CN114299079B - Dense point cloud data-oriented engine blade section line data acquisition method - Google Patents
Dense point cloud data-oriented engine blade section line data acquisition method Download PDFInfo
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Abstract
The invention provides a dense point cloud-oriented engine blade section line data acquisition method, which is characterized in that blade plane characteristics are applied to the establishment of a blade part coordinate system, and the establishment of the blade part coordinate system and the section line data acquisition of an unknown blade model can be completed. Firstly, solving centroid and covariance matrixes of measured point cloud data, constructing a rigid body transformation matrix according to eigenvectors of the covariance matrixes, and down-converting the point cloud data from a coordinate system of a measuring system to a coordinate system of an initial part; secondly, dividing plane point cloud data in the blade, performing plane fitting to obtain a plane normal vector, performing cross product operation according to the plane normal vector and a direction vector of a Z axis of a standard part coordinate system to obtain a rotation axis of coordinate transformation from an initial part coordinate system to the part coordinate system, and calculating according to a cosine theorem to obtain a rotation angle; constructing a rotation matrix according to the rotation shaft and the rotation angle again, and realizing the conversion from the initial part coordinate system to the part coordinate system; then, intercepting blade measurement data under a part coordinate system by a point cloud data intercepting method to obtain three-dimensional section line data; and finally, projecting the three-dimensional section point cloud data to a section plane to obtain two-dimensional section point cloud data, thereby realizing acquisition of the blade section point cloud data under an unknown blade part coordinate system. The invention provides a dense three-dimensional point cloud-oriented blade section line data acquisition method, which provides standard section line data for detection and data partitioning of blade characteristic parameters and an effective method for establishing a part coordinate system of an unknown engine blade model.
Description
Technical Field
The invention provides a dense point cloud-oriented engine blade section line data acquisition method, which is characterized in that blade plane characteristics are applied to the establishment of a blade part coordinate system, and the establishment of the blade part coordinate system and the section line data acquisition of an unknown blade model can be completed. The invention belongs to the technical field of three-dimensional vision measurement.
Technical Field
The section line data acquisition of the engine blade is a precondition for the detection of the characteristic parameters of the engine blade. The evaluation indexes of the geometric processing precision of the engine blade in China are basically detected and calculated through the section data of the engine blade, and the traditional detection method mainly adopts a three-coordinate machine for measurement.
The method has the advantages that dense three-dimensional point cloud data of the blade can be obtained through measurement by the three-dimensional measurement method of binocular structured light, the obtained point cloud data is large in quantity and high in measurement efficiency, automatic measurement is easy to achieve, the obtained point cloud data is dense, the obtained point cloud data is not single-contour point cloud data obtained by the traditional method, and a part coordinate system of the blade is difficult to establish, so that the acquisition of blade section line data in the dense point cloud data is difficult. Under the condition of unknown blade design models and part coordinate systems, the invention provides the engine blade section line data acquisition method facing the dense point cloud data, which can provide available two-dimensional section data for the detection and extraction of the characteristic parameters of the engine blade.
Disclosure of Invention
The invention provides a dense point cloud-oriented blade section line data acquisition method, which applies blade plane characteristics to the establishment of a blade part coordinate system and can finish the establishment of the blade part coordinate system and the section line data acquisition of an unknown blade model. A flow chart of the blade section line data acquisition method for the dense point cloud is shown in the attached figure 1.
The basic principle of the method is that firstly, a normalized covariance matrix of measurement point cloud data is calculated, a eigenvector of the covariance matrix is solved by a eigenvalue decomposition method, a rigid body transformation matrix is constructed according to the eigenvector, and the measurement data is converted into an initial part coordinate system; secondly, calculating a rotation angle and a rotation axis required by correcting the part coordinate system by using a plane normal vector in the blade data and a Z-axis direction vector in the standard part coordinate system; calculating a rotation matrix for correcting the part coordinate system according to the rotation shaft and the rotation angle, and carrying out coordinate transformation on the blade point cloud data under the initial part coordinate system by using the rotation matrix; then, intercepting the blade data through point cloud data processing to obtain three-dimensional section line data; and finally, projecting the three-dimensional section line data to a section plane to obtain two-dimensional section line data of the blade.
The invention is different from other blade section line acquisition methods in that the invention realizes the interception of the blade section line data from the measured dense point cloud data, and is unique in that the invention is unknown to the part coordinate system of the measured blade, and has no blade theoretical design model as the reference for data alignment, and the invention has the most obvious and leading advantages of establishing the blade part coordinate system and acquiring the section line data aiming at the blade measurement data of the unknown blade model.
The technical solution of the invention is as follows: firstly, calculating eigenvalues and eigenvectors of a normalized covariance matrix of measurement data obtained by a binocular structured light measurement system, constructing a transformation matrix T according to the eigenvalues and the eigenvectors, and transforming the measurement data through the T matrix to enable blade data to be down-converted from a measurement system coordinate system to an initial part coordinate system; after the initial part coordinate system is established, correcting the initial part coordinate system by using a plane normal vector in the blade and a direction vector of a Z axis of the standard part coordinate system, wherein in the corrected part coordinate system, the bottom plane of the blade coincides with an XOY plane of the standard part coordinate system; intercepting the point cloud data at a certain height to obtain three-dimensional blade section line point cloud data, and projecting the three-dimensional blade section line point cloud data to a two-dimensional plane where the intercepting height is located to obtain the two-dimensional section line point cloud data of the blade. The method mainly comprises the following steps:
(1) Calculating centroid and normalized covariance matrix of the three-dimensional point cloud data, calculating eigenvectors and eigenvalues of the covariance matrix by utilizing an eigenvalue decomposition method, arranging the eigenvectors into a matrix P according to the sequence of the eigenvalues from large to small, constructing a rigid transformation matrix T according to the P and centroid coordinates, and applying the transformation matrix T to the measurement data to transform to an initial part coordinate system;
(2) The method for segmenting the point cloud data of the bottom surface of the blade comprises the following steps: firstly establishing an adjacency relation for point clouds through KD-Tree, secondly randomly selecting a point in the point clouds as a starting point of P search, obtaining the distance from each point to P point through KD-Tree neighbor searching algorithm, judging whether the distances from the adjacent points to P meet the condition or not through a distance threshold, storing the adjacent points and P in Q clusters if the distances are smaller than the threshold, selecting points except P in Q, repeating the above operation until the points in Q are not increased, and finally counting the number of the point clouds in a point set Q, wherein the planar point cloud data of the point set number within a specified number range is the planar point cloud data of the bottom of the blade. Fitting the plane point cloud data at the bottom of the blade by adopting a RANSAC algorithm to obtain a plane equation, calculating a cross product between a plane normal vector and a Z-axis direction vector in a standard part coordinate system to obtain a rotating shaft, and obtaining the rotating angle according to a cosine theorem;
(3) After the rotation axis and the rotation angle are known, a rotation transformation matrix is constructed according to a Rodrigues rotation formula, and measurement data is converted from an initial part coordinate system to a new part coordinate system, so that the correction of the initial part coordinate system is completed;
(4) In the dense three-dimensional blade point cloud data under the corrected part coordinate system, a plane parallel to the Z axis is a section plane, the position of the section plane can be flexibly set according to detection requirements, and three-dimensional section line point cloud data of the blade with a certain thickness is intercepted at the section plane;
(5) And projecting the three-dimensional section line point cloud data onto a section plane to obtain the two-dimensional section line point cloud data of the blade.
The expression of the normalized covariance matrix mentioned in step (1) is:
Wherein Cov (x, x), cov (y, y) and Cov (z, z) are covariances between data of the same dimension, essentially differences between one-dimensional features, i.e., variances, and the remainder are covariances between two-dimensional features, and the normalized covariance matrix can be found to be a real symmetric matrix, and feature values and feature vectors can be solved by a feature value decomposition method. The final constructed rigid body transformation matrix is expressed as:
wherein R is the transposed matrix of P, t= -r×s, s is the centroid coordinates of the measurement point cloud data. After the point cloud under the measurement system is subjected to matrix T transformation, the point cloud data under the initial part coordinate system is obtained.
In the step (2), the blade bottom plane is the planar structure with the largest area and the most flat in the blade point cloud data, the blade bottom plane point cloud data is easier to divide and has the highest flatness, and in the standard part coordinate system, the blade bottom plane should be parallel or coincident with the XOY plane of the standard part coordinate system, so that the rotation axis and the rotation angle can be calculated according to the normal vector n= (a, B, C) of the blade bottom plane and the Z-axis direction vector v= (0, 1) in the standard part coordinate system, the rotation axis can be obtained by calculating the cross product of n and v, and the two-vector included angle can be known according to the cosine theorem, and the included angle is the rotation angle.
The rigid transformation matrix algorithm is constructed in the step (3), wherein the rotation formula of the Reed-Giss is as follows:
R＝I+(sinθ)K+(1-cosθ)K2
Wherein R is a three-dimensional rotation matrix, I is a three-dimensional unit matrix, theta is a rotation angle, K is an antisymmetric matrix constructed after rotation vector unitization, and the rotation matrix of the correction part coordinate system can be calculated according to the formula.
The method for intercepting the three-dimensional section line of the blade in the step (4) is characterized in that the normal vector direction of the appointed section plane in the program is parallel to the Z-axis direction, and three-dimensional point clouds with the thickness of 0.08mm are intercepted on the upper part and the lower part of the section plane respectively, so that complete three-dimensional section line point cloud data of the blade can be obtained.
The method for acquiring the two-dimensional section line point cloud data in the step (5) projects the three-dimensional section line data to the section plane designated in the step (4) to obtain the two-dimensional plane section line point cloud data.
The invention has the advantages that:
The invention aims at dense point cloud data measured by a binocular structured light measuring system, and can complete the establishment of a blade coordinate system and the acquisition of section line data on the premise of not knowing a part coordinate system and a design model. This is different from the conventional study of obtaining the section line of the engine blade, and in the past, the section line data of the blade is obtained either based on a theoretical design model or a conversion relationship between a known measurement system and a part coordinate system, or two-dimensional section line data of the blade can be directly obtained through measurement equipment. The method can help reverse engineering design to recover a more accurate blade model by acquiring blade section line data, and provides accurate point cloud data for detecting engine blade section characteristic parameters of dense point cloud data.
In summary, the invention provides a dense point cloud-oriented engine blade section line data acquisition method, which is based on transformation matrix information obtained by calculation of measurement data, and corrects a part coordinate system by combining plane characteristics in a blade, so that a blade bottom plane coincides with an XOY plane in a standard part coordinate system, a point cloud plane interception method is adopted, and three-dimensional section line point cloud is projected to the section plane, so that the acquisition of the engine blade section line data is realized, and an acquisition result is displayed by two-dimensional point cloud data.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is bottom-blade planar point cloud data obtained by point cloud segmentation in blade measurement point cloud data.
FIG. 3 is a schematic illustration of the location of engine blade point cloud data in an initial part coordinate system and a corrected part coordinate system. In the figure, 1 is a standard part coordinate system, which is an unknown coordinate system, 2 is point cloud data of the engine blade under the initial part coordinate system, and 3 is point cloud data of the engine blade after the initial part coordinate system is corrected by the plane characteristics.
FIG. 4 is a schematic view of intercepting three-dimensional point cloud data of a designated position of an engine blade. In the figure, 1 is engine blade point cloud data, and 2 is an effect graph taken at different blade heights.
Fig. 5 is a front-back schematic view of the projection of point cloud data onto a two-dimensional plane. In the figure, 1 is three-dimensional section line point cloud data of an engine blade, and 2 is two-dimensional section line point cloud data of the blade obtained after projection.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and the specific embodiments.
The invention provides an engine blade section line data acquisition method for dense point cloud data, which is implemented by a flow chart shown in figure 1, and comprises the steps of calculating centroid and normalized covariance matrix of measured three-dimensional point cloud data, calculating eigenvectors and eigenvalues of the covariance matrix by using an eigenvalue decomposition method, constructing a rigid body transformation matrix T according to the eigenvectors, and converting the measured data into an initial part coordinate system; the method comprises the steps of obtaining plane data in a blade by adopting a point cloud segmentation method, as shown in fig. 2, fitting a plane by adopting a RANSAC algorithm to obtain a plane normal vector, calculating a rotation axis and a rotation angle of a correction matrix according to the plane normal vector and a direction vector of a Z axis of a standard part coordinate system, and further determining the rotation matrix to realize correction of an initial part coordinate system; the corrected blade measurement data adopts a point cloud plane interception method to obtain three-dimensional section line data, and a projection method is adopted to obtain two-dimensional section line data. A schematic of the initial blade-part coordinate system and the corrected blade-part coordinate system is shown in fig. 3. The invention specifically operates as follows:
1. Calculating centroid s of blade measurement data, normalizing the measurement data according to centroid coordinates to obtain normalized data, and calculating covariance matrix C of the normalized data, wherein the expression of the normalized covariance matrix is as follows:
The Cov (x, x), cov (y, y) and Cov (z, z) are covariances between data in the same dimension, the differences between one-dimensional features are essential, namely variances, the rest are covariances between two-dimensional features, eigenvalue decomposition is carried out on a covariance matrix to obtain three eigenvalues and eigenvectors thereof, the eigenvectors are ordered in the order from large to small of the eigenvalues to obtain a matrix P, the transposition of the matrix P is a rotation matrix R in rigid transformation, the translation vector in the rigid matrix is-Rxs, and the final rigid transformation matrix is:
After the measurement data is transformed by the rigid transformation matrix T, the blade point cloud data in the initial part coordinate system shown as 2 in fig. 2 can be obtained.
2. The bottom plane of the blade is a plane structure with the largest area and the flattest area in the point cloud data of the blade, and the point cloud data of the bottom plane of the blade is easier to divide and has the highest flatness. In the master part coordinate system, the blade bottom plane should be parallel or coincident with the XOY plane of the master part coordinate system, so that the blade initial part coordinate system can be corrected according to the normal vector of the blade bottom plane. The method for segmenting the point cloud data of the bottom surface of the blade comprises the following steps: firstly establishing an adjacency relation for point clouds through KD-Tree, secondly randomly selecting a point in the point clouds as a starting point of P search, obtaining the distance from each point to P point through KD-Tree neighbor searching algorithm, judging whether the distances from the adjacent points to P meet the condition or not through a distance threshold, storing the adjacent points and P in Q clusters if the distances are smaller than the threshold, selecting points except P in Q, repeating the above operation until the points in Q are not increased, and finally counting the number of the point clouds in a point set Q, wherein the planar point cloud data of the point set number within a specified number range is the planar point cloud data of the bottom of the blade. The segmented blade bottom plane data is shown in figure 2. And (3) fitting the plane point cloud data of the bottom of the blade by adopting a RANSAC algorithm to obtain a plane equation, wherein the normal vector of the plane of the bottom of the blade is n= (A, B and C), the direction vector of the Z axis in a standard part coordinate system is v= (0, 0 and 1), a rotation axis can be obtained by solving a cross product of n and v, and the included angle of the two vectors can be known according to a cosine theorem, and the included angle is the rotation angle.
3. The rotation matrix is constructed from the rotation axis and the rotation angle according to the rondrigas rotation formula. According to the obtained unit rotation vector of the Rode+, u Λ is an antisymmetric matrix constructed according to u, and according to the formula, a rotation matrix R' for correcting the coordinate system of the part can be calculated. And constructing a rigid body transformation matrix T 'by using the rotation matrix R', wherein R in the formula (2) is replaced by R ', T is replaced by a three-dimensional column vector of all 0, and the transformation matrix T' is adopted to correct the point cloud data under the initial part coordinate system, so that the blade point cloud data under the corrected part coordinate system as shown in 3 in figure 3 can be obtained.
4. According to the plane intercepting method in the point cloud data processing, the point cloud data with specified dimension and specific range in the point cloud data can be acquired, in the process of acquiring the section line of the blade, the intercepted dimension is in the z direction, the intercepting range can be set through a program, and the section thickness is set to be 0.16mm after experimental verification, so that the problem of low processing speed caused by the fact that the quantity of the point cloud data of the section line of the blade is not excessive can be ensured, and the integrity of the section data is considered. A schematic of blade section line data is taken at different heights as shown in fig. 4. The three-dimensional section line point cloud data obtained finally are shown as 1 in fig. 5, and it can be seen that the blade section data have a certain thickness.
5. Because the point cloud data measured by the binocular structured light three-dimensional measurement method is three-dimensional dense point cloud data and is uniformly distributed in space, the intercepted three-dimensional section line data can be projected to a section plane, so that the projection point of the three-dimensional point cloud on the two-dimensional plane is obtained. In the point cloud data processing, the projection model type and the parameters of the projection model can be set, any point cloud is projected onto the set parameter model, the obtained cross-section point cloud data is projected by using the method, the 1-direction cross-section plane in fig. 5 is projected, the coordinate value of the obtained blade cross-section point cloud data is in a two-dimensional plane rectangular coordinate system, and the result is shown as 2 in fig. 5.
Claims (5)
1. The engine blade section line data acquisition method for dense point cloud data is characterized by comprising the following steps of:
(1) Calculating centroid and normalized covariance matrix of three-dimensional point cloud data of blade measurement, calculating eigenvectors and eigenvalues of the covariance matrix by utilizing an eigenvalue decomposition method, arranging the eigenvectors into a matrix P according to the sequence of the eigenvalues from large to small, constructing a rigid transformation matrix T according to the P and centroid coordinates, and applying the transformation matrix T to the measurement data to transform to an initial part coordinate system;
(2) Dividing plane point cloud data in the blade into Ping Miandian clouds at the bottom of the blade by adopting a point cloud data processing method, performing plane fitting on the plane point cloud data, calculating a cross product between a plane normal vector and a Z-axis direction vector in a standard part coordinate system to obtain a rotation axis, and calculating according to a cosine theorem to obtain a rotation angle;
(3) Constructing a rotation transformation matrix according to the Rodrigues rotation formula, and converting measurement data from an initial part coordinate system to a finally established part coordinate system, thereby completing the correction of the initial part coordinate system;
(4) Filtering the point cloud data under the part coordinate system, and intercepting three-dimensional section line point cloud data of the blade with a certain thickness at a specified height of the blade;
(5) Projecting the three-dimensional section line point cloud data onto a section plane to obtain the two-dimensional section line point cloud data of the blade, wherein the expression of the normalized covariance matrix mentioned in the step (1) is as follows:
Wherein Cov (x, x), cov (y, y) and Cov (z, z) are covariances between data of the same dimension, essentially differences between one-dimensional features, namely variances, and the remainder are covariances between two-dimensional features, finding that the normalized covariance matrix is a real symmetric matrix, solving eigenvalues and eigenvectors by a eigenvalue decomposition method, and finally forming a rigid transformation matrix expressed as:
wherein R is the transposed matrix of P, t= -R×s, s= (x, y, z) is a vector represented by the centroid of the measured point cloud data, and the point cloud under the measurement system is obtained after the point cloud under the measurement system is subjected to matrix T transformation, namely the point cloud data under the initial part coordinate system.
2. The method according to claim 1, characterized in that: in the step (2), the blade bottom plane is the planar structure with the largest area and the most flat in the blade point cloud data, the blade bottom plane point cloud data is easier to divide and has the highest flatness, in the standard part coordinate system, the blade bottom plane should be parallel or coincident with the XOY plane of the standard part coordinate system, so the rotation axis and the rotation angle are calculated according to the normal vector n= (a, B, C) of the blade bottom plane and the Z-axis direction vector v= (0, 1) in the standard part coordinate system, the rotation axis is obtained by calculating the cross product of n and v, and the two vector included angles are known according to the cosine theorem, and the included angle is the rotation angle.
3. The method according to claim 1, characterized in that: the formula of the Reed-Solomon rotation matrix of the rigid transformation matrix algorithm constructed in the step (3) is as follows:
R＝cosθI+(1-cosθ)uuT+sinθuΛ，
Wherein R is a three-dimensional rotation matrix, I is a three-dimensional unit matrix, theta is a rotation angle, u is a unit rotation vector obtained by solving cross products of n and v, u Λ is an antisymmetric matrix constructed according to u, and the rotation matrix of the coordinate system of the correction part is calculated according to the formula.
4. The method according to claim 1, characterized in that: and (3) performing point cloud filtering processing in the step (4), wherein a field for point cloud screening is designated as a coordinate in the Z direction, and point cloud data with the thickness of 0.08mm is intercepted on the upper and lower sides of the section plane, so that complete three-dimensional section line point cloud data of the blade are obtained.
5. The method according to claim 1, characterized in that: the projection of the three-dimensional point cloud onto the cross-sectional plane in the step (5) is to project the three-dimensional cross-sectional line data onto the cross-sectional plane designated in the step (4) to obtain two-dimensional plane cross-sectional line point cloud data.
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