CN112015138B - Blade contour error evaluation method based on K nearest neighbor iterative nearest grid algorithm - Google Patents

Blade contour error evaluation method based on K nearest neighbor iterative nearest grid algorithm Download PDF

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CN112015138B
CN112015138B CN202010918692.3A CN202010918692A CN112015138B CN 112015138 B CN112015138 B CN 112015138B CN 202010918692 A CN202010918692 A CN 202010918692A CN 112015138 B CN112015138 B CN 112015138B
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point
blade
patch
profile
point cloud
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CN112015138A (en
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樊炜
闵康
刘晓卓
张云飞
周涛
黄文�
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Institute of Mechanical Manufacturing Technology of CAEP
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/408—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by data handling or data format, e.g. reading, buffering or conversion of data
    • G05B19/4086—Coordinate conversions; Other special calculations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0004—Industrial image inspection
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/13—Edge detection
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35356—Data handling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10028—Range image; Depth image; 3D point clouds
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30108—Industrial image inspection
    • G06T2207/30164—Workpiece; Machine component

Abstract

The invention discloses a blade contour error evaluation method based on a K nearest neighbor iterative nearest grid algorithm, wherein a five-axis measurement system is adopted in the blade surface contour error evaluation method to obtain measurement point cloud of the whole blade surface, the maximum and minimum distance from the measurement point cloud to an ideal profile triangular patch is taken as a target function, and the KNN-ICM algorithm is used for matching and analyzing the measurement point cloud and a triangulated CAD model; the method solves the problem of incomplete analysis of the key section method, and completely reflects the deviation distribution of the whole and all parts of the blade profile.

Description

Blade contour error evaluation method based on K nearest neighbor iterative nearest grid algorithm
Technical Field
The invention relates to the technical field of computer-aided manufacturing and numerical control machining, in particular to a blade contour error evaluation method based on a K nearest neighbor iterative nearest grid algorithm.
Background
The blade part is used as a high-fault part in the power device, and the working performance and the service life of the whole machine are seriously influenced. The shape error of the blade profile has great influence on the secondary flow loss, directly influences the energy conversion rate of the air compressor and further influences the working efficiency, plays a very important role in the performance of the engine, and therefore the processing of the blade parts and the detection of the profile quality have very important significance in the detection of engine parts.
With the continuous development and improvement of the measuring technology, the technology and means for analyzing the surface profile of the blade are more and more. The contour information of the key part of the blade can be obtained based on a key section analysis method of a three-coordinate measuring machine. However, the three-coordinate measuring machine has low measuring efficiency, and the key section method cannot acquire all profile information of the molded surface. The five-axis coordinate measuring system can keep the probe continuously sweeping on the curved surface in the measuring process, can obtain all contour information of the surface of the workpiece, and then registers the measured point cloud with an ideal CAD model so as to evaluate the contour error of the molded surface. However, the existing round error evaluation method has the problems of low evaluation precision, low calculation efficiency, large memory consumption and the like.
Non-patent document A method for registration of 3-D maps proposes a point cloud matching method, but the efficiency of finding the closest point is very low, and the calculation fails when the point cloud is large in scale. In order to improve the calculation efficiency, a K Nearest Neighbor (KNN) algorithm is introduced into point cloud matching in non-patent document Tunnel development Analysis using KNNs-ICP Method Based on terrestial Laser Scanning Data to form a nearest neighbor point cloud matching Method (KNN-ICP), and the Method can efficiently acquire the nearest point of each point in the point cloud. However, the existing evaluation methods for profile contour errors still have defects, point clouds are adopted to describe a CAD model, data points which are dense enough are needed to ensure the accuracy of the distance between a calculation point and an ideal curved surface, the requirement on a memory is high, and the calculation efficiency is low. In addition, the existing contour error evaluation method adopts the distance between the measured point cloud and the ideal point cloud as an optimization target, but the index cannot accurately reflect the real contour error of the surface of the workpiece.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the existing contour error evaluation method adopts the distance between a measured point cloud and an ideal point cloud as an optimization target, but the index cannot accurately reflect the real contour error of the surface of a workpiece; the method adopts point cloud to describe the CAD model, needs the point cloud with enough density to ensure the precision of the distance between the calculation point and the ideal curved surface, and has high requirement on the memory and low calculation efficiency.
The invention solves the technology through the following technical scheme:
the scheme provides a blade contour error evaluation method based on a K nearest neighbor iterative nearest grid (KNN-ICM) algorithm, which comprises the following steps:
s1: triangulating each molded surface part of the compressor blade according to the machining tolerance to generate a triangular surface patch of each molded surface part, and acquiring a triangular surface patch discrete point cloud set of each molded surface part;
s2: measuring points of each molded surface part of the compressor blade are obtained by using an REVO five-axis scanning measuring system, and all measuring point cloud data sets are obtained;
s3: aiming at the discrete point cloud set and all the measured point cloud sets of the triangular surface patches of the parts of the molded surfaces, calculating the closest point and the corresponding distance from each measured point to the triangular surface patch by adopting a KNN algorithm and spreading search;
s4: if the absolute value of the difference between the average value of the distances from all the current measuring point positions to the triangular patch and the last calculated value is smaller than the iteration termination precision, the step S6 is entered, otherwise, the step S5 is continuously executed;
s5: calculating a rotation matrix and a translation matrix by using a quaternion method, enabling the current position of each measuring point to approach the position of the closest point on the corresponding triangular patch to obtain a new measuring point cloud data set, and returning to S3;
s6: and stopping the iterative calculation, and outputting the maximum contour error of the whole blade, the maximum contour error of each profile part, the average contour error of the whole blade and the average contour error of each profile part.
The further optimization scheme is that the machining tolerance of a workpiece is set to be tau, and the parts of the molded surfaces of the blades of the compressor are triangulated with the discrete precision of omega tau, wherein 0< omega < 1.
The further optimization scheme is that the compressor blade comprises: a bucket profile portion, a trailing edge profile portion, a back profile portion, and a leading edge profile portion.
The further optimization scheme is that when the triangular dissection is carried out on each section of the compressor blade, each section is dissected independently.
The further optimization scheme is that the mark numbers of a blade basin (CC) profile part, a rear edge (TE) profile part, a blade back (CV) profile part and a front edge (LE) profile part are sequentially 1,2,3 and 4;
by using
Figure BDA0002665906660000021
The number of discrete points representing the t-profile portion; k denotes the number of iterations of the KNN algorithm calculation, the initial case k is 0,
Figure BDA0002665906660000022
corner mark i 1 … nt，ntIndicates the number of partial measuring points of the t-shaped surface, N ═ Sigmatnt；
The set of the triangular patch discrete point clouds of all the profile parts is as follows:
Figure BDA0002665906660000023
all measured point cloud data sets are:
Figure BDA0002665906660000024
setting measuring points
Figure BDA0002665906660000025
The closest point to the triangular patch is:
Figure BDA0002665906660000026
the corresponding distance is:
Figure BDA0002665906660000027
wherein
Figure BDA0002665906660000028
The new measured point cloud data set obtained in S5 is
Figure BDA0002665906660000029
Wherein
Figure BDA00026659066600000210
Returning to S3 when k is k + 1;
the overall maximum profile error of the blade is as follows:
Figure BDA0002665906660000031
the maximum profile error for each profile section is:
Figure BDA0002665906660000032
the overall average profile error of the blade is as follows:
Figure BDA0002665906660000033
the average profile error for each profile section is:
Figure BDA0002665906660000034
the further optimization scheme is that the method for calculating the closest point and the corresponding distance from each measuring point to the triangular patch by adopting the KNN algorithm and the spreading search comprises the following steps:
t1: firstly, the discrete point cloud of the triangular surface patch of a certain molded surface part
Figure BDA0002665906660000035
Storing according to a k-d tree structure, and recording the triangular patch set as
Figure BDA0002665906660000036
mtThe number of patches of each part;
t2: calculating the position of the current measuring point
Figure BDA0002665906660000037
To the closest point on the triangular patch
Figure BDA0002665906660000038
To obtain
Figure BDA0002665906660000039
Distance to the closest point of the triangular patch
Figure BDA00026659066600000310
The further optimization scheme is that the T2 comprises the following specific steps:
t2.1 definition: if M istIf at least one vertex of the middle triangular patch is a certain element in the discrete point set V, the patch is called as a V associated patch, and a set formed by all the V associated patches is marked as CM (V); point cloud
Figure BDA00026659066600000311
The first K points with the distance from the middle point P to the middle point P from small to large are called as K nearest neighbor points of P, and the set formed by the K points is recorded as
Figure BDA00026659066600000312
Setting j as an iteration counter for calculating the closest point; let j be 1 and j be equal to 1,
Figure BDA00026659066600000313
note the book
Figure BDA00026659066600000314
Figure BDA00026659066600000315
To
Figure BDA00026659066600000316
The minimum value of the distances of each patch is
Figure BDA00026659066600000317
It corresponds to
Figure BDA00026659066600000318
Point of is
Figure BDA00026659066600000319
Discrete point cloud on triangular patch using KNN algorithm
Figure BDA00026659066600000320
Middle search
Figure BDA00026659066600000321
A nearest neighbor, calculating
Figure BDA00026659066600000322
T2.2: order
Figure BDA00026659066600000323
Discrete point cloud on triangular patch by KNN algorithm
Figure BDA00026659066600000324
Middle search
Figure BDA00026659066600000325
A nearest neighbor, calculating
Figure BDA00026659066600000326
And
Figure BDA00026659066600000327
Figure BDA00026659066600000328
t2.3 ifj<0, j ═ j +1, return T2.2; if not, then,
Figure BDA00026659066600000329
the further optimization scheme is that a measuring point is calculated
Figure BDA00026659066600000330
To
Figure BDA00026659066600000331
All the associated patch distances of the nearest neighbors take the minimum value of the distances
Figure BDA00026659066600000332
The method comprises the following specific steps:
k1: calculating data points
Figure BDA00026659066600000333
All relations to vertices containing a nearest neighborThe distance of the connected pieces;
k2: traverse in sequence
Figure BDA00026659066600000334
A nearest neighbor, calculating
Figure BDA00026659066600000335
The distance from each nearest neighbor point to all the associated patches with the vertex, and the minimum value of all the distances is taken as the minimum value
Figure BDA00026659066600000336
The further optimization scheme is that the K1 comprises the following specific steps:
k1.1: discrete point cloud with triangular patch
Figure BDA0002665906660000041
Median data point
Figure BDA0002665906660000042
Finding a triangular patch set M with a certain nearest neighbor point of CtAll the related patches CM (C) taking C as a vertex;
k1.2: calculating points
Figure BDA0002665906660000043
Distances to each triangular patch in the set CM (C), and taking the minimum value as a point
Figure BDA0002665906660000044
Distance to patch CM (C).
Calculating data points
Figure BDA0002665906660000045
Distance d to all associated patches CM (C) containing a nearest neighbor C as a vertexCM(C)(ii) a The method comprises the following steps:
(1) setting the intermediate and data points of the surface patch vertex of the CAD model
Figure BDA0002665906660000046
Finding all the related patches taking C as a vertex, wherein the nearest neighbor point of C is C;
(2) let one of the patches with C as the vertex be ABC. Separately calculating vectors
Figure BDA0002665906660000047
And
Figure BDA0002665906660000048
the included angle between is theta1And theta2. If it is
Figure BDA0002665906660000049
Or
Figure BDA00026659066600000410
Then calculate
Figure BDA00026659066600000411
Distance d to triangle patch ABCABC(ii) a If not, then,
Figure BDA00026659066600000412
as a point
Figure BDA00026659066600000413
Distance to triangle patch ABC.
Wherein, calculating
Figure BDA00026659066600000414
Distance d to triangle patch ABCABCThe process is as follows:
(a) is provided with
Figure BDA00026659066600000415
The point coordinate is (x)0,y0,z0) The coordinate of point A is (x)1,y1,z1) And the coordinate of the point B is (x)2,y2,z2) And the coordinate of the point C is (x)3,y3,z3). Let t1＝(y2-y1)(z3-z1)-(y3-y1)(z2-z1)，t2＝(z2-z1)(x3-x1)-(z3-z1)(x2-x1)，t3＝(x2-x1)(y3-y1)-(x3-x1)(y2-y1)，t4＝-(t1x1+t2y1+t3z1) Calculating
Figure BDA00026659066600000416
The projection point S of the plane where the triangular patch ABC is located is (x)S,yS,zS)：
Figure BDA00026659066600000417
Figure BDA00026659066600000418
Figure BDA00026659066600000419
(b) Is provided with
Figure BDA00026659066600000420
If the sequence of alpha, beta, gamma is not changed, the projection point is positioned in the triangular patch, and the projection point is taken
Figure BDA00026659066600000421
Otherwise, go to step (c);
(c) respectively calculating points
Figure BDA00026659066600000422
The distance from the three line segments AB, BC and CA of the patch is taken as the minimum value dABC. Therein, a point
Figure BDA0002665906660000051
To each stripThe calculation method of the edge distance is as follows: taking AB edge as an example, first calculate
Figure BDA0002665906660000052
Projected point D on line AB:
Figure BDA0002665906660000053
order to
Figure BDA0002665906660000054
When 0 is present<r<1, the projection point is inside the line segment; otherwise, the projection point is outside the line segment, point
Figure BDA0002665906660000055
Distance d to line segment ABABThe calculation formula of (2) is as follows:
Figure BDA0002665906660000056
similarly, d is calculatedBC，dCAGet dABC＝min{dAB,dBC,dCA}。
(3) Traversing all the associated patches with C as the vertex, respectively calculating the distances from the data points to all the associated patches with C as the vertex by adopting the steps, and taking the minimum value as dCM(C)。
Traverse in sequence
Figure BDA0002665906660000057
A nearest neighbor, calculating
Figure BDA0002665906660000058
The distance to the associated patch of each neighboring point is taken as the minimum value of all the distances and recorded as
Figure BDA0002665906660000059
Further, in S5, a quaternion method is used to calculateA rotation matrix and a translation vector. Note the book
Figure BDA00026659066600000510
Figure BDA00026659066600000511
The rotation matrix is R(k)Translation matrix is T(k)The specific calculation steps are as follows:
(1) set of computation points P(k)And Q(k)Central position of
Figure BDA00026659066600000512
And
Figure BDA00026659066600000513
and carrying out centralized processing:
Figure BDA00026659066600000514
(2) calculating a covariance matrix C from the centralized data point setmAnd constructing a positive definite matrix N through the covariance matrix:
Figure BDA00026659066600000515
Figure BDA00026659066600000516
(3) calculating the eigenvalue of the positive definite matrix N, wherein the eigenvector corresponding to the maximum eigenvalue corresponds to the rotation quaternion as follows:
q＝(q0,q1,q2,q3)T
(4) using a rotating quaternion q ═ q (q)0,q1,q2,q3)TThe rotation matrix is represented as:
Figure BDA0002665906660000061
(5) according to
Figure BDA0002665906660000062
Computing a translation vector T(k)。
The working principle of the method is as follows: in order to more accurately and comprehensively evaluate the precision of the whole surface of a part, the technical scheme adopts an REVO five-axis measuring system to obtain the measuring point cloud data of the whole blade surface and provides a K nearest neighbor iterative nearest grid algorithm to calculate the profile error between the measuring point cloud and a CAD model (the CAD model is divided into four parts, namely a CC profile part, a CV profile part, an LE profile part and a TE profile part).
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. according to the blade contour error evaluation method based on the K nearest neighbor iterative nearest grid algorithm, the five-axis measurement system is adopted in the blade surface contour error evaluation method to obtain the measurement point cloud of the whole blade surface, the speed is high, the precision is high, and the point cloud data obtaining efficiency is improved; the method solves the problem of incomplete analysis of the key section method, and completely reflects the deviation distribution of the whole and all parts of the blade profile.
2. According to the blade contour error evaluation method based on the K nearest neighbor iterative nearest grid algorithm, the maximum and minimum distance from the measured point cloud to the triangular surface patch of the ideal profile is used as a target function, the measured point cloud is matched and analyzed with the triangulated CAD model through the KNN-ICM algorithm, memory consumption during calculation is reduced, calculation accuracy and efficiency of the distance from the measured point to the ideal profile are improved, and the contour error of a workpiece can be reflected more accurately.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention.
FIG. 1 is a flow chart of a blade contour error evaluation method based on a K nearest neighbor iterative nearest grid algorithm;
FIG. 2 is a schematic structural diagram of a tablet press blade;
FIG. 3 is a schematic diagram of a REVO five-axis scanning measurement system;
FIG. 4 is a dot
Figure BDA0002665906660000063
Corresponding closest point
Figure BDA0002665906660000064
And with
Figure BDA0002665906660000065
An associated triangular patch being a vertex;
FIG. 5 shows measurement points
Figure BDA0002665906660000066
Schematic diagram of the position relation with the triangular patch;
FIG. 6 shows measurement points
Figure BDA0002665906660000067
Schematic diagram of the projection point of (a) in the triangular patch;
FIG. 7 shows measurement points
Figure BDA0002665906660000068
The projected point of (a) is outside the triangular patch;
FIG. 8 shows measurement points
Figure BDA0002665906660000071
A schematic diagram of the position relationship between the projection point and the triangular patch;
FIG. 9 shows measurement points
Figure BDA0002665906660000072
Projection point and triangular surfaceThe position relationship of the segment AB is shown schematically.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1
As shown in fig. 1, a method for evaluating a blade surface contour error based on a K-nearest neighbor iterative nearest grid algorithm includes the following steps:
s1, triangulation (0) is carried out on the CAD molded surface of the blade with the discrete precision of omega & tau, and the machining tolerance of the workpiece is set to be tau<ω<1) The set of discrete point clouds constituting the triangular patch is
Figure BDA0002665906660000073
Where t denotes the identification number of the respective part of the blade,
Figure BDA0002665906660000074
indicating the number of discrete points of the part plane.
S2: as shown in FIG. 3, a REVO five-axis measurement system is adopted to obtain measurement points on the surface of the whole blade, and a measurement point cloud data set is recorded as
Figure BDA0002665906660000075
ntRepresents the number of the measuring points of the part, and N is sigmat nt. k denotes the number of iterations, the initial case k is 0,
Figure BDA0002665906660000076
i＝1…nt。
s3: respectively calculating the current position of all measuring points for each part of the blade
Figure BDA0002665906660000077
To the closest point on the triangular patch
Figure BDA0002665906660000078
And corresponding distance
Figure BDA0002665906660000079
S4: when k is more than or equal to 1, calculating
Figure BDA00026659066600000710
If e<E (where e is the given iteration termination precision), go to step S6; otherwise, the step S5 is continued.
S5: rotation matrix R is calculated by adopting quaternion method(k)And translation matrix T(k)So that the current measurement point cloud
Figure BDA00026659066600000711
Approximation
Figure BDA00026659066600000712
Obtaining new measuring point cloud position
Figure BDA00026659066600000713
Wherein
Figure BDA00026659066600000714
Let k be k +1, return to step S3.
S6: stopping iteration, and respectively outputting maximum profile errors of the whole blade and each part
Figure BDA00026659066600000715
And
Figure BDA00026659066600000716
and average profile error of the whole and each part of the blade
Figure BDA00026659066600000717
And
Figure BDA00026659066600000718
further, in step S1, the blade profile is composed of four parts, i.e., a blade basin (CC), a blade back (CV), a Leading Edge (LE), and a Trailing Edge (TE), as shown in fig. 2. When the CAD model is triangulated, the four parts are separately subdivided.
Further, in step S3, the nearest point of each point cloud data in the triangular patch is found by using the KNN algorithm
Figure BDA00026659066600000719
The method comprises the following steps:
firstly, acquiring point cloud data of a blade profile by using a REVO five-axis scanning measurement system; the actual measurement point cloud consists of four parts of CC, CV, LE and TE. Recording the current position of some part of the measured point cloud data of the blade as follows:
Figure BDA0002665906660000081
k represents the number of iterations and the initial value is 0.
Second, the discrete point clouds that will form the triangular patch
Figure BDA0002665906660000082
Storing according to a k-d tree structure, and recording a part of triangular patch set as
Figure BDA0002665906660000083
mtThe number of partial triangular patches.
Thirdly, calculating the current position of the measuring point
Figure BDA0002665906660000084
To the closest point of the triangular patch
Figure BDA0002665906660000085
To a corresponding distance
Figure BDA0002665906660000086
Figure BDA0002665906660000087
i＝1...nt. Defining: if M istIf at least one vertex of the medium triangular patch is an element in the discrete point set V, the patch is calledV associated patch, the set formed by all associated patches of V is marked as CM (V); point cloud
Figure BDA0002665906660000088
The first K points with the distance from the middle point P to the middle point P from small to large are called as K nearest neighbor points of P, and the set formed by the K points is recorded as
Figure BDA0002665906660000089
Calculating the closest point
Figure BDA00026659066600000810
The specific procedure for the corresponding distances is as follows:
(1) let j be the calculation
Figure BDA00026659066600000811
To triangular patch MtIteration counter of the closest point. Let j be 1 and j be equal to 1,
Figure BDA00026659066600000812
note the book
Figure BDA00026659066600000813
Figure BDA00026659066600000814
To
Figure BDA00026659066600000815
The minimum value of the distances of each patch is
Figure BDA00026659066600000816
It corresponds to
Figure BDA00026659066600000817
Point of is
Figure BDA00026659066600000818
Point cloud using KNN algorithm
Figure BDA00026659066600000819
Middle search
Figure BDA00026659066600000820
A closest point, calculating
Figure BDA00026659066600000821
(2) Order to
Figure BDA00026659066600000822
Using KNN algorithm in
Figure BDA00026659066600000823
Middle search
Figure BDA00026659066600000824
A closest point, calculating
Figure BDA00026659066600000825
And
Figure BDA00026659066600000826
Figure BDA00026659066600000827
(3) if Δj<0, j ═ j +1, return (2); if not, then,
Figure BDA00026659066600000828
similarly, the four parts of the blade calculate the closest point on the patch and the corresponding distance in the same way. (As shown in FIG. 4, the triangle of the dotted line is
Figure BDA00026659066600000829
For the associated patch of the vertex, the point is determined by calculation
Figure BDA00026659066600000830
Is the closest point to the point of the image,
Figure BDA00026659066600000831
to threeThe distance of the corner pieces is
Figure BDA00026659066600000832
)
Further, the points are calculated
Figure BDA00026659066600000833
And
Figure BDA00026659066600000834
minimum of distances of all associated patches of the nearest neighbors
Figure BDA00026659066600000835
Comprises the following steps:
first, calculate the data point
Figure BDA00026659066600000836
Distance d to all associated patches CM (C) containing a nearest neighbor C as a vertexCM(C)；
(1) Setting the intermediate and data points of the surface patch vertex of the CAD model
Figure BDA00026659066600000837
Finding all related patches taking C as a vertex, wherein the nearest neighbor point of C is C;
(2) let one of the patches with C as the vertex be ABC. Separately calculating vectors
Figure BDA00026659066600000838
And
Figure BDA00026659066600000839
the included angle between is theta1And theta2. If it is
Figure BDA0002665906660000091
Or
Figure BDA0002665906660000092
Then calculate
Figure BDA0002665906660000093
Distance d to triangle patch ABCABC(ii) a If not, then,
Figure BDA0002665906660000094
as a point
Figure BDA0002665906660000095
Distance to triangle patch ABC.
Wherein, calculating
Figure BDA0002665906660000096
Distance d to triangle patch ABCABCThe process is as follows:
(a) as shown in fig. 8, let
Figure BDA0002665906660000097
The point coordinate is (x)0,y0,z0) The coordinate of point A is (x)1,y1,z1) And the coordinate of the point B is (x)2,y2,z2) And the coordinate of the point C is (x)3,y3,z3). Let t1＝(y2-y1)(z3-z1)-(y3-y1)(z2-z1)，t2＝(z2-z1)(x3-x1-(z3-z1)(x2-x1)，t3＝(x2-x1)(y3-y1)-(x3-x1)(y2-y1)，t4＝-(t1x1+t2y1+t3z1) Calculating
Figure BDA0002665906660000098
The projection point S of the plane where the triangular patch ABC is located is (x)S,yS,zS)：
Figure BDA0002665906660000099
Figure BDA00026659066600000910
Figure BDA00026659066600000911
(b) Is provided with
Figure BDA00026659066600000912
If the sequence of alpha, beta, gamma and alpha does not change sign, the projection point is positioned inside the triangular patch (as shown in figure 6), and the projection point is taken
Figure BDA00026659066600000913
Otherwise (the projection point is not inside the triangular patch, as shown in fig. 7), go to step (c);
(c) calculating points
Figure BDA00026659066600000914
The distance from the three line segments AB, BC and CA of the patch is taken as the minimum value dABC. Dot
Figure BDA00026659066600000915
The distance to each edge is calculated as follows: taking the AB edge as an example (as shown in FIG. 9, there are two cases that the projection point is inside the line segment and outside the line segment), first, calculate
Figure BDA00026659066600000916
Projected point D on line AB:
Figure BDA00026659066600000917
order to
Figure BDA00026659066600000918
When 0 is present<r<1, the projection point is inside the line segment; otherwise, the projection point is outside the line segment, point
Figure BDA00026659066600000919
Distance d to line segment ABABThe calculation formula of (2) is as follows:
Figure BDA00026659066600000920
similarly, d is calculatedBC，dCAGet dABC＝min{dAB,dBC,dCA}。
(3) Traversing all the associated patches with C as the vertex, respectively calculating the distances from the data points to all the associated patches with C as the vertex by adopting the steps, and taking the minimum value as dCM(c)。
Two, sequentially traverse
Figure BDA0002665906660000101
The nearest neighbor point is calculated by the method
Figure BDA0002665906660000102
The distance to the associated patch of each neighboring point is taken as the minimum value of all the distances and recorded as
Figure BDA0002665906660000103
Further, in step S5, a rotation matrix and a translation vector are calculated by a quaternion method. Note the book
Figure BDA0002665906660000104
Figure BDA0002665906660000105
The rotation matrix is R(k)Translation matrix is T(k)The specific calculation steps are as follows:
(1) set of computation points P(k)And Q(k)Central position of
Figure BDA0002665906660000106
And
Figure BDA0002665906660000107
and carrying out centralized processing:
Figure BDA0002665906660000108
(2) calculating a covariance matrix C from the centralized data point setmAnd constructing a positive definite matrix N through the covariance matrix:
Figure BDA0002665906660000109
Figure BDA00026659066600001010
(3) calculating the eigenvalue of the positive definite matrix N, wherein the eigenvector corresponding to the maximum eigenvalue corresponds to the rotation quaternion as follows:
q＝(q0,q1,q2,q3)T
(4) using a rotating quaternion q ═ q (q)0,q1,q2,q3)TThe rotation matrix is represented as:
Figure BDA00026659066600001011
(5) according to
Figure BDA00026659066600001012
Computing a translation vector T(k)。
Example 2
The specific implementation mode of the blade contour error evaluation method based on the K nearest neighbor iterative nearest grid algorithm comprises the following steps of:
marking the marks of four parts CC, CV, LE and TE of a blade CAD molded surface of an air compressor as t1, 2,3 and 4 respectively, taking the machining tolerance tau of a workpiece as 0.01mm, taking omega as 0.1, triangulating the blade CAD molded surface with the discrete precision of 0.1 tau, and integrating the discrete point clouds forming a triangular surface patch into a discrete point cloud set
Figure BDA00026659066600001013
The data amount of the discrete point cloud of each part is respectively
Figure BDA0002665906660000111
154966 in total. The discrete point clouds constituting the triangular patch
Figure BDA0002665906660000112
Storing according to k-d tree structure, each part of triangular patch is collected into
Figure BDA0002665906660000113
The number of each is m1＝69531、m2＝75043、m3＝59688、m4102331 and 306593 pieces in total. Adopting an REVO five-axis measuring system to obtain measuring points on the surface of the whole blade, and collecting the measuring point cloud data into a data set
Figure BDA0002665906660000114
The data quantity of the measured point clouds of each part is n1＝2866、n2＝2496、n3＝856、n41973, 8191 in total.
And step two, solving the closest point and the corresponding distance from the current measuring point positions to the triangular patch. Setting iteration termination precision as 0.001mm in the form of ∈, if the absolute value of the difference between the average value of the distances from all the current measuring points to the triangular patch and the last calculated value is smaller than the ∈, entering a fourth step, otherwise, continuing to execute a third step;
and thirdly, calculating a rotation matrix and a translation matrix by adopting a quaternion method, enabling the position of the current measurement point cloud to approach the nearest position on the triangular surface patch of the CAD model, and updating the position of the measurement point cloud. Returning to the step two;
and step four, terminating iteration, and respectively outputting the maximum contour error of the whole blade and each part and the average contour error of the whole blade and each part, as shown in table 1.
TABLE 1 average and maximum profile errors of the entire blade from section to section
Figure BDA0002665906660000115
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. The blade contour error evaluation method based on the K nearest neighbor iterative nearest grid algorithm is characterized by comprising the following steps of:
s1: triangulating each molded surface part of the compressor blade according to the machining tolerance to generate a triangular surface patch of each molded surface part, and acquiring a triangular surface patch discrete point cloud set of each molded surface part;
s2: measuring points of each molded surface part of the compressor blade are obtained by using an REVO five-axis scanning measuring system, and all measuring point cloud data sets are obtained;
s3: aiming at the discrete point cloud set and all measured point cloud data sets of the triangular surface patches of the parts of the molded surfaces, searching and calculating the closest point and the corresponding distance from each measured point to the triangular surface patch through a KNN algorithm;
s4: if the absolute value of the difference between the average value of the distances from all the current measuring point positions to the triangular patch and the last calculated value is smaller than the iteration termination precision, the step S6 is entered, otherwise, the step S5 is continuously executed;
s5: calculating a rotation matrix and a translation matrix by using a quaternion method, enabling the current position of each measuring point to approach the position of the closest point on the corresponding triangular patch to obtain a new measuring point cloud data set, and returning to S3;
s6: and stopping the iterative calculation, and outputting the maximum contour error of the whole blade, the maximum contour error of each profile part, the average contour error of the whole blade and the average contour error of each profile part.
2. The blade profile error evaluation method based on the K-nearest neighbor iterative nearest grid algorithm according to claim 1, wherein the machining tolerance of a workpiece is set to be tau, and each profile part of the compressor blade is triangulated with discrete precision of omega-tau, wherein 0< omega < 1.
3. The blade contour error evaluation method based on the K-nearest neighbor iterative nearest grid algorithm according to claim 1, wherein a compressor blade comprises: a bucket profile portion, a trailing edge profile portion, a back profile portion, and a leading edge profile portion.
4. The blade contour error evaluation method based on the K-nearest neighbor iterative nearest grid algorithm according to claim 2 or 3, wherein when triangulating each profile part of the compressor blade, each profile part is separately subdivided.
5. The blade contour error evaluation method based on the K-nearest neighbor iterative nearest grid algorithm according to claim 3, wherein the labels of the leaf basin profile part, the trailing edge profile part, the leaf back profile part and the leading edge profile part are t ═ 1,2,3 and 4 in sequence;
Figure FDA0003068641470000011
the number of discrete points representing the t-profile portion; k denotes the number of iterations of the KNN algorithm calculation, the initial case k is 0,
Figure FDA0003068641470000012
corner mark i 1 … nt，ntExpressing the number of partial measuring points of the t-shaped surface, wherein N is sigmatnt；
The set of the triangular patch discrete point clouds of all the profile parts is as follows:
Figure FDA0003068641470000013
all measured point cloud data sets are:
Figure FDA0003068641470000014
setting measuring points
Figure FDA0003068641470000015
The closest point to the triangular patch is:
Figure FDA0003068641470000016
the corresponding distance is:
Figure FDA0003068641470000017
wherein
Figure FDA0003068641470000021
The new measured point cloud data set obtained in S5 is
Figure FDA0003068641470000022
Wherein
Figure FDA0003068641470000023
R(k)Rotation matrix, T, for a measurement point cloud data set(k)A translation vector of the measurement point cloud data set; returning to S3 when k is k + 1;
the overall maximum profile error of the blade is as follows:
Figure FDA0003068641470000024
the maximum profile error for each profile section is:
Figure FDA0003068641470000025
the overall average profile error of the blade is as follows:
Figure FDA0003068641470000026
the mean profile error of each profile section is：
Figure FDA0003068641470000027
6. The method for evaluating the blade contour error based on the K-nearest neighbor iterative nearest grid algorithm according to claim 5, wherein the method for iteratively calculating the nearest point and the corresponding distance from each measuring point to the triangular patch by using the KNN algorithm comprises the following steps:
t1: firstly, the discrete point cloud of the triangular surface patch of a certain molded surface part
Figure FDA0003068641470000028
Storing according to a k-d tree structure, and recording the triangular patch set as
Figure FDA0003068641470000029
mtThe number of patches of each part;
t2: calculating the position of the current measuring point
Figure FDA00030686414700000210
To the closest point on the triangular patch
Figure FDA00030686414700000211
To obtain
Figure FDA00030686414700000212
Distance to the closest point of the triangular patch
Figure FDA00030686414700000213
7. The blade contour error evaluation method based on the K-nearest neighbor iterative nearest grid algorithm according to claim 6, wherein T2 comprises the following specific steps:
t2.1 definition: if M istAt least one vertex of the medium triangular patch is an element of the discrete point set V,the patch is called as the associated patch of V, and the set of all associated patches of V is denoted as cm (V); point cloud
Figure FDA00030686414700000214
The first K points with the distance from the middle point P to the middle point P from small to large are called as K nearest neighbor points of P, and the set formed by the K points is recorded as
Figure FDA00030686414700000215
Setting j as an iteration counter for calculating the closest point; let j be 1 and j be equal to 1,
Figure FDA00030686414700000216
note the book
Figure FDA00030686414700000217
Figure FDA00030686414700000218
To
Figure FDA00030686414700000219
The minimum value of the distances of each patch is
Figure FDA00030686414700000220
It corresponds to
Figure FDA00030686414700000221
Point of is
Figure FDA00030686414700000222
Discrete point cloud on triangular patch using KNN algorithm
Figure FDA00030686414700000223
Middle search
Figure FDA00030686414700000224
A nearest neighbor, calculating
Figure FDA00030686414700000225
T2.2: order
Figure FDA00030686414700000226
Discrete point cloud on triangular patch by KNN algorithm
Figure FDA00030686414700000227
Middle search
Figure FDA00030686414700000228
A nearest neighbor, calculating
Figure FDA00030686414700000229
And
Figure FDA00030686414700000230
Figure FDA00030686414700000231
t2.3 ifj<0, j ═ j +1, return T2.2; if not, then,
Figure FDA0003068641470000031
8. the method for evaluating the blade profile error based on the K-nearest neighbor iterative nearest grid algorithm according to claim 7, wherein a measuring point is calculated
Figure FDA0003068641470000032
To
Figure FDA0003068641470000033
The distance of all the related patches of the nearest neighbors is taken as the minimum value
Figure FDA0003068641470000034
The method comprises the following specific steps:
k1: calculating data points
Figure FDA0003068641470000035
Distances to all associated patches containing a certain nearest neighbor point as a vertex;
k2: traverse in sequence
Figure FDA0003068641470000036
A nearest neighbor, calculating
Figure FDA0003068641470000037
The distance from each nearest neighbor point to all the associated patches with the vertex, and the minimum value of all the distances is taken as the minimum value
Figure FDA0003068641470000038
9. The method for evaluating the blade contour error of the K-nearest neighbor iterative nearest grid algorithm according to claim 8, wherein K1 comprises the following steps:
k1.1: discrete point cloud with triangular patch
Figure FDA0003068641470000039
Median data point
Figure FDA00030686414700000310
Finding a triangular patch set M with a certain nearest neighbor point of CtAll the related patches CM (C) taking C as a vertex;
k1.2: calculating points
Figure FDA00030686414700000311
Distances to each triangular patch in the set CM (C), and taking the minimum value as a point
Figure FDA00030686414700000312
Distance to patch CM (C).
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