CN112884897A - Cylindrical rod three-dimensional contour geometric reconstruction method prepared by selective laser melting - Google Patents
Cylindrical rod three-dimensional contour geometric reconstruction method prepared by selective laser melting Download PDFInfo
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Abstract
The invention discloses a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting, which comprises the following steps of: obtaining a reverse three-dimensional geometric model of the cylindrical rod manufactured by selective laser melting; capturing ellipse size data to be fitted of the cross section of the cylinder according to the reverse three-dimensional model; from the ellipse size data, the cylinder is reconstructed from the ellipse cross-section. Aiming at the fact that the cylindrical structure printed by selective laser melting has geometric defects influencing mechanical properties, namely the surface profile is irregular, the cross section shape of the cylindrical structure is simulated through an ellipse, a cylindrical model is reconstructed, the cross section profile of the selective laser melting is accurately described by adopting five parameters, the method is simple and easy to implement, the subsequent simulation application of the model is facilitated, and the method has a good application prospect in the aspect of material increase manufacturing.
Description
Technical Field
The invention relates to the field of additive manufacturing, in particular to a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting.
Background
The additive manufacturing technology is gradually a new favorite for engineering manufacturers, which not only can overcome the defect that complex parts cannot be manufactured by traditional processing, but also can obtain parts with more excellent mechanical properties. But there are some problems that conventional machining does not have, most notably surface profile accuracy. Lattice structures are also a focus of research today. In the aspects of structures such as light weight, shock absorption and energy absorption, the dot matrix shows excellent functions and has important application prospects. Whereas complex structures can be perfectly realized by additive manufacturing.
In Selective Laser Melting (SLM), metal powder is irradiated by a Laser beam to melt the powder into a solid, which is stacked layer by layer to form a three-dimensional solid part. But the factors of unstable molten pool and uneven cooling in the printing process cause the defects of the parts. Defects in the SLM process result in stress concentrations in the fabricated part, which can lead to part failure.
In the three-dimensional lattice, the cylindrical rods are basic composition units, and when the cylindrical structure is manufactured through the SLM, the surface profile has deviation, and particularly when the dimension of a workpiece is small, the performance is seriously influenced by geometric defects. The density of the SLM prepared test piece is very high, and the manufacturing defects influencing the dot matrix performance are mainly surface geometric defects. At present, an ideal cylinder model is generally used for simulating the stress condition of an actual cylinder structure, the ideal cylinder model is greatly different from the actual SLM manufactured cylinder structure, and the conclusion obtained by mechanical analysis of a cylinder deviates from the actual manufactured lattice. Therefore, it is necessary to consider the geometrical defects into the performance study of the lattice. The addition of manufacturing geometric defects to the cylindrical structure model can improve the simulation accuracy, thereby enhancing the prediction capability of the model.
For the actually manufactured cylinder, the surface profile is complex, accurate prediction and reconstruction are difficult to realize, and if the scanning data is directly used for analysis, the model construction difficulty is high, the efficiency is low, the calculation processing time is long, and the subsequent software operation is not convenient. Some researchers have reconstructed cylinders using cylinders of different diameters, but this method does not take into account the variations in the shape of the cross-section of the real cylinder. How to construct the three-dimensional outline of the cylinder under the SLM can meet the requirements of high precision and high efficiency and needs to be solved.
In conclusion, the 3D real outline geometric modeling method for geometrically reconstructing the formed lattice structure has practical significance by considering the manufacturing geometric defects under the SLM, provides powerful reference for mechanical property simulation analysis of 3D forming manufacturing parts, and has good application prospect in the aspect of additive manufacturing.
Disclosure of Invention
Aiming at the problems that the cylinder generates geometric defects and lacks a profile characterization model for construction in the selective laser manufacturing process, the invention aims to provide a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting.
The invention provides a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting, which comprises the following steps of:
step 1: obtaining a cylindrical rod three-dimensional model with a real outline according to point cloud data of a selected area laser melting manufactured cylinder, and the specific steps comprise:
step 11: acquiring cylindrical point cloud data manufactured by selective laser melting;
step 12: removing excessively discrete points in the point cloud data, and cutting off two ends of the cylinder to improve the accuracy of the cross section data;
step 13: performing reverse modeling to obtain a reverse model, namely a cylindrical three-dimensional model with a real outline;
step 2: sectioning the three-dimensional model to obtain m cross section pictures, and simulating an elliptical graph of the cross section outline according to the pictures to obtain fitted elliptical cross section data;
the fitted elliptical cross-section data comprises: the offset (dx, dy) of the actual circle center o ', the actual circle center o' and the ideal circle center o, an actual coordinate system x '-y', an ideal coordinate system x-y deflection angle theta, the ellipse major axis length a and the ellipse minor axis length b;
the specific expression is as follows:
let a point (x) on the cross-sectional profilei，yi) (i ═ 1, 2.., n), according to any elliptical equation:
x2+Axy+By2+Cx+Dy+E＝0
wherein A, B, C, D, E is any real number;
by the principle of least squares, we obtain:
dx＝x0-x
dy＝y0-y
wherein x and y are the coordinates of the center of a circle of the ideal cylindrical cross section, and x0，y0The coordinate of the center of the fitted ellipse is shown, wherein a is the length of the major axis of the ellipse, and b is the length of the minor axis of the ellipse; theta is an offset angle of an actual coordinate system x '-y' and an ideal coordinate system x-y, the anticlockwise direction is positive, dx is the x-axis offset of an actual circle center o 'and an ideal circle center o, and dy is the y-axis offset of the actual circle center o' and the ideal circle center o;
and step 3: obtaining a three-dimensional solid model of geometric representation of the real outline of the cylinder according to the fitted elliptical cross section data, and the specific steps comprise:
step 31: drawing an elliptic curve at the height of the coordinate system 0 according to the fitted elliptic cross section data;
step 32: determining the height of the next cross section and drawing an elliptic curve according to the interval between the cross sections of the model to be reconstructed;
step 33: repeating the step 32, determining an actual coordinate system x '-y' by the circle center offset (dx, dy) and the offset angle theta at different heights, and drawing an elliptic curve according to the major axis a and the minor axis b of the ellipse until the drawing height is greater than or equal to the height of the model cylinder;
step 34: and sequentially selecting all the elliptic curves from bottom to top, smoothly transiting the drawn elliptic curves, and connecting the elliptic curves into a cylindrical entity to obtain a three-dimensional entity model of the geometric representation of the real outline of the cylinder.
Further, the number m of the cross-section pictures in the step 2 is determined according to the reconstruction accuracy.
Further, the step 31 is specifically to randomly select data according to the fitted elliptical cross section data, start from 0 height in CAD software, take the world coordinate system as an ideal coordinate system x-y with 0 height, take the circle center offset (dx, dy) as an actual coordinate origin 0 ', and change the offset angle 0 of the coordinate system x-y, thereby determining an actual coordinate system x ' -y '; under the actual coordinate system x '-y', an ellipse is drawn according to the major and minor axis lengths a, b.
Further, the step 32 specifically includes: the coordinate system is regressed to the world coordinate system, the height of the next cross section is determined according to the interval between the cross sections of the required reconstruction model, the world coordinate is moved to the height, thereby determining the ideal coordinate system x-y on the height, the actual coordinate system x '-y' of a certain height is determined by the circle center offset (dx, dy) and the deflection angle theta, and the elliptic curve of the certain height is determined by the major and minor axes a, b of the ellipse.
Further, the interval between the cross sections of the reconstructed model in the step 32 is determined according to the characterization accuracy requirement.
Further, step 34 selects each elliptic curve through a lofting operation in the CAD software.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the manufacturing geometric defect of selective laser melting is considered in the cylindrical three-dimensional profile model, so that the reconstructed simulation model is combined with the actual model, and the lattice junction model has higher precision on the basis of guiding the theoretical model by the actual test.
2. The invention adopts the elliptic cross section to represent the cross section of the cylinder, can simulate the geometrical defects of uneven diameter, circle center deviation, cross section shape change and the like of the real cylinder in the manufacturing process, and takes the geometrical outline deviation into the cylindrical geometrical model.
3. The method adopts the least square method to simulate the actually manufactured cylindrical cross section into an elliptical shape, fully considers all data points on the actual cross section, has high simulation precision, and has high similarity between the shape of the fitted elliptical cross section and the shape of the actual cross section.
Drawings
FIG. 1 is a flow chart of a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting according to the present invention;
FIG. 2 is a schematic illustration of ellipse data of the present invention;
FIG. 3 is a schematic view of an ideal model of a body centered cylinder of the present invention;
FIG. 4 is a schematic representation of a cylindrical reverse model of the present invention;
FIG. 5 is a schematic cross-sectional view of a cylindrical reverse model of the present invention;
FIG. 6 is a schematic diagram of a cylindrical model based on elliptical characterization according to the present invention.
Detailed Description
In order to better understand the technical scheme of the invention, the following detailed description is made on the specific implementation mode of the invention by combining the accompanying drawings 1-6 and the embodiment.
The invention provides a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting, which comprises the following steps of:
step 1: when acquiring geometric defect data of a selected area laser melting formed round bar column, acquiring point cloud data of a cylindrical outline by adopting geometric scanning equipment, removing excessively discrete points in the point cloud data, cutting off two ends of the cylinder to directly serve as outlines at two ends of a simulation model, and then performing reverse modeling to obtain a reverse model, namely a cylindrical three-dimensional model with a real outline;
step 2: sectioning the cylindrical three-dimensional model with the real outline to obtain 100 cylindrical cross-section pictures with maximum pixels of 1680 x 1200, wherein in order to ensure the data accuracy, the number of the cross-section pictures is determined according to reconstruction accuracy, the higher the reconstruction accuracy requirement is, the higher the value is, the example is only for explaining the implementation process, and 100 cross sections are taken; simulating an elliptic curve of the cross section by adopting a least square method, wherein the elliptic curve comprises an actual circle center o ' and an ideal circle center o offset (dx, dy), an actual coordinate system x ' -y ' and an ideal coordinate system x-y offset angle theta (the anticlockwise direction is positive), and the lengths a and b of the major axis and the minor axis of the ellipse; the center offset (dx, dy) represents the centroid offset of the real cylinder, the lengths a and b of the major axis and the minor axis of the ellipse reflect the diameter deviation of the real cylinder, and the five parameters comprehensively represent the axial waviness of the real cylinder and accurately reflect the three-dimensional real outline of the cylinder;
the specific expression is as follows:
let a point (x) on the cross-sectional profilei，yi) (i ═ 1, 2.., n), according to any elliptical equation:
x2+Axy+By2+Cx+Dy+E＝0 (1)
wherein A, B, C, D, E is any real number;
by the principle of least squares, we obtain:
dx＝x0-x
dy＝y0-y
wherein x and y are the coordinates of the center of a circle of the ideal cylindrical cross section, and x0，y0The coordinate of the center of the fitted ellipse is shown, wherein a is the length of the major axis of the ellipse, and b is the length of the minor axis of the ellipse; theta is an offset angle of an actual coordinate system x '-y' and an ideal coordinate system x-y, the anticlockwise direction is positive, dx is the x-axis offset of an actual circle center o 'and an ideal circle center o, and dy is the y-axis offset of the actual circle center o' and the ideal circle center o;
and step 3: according to the fitted elliptical cross section data, starting from 0 height in CAD software, taking an ideal coordinate system x-y with a world coordinate system of 0 height, taking the circle center offset (dx, dy) as an actual coordinate origin 0 ', and simultaneously changing the offset angle theta of the coordinate system x-y so as to determine an actual coordinate system x ' -y '; drawing an ellipse according to the lengths a and b of the major axis and the minor axis under an actual coordinate system x '-y'; returning the coordinate system to a world coordinate system, determining the height of the next cross section according to the interval between the cross sections, moving the world coordinate to the height, thereby determining an ideal coordinate system x-y on the height, and repeating the steps, wherein the circle center offset (dx, dy) and the offset angle theta determine an actual coordinate system x '-y' at different heights, and the major and minor axes a and b of the ellipse determine an elliptic curve; and finally, sequentially selecting all the elliptic curves from bottom to top through lofting operation in CAD software, smoothly transiting the drawn elliptic curves, and connecting the elliptic curves into a three-dimensional entity, namely a three-dimensional model of geometric representation of the real outline of the cylinder.
The invention relates to a method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting and a basic principle thereof.
The following description is given with reference to specific examples to illustrate how the present invention may be applied in practice:
taking a body center lattice with a cylindrical rod diameter of 1mm as an example, as shown in fig. 3, after a cylinder with a diameter of 1mm and a height of 6mm is manufactured through selective laser melting, the surface of the cylinder is rough, powder is obviously adhered, the diameter is not uniform, and the difference from an ideal smooth cylinder is very large.
The requirement of establishing a three-dimensional cylindrical geometric model with higher precision can characterize the geometric defects in the manufacturing process.
Firstly, acquiring the geometric defect data of the cylinder formed by selective laser melting. Adopting a geometric scanning device to obtain 1mm cylindrical point cloud data manufactured by selective laser melting, removing excessively discrete points in the point cloud data, removing data at two ends of a cylinder to avoid influencing the data accuracy of a cross section, then carrying out reverse modeling, materializing the point cloud data to obtain a reverse model, namely a cylindrical three-dimensional model with a real outline, and storing the model in an x-t format as shown in figure 4;
then, the cylindrical three-dimensional model with the real outline is imported into CAD software, and the model is converted into an editable state by adopting an x decomposition command. The bottom surface of the model is placed near the origin on the x-y plane by the alignment command to determine the reference plane. The cutting process will be performed at 0.06mm intervals starting from the top of the model using the cutting command again, and 100 cylindrical cross sections are obtained. And respectively moving the cylindrical cross sections of the unified x-y plane position passing through the reference plane into a rectangular frame of 1.68mm x 1.2mm at the same determined position so as to ensure that the relative positions of the cylindrical cross sections can be determined by selecting the rectangular frame. Then outputting a rectangular frame containing a cylindrical cross section as a cylindrical cross section picture by issuing a command so as to ensure the accuracy of data, wherein the picture pixel is 1680 × 1200 as the maximum pixel of the CAD software, as shown in FIG. 5;
according to the output picture, calculating the ellipse size of the cross section outline by adopting a least square method in programming software, wherein the ellipse size comprises an actual circle center o ' and an ideal circle center o offset (dx, dy), an actual coordinate system x ' -y ' and an ideal coordinate system x-y offset angle theta (the anticlockwise direction is positive) and the lengths a and b of the major axis and the minor axis of the ellipse; the center offset (dx, dy) represents the centroid offset of the real cylinder, the lengths a and b of the major axis and the minor axis of the ellipse reflect the diameter deviation of the real cylinder, and the five parameters comprehensively represent the axial waviness of the real cylinder and accurately reflect the cross section profile of the cylinder;
the specific expression is as follows:
let a point (x) on the cross-sectional profilei，yi) (i ═ 1, 2.., n), according to any elliptical equation:
x2+Axy+By2+Cx+Dy+E＝0
wherein A, B, C, D, E is any real number;
by the principle of least squares, we obtain:
dx＝x0-x
dy＝y0-y
wherein, the center of the elliptic cross section at the bottommost end of the cylinder is taken as the center coordinate x of the cylindrical cross section which is 0.753, y is 0.536, and x is0，y0And fitting the coordinates of the center of the ellipse to obtain ellipse fitting data of the cylindrical cross section. As shown in the following table:
TABLE 1
Finally, starting from the height of 0 in CAD software, taking the ideal coordinate system x-y with the height of the world coordinate system of 0, taking the circle center offset (-0.164, -0.229) as the actual coordinate origin o ', and simultaneously changing the offset angle of the coordinate system x-y to-2.149, thereby determining the actual coordinate system x ' -y '; drawing a first ellipse according to the length a of the major axis and the minor axis being 0.500 and b being 0.459 under an actual coordinate system x '-y'; returning the coordinate system to the world coordinate system, moving the coordinate system to (-0.158, -0.217, 0.6), thereby determining an ideal coordinate system x-y of the second cross section, and drawing a second ellipse according to the length a of the major and minor axes being 0.505 and b being 0.430; repeating the steps, determining an actual coordinate system x '-y' by the circle center offset (dx, dy, h) and the offset angle theta, and determining an elliptic curve by the major axis and the minor axis a, b of the ellipse until the drawing of the 101 th elliptic cross section curve is completed; and finally, sequentially selecting all the elliptic curves from bottom to top through lofting operation in CAD software, smoothly transiting the drawn elliptic curves, and connecting the elliptic curves into a three-dimensional entity, namely a three-dimensional cylindrical model for representing a real contour, as shown in FIG. 6.
A smooth cylindrical model of 1mm diameter and 6mm height was created in CAD software as shown in figure 3. And importing the reverse model, the smooth cylinder model and the three-dimensional entity model of the geometric representation of the real outline of the cylinder into ANSYS software. The static simulation is carried out, the three models are similarly fixed on one end face, the other end face is stressed by 10 newton of pressure, and the maximum stress result obtained by the simulation is shown in the following table:
compared with an ideal cylinder model, the three-dimensional solid model for geometrically characterizing the real outline of the cylinder has the advantages that the maximum stress relative error is reduced by 46.46%, the three-dimensional solid model is closer to a reverse model, and the stress distribution unevenness caused by the axis deviation can be simulated. Therefore, compared with an ideal cylinder model, the mechanical property of the three-dimensional reconstruction model is closer to that of a cylinder manufactured by laser melting in an actual selected area.
The above examples are merely illustrative of the effectiveness of the method, and do not limit the scope of the invention, and all equivalent methods or equivalent flow transformations that may be applied directly or indirectly to other related art by using the contents of the specification and drawings are included in the scope of the invention.
Claims (6)
1. A method for geometrically reconstructing a three-dimensional profile of a cylindrical rod prepared by selective laser melting is characterized by comprising the following steps:
step 1: according to the cylindrical point cloud data manufactured by selective laser melting, a cylindrical rod three-dimensional model with a real outline is obtained, and the specific steps comprise:
step 11: acquiring cylindrical point cloud data manufactured by selective laser melting;
step 12: removing excessively discrete points in the point cloud data, and cutting off two ends of the cylinder to improve the accuracy of the cross section data;
step 13: performing reverse modeling to obtain a reverse model, namely a cylindrical three-dimensional model with a real outline;
step 2: sectioning the three-dimensional model to obtain m cross section pictures, and simulating an elliptical graph of the cross section outline according to the pictures to obtain fitted elliptical cross section data;
the fitted elliptical cross-section data comprises: the offset (dx, dy) of the actual circle center o ', the actual circle center o' and the ideal circle center o, an actual coordinate system x '-y', an ideal coordinate system x-y deflection angle theta, the ellipse major axis length a and the ellipse minor axis length b;
the specific expression is as follows:
let a point (x) on the cross-sectional profilei，yi) (i ═ 1, 2.., n), according to any elliptical equation:
x2+Axy+By2+Cx+Dy+E＝0
wherein A, B, C, D, E is any real number;
by the principle of least squares, we obtain:
dx＝x0-x
dy＝y0-y
wherein x and y are the coordinates of the center of a circle of the ideal cylindrical cross section, and x0，y0The coordinate of the center of the fitted ellipse is shown, wherein a is the length of the major axis of the ellipse, and b is the length of the minor axis of the ellipse; theta is an offset angle of an actual coordinate system x '-y' and an ideal coordinate system x-y, the anticlockwise direction is positive, dx is the x-axis offset of an actual circle center o 'and an ideal circle center o, and dy is the y-axis offset of the actual circle center o' and the ideal circle center o;
and step 3: obtaining a three-dimensional solid model of geometric representation of the real outline of the cylinder according to the fitted elliptical cross section data, and the specific steps comprise:
step 31: drawing an elliptic curve at the height of the coordinate system 0 according to the fitted elliptic cross section data;
step 32: determining the height of the next cross section and drawing an elliptic curve according to the interval between the cross sections of the model to be reconstructed;
step 33: repeating the step 32, determining an actual coordinate system x '-y' by the circle center offset (dx, dy) and the offset angle theta at different heights, and drawing an elliptic curve according to the major axis a and the minor axis b of the ellipse until the drawing height is greater than or equal to the height of the model cylinder;
step 34: and sequentially selecting all the elliptic curves from bottom to top, smoothly transiting the drawn elliptic curves, and connecting the elliptic curves into a cylindrical entity to obtain a three-dimensional entity model of the geometric representation of the real outline of the cylinder.
2. The method for geometrically reconstructing the three-dimensional profile of a cylindrical rod prepared by selective laser melting according to claim 1, wherein: and the number m of the cross-section pictures in the step 2 is determined according to the reconstruction precision.
3. The method for geometrically reconstructing the three-dimensional profile of a cylindrical rod prepared by selective laser melting according to claim 1, wherein: step 31 is specifically to randomly select data according to the fitted elliptical cross section data, start from 0 height in CAD software, take the world coordinate system as an ideal coordinate system x-y with 0 height, take the circle center offset (dx, dy) as an actual coordinate origin o ', and change the offset angle theta of the coordinate system x-y, thereby determining an actual coordinate system x ' -y '; under the actual coordinate system x '-y', an ellipse is drawn according to the major and minor axis lengths a, b.
4. The method for geometrically reconstructing the three-dimensional profile of a cylindrical rod prepared by selective laser melting according to claim 1, wherein: the step 32 is specifically: the coordinate system is regressed to a world coordinate system, the height of the next cross section is determined according to the interval between the cross sections of the required reconstruction model, the world coordinate is moved to the height, thereby determining an ideal coordinate system x-y on the height, an actual coordinate system x '-y' of a certain height is determined by the circle center offset (dx, dy) and the deflection angle theta, and an elliptic curve of the certain height is determined by the major and minor axes a, b of the ellipse.
5. The method for geometrically reconstructing the three-dimensional profile of a cylindrical rod prepared by selective laser melting according to claim 1, wherein: the spacing between the cross-sections of the reconstructed model in step 32 is determined according to characterization accuracy requirements.
6. The method for reconstructing the three-dimensional profile geometry of a cylindrical rod by selective laser melting according to claim 1, wherein said step 34 is performed by selecting each elliptic curve through a lofting operation in a CAD software.
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Application publication date: 20210601 |