Blade profile contour line cosine error-free solving method based on sweep measurement

Abstract

The invention relates to a blade profile contour line cosine-error-free solving method based on sweep measurement, and the method comprises the steps: building a section plane and planes at two sides in a measurement coordinate system, taking a sampling point in a region defined by the two planes as a candidate point for constructing a blade profile contour line, the section plane intersects with the candidate sphere corresponding to each candidate point to obtain a plurality of section circles with different radiuses, an area formed by a set of the plurality of section circles is a union set area, and the inner boundary of the union set area is calculated according to the relation between the circle center distance between a target circle in the union set area and other section circles and the circle radiuses, so that the blade profile contour line is obtained. According to the method, the innovative blade profile contour line solving method is provided, the arc segment representation method is adopted, the calculation process is simple, and the method has high solving precision and wide applicability in contour line solving of a complex curved surface.

Description

Technical Field

[0001] The invention relates to the field of measurement technology data processing and a method for calculating blade profile lines. Background Art

[0002] Blade disks are key engine components, and their machining precision and blade profile measurement accuracy play a vital role in overall engine performance. Coordinate measuring machines (CMMs), the leading contact measurement technology, have long dominated blade profile measurement due to their high precision and stability.

[0003] However, with the increasing complexity of aero-engine design and the stringent requirements for machining accuracy, the efficiency limitations of three-dimensional coordinate measuring machines have gradually become apparent, making it difficult to meet the needs of fast and efficient inspection. To overcome this bottleneck, five-axis swing scanning measurement technology has emerged. Through the flexibility and high precision of five-axis linkage, this technology can capture high-density, high-precision spherical center point cloud data on the blade surface in a very short time, providing unprecedented data support for accurate blade shape measurement.

[0004] However, existing blade profile solution methods, such as the "fit-intersect-compensate" approach, face significant shortcomings in the face of the massive amounts of data generated by five-axis sweep measurements. When dealing with complex curved surfaces and high-precision requirements, significant accuracy loss and profile anomalies (such as bending and self-intersection) often occur. Especially when dealing with blades with small torsional features, it is difficult to accurately capture subtle morphological changes. This results in significant deviations between the solved profile and the actual shape, seriously affecting the blade's inspection accuracy and the reliability of the assessment.

[0005] In addition, existing methods often encounter contour anomalies when processing non-overlapping sampling points, resulting in the solved contour lines being unable to truly reflect the actual shape of the blade, which hinders the aviation engine manufacturing industry from moving towards a higher level. Summary of the Invention

[0006] The purpose of the present invention is to avoid the shortcomings of the existing technology and provide a cosine error-free solution method for blade profile lines based on swing scanning measurement, which can reflect the true shape of the blade, is simple to calculate, improves blade detection accuracy and evaluation feasibility, and has high solution accuracy and wide applicability.

[0007] To achieve the above object, the technical solution adopted by the present invention is: a method for solving the blade profile line without cosine error based on swing scanning measurement, comprising the following steps: Step 1: Based on the swing scanning measurement, obtain the sampling points of the entire blade surface to be measured in the measurement coordinate system. The coordinate information of the sampling points is , i is an integer greater than 1; Given a coordinate system parallel to the contour section and with the origin of the distance measurement being The plane is the cutting plane , on the cutting plane Both sides, built to the cutting plane The distance is equal to the radius r of the probe ball used for the sweep measurement and is Two parallel planes, the sampling points in the area enclosed by the two planes are used as candidate points for constructing the leaf contour line, and the coordinate information of the candidate points is recorded as ; At the same time, each candidate point corresponds to a sphere with the candidate point as the center and the radius of the sphere A candidate sphere with radius ; Step 2: On the cutting plane Upper cutting plane With candidate spheres The intersection obtains multiple cross-sectional circles with different radii, and the area formed by the set of multiple cross-sectional circles is the union area; Any cross-sectional circle is recorded as the target circle. When the target circle intersects with other cross-sectional circles, the arc on the target circle that is inside the other cross-sectional circles is defined as the inner arc, and the remaining arc on the target circle is defined as the outer arc. Then, the angle domains of the inner and outer arcs of the intersecting circles are obtained by the relationship between the center distance and the radius of the target circle and other cross-sectional circles. The cross-sectional circles that cannot provide outer arcs are eliminated, and the cross-sectional circles that have outer arc angle domains are retained. That is, all outer arcs in the union area are solved. The union region is closed and has inner and outer boundaries, and the inner and outer boundaries are the two boundary lines of all the outer arcs on the union region, and the inner boundary is the desired leaf contour line; Step 3: Screen the cross-sectional circles with outer arc angle domains again, retain only the cross-sectional circles that can truly reflect the blade profile characteristics, and establish the topological connection relationship between the cross-sectional circles; According to the topological relationship, the selected cross-sectional circles are connected one by one in sequence to obtain the complete contour curve of the blade.

[0008] Furthermore, the multiple cross-section circles described in step 2 The specific construction process is: Establishing an evaluation coordinate system , evaluation coordinate system The coordinate axes of the measurement coordinate system are parallel to the coordinate axes of the measurement coordinate system, and the origin is located between the X axis of the measurement coordinate system and the section plane. At the intersection of In the evaluation coordinate system Middle, cross-section circle The coordinates of the center of the circle are , the radius is , then the cross-section circle The equation is expressed as: ; This means that the cross-sectional circle The point of the equation ( y,z ) are located in the cross-sectional circle superior.

[0009] Furthermore, the steps for solving the outer arc in step 2 are: First, the target circle The center of the circle As the origin, establish the target circle coordinate system , choose any cross-section circle , the target circle Center and cross-section circle The line connecting the circle centers is used as the target circle coordinate system The Xt axis is rotated 90° counterclockwise as the target circular coordinate system. Yt axis; Then, choose a cross-section circle , with the target circle The center of the circle is the origin, and a temporary coordinate system is established , target circle Center and cross-section circle The line connecting the centers of the circles is the temporary coordinate system Xk axis, temporary coordinate system The Xk axis and the target circle coordinate system The angle between the Xt axis is ; Next, in the temporary coordinate system Next, target circle and cross-section circle The center distance of , target circle and cross-section circle The radius is and , compare the relationship between the center distance and the circle radius, that is, to determine the intersection of the two circles: If the center distance is greater than the target circle and cross-section circle The sum of the radii, the two circles do not intersect; if the center distance is less than the target circle and cross-section circle The sum of the radii, then the two circles intersect; The intersection points are denoted as and , the intersection point and the target circle coordinate system The angle between the line connecting the origin and the Xk axis is ,but Expressed as: , Therefore, the target circle The arc between the two intersection points is the inner arc, and the center angle domain corresponding to the inner arc is for: , If the target circle exist intersecting circles, the inner arc angle domain of each intersecting circle is , then the target circle Inner arc angle domain for: , Next, compare the inner arc angle domain of the target circle With the whole domain Relationship: like , then the target circle is completely inside the other cross-sectional circles and no outer arc can be provided; like , then there is an outer arc on the target circle, and the outer arc angle domain is the complement of the inner arc angle domain; Eliminate the cross-section circles that cannot provide outer arcs, and only retain the angle domains that have outer arcs. The cross-sectional circle of , at this time, the inner and outer boundaries of the union area are obtained.

[0010] Furthermore, the step three specifically includes the following steps: First, construct a leaf profile center point The center of the cross-section circle is taken as the object, and the matrix calculation is used to devalue the center of the cross-section circle, and the eigenvalue of the covariance matrix is ​​calculated. The eigenvector corresponding to the eigenvalue with the largest absolute value is the direction of the blade chord length, and the eigenvector corresponding to the eigenvalue with the smallest absolute value is the direction of the blade thickness. Then, the projections of the center of the cross-section circle in the direction of the blade chord length and the blade thickness are calculated respectively, and the two points with the largest projection distance in the direction of the blade chord length are selected and connected to form a straight line. , take the two points with the largest projection distance in the thickness direction of the blade, and connect the two points to form a straight line ,straight line and straight lines The intersection point is recorded as the contour center point ; Next, find the center point of the contour from all cross-section circles The closest cross-sectional circle is used as the first target circle. Then, the outer arc of the first target circle is obtained, that is, the first contour arc segment is obtained. ; According to the characteristics of the blade profile being a closed curve, the first arc segment of the profile is The end Should be the starting point of the contour arc on the second target circle , in order to track the target circle and filter out all the contour arcs , that is, the contour center point is used to reduce the number of target circles and, at the same time, to determine the topological relationship between the blade profile arcs; The contour arcs are connected in sequence to obtain a blade profile that reflects the actual shape of the blade and embodies the blade detection accuracy.

[0011] Furthermore, the outer arc of the target circle in the step is obtained by the method of step two.

[0012] The beneficial effects of the present invention are as follows: the present invention aims to simplify the calculation process by proposing an innovative method for solving blade profile contours and adopting a circular arc segment representation method. It also has high solution accuracy and wide applicability in solving contours of complex surfaces, is easy to implement and deploy in practical engineering applications, and effectively avoids the cosine error in traditional compensation reconstruction strategies, thereby solving the shortcomings of existing measurement technologies in blade profile detection and improving blade detection accuracy, which is of great significance to promoting the development of the aviation engine manufacturing industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Schematic diagram of obtaining candidate points of the present invention; Figure 2 It is a schematic diagram of generating a cross-section circle of the present invention; Figure 3 It is a schematic diagram of the calculation method of the inner and outer arcs of the present invention; Figure 4 It is a schematic diagram of the structure of the center point of the contour of the present invention; Figure 5 Schematic diagram of the screening process of the contour arc of the present invention; Figure 6 It is a schematic diagram of the complete blade profile obtained by calculation in the present invention. DETAILED DESCRIPTION

[0014] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0015] In order to achieve the above object, the present invention provides the following specific implementation methods: Example 1: Figures 1-6 As shown, a method for solving blade profile line without cosine error based on swing scanning measurement includes the following steps: S01. Based on the swing scanning measurement, the sampling points of the entire blade surface to be measured are obtained in the measurement coordinate system. The coordinate information of the sampling points is , i is an integer greater than 1; like Figure 1 As shown, the given is parallel to the contour section, and the origin of the distance measurement coordinate system is The plane is the cutting plane , on the cutting plane Both sides, built to the cutting plane The distance is equal to the radius r of the probe ball used for the sweep measurement and is Two parallel planes, the sampling points in the area enclosed by the two planes are used as candidate points for constructing the leaf contour line, and the coordinate information of the candidate points is recorded as ; Each candidate point corresponds to a sphere with the candidate point as the center and the radius of the sphere as the measurement point. A candidate sphere with radius ; S02, on the cutting plane Upper cutting plane With candidate spheres Intersection to obtain multiple cross-sectional circles with different radii, multiple cross-sectional circles The specific construction process is: like Figure 2 As shown, establish the evaluation coordinate system , evaluation coordinate system The coordinate axes of the measurement coordinate system are parallel to the coordinate axes of the measurement coordinate system, and the origin is located between the X axis of the measurement coordinate system and the section plane. At the intersection of In the evaluation coordinate system Middle, cross-section circle The coordinates of the center of the circle are , the radius is , then the cross-section circle The equation is expressed as: ; This means that the cross-sectional circle The point of the equation ( y,z ) are located in the cross-sectional circle superior; Multiple cross-section circles The area formed by the set of is the union area.

[0016] S03, such as Figure 3 As shown in the figure, any cross-section circle is recorded as the target circle. When the target circle intersects with other cross-section circles, the arc on the target circle that is inside the other cross-section circles is defined as the inner arc, and the remaining arc on the target circle is defined as the outer arc. The center of the circle As the origin, establish the target circle coordinate system , choose any cross-section circle , the target circle Center and cross-section circle The line connecting the circle centers is used as the target circle coordinate system The Xt axis is rotated 90° counterclockwise as the target circular coordinate system. Yt axis.

[0017] S04, choose another cross-section circle , with the target circle The center of the circle is the origin, and a temporary coordinate system is established. , target circle Center and cross-section circle The line connecting the centers of the circles is the temporary coordinate system Xk axis, temporary coordinate system The Xk axis and the target circle coordinate system The angle between the Xt axis is .

[0018] S05, in the temporary coordinate system Next, target circle and cross-section circle The center distance of , target circle and cross-section circle The radius is and , compare the relationship between the center distance and the circle radius, that is, to determine the intersection of the two circles: If the center distance is greater than the target circle and cross-section circle The sum of the radii, the two circles do not intersect; if the center distance is less than the target circle and cross-section circle The sum of the radii, then the two circles intersect; The intersection points are denoted as and , the intersection point and the target circle coordinate system The angle between the line connecting the origin and the Xk axis is ,but Expressed as: , Therefore, the target circle The arc between the two intersection points is the inner arc, and the center angle domain corresponding to the inner arc is for: , If the target circle exist intersecting circles, the inner arc angle domain of each intersecting circle is , then the target circle Inner arc angle domain for: .

[0019] S06. Compare the inner arc angle domain of the target circle With the whole domain Relationship: like , then the target circle is completely inside the other cross-sectional circles and no outer arc can be provided; like , then there is an outer arc on the target circle, and the outer arc angle domain is the complement of the inner arc angle domain; Eliminate the cross-section circles that cannot provide outer arcs, and only retain the angle domains that have outer arcs. The cross-sectional circle of the union area is obtained at this time. The inner and outer boundaries of the union area are closed and have inner and outer boundaries. The inner and outer boundaries are the two boundary lines of all the outer arcs on the union area, and the inner boundary is the desired blade contour line.

[0020] S07, such as Figure 4 As shown, construct a blade profile center point The center of the cross-section circle is taken as the object, and the matrix calculation is used to devalue the center of the cross-section circle, and the eigenvalue of the covariance matrix is ​​calculated. The eigenvector corresponding to the eigenvalue with the largest absolute value is the direction of the blade chord length, and the eigenvector corresponding to the eigenvalue with the smallest absolute value is the direction of the blade thickness. S08. Calculate the projection of the center of the cross-section circle in the direction of the blade chord length and the blade thickness direction respectively, select the two points with the largest projection distance in the direction of the blade chord length, and connect the two points to form a straight line. , take the two points with the largest projection distance in the thickness direction of the blade, and connect the two points to form a straight line ,straight line and straight lines The intersection point is recorded as the contour center point ; S09, such as Figure 5 As shown, find the center point of the contour from all cross-section circles The closest cross-sectional circle is used as the first target circle. Then, the outer arc of the first target circle is obtained. The outer arc of the target circle is calculated by S03-S06, that is, the first contour arc segment is obtained. ; S10. According to the characteristic that the blade profile is a closed curve, the first arc segment of the profile is The end Should be the starting point of the contour arc on the second target circle , in order to track the target circle and filter out all the contour arcs , that is, the contour center point is used to reduce the number of target circles and, at the same time, to determine the topological relationship between the blade profile arcs; like Figure 6 As shown, the contour arcs are connected in sequence to obtain a blade profile that reflects the actual shape of the blade and embodies the blade detection accuracy.

[0021] like Figure 1-6 In order to further illustrate the technical solutions and technical effects of the present invention, the following specific examples are provided: Step 1: Preprocessing of sampling points, First, based on the massive sampling points obtained by the sweep measurement, the storage format of the sampling points is analyzed and the coordinate information of the sampling points is obtained. .

[0022] Then according to the given cutting plane , filter the sampling points, usually the cutting plane is perpendicular to the X axis of the measurement coordinate system and the distance from the coordinate origin is plane.

[0023] The principle of screening is to select sampling points whose distance from the sampling point to the cutting plane is less than the radius of the measuring sphere. The screened points are called candidate points. The candidate points are used to calculate the blade profile. Each candidate point can correspond to a is the center of the sphere and the radius is the tip radius sphere, also called a candidate sphere .

[0024] Step 2: Generation of cross-section circle, According to the cutting plane in step 1, establish the evaluation coordinate system on the cutting plane , the axes of the evaluation coordinate system are parallel to the measurement coordinate system, and the origin is located at the intersection of the X-axis of the measurement coordinate system and the plane.

[0025] In the evaluation coordinate system, Figure 2 As shown, the intersection of the cutting plane and the candidate sphere can obtain cross-sectional circles with different radii. , the coordinates of the circle center are , the radius is The equation of the cross-section circle can be expressed as: , Each candidate sphere can be cut into a cross-sectional circle, and the set of all multiple cross-sectional circles constitutes a region union region. The union region is closed and has an inner boundary and an outer boundary. The inner and outer boundaries can be composed of arc segments on the cross-sectional circle, where the inner boundary is the desired blade profile contour line.

[0026] Step 3: Solution method for inner and outer arcs, According to step 2, the radius of the obtained cross-section circles is different, and there are complex intersection relationships between the circles. Figure 3 As shown in the figure, for any cross-sectional circle, it is recorded as the target circle. When the target circle intersects with other circles, part of the arc on the target circle will be inside the other circle. This part of the arc is called the inner arc, and the arc that is not inside the other circle is called the outer arc. The inner and outer boundaries of the union area formed by the cross-sectional circles are both outer arcs. The solution for the outer arc is given here: First, the target circle The center of the circle As the origin, establish the target circle coordinate system . Choose any cross-section circle , the line connecting the center of the target circle and the center of the cross section circle is used as the X coordinate of the target circle coordinate system. t Axis, X t The axis is rotated 90° counterclockwise as Y t Axis. Then traverse other section circles, with section circles For example, take the center of the target circle as the origin and establish a temporary coordinate system .

[0027] Target circle center and cross-section circle The line connecting the centers of the circles is the X coordinate system of the temporary coordinate system. k Axis. Temporary coordinate system X k Axis and target circle coordinate system X t The angle between the axes is .

[0028] In the temporary coordinate system, the target circle and cross-section circle The center distance of The radii of the two circles are and , compare the relationship between the center distance and the radius of the two circles to determine the intersection of the two circles.

[0029] If the distance between the centers of the two circles is greater than the sum of the radii of the two circles, then the two circles do not intersect. If the distance between the centers of the two circles is less than the sum of the radii of the two circles, then the two circles intersect.

[0030] The intersection points are denoted as and , the line connecting the intersection point and the origin of the target circle coordinate system and X k The angle between the axes is , It can be expressed as: , Therefore, the arc of the target circle between the two intersection points is the inner arc, and the center angle domain corresponding to the inner arc is: , If the target circle exists intersecting circles, the inner arc angle domain of each intersecting circle is , then the inner arc angle domain of the target circle is: , Then compare the inner arc angle domain With the whole domain relationship.

[0031] like , then the target circle is completely inside the other cross-sectional circles and no outer arc can be provided; like , then there is an outer arc on the target circle, and the angle domain of the outer arc is is the complement of the inner arc angle domain. Circles that cannot provide an outer arc are eliminated, and only circles that have an outer arc angle domain are retained. This gives the inner and outer boundaries of the union region.

[0032] Step 4: Screening and construction of contour arcs, According to the calculation in step 3, the boundary of the union area can be obtained, that is, the outer arcs of all cross-sectional circles. However, there is no topological relationship between the outer arcs at this time, so it is necessary to filter the outer arcs, find the inner boundary arcs, and connect the inner boundary arcs in sequence to obtain the blade profile to be solved. The screening method is: First, construct a leaf contour center point ,like Figure 4 As shown, the construction method can be described as follows: using the principal component analysis method, the object of analysis is the center of the cross-section circle, using matrix calculation, de-valued processing of the samples, and calculating the eigenvalues ​​of the covariance matrix. The eigenvector corresponding to the eigenvalue with the largest absolute value is the principal component direction, that is, the direction of the blade chord length (referred to as the blade chord direction), and the other eigenvector is in the direction of the blade thickness (referred to as the blade thickness direction). Then calculate the projection of the center of the cross-section circle in the blade chord direction and the blade thickness direction respectively, take the two points with the largest projection distance in the blade chord direction, and connect the two points to form a straight line. , take the two points with the largest projection distance in the leaf thickness direction, and connect the two points to form a straight line , the intersection of the two straight lines is recorded as the center point of the contour .

[0033] like Figure 5 As shown, after obtaining the contour center point, find the contour center point from all cross-section circles The closest cross-sectional circle is used as the first target circle, and then the outer arc of the target circle is obtained by the calculation method in step 3. The outer arc obtained at this time is the first contour arc segment required. According to the characteristics of the blade profile being a closed curve, the end point of the contour arc on the first target circle is Should be the starting point of the contour arc on the second target circle .

[0034] In this way, the target circle is tracked and all contour arcs are screened out. The introduction of the contour center point not only reduces the number of target circles, but also determines the topological relationship between the arcs of the blade contour. Figure 6 As shown in FIG, the contour arcs are connected in sequence to form the desired blade profile. The desired blade profile can also be used to evaluate blade parameters such as profile degree, blade thickness, and chord length.

[0035] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating blade profile without cosine error based on sweep measurement, characterized in that: The following steps are involved: Step 1: Based on the swing scanning measurement, obtain the sampling points of the entire blade surface to be measured in the measurement coordinate system. The coordinate information of the sampling points is , i is an integer greater than 1; Given a coordinate system parallel to the contour section and with the origin of the distance measurement being The plane is the cutting plane , on the cutting plane Both sides, built to the cutting plane The distance is equal to the radius r of the probe ball used for the sweep measurement and is Two parallel planes, the sampling points in the area enclosed by the two planes are used as candidate points for constructing the leaf contour line, and the coordinate information of the candidate points is recorded as ; At the same time, each candidate point corresponds to a sphere with the candidate point as the center and the radius of the sphere A candidate sphere with radius ; Step 2: On the cutting plane Upper cutting plane With candidate spheres The intersection obtains multiple cross-sectional circles with different radii, and the area formed by the set of multiple cross-sectional circles is the union area; Any cross-sectional circle is recorded as the target circle. When the target circle intersects with other cross-sectional circles, the arc on the target circle that is inside the other cross-sectional circles is defined as the inner arc, and the remaining arc on the target circle is defined as the outer arc. Then, the angle domains of the inner and outer arcs of the intersecting circles are obtained by the relationship between the center distance and the radius of the target circle and other cross-sectional circles. The cross-sectional circles that cannot provide outer arcs are eliminated, and the cross-sectional circles that have outer arc angle domains are retained. That is, all outer arcs in the union area are solved. The union region is closed and has inner and outer boundaries, and the inner and outer boundaries are the two boundary lines of all the outer arcs on the union region, and the inner boundary is the desired leaf contour line; Step 3: Screen the cross-sectional circles with outer arc angle domains again, retain only the cross-sectional circles that can truly reflect the blade profile characteristics, and establish the topological connection relationship between the cross-sectional circles; According to the topological relationship, the selected cross-sectional circles are connected one by one in sequence to obtain the complete contour curve of the blade.

2. The method for solving blade profile line without cosine error based on swing scanning measurement according to claim 1, characterized in that: Multiple cross-section circles described in step 2 The specific construction process is: Establishing an evaluation coordinate system , evaluation coordinate system The coordinate axes of the measurement coordinate system are parallel to the coordinate axes of the measurement coordinate system, and the origin is located between the X axis of the measurement coordinate system and the section plane. At the intersection of In the evaluation coordinate system Middle, cross-section circle The coordinates of the center of the circle are , the radius is , then the cross-section circle The equation is expressed as: ； This means that the cross-sectional circle The point of the equation ( y,z ) are located in the cross-sectional circle superior.

3. The method for solving blade profile line without cosine error based on swing scanning measurement according to claim 1, characterized in that: The steps for solving the outer arc in step 2 are: First, the target circle The center of the circle As the origin, establish the target circle coordinate system , choose any cross-section circle , the target circle Center and cross-section circle The line connecting the circle centers is used as the target circle coordinate system The Xt axis is rotated 90° counterclockwise as the target circular coordinate system. Yt axis; Then, choose a cross-section circle , with the target circle The center of the circle is the origin, and a temporary coordinate system is established , target circle Center and cross-section circle The line connecting the centers of the circles is the temporary coordinate system Xk axis, temporary coordinate system The Xk axis and the target circle coordinate system The angle between the Xt axis is ; Next, in the temporary coordinate system Next, target circle and cross-section circle The center distance of , target circle and cross-section circle The radius is and , compare the relationship between the center distance and the circle radius, that is, to determine the intersection of the two circles: If the center distance is greater than the target circle and cross-section circle The sum of the radii, the two circles do not intersect; if the center distance is less than the target circle and cross-section circle The sum of the radii, then the two circles intersect; The intersection points are denoted as and , the intersection point and the target circle coordinate system The angle between the line connecting the origin and the Xk axis is ,but Expressed as: ， Therefore, the target circle The arc between the two intersection points is the inner arc, and the center angle domain corresponding to the inner arc is for: ， If the target circle exist intersecting circles, the inner arc angle domain of each intersecting circle is , then the target circle Inner arc angle domain for: ， Next, compare the inner arc angle domain of the target circle With the whole domain Relationship: like , then the target circle is completely inside the other cross-sectional circles and no outer arc can be provided; like , then there is an outer arc on the target circle, and the outer arc angle domain is the complement of the inner arc angle domain; Eliminate the cross-section circles that cannot provide outer arcs, and only retain the angle domains that have outer arcs. The cross-sectional circle of , at this time, the inner and outer boundaries of the union area are obtained.

4. The method for solving blade profile line without cosine error based on swing scanning measurement according to any one of claims 1 to 3, characterized in that: The step three specifically includes the following steps: First, construct a leaf profile center point The center of the cross-section circle is taken as the object, and the matrix calculation is used to devalue the center of the cross-section circle, and the eigenvalue of the covariance matrix is ​​calculated. The eigenvector corresponding to the eigenvalue with the largest absolute value is the direction of the blade chord length, and the eigenvector corresponding to the eigenvalue with the smallest absolute value is the direction of the blade thickness. Then, the projections of the center of the cross-section circle in the direction of the blade chord length and the blade thickness are calculated respectively, and the two points with the largest projection distance in the direction of the blade chord length are selected and connected to form a straight line. , take the two points with the largest projection distance in the thickness direction of the blade, and connect the two points to form a straight line ,straight line and straight lines The intersection point is recorded as the contour center point ; Next, find the center point of the contour from all cross-section circles The closest cross-sectional circle is used as the first target circle. Then, the outer arc of the first target circle is obtained, that is, the first contour arc segment is obtained. ; According to the characteristics of the blade profile being a closed curve, the first arc segment of the profile is The end Should be the starting point of the contour arc on the second target circle , in order to track the target circle and filter out all the contour arcs , that is, the contour center point is used to reduce the number of target circles and, at the same time, to determine the topological relationship between the blade profile arcs; The contour arcs are connected in sequence to obtain a blade profile that reflects the actual shape of the blade and embodies the blade detection accuracy.

5. The method for solving blade profile line without cosine error based on swing scanning measurement according to claim 4, characterized in that: The outer arc of the target circle in the step is obtained by the method of step two.

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