CN115464745A - Concrete 3D printing path optimization method with variable path width - Google Patents

Concrete 3D printing path optimization method with variable path width Download PDF

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Publication number
CN115464745A
CN115464745A CN202211191646.3A CN202211191646A CN115464745A CN 115464745 A CN115464745 A CN 115464745A CN 202211191646 A CN202211191646 A CN 202211191646A CN 115464745 A CN115464745 A CN 115464745A
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printing
concrete
model
geometric
geometric model
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马宗方
万伟鹏
宋琳
段明
刘超
刘化威
武怡文
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Xian University of Architecture and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B28—WORKING CEMENT, CLAY, OR STONE
    • B28B—SHAPING CLAY OR OTHER CERAMIC COMPOSITIONS; SHAPING SLAG; SHAPING MIXTURES CONTAINING CEMENTITIOUS MATERIAL, e.g. PLASTER
    • B28B1/00—Producing shaped prefabricated articles from the material
    • B28B1/001—Rapid manufacturing of 3D objects by additive depositing, agglomerating or laminating of material
    • 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
    • B33Y10/00—Processes of 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Abstract

The invention discloses a concrete 3D printing path optimization method with variable path width, which comprises the following steps: step 1): printing a component model slice by concrete; step 2): converting the concrete printing component section model into a geometric model; step 3): initializing position information in a geometric model, and dividing the geometric model into a plurality of once-through connected domains; step 4): calculating the widths of different areas of the concrete member by using a distance formula between two points; step 5): solving the relation among the diameter of the spray head, the blanking speed and the width of the concrete member by utilizing a multiple linear regression equation; step 6): and marking the specific blanking speeds with different printing widths by using different colors, refining the specific printing state of the component, and completing the 3D printing process of the concrete with the variable path width. The invention reasonably arranges the whole printing process and effectively improves the forming time and quality.

Description

Concrete 3D printing path optimization method with variable path width
Technical Field
The invention relates to the technical field of concrete 3D printing, in particular to a path width-variable concrete 3D printing path optimization method.
Background
The current concrete 3D printing technology still needs to overcome many difficulties. In the traditional concrete 3D printing process, because the spray head is fixed and the diameter of the spray head is not changed, the printing of a given simple component can be normally finished, but when some complex patterns are met, due to the fact that the width is changed continuously, frequent jumping of the spray head and frequent change of the blanking speed can be caused, and therefore the 3D printing component has obvious uneven forming conditions, and forming time and quality of the component are affected seriously.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a concrete 3D printing path optimization method with variable path width, which marks the printing speed of specific points by different colors and reasonably arranges the whole printing process, so that the printing spray head does not need to be replaced and repeated printing can be carried out within the effective width range, and the forming time and quality are effectively improved.
In order to achieve the purpose, the invention adopts the technical scheme that:
a path width variable concrete 3D printing path optimization method comprises the following steps;
step 1): printing a component model slice by concrete;
step 2): converting the concrete printing component section model in the step 1) into a geometric model;
and step 3): initializing position information of each point and eight vector directions (respectively, upper, lower, left, right, upper left, lower left, upper right and lower right) in the geometric model obtained in the step 2), and dividing the geometric model into a plurality of connected domains which can be traversed once by using a model parting method;
and step 4): finding out the middle point based on the vector direction by using a distance formula between the two points, connecting the middle points to find out the central axis of the member during printing, and solving the widths of different areas of the concrete member;
and step 5): solving the relation among the diameter of the spray head, the blanking speed and the width of the concrete member by utilizing a multiple linear regression equation;
step 6): and marking the concrete blanking speeds with different printing widths by using different colors, refining the printing state of a concrete member, and finishing the 3D printing process of the concrete with variable path width.
The model transformation step of the step 2):
(1) Extracting the area of the printing nozzle needing blanking in the geometric model, and deleting the rest information;
(2) Giving coordinate values of each geometric point (x, y) according to the geometric model proportion, marking the geometric points of the geometric model, marking each geometric vertex, and then marking the points intersected by each printing path in the geometric model;
(3) Connecting the marked geometric points proportionally according to the width of the printing path;
(4) And after the conversion is finished, scaling the geometric model in an equal proportion mode.
And 3) importing the geometric model image into a computer, converting the geometric model image into a binary image, obtaining a pixel matrix of the binary image, traversing each point on the geometric model after the thinning processing, and classifying the geometric points according to different connected domains processed by the classification model.
The step 4) calculates the modular length of the vector based on a two-point distance formula so as to calculate the midpoint, wherein the modular length formula is as follows:
Figure BDA0003869691080000031
and 5) solving the relation among the diameter of the spray head, the blanking speed and the width of the concrete member by using a multiple linear regression equation, wherein the concrete process comprises the following steps:
(1) There are now three independently observed data (y, x) i1 ，x i2 ) Respectively, the diameter (x) of the nozzle i1 ) Feeding speed (x) i2 ) A print diameter (y); from a multiple linear regression equation (as follows):
y＝β 0 +β 1 x i1 +β 2 x i2 +ε
note the book
Figure BDA0003869691080000032
β＝[β 0 β 1 β 2 ] T
The multiple linear regression equation can be expressed as:
y i ＝Xβ+ε
wherein beta is 0 ，β 1 ，β 2 Respectively, the unknown parameters required to be taken in the multiple linear regression equation.
(2) And for the parameter estimation part of the multiple linear regression equation, estimating by using a least square method to solve the minimum value of the sum of squares of errors, wherein the basic principle of the least square method is as follows: let (x, y) be a pair of observations, and x = [ x ] 1 ,x 2 ,x 3 ,x 4 …x n ]E R, y = R satisfies the following theoretical function:
y＝f(x,β)
β＝[β 1 ,β 2 ,β 3 ,β 4 …β n ]to find the optimum estimate of the parameter β for the function y = f (x, β) for the pending parameters, for a given set of m (typically m)>n) observing data, solving the objective function
Figure BDA0003869691080000041
Parameter beta of minimum value i (i＝1,2,3,4……n)；
(3) The hypothesis test using regression analysis verifies whether the model is reasonable, and as with the hypothesis test of the unitary linear regression equation, hypotheses are made for each beta, let H 0 ：β j =0 (j = 2) was also checked with F, but note that H was accepted 0 Only y and x can be illustrated i1 .x i2 The linear relationship of (a) is not obvious, and a nonlinear relationship may exist; some measures of y and x i1 ，x i2 An index of degree of correlation, such as a complex decision coefficient defined using the ratio of the regression squares in the sum of the total squares;
Figure BDA0003869691080000042
wherein U is the sum of the squares of the residuals of y and SST is x i1 ，x i2 The sum of squares.
Figure BDA0003869691080000043
Called the complex correlation coefficient, the larger R, y and x i1 ，x i2 The more closely the correlation, R is greater than 0.8 or 0.9 to consider the correlation true.
The invention has the beneficial effects that:
aiming at the problem that the printing shape and width of a complex component are changed in the printing process, the invention provides a 3D (three-dimensional) concrete variable-width printing algorithm, the central axis of each area is found out based on printing vector point calculation, and the diameter (x) of a spray head is obtained according to a linear regression model i1 ) Feeding speed (x) i2 ) The relation between the printing diameter (y) three is printed, the printing speed of specific points of different color marks is used, and the whole printing process is reasonably arranged, so that the printing nozzle can be replaced and repeated printing can be carried out within the effective width range, and the forming time and quality are effectively improved.
Drawings
FIG. 1 is a geometric model of a concrete member according to the present invention.
FIG. 2 is a graph showing the results of the extraction of the central axis of the concrete member of the present invention.
Fig. 3 is a graph of specific feed rates for marking different print widths with different colors according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Example (b):
the method comprises the following steps: and slicing the printed piece model.
The first step is as follows: in the acquisition process of the method, the geometric data (length, width, height and the like) of the printing component is read by using a measuring tool, then a printing model is established according to the acquired data, and finally the established model is sliced by using Cura software.
Step two: the slice model is converted into a geometric model.
The second step is as follows: (1) Deleting the information of the part which does not need to be printed in the slice model; (2) extracting each geometric point in the slice model; (3) The geometric data of the acquired slice model is reduced in equal proportion (as shown in figure 1), so that the established geometric model is convenient to process.
Step three: initializing position information of each point and eight vector directions in the geometric model, and dividing the geometric model into a plurality of connected domains which can be traversed once by using a model parting method.
Step four: the distance formula between the two points is used for finding the middle point in the vector-based direction, and the middle point is connected to find the central axis of the component during printing (as shown in figure 2).
The fourth step is that: and solving the modular length of the vector based on a two-point distance formula so as to obtain a midpoint, wherein the modular length formula is as follows:
Figure BDA0003869691080000061
step five: and solving the relation among the diameter of the spray head, the blanking speed and the printing diameter by utilizing a multiple linear regression equation, and determining the printing speed of each point.
Determining a regression coefficient by utilizing a multiple linear regression model in the step (1),β 0 、β 1 、β 2 selecting three groups of data (y, x) in printing experiment i1 ，x i2 ) The diameters (x) of the nozzles are shown in the following tables i1 ) Feeding speed (x) i2 ) And a print diameter (y).
Nozzle diameter (mm) Blanking speed (r/min) Printing diameter (mm)
10 7000 10
10 7200 11.3
10 7500 12.1
10 8000 13.2
10 8400 13.9
20 7000 20.2
20 7200 21.4
20 7500 22.6
20 8000 23.9
20 8400 25.1
40 7000 40.8
40 7200 42.1
40 7500 43.9
40 8000 45.3
40 8400 47.1
The parameter estimation part uses least square method to estimate, and calculates the minimum value of the error square sum. The available relationship model is as follows:
Figure BDA0003869691080000062
Figure BDA0003869691080000071
in the table, intercept represents an Intercept (herein, the distance from the intersection of the function graph and the Y axis to the origin is specified), namely a constant term of the multiple regression equation, and has a value of-24.5159; XVable 1 represents independent variable x1, and the parameter estimation value is 1.058286, i.e. the coefficient in front of variable x1 of the multiple regression equation; XVariable2 denotes the independent variable x2 and the parameter estimate is 0.003414, the coefficient preceding variable x2 of the multiple regression equation. Thus, the multiple regression equation is: y = -24.5159 +1.058286x1+0.003414x2. (3) The model was tested for plausibility using hypothesis testing of regression analysis, as with hypothesis testing of a one-dimensional linear regression equation, with hypotheses being performed for each β. Let H 0 ：β j =0 (j = 2) was likewise checked using F. Note, however, that H is accepted 0 Only y and x can be illustrated i1 .x i2 The linear relationship of (a) is not obvious and a nonlinear relationship may exist.
Some measures of y and x i1 ，x i2 An index of the degree of correlation, such as a complex decision coefficient defined using the ratio of the regression squares in the sum of the total squares.
Figure BDA0003869691080000072
Wherein U is the sum of the squared residuals of y, SST is x i1 ，x i2 The sum of squares.
Figure BDA0003869691080000073
Called the complex correlation coefficient, the larger R, y and x i1 ，x i2 The more closely the correlation, R is greater than 0.8 or 0.9 to consider the correlation true.
Also for the check of the regression coefficients, each β was checked with the t-distribution.
The multiple linear regression results are shown in the following table:
Figure BDA0003869691080000074
Figure BDA0003869691080000081
as can be seen from the regression statistical table, the value of the correlation coefficient MultipleR (the value range is (-1,1)) is 0.999393, which indicates that the regression model has a high positive correlation. The determinant coefficient rsquad (i.e., the decision coefficient, the measurement coefficient, and the goodness of fit, which is the square of the correlation coefficient multiplet) has a value of 0.998787, which indicates that 99.88% of the total variation of the dependent variable y is due to the variation of the independent variable, i.e., the regression model can account for 99.88% of the total variation of the dependent variable. The corrected decision coefficient AdjustedRSquare (i.e., the corrected decision coefficient) is used to test the goodness of fit of the multiple regression model in order to avoid overestimating the decision coefficient RSquare (i.e., goodness of fit) due to the addition of independent variables. The standard error value is 0.518795, which is the residual error from the ANOVA table
Figure BDA0003869691080000082
To obtain, i.e.
Figure BDA0003869691080000083
And the distance between the true value and the regression line is represented, and the smaller the value is, the better the fitting degree of the regression model and the actual data is.
Step six: and marking the specific printing speed of each printing point by different colors, refining the specific printing state of the component, and finishing the printing process of the 3D concrete with variable width.
The algorithm adopted by the invention is tested by using a MATLABR2018a development tool under an operation platform of Windows10, and the specific software and hardware environments are shown in the following table:
Figure BDA0003869691080000084
。

Claims (5)

1. a path width variable concrete 3D printing path optimization method is characterized by comprising the following steps;
step 1): printing a component model slice by concrete;
step 2): converting the concrete printing component section model in the step 1) into a geometric model;
step 3): initializing position information of each point and eight vector directions (respectively, upper, lower, left, right, upper left, lower left, upper right and lower right) in the geometric model obtained in the step 2), and dividing the geometric model into a plurality of connected domains which can be traversed once by using a model parting method;
step 4): finding out the middle point based on the vector direction by using a distance formula between the two points, connecting the middle points to find out the central axis of the member during printing, and solving the widths of different areas of the concrete member;
step 5): solving the relation among the diameter of the spray head, the blanking speed and the width of the concrete member by utilizing a multiple linear regression equation;
step 6): and marking the concrete blanking speeds with different printing widths by using different colors, refining the printing state of a concrete member, and finishing the 3D printing process of the concrete with variable path width.
2. The method for optimizing the 3D printing path of the concrete with the variable path width as claimed in claim 1, wherein the model transformation step of the step 2) comprises the following steps:
(1) Extracting a region needing blanking of a printing nozzle in the geometric model, and deleting the rest information;
(2) Giving coordinate values of each geometric point (x, y) according to the geometric model proportion, marking the geometric points of the geometric model, marking each geometric vertex, and then marking the points intersected by each printing path in the geometric model;
(3) Connecting the marked geometric points proportionally according to the width of the printing path;
(4) And after the conversion is finished, scaling the geometric model in an equal proportion mode.
3. The method for optimizing the concrete 3D printing path with the variable path width according to claim 1, wherein in the step 3), the geometric model image is imported into a computer, converted into a binary image, a pixel matrix of the binary image is obtained, each point on the geometric model after the refining processing is traversed, and the geometric points are classified according to different connected domains after the classification model processing.
4. The method for optimizing the concrete 3D printing path with the variable path width according to claim 1, wherein the step 4) is to calculate the module length of the vector based on a two-point distance formula to calculate the midpoint, wherein the module length formula is as follows:
Figure FDA0003869691070000021
5. the method for optimizing the concrete 3D printing path with the variable path width according to claim 1, wherein the step 5) utilizes a multiple linear regression equation to solve the relationship among the nozzle diameter, the blanking speed and the width of the concrete member, and the specific process is as follows:
(1) There are now three independently observed data (y, x) i1 ，x i2 ) Respectively, the diameter (x) of the nozzle i1 ) Feeding speed (x) i2 ) A print diameter (y); from a multiple linear regression equation (as follows):
y＝β 0 +β 1 x i1 +β 2 x i2 +ε
note the book
Figure FDA0003869691070000022
β＝[β 0 β 1 β 2 ] T
The multiple linear regression equation can be expressed as:
y i ＝Xβ+ε
wherein, beta 0 ，β 1 ，β 2 Respectively, the unknown parameters required to be taken in the multiple linear regression equation.
(2) And for the parameter estimation part of the multiple linear regression equation, estimating by using a least square method to solve the minimum value of the sum of squares of errors, wherein the basic principle of the least square method is as follows: let (x, y) be a pair of observations, and x = [ x ] 1 ,x 2 ,x 3 ,x 4 …x n ]Epsilon R, y = R satisfies the following theoretical function:
y＝f(x,β)
β＝[β 1 ,β 2 ,β 3 ,β 4 …β n ]to find the optimum estimate of the parameter β for the function y = f (x, β) for the pending parameters, for a given set of m (typically m)>n) observing data, solving an objective function
Figure FDA0003869691070000031
Parameter beta of minimum value i (i＝1,2,3,4……n)；
(3) The hypothesis test using regression analysis verifies whether the model is reasonable, and as with the hypothesis test of the unitary linear regression equation, hypotheses are made for each beta, let H 0 ：β j =0 (j = 2) was also checked with F, but note that H was accepted 0 Only y and x can be illustrated i1 .x i2 The linear relationship of (a) is not obvious, and a nonlinear relationship may exist; some measures of y and x i1 ，x i2 An index of the degree of correlation, such as a complex decision coefficient defined using the ratio of regression squares in the sum of the squares;
Figure FDA0003869691070000032
wherein U is the sum of the squares of the residuals of y and SST is x i1 ，x i2 And (4) summing the squares.
Figure FDA0003869691070000041
Called the complex correlation coefficient, the larger R, y and x i1 ，x i2 The more closely the correlation, the more R than 0.8 or 0.9 the correlation is considered to be true.
CN202211191646.3A 2022-09-28 2022-09-28 Concrete 3D printing path optimization method with variable path width Pending CN115464745A (en)

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