Aero-engine blade profile mean camber line construction method

Abstract

The invention discloses an aero-engine blade profile mean camber line construction method which comprises the steps that a blade profile contour line formed by connecting a plurality of arc sections end to end is obtained according to the blade profile condition, the demarcation point of a blade basin profile line and a blade back profile line on the blade profile contour line is determined, the arc section on one side of the blade basin profile line is a blade basin arc section, and the arc section on the other side of the blade basin profile line is a blade back arc section; the arc section on one side of the blade back molded line is a blade back arc section; a plurality of common tangent circles are created in the blade profile contour line in the clockwise or anticlockwise direction, and in the creation direction of the common tangent circles, each common tangent circle is tangent to the middle point of the blade basin arc section and the blade back arc section which are sequentially distributed; and common tangent circles which are not intersected with the blade profile contour line are screened out to serve as inscribed circles, the circle centers of all the inscribed circles are fitted, and a mean camber line is obtained. The blade profile contour line is composed of limited arc sections connected end to end, the common tangent circle is constructed based on the blade profile contour line, the radius value is directly calculated through the blade basin arc section, the blade back arc section and the like, the center coordinate of the inscribed circle is accurately calculated, and the high-precision blade profile mean camber line is rapidly constructed.

Description

Technical Field

[0001] The invention relates to the technical field of aero-engine blade profile detection, and in particular to a method for constructing a mid-camber line of an aero-engine blade profile. Background Art

[0002] The blades on aircraft engines are precision parts that play a vital role in the reliability of aircraft engines. Therefore, the processing accuracy of blades is extremely high. The blade profile is controlled by a series of blade profiles (blade cross sections), and the blade profiles are mostly free curves with numerous cross-sectional characteristic parameters and geometric tolerance requirements, and there is no fixed rule for the parameters of the profile. According to the provisions of the navigation mark HB 5647-98, the center arc line of the blade profile is composed of the center of all inscribed circles in the blade profile. The center arc line is the basis for calculating the blade profile thickness and is also one of the important bases for judging the blade profile processing quality. The high-precision blade profile center arc line is an important prerequisite for completing the evaluation of blade profile characteristics such as leading and trailing edge points, blade profile thickness, and blade profile maximum thickness. It is also a solid foundation for guiding the optimization of blade profile manufacturing process.

[0003] At present, the inspection of blades is usually carried out by using a three-dimensional coordinate measuring machine (CMM). With the help of a multi-degree-of-freedom probe, the blade profile can be continuously and automatically measured, and the processing errors of the blades can be accurately calculated and separated. Based on this, the processing parameters can be adjusted to improve the accuracy of the blade manufacturing system. However, the expression of the blade profile obtained by this traditional measurement method is discrete. When judging the tangent relationship between the inscribed circle and the blade profile, a large number of approximate errors need to be introduced, resulting in the inability to construct a mid-arc line that reflects the actual blade profile. The mid-arc line with large deviations cannot provide an effective reference for improving the processing quality of the blade.

[0004] The patent with the publication number CN111062099A discloses a method for constructing the median arc of a blade profile based on equal-radius search. This method is proposed based on the definition of the median arc in response to the problems in practical applications of median arc construction. The method mainly includes two steps: 1) Construct a continuous blade profile model, including step 1.1, preprocessing: the curve is segmented into two segments by the extreme values of the X coordinates of the measurement points, and the two segmented segments are re-sorted according to the X coordinates respectively; step 1.2, parameterize the knot vector: the data points of the blade profile correspond to the knots within the domain, and the cumulative chord length parameterization method can be used to determine the knots within the domain; step 1.3, back-calculate the control vertices of the B-spline: the final interpolation result of the blade profile curve is jointly represented by the determined knot vector and the back-calculated control vertices. 2) Based on the continuous blade profile model obtained in step 1), construct the median arc of the blade profile based on radius search, including step 2.1, determine the starting search conditions, radius r, starting point and its normal direction, and calculate the normal distance d from the center of the circle to the back blade profile; step 2.2, construct an auxiliary search circle, that is, construct an auxiliary search circle passing through the points of the lower half segment curve with a radius r equal to the leading edge radius; step 2.3, use the normal vector direction at the segmentation point of the leading edge as the search direction, and continuously adjust the search direction according to the difference between the normal distance d from the center of the circle to the upper half blade profile and the radius r of the auxiliary search circle; when d>r, there is no intersection between the search circle 1 and the back blade profile, and r′ = r + δ is taken as the radius size of the new search circle; when d<r, the search circle 2 has two intersections with the back, and r′ = r - δ is taken as the radius size of the new search circle; repeat the above judgment conditions until the set threshold condition |d - r| < e is satisfied; at this point, a point on the median arc and the radius size of the tangent circle at this point have been determined; after completing the construction process of one inscribed circle, move a little towards the trailing edge direction and repeat the above construction process; step 2.4, construct the continuity model of the median arc. The centers of all the inscribed circles obtained from the above search constitute the discretized model of the median arc. On this basis, the continuity model of the median arc is constructed by using the cubic spline interpolation method, and it is extended tangentially at the leading edge center to intersect with the blade profile spline to obtain the final complete median arc of the blade profile.

[0005] Although the above patent is also for the construction of the median arc of an aero-engine blade profile, according to the description in the text, this technical solution searches for the radius value by adding or subtracting a δ value, and the basis for calculating the median arc is the profile points. These measures also cannot avoid the introduction of approximate errors and cannot truly construct a median arc with high accuracy. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for constructing the median arc of an aero-engine blade profile that can accurately calculate the inscribed circle and construct a high-precision median arc of the blade profile in view of the defects of the prior art.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A method for constructing a mid-arc line of an aero-engine blade profile comprises the following steps: obtaining a blade profile contour line composed of a plurality of arc segments connected end to end according to a blade profile condition, determining a dividing point between a blade basin profile line and a blade back profile line on the blade profile contour line, wherein the arc segment on one side of the blade basin profile line is the blade basin arc segment, and the arc segment on one side of the blade back profile line is the blade back arc segment; creating a plurality of tangent circles in a clockwise or counterclockwise direction within the blade profile contour line, wherein each of the tangent circles is tangent to the midpoint of the blade basin arc segment and the blade back arc segment distributed in sequence along the direction in which the tangent circles are created; selecting tangent circles that do not intersect the blade profile contour line as inscribed circles, fitting the centers of the inscribed circles, and obtaining a mid-arc line.

[0009] Furthermore, the arc segment is formed by projecting the three-dimensional point cloud of the blade profile onto a cross section using a measuring device, and then intersecting the surface contour of a measuring ball of the measuring device with the cross section.

[0010] Furthermore, the measuring device is a five-axis measuring device.

[0011] Furthermore, the process of determining the demarcation point is as follows: constructing a point set with arc starting points of all arc segments on the blade profile contour line, and determining two points with the farthest distance in the point set as demarcation points.

[0012] Furthermore, the blade basin arc segment Arc i The midpoint P im The coordinates of are determined as follows: i The center of the circle P i (y i , z i ), arc radius r i 、Arc starting point P is (y is , z is ) and the arc end point P ie (y ie , z ie ), Arc segment on the back of the leaf j The center of the circle P j (y j , z j ), arc radius r j 、Arc starting point P js (y js , z js ) and the arc end point P je (y je , z je ), by deriving the straight line P i P im Direction vector And normalize the direction vector to According to the relation r i , find P im Coordinate value.

[0013] Furthermore, the tangent circle Cir ij The center coordinates P ijo (y ijo ,z ijo ) is determined by: finding the radius r of the tangent circle ij The expression of and About the radius r of the tangent circle ij , and the radius of the arc segment on the back of the leaf r j The system of equations, that is, to find the center P ijo The coordinates of .

[0014] Furthermore, the center point fitting of each inscribed circle is achieved by constructing a cubic spline interpolation function using the center points of each inscribed circle.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] In the present invention, the blade profile contour line is no longer expressed in the form of a discrete point set, but a finite number of arc segments connected end to end. A common tangent circle is constructed based on the blade profile contour line, and the radius value is directly calculated through the blade basin arc segment and the blade back arc segment, thereby accurately calculating the center coordinates of the inscribed circle and quickly constructing a high-precision blade profile center arc line. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of the blade profile line according to Embodiment 1 of the present invention;

[0018] Figure 2 This is a schematic diagram of solving the center and radius of a tangent circle in Embodiment 1 of the present invention;

[0019] Figure 3 is a schematic diagram of all the inscribed circles solved in Example 1 of the present invention;

[0020] Figure 4 This is a schematic diagram of the camber line of the blade profile described in Example 1 of the present invention. DETAILED DESCRIPTION

[0021] In order to clearly illustrate the technical features of the present solution, the present technical solution is described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0022] In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present application is not limited to the specific embodiments disclosed below.

[0023] In addition, in the description of the present application, it should be understood that the terms "center", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first" and "second" are used only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0024] In this application, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, or a communication; it can be a direct connection, or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0025] In the present application, unless otherwise clearly specified and limited, a first feature "above" or "below" a second feature may be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in an appropriate manner in any one or more embodiments or examples.

[0026] A method for constructing the mid-camber line of an aero-engine blade profile includes three steps:

[0027] 1. Determine the dividing point between the leaf basin line and the leaf back line;

[0028] 2. Create an inscribed circle between the leaf basin and leaf back lines;

[0029] 3. Fit the center of the inscribed circle into the median arc.

[0030] The above three steps are described in three embodiments below.

[0031] Example 1

[0032] After the three-dimensional point cloud of the blade profile is projected onto a cross section using a five-axis measuring device, the surface contour of the measuring ball of the measuring device intersects the cross section to form multiple arc segments 1, and the ends of the multiple arc segments 1 are sequentially connected to form a curve, such as Figure 1 As shown in , the curve is the blade profile 2. The information of each arc segment 1 includes the coordinates of the center of the circle, the radius of the arc, the starting point of the arc and the end point of the arc. Figure 2 As shown, relative to the center of the circle, the end point of the arc is in the counterclockwise direction of the starting point of the arc, so the arc segments constituting the blade profile line 2 are arranged in a clockwise direction.

[0033] A point set is constructed from the arc starting points of all arc segments on the blade profile line 2, recorded as point set S. The two points with the farthest distance in point set S are determined by traversal calculation, such as Figure 3 As shown, the point located at the front edge is called the front edge marking point P le , the point located at the trailing edge is called the trailing edge marker point P te These two points are used as the dividing points between the blade basin line and the blade back line. The arc segment 1 located on one side of the blade basin line is recorded as the blade basin arc segment, with a total of m arc segments; the arc segment 1 located on the side of the blade back line is recorded as the blade back arc segment, with a total of n arc segments.

[0034] Example 2

[0035] A plurality of tangent circles 3 are created in the blade profile 2 obtained in Example 1 in a clockwise or counterclockwise direction, as shown in FIG. Figure 2 As shown, along the creation direction of the tangent circle 3, each tangent circle 3 is composed of successively distributed leaf basin arc segments Arc i The midpoint P im The leaf basin side tangent point is the leaf back arc segment Arc j The circle is the tangent circle of the back of the leaf. The calculation method of the common tangent circle is as follows:

[0036] The arc segment of the blade basin is known. i The center of the circle P i (y i ,z i ), arc radius r i 、Arc starting point P is (y is ,zis ) and the arc end point P ie (y ie , z ie );Arc on the back of the leaf j The center of the circle P j (y j , z j ), arc radius r j 、Arc starting point P js (y js , z js ) and the arc end point P je (y je , z je ), where 1≤i≤m; 1≤j≤n. If the tangent point of the common tangent circle and the blade basin arc Arci is at the midpoint of the arc segment, then the straight line P i P im The direction vector is

[0037]

[0038] The straight line P i P im The direction vector is normalized to

[0039]

[0041] remember

[0042] According to the relation Arc segment of leaf basin i Midpoint P im (y im , z im ) is solved.

[0043] Let the tangent circle to be found be Cir ij The center of the circle is P ijo (y ijo , z ijo ), with a radius of r ij , the point of tangency with the arc on the back of the leaf is P jt (y jt , z jt ). Since the center of the tangent circle P ijo On the straight line P i P im On the top, construct the equation system:

[0044]

[0045] The radius of the tangent circle is r ij The expression is

[0046]

[0047] Common tangent circle Cir ij The radius r ij If it is a negative value, it is discarded; if it is a positive value, the center of the circle P ijo The coordinates of can be obtained by solving any of the above equations.

[0048] After the tangent circle 3 is created, the inscribed circle of the blade profile contour line 2 requires that the created tangent circle 3 cannot intersect with the blade profile contour line 2. Therefore, the criterion of "if the distance between the centers of the two circles is less than the sum of the radii and greater than the difference in radii, then the two circles intersect" is adopted to select the tangent circle that does not intersect with the blade profile contour line from several tangent circles 3, which is the required inscribed circle 4.

[0049] Traverse the arc segment of the leaf basin i , with the leaf basin arc segment Arc i The midpoint of is the tangent point (i = 1, 2, ..., m) to create an inscribed circle, and all the inscribed circles 4 between the blade basin line and the blade back line are obtained. Draw a line P connecting the front and rear edge marking points le P te , the center of each inscribed circle 4 is vector Direction arrangement.

[0050] Example 3

[0051] In this embodiment, the center of each inscribed circle 4 is fitted, which is specifically achieved by constructing a cubic spline interpolation function from the center of each inscribed circle. The definition and solution process of the cubic spline interpolation function are as follows:

[0052] Given a partition Δ of the interval [a, b]: a = x0 <x1<…<x n-1 <x n = b, if the real-valued function s(x) satisfies: a) in every interval [x i-1 , x i ] is a polynomial of degree not more than m; b) at the internal node x i (1≤i≤n-1) has an m-1 order continuous derivative; c)s(x i )=f(x i ), (0≤i≤n), then the function s(x) is called the m-order spline interpolation function of f(x) with respect to the partition Δ.

[0053] The cubic spline interpolation function s(x) is a polynomial of no more than three degrees in each small interval, containing four undetermined coefficients. Thus, there are 4n undetermined coefficients in the entire interpolation interval. According to the definition of cubic spline interpolation, there are 4n-2 constraints as follows:

[0054] Internal node x i Department

[0055] At all nodes s(x i )=f(x i ), (0≤i≤n),

[0056] Add two natural boundary conditions to constrain s″(0)=s″(x n )=0.

[0057] Assume i (x) = a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , step length h i =x i+1 -x i ,s i (x i+1 )=y i+1 , construct the matrix equation:

[0058]

[0059] Use LU decomposition to solve the matrix equation and calculate the coefficients of the spline curve:

[0060]

[0061] Substituting the coefficients back, function s i (x) is the cubic spline curve s(x) in the interval [x i -1,xi].

[0062] The cubic spline interpolation curve s(x) obtained by fitting the center of the inscribed circle 4 is the blade profile mid-arc 5.

[0063] Obviously, the above embodiments are merely examples for clearly illustrating the technical solutions of the present invention, and are not intended to limit the implementation methods of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all implementation methods here. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for constructing a mid-camber line of an aero-engine blade, characterized in that: According to the blade shape, a blade contour line consisting of multiple arc segments connected end to end is obtained, and the dividing point between the blade basin line and the blade back line on the blade contour line is determined. The arc segment on one side of the blade basin line is the blade basin arc segment, and the arc segment on the side of the blade back line is the blade back arc segment; multiple tangent circles are created in a clockwise or counterclockwise direction within the blade contour line, and along the creation direction of the tangent circles, each of the tangent circles is tangent to the midpoint of the blade basin arc segment and the blade back arc segment distributed in sequence; the tangent circles that do not intersect with the blade contour line are selected as inscribed circles, and the centers of the inscribed circles are fitted to obtain the median arc line.

2. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 1, characterized in that: The arc segment is formed by projecting the three-dimensional point cloud of the blade profile onto a cross section using a measuring device, and then the surface contour of the measuring ball of the measuring device intersects the cross section.

3. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 2, characterized in that: The measuring device is a five-axis measuring device.

4. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 1, characterized in that: The process of determining the demarcation point is as follows: constructing a point set with the arc starting points of all arc segments on the blade profile line, and determining the two points with the farthest distance in the point set as the demarcation points.

5. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 1, characterized in that: Arc segment of leaf basin i The midpoint P im The coordinates of are determined as follows: i The center of the circle P i (y i , z i ), arc radius r i 、Arc starting point P is (y is , z is ) and the arc end point P ie (y ie , z ie ), Arc segment on the back of the leaf j The center of the circle P j (y j , z j ), arc radius r j 、Arc starting point P js (y js , z js ) and the arc end point P je (y je , z je ), by deriving the straight line P i P im Direction vector And normalize the direction vector to According to the relation Find P im Coordinate value.

6. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 5, characterized in that: Common tangent circle Cir ij The center coordinates P ijo (y ijo , z ijo ) is determined by: finding the radius r of the tangent circle ij The expression of and About the radius r of the tangent circle ij , and the radius of the arc segment on the back of the leaf r j The system of equations, that is, to find the center P ijo The coordinates of .

7. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 6, characterized in that: The radius of the tangent circle r ij If it is a negative value, it should be discarded.

8. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 6, characterized in that: The system of equations is:

9. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 6, characterized in that: The radius of the tangent circle r ij The expression is:

10. The method for constructing the mid-camber line of an aircraft engine blade profile according to claim 1, characterized in that: The center fitting of each inscribed circle is achieved by constructing a cubic spline interpolation function using the center of each inscribed circle.

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