the actual 3D printing of the printing equipment.
Fig. 9 shows the actual printed real effect diagram of the model complete path planning path generated by the three-dimensional printing path planning method based on the free-form surface slice according to the present disclosure.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A three-dimensional printing path planning method based on free-form surface slices is characterized by comprising the following steps:
(1) Taking the ratio of the pressurizing deformation quantity of each layer of material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer as the gravity settling influence weight of each layer of material beam, taking the extrusion time of each layer of material beam to the material beam on the lower layer as the material beam hardening time weight of each layer of material beam, and dividing the three-dimensional printing model into a plurality of free-form surface sliced layers from the longitudinal direction according to the product of the gravity settling influence weight of each layer of material beam and the material beam hardening time weight;
(2) And carrying out curved surface discretization on each free-form surface sliced layer to obtain a discrete point set of each free-form surface sliced layer, selecting discrete points in the discrete point set of each free-form surface sliced layer by taking the shortest path as a target to form a printing path of each free-form surface sliced layer, and connecting the printing paths of all the free-form surface sliced layers to form a three-dimensional printing path.
2. The method for planning a three-dimensional printing path based on a free-form surface slice according to claim 1, wherein the step (1) comprises:
dividing the three-dimensional printing model into a plurality of vertical analysis units in the longitudinal direction;
the method comprises the following steps of pre-dividing a vertical analysis unit into a plurality of cuboids with equal intervals from bottom to top, regarding a first cuboid, taking the ratio of the compression deformation quantity of a previous layer of material beams to the height direction of a lowest layer of material beams corresponding to the cuboid to the height direction of the lowest layer of material beams to the height of the lowest layer of material beams as the gravity sedimentation influence weight of the previous layer of material beams, taking the extrusion time of the previous layer of material beams to the lowest layer of material beams as the material beam hardening time weight of the previous layer of material beams, and performing re-division according to the integral distribution height of the gravity sedimentation influence weight of the previous layer of material beams and the material beam hardening time weight;
the other parts of the first cuboid which is divided again are removed by the vertical analysis unit for re-pre-division, the ratio of the pressurizing deformation quantity of the layer of material beam corresponding to the cuboid in the height direction of all material beams at the lower layer of the cuboid to the height of all material beams at the lower layer of the cuboid is used as the gravity settling influence weight of the layer of material beam, the extrusion time of the layer of material beam to all material beams at the lower layer of the cuboid is used as the material beam hardening time weight of the layer of material beam, the vertical analysis unit is divided into a plurality of cuboids according to the integral distribution height of the gravity settling influence weight of the layer of material beam and the material beam hardening time weight, and the height of the vertical analysis unit is divided into a plurality of cuboids;
and splicing the central points of the cuboids in all the vertical analysis units from bottom to top to form a plurality of free-form surface sliced layers.
3. The method for planning a three-dimensional printing path based on a free-form surface slice of claim 2, wherein the height of the re-divided cuboid is:
wherein k is the number of the re-pre-divided cuboids above the re-divided cuboids, h D Height of subdivided cuboid,. DELTA.Hg i Is the weight of gravity settling influence, Δ T, of the ith layer of the batch i And D is the diameter of the printing nozzle.
4. The method for planning a three-dimensional printing path based on a free-form surface slice according to claim 2, wherein the height of the pre-divided cuboid is as follows: the diameter of the printing nozzle is as follows: the ratio of the height of the vertical analysis unit to the diameter of the printing nozzle, and the height of the cuboid pre-divided again are as follows: printing the diameter of the spray head, wherein the number of the cuboid subjected to pre-segmentation again is as follows: the vertical analysis unit removes a ratio of a height of the other portion of the first rectangular parallelepiped to a diameter of the print head which is subdivided.
5. A method for planning a three-dimensional printing path based on a free-form surface slice according to claim 3, wherein the specific way of surface discretization is as follows:
describing the free-form surface sliced layer as a curved surface constructed by a plurality of curves in the u and v directions;
the coordinates in the v direction on the curved surface are made to be the same, interpolation is carried out in the u direction to obtain a u-direction parameter line, the coordinates in the u direction on the curved surface are made to be the same, and interpolation is carried out in the v direction to obtain a v-direction parameter line;
all the intersection points of all the parameter lines in the u direction and the v direction form a discrete point set of the free-form surface sliced layer;
and carrying out curved surface discretization on the free curved surface sliced layers from bottom to top to obtain a discrete point set of each free curved surface sliced layer.
6. The method according to claim 5, wherein the distance during interpolation is a beam extrusion width l D ，
7. The method for planning a three-dimensional printing path based on free-form surface slices as claimed in any one of claims 1 to 6, wherein the printing path of the free-form surface slice layer corresponding to the upper top surface and the lower bottom surface in the three-dimensional printing model is composed by the following steps:
setting the current point as i, and searching in the previous stepThe cable direction is
The search direction deviation angle θ of the next target point is:
θ＝arccosθ
multiplying the search direction deflection angle theta of the next target point by the weight coefficient omega, and calculating the distance D between the current point and the next target point after the search direction correction next ：
Wherein d is next Is the straight-line distance between the current point and the candidate target point,
searching direction for the next step;
selecting D in discrete point set of free-form surface sliced layer next The smallest point is taken as the next target point;
and sequentially connecting all target points from the discrete points of the free-form surface sliced layer to the starting point to the end point to form a printing path.
8. The method for planning a three-dimensional printing path based on free-form surface slices as claimed in any one of claims 1 to 6, wherein the printing path of the free-form surface slice layer corresponding to the middle layer of the three-dimensional printing model is composed by the following steps:
the shortest path is taken as a target, the rotation angle is limited to be 60-120 degrees, the length from the printing nozzle to the material beam section before the nozzle turns is limited to be more than 10 times of the diameter of the printing nozzle, discrete points are selected from the discrete points of the free-form surface slice layer in a concentrated mode, and the printing path of the free-form surface slice layer is formed.
9. The method for three-dimensional printing path planning based on free-form surface slices according to any one of claims 1-6, wherein the step (2) further comprises:
detecting whether a cross point exists in the printing path in each free-form surface sliced layer, if so, exchanging the end point of the first section of path in two cross path sections corresponding to the cross point with the start point of the second section of path to generate a printing path for eliminating the local cross point, and if not, connecting the start point of the printing path of the free-form surface sliced layer i with the end point of the printing path of the free-form surface sliced layer i-1 to form a three-dimensional printing path, wherein i is more than or equal to 2.
10. A three-dimensional printing path planning system based on free-form surface slicing is characterized by comprising:
the model slicing module is used for taking the ratio of the pressurizing deformation quantity of each layer of material beam extruded by the printing nozzle to the material beam on the lower layer in the longitudinal direction to the height of the material beam on the lower layer as the gravity sedimentation influence weight of each layer of material beam, taking the extrusion time of each layer of material beam to the material beam on the lower layer as the material beam hardening time weight of each layer of material beam, and dividing the three-dimensional printing model into a plurality of free-form surface slicing layers from the longitudinal direction according to the product of the gravity sedimentation influence weight of each layer of material beam and the material beam hardening time weight;
the curved surface layer discrete module is used for carrying out curved surface discrete on each free curved surface slice layer to obtain a discrete point set of each free curved surface slice layer;
and the path planning module is used for selecting discrete points in the discrete point set of each free-form surface sliced layer by taking the shortest path as a target, forming the printing paths of each free-form surface sliced layer, and connecting the printing paths of all the free-form surface sliced layers to form a three-dimensional printing path.
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