A method for solving blade profile geometry parameters of an impeller machine

Abstract

The application discloses a kind of impeller mechanical blade profile geometric parameter solving method, according to the curvature mutation value of blade back, blade basin two profile lines, segment is divided to blade profile, is fitted to the front trailing edge arc segment by least square method, and the front trailing edge radius and front trailing edge point are solved;Then, golden section method is used to obtain middle camber line;Finally, according to the front edge, trailing edge coordinates, the installation angle of blade profile and chord length are solved, according to the thickness distribution, the maximum thickness and its relative position are solved, according to the obtained middle camber line distribution, geometric inlet angle, geometric outlet angle, blade profile front edge angle, blade profile trailing edge angle and bend angle are solved.The method changes the repeated solving problem of circle and profile intersection point into optimization problem, only needs to solve the distance between point and point constantly, that is, the purpose of quickly solving blade profile middle camber line can be achieved, which greatly simplifies the solving process of blade profile middle camber line.

Description

Technical Field

[0001] This invention belongs to the field of mechanical technology, specifically relating to a method for solving the geometric parameters of impeller blades in turbomachinery. Background Technology

[0002] Axial compressors are one of the three core components of aero engines. Currently, compressor performance based on traditional aerodynamic design methods is approaching its limits. To break through these limits and broaden the stable operating range of compressors, it is necessary to develop advanced compressor flow control technologies, such as casing treatment, endwall styling, and boundary layer extraction. Among these, the application of control methods such as blade profile optimization design, biomimetic blade leading-edge knots, and teardrop-shaped leading edges all require corresponding modeling based on known blade geometry parameters. Therefore, accurately solving for its geometry parameters when the blade profile is known is crucial.

[0003] The key to solving the blade profile geometry parameters lies in determining the mid-curve. Currently, the main method for determining the mid-curve is based on the equal radius method. The solution is as follows: Take a point (point A) on either the blade tip or the blade back, find the intersection point (point B) of the normal line (line 1) of this point and another profile line, and then find a point (point C) between these two points such that its distance to the blade tip and the blade back is equal. This point is a point on the mid-curve.

[0004] There are two existing methods to solve for point C. One method involves finding a point D at an appropriate position on the normal line (line 1) passing through point A, and constructing a circle with D as the center and AD as the radius, such that the circle intersects another profile line at two points. The radius is gradually decreased, and the solution ends when the difference between the distance between the intersection points of the circle and the other profile line and the length of AD is less than a given error. This method has obvious drawbacks: it requires continuously solving for the intersection points of the circle and the profile line, resulting in a large computational load, numerous iterations, and a long computation cycle.

[0005] Another method (see patents CN 101813004 B and CN 109948299 A) involves taking the midpoint D of the normal segment AB, using D as the center and AD as the radius, and finding the intersection point of this circle with another profile. If there is one intersection point (i.e., point B), then the midpoint is a point on the middle arc. If there are two intersection points, point B and another point E, a point (let's call it point F) is found on the profile BE using an iterative method, such that the difference between the distance from point O, the intersection point of the normal line (line 2) passing through point F and line 1, to points F and A is less than a given error; then point O is a point on the middle arc. Although this method significantly reduces the number of times the intersection point of the circle and the profile is calculated compared to the first method, it does not fundamentally solve the problem of a large number of iterations and a long computation period. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a method for solving the geometric parameters of turbomachinery blade profiles. The blade profile is segmented based on the abrupt curvature changes of the blade back and blade base lines. The leading and trailing edge radii and points are calculated by fitting the leading and trailing edge arcs using the least squares method. Then, a point A is selected on the middle section of the blade back, and the normal to point A is calculated. The golden section method is used to calculate the intersection point B of this normal with the blade base, and the distance disOP from point O in the AM interval to the blade base. Based on this, the AM interval is continuously reduced until its length is less than a pre-set error, ultimately obtaining point C on the mid-arc line and the thickness distribution disAC. Finally, the blade profile installation angle and chord length are calculated based on the leading and trailing edge coordinates. The maximum thickness and its relative position are calculated based on the thickness distribution. The geometric inlet angle, geometric outlet angle, leading edge angle, trailing edge angle, and bend angle are calculated based on the obtained mid-arc line distribution. This method transforms the iterative problem of finding the intersection points of a circle and the profile into an optimization problem. By simply solving for the distances between points, the curvature of the airfoil can be quickly determined, greatly simplifying the process. Furthermore, the use of the golden section method and least squares fitting method significantly addresses the issues of numerous iterations, long computation cycles, and low accuracy, further improving the speed and accuracy of airfoil parameter calculation.

[0007] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0008] Step 1: Read in the leaf shape data and divide the shape into two parts, the leaf base and the leaf back, based on the minimum and maximum values ​​of the horizontal coordinate.

[0009] Step 2: Perform cubic spline curve fitting on the leaf base and leaf back, and solve the curvature of the two profiles on the leaf base and leaf back respectively. According to the abrupt change point of the curvature value, divide the leaf base and leaf back into leading edge segment, middle segment and trailing edge segment respectively.

[0010] Step 3: Merge the leading edge segments of the leaf base and the leaf back, and merge the trailing edge segments of the leaf base and the leaf back. Apply the least squares method to fit the merged leading edge arc segments and trailing edge arc segments respectively, and calculate the leading edge radius, the center of the leading edge arc segment, the trailing edge radius, and the center of the trailing edge arc segment.

[0011] Step 4: Draw a circle with the center of the leading edge arc segment as the center and the leading edge radius as the radius; traverse the points on the leaf base and leaf back profile lines, calculate the distances from these points to the center of the leading edge arc segment, and find the critical points Criticalpoint 1 and Criticalpoint 2. Along the leaf base and leaf back profile lines, the distance from one side of the points between Criticalpoint 1 and Criticalpoint 2 to the center of the leading edge arc segment is equal to the leading edge radius, and the distance from the other side of the points to the center of the leading edge arc segment is greater than the leading edge radius; Draw a circle with the center of the trailing edge arc segment as the center and the trailing edge radius as the radius, traverse the points on the leaf base and leaf back profile lines, calculate the distances from these points to the center of the trailing edge arc segment, and find the critical points Criticalpoint 3 and Criticalpoint 4. Along the leaf base and leaf back profile lines, the distances from Criticalpoint 3 and Criticalpoint 4 are equal to the leading edge radius. The distance from one side of the point between points 4 to the center of the trailing arc is equal to the trailing radius, while the distance from the other side to the center of the trailing arc is greater than the trailing radius; these four intersection points re-divide the leaf basin and leaf back profile into the leading edge segment, the middle segment, and the trailing edge segment.

[0012] Step 5: Merge the leading edge segments of the leaf base and leaf back obtained in Step 4, and merge the trailing edge segments of the leaf base and leaf back. Calculate the midpoint coordinates of the merged leading edge arc segment and trailing edge arc segment, and define them as the leading edge point coordinates and trailing edge point coordinates, respectively.

[0013] Step 6: Perform cubic spline fitting on the middle section of the leaf base and leaf back. Select any point A on the leaf back, find the normal line of the leaf back at point A, and use the golden section method to find the intersection point B of the normal line and the leaf base.

[0014] Step 7: Let M be the midpoint of normal AB, select a point O on line segment AM, and find the distance disOP from point O to the leaf-shaped line. P is a point on the leaf-shaped line.

[0015] Step 8: Solve the minimum problem: min f(O)=(|(disAO)) 2 -(disOP) 2 |), the result is defined as point C, and the distance between points A and C, disAC, is calculated;

[0016] Step 9: For all points on the middle section of the back of the leaf, find the corresponding point C according to the method in steps 6 to 8. All points C form the middle arc line. The distance disAC between the back of the leaf and the middle arc line constitutes the leaf thickness distribution.

[0017] Step 10: Merge the leading edge point, the center point of the leading edge arc segment, all points on the middle arc obtained in Step 9, the center point of the trailing edge arc segment, and the trailing edge point into a complete middle arc; fit the complete middle arc with a cubic spline curve, check the curvature of each point, and if there are abrupt points, discard these points to obtain the final middle arc.

[0018] Step 11: Determine the blade installation angle and chord length based on the coordinates of the leading and trailing edges;

[0019] Step 12: Determine the maximum thickness and its relative position based on the thickness distribution;

[0020] Step 13: Fit the middle arc with a cubic spline curve to find the tangent angles at the beginning and end of the middle arc, and then obtain the geometric inlet angle, geometric outlet angle, blade leading edge angle, blade trailing edge angle and bend angle.

[0021] Preferably, finding the intersection point B of the normal and the leaf base using the golden section method is an optimization problem, that is, there exists a point B in the leaf base profile where the distance from this point to the normal passing through point A is minimized; this problem can be expressed mathematically as a minimum value problem. Where Ax+By+C=0 is the equation of the normal line passing through point A, and x0 and y0 are the coordinates of points on the leaf basin.

[0022] Preferably, in step seven, the coordinates of point P are obtained using the golden section method;

[0023] Step 7-1: Assume there exist two points P s and P e P s P e If the absolute value of the difference between the x-coordinate of point P and the x-coordinate of point B is disAB, then point P must be located at point P. s P e Within the range;

[0024] Step 7-2: Calculate the golden section point, P1 = P e -0.618*(P e -P s P2 = Ps + 0.618 * (P e -P s ), calculate the distances disOP1 and disOP2 from these two points to point O respectively;

[0025] Step 7-3: Compare the sizes of disOP1 and disOP2. If disOP1 > disOP2, narrow the interval to P1P. e Conversely, if disOP1 < disOP2, the interval is reduced to P. s P2;

[0026] Step 7-4: Recalculate the new golden section point and its distance to point O, iteratively narrowing the interval until the length of the interval is less than the preset error. Finally, the coordinates of P are the midpoint of the interval.

[0027] Preferably, the method for solving the minimum problem in step 8 is the golden section method.

[0028] The beneficial effects of this invention are as follows:

[0029] This invention transforms the iterative problem of finding the intersection points of a circle and a profile into an optimization problem. This process only requires continuously calculating the distances between points to quickly solve for the arc of the airfoil, greatly simplifying the process. Furthermore, the use of the golden section method and least squares fitting method significantly addresses the issues of numerous iterations, long computation cycles, and low accuracy, further improving the speed and accuracy of airfoil parameter calculation. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the blade cascade geometry in an embodiment of the present invention.

[0031] Figure 2 The diagram shows the variation of the curvature of the leaf back and leaf basin with chord length and the point of curvature change in an embodiment of the present invention. (a) Leaf back, (b) Leaf basin.

[0032] Figure 3 The diagram shows the specific location of the curvature abrupt change point in the blade cascade and the fitting of the leading and trailing edges in an embodiment of the present invention, (a) near the leading edge, (b) near the trailing edge.

[0033] Figure 4 The diagram shows four critical points and blade cascade divisions in an embodiment of the present invention: (a) near the leading edge, and (b) near the trailing edge.

[0034] Figure 5 This is a schematic diagram illustrating the calculation principle of point P in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] In view of the shortcomings of existing solution methods, the technical problem to be solved by the present invention is to provide a method for solving air profile parameters that avoids solving for the intersection of the circle and the profile as much as possible, and improves the calculation accuracy and speed.

[0037] The present invention provides a method for solving the geometric parameters of impeller blades in turbomachinery, comprising the following specific steps:

[0038] Step 1: Read in the leaf shape data and divide the shape into two parts, the leaf base and the leaf back, based on the minimum and maximum values ​​of the horizontal coordinate.

[0039] Step 2: Perform cubic spline curve fitting on the leaf base and leaf back, and solve the curvature of the two profiles of the leaf base and leaf back respectively. According to the abrupt change point of the curvature value, divide the leaf base / leaf back into the leading edge segment, the middle segment, and the trailing edge segment.

[0040] Step 3: Merge the leading edge segments of the leaf base and the leaf back, and merge the trailing edge segments of the leaf base and the leaf back. Apply the least squares method to fit the merged leading edge arc segment and trailing edge arc segment respectively, and find the leading edge radius, the center of the leading edge arc segment, the trailing edge radius, and the center of the trailing edge arc segment.

[0041] Step 4: Draw a circle with the center of the leading edge arc segment as the center and the leading edge radius as the radius. Traverse the points on the leaf base and leaf back profile lines, calculating the distances from these points to the center of the leading edge arc segment. More precisely identify the critical points Criticalpoint1 and Criticalpoint2 (points on one side of these critical points are equal to the leading edge radius, while points on the other side are greater than the leading edge radius). Draw a circle with the center of the trailing edge arc segment as the center and the trailing edge radius as the radius. Traverse the points on the leaf base and leaf back profile lines, calculating the distances from these points to the center of the trailing edge arc segment. Identify the critical points Criticalpoint3 and Criticalpoint4 (points on one side of these critical points are equal to the trailing edge radius, while points on the other side are greater than the trailing edge radius). These four intersection points re-divide the leaf base and leaf back profile lines into leading edge, middle, and trailing edge segments.

[0042] Step 5: Merge the leading edge segments of the leaf base and leaf back obtained in Step 4, and merge the trailing edge segments of the leaf base and leaf back. Find the coordinates of the midpoints of the merged leading and trailing edge arc segments. These coordinates are the coordinates of the leading edge point and the trailing edge point.

[0043] Step 6: Perform cubic spline fitting on the middle section of the leaf base and leaf back. Select a point A on the leaf back, find the normal line of the leaf back at point A, and use the golden section method to find the intersection point B of the normal line and the leaf base.

[0044] Step 7: Let M be the midpoint of normal AB, select a point O on line segment AM, and find the distance disOP from point O to the leaf-shaped line;

[0045] Step 8: Since point C on the middle arc must lie on the normal AB and must be located on the line segment between point A and M; the distance from point C to A on the middle arc must be equal to the distance to the leaf-shaped curve. Using this characteristic, the problem can be transformed into finding a point on the normal AM such that the absolute value of the difference between the square of the distance from that point to A and the square of the distance to the leaf-shaped curve is minimized. Mathematically, this can be expressed as: solving the minimum problem, min f(O)=(|(disAO)) 2 -(disOP) 2|), point O is located in the middle of line segment AM; the problem is solved using the golden section method to obtain point C on the middle arc, and the distance between points A and C, disAC, is calculated;

[0046] Step 9: For all points on the middle section of the leaf back, follow the methods in steps 6 to 8 to find the corresponding points on the middle arc (coordinates of point C) and the thickness distribution (distance between points A and C);

[0047] Step 10: Merge the leading edge point, the center point of the leading edge arc segment, all the points of the middle arc obtained in Step 9, the center point of the trailing edge arc segment, and the trailing edge point into a complete middle arc; fit the middle arc with a cubic spline curve, check the curvature of each point, and if there are abrupt points, discard these points to obtain the final middle arc.

[0048] Step 11: Determine the blade installation angle and chord length based on the coordinates of the leading and trailing edges;

[0049] Step 12: Determine the maximum thickness and its relative position based on the thickness distribution;

[0050] Step 13: Fit the mid-arc line with a cubic spline curve to find the tangent angles at the beginning and end of the mid-arc line, and then obtain the geometric inlet angle, geometric outlet angle, blade leading edge angle, blade trailing edge angle, and bend angle.

[0051] Preferably, in step six, solving for the coordinates of point B is not the traditional method of finding the intersection of the normal line passing through point A and the leaf-shaped profile. Instead, the problem is transformed into an optimization problem: finding a point B within the leaf-shaped profile whose distance to the normal line passing through point A is minimized. Mathematically, this problem can be expressed as a minimum value problem. Where Ax+By+C=0 is the equation of the normal line passing through point A, and x0 and y0 are the coordinates of points on the leaf basin.

[0052] Preferably, in step seven, the coordinates of point P are obtained using the golden section method. Assume there exist two points P... s and P e P s P e If the absolute value of the difference between the x-coordinate of point P and the x-coordinate of point B is disAB, then point P must be located at point P. s P e Within the interval. First, calculate the golden section point, P1 = P... e -0.618*(P e -P s P2 = Ps + 0.618 * (P e -P sCalculate the distances disOP1 and disOP2 from these two points to point O. Then compare the values ​​of disOP1 and disOP2. If disOP1 > disOP2, reduce the interval to P1P. e Conversely, if disOP1 < disOP2, the interval is reduced to P. s P2. Finally, recalculate the new golden section point and its distance to point O, iteratively narrowing the interval until the length of the interval is less than the preset error. The final coordinates of P are the midpoint of the interval. Specific implementation examples:

[0054] This embodiment is applied to the blade stack of a high-load, low-speed compressor. Figure 1 This is a geometric schematic diagram of the blade cascade. The known geometric parameters of the blade cascade include chord length, mounting angle, inlet geometric angle, and outlet geometric angle. This embodiment will first solve for the geometric parameters of the blade cascade, and then compare them with its known geometric parameters to demonstrate the effectiveness of the invention. The implementation process for solving the blade geometry parameters is as follows:

[0055] 1) Read in the leaf shape data, and divide the shape into two parts, the leaf base and the leaf back, based on the minimum and maximum values ​​of the horizontal axis. Figure 1 As shown;

[0056] 2) Perform cubic spline curve fitting on the leaf base and leaf back, and solve for the curvature of the two profile lines for the leaf base and leaf back respectively. (Refer to...) Figure 2 The results are shown. The points of abrupt change in curvature value are plotted at specific locations within the leaf shape. (See [reference needed]). Figure 3 Based on this mutation point, the leaf base / leaf back is divided into a leading edge segment, a middle segment, and a trailing edge segment. The leading edge segments of the leaf base and leaf back are merged, as are the trailing edge segments. The least squares method is used to fit the merged leading edge arc segment and trailing edge arc segment respectively, and the leading edge radius, the center of the leading edge arc segment, the trailing edge radius, and the center of the trailing edge arc segment are calculated. Figure 3 As shown;

[0057] 3) Draw a circle with the center of the leading / tail edge arc segment as the center and the radius of the leading edge as the radius. Traverse the points on the leaf base and leaf back profile lines, calculate the distances from these points to the center of the leading edge arc segment, and then more accurately identify the critical points Criticalpoint 1, Criticalpoint 2, Criticalpoint 3, and Criticalpoint 4, as follows: Figure 4 As shown, these four intersection points re-divide the leaf basin and leaf back profile into the leading edge segment, the middle segment, and the trailing edge segment;

[0058] 4) See Figure 5A cubic spline fit is performed on the middle section of the leaf base and leaf back. A point A is selected on the middle section of the leaf back, and the intersection point B of the normal line of the leaf back at point A and the leaf base is found. Let M be the midpoint of the normal line AB, and select a point O on the line segment AM. The distance disOP from point O to the leaf base profile is found using the golden section method.

[0059] Based on this, the AM interval is continuously reduced until the length of the interval is less than the preset error. Finally, the coordinates of C are the midpoint of the interval, and the distance from this point to A is equal to the distance to the leaf basin line.

[0060] 5) For all points on the middle section of the leaf back, follow step 4) to find the corresponding points on the middle arc (coordinates of point C).

[0061] And the thickness distribution (the distance between points A and C);

[0062] 6) Merge the leading edge point, the center point of the leading edge arc segment, all the points of the middle arc obtained in step 5), the center point of the trailing edge arc segment, and the trailing edge point into a complete middle arc; fit the middle arc with a cubic spline curve, check the curvature of each point, and if there are abrupt points, discard these points to obtain the final middle arc.

[0063] 7) Finally, the blade installation angle and chord length are determined based on the coordinates of the leading and trailing edges. The maximum thickness and its relative position are determined based on the thickness distribution. The geometric inlet angle, geometric outlet angle, blade leading edge angle, blade trailing edge angle, and bend angle are determined based on the obtained mid-curve distribution.

[0064] The final geometric parameters obtained according to this invention and the known geometric parameters of the airfoil are shown in Table 1. The data in the table shows that the geometric parameters of the airfoil obtained by this invention are very close to the actual geometric parameters of the airfoil, and the errors are all below 0.9%, which fully demonstrates the effectiveness and reliability of this invention.

[0065] Table 1 Comparison of Leaf Shape Geometric Parameters

[0066]

Claims

1. A method for solving the geometric parameters of turbomachinery blade profiles, characterized in that, Includes the following steps: Step 1: Read in the leaf shape data and divide the shape into two parts, the leaf base and the leaf back, based on the minimum and maximum values ​​of the horizontal coordinate. Step 2: Perform cubic spline curve fitting on the leaf base and leaf back, and solve the curvature of the two profiles on the leaf base and leaf back respectively. According to the abrupt change point of the curvature value, divide the leaf base and leaf back into leading edge segment, middle segment and trailing edge segment respectively. Step 3: Merge the leading edge segments of the leaf base and the leaf back, and merge the trailing edge segments of the leaf base and the leaf back. Apply the least squares method to fit the merged leading edge arc segments and trailing edge arc segments respectively, and calculate the leading edge radius, the center of the leading edge arc segment, the trailing edge radius, and the center of the trailing edge arc segment. Step 4: Draw a circle with the center of the leading edge arc segment as the center and the leading edge radius as the radius; traverse the points on the leaf base and leaf back profile lines, calculate the distances from these points to the center of the leading edge arc segment, and find the critical points Criticalpoint 1 and Criticalpoint 2. Along the leaf base and leaf back profile lines, the distances from one side of the points between Criticalpoint 1 and Criticalpoint 2 to the center of the leading edge arc segment are all equal to the leading edge radius, and the distances from the other side of the points to the center of the leading edge arc segment are all greater than the leading edge radius; Draw a circle with the center of the trailing edge arc segment as the center and the trailing edge radius as the radius, traverse the points on the leaf base and leaf back profile lines, calculate the distances from these points to the center of the trailing edge arc segment, and find the critical points Criticalpoint 3 and Criticalpoint 4. Along the leaf base and leaf back profile lines, the distances from Criticalpoint 3 and Criticalpoint 4 are all equal to the leading edge radius. The distance from one side of the point between points 4 to the center of the trailing arc is equal to the trailing radius, while the distance from the other side to the center of the trailing arc is greater than the trailing radius; these four intersection points re-divide the leaf basin and leaf back profile into the leading edge segment, the middle segment, and the trailing edge segment. Step 5: Merge the leading edge segments of the leaf base and leaf back obtained in Step 4, and merge the trailing edge segments of the leaf base and leaf back. Calculate the midpoint coordinates of the merged leading edge arc segment and trailing edge arc segment, and define them as the leading edge point coordinates and trailing edge point coordinates, respectively. Step 6: Perform cubic spline fitting on the middle section of the leaf base and leaf back. Select any point A on the leaf back, find the normal line of the leaf back at point A, and use the golden section method to find the intersection point B of the normal line and the leaf base. Step 7: Let M be the midpoint of normal AB, select a point O on line segment AM, and find the distance disOP from point O to the leaf-shaped line. P is a point on the leaf-shaped line. Step 8: Solve the minimum problem: min f(O)=(|(disAO)) 2 -(disOP) 2 |), the result is defined as point C, and the distance between points A and C, disAC, is calculated; Step 9: For all points on the middle section of the back of the leaf, find the corresponding point C according to the method in steps 6 to 8. All points C form the middle arc line. The distance disAC between the back of the leaf and the middle arc line constitutes the leaf thickness distribution. Step 10: Merge the leading edge point, the center point of the leading edge arc segment, all points on the middle arc obtained in Step 9, the center point of the trailing edge arc segment, and the trailing edge point into a complete middle arc; fit the complete middle arc with a cubic spline curve, check the curvature of each point, and if there are abrupt points, discard these points to obtain the final middle arc. Step 11: Determine the blade installation angle and chord length based on the coordinates of the leading and trailing edges; Step 12: Determine the maximum thickness and its relative position based on the thickness distribution; Step 13: Fit the middle arc with a cubic spline curve to find the tangent angles at the beginning and end of the middle arc, and then obtain the geometric inlet angle, geometric outlet angle, blade leading edge angle, blade trailing edge angle and bend angle.

2. The method for solving the geometric parameters of turbomachinery blades according to claim 1, characterized in that, The method of using the golden section to find the intersection point B of the normal and the leaf base is an optimization problem, that is, there exists a point B in the leaf base shape line such that the distance from this point to the normal passing through point A is minimized; this problem can be expressed mathematically as a problem of finding the minimum value. Where Ax+By+C=0 is the equation of the normal line passing through point A, and x0 and y0 are the coordinates of points on the leaf basin.

3. The method for solving the geometric parameters of turbomachinery blades according to claim 1, characterized in that, In step 7, the coordinates of point P are obtained using the golden section method; Step 7-1: Assume there exist two points P s and P e P s P e If the absolute value of the difference between the x-coordinate of point P and the x-coordinate of point B is disAB, then point P must be located at point P. s P e Within the range; Step 7-2: Calculate the golden section point, P1 = P e -0.618*(P e -P s P2 = Ps + 0.618 * (P e -P s ), calculate the distances disOP1 and disOP2 from these two points to point O respectively; Step 7-3: Compare the sizes of disOP1 and disOP2. If disOP1 > disOP2, narrow the interval to P1P. e Conversely, if disOP1 < disOP2, the interval is reduced to P. s P2; Step 7-4: Recalculate the new golden section point and its distance to point O, iteratively narrowing the interval until the length of the interval is less than the preset error. Finally, the coordinates of P are the midpoint of the interval.

4. The method for solving the geometric parameters of turbomachinery blades according to claim 1, characterized in that, The method for solving the minimum problem in step 8 is the golden section method.

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