CN106021782A - Mean-line-based blade front and back edge fitting and section line smooth reconstruction method - Google Patents

Abstract

The invention discloses a mean-line-based blade front and back edge fitting and section line smooth reconstruction method. The method is used for solving the technical problem that an existing method is poor in practicability. According to the technical scheme, on the basis of a fitting problem of front and back edge measuring points, a restrained least square fitting method is built for fitting of front and back edges meeting the design requirement. Different from unrestraint least square method front and back edge fitting, the method adopts a mean line as constraint conditions for front and back edge fitting, the restrained least square method is built, a Gauss-Newton method is used for iterative solving, finally, a fitting front and back edge curve approximating the designed front and back edges is obtained, front edge radius errors are lowered to 0.007% from original 0.670%, and the back edge radius errors are lowered to 0.062% from original 1.018%. The fitting front and back edge and the blade back and blade basin achieve smooth connection, and the smooth section line curve is built. The method has the advantages of being high in calculation precision, high in convergence rate and effective in constraint.

Description

Blade front and rear edge matching based on mean camber line and section line smooth reconstruction method

Technical field

The invention belongs to gas turbine blades and manufacture field, intend particularly to a kind of blade front and rear edge based on mean camber line Close and section line smooth reconstruction method.

Background technology

Blade is the strength member in aero-engine, is the major part of compressor and turbine.Both operation principles are not With, but the requirement to high-quality blade is consistent.Blade off quality not only profile errors can not meet design public affairs Difference requirement, aerodynamic parameter can not reach to design requirement.The result caused not only makes the inefficiency of calming the anger of compressor, turbine Duty be also affected.Therefore, manufacturing high-quality blade is current aerospace manufacturing industry problem demanding prompt solution.

The Accurate Model of blade profile is not only the guarantee that high-quality manufactures, and is also the basis of Error analysis of machining.Air inlet Angle, the blade profile aerodynamic parameter such as efflux angles is the important parameter affecting blade working efficiency, and its position is in edge district before and after blade profile Territory.Particularly front edge area, while affecting flow inlet angle, the air-flow that different leading edge precision can affect under the different angle of attack divides From.Accordingly, it would be desirable to blade profile is carried out Accurate Model and is applied in aerodynamic parameter extraction and error analysis.In reverse-engineering In, existing blade is measured and rebuilds the inevitable requirement being to simplify design complexity.In order to obtain and product equal accuracy Copy, it is desirable to blade is carried out high accuracy model.In addition, damaged blade is also required to when repairing use accurate leaf Sheet Model Reconstruction, in order to the damaged area of reblading.

It is error analysis even reverse-engineering just because of blade profile modeling, the most basic in the various fields such as blade reparation Project, each experts and scholars have carried out much research to it.Artificial modeling pattern is the nascent product of CAD, although build Mould is directly perceived, convenient, but takes time and effort, high cost.Document " Chen Zhiqiang, Zhang Dinghua, Jin Yanfang, etc. based on measurement data Blade profile characteristic parameter extraction [J]. science and technology and engineering, 2007,7 (9): 1972-1975. " make when front and rear edge reconstructs By the method for least square fitting circular arc, obtain, by constantly adjusting the number of leading edge point, the fitting circle conduct that change is minimum Front and rear edge circular arc.Although the method can obtain high-precision fitting circle, but does not accounts for front and rear edge curve and blade back curve The smooth connection of leaf pelvic curvature line, has some limitations.

Summary of the invention

In order to overcome the deficiency of existing method poor practicability, the present invention provides a kind of blade front and rear edge based on mean camber line to intend Close and section line smooth reconstruction method.The method measures the fitting problems of point for front and rear edge, sets up the least square of belt restraining Fitting process, meets edge before and after design requires for matching.It is different from without edge matching before and after Constraint least square algorithm, the method With the constraints of mean camber line front and rear edge matching the most, set up the method for least square of belt restraining, use Gauss-Newton method repeatedly In generation, solves, and finally gives the matching front and rear edge curve approaching design front and rear edge, and leading-edge radius error is by 0.670% fall before As little as 0.077%, trailing edge radius error is reduced to 0.062% by 1.018% before.Moreover, matching front and rear edge and leaf Notopodium pelvic curvature line has reached to be smoothly connected, and establishes smooth section line curve.It is high that the method has computational accuracy, convergence rate Hurry up, retrain more effective advantage.

The technical solution adopted for the present invention to solve the technical problems: a kind of blade front and rear edge matching based on mean camber line and Section line smooth reconstruction method, is characterized in comprising the following steps:

Step one, the selection a certain section line of blade measure point for object, wherein leading edge point set P_lFor matching object.Select former The blade back curve C begun_vWith leaf pelvic curvature line C_cFor back-up curve.

Step 2, at blade back curve C_vWith leaf pelvic curvature line C_cOn the basis of, utilize mean camber line and Gauss-Newton method to front Edge point set P_lIt is fitted, is met leaf basin, leading edge curve C that blade back is smoothly connected with leading edge_l。

1. to initial blade back curve C_vWith leaf pelvic curvature line C_cApplication mean camber line extraction algorithm, obtains initial mean camber line C_m。

2. initial blade back curve and leaf pelvic curvature line are carried out curvature continuous print prolongation, the blade back curve C after being extended_veWith Leaf pelvic curvature line C_ce.To this to curve application mean camber line extraction algorithm, the mean camber line C after being extended_me。

3. the leading edge circular arc least square fitting equation of belt restraining is set up.In order to meet the leading edge curve C after matching_lNot only Error of fitting is minimum, in addition it is also necessary to ensure and blade back curve C_veWith leaf pelvic curvature line C_ceReach to smoothly transit.Therefore, mean camber line is utilized As the transition in the circular arc center of circle Yu radius, i.e. with the point on mean camber line as the center of circle, the inscribed circle obtained meets leading edge curve C_lWith Blade back curve C_veLeaf pelvic curvature line C_ceTangent condition, sets up following least square fitting expression formula.

$\min f\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{e}_i^2\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(\sqrt{{(P_{ix}-O_x(s\left)\right)}^2+{(P_{iy}-O_y(s\left)\right)}^2}-R(s\left)\right)}^2$

Wherein, s is for extending mean camber line C_meArc length parameters, O_x(s),O_yS (), R (s) is respectively center of circle X-coordinate, center of circle Y Coordinate, matching garden radius.P_ix, P_iyIt is X-coordinate and the Y coordinate of leading edge measurement point respectively.

4. utilize Gauss-Newton method to carry out least-squares calculation, calculate aboutJacobian matrix,

$J\left(s\right)=\left[\begin{array}{c}\frac{(P_{1x}-O_x(s\left)\right)\·O_x^{\′}\left(s\right)+(P_{1y}-O_y(s\left)\right)\·O_y^{\′}\left(s\right)}{\sqrt{{(P_{1x}-O_x(s\left)\right)}^2+{(P_{1y}-O_y(s\left)\right)}^2}}-R^{\′}\left(s\right)\\ .\\ .\\ .\\ \frac{(P_{nx}-O_x(s\left)\right)\·O_x^{\′}\left(s\right)+(P_{ny}-O_y(s\left)\right)\·O_y^{\′}\left(s\right)}{\sqrt{{(P_{nx}-O_x(s\left)\right)}^2+{(P_{ny}-O_y(s\left)\right)}^2}}-R^{\′}\left(s\right)\end{array}\right]$

Set up iterative computation formula s^(k+1)=s^(k)-(J^T·J)^-1·J^T·e(s^(k)), wherein, e (s)=(e₁(s),…,e_n (s))^T；

5. original mean camber line C is extracted_mExtreme coordinates P_e, and by this coordinate P_eExtending C on mean camber line_meArc length parameters s_l Initial value as iteration is iterated.After m iteration, this arc length parameters s_mRepresented inscribed circle is and meets error With minimum and with blade back curve C_veLeaf pelvic curvature line C_ceThe leading edge curve C being smoothly connected_l。

Step 3, to trailing edge curve C_tIt is fitted, obtains the trailing edge curve C after matching_t。

Step 4, using the beginning and end of the leading edge curve after matching and trailing edge curve as leading edge curve, trailing edge curve With blade back curve, the junction point of leaf pelvic curvature line, four curves constitute the section line of blade profile.

The invention has the beneficial effects as follows: the method measures the fitting problems of point for front and rear edge, sets up the minimum of belt restraining Two take advantage of fitting process, meet edge before and after design requires for matching.It is different from without edge matching before and after Constraint least square algorithm, should Method, with the constraints of mean camber line front and rear edge matching the most, sets up the method for least square of belt restraining, uses Gauss-Newton Method iterative, finally gives the matching front and rear edge curve approaching design front and rear edge, and leading-edge radius error is by before 0.670% is reduced to 0.077%, and trailing edge radius error is reduced to 0.062% by 1.018% before.Moreover, before matching Trailing edge has reached to be smoothly connected with blade back leaf pelvic curvature line, establishes smooth section line curve.It is high that the method has computational accuracy, Fast convergence rate, retrains more effective advantage.

With detailed description of the invention, the present invention is elaborated below in conjunction with the accompanying drawings.

Accompanying drawing explanation

Fig. 1 is arc in present invention blade based on mean camber line front and rear edge matching and section line smooth reconstruction embodiment of the method band The leading edge circular fitting schematic diagram of line constraint.

Detailed description of the invention

With reference to Fig. 1.Present invention blade based on mean camber line front and rear edge matching and section line smooth reconstruction method concrete steps As follows:

Step 1. selects a certain section line of blade to measure point for goal in research, wherein leading edge point set P_lFor matching object.Choosing Select original blade back curve C_vWith leaf pelvic curvature line C_cFor back-up curve.

Step 2. is at this blade back curve C_vWith leaf pelvic curvature line C_cOn the basis of, utilize mean camber line and Gauss-Newton method pair Leading edge point set P_lIt is fitted, is met leaf basin, leading edge curve C that blade back is smoothly connected with leading edge_l, detailed process is as follows:

1. to initial blade back curve C_vWith leaf pelvic curvature line C_cApplication mean camber line extraction algorithm, obtains initial mean camber line C_m。

2. initial blade back curve and leaf pelvic curvature line are carried out curvature continuous print prolongation, the blade back curve C after being extended_veWith Leaf pelvic curvature line C_ce.To this curve group application mean camber line extraction algorithm, the mean camber line C after being extended_me。

3. the leading edge circular arc least square fitting equation of belt restraining is set up.In order to meet the leading edge curve C after matching_lNot only Error of fitting is minimum, in addition it is also necessary to ensure and blade back curve C_veWith leaf pelvic curvature line C_ceReach to smoothly transit.Therefore, mean camber line is utilized As the transition in the circular arc center of circle Yu radius, i.e. with the point on mean camber line as the center of circle, the inscribed circle obtained meets leading edge curve C_lWith Blade back curve C_veLeaf pelvic curvature line C_ceTangent condition, sets up following least square fitting expression formula.

$\min f\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{e}_i^2\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(\sqrt{{(P_{ix}-O_x(s\left)\right)}^2+{(P_{iy}-O_y(s\left)\right)}^2}-R(s\left)\right)}^2$

Wherein, s is for extending mean camber line C_meArc length parameters, O_x(s),O_yS (), R (s) is respectively center of circle X-coordinate, center of circle Y Coordinate, matching garden radius.P_ix, P_iyIt is X-coordinate and the Y coordinate of leading edge measurement point respectively.

4. Gauss-Newton method is utilized to carry out least-squares calculation.Calculate aboutJacobian matrix.

$J\left(s\right)=\left[\begin{array}{c}\frac{(P_{1x}-O_x(s\left)\right)\·O_x^{\′}\left(s\right)+(P_{1y}-O_y(s\left)\right)\·O_y^{\′}\left(s\right)}{\sqrt{{(P_{1x}-O_x(s\left)\right)}^2+{(P_{1y}-O_y(s\left)\right)}^2}}-R^{\′}\left(s\right)\\ .\\ .\\ .\\ \frac{(P_{nx}-O_x(s\left)\right)\·O_x^{\′}\left(s\right)+(P_{ny}-O_y(s\left)\right)\·O_y^{\′}\left(s\right)}{\sqrt{{(P_{nx}-O_x(s\left)\right)}^2+{(P_{ny}-O_y(s\left)\right)}^2}}-R^{\′}\left(s\right)\end{array}\right]$

Set up iterative computation formula.

s^(k+1)=s^(k)-(J^T·J)^-1·J^T·e(s^(k)), wherein, e (s)=(e₁(s),…,e_n(s))^T。

5. original mean camber line C is extracted_mExtreme coordinates P_e, and by this coordinate P_eExtending C on mean camber line_meArc length parameters s_l Initial value as iteration is iterated.After 5 iteration, this arc length parameters s_mRepresented inscribed circle is and meets error With minimum and with blade back curve C_veLeaf pelvic curvature line C_ceThe leading edge curve C being smoothly connected_l。

The same method of step 3. is applied to trailing edge curve C_tMatching, obtain the trailing edge curve C after matching_t。

Step 4. using the beginning and end of the leading edge curve after matching and trailing edge curve as leading edge curve, trailing edge curve with Blade back curve, the junction point of leaf pelvic curvature line.These four curves constitute the section line of this blade profile.Before and after the present embodiment matching Edge effect is as shown in table 1, and is contrasted with without Constraint least square algorithm.

Table 1 this method compares with theoretical model with without Constraint least square algorithm

Simulation result shows, uses the blade front and rear edge matching based on mean camber line of present invention proposition and section line smooth heavy Structure method matching can meet edge circular arc before and after design requires.In addition, matching front and rear edge and blade back curve leaf pelvic curvature line It is smoothly connected, meets pneumatic requirement.

Claims (1)

1. a blade front and rear edge matching based on mean camber line and section line smooth reconstruction method, it is characterised in that include following step Rapid:

Step one, the selection a certain section line of blade measure point for object, wherein leading edge point set P_lFor matching object；Select original Blade back curve C_vWith leaf pelvic curvature line C_cFor back-up curve；

Step 2, at blade back curve C_vWith leaf pelvic curvature line C_cOn the basis of, utilize mean camber line and Gauss-Newton method to leading edge point Collection P_lIt is fitted, is met leaf basin, leading edge curve C that blade back is smoothly connected with leading edge_l；

1. to initial blade back curve C_vWith leaf pelvic curvature line C_cApplication mean camber line extraction algorithm, obtains initial mean camber line C_m；

2. initial blade back curve and leaf pelvic curvature line are carried out curvature continuous print prolongation, the blade back curve C after being extended_veWith leaf basin Curve C_ce；To this to curve application mean camber line extraction algorithm, the mean camber line C after being extended_me；

3. the leading edge circular arc least square fitting equation of belt restraining is set up；In order to meet the leading edge curve C after matching_lNot only matching Error is minimum, in addition it is also necessary to ensure and blade back curve C_veWith leaf pelvic curvature line C_ceReach to smoothly transit；Therefore, mean camber line conduct is utilized The circular arc center of circle and the transition of radius, i.e. with the point on mean camber line as the center of circle, the inscribed circle obtained meets leading edge curve C_lWith blade back Curve C_veLeaf pelvic curvature line C_ceTangent condition, sets up following least square fitting expression formula；

$\min f\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{e}_i^2\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(\sqrt{{(P_{ix}-O_x(s\left)\right)}^2+{(P_{iy}-O_y(s\left)\right)}^2}-R(s\left)\right)}^2$

Wherein, s is for extending mean camber line C_meArc length parameters, O_x(s),O_y(s), R (s) respectively center of circle X-coordinate, center of circle Y coordinate, Matching garden radius；P_ix, P_iyIt is X-coordinate and the Y coordinate of leading edge measurement point respectively；

4. utilize Gauss-Newton method to carry out least-squares calculation, calculate aboutJacobian matrix,

$J\left(s\right)=\left[\begin{array}{c}\frac{(P_{1x}-O_x(s\left)\right)\·O_x^{\′}\left(s\right)+(P_{1y}-O_y(s\left)\right)\·O_y^{\′}\left(s\right)}{\sqrt{{(P_{1x}-O_x(s\left)\right)}^2+{(P_{1y}-O_y(s\left)\right)}^2}}-R^{\′}\left(s\right)\\ .\\ .\\ .\\ \frac{(P_{nx}-O_x(s\left)\right)\·O_x^{\′}\left(s\right)+(P_{ny}-O_y(s\left)\right)\·O_y^{\′}\left(s\right)}{\sqrt{{(P_{nx}-O_x(s\left)\right)}^2+{(P_{ny}-O_y(s\left)\right)}^2}}-R^{\′}\left(s\right)\end{array}\right]$

Set up iterative computation formula s^(k+1)=s^(k)-(J^T·J)^-1·J^T·e(s^(k)), wherein, e (s)=(e₁(s),…,e_n(s) )^T；

5. original mean camber line C is extracted_mExtreme coordinates P_e, and by this coordinate P_eExtending C on mean camber line_meArc length parameters s_lAs The initial value of iteration is iterated；After m iteration, this arc length parameters s_mRepresented inscribed circle is and meets error and Little and with blade back curve C_veLeaf pelvic curvature line C_ceThe leading edge curve C being smoothly connected_l；

Step 3, to trailing edge curve C_tIt is fitted, obtains the trailing edge curve C after matching_t；

Step 4, using the beginning and end of the leading edge curve after matching and trailing edge curve as leading edge curve, trailing edge curve and leaf The back of the body curve, the junction point of leaf pelvic curvature line, four curves constitute the section line of blade profile.