A method for measuring an inner tangent circle of a blade profile

Abstract

This invention discloses a method for calculating the inscribed circle of an airfoil, comprising the following steps: determining an airfoil curve based on a series of airfoil reference points; selecting an airfoil reference point on one side of the airfoil curve as an initial point; selecting an optimal control point on the other side; determining an initial circle passing through these three points based on the two airfoil reference points and the optimal control point; and then determining an inscribed circle that is tangent to the airfoil curve at the initial point and also tangent to the initial circle. Finally, selecting another airfoil reference point on one side of the initial point of the airfoil curve as a new initial point, and repeating the above steps to determine the inscribed circle of the airfoil curve at the new initial point. This invention avoids the iterative methods commonly used in determining the inscribed circle, making the analysis of the inscribed circle faster, simpler, and more efficient.

Description

Technical Field

[0001] This invention belongs to the field of blade geometry analysis technology, and specifically relates to a method for calculating the inscribed circle of a blade. Background Technology

[0002] Geometric analysis of compressor blade profiles is a crucial task for both industrial design and manufacturing. Modern axial compressor blade design often employs a method that shapes the leading and trailing edge pressure and suction surfaces. This requires geometric analysis to calculate the blade's mid-curve and thickness distribution, thereby obtaining key geometric parameters, including the maximum thickness and its location. During manufacturing, blade inspection necessitates further geometric analysis to determine if the machining meets design requirements.

[0003] In the process of blade profile geometric analysis, the main task is to calculate the parameters (coordinates and radius) of the blade profile's inscribed circle. Previously, the calculation of the inscribed circle typically employed iterative methods, such as repeatedly attempting bisections on the data to arrive at a relatively accurate parameter, or constructing the blade profile's mid-curve based on an equal-radius search. However, while these iterative methods can yield relatively accurate analytical solutions for the inscribed circle, the calculation methods are complex and computationally inefficient. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology in that the calculation method of the airfoil inscribed circle parameter is complicated and the calculation efficiency is low, and to provide a new method for calculating the airfoil inscribed circle.

[0005] The present invention solves the above-mentioned technical problems through the following technical solution:

[0006] A method for calculating the inscribed circle of a leaf shape, characterized by the following steps:

[0007] Step 0: Determine the leaf shape curve based on a series of leaf shape reference points;

[0008] Step 1: Select a reference point on one side of the airfoil curve as the initial point;

[0009] Step 2: Select any reference point for the leaf shape on the other side of the leaf shape curve as a control point.

[0010] Set the first connection line as the line connecting the initial point and the control point.

[0011] Define the first tangent line as the tangent line at the initial point.

[0012] Set a second tangent line, which is the tangent line at the location of the control point.

[0013] And obtain the first included angle between the first tangent and the first connecting line, the second included angle between the second tangent and the first connecting line, and select the control point with the smallest absolute value of the difference between the first included angle and the second included angle as the optimal control point;

[0014] Step 3: Select two leaf shape reference points located on both sides of the optimal control point on one side of the leaf shape curve, and determine the initial circle passing through the three points using the two leaf shape reference points and the optimal control point;

[0015] Step 4: Determine the inscribed circle that is tangent to the leaf-shaped curve at the initial point and also tangent to the initial circle;

[0016] Step 5: If the inscribed circle intersects one side of the optimal reference point of the leaf shape curve, discard the inscribed circle; otherwise, the inscribed circle is the desired inscribed circle of the leaf shape curve at the initial point.

[0017] Step 6: Select another blade reference point on one side of the initial point of the blade profile curve as a new initial point, and then repeat steps 2 to 5 to determine the inscribed circle of the blade profile curve at the new initial point.

[0018] In this scheme, by selecting an initial point and an optimal control point on different sides of the blade profile, and drawing an initial circle to simulate the arc at the optimal control point, and then determining the inscribed circle that is tangent to both the blade profile curve and the initial circle, a new scheme for obtaining the parameters of the inscribed circle analytically is provided. The analytical parameter extraction process no longer involves iterative approximation, the calculation method is simple, and the efficiency is higher.

[0019] Furthermore, in step 1, a leaf shape reference point is selected on the underside of the leaf on the leaf shape curve as the initial point; in step 2, any leaf shape reference point is selected on the leaf base side of the leaf shape curve as the control point.

[0020] In this scheme, by further clarifying the relative positions of the initial point and the control point on the airfoil curve, the scheme of obtaining the inscribed circle parameters analytically becomes more specific and clear.

[0021] Furthermore, in step 1, a leaf shape reference point is selected on the leaf base side of the leaf shape curve as the initial point; in step 2, any leaf shape reference point is selected on the leaf back side of the leaf shape curve as the control point.

[0022] In this scheme, by further clarifying the relative positions of the initial point and the control point on the airfoil curve, the scheme of obtaining the inscribed circle parameters analytically becomes more specific and clear.

[0023] Furthermore, in step 3, the arc of the initial circle at the three points of the two blade reference points and the optimal control point is a hypothetical arc, and the curve of the blade curve at these three points is the actual curve. The initial circle corresponding to the hypothetical arc that is closest to the actual curve is selected as the optimal initial circle.

[0024] In this scheme, the optimal initial circle is determined by selecting the assumed arc that is closest to the actual curve, making the calculation results of the scheme more accurate.

[0025] Furthermore, in step 3, two adjacent leaf shape reference points located on both sides of the optimal control point are selected on one side of the optimal control point of the leaf shape curve, and the initial circle passing through the three points is determined by the two leaf shape reference points and the optimal control point.

[0026] In this scheme, by selecting two adjacent leaf shape reference points on both sides of the optimal control point and then determining the initial circle, the calculation process of the scheme is made simpler.

[0027] Further, in step 6, another blade reference point adjacent to the initial point is selected on one side of the initial point of the blade curve as a new initial point. Then, steps 2 to 5 are repeated to determine the inscribed circle of the blade curve at the new initial point.

[0028] In this scheme, by selecting another blade reference point adjacent to the initial point on one side of the blade curve as a new initial point, and then determining a new inscribed circle, the calculation process of the scheme becomes simpler and clearer.

[0029] Furthermore, in step 6, steps 2 to 5 are repeated until all the pre-selected airfoil reference points on one side of the initial point of the airfoil curve have been used as the initial point.

[0030] In this scheme, it is clarified that the process of calculating the inscribed circle terminates after all the pre-selected blade reference points of the blade profile curve have been used as the initial points, making the calculation process of the scheme simpler.

[0031] Furthermore, in step 4, the distance from the initial point to the center of the initial circle is the initial distance. If the initial distance is less than the radius of the initial circle, it is determined that the leaf-shaped curve is tangent to the initial point and inscribed within the inscribed circle of the initial circle.

[0032] If the initial distance is greater than or equal to the initial circle radius, it is determined that the leaf-shaped curve is tangent to the initial point and externally tangent to the inscribed circle of the initial circle.

[0033] In this scheme, the process of determining the inscribed circle is divided into two cases based on the relationship between the initial distance and the initial circle radius, which further improves the efficiency of determining the inscribed circle.

[0034] Furthermore, step 6 is followed by step 7: determining the mid-arc line and thickness distribution of the leaf-shaped curve based on the obtained inscribed circle.

[0035] In this scheme, the mid-curve and thickness distribution can be determined more efficiently by using a known inscribed circle.

[0036] Furthermore, step 7 is followed by step 8: based on the obtained mid-arc line and thickness distribution of the airfoil curve, the inlet and outlet metal angles, maximum thickness and their positions of the airfoil curve are further determined.

[0037] In this scheme, the mid-circle, mid-arc line, and thickness distribution can be determined more efficiently by knowing the inscribed circle, mid-arc line, and thickness distribution.

[0038] The significant advantages of this invention are as follows: By selecting initial points and optimal reference points on different sides of the airfoil, and taking an appropriate arc on the side of the optimal reference point, and then using analytical methods to calculate and determine the inscribed circle, this solution provides a new method for determining the inscribed circle. In the process of obtaining the inscribed circle parameters, the new steps avoid the iterative methods typically used in determining the inscribed circle, making the analytical calculation of the inscribed circle faster, simpler, and more efficient, effectively overcoming the shortcomings of current methods for calculating the inscribed circle of airfoils. Attached Figure Description

[0039] Figure 1 This is a flowchart of the leaf-shaped inscribed circle calculation method in this invention.

[0040] Figure 2 This is a schematic diagram illustrating the selection of the initial point and the optimal control point in this invention.

[0041] Figure 3 This is a schematic diagram illustrating the determination of the inscribed circle when the initial distance is less than the initial circle radius in this invention.

[0042] Figure 4 This is a schematic diagram illustrating the determination of the inscribed circle when the initial distance is greater than the initial circle radius in this invention.

[0043] Figure 5 This is a schematic diagram of the construction of the arc line 1 in the leaf shape in this invention.

[0044] Figure 6 for Figure 5 A diagram on the left.

[0045] Figure 7 for Figure 5 A schematic diagram of the middle section.

[0046] Figure 8 for Figure 5 The diagram on the right.

[0047] Figure 9 This is a schematic diagram of the construction of the second arc line in the leaf shape in this invention.

[0048] Figure 10 for Figure 9 A diagram on the left.

[0049] Figure 11 for Figure 9 A schematic diagram of the middle section.

[0050] Figure 12 for Figure 9 The diagram on the right.

[0051] Explanation of reference numerals in the attached figures:

[0052] Leaf-shaped curve 1

[0053] Top side 11

[0054] Bottom side 12

[0055] Initial circle 2

[0056] Inscribed circle 3

[0057] Mid-arc line 4

[0058] Initial point B

[0059] Control point M

[0060] Initial circle center D

[0061] Initial circle radius r2

[0062] Incenter A

[0063] Inscribed circle radius r1

[0064] Tangent point C

[0065] First connection BM

[0066] First bisector BB2

[0067] Second tangent MM2

[0068] First included angle α1

[0069] Second included angle α2 Detailed Implementation

[0070] The present invention will be further illustrated by way of embodiments below, but the present invention is not limited to the scope of the embodiments described herein.

[0071] The present invention will be further described below with reference to the accompanying drawings. An embodiment of the present invention implements a method for calculating the inscribed circle of a leaf shape, comprising the following steps:

[0072] Step 0: Based on a series of leaf shape reference points, a leaf shape curve 1 is formed, which includes two sides: an upper side 11 and a lower side 12.

[0073] Step 1: As Figure 2 As shown, a reference point for the airfoil is selected on the upper side 11 of the airfoil curve 1 as the initial point B;

[0074] Step 2: As Figure 2 As shown, an arbitrary leaf shape reference point is selected on the lower side 12 of leaf shape curve 1 as the control point M.

[0075] Set the first line BM as the line connecting the initial point B and the control point M.

[0076] Set the first tangent line BB2 as the tangent line at the initial point B.

[0077] Set the second tangent MM2 as the tangent at the control point M.

[0078] The first included angle α1 between the first tangent BB2 and the first connecting line BM, and the second included angle α2 between the second tangent MM2 and the first connecting line BM are obtained. The absolute value of the difference between the first included angle α1 and the second included angle α2 is calculated. On the lower side 12 of the leaf shape curve 1, the absolute value of the difference between the first included angle α1 and the second included angle α2 corresponding to different control points M is obtained and compared. The control point M corresponding to the minimum absolute value is taken as the optimal control point M.

[0079] Step 3: As Figure 2 As shown, two leaf shape reference points N and P are selected on the lower side 12 of the leaf shape curve 1, located on both sides of the optimal control point M, and the initial circle 2 passing through these three points is determined by the two leaf shape reference points N and P and the optimal control point M.

[0080] Step 4: As Figure 3 (internal incision) and Figure 4 (External tangency case) As shown, determine the inscribed circle 3 that is tangent to the leaf-shaped curve 1 at the initial point B, and tangent to the initial circle 2 at the tangency point C;

[0081] Step 5: If the inscribed circle 3 intersects the lower side of the reference point M of the leaf curve 1, discard the determined inscribed circle 3; otherwise, the inscribed circle 3 determined in step 4 is the inscribed circle 3 of the leaf curve 1 at the initial point B.

[0082] Step 6: Select another blade reference point on the upper side of the initial point B of the blade curve 1 as the new initial point B. Then repeat steps 2 to 5 to determine the inscribed circle 3 of the blade curve 1 at the new initial point B.

[0083] In this embodiment, the formulation of the blade profile curve 1, the comparison of the absolute value of the included angle difference to determine the optimal control point M, the determination of the initial circle 2 and the determination of the inscribed circle 3, and the selection of the inscribed circle 3 in step 5 can all be calculated either manually using methods commonly chosen by those skilled in the art, or by using computer-aided methods. In this embodiment, by selecting the initial point B and the control point M on the upper and lower sides of the blade profile respectively, then determining the optimal control point M, and constructing the initial circle 2 to simulate the arc segment of the blade profile curve 1 at the optimal control point M, and then determining the inscribed circle 3 that is tangent to both the blade profile curve 1 and the initial circle 2, a new scheme for obtaining the parameters of the inscribed circle 3 analytically is provided. The process of analytically obtaining the parameters no longer involves iterative calculation methods, and the overall calculation method is simpler and more efficient.

[0084] In this embodiment, a leaf shape reference point needs to be selected on the upper side 11 of the leaf shape curve 1 as the initial point B, and then any leaf shape reference point needs to be selected on the lower side 12 of the leaf shape curve 1 as the control point M. In this embodiment, the upper side is the leaf back side and the lower side is the leaf base side. In other embodiments, the upper side can also be the leaf base side and the lower side can be the leaf back side. In other embodiments, when the spatial arrangement of the two sides of the leaf shape curve 1 is not the vertical relationship in this embodiment, for example, when the two sides of the leaf shape curve 1 are in a horizontal relationship, steps 1 and 2 can also be other methods that can be understood and conceived by those skilled in the art, such as selecting the initial point B on one side of the leaf shape curve 1 and then selecting the control point M on the other side.

[0085] In this embodiment, in step 3, the arcs of the initial circle 2 at the two blade reference points N and P and the optimal control point M are assumed arcs, and the curve of the blade curve 1 at these three points is the actual curve. The assumed arc that is closest to the actual curve is selected using methods commonly used by those skilled in the art or computer-aided methods. The initial circle 2 corresponding to the assumed arc that is closest to the actual curve is the optimal initial circle 2. By selecting the optimal initial circle 2, the calculation results of the blade inscribed circle 3 in subsequent steps are more accurate.

[0086] In other embodiments, in step 3, two leaf shape reference points N and P, located on either side of the optimal reference point M and adjacent to the reference point M, are selected on one side of the reference point M of the leaf shape curve 1. An initial circle 2 passing through these three points is determined using the two reference points N and P and the optimal reference point M. By selecting two adjacent reference points N and P on either side of the optimal reference point M to calculate and determine the initial circle 2, the calculation process for the inscribed circle 3 of the leaf shape does not require determining the optimal initial circle 2, making the calculation process simpler.

[0087] In this embodiment, in step 6, another blade reference point adjacent to the initial point B is selected on one side of the initial point B of the blade curve 1 as the new initial point B. Then, steps 2 to 5 are repeated to determine the inscribed circle 3 of the blade curve 1 at the new initial point B. In this embodiment, the relationship between the initial point B and the next initial point B is relatively clear and simple, which also makes the determination and calculation process of the inscribed circle 3 relatively clear and simple.

[0088] In other embodiments, steps 2 through 5 are repeated in step 6 until all pre-selected airfoil reference points on one side of the initial point B of the airfoil curve 1 have been used as the initial point B. The pre-selection of airfoil reference points can be performed in step 6 when calculating the inscribed circle 3 at the first initial point B, and can be done using methods commonly conceived by those skilled in the art or computer-aided methods to pre-select a portion of the airfoil reference points constituting the airfoil curve for calculating the inscribed circle 3. In step 6, by using the pre-selected airfoil reference points of the airfoil curve 1 as the initial point B, the process of calculating the inscribed circle 3 is simplified.

[0089] In this embodiment, in step 4, the distance from the initial point B to the center D of the initial circle 2 is the initial distance. If the initial distance is less than the radius r2 of the initial circle 2, it is determined that the leaf-shaped curve 1 is tangent to the initial point B and inscribed in the inscribed circle 3 of the initial circle 2.

[0090] If the initial distance is greater than or equal to the radius r2 of the initial circle 2, it is determined that it is tangent to the leaf-shaped curve 1 at the initial point B, and is externally tangent to the inscribed circle 3 of the initial circle 2.

[0091] In this embodiment, the process of determining the inscribed circle 3 is divided into the above two cases based on the relationship between the initial distance and the radius r2 of the initial circle 2, thereby improving the accuracy of the inscribed circle calculation.

[0092] Specifically, in this embodiment, the coordinates of the initial point B are (x... B y B The coordinates of the center D of the initial circle 2 are (x, y). D y D The coordinates of the center A of the inscribed circle 3 are (x, y). A yA ), k B It is the slope value of the initial point B on the leaf-shaped curve 1, and the tangent point C is the tangent point between the initial circle 2 and the inscribed circle 3.

[0093] In step 4, the coordinates (x, y) of the center A of the inscribed circle 3 are... A y A The calculation process for ) and radius r1 is as follows:

[0094] If the initial distance is less than the initial circle radius r2, such as Figure 3 As shown: θ1 is the angle between AC and the horizontal axis, θ2 is the angle between CD and the horizontal axis, and θ3 is the angle between AB and the horizontal axis.

[0095] x A +r1cos(θ1)=x D +r2cos(θ2) (1)

[0096] y A +r1sin(θ1)=y D +r2sin(θ2) (2)

[0097] -ctan(θ1)=-ctan(θ2) (3)

[0098] θ1=θ2 (4)

[0099] x B =x A +r1cos(θ3) (5)

[0100] y B =y A +r1sin(θ3) (6)

[0101] θ3=atan(k B )+π / 2 (7)

[0102] Substituting equation 4 into equations 1 and 2 respectively, we get:

[0103] x A +r1cos(θ1)=x D +r2cos(θ1) (8)

[0104] y A +r1sin(θ1)=y D +r2sin(θ1) (9)

[0105] Substituting equation 7 into equations 5 and 6 respectively, we get:

[0106] x B =x A +r1cos(atan(kB (10) + π / 2)

[0107] y B =y A +r1sin(atan(k B (11) + π / 2)

[0108] Solving equations 8, 9, 10, and 11 simultaneously yields:

[0109]

[0110] Substituting r1 into equations 10 and 11, we can obtain x. A and y A ;

[0111] Let r1,x A and y A Substituting into equations 8 and 9, we can obtain θ1;

[0112] Substituting θ1 into equation 4 yields θ2.

[0113] Therefore, the coordinates (x, y) of the center A of the inscribed circle 3 can be obtained. A ,y A ) and radius r1.

[0114] If the initial distance is greater than or equal to the initial circle radius r2, such as Figure 4 As shown: θ1 is the angle between AC and the horizontal axis, θ2 is the angle between CD and the horizontal axis, and θ3 is the angle between AB and the horizontal axis.

[0115] θ2=θ1-π (13)

[0116] x A +r1cos(θ1)=x D +r2cos(θ1-π) (14)

[0117] y A +r1sin(θ1)=y D +r2sin(θ1-π) (15)

[0118] Similar to the derivation above, solving equations 14, 15, 10, and 11 simultaneously yields:

[0119]

[0120] Substituting r1 into equations 10 and 11, we can obtain x. A and y A ;

[0121] Let r1,x A and y ASubstituting into equations 14 and 15, we can obtain θ1;

[0122] Substituting θ1 into equation 13 yields θ2.

[0123] Therefore, the coordinates (x, y) of the center A of the inscribed circle 3 can be obtained. A ,y A ) and radius r1.

[0124] In this embodiment, a concise and clear calculation method for the parameters of the inscribed circle 3 is provided, avoiding the iterative methods typically used in calculating the inscribed circle 3. This makes the determination of the parameters of the inscribed circle 3 faster, simpler, and more efficient. In other embodiments, the method for determining the inscribed circle 3, which is tangent to the leaf-shaped curve 1 at the initial point B and also tangent to the initial circle 2, in step 4 can also employ other methods that can be understood and conceived by those skilled in the art to calculate the coordinates (x, y) of the center A of the inscribed circle 3. A ,y A ) and radius r1.

[0125] In this embodiment, step 6 is followed by step 7: based on the inscribed circles 3 at different initial points B that have been obtained, the middle arc line 4 and thickness distribution of the leaf-shaped curve 1 are determined by means commonly conceivable to those skilled in the art or by computer-aided methods.

[0126] In this embodiment, step 8 is included after step 7: based on the inscribed circle 3, the middle arc line 4 and the thickness distribution of the blade profile curve 1 already obtained, the inlet and outlet metal angles, maximum thickness and their positions of the blade profile curve 1 are further determined by means of methods commonly conceived by those skilled in the art or by computer-aided methods.

[0127] The above embodiments can all be applied to blade reverse engineering or blade processing inspection to calculate the inscribed circle, mid-arc line, thickness distribution, inlet and outlet metal angles, maximum thickness and their positions of the corresponding blade device.

[0128] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A method for calculating an inscribed circle of a profile, characterized in that, Includes the following steps: Step 0: Determine the leaf shape curve based on a series of leaf shape reference points; Step 1: Select a reference point on one side of the airfoil curve as the initial point; Step 2: Select any reference point for the leaf shape on the other side of the leaf shape curve as a control point. Set the first connection line as the line connecting the initial point and the control point. Define the first tangent line as the tangent line at the initial point. Set a second tangent line, which is the tangent line at the location of the control point. And obtain the first included angle between the first tangent and the first connecting line, the second included angle between the second tangent and the first connecting line, and select the control point with the smallest absolute value of the difference between the first included angle and the second included angle as the optimal control point; Step 3: Select two leaf shape reference points located on both sides of the optimal control point on one side of the leaf shape curve, and determine the initial circle passing through the three points using the two leaf shape reference points and the optimal control point; Step 4: Determine the inscribed circle that is tangent to the leaf-shaped curve at the initial point and also tangent to the initial circle; Step 5: If the inscribed circle intersects one side of the optimal reference point of the leaf shape curve, discard the inscribed circle; otherwise, the inscribed circle is the desired inscribed circle of the leaf shape curve at the initial point. Step 6: Select another blade reference point on one side of the initial point of the blade profile curve as a new initial point, and then repeat steps 2 to 5 to determine the inscribed circle of the blade profile curve at the new initial point.

2. The method for calculating the inscribed circle of the airfoil according to claim 1, characterized in that, In step 1, a leaf shape reference point is selected on the underside of the leaf shape curve as the initial point; In step 2, select any leaf shape reference point on the leaf basin side of the leaf shape curve as a control point.

3. The method for calculating the inscribed circle of the airfoil according to claim 1, characterized in that, In step 1, a leaf shape reference point is selected on one side of the leaf basin of the leaf shape curve as the initial point; In step 2, select any leaf shape reference point on the underside of the leaf shape curve as a control point.

4. The method of claim 1, wherein, In step 3, the arc of the initial circle at the three points of the two blade reference points and the optimal control point is the assumed arc, and the curve of the blade curve at the three points is the actual curve. The initial circle corresponding to the assumed arc that is closest to the actual curve is selected as the optimal initial circle.

5. The method of claim 1, wherein, In step 3, on one side of the optimal control point of the leaf shape curve, two leaf shape reference points located on both sides of the optimal control point and adjacent to the optimal control point are selected, and the initial circle passing through the three points is determined by the two leaf shape reference points and the optimal control point.

6. The method of claim 1, wherein, In step 6, another blade reference point adjacent to the initial point is selected on one side of the initial point of the blade curve as a new initial point. Then, steps 2 to 5 are repeated to determine the inscribed circle of the blade curve at the new initial point.

7. The method of claim 1, wherein, In step 6, steps 2 to 5 are repeated until all the pre-selected air profile reference points on one side of the initial point of the air profile curve have been used as the initial point.

8. The method of claim 1, wherein, In step 4, the distance from the initial point to the center of the initial circle is the initial distance. If the initial distance is less than the radius of the initial circle, it is determined that the leaf-shaped curve is tangent to the initial point and inscribed in the inscribed circle of the initial circle. If the initial distance is greater than or equal to the initial circle radius, it is determined that the leaf-shaped curve is tangent to the initial point and externally tangent to the inscribed circle of the initial circle.

9. The method of claim 1-8, wherein, Step 6 is followed by step 7, which determines the mid-arc line and thickness distribution of the leaf-shaped curve based on the obtained inscribed circle.

10. The method of claim 9, wherein, Step 7 is followed by step 8, which further determines the inlet and outlet metal angles, maximum thickness and their positions of the airfoil curve based on the obtained mid-arc line and thickness distribution of the airfoil curve.

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