CN111062099B - Leaf mean camber line construction method based on equal radius search - Google Patents

Abstract

The invention discloses a method for constructing the center arc line of a blade based on equal radius search. This method is proposed based on the definition of the center arc line in view of the problems of the construction of the center arc line in practical applications. The method mainly includes two steps: 1) Construct a continuous model of the blade shape, 2) Based on the continuous model of the blade shape obtained in step 1), construct the central arc line of the blade shape based on radius search. The method of constructing the mid-arc line adopted in the present invention can accurately determine the inscribed circle defined by the mid-arc line. Due to the adoption of the idea of variable step size, the search efficiency is accelerated and the convergence accuracy of the inscribed circle is improved. The final mid-arc line can more accurately reflect the actual processing conditions of the blade.

Description

Method for constructing blade mid-arc lines based on equal radius search

Technical field

The invention belongs to the field of precision measurement, and specifically relates to a method for constructing a blade center arc based on equal radius search.

Background technique

Blades are a core component of aeroengines, accounting for about 30% of the entire engine manufacturing. Blades are thin-walled parts and work in severe working conditions such as high load and complex stress. In order to ensure its special performance, the airfoil surface is usually designed as a free-form surface, and has strict size and shape accuracy requirements, strict surface integrity, and high manufacturing precision requirements. The overall size span of the blade is large and the shape is complex, and processing such as casting or milling can easily cause deformation. The quality of the blades has a great influence on the secondary flow loss of the engine, which directly determines its energy conversion efficiency. Therefore, strictly controlling the geometric accuracy of aerospace blades after processing is of great significance to achieve precision manufacturing of aeroengines and ensure the overall level of the engine. 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-section characteristic parameters and geometric tolerance requirements, and there are no fixed rules for profile parameters.

In recent years, as the performance and demand of aerospace engines continue to improve, more stringent requirements have been put forward for the profile accuracy and product consistency of batch manufacturing of blades. Using blade precision detection technology to accurately calculate the processing error of separated blades and adjust the processing process parameters based on this is an important way to improve the accuracy of the blade manufacturing system. The main content of blade inspection is the processing geometric error of the profile, including items such as characteristic parameters that control the blade profile and contour errors.

With the gradual maturity of Coordinate Measuring Machine (CMM) technology, continuous automated measurement of blade profiles can be carried out with multi-degree-of-freedom probes. The four-coordinate measuring system developed on this basis adds a high-precision rotary spindle to the three linear axes of the CMM. Relevant research institutions combined the four-coordinate measurement system with the trigger probe to develop a special blade measuring instrument. The control software drives the motion mechanism, adjusts the trigger probe to measure the blade shape point by point, and finally obtains the blade accuracy through the analysis system.

Optical scanning measurement can be used to achieve discrete sampling of blade profiles. However, due to the limitation of sampling density, it is difficult to accurately obtain the profile data of the specified blade section (blade profile). The usual method is to take a certain height range near the blade section. The point cloud is projected to obtain the leaf profile point cloud data, and then the precise leaf profile data is extracted. At the same time, due to the influence of various measurement errors, calculating the profile error requires accurately matching the blade measurement points with the theoretical model to isolate the single error of the profile shape, and requires segmentation of the blade cross-section profile line edge head profile.

The leading and trailing edges of the blades are the arc portions at both ends of the blade profile. Their size and shape determine the aerodynamic performance of the engine. The commonly used edge shape in engineering is arc-shaped. The edge edge is tangent to the free curves of the leaf basin and leaf back section, and together form a complete leaf shape. In order to solve the dimensional deviation of the edge head, it is necessary to separate the edge head from the leaf basin and leaf back profile lines in the blade profile measurement data. Due to the complexity of the blade profile profile, it is difficult to accurately analyze the above elements. Difficulties.

According to the regulations of navigation mark HB 5647-98, the central arc line of the airfoil is composed of the centers of all inscribed circles within the airfoil. The mid-arc line is the basis for calculating the blade thickness and is also one of the important basis for judging the processing quality of the blade. The traditional method is to enlarge the profile line in equal proportions through drawing and draw a rough tangent circle. The mid-arc line is composed of connecting the centers of all tangent circles. However, this method is inefficient and has large errors. At present, the methods for solving mid-arc lines mainly include analytical methods, methods based on equal angles or equal radii, and methods based on equidistant lines. The solution conditions of the analytical method are relatively harsh, requiring the leaf basin and leaf back curves to have analytical expressions of fifth-order equations, and its applicable range is narrow. The discrete model of the blade is used for calculation based on the equal angle or equal radius method, and the error is large. The implementation of the isometric line method is relatively complex and requires a large number of leaf-shaped isometric line intersections.

Contents of the invention

Aiming at the problem of constructing the mid-camber line in practical applications, the present invention provides a method for constructing the mid-camber line of a blade based on equal radius search based on the definition of the mid-camber line.

The present invention is implemented by adopting the following technical solutions:

The method of constructing the blade center arc line based on equal radius search includes the following steps:

1) Construct a leaf shape continuous model;

2) According to the continuous model of the blade obtained in step 1), the central arc of the blade is constructed based on the radius search.

A further improvement of the present invention is that the specific implementation method of step 1) is as follows:

Step 1.1, preprocessing

Divide the curve into two segments by using the extreme value of the X coordinate of the measurement point, and reorder the two segments according to the X coordinate;

Step 1.2. Parameterize the node vectors

Using the cumulative chord length parameterization method, let d be the total chord length:

Then there are:

The data points of the leaf shape correspond to the nodes in the definition domain, and the nodes in the definition domain can be determined by using the cumulative chord length parameterization method;

Step 1.2, back-calculate the control vertices of the B-spline

The interpolation curve used is cubic B-spline, let k=3; according to the principle of curve interpolation, the nodes in the definition domain [u ₃ , u _n+1 ] are substituted into the expression of B-spline:

Get a system of m+1 linear equations:

For the C ² continuous B-spline closed curve, since the first and last measurement points of the blade shape are repeated, Equation (4) has m effective equations; the k = 3 control points at the first and last ends are the same in sequence, and Equation (4) is about There are n-2 equations remaining for the control points; the value of N _j,3 (u _i ) is determined based on the constructed node vector U and the basis function recursion formula; therefore, just calculate the equations of the remaining m unknown control points, Eq. The matrix form of is as follows:

The final blade curve interpolation result is jointly represented by the above-mentioned determined node vector U and the back-calculated control vertex.

A further improvement of the present invention is that the specific implementation method of step 2) is as follows:

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 leaf back line;

Step 2.2. Construct an auxiliary search circle, that is, construct an auxiliary search circle that passes through the lower half of the curve point and has a radius r equal to the radius of the front edge;

Step 2.3. Use the normal vector direction at the dividing point of the front edge as the search direction, and continuously adjust the search direction according to the difference between the normal distance d between the center of the circle and the upper half of the blade shape and the radius r of the auxiliary search circle;

When d>r, the search circle 1 has no intersection with the leaf back line, and r'=r+δ is the radius of the new search circle; when d<r, there are two intersections between the search circle 2 and the leaf back, with r '=r-δ is the new search circle radius; repeat the above judgment conditions until the set threshold condition |d-r|<ε is met; so far, a point on the mid-arc line and the tangent circle at that point have been determined Radius size; after completing the construction process of the inscribed circle, move a little toward the trailing edge and repeat the above construction process;

Step 2.4. Construct the continuity model of the middle arc

The centers of all inscribed circles obtained by the above search constitute the discretized model of the mid-arc line. Based on the above, the cubic spline interpolation method is used to construct the continuity model of the mid-arc line, and the center of the edge head circle is along the tangent. Expand to intersect with the leaf spline to obtain the final complete leaf center arc.

The present invention has the following beneficial technical effects:

The method of constructing the blade center arc line adopted by the present invention can accurately determine the inscribed circle defined by the center arc line. Due to the adoption of the idea of variable step size, the search efficiency is accelerated and the convergence accuracy of the inscribed circle is improved. The final mid-arc line can more accurately reflect the actual processing conditions of the blade.

Description of the drawings

Figure 1 is the B-spline interpolation flow chart of the leaf curve.

Figure 2 is a schematic diagram of the control points of the blade curve.

Figure 3 is a schematic diagram of the blade shape continuity model.

Figure 4 is a schematic diagram of the inscribed circle search process.

Figure 5 is a flow chart for constructing the central arc line of the blade shape.

Figure 6 is a schematic diagram of the construction of the arc line in the blade shape.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

The present invention aims at problems in the practical application of the center arc line construction, and based on the definition of the center arc line, implements a method for constructing the blade center arc line based on equal radius search.

B-spline curves have a series of excellent properties, such as geometric invariance and affine invariance, and can ensure that the local shape of the blade is only affected by local measurement data. In engineering calculations, in order to ensure that C ² is continuous at the interpolation point, a cubic B-spline needs to be used as the interpolation curve. The leaf shape is a closed curve, and the leaf shape data measurement point is q _i (i=0,1,...,m). When separating the edge, the leaf profile measurement data points have been split into two segments and reordered. In order to realize the closed B-spline interpolation of the leaf shape, it is necessary to connect the measured points of the two sections end to end and add a starting measurement point at the end of the data point set. The inverse interpolation leaf interpolation B-spline is composed of the control vertex d _i (i=0,1,...,n) and the node vector U={u ₀ ,u ₁ ,...,u _n+k+1 } It is jointly determined to satisfy n=m+k-1. Let d _i (i=0,1,...,n) be the control vertex, N _i,k (u)(i=1,2,...,n) be the basis function of the k-order B-spline, The corresponding node vector is U={u ₀ , u ₁ ,..., u _n+k+1 }, which satisfies u ₀ ≤ _{u 1} ≤···≤u _n+k+1 . The expression of B-spline is:

It is stipulated that within the interval u _i ≤ u < u _i+1 , the zero-order B-spline basis function is N _i,0 (u) = 1, and the remaining intervals are zero. According to the De Boer-Cox formula and stipulating that 0/0=0 in the formula, the B-spline basis function has the following recursion relationship:

The method mainly includes the following steps:

1) Construct a leaf shape continuous model;

2) According to the continuous model of the blade obtained in step 1), the central arc of the blade is constructed based on the radius search.

The specific implementation method of step 1) is as follows:

Step 1.1, preprocessing

The curve is divided into two segments by the extreme value of the X coordinate of the measurement point, and the two divided segments are reordered according to the X coordinate.

Step 1.2. Node vector parameterization

Using the cumulative chord length parameterization method, let d be the total chord length:

Then there are:

The data points of the leaf shape correspond to the nodes in the definition domain. Using the cumulative chord length parameterization method to determine the nodes in the definition domain can effectively avoid the problem of large changes in the density of measured data points and better reflect the true shape of the leaf shape. For the nodes in the definition domain, there are In order to make the leaf-shaped B-spline curve closed, the other 2k nodes are determined as: u ₀ =u _n-k+1 -1,u ₁ =u _n-k+2 -1,…,u _k-1 = u _n -1; u _n+2 ＝1+u _k+1 , u _n+3 ＝1+u _k+2 ,…, u _n+k+1 ＝1+u _2k . When constructing the node vector, first determine the nodes in the definition domain through the cumulative chord length parameterization method, and then supplement the values of 2k remaining nodes. The two jointly determine the node vector U of the leaf interpolation curve.

Step 1.2, back-calculate the control vertices of the B-spline

The interpolation curve used in the present invention is a cubic B-spline, assuming k=3. According to the principle of curve interpolation, the nodes in the domain [u ₃ , u _n+1 ] are substituted into the expression of B-spline:

A system of m+1 linear equations can be obtained:

For the C ² continuous B-spline closed curve, since the first and last measurement points of the blade shape are repeated, Equation (4) has m effective equations. The k = 3 control points at the first and last ends are the same in sequence, and the number of equations related to the control points in equation (4) is n-2. The value of N _j,3 (u _i ) can be determined based on the constructed node vector U and the basis function recursive formula. Therefore, we only need to calculate the equations of the remaining m unknown control points. The matrix form of the equation is as follows:

The final blade curve interpolation result is jointly represented by the above-mentioned determined node vector U and the back-calculated control vertex. The flow chart of the blade curve B-spline interpolation is shown in Figure 1. The measured leaf shape data is parameterized by node vectors and the control points are back-calculated, as shown in Figure 2. In the transition area where the curvature changes greatly, the density of measuring points changes drastically, but the interpolation curve still passes through each blade point smoothly, and a continuous model is accurately constructed, as shown in Figure 3.

The specific implementation method of step 2) is as follows:

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 leaf back line.

Step 2.2. Construct an auxiliary search circle.

Construct an auxiliary search circle that passes through the lower half curve point and has a radius r equal to the leading edge radius.

Step 2.3. Use the normal vector direction at the dividing point of the front edge as the search direction. Continuously adjust the search direction according to the difference between the normal distance d between the center of the circle and the upper half of the blade shape and the radius r of the auxiliary search circle. The inscribed circle The search process is shown in Figure 4.

When d>r, there is no intersection between the search circle 1 and the leaf back line, and r'=r+δ is the radius of the new search circle. When d<r, there are two intersection points between the search circle 2 and the leaf back, and r'=r-δ is the new search circle radius. Repeat the above judgment conditions until the set threshold condition |d-r|<ε is met. So far, a point on the mid-arc line and the radius of the tangent circle at that point have been determined.

After completing the construction process of the inscribed circle, move a little toward the trailing edge and repeat the above construction process. In order to improve the efficiency of the search, set the starting radius of the auxiliary circle to be equal to the radius of the tangent circle in the previous step. In addition, in the search process, in order to speed up the convergence to the inscribed circle, the idea of variable step size is adopted. When the value of |d-r| is large, it means that the search circle and the inscribed circle are quite different. At this time, a larger step size δ is used to accelerate the approach to the inscribed circle. When |d-r| is a small value, a smaller search step size δ is used to accurately converge to a result that satisfies the termination threshold. The flow chart of the arc construction method in equal radius search based on B-spline interpolation is shown in Figure 5.

Step 2.4. Construct the continuity model of the middle arc

The centers of all inscribed circles obtained by the above search constitute the discretized model of the mid-arc line. Based on the above, the cubic spline interpolation method is used to construct the continuity model of the mid-arc line, and the center of the edge head circle is along the tangent. Expand to intersect with the leaf spline to obtain the final complete leaf center arc.

An equal-radius search mid-arc construction method based on cubic non-uniform closed B-spline interpolation was used to process the measured data of aviation blade profiles. The results are shown in Figure 6. The search process continues along the inlet side to the exhaust side, and all inscribed circles in the picture are the final search results. The continuous model of the center of the inscribed circle and the extension line form the central arc line of the blade. It can be seen from the search results at the inlet and exhaust edges, the leaf basin and the leaf back that the center arc line construction method used in the present invention can accurately determine the inscribed circle defined by the center arc line. Due to the adoption of the idea of variable step size, the search efficiency is accelerated and the convergence accuracy of the inscribed circle is improved. The final mid-arc line can more accurately reflect the actual processing conditions of the blade.

Claims (1)

1. The method of constructing the blade center arc line based on equal radius search is characterized by including the following steps: 1) Construct a leaf shape continuous model; the specific implementation method is as follows: Step 1.1, preprocessing Divide the curve into two segments by using the extreme value of the X coordinate of the measurement point, and reorder the two segments according to the X coordinate; Step 1.2. Parameterize the node vectors Using the cumulative chord length parameterization method, let d be the total chord length: Then there are: The data points of the leaf shape correspond to the nodes in the definition domain, and the nodes in the definition domain can be determined by using the cumulative chord length parameterization method; Step 1.2, back-calculate the control vertices of the B-spline The interpolation curve used is cubic B-spline, let k=3; according to the principle of curve interpolation, the nodes in the definition domain [u ₃ , u _n+1 ] are substituted into the expression of B-spline: Get a system of m+1 linear equations: For the C ² continuous B-spline closed curve, since the first and last measurement points of the blade shape are repeated, Equation (4) has m effective equations; the k = 3 control points at the first and last ends are the same in sequence, and Equation (4) is about The number of equations of control points remains n-2; The value of N _j,3 (u _i ) is determined based on the constructed node vector U and the basis function recursion formula; therefore, just calculate the equations of the remaining m unknown control points. The matrix form of the equation is as follows: The final leaf curve interpolation result is jointly represented by the above-mentioned determined node vector U and the back-calculated control vertex; 2) Based on the continuous model of the blade obtained in step 1), construct the central arc of the blade based on radius search; the specific implementation method is as follows: 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 leaf back line; Step 2.2. Construct an auxiliary search circle, that is, construct an auxiliary search circle that passes through the lower half of the curve point and has a radius r equal to the radius of the front edge; Step 2.3. Use the normal vector direction at the dividing point of the front edge as the search direction, and continuously adjust the search direction according to the difference between the normal distance d between the center of the circle and the upper half of the blade shape and the radius r of the auxiliary search circle; When d>r, the search circle 1 has no intersection with the leaf back line, and r'=r+δ is the radius of the new search circle; when d<r, there are two intersections between the search circle 2 and the leaf back, with r '=r-δ is the new search circle radius; repeat the above judgment conditions until the set threshold condition |d-r|<ε is met; so far, a point on the mid-arc line and the tangent circle at that point have been determined Radius size; after completing the construction process of the inscribed circle, move a little toward the trailing edge and repeat the above construction process; Step 2.4. Construct the continuity model of the middle arc The centers of all inscribed circles obtained by the above search constitute the discretized model of the mid-arc line. Based on the above, the cubic spline interpolation method is used to construct the continuity model of the mid-arc line, and the center of the edge head circle is along the tangent. Expand to intersect with the leaf spline to obtain the final complete leaf center arc.