A calibration method for aero-engine blade surface measurement system based on sphere center feature point transformation

Abstract

The invention relates to a calibration method for an aero-engine blade profile measurement system based on sphere center feature point transformation, and belongs to the field of precision measurement and instrument technology. The method comprises the following steps: fixing the relative positions of a line structured light sensor A (1) and a line structured light sensor B (2), and placing a standard sphere (3) within the measurement range of the line structured light sensor A (1) and the line structured light sensor B (2); placing the standard sphere (3) at N different positions on a guide rail (5), and measuring N groups of cross-sectional arc data at different positions; fitting the arc profile of the standard sphere (3), obtaining the center coordinates and radius of a fitting circle (6), and obtaining a sphere center point set of the standard sphere (3), and then fitting the motion equation of the guide rail (5), and evaluating the calibration result through a precision polyhedron (7). The invention can realize the precise calibration of the aero-engine blade profile measurement system and improve the aero-engine blade profile measurement accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of precision measurement and instrumentation, and in particular relates to a calibration method for an aero-engine blade profile measurement system based on sphere center feature point transformation. Background Art

[0002] Blades are the core components of aircraft engines, accounting for over one-third of the total manufacturing volume. They are the most numerous and diverse parts in an engine. The quality of the blade profile directly impacts the engine's energy conversion efficiency, so the profile and structural parameters need to be inspected at each stage of blade processing to control the quality of the blade's machining. In actual testing, errors in the relative positioning of the guide rails and sensors can occur due to factors such as labor and equipment. This can cause the measured object placed on the guide rail to deviate from its intended direction during movement, resulting in significant deviations in the data measured by the sensor. Therefore, conducting research on the calibration of the guide rail's movement direction and accurately assessing the measured object's movement direction are crucial for improving the accuracy of the entire measurement system.

[0003] Currently, the more commonly used installation posture calibration method is the fixed-point posture change method. The fixed-point posture change method is to change the posture of the robot to measure the fixed sphere center, and solve the posture relationship between the robot and the sensor based on the principle of unchanged sphere center position. Although the fixed-point posture change method is simple, the posture of the measurement system with a mobile mechanism as the carrier cannot be changed arbitrarily, and it is sensitive to geometric errors.

[0004] The paper (Wuxunbo Y, Kejun Z, Yanjun F, et al. Demonstration of a simple and flexible calibration method for structured light system[J]. Optik, 2023, 276.) uses a calibration method in which a circular calibration plate is moved arbitrarily multiple times within the depth of field of the camera and projector. Leveraging existing camera calibration methods, the position and attitude of each calibration plate are derived, while phase and height data for each pixel are simultaneously established.

[0005] Patent CN217932765U, "A Robotic Surface Structured Light Stereo Camera Online Calibration Device," proposes an online calibration device for a robot surface structured light stereo camera. An industrial robot drives a surface structured light stereo camera to various calibration poses. The surface structured light stereo camera captures images of a calibration partner. Based on the pose changes of the calibration partner at each calibration pose, pose conversion information between the surface structured light stereo camera and the industrial robot is obtained. However, the calibration sensor uses surface structured light, making it impossible to calibrate the guide rail pose using line structured light.

[0006] A comprehensive analysis of the above methods reveals significant limitations in existing measurement system calibration methods. They cannot meet the requirements of using a unidirectional cursor to determine the direction of guide rail motion. While the fixed-point variable pose method is simple and sufficient for guide rail pose calibration, it is sensitive to geometric errors, significantly impacting the accuracy and efficiency of spherical profile measurement. Summary of the Invention

[0007] To address the challenges of existing technologies, the present invention discloses a calibration method for an aircraft engine blade profile measurement system based on sphere center feature point transformation. This method utilizes two linear structured light sensors, places a standard sphere on a guide rail, moves the guide rail, measures the spherical surface of the standard sphere, and fits the sphere center. The relative position of the guide rail relative to the sensors is then determined using a corresponding mathematical algorithm. This method improves the accuracy of guide rail relative position calibration and provides a feasible method for calibrating guide rail position using dual-line structured light.

[0008] The technical solution of the present invention is:

[0009] 1) Fix the relative positions of the line structured light sensor A (1) and the line structured light sensor B (2), and place the standard ball (3) within the measurement range of the line structured light sensor A (1) and the line structured light sensor B (2);

[0010] 2) The standard ball (3) is placed at N different positions on the guide rail (5), and the line structured light sensor A (1) and the line structured light sensor B (2) are used to measure the cross-sectional arc data of the standard ball (3) at N different positions, and the measurement point set (X ij ,Z ij ), i = 1, 2, ..., N, j = 1, 2, ..., n, where N is the number of cross-sectional arc data sets at different positions, and n is the number of data points measured in each set of arc segments;

[0011] 3) Fitting the arc profile of the standard sphere (3) by the cross-sectional arc data, and converting the arc measurement point set (X ij ,Z ij ) The center coordinates of each set of fitting circles (6) are obtained by mathematical fitting. i =(x i ,z i ), the circle radius is r i ;

[0012] 4) According to the known radius R of the standard sphere (3), the point set (X ij ,Z ij ) corresponds to the center point set P of the standard sphere (3) i ;

[0013] 5) Through the sphere center point set P i, the spatial straight line equation of the center of the standard sphere (3) in the measurement coordinate system is fitted, and the direction vector of the spatial straight line is obtained as (a, c, 1), that is, the movement direction of the guide rail (5), where a is the component of the movement direction of the guide rail (5) along the x-axis, c is the component of the movement direction of the guide rail (5) along the y-axis, and 1 is the component of the movement direction of the guide rail (5) along the z-axis.

[0014] 6) The movement direction of the guide rail (5) is calibrated and the calibration result is evaluated by a precision polyhedron (7).

[0015] In step 2), the data measured by the two line structured light sensors are along the x-direction and the z-direction, where the data in the x-direction reflects the vertical distance from the measuring point to the sensor, representing the width information of the measured point; the data in the z-direction reflects the lateral distance from the measuring point to the sensor, representing the depth information of the measured point. The y-axis direction is obtained by establishing a spatial rectangular coordinate system according to the right-hand coordinate system principle.

[0016] The coordinates of the center of the fitting circle (6) in step 3) are obtained by minimizing the square error sum fitting principle.

[0017] Let the curve of the fitted circle be:

[0018]

[0019] Here, x i is the coordinate of the center of the fitting circle (6) corresponding to each set of arc segments along the x-axis, z i is the coordinate of the center of the fitting circle (6) corresponding to each set of arc segments along the z-axis, p = -2x i ,q=-2z i , s = x i 2 +z i 2 , r i is the radius of the fitting circle (6) corresponding to each set of arc segments;

[0020] Measuring point (X ij ,Y ij ) to the center of the fitted circle (6) ij and the radius r of the fitting circle (6) i The squared difference is:

[0021]

[0022] Let the objective function f i (p,q,s) is:

[0023]

[0024] The objective function is optimized and solved, and the corresponding circular curve when it takes the minimum value is the optimal fitting circle.

[0025] The center P of the standard sphere (3) obtained in step 4) i for:

[0026]

[0027] Where y i is the coordinate of the center of the standard sphere (3) corresponding to each set of fitting circles (6) along the y-axis direction, The sign of is determined by the intersection of the light plane and the standard sphere (3), and R is the radius of the standard sphere (3).

[0028] In step 5), the motion direction of the guide rail (5) is solved by the least squares fitting method.

[0029] When the space line is not parallel to the XOY plane, the equation of the space line is:

[0030]

[0031] Right now:

[0032] Here, a is the component of the motion direction of the guide rail (5) along the x-axis, c is the component of the motion direction of the guide rail (5) along the y-axis, and (b, d, 0) is a point on the equation of the straight line of motion of the guide rail.

[0033] Through step 4) we get the center space coordinate point set {P i}, i=1,2,…,N, and substitute it into the equation of the line in space, we have:

[0034]

[0035] Where x′ i The z-axis coordinate under the equation of the space line is z i The coordinate of the corresponding point along the x-axis, y′ i The z-axis coordinate under the equation of the space line is z i The coordinate of the corresponding point along the y-axis.

[0036] make:

[0037]

[0038] Find the partial derivatives of a, b, c, and d respectively:

[0039]

[0040] Rearranging the equations yields:

[0041]

[0042] make Then we have:

[0043] That is:

[0044]

[0045] In step 6), the precision polyhedron (7) is a standard regular 12-sided prism. The accuracy of the spatial motion direction of the translation stage is analyzed by comparing the measured plane angle value with the nominal angle value of the standard regular prism. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The schematic diagram of the calibration method for the aero-engine blade profile measurement system based on the transformation of sphere center feature points.

[0047] Figure 2 The diagram is a system diagram of the calibration method of the aero-engine blade profile measurement system based on the transformation of the sphere center feature points;

[0048] Figure 3 It is the geometric relationship diagram between the fitting circle and the center of the measured sphere;

[0049] Figure 4 It is a precise polyhedron;

[0050] In the figure: 1. Line structured light sensor A; 2. Line structured light sensor B; 3. Standard sphere; 4. Sliding table; 5. Guide rail; 6. Fitting circle; 7. Precision polyhedron.

[0051] The present invention has the following characteristics and beneficial effects:

[0052] 1. In the present invention, the movement direction of the guide rail is calibrated by fitting the center of the standard sphere. The standard sphere is made by high-precision processing, so the measured data has high accuracy, reducing the calibration error.

[0053] 2. In this invention, the relative position of the guide rail is measured by sliding a standard ball on the guide rail. This method is simple and can directly obtain the relative position of the guide rail in the sensor coordinate system. After obtaining the relative position of the guide rail, the three-dimensional measurement of the object under test can be performed.

[0054] The invention has a wide range of uses and is particularly suitable for three-dimensional measurement of the surface profile of aero-engine blades. DETAILED DESCRIPTION

[0055] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0056] A method for calibrating an aero-engine blade profile measurement system based on sphere center feature point transformation, the method comprising the following steps:

[0057] 1) Fix the relative positions of the line structured light sensor A1 and the line structured light sensor B2, and place the standard ball 3 within the measurement range of the line structured light sensor A1 and the line structured light sensor B2;

[0058] 2) The standard ball 3 is placed at N different positions on the guide rail 5, and the line structured light sensor A1 and the line structured light sensor B2 are used to measure the cross-sectional arc data of the standard ball 3 at N different positions, and the measurement point set (X ij ,Z ij ), i = 1, 2, ..., N, j = 1, 2, ..., n, where N is the number of cross-sectional arc data sets at different positions, and n is the number of data points measured in each set of arc segments;

[0059] 3) Fit the arc profile of the standard sphere 3 through the cross-section arc data, and convert the standard sphere arc measurement point set (X ij ,Z ij ) The coordinates of the center of each fitting circle 6 are obtained by mathematical fitting as O′ i =(x i ,z i ), the circle radius is r i Since the line structured light sensor measures the two-dimensional coordinate points of the standard spherical contour, the center of the circle is obtained in two dimensions. Therefore, it is necessary to expand the coordinates of the sphere center to three dimensions based on the geometric relationship.

[0060] 4) Through the coordinates of the center of each set of fitting circles and the radius r of each set of fitting circles i , according to the known radius R of the standard sphere, we get the point set (X ij ,Z ij ) corresponds to the center point set P of the standard ball 3 i ,

[0061] Standard ball center O i for:

[0062]

[0063] The sign is determined by the intersection of the light plane and the standard sphere 3, and R is the radius of the standard sphere.

[0064] 5) Using the sphere center point set and radius obtained in step 4), the spatial straight line equation of the sphere center in the measurement coordinate system can be fitted using the least squares method. The direction vector of the spatial straight line obtained by fitting is (a, c, 1), which is the movement direction of the guide rail 5. Here, a is the unit displacement of the guide rail along the x-axis, c is the unit displacement of the guide rail along the y-axis, and 1 is the unit displacement of the guide rail along the x-axis.

[0065] 6) The motion direction of the guide rail 5 is calibrated and evaluated using a precision polyhedron 7, which is a standard regular 12-sided prism. The accuracy of the spatial motion direction of the translation stage is analyzed by comparing the measured plane angle value with the nominal angle value of the standard regular prism.

Claims

1. A calibration method for an aero-engine blade profile measurement system based on spherical center feature point transformation, characterized by: The method comprises the following steps: 1) Fix the relative positions of the line structured light sensor A (1) and the line structured light sensor B (2), and place the standard ball (3) within the measurement range of the line structured light sensor A (1) and the line structured light sensor B (2); 2) The standard ball (3) is placed at N different positions on the guide rail (5), and the line structured light sensor A (1) and the line structured light sensor B (2) are used to measure the cross-sectional arc data of the standard ball (3) at N different positions, and the measurement point set (X ij ,Z ij ), i = 1, 2, ..., N, j = 1, 2, ..., n, where N is the number of cross-sectional arc data sets at different positions, and n is the number of data points measured in each set of arc segments. The data in the x-direction reflects the vertical distance from the measuring point to the sensor, representing the width information of the measured point. The data in the z-direction reflects the horizontal distance from the measuring point to the sensor, representing the depth information of the measured point. The y-axis direction is obtained by establishing a spatial rectangular coordinate system based on the right-hand coordinate system principle. 3) Fitting the arc profile of the standard sphere (3) by the cross-sectional arc data, and converting the arc measurement point set (X ij ,Z ij ) The center coordinates of each set of fitting circles (6) are obtained by mathematical fitting. i =(x i ,z i ), the circle radius is r i ; 4) According to the known radius R of the standard sphere (3), the point set (X ij ,Z ij ) corresponds to the center point set P of the standard sphere (3) i for: Where y i is the coordinate of the center of the standard sphere (3) corresponding to each set of fitting circles (6) along the y-axis direction, The sign of is determined by the intersection of the light plane and the standard sphere (3), and R is the radius of the standard sphere (3); 5) Through the sphere center point set P i , fit the spatial straight line equation of the center of the standard sphere (3) in the measurement coordinate system, and obtain the direction vector of the spatial straight line as (a, c, 1), that is, the movement direction of the guide rail (5), where a is the component of the movement direction of the guide rail (5) along the x-axis, c is the component of the movement direction of the guide rail (5) along the y-axis, and 1 is the component of the movement direction of the guide rail (5) along the z-axis; 6) The movement direction of the guide rail (5) is calibrated and the calibration result is evaluated by a precision polyhedron (7).

2. The method for calibrating an aero-engine blade profile measurement system based on spherical center feature point transformation according to claim 1, characterized in that: The center coordinates of the fitting circle (6) in step 3) are obtained by minimizing the square sum of errors. Let the curve of the fitted circle be: Here, x i is the coordinate of the center of the fitting circle (6) corresponding to each set of arc segments along the x-axis, z i is the coordinate of the center of the fitting circle (6) corresponding to each set of arc segments along the z-axis, p = -2x i ,q=-2z i , r i is the radius of the fitting circle (6) corresponding to each set of arc segments; Measuring point (X ij ,Y ij ) to the center of the fitted circle (6) ij and the radius r of the fitting circle (6) i The squared difference is: Let the objective function f i (p,q,s) is: The objective function is optimized and solved, and the corresponding circular curve when it takes the minimum value is the optimal fitting circle.

3. The method for calibrating an aero-engine blade profile measurement system based on spherical center feature point transformation according to claim 1, characterized in that: The method for solving the movement direction of the guide rail (5) in step 5) adopts the least square fitting method. When the space line is not parallel to the XOY plane, the equation of the space line is: Right now: Here, a is the component of the motion direction of the guide rail (5) along the x-axis, c is the component of the motion direction of the guide rail (5) along the y-axis, and (b, d, 0) is a point on the equation of the straight line of motion of the guide rail. Through step 4) we get the center space coordinate point set {P i }, i=1,2,…,N, and substitute it into the equation of the line in space, we have: Where x i 'The z-axis coordinate under the equation of the space line is z i The coordinates of the corresponding point along the x-axis, y i 'The z-axis coordinate under the equation of the space line is z i The coordinates of the corresponding point along the y-axis; make: Find the partial derivatives of a, b, c, and d respectively: Rearranging the equations yields: make Then we have: Right now:

4. The method for calibrating an aero-engine blade profile measurement system based on spherical center feature point transformation according to claim 1, characterized in that: In the step 6), the precision polyhedron (7) is a standard regular 12-sided prism, and the accuracy of the spatial motion direction of the translation stage is analyzed by comparing the measured plane angle value with the nominal angle value of the standard regular prism.

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