CN111169016B - 3+2 shaft unsupported 3D printing manufacturing method for blade parts - Google Patents

3+2 shaft unsupported 3D printing manufacturing method for blade parts Download PDF

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CN111169016B
CN111169016B CN201911310642.0A CN201911310642A CN111169016B CN 111169016 B CN111169016 B CN 111169016B CN 201911310642 A CN201911310642 A CN 201911310642A CN 111169016 B CN111169016 B CN 111169016B
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clustering
sub
printing
blade
initial clustering
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CN111169016A (en
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吴宝海
李成林
张莹
郑海
张阳
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Northwestern Polytechnical University
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Northwestern Polytechnical University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/30—Auxiliary operations or equipment
    • B29C64/386—Data acquisition or data processing for additive manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00—Data acquisition or data processing for additive manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29L—INDEXING SCHEME ASSOCIATED WITH SUBCLASS B29C, RELATING TO PARTICULAR ARTICLES
    • B29L2031/00—Other particular articles
    • B29L2031/08—Blades for rotors, stators, fans, turbines or the like, e.g. screw propellers
    • B29L2031/082—Blades, e.g. for helicopters

Abstract

The invention discloses a 3+ 2-axis unsupported 3D printing manufacturing method for blade parts, which is used for solving the technical problem that the existing multi-axis 3D printing manufacturing method for the blade parts is complex. According to the technical scheme, a blade part is divided into a plurality of sub-blocks through an improved spectral clustering algorithm, compared with a Z plane simple direct division method adopted in the background technology, the similarity and the adjacent degree of blades in different Z directions are considered, so that the surface normal vectors of the divided sub-blocks are more uniform, the step effect during printing is avoided, the clustering number can be automatically determined according to the clustering algorithm, the defects of the traditional spectral clustering algorithm are overcome, meanwhile, an iterative algorithm based on two criteria can also automatically give out the optimal clustering number, the defect that the traditional spectral clustering algorithm needs to manually give out the clustering number is overcome, the sub-blocks are printed in the main printing direction calculated by the method, a supporting structure is avoided in the whole 3D printing and forming process of the blade, and the method is simple and reliable.

Description

3+2 shaft unsupported 3D printing manufacturing method for blade parts
Technical Field
The invention relates to a multi-axis 3D printing manufacturing method of blade parts, in particular to a 3+2 axis unsupported 3D printing manufacturing method of blade parts.
Background
At present, many researchers put emerging manufacturing technologies into the manufacturing research of blisks and impeller parts for obtaining manufacturing and processing methods with higher efficiency and lower cost, and 3D printing of the blisks and the impeller parts is one of effective solutions, so that the blisks and the impeller parts have the advantages of saving materials and time; on the other hand, the manufacturing of the blades is the key for printing and manufacturing the impeller parts of the blisk, but the blades belong to curved surface parts, so that the problems of complex structure, serious surface bending and twisting and the like exist, and when a 3-axis 3D printer is used for printing, the following two problems mainly exist; one is the sharp height error caused by the non-perpendicularity of the printing direction and the normal vector of the surface of the part, namely the 'step effect': the printed part surface has sharp height (see figure 3), and the ladder effect is more obvious when the non-perpendicularity degree is larger; secondly, the part suspension area may need to be added with a support to form the part, the introduction of the support structure will increase the time of the whole forming process, and in addition, the processing time is needed to remove the support structure, and meanwhile, the existence of the support structure also causes the waste of materials, which is obviously contrary to the original purpose of 3D printing; in addition, the process of removing the support structure can also result in a loss of surface quality at the support structure and part contact.
Document 1 "w.wang, c.zanni, and l.kobbelt," Improved surface quality In 3D printing by optimizing the printing direction, "In Computer Graphics form, vol.35, No.2.wiley Online Library, pp.59-70,2016," proposes that sequential printing by dividing parts and finally manual butt-joining "stitching" achieve less support and surface perpendicular printing, but the application to thin-wall cranked heavy blade-like parts corresponding to the present invention is not ideal In dividing effect and still requires partial support.
Document 2, "chinese patent application publication No. CN 105149582A" discloses a multi-axis 3D printing and forming method for blade parts, but the blade is divided in a plane only in the Z direction, which is too simple to be suitable for the case of large bending degree, and the printing process still needs a certain support.
Disclosure of Invention
In order to overcome the defect that the existing multi-axis 3D printing manufacturing method of the blade parts is complex, the invention provides a 3+ 2-axis unsupported 3D printing manufacturing method of the blade parts. According to the method, the blade parts are divided into a plurality of sub-blocks through an improved spectral clustering algorithm, compared with a Z plane simple direct division method adopted in the background technology, the similarity and the adjacency degree of the blades in different Z directions are considered, so that the surface normal vectors of the divided sub-blocks are more uniform, the step effect during printing is avoided, the clustering number can be automatically determined according to the clustering algorithm, the defects of the traditional spectral clustering algorithm are overcome, meanwhile, an iterative algorithm based on two criteria can also automatically give out the optimal clustering number, the defect that the traditional spectral clustering algorithm needs to manually give out the clustering number is overcome, the sub-blocks are printed in the main printing direction calculated by the method, a supporting structure is avoided in the whole 3D printing and forming process of the blade, and the method is simple and reliable.
The technical scheme adopted by the invention for solving the technical problems is as follows: a3 +2 shaft unsupported 3D printing manufacturing method of blade parts is characterized by comprising the following steps:
step one, importing a leaf part three-dimensional model in an STL format, and simultaneously importing 134 point sets and 994 point sets which are distributed on a unit sphere in a grid mode and respectively used as printing voting vector sets D of an algorithm0And a set of candidate printing direction vectors D1；
Step two, performing over-segmentation on the triangular patch to realize the pretreatment of the model; according to the three-dimensional model of the blade to be manufactured, software measures to obtain the maximum thickness d of the blade, and the maximum collapse angle theta of the blade is found according to the printing material used by the partcThe included angle threshold value is used as whether the normal vector of the triangular patch votes for the voting printing direction vector or not;
traversing the whole set of triangular patches and the set of candidate printing direction vectors D1Calculating the included angle between the two, if a certain triangular patch TriAnd a certain candidate printing direction vector
Figure GDA0003274841570000021
Angle of inclusion at threshold thetacInternal, then TriTo pair
Figure GDA0003274841570000022
And (5) casting 1 ticket. After the voting process is finished, pair D1Classifying triangular patches with consistent printing direction vector conditions of medium votes together, then calculating whether the centroid distance between the classified triangular patches is less than or equal to 2D, if so, dividing the classified triangular patches into 1 initial clustering unit, otherwise, forming an initial clustering unit by the classified triangular patches respectively, and otherwise, if a certain triangular patch and other patch pairs D are in the same pair1If the vectors in (1) have no same vote, the triangular patch alone forms 1 voteAn initial clustering unit;
thirdly, constructing a similarity matrix W for the given blade part B to describe the similarity relation between each initial clustering unit as a basis for next clustering segmentation, and then calculating a normalization matrix D to further obtain a normalized Laplacian matrix L of the blade part;
the size of the similarity matrix W is n2×n2Wherein n is2Element w as the number of initial clustering unitsijRepresents an initial clustering unit CiAnd CjA rule relation is established between the initial clustering units, and w is used for eliminating the self similarity of the initial clustering unit Cii＝0；
The similarity matrix establishment criterion of the blade parts is as follows:
step error is minimum: from the above, in the absence of a support structure, the error of the 3D printed part is caused by a step error caused by the fact that the printing direction and the normal vector of the surface of the part are not completely perpendicular to each other
Figure GDA0003274841570000031
Denotes the printing direction, h denotes the cross-sectional layer thickness, niIs the normal vector at the ith triangular patch in the printed part STL model. Definition of tip height ciComprises the following steps:
Figure GDA0003274841570000032
step error E of single initial clustering unitiComprises the following steps:
Ei＝ci·S(Ci) (2)
wherein S (C)i) Represents an initial clustering unit CiThe area of (d);
calculating an initial clustering unit CiAnd CjThe step error between is expressed as:
Figure GDA0003274841570000033
wherein the content of the first and second substances,
Figure GDA0003274841570000034
to minimize the step error, there are
Figure GDA0003274841570000035
Wherein the sum of the areas of the two is divided by S (C)i)+S(Cj) Homogenizing the area of the initial clustering unit;
the adjacent closeness degree between the adjacent initial clustering units is maximized: obviously, if two initial clustering units are to be divided into the same sub-block, the two initial clustering units must be adjacent, and under the condition that the step errors are the same, the greater the adjacent degree is, the more the priority is for dividing into the same sub-block, and any two adjacent initial clustering units C are divided intoi、CjDegree of adjacency Ne ofijIs represented as follows:
Figure GDA0003274841570000036
Figure GDA0003274841570000037
Figure GDA0003274841570000038
Figure GDA0003274841570000039
wherein x isiIs represented by CiSet of x coordinates of vertices, y, of all triangular patches in the seti、zi、xj、yj、zjFor the same reason, xijThen is Ci、CjAll triangle surfaces inA set of x coordinates of patch vertices;
through the two steps, the similarity matrix is established in the following way:
Figure GDA0003274841570000041
wherein wijIs the ith row and j column element, lambda in the similarity matrix1、λ2Respectively debugging parameters
The normalized matrix D is calculated as follows:
Figure GDA0003274841570000042
the normalized Laplace matrix L of the blade parts has the formula:
Figure GDA0003274841570000043
step four, clustering the initial clustering units of the similarity matrix by using an improved clustering algorithm to obtain the optimal sub-block division B (B)1,B2,…BN) Calculating a main printing direction vector of each sub-block and each parameter representing theoretical printing error;
converting the clustering problem between initial clustering units in the solved similarity matrix into N classification problems of the feature vectors f corresponding to the first N feature values with the minimum L by adopting an Ncut method;
then standardizing the characteristic matrix composed of the N characteristic vectors into F according to rows, wherein each row is used as a N-dimensional sample, m samples are totally obtained, K-means clustering is adopted, the clustering dimension is N, and finally the optimal subblock division B (B) is obtained1,B2,…BN)；
Calculating a main printing direction vector of each sub-block: firstly, traversing 994 candidate printing direction vector sets D generated before for each sub-block in turn0Taking out one element of the
Figure GDA0003274841570000044
Satisfy the requirement of
Figure GDA0003274841570000045
The error of the included angle value of all triangular patches in the corresponding sub-block is
Figure GDA0003274841570000046
The minimum error value of the included angle between the sub-block and the sub-block;
various parameters representing theoretical printing errors are calculated: the method specifically comprises the steps that the sum of included angle values of normal vectors of each triangular surface patch in all sub-blocks and main printing direction vectors of the corresponding sub-blocks is recorded as sum _ ang, the average value of the total included angle, ave _ ang and the variance of the total included angle, var _ ang and the maximum value of the included angle in a part is recorded as ext _ ang, and the expression is as follows;
Figure GDA0003274841570000047
Figure GDA0003274841570000048
Figure GDA0003274841570000049
Figure GDA0003274841570000051
ext_ang＝max(angij) (16)
for convenient postamble expression, unify these parameters to the parameter set Par of the output result;
step five, determining the number of the optimal clustering sub-blocks, the theoretical printing error and the blade segmentation information under the current clustering number by an iterative algorithm;
two criteria for the iterative algorithm to perform:
the included angle between the normal vector of all triangular patches in the sub-block and the main printing direction of the sub-block is less than the material collapse angle thetac(ii) a The formula for calculating the included angle is as follows:
θi＝arccos|niPi|≤θc (17)
wherein, thetaiExpressing the normal vector N of any triangular patch when the number of clusters is NiCorresponding to the main printing direction PiThe included angle of (A);
theoretical printing error E of each initial clustering unittAll within a given manufacturing tolerance requirement E of the bladedWithin the range;
if the blade is divided into 2 sub-blocks B1、B2Then, the algorithm divides the initial clustering units included in each sub-block, and B is assumed1In m initial clustering units, B2N, while giving the main printing direction vector P of each sub-blocki(ii) a Calculating theoretical printing error of any one initial clustering unit of the blades by the following formula
Figure GDA0003274841570000052
At this time j ∈ [1, m + n ]]，njIs the normal vector at the jth triangular patch in the printed part STL model;
Figure GDA0003274841570000053
the specific flow of the iterative algorithm is as follows:
the clustering number N is an initial value, the clustering number N is substituted into a clustering algorithm to obtain output of a partitioning result of an initial clustering unit, an output result parameter set Par and the like, if elements in the current Par are all smaller than the Par output by the last N value, the next step is carried out, otherwise, clustering partitioning is carried out again until the condition is met;
two iteration criteria are judged:
Figure GDA0003274841570000054
θi≤θcif yes, outputting the convergenceThe cluster number of the cluster result is the optimal cluster number N; if not, N is equal to N +1, and then the step four is returned to cluster again until the condition is met;
and step six, applying the result output by the algorithm to 3+ 2-axis 3D printing of the blade part to complete the solid printing of the blade part.
When each subblock is printed, the printer needs to adjust the position and posture of the printed part, so that the main printing direction of the current printed subblock given by the algorithm is consistent with the printing direction of the multi-axis 3D printer, the subblocks divided by the clustering algorithm are sequentially printed from bottom to top, and the unsupported high-quality blocked 3D multi-axis printing of the blade parts is realized.
The invention has the beneficial effects that: according to the method, the blade parts are divided into a plurality of sub-blocks through an improved spectral clustering algorithm, compared with a Z plane simple direct division method adopted in the background technology, the similarity and the adjacency degree of the blades in different Z directions are considered, so that the surface normal vectors of the divided sub-blocks are more uniform, the step effect during printing is avoided, the clustering number can be automatically determined according to the clustering algorithm, the defects of the traditional spectral clustering algorithm are overcome, meanwhile, an iterative algorithm based on two criteria can also automatically give out the optimal clustering number, the defect that the traditional spectral clustering algorithm needs to manually give out the clustering number is overcome, the sub-blocks are printed in the main printing direction calculated by the method, a supporting structure is avoided in the whole 3D printing and forming process of the blade, and the method is simple and reliable.
Specifically, the invention combines the structural characteristics of the blade parts and the technological characteristics of multi-axis 3D printing, improves the spectral clustering algorithm of the background technology, enables the spectral clustering algorithm to be applied to the STL model of the blade parts, and performs segmentation according with the 3D printing technology;
when the triangular patch of the STL model of the blade part is processed, the triangular patch is initially clustered into a smaller number of initial clustering units by adopting an over-segmentation step, so that the efficiency of a subsequent clustering algorithm is effectively improved;
the invention also provides a method for automatically giving the optimal clustering number according to the blade part additive manufacturing process, and overcomes the defect that the clustering number needs to be given by the traditional spectral clustering algorithm;
according to the invention, the method of sub-block step-by-step printing is adopted for 3D printing of the blades, and each sub-block is printed in the main printing direction according to the algorithm, so that the problems that a large number of supporting structures are needed in the printing process and the printing quality of partial areas is poor due to the fact that the blade parts are generally bent seriously are solved.
The method can automatically divide the blade into a plurality of sub-blocks for realizing optimal printing, and has the advantages of no support and high printing quality compared with the traditional 3-axis 3D printing.
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Drawings
FIG. 1 is a flow chart of a 3+ 2-axis unsupported 3D printing manufacturing method of the blade type part.
FIG. 2 is a schematic representation of the results of the blade division obtained by the method of the present invention.
FIG. 3 is a schematic diagram of a step effect formed by a prior art method.
Detailed Description
Reference is made to fig. 1-2. The 3+2 shaft unsupported 3D printing manufacturing method of the blade parts comprises the following specific steps:
step 1, preparation: introducing a leaf part three-dimensional model in STL format (675 triangular patches in total), and simultaneously introducing a 134 point set and a 994 point set which are distributed on a unit sphere in a grid manner as a printing voting vector set D of an algorithm respectively0And a set of candidate printing direction vectors D1；
Step 2, segmentation pretreatment: because the calculated amount of the segmentation algorithm directly acted by the triangular patch of the blade model as the minimum unit is huge and redundant, the model is preprocessed firstly to improve the algorithm efficiency.
According to the three-dimensional model of the blade to be manufactured, software measures the maximum thickness d of the blade, wherein d is 18mm, and the maximum collapse angle | delta theta is found according to the printing material used by the partcIf it is 30 deg. as a triangle patch normal vector pair votePrinting an included angle threshold value of the direction vector voting;
traversing the whole set of triangular patches and the set of candidate printing direction vectors D1Calculating the included angle between the two, if a certain triangular patch TriAnd a certain candidate printing direction vector
Figure GDA0003274841570000071
Angle of inclusion at threshold thetacIn, i.e.
Figure GDA0003274841570000072
Figure GDA0003274841570000073
Then TriTo pair
Figure GDA0003274841570000074
And (5) casting 1 ticket. After the voting process is finished, pair D1Classifying the triangular patches with consistent printing direction vector conditions of the medium votes together, then calculating whether the centroid distance between the triangular patches is less than or equal to 36mm, if so, dividing the classified triangular patches into 1 initial clustering unit, otherwise, independently forming an initial clustering unit between the classified triangular patches, and otherwise, if a certain triangular patch and other patch pairs D are in charge of1If the vectors in the three-dimensional space vector have no same vote, the triangular patch alone forms 1 initial clustering unit, and finally 279 initial clustering units are obtained;
step 3, constructing a similarity matrix and a Laplace matrix of the triangular patch of the blade: for a given blade part B, constructing a similarity matrix W for describing the magnitude of similarity relation among initial clustering units as a basis for next clustering segmentation, and then calculating a normalization matrix D to further obtain a Laplacian matrix L for blade part normalization;
the size of the similarity matrix W is n2×n2(wherein n is2279, the number of initial clustering units), wherein the element wijRepresents an initial clustering unit CiAnd CjA criterion relation (kernel function) is established between the twoThe similarity of the initial clustering unit C itself, let wii＝0；
The similarity matrix establishment criterion of the blade parts is as follows:
step error is minimum: from the above, in the absence of a support structure, the error of a 3D printed part is caused by a step error (step effect) generated by incomplete perpendicularity of the printing direction and the normal vector of the surface of the part, wherein the step error is generated
Figure GDA0003274841570000075
Denotes the printing direction, h denotes the cross-sectional layer thickness, 0.3 is taken, niIs the normal vector at the ith triangular patch in the printed part STL model. Definition of tip height ciComprises the following steps:
Figure GDA0003274841570000076
step error E of single initial clustering unitiComprises the following steps:
Ei＝ci·S(Ci) (2)
wherein, S (C)i) Represents an initial clustering unit CiThe area of (d);
calculating an initial clustering unit CiAnd CjThe step error between is expressed as:
Figure GDA0003274841570000081
wherein the content of the first and second substances,
Figure GDA0003274841570000082
to minimize the step error, there are
Figure GDA0003274841570000083
Wherein, the sum of the areas of the two is divided by S (C)i)+S(Cj) Is to cluster the area of the unit initiallyHomogenizing;
the adjacent closeness degree between the adjacent initial clustering units is maximized: obviously, if two initial clustering units are to be divided into the same sub-block, the initial clustering units must be adjacent to each other, and under the condition that the step errors are the same, the greater the adjacent degree is, the more the priority is for dividing the two initial clustering units into the same sub-block, and any two adjacent initial clustering units C are divided intoi、CjDegree of adjacency Ne ofijIs represented as follows:
Figure GDA0003274841570000084
Figure GDA0003274841570000085
Figure GDA0003274841570000086
Figure GDA0003274841570000087
wherein x isiIs represented by CiSet of x coordinates of vertices, y, of all triangular patches in the seti、zi、xj、yj、zjFor the same reason, xijThen is Ci、CjThe x coordinate set of the vertexes of all the triangular patches;
through the two steps, the similarity matrix is established in the following way:
Figure GDA0003274841570000088
wherein λ is1Take 0.7, λ2Take 0.3
The normalized matrix D is calculated as follows:
Figure GDA0003274841570000089
the normalized Laplace matrix L of the blade parts has the formula:
Figure GDA0003274841570000091
and 4, dividing triangular patches of the blade parts: clustering the initial clustering units of the similarity matrix by using an improved clustering algorithm to obtain the optimal sub-block division B (B)1,B2,…BN) Calculating a main printing direction vector of each sub-block and each parameter representing theoretical printing error;
converting the clustering problem between initial clustering units in the solved similarity matrix into N classification problems of the feature vectors f corresponding to the first N feature values with the minimum L by adopting an Ncut method;
then standardizing the characteristic matrix composed of the N characteristic vectors into F according to rows, wherein each row is used as a N-dimensional sample, m samples are totally obtained, K-means clustering is adopted, the clustering dimension is N, and finally the optimal subblock division B (B) is obtained1,B2,…BN)；
Calculating a main printing direction vector of each sub-block: traversing the 994 candidate printing direction vector sets D generated before for each sub-block in turn0Taking out one element of the
Figure GDA0003274841570000092
Satisfy the requirement of
Figure GDA0003274841570000093
The error of the included angle value of all triangular patches in the corresponding sub-block is
Figure GDA0003274841570000094
The minimum error value of the included angle between the sub-block and the sub-block;
various parameters representing theoretical printing errors are calculated: specifically, the method comprises the following steps of obtaining information such as the sum (recorded as sum _ ang) of included angle values of normal vectors of each triangular patch in all sub-blocks and main printing direction vectors of the corresponding sub-blocks, the average (recorded as ave _ ang) of total included angles, the variance (recorded as var _ ang) of the total included angles, the maximum (recorded as ext _ ang) of included angles in parts and the like, wherein the expression is as follows;
Figure GDA0003274841570000095
Figure GDA0003274841570000096
Figure GDA0003274841570000097
Figure GDA0003274841570000098
ext_ang＝max(angij) (16)
for convenient expression, unifying the parameters into an output result parameter set Par;
step 5, determining the number of the optimal clustering sub-blocks, theoretical printing errors and blade segmentation information under the current clustering number by an iterative algorithm;
two criteria for the iterative algorithm to perform:
the normal vectors of all triangular patches in a sub-block are all less than the material collapse angle thetac＝30°；
The formula for calculating the included angle is as follows:
θi＝arccos|niPi|≤θc (17)
wherein, thetaiExpressing the normal vector N of any triangular patch when the number of clusters is NiCorresponding to the main printing direction PiThe included angle of (A);
to ensure the quality of the manufactured blade, theoretical printing errors of each initial clustering unit are specifiedDifference EtAll within a given manufacturing tolerance requirement E of the bladedH cos20 ° -0.28 mm;
if the blade is divided into 2 sub-blocks B1、B2The algorithm divides the initial clustering unit included in each sub-block (assume B)1In m initial clustering units, B2N) in the sub-block while giving a main printing direction vector P of each sub-blocki(ii) a Calculating theoretical printing error of any one initial clustering unit of the blades by the following formula
Figure GDA0003274841570000101
At this time j ∈ [1, m + n ]]
Figure GDA0003274841570000102
The specific flow of the iterative algorithm is as follows:
the clustering number N is an initial value, the clustering number N is substituted into a clustering algorithm to obtain output of a partitioning result of an initial clustering unit, an output result parameter set Par and the like, if elements in the current Par are all smaller than the Par output by the last N value, the next step is carried out, otherwise, clustering partitioning is carried out again until the condition is met;
two iteration criteria are judged:
Figure GDA0003274841570000103
θi≤θcif yes, outputting a clustering result, wherein the clustering number at the moment is the optimal clustering number N; if not, N is equal to N +1, and then the step 4 is returned to cluster again until the condition is met;
when the iteration is carried out until the N is 3, the conditions are met, namely, the impeller blade is divided into 3 sub-blocks, and sum _ ang is 4092.4622 degrees, the average value ave _ ang is 6.0943 degrees, the variance var _ ang is 20.1656 degrees, the maximum value ext _ ang in the part is 19.935 degrees, and the main printing directions of the 4 sub-blocks are P1(-0.1379,0.6935,0.7071)、P2(0，-0.9569，-0.2903)、P3(-0.1379，0.6935，0.7071)、P4(0.1622，0.8155，0.5556)
Step 6, applying the result output by the algorithm to 3+ 2-axis 3D printing of the blade part to complete the solid printing of the blade part;
when each subblock is printed, the 3+ 2-axis 3D printer needs to adjust the position and posture of the printed part, so that the main printing direction of the currently printed subblock given by the algorithm is consistent with the printing direction of the multi-axis 3D printer, the subblocks divided by the clustering algorithm are sequentially printed from bottom to top, and the unsupported high-quality blocked 3D multi-axis printing of the blade parts is realized.

Claims (1)

1. A3 +2 shaft unsupported 3D printing manufacturing method of a blade part is characterized by comprising the following steps:
step one, importing a leaf part three-dimensional model in an STL format, and simultaneously importing 134 point sets and 994 point sets which are distributed on a unit sphere in a grid mode and respectively used as printing voting vector sets D of an algorithm0And a set of candidate printing direction vectors D1；
Step two, performing over-segmentation on the triangular patch to realize the pretreatment of the model; according to the three-dimensional model of the blade to be manufactured, software measures to obtain the maximum thickness d of the blade, and the maximum collapse angle theta of the blade is found according to the printing material used by the partcThe included angle threshold value is used as whether the normal vector of the triangular patch votes for the voting printing direction vector or not;
traversing the whole set of triangular patches and the set of candidate printing direction vectors D1Calculating the included angle between the two, if a certain triangular patch TriAnd a certain candidate printing direction vector
Figure FDA0003274841560000011
Angle of inclusion at threshold thetacInternal, then TriTo pair
Figure FDA0003274841560000012
1, casting a ticket; after the voting process is finished, pair D1Triangular patch categorization with consistent print direction vector conditions for medium votesThe method comprises the steps of obtaining a triangular patch pair D, calculating whether the centroid distance between the triangular patches is smaller than or equal to 2D, if so, dividing the triangular patch into 1 initial clustering unit, otherwise, forming an initial clustering unit by the triangular patches, and otherwise, forming an initial clustering unit by a certain triangular patch and other patch pairs D1If the vectors in the three-dimensional space vector have no same vote, the triangular patch alone forms 1 initial clustering unit;
thirdly, constructing a similarity matrix W for the given blade part B to describe the similarity relation between each initial clustering unit as a basis for next clustering segmentation, and then calculating a normalization matrix D to further obtain a normalized Laplacian matrix L of the blade part;
the size of the similarity matrix W is n2×n2Wherein n is2Element w as the number of initial clustering unitsijRepresents an initial clustering unit CiAnd CjA rule relation is established between the initial clustering units, and w is used for eliminating the self similarity of the initial clustering unit Cii＝0；
The similarity matrix establishment criterion of the blade parts is as follows:
step error is minimum: from the above, in the absence of a support structure, the error of the 3D printed part is caused by a step error caused by the fact that the printing direction and the normal vector of the surface of the part are not completely perpendicular to each other
Figure FDA0003274841560000013
Denotes the printing direction, h denotes the cross-sectional layer thickness, niIs the normal vector at the ith triangular patch in the printed part STL model; definition of tip height ciComprises the following steps:
Figure FDA0003274841560000014
step error E of single initial clustering unitiComprises the following steps:
Ei＝ci·S(Ci) (2)
wherein S (C)i) Represents an initial clustering unit CiThe area of (d);
calculating an initial clustering unit CiAnd CjThe step error between is expressed as:
Figure FDA0003274841560000021
wherein the content of the first and second substances,
Figure FDA0003274841560000022
to minimize the step error, there are
Figure FDA0003274841560000023
Wherein the sum of the areas of the two is divided by S (C)i)+S(Cj) Homogenizing the area of the initial clustering unit;
the adjacent closeness degree between the adjacent initial clustering units is maximized: obviously, if two initial clustering units are to be divided into the same sub-block, the two initial clustering units must be adjacent, and under the condition that the step errors are the same, the greater the adjacent degree is, the more the priority is for dividing into the same sub-block, and any two adjacent initial clustering units C are divided intoi、CjDegree of adjacency Ne ofijIs represented as follows:
Figure FDA0003274841560000024
Figure FDA0003274841560000025
Figure FDA0003274841560000026
Figure FDA0003274841560000027
wherein x isiIs represented by CiSet of x coordinates of vertices, y, of all triangular patches in the seti、zi、xj、yj、zjFor the same reason, xijThen is Ci、CjThe x coordinate set of the vertexes of all the triangular patches;
through the two steps, the similarity matrix is established in the following way:
Figure FDA0003274841560000028
wherein wijIs the ith row and j column element, lambda in the similarity matrix1、λ2Respectively debugging parameters
The normalized matrix D is calculated as follows:
Figure FDA0003274841560000029
the normalized Laplace matrix L of the blade parts has the formula:
Figure FDA0003274841560000031
step four, clustering the initial clustering units of the similarity matrix by using an improved clustering algorithm to obtain the optimal sub-block division B (B)1,B2,…BN) Calculating a main printing direction vector of each sub-block and each parameter representing theoretical printing error;
converting the clustering problem between initial clustering units in the solved similarity matrix into N classification problems of the feature vectors f corresponding to the first N feature values with the minimum L by adopting an Ncut method;
then standardizing the characteristic matrix composed of the N characteristic vectors into F according to rows, wherein each row is used as a N-dimensional sample, m samples are totally obtained, K-means clustering is adopted, the clustering dimension is N, and finally the optimal subblock division B (B) is obtained1,B2,…BN)；
Calculating a main printing direction vector of each sub-block: firstly, traversing 994 candidate printing direction vector sets D generated before for each sub-block in turn0Taking out one element of the
Figure FDA0003274841560000032
Satisfy the requirement of
Figure FDA0003274841560000033
The error of the included angle value of all triangular patches in the corresponding sub-block is
Figure FDA0003274841560000034
The minimum error value of the included angle between the sub-block and the sub-block;
various parameters representing theoretical printing errors are calculated: the method specifically comprises the steps that the sum of included angle values of normal vectors of each triangular surface patch in all sub-blocks and main printing direction vectors of the corresponding sub-blocks is recorded as sum _ ang, the average value of the total included angle, ave _ ang and the variance of the total included angle, var _ ang and the maximum value of the included angle in a part is recorded as ext _ ang, and the expression is as follows;
Figure FDA0003274841560000035
Figure FDA0003274841560000036
Figure FDA0003274841560000037
Figure FDA0003274841560000038
ext_ang＝max(angij) (16)
for convenient postamble expression, unify these parameters to the parameter set Par of the output result;
step five, determining the number of the optimal clustering sub-blocks, the theoretical printing error and the blade segmentation information under the current clustering number by an iterative algorithm;
two criteria for the iterative algorithm to perform:
the included angle between the normal vector of all triangular patches in the sub-block and the main printing direction of the sub-block is less than the material collapse angle thetac；
The formula for calculating the included angle is as follows:
θi＝arccos|niPi|≤θc (17)
wherein, thetaiExpressing the normal vector N of any triangular patch when the number of clusters is NiCorresponding to the main printing direction PiThe included angle of (A); n isiIs the normal vector at the ith triangular patch in the printed part STL model; theoretical printing error E of each initial clustering unittAll within a given manufacturing tolerance requirement E of the bladedWithin the range;
if the blade is divided into 2 sub-blocks B1、B2Then, the algorithm divides the initial clustering units included in each sub-block, and B is assumed1In m initial clustering units, B2N, while giving the main printing direction vector P of each sub-blocki(ii) a Calculating theoretical printing error of any one initial clustering unit of the blades by the following formula
Figure FDA0003274841560000041
At this time j ∈ [1, m + n ]]，njIs the normal vector at the jth triangular patch in the printed part STL model;
Figure FDA0003274841560000042
the specific flow of the iterative algorithm is as follows:
the clustering number N is an initial value, the clustering number N is substituted into a clustering algorithm to obtain output of a partitioning result of an initial clustering unit, an output result parameter set Par and the like, if elements in the current Par are all smaller than the Par output by the last N value, the next step is carried out, otherwise, clustering partitioning is carried out again until the condition is met;
two iteration criteria are judged:
Figure FDA0003274841560000043
θi≤θcif yes, outputting a clustering result, wherein the clustering number at the moment is the optimal clustering number N; if not, N is equal to N +1, and then the step four is returned to cluster again until the condition is met;
step six, applying the result output by the algorithm to 3+ 2-axis 3D printing of the blade part to complete the solid printing of the blade part;
when each subblock is printed, the printer needs to adjust the position and posture of the printed part, so that the main printing direction of the current printed subblock given by the algorithm is consistent with the printing direction of the multi-axis 3D printer, the subblocks divided by the clustering algorithm are sequentially printed from bottom to top, and the unsupported high-quality blocked 3D multi-axis printing of the blade parts is realized.
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