CN115455588A - Turbine blade precision casting mold surface reversible deformation design method - Google Patents
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Abstract
A turbine blade precision casting mold molded surface reversible deformation design method relates to the field of machinery. 1) Encrypting discrete points of a curve; 2) B, fitting a design curve by a spline; 3) Searching a corresponding point of the measured data based on a curve subdivision method; 4) Constructing a free deformation grid: deforming the object by manipulating the design grid control points; 5) And (3) iteratively calculating displacement deformation: establishing a series of fitting curves by iteratively adjusting control points of the design curve, wherein in each iteration, a difference vector of each control point is a weighted sum of data points of the target curve and some difference vectors of corresponding points on the fitting curve, and the weighted sum of the difference vectors is iteration calculation displacement deformation; 6) And performing inverse deformation on the design curve by adopting the iterative deformation. On the basis of keeping the design intention, the molded surface of the turbine blade precision casting mold is subjected to inverse deformation optimization design according to the deviation of the measuring point data, the curved surface reconstruction precision and the practicability of the molded surface of the turbine blade precision casting mold are improved, and the cavity inverse deformation optimization of the precision casting turbine blade based on the B spline characteristic is realized.
Description
Technical Field
The invention relates to the field of machinery, in particular to a turbine blade precision casting mold molded surface reverse deformation design method based on B spline curve subdivision.
Background
Turbine blades are typically precision cast using directional crystallization or single crystal net shape. In the design and manufacturing process of the precision casting turbine blade of the aero-engine in China, the problems of low profile precision, unstable quality and high rejection rate of the precision casting turbine blade caused by unreasonable size of the mold design are not solved. The main foreign engine companies have established directional solidification and single crystal turbine blade precision casting production lines, the casting process is mature, and the problem of accurate shape control of the molded surface of the turbine blade casting is urgently solved. In the process of precision casting of the turbine blade, after high-temperature liquid alloy is injected into a shell, deformation can be generated along with the reduction of temperature. The turbine blade has a complex structural shape, so that heat dissipation is uneven when a casting is cooled, deformation of each point of the blade is uneven, actual deformation of the casting is nonlinear, the casting size is out of tolerance, and qualified turbine blades cannot be cast. This has become a big pain point in the field of turbine blade net-shape precision casting, so it is necessary to propose a turbine blade precision casting mold surface reverse deformation optimization design method which can combine design intention and measured data.
The design of the reverse deformation of the molded surface of the precision casting mold needs to compensate the deformation of the casting in the solidification cooling process. In China, a profile scaling method is firstly adopted for compensation and is divided into a uniform scaling method, a chord length scaling method, a mean camber line scaling method and a shrinkage center scaling method, the shrinkage rates of the four scaling methods still adopt constants, and the difference is that the selection of the shrinkage center and the shrinkage direction is inconsistent. Although this method is simple, it has obvious disadvantages: firstly, the uniform shrinkage of the turbine blade is approximate, namely, the shrinkage rate values at different parts are assumed to be the same, secondly, the proportion of the volume shrinkage of the turbine blade is approximate, the coordinate line of the design molded surface of the turbine blade is thickened or reduced along the normal proportion to realize the compensation of a mold cavity, and the non-rigid deformation of the turbine blade is ignored. In view of the disadvantages of the profile scaling method, some researchers propose to assign different shrinkage rates in the x, y and z directions to obtain certain effects. However, the disadvantages are that the shrinkage rate is still assigned as a constant or linear value in all directions, and the casting model needs to be continuously corrected according to the shape and size of the cast part. With the maturity of the numerical simulation technology in the casting process, a method for reversely superposing the deformation obtained by numerical simulation on the node is provided, and the shape of the turbine blade after shrinkage deformation is very close to the ideal design shape through multiple iterations. The method has the disadvantages that the quality of the grid is reduced at the position where the casting deformation is large, so that the convergence of numerical simulation calculation and the correctness of a simulation result are influenced. And then, a precision casting mold surface reversible deformation method based on displacement field simulation and characteristic parameter extraction is proposed, and compensation of nonlinear shrinkage deformation is realized by extracting characteristic parameters of a reflecting blade profile and restoring and adjusting the blade profile. The method has the disadvantages that the deviation amount before and after solidification is linearly and reversely superposed in reverse adjustment, and the deformation caused by superposition is ignored; reversely adjusting a plurality of characteristic parameters at the same time, and ignoring the coupling relation among the parameters; and the geometrical characteristic parameters of different sections are reversely adjusted, so that the reconstruction of the final curved surface is difficult.
Disclosure of Invention
The invention aims to provide a method for designing the reverse deformation of the profile of the turbine blade precision casting mold based on B-spline curve subdivision, which carries out reverse deformation optimization design on the profile of the turbine blade precision casting mold according to the deviation of measuring point data on the basis of keeping the design intention, aims to optimize the design size of the precision casting mold based on coupling deformation, ensures that the casting size does not generate out-of-tolerance, improves the curved surface reconstruction precision and the practicability of the profile of the turbine blade precision casting mold, and realizes the net-forming precision casting of the turbine blade.
The invention comprises the following steps:
1) Discrete points of the encryption curve: gridding a fitting area of a curve to be encrypted, determining the size of an influence area of a grid point x and a node contained in the influence area, calculating a node value at the grid point x after determining a shape function, performing the above processing on each grid point, and encrypting the curve;
2) B spline fitting design curve: parameterizing discrete points on the design curve according to an accumulative chord length parameterization method, requiring the head and tail end points of the design curve to pass through the head and tail end points of the B spline curve, fitting the rest of the discrete points on the design curve through the B spline curve by using a least square thought, and iteratively reducing the fitting deviation for multiple times so as to determine the number of control points, thereby completing the fitting of the design curve by using the B spline;
3) Solving the corresponding points of the measured data points on the design curve: searching corresponding points based on a curve subdivision method, and subdividing a B spline curve into a group of Bezier curves by using a node insertion algorithm of the B spline curve; subdividing each Bezier curve again in the binary tree searching process, judging whether the condition is met, if so, subdividing again until the curve segment is smaller than a set threshold value, and judging the minimum value in the candidate points to obtain the corresponding point of the actually measured data point on the design curve;
4) Constructing a free deformation grid: the object is deformed by manipulating the control points of the design grid, and local free deformation can be realized by adopting a B-spline basis function with local support; considering that the object of the current time is a two-dimensional B spline, defining the simplest designed grid as an axial grid with a control point grid, and expressing the axial grid as a B spline surface;
5) And (3) iteratively calculating displacement deformation: establishing a series of fitting curves by iteratively adjusting control points of the design curve, wherein in each iteration, a difference vector of each control point is a weighted sum of a target curve data point and some difference vectors of corresponding points on the fitting curve, and the weighted sum of the difference vectors is the displacement deformation of iterative calculation;
6) Carrying out inverse deformation on the design curve by adopting iterative deformation: and under the condition that the deformed B-spline control points correspond to the control points before deformation, accumulating the weighted difference vectors of the data points as inverse deformation parameters, calculating a deformation matrix of the control points embedded in the grid, and performing inverse deformation on the design curve by manipulating the grid.
In step 3), taking a point on the actual measurement curve as an example (hereinafter referred to as an actual measurement point), the distance from the actual measurement point to the corresponding point on the design curve may be converted into the distance from the actual measurement point to a set of Bezier curves, and then the problem of the minimized distance function is converted into the zero point problem of the polynomial function related to the parameter t. And in the binary tree searching process, along with depth subdivision of a Bezier curve, judging whether the polynomial function of the parameter t is on the same side of the t axis, excluding the same side, marking the different side as candidate points, and finally taking the minimum value in the candidate points as the closest point of the actual measuring points on the design curve.
In step 4), the constructing a free deformation mesh includes constructing a two-dimensional free deformation mesh including a model, and the deformation operation does not directly act on the object but acts on the embedded deformation space, and the constructing a two-dimensional free deformation mesh including a model mainly includes the following two steps: constructing a local two-dimensional coordinate system, then calculating local coordinates corresponding to each vertex coordinate of the model, and embedding the curve model into a frame; based on a ternary Bernstein multivariate power function, moving a control point, recalculating the world coordinate of each vertex of the model by using the local coordinate of the vertex of the model, the world coordinate of the control point and a Bernstein polynomial, and pulling the model by the framework to realize deformation.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a B-spline curve subdivision-based turbine blade precision casting mold surface reverse deformation design method which effectively achieves the optimal compromise of retaining design intention to the maximum extent through measured data, achieves B-spline characteristic-based cavity reverse deformation optimization of precision casting turbine blades, provides a convenient preposed foundation for subsequent two-dimensional superposition to three-dimensional reconstruction, and saves a large amount of fairing cost and time compared with discrete point three-dimensional reconstruction work. Because the adopted Free Form Deformation (FFD) algorithm is closely related to the turbine blade profile parameterization design method, all related technologies such as turbine blade design, modeling, machining and the like can be conveniently integrated on any CAD platform, and the turbine blade profile parameterization operation is efficiently realized.
Drawings
FIG. 1 is a graph of the encryption effect of the leaf back curve of the leaf basin with sparse point cloud;
FIG. 2 is a schematic diagram of a design model blade back curve fitting of the present invention;
FIG. 3 is a graph of the effect of curve subdivision according to the present invention;
FIG. 4 is a free-form mesh effect diagram of the present invention;
FIG. 5 is a schematic diagram of an iterative fitting error vector according to the present invention.
Detailed Description
The following examples will allow one skilled in the art to more fully understand the present invention, but do not limit the invention in any way.
The method of the invention comprises the following implementation approaches:
(1) Given the similar complexity of discrete points in preserving turbine blade design intent, it is often reduced to a series of two-dimensional cross-sectional stacking problems. The method adopts two sections of B splines and two sections of circular arcs to represent the blade basin and the blade back of the section of the turbine blade, and when point clouds at the blade basin and the blade back are sparse and discrete point data does not interfere with noise points, the fitting error is zero when an implicit function curve obtained by calculation passes through an original data point. And for the noise point data, the influence of the noise point is weakened through moving least squares with influence domains. The curve surface fitting is carried out by using a moving least square method, namely, firstly, a fitting area is gridded, then, a node value on each grid point is solved by using a formula, and curve encryption is carried out;
(2) Fitting a blade basin blade back curve of the encrypted turbine blade section by using a B spline, carrying out accumulated chord length parameterization on discrete points on the curve, pre-calculating parameter values and node vectors, solving control points and a basic function by using a least square method to meet the condition that the curve is as close as possible to data points, and iteratively obtaining the number of the control points according to an error limit defined by a user;
(3) In order to avoid the disadvantages of the conventional numerical method and the requirement of providing a good initial value for Newton iteration to obtain correct results, a method based on curve subdivision is proposed to find the closest point, i.e. the point on the curve where a given point is closest to the given point, and the method does not involve any iterative processing. Firstly, subdividing a B spline of a leaf back basin curve into Bezier curves, screening qualified curves according to the fact whether a constructed curve is intersected with a t axis or not, subdividing the Bezier curves, searching the closest point of an actually measured data point on a design curve by adopting binary tree decomposition, and defining the search depth through an error limit given by a user;
(4) The deformation operation of the FFD is not directly applied to the object but applied to the embedded deformation space, and if the deformation space is changed, the object embedded therein is naturally changed. The FFD algorithm mainly comprises two steps: embedding the curve model into a frame consisting of control points; when the position of the control point is changed, the frame pulls the model, so that the deformation is realized;
(5) A group of bases and a group of discrete data points to be fitted are given and marked as initial control vertexes, an initial fitting curve is generated, fitting error vectors from each initial control vertex to the initial curve are calculated, the control vertexes are moved along the direction of the fitting error vectors, new control vertexes are generated, a curve line with the fitting accuracy being improved continuously can be obtained through the circulation, and when the fitting bases are NTP bases, the fitting error can be ensured to be small at will, namely the fitting limit curves interpolate the initial control vertexes, a very large data set can be fitted efficiently and stably by means of the method, and meanwhile, in the incremental data fitting process of the method, a new round of iteration can be started from the fitting result of the previous round of iteration, and therefore a large number of calculations are saved;
(6) And under the condition that the deformed B-spline control points correspond to the control points before deformation, accumulating the weighted difference vectors of the data points as inverse deformation parameters, calculating a deformation matrix of the control points embedded in the grid, and performing inverse deformation on the design curve by manipulating the grid.
The specific implementation steps are given in the following with reference to the attached drawings.
The method comprises the following steps: discrete points of encryption curve
By taking an aeroengine turbine blade casting line laser scanning model as an example, aiming at the problem that point clouds at a blade basin and a blade back of a turbine blade section are sparse, moving least squares are introduced to encrypt discrete points on a curve. The basic idea of curve encryption using the moving least squares method is to first grid the fitting area, determine the size of the area of influence of grid point x toAnd nodes contained in the affected area, after determining the shape function, calculating a node value at a grid point x, performing the above processing on each grid point, and performing curve encryption, wherein the encryption effect is shown in fig. 1. Wherein the shape function is expressed as phi = P T (P T ωP) -1 P T ω, basis function P = [1, x = 2 ] T ，P T Is the transposition of P, P -1 Is the inverse matrix of P. The weight function ω is related to the radius of the domain of influence
Cubic spline function curve of (1):
step two: b spline fitting design curve
Fitting the blade back curve of the blade basin with the encrypted turbine blade section by using a B spline, taking the design of a model blade back curve as an example, and taking a discrete point q as the blade back curve r (r =0, …, m) and fitting the leaf back curve with 3-degree B-spline, the first section design model leaf back curve is recorded as
Wherein b represents the leaf back, ls represents the curve of the ith section, t is the normalized parameter, and the expression is
Wherein P is i b For the ith control vertex of the leaf back curve, N i,3 And (t) is a basis function of the cubic B spline corresponding to the ith control vertex. Satisfy the requirement of
The remaining points q k (k =1, …, m-1) is approximated with a least squares fit, i.e.
Is for n +1 variables P i b Is the most important ofSmall value, where t r Is q r (r =0, …, m) node vector t, a pre-computed parameter value parameterized by cumulative chord length j ＝{0,0,0,0,t r ,1,1,1,1}. The effect of the fit is shown in figure 2.
Step three: calculating the corresponding point of the measured data point on the design curve
Subdividing the B splines of the design curve into Bezier curves by a de Boor recursion algorithm, wherein the subdivision effect is shown as figure 3, and the subdivided jth sub-curve is shown as
Wherein P is i For the ith control point of the sub-curve, B i,3 Is the cubic Bernstein basis function corresponding to the ith control vertex. The corresponding points can be described as: calculating actual measuring point q of turbine blade casting line laser scanning model r (r =0, …, m) in design sub-curve C i Corresponding point p on (t) r (r＝0,…,m)，q r Corresponding point p thereof r The distance between is minimal and the function of minimizing is:
can be expressed as a Bezier curve on a t axis, and the minimization solving problem can be converted into a zero point solving problem. For is to
And performing recursive subdivision by using a deCasteljau algorithm, and simultaneously checking whether the control points of the subdivided sub-curves are on the same side of the t axis (namely the sub-curves have no intersection point with the t axis), wherein if the control points are on the same side, the corresponding interval is marked as the interval excluding the closest point. And searching candidate points in the unmarked node interval with the given depth by using a binary tree method while excluding the unqualified curve. Finally, taking the minimum value in the candidate points as the corresponding point p r 。
Step four: construction free deformation grid
Constructing a two-dimensional local coordinate system, and combining the design curves and the real curvesEmbedding the measuring curve into the coordinate system, and then calculating the local coordinate corresponding to each vertex coordinate of the model
Local coordinates regardless of changes in world coordinates of control points
Are all fixed, provided that p is 0 Is the local coordinate system origin and p is the model vertex coordinates. Moving the control point by using the local coordinates of the model vertex, the world coordinates of the control point and the Bernstein polynomial B i,m Recalculating the world coordinates of each vertex of the model:
the effect of driving the curve to deform by using the grid space is realized, as shown in fig. 4; wherein u/v is a horizontal/vertical grid parameter, B i,m Is the Bernstein basis function corresponding to the ith m-th order, B j,n Is the Bernstein basis function corresponding to the jth n-th order, P i,j Is a vector matrix of (n + 1) × (m + 1), and embeds grid nodes with the sequence (i, j).
Step five: iteratively calculating displacement deformation
Actual measuring point q of line laser scanning model of turbine blade casting of aero-engine r (r =0, …, m) as an example, at the start of the iteration, the design curve B-spline function is taken as the first (noted as 0 th) fit curve
As shown in fig. 5, the first deviation of the jth parameter from its corresponding point
Wherein t is j Is q r Corresponding to the parameters, designing the first adjustment vector of the ith control point on the curve B spline as
One iteration post-curve control points P embedded in the grid S (u, v) k Can representIs composed of
Wherein u/v is a horizontal/vertical grid parameter, B i',m Is the Bernstein basis function corresponding to the i' th m-th order, B j',n Is the Bernstein basis function corresponding to the j' th n-th order, P i',j' A vector matrix of (n + 1) × (m + 1) with grid nodes of (i ', j') sequence built in; the deformation of the fitted curve can be replaced by operating its control points, and the above equation can be converted into
Where s represents the number of control points. Obtaining new control points and new curves by using the grid deformation method in the step four;
similarly, the kth curve f is obtained after the kth iteration k (t) satisfies
The method depends on the parameter distance between a data point and a corresponding point on the same parameter curve, the parameter t of iterative operation is a chord length parameter calculated by a real measuring point of a line laser scanning model, and the iteration is to design a control point of a B spline of the curve, so that the B spline control point of the deformation curve corresponds to the real measuring point by using the method of the third step.
Step six: inverse deformation of design curve by iterative deformation
The weighted sum of the difference vectors of each iteration approximation can be obtained from the step five
By using
The design model leaf basin leaf back curve is subjected to inverse deformation, w times of iterative approximation are carried out on the design model leaf basin curve as an example, and the expression of the deformed leaf basin curve is
The foregoing description is only exemplary of the preferred embodiments of the invention and is illustrative of the principles of the technology employed. It will be appreciated by persons skilled in the art that the scope of the disclosure herein is not limited to the particular combination of features described above, but also encompasses other combinations of features described above or their equivalents. For example, the above features and the features having similar functions disclosed in the present invention are mutually replaced to form the technical solution.
Claims (6)
1. The method for designing the molded surface reverse deformation of the turbine blade precision casting mold is characterized by comprising the following steps of:
1) Encrypting discrete points of a curve;
2) B spline fitting a design curve;
3) Solving the corresponding points of the measured data points on the design curve: searching corresponding points based on a curve subdivision method, and subdividing a B spline curve into a group of Bezier curves by using a node insertion algorithm of the B spline curve; subdividing each Bezier curve again in the binary tree searching process, judging whether the condition is met, if so, subdividing again until the curve segment is smaller than a set threshold value;
4) Constructing a free deformation grid: the object is deformed by manipulating the control points of the design grid, and local free deformation can be realized by adopting a B spline basis function with local support;
5) And (3) iteratively calculating displacement deformation: establishing a series of fitting curves by iteratively adjusting control points of the design curve, wherein in each iteration, a difference vector of each control point is a weighted sum of difference vectors of data points of the target curve and corresponding points on the fitting curve, and the weighted sum of the difference vectors is the iterative computation displacement deformation;
6) Performing inverse deformation on the design curve by adopting iterative deformation: under the condition that B spline control points of the design curve correspond to control points of the measured data curve, the accumulated sum of weighted difference vectors of the data points is used as an inverse deformation parameter, a deformation matrix of the control points embedded in the grid is calculated, and the design curve is subjected to inverse deformation through manipulating the grid.
2. The method for designing the reverse deformation of the profile of the turbine blade precision casting mold according to claim 1, wherein in the step 1), the specific method for encrypting the discrete points of the curve is as follows: and gridding a fitting area of a curve to be encrypted, determining the size of an influence area of a grid point x and a node contained in the influence area, calculating a node value at the grid point x after determining a shape function, performing the above processing on each grid point, and encrypting the curve.
3. The turbine blade precision casting mold surface reverse deformation design method as claimed in claim 1, wherein in step 2), the specific method of B-spline fitting the design curve is as follows: and (3) parameterizing discrete points on the design curve according to an accumulative chord length parameterizing method, requiring the head and tail end points of the design curve to pass through the head and tail end points of the B spline curve, fitting the rest of the discrete points on the design curve through the B spline curve by using a least square thought, and iteratively reducing the fitting deviation for multiple times so as to determine the number of control points, thereby completing the fitting of the design curve by using the B spline.
4. The method for designing the reverse deformation of the turbine blade precision casting mold according to claim 1, wherein in the step 3), the specific method for determining the corresponding point of the measured data point on the design curve is as follows: converting the distance from the measured data point to the corresponding point on the design curve into the distance from the measured data point to a group of Bezier curves, and converting the problem of the minimized distance function into the zero point problem of the polynomial function related to the parameter t; and in the binary tree searching process, along with depth subdivision of a Bezier curve, judging whether a polynomial function of a parameter t is on the same side of a t axis, if so, excluding the polynomial function, if not, marking the polynomial function as a candidate point, and finally, taking the minimum value in the candidate points as a corresponding point of a measured data point on a design curve.
5. The method for designing the reverse deformation of the profile of a turbine blade casting mold according to claim 1, wherein in the step 4), the free deformation mesh is constructed, and the design simple mesh is defined as an axial mesh with a control point mesh based on a two-dimensional B spline and is expressed as a B spline surface.
6. The method for designing the reverse deformation of the profile of the turbine blade precision casting mold according to claim 1, wherein in the step 4), the constructing of the free deformation mesh comprises constructing a two-dimensional free deformation mesh containing a model, and the specific steps are as follows:
(1) Constructing a local two-dimensional coordinate system, calculating local coordinates corresponding to each vertex coordinate of the model, and embedding the curve model into a frame;
(2) And moving the control point based on the ternary Bernstein multivariate power function, recalculating the world coordinate of each vertex of the model by using the local coordinates of the vertices of the model, the world coordinates of the control point and the Bernstein polynomial, and pulling the model by the framework to realize deformation.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116522546A (en) * | 2023-07-04 | 2023-08-01 | 太原理工大学 | Container configuration reverse solving method for uniformly removing blade part through barreling finishing |
| CN117726710A (en) * | 2024-02-18 | 2024-03-19 | 粤港澳大湾区数字经济研究院(福田) | Curve dispersion-based drawing method and related device |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116522546A (en) * | 2023-07-04 | 2023-08-01 | 太原理工大学 | Container configuration reverse solving method for uniformly removing blade part through barreling finishing |
| CN116522546B (en) * | 2023-07-04 | 2023-09-15 | 太原理工大学 | Container configuration reverse solving method for uniformly removing blade part through barreling finishing |
| CN117726710A (en) * | 2024-02-18 | 2024-03-19 | 粤港澳大湾区数字经济研究院(福田) | Curve dispersion-based drawing method and related device |
| CN117726710B (en) * | 2024-02-18 | 2024-06-04 | 粤港澳大湾区数字经济研究院(福田) | Curve dispersion-based drawing method and related device |
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