CN111062099A - Equal-radius search based blade profile mean camber line construction method - Google Patents
Equal-radius search based blade profile mean camber line construction method Download PDFInfo
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Abstract
The invention discloses a blade type mean camber line construction method based on equal radius search, which aims at the problem of mean camber line construction in practical application and is provided based on the definition of the mean camber line, and the method mainly comprises two steps: 1) constructing a blade profile continuous model, and 2) constructing a blade profile mean camber line based on radius search according to the blade profile continuous model obtained in the step 1). The method for constructing the mean camber line can accurately determine the inscribed circle defined by the mean camber line. Due to the adoption of the step length changing idea, the search efficiency is accelerated, and meanwhile, the convergence precision of the inscribed circle is improved. The final camber line can reflect the actual processing condition of the blade more accurately.
Description
Technical Field
The invention belongs to the field of precision measurement, and particularly relates to a blade profile mean camber line construction method based on equal radius search.
Background
The blade is a core component of an aircraft engine and accounts for approximately 30% of the total engine manufacturing. The blade belongs to a thin-wall part and works under severe working conditions of high load, complex stress and the like. In order to ensure special performance, the blade body profile is usually designed into a free-form surface, and has strict requirements on size, shape precision and surface integrity, and the manufacturing precision is high. The whole size span of the blade is large, the profile is complex, and the deformation is easily caused by casting or milling and other processing. The mass of the blade has a large influence on the secondary flow loss of the engine, and directly determines the energy conversion efficiency of the engine. Therefore, the geometric accuracy of the aviation blade after machining is strictly controlled, and the method has important significance for realizing the precise manufacturing of the aviation engine and ensuring the integral level of the engine. The blade profile is controlled by a series of blade profiles (blade sections), and the blade profiles are mostly free curves, have numerous section characteristic parameters and geometric tolerance requirements, and the parameters of the profile have no fixed rule.
In recent years, as the performance and demand of aircraft engines have been increased, more stringent requirements have been placed on the accuracy of the profile of blade mass production, the consistency of products, and the like. The precise calculation and separation of the blade machining error through the blade precise detection technology and the completion of the machining process parameter adjustment based on the blade precise detection technology are important ways for improving the precision of a blade manufacturing system. The main content of the blade detection is the processing geometric error of the molded surface, including items such as characteristic parameters and profile tolerance errors of the control blade profile.
With the gradual maturity of the technology of a Coordinate Measuring Machine (CMM), the blade profile can be continuously and automatically measured by matching with a multi-freedom Measuring head. A four-coordinate measuring system developed on the basis is that a high-precision rotary main shaft is additionally arranged on the basis of three linear shafts of the CMM. A related research mechanism combines a four-coordinate measuring system with a trigger measuring head, and a special blade measuring instrument is developed. The control software drives the movement mechanism, the trigger measuring head is adjusted to measure the blade profile point by point, and finally the blade precision is obtained through the analysis system.
The method is characterized in that the discretization sampling of the blade profile can be realized by using optical scanning measurement, but the sampling density is limited, so that the accurate acquisition of the profile data of the specified section (blade profile) of the blade is difficult to ensure. Meanwhile, due to the influence of various measurement errors, the blade profile measurement point and a theoretical model need to be accurately matched to separate the single error of the profile shape when calculating the profile error, and the profile of the profile type line edge head of the cross section of the blade needs to be segmented.
The size and shape of the front edge and the rear edge of the blade, namely the circular arc parts at the two ends of the profile of the blade determine the aerodynamic performance of the engine. The edge head commonly used in engineering is in a circular arc shape, and the edge head is tangent with the free curves of the leaf basin and the leaf back section to jointly form a complete leaf profile. In order to solve the size deviation of the edge head, the edge head needs to be separated from two molded lines of a blade basin and a blade back in blade profile measurement data, and due to the complexity of the blade profile molded lines, the accurate analysis of all the elements has great difficulty.
According to the specification of the navigation mark HB 5647-98, the blade profile mean camber line is formed from the centre of all inscribed circles in the blade profile. The mean camber line is the basis of blade profile thickness calculation and is also one of the important bases for judging the processing quality of the blade profile. In the traditional method, the molded line is amplified in equal proportion through drawing to draw a rough tangent circle, and a middle arc line is formed by connecting the centers of all tangent circles, but the method has low efficiency and large error. The existing method for solving the mean camber line mainly comprises an analytic method, an equiangular or equiradial method, an equidistant line method and the like. The solving condition of the analytic method is relatively harsh, the leaf basin and leaf back curves are required to have a quintic equation analytic expression, and the application range is narrow. And the calculation is carried out by adopting a discrete model of the blade profile based on an equal angle or equal radius method, so that the error is large. The equidistant line method is complex to implement and needs to carry out intersection of a large number of blade profile equidistant lines.
Disclosure of Invention
The invention provides a blade type mean camber line construction method based on equal radius search, aiming at the problem of mean camber line construction in practical application and based on the definition of mean camber line.
The invention is realized by adopting the following technical scheme:
the blade profile mean camber line construction method based on equal radius search comprises the following steps:
1) constructing a leaf-shaped continuous model;
2) constructing a blade profile mean camber line based on radius search according to the blade profile continuous model obtained in the step 1).
The further improvement of the invention is that the specific implementation method of the step 1) is as follows:
step 1.1, pretreatment
Dividing the curve into two sections through an extreme value of the X coordinate of the measuring point, and respectively reordering the two divided sections according to the X coordinate;
step 1.2 parameterizing node vectors
And d is a total chord length by using an accumulated chord length parameterization method:
then there are:
the data points of the leaf shapes correspond to the nodes in the definition domain, and the nodes in the definition domain can be determined by using an accumulative chord length parameterization method;
step 1.2, back-computing the control vertex of the B-spline
The adopted interpolation curve is a cubic B spline, and k is made to be 3; according to the principle of curve interpolation, a domain [ u ] is defined3,un+1]Substituting the nodes in the B spline into an expression:
m +1 linear equation sets are obtained:
for C2A continuous B-spline closed curve, wherein the equation (4) has m effective equations due to the repetition of the first and last measuring points of the leaf profile; the k at the first end and the k at the last end are the same as 3 control points in sequence, and n-2 residual equations about the control points in the formula (4) are left; determining N according to constructed node vector U and basis function recursionj,3(ui) A value of (d); therefore, the equations for the remaining m unknown control points can be calculated, and the matrix form of the equations is as follows:
the final leaf curve interpolation result is represented by the determined node vector U and the back-calculated control vertex.
The further improvement of the invention is that the specific implementation method of the step 2) is as follows:
step 2.1, determining an initial search condition, a radius r, an initial point and a normal direction thereof, and calculating a normal distance d from a circle center to a blade back profile;
2.2, constructing an auxiliary search circle, namely constructing an auxiliary search circle which passes through a lower half section of curve point and has the radius r equal to the radius of the front edge;
step 2.3, taking the normal vector direction of the division point of the front edge as a search direction, and continuously adjusting the search direction according to the difference value of the normal distance d between the circle center and the upper half leaf profile and the radius r of the auxiliary search circle;
when d is larger than r, the searching circle 1 and the blade back molded line have no intersection point, and r ═ r + delta is used as the radius of a new searching circle; when d is less than r, two intersection points are formed between the search circle 2 and the leaf back, and r' is r-delta and is used as the radius of a new search circle; repeating the judgment condition until the set threshold value condition | d-r | is less than epsilon; to this end, a point on the mean camber line and the size of the tangent circle radius at that point have been determined; after the construction process of the inscribed circle is completed once, moving a point in the direction of the rear edge, and repeating the construction process;
step 2.4, constructing a continuous model of the mean camber line
The circle centers of all the inscribed circles obtained through the search form a discretization model of the mean camber line, a continuity model of the mean camber line is constructed by adopting a cubic spline interpolation method on the basis, and the circle centers of the edges are expanded to intersect with the leaf-shaped splines along the tangential direction, so that the final complete leaf-shaped mean camber line is obtained.
The invention has the following beneficial technical effects:
the method for constructing the blade-shaped mean camber line can accurately determine the inscribed circle defined by the mean camber line. Due to the adoption of the step length changing idea, the search efficiency is accelerated, and meanwhile, the convergence precision of the inscribed circle is improved. The final camber line can reflect the actual processing condition of the blade more accurately.
Drawings
FIG. 1 is a flow chart of B-spline interpolation of a leaf curve.
FIG. 2 is a schematic diagram of control points of a profile curve.
FIG. 3 is a schematic view of a leaf pattern continuity model.
Fig. 4 is a schematic diagram of an inscribed circle search process.
FIG. 5 is a flow chart of the construction of the camber line of the blade profile
FIG. 6 is a schematic diagram of the construction of the camber line of the blade profile.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention aims at the problem of camber line construction in practical application, and realizes a blade type camber line construction method based on equal radius search based on the definition of the camber line.
The B-spline curve has a series of excellent properties such as geometric invariance and affine invariance, and can ensure that the local shape of the leaf profile is only influenced by local measurement data. In engineering calculations, to ensure that C is at the interpolation point2And continuously, three B-sample strips are adopted as interpolation curves. The blade profile is a closed curve, and the measurement point of the blade profile data is set as qi(i ═ 0, 1.., m). Upon separation of the margin, the leaf-type measurement data points have been segmented into two segments and reordered. In order to realize closed B-spline interpolation of the leaf type, two sections of measured points are connected end to end, and an initial measured point is added at the tail end of a data point set. Control vertex d of inverse interpolation leaf type interpolation B splinei(i-0, 1.. times.n) and node vector U-U0,u1,...,un+k+1Are determined together, and satisfy n ═ m + k-1. Let di(i ═ 0, 1.. times, N) is the control vertex, Ni,k(U) (i ═ 1, 2.., n) is the basis function of a k-th order B spline, and the corresponding node vector is U ═ U ·0,u1,...,un+k+1Satisfy u0≤u1≤···≤un+k+1. The expression of B-spline is:
is defined in the interval ui≤u＜ui+1Inner, zero-order B-spline basis function is Ni,0(u) is 1, and the remaining intervals are zero. According to the de-boolean-cox formula, and specifying that 0/0 is 0, the B-spline basis function has the following recurrence relation:
the method mainly comprises the following steps:
1) constructing a leaf-shaped continuous model;
2) constructing a blade profile mean camber line based on radius search according to the blade profile continuous model obtained in the step 1).
The specific implementation method of the step 1) is as follows:
step 1.1, pretreatment
And dividing the curve into two sections through the extreme value of the X coordinate of the measuring point, and reordering the two divided sections according to the X coordinate.
Step 1.2, node vector parameterization
And d is a total chord length by using an accumulated chord length parameterization method:
then there are:
the data points of the leaf profile correspond to the nodes in the definition domain, and the nodes in the definition domain are determined by using an accumulated chord length parameterization method, so that the problem of large density change of the measured data points can be well solved, and the real shape of the leaf profile can be reflected better. For nodes in a defined domain there are
To allow the leaf B-spline curve to be closed, for the other 2k nodes: u. of0＝un-k+1-1,u1＝un-k+2-1,…,uk-1＝un-1；un+2＝1+uk+1,un+3＝1+uk+2,…,un+k+1＝1+u2k. When constructing the node vector, firstly determining the node in the definition domain by an accumulated chord length parameterization method, then supplementing the values of 2k other nodes, and determining the node vector U of the leaf-shaped interpolation curve by the two nodes together.
Step 1.2, back-computing the control vertex of the B-spline
The interpolation curve adopted in the invention is cubic B-spline, and k is 3. According toPrinciple of curve interpolation, domain [ u ] will be defined3,un+1]Substituting the inner nodes into the expression of the B spline:
m +1 linear equation sets can be obtained:
for C2And (3) a continuous B-spline closed curve, wherein the equation (4) has m effective equations because the first and last measuring points of the leaf profile are arranged repeatedly. The k at the first end and the k at the last end are the same as 3 control points in sequence, and the equation (4) has the residual n-2 equations about the control points. N can be determined according to the constructed node vector U and the basis function recursionj,3(ui) The value of (c). Therefore, only the equations of the remaining m unknown control points need to be calculated, and the matrix form of the equations is as follows:
the final interpolation result of the leaf curve is represented by the determined node vector U and the back-calculated control vertex, and the flow chart of the leaf curve B-spline interpolation is shown in fig. 1. The measured leaf data is parameterized by node vectors and control points are calculated back, as shown in fig. 2. In the transition region with large curvature change, the density of the measured points changes violently, but the interpolation curve still passes through each leaf-shaped point smoothly, and a continuous model is accurately constructed, as shown in fig. 3.
The specific implementation method of the step 2) is as follows:
and 2.1, determining an initial search condition, the radius r, the initial point and the normal direction thereof, and calculating the normal distance d from the circle center to the blade back profile.
And 2.2, constructing an auxiliary search circle.
And constructing an auxiliary search circle which passes through the curve point of the lower half segment and has the radius size r equal to the radius of the front edge.
And 2.3, taking the normal vector direction of the division point of the front edge as a search direction, and continuously adjusting the search direction according to the difference value between the normal distance d between the circle center and the upper half leaf profile and the radius r of the auxiliary search circle, wherein the search process of the inscribed circle is shown in fig. 4.
When d is larger than r, the search circle 1 has no intersection point with the blade back line, and r' is r + delta and is the radius of the new search circle. When d is less than r, the search circle 2 has two intersection points with the leaf back, and r' is r-delta as the radius of the new search circle. And repeating the judgment condition until a set threshold value condition | d-r | is less than epsilon. To this end, a point on the mean camber line and the size of the radius of the tangent circle at that point have been determined.
And after the construction process of the inscribed circle is completed once, moving a little toward the direction of the rear edge, and repeating the construction process. In order to improve the searching efficiency, the radius of the initial auxiliary circle is set to be equal to the radius of the tangent circle of the previous step. In addition, in the searching process, in order to accelerate the speed of converging to the inscribed circle, a step length changing idea is adopted. When the value of | d-r | is a larger value, the difference between the search circle and the inscribed circle is larger, and a larger step length delta is adopted to accelerate to approach the inscribed circle. When | d-r | is a smaller value, a smaller search step δ is used to converge exactly to a result that satisfies the termination threshold. The flow chart of the equal radius search camber line construction method based on B-spline interpolation is shown in FIG. 5.
Step 2.4, constructing a continuous model of the mean camber line
The circle centers of all the inscribed circles obtained through the search form a discretization model of the mean camber line, a continuity model of the mean camber line is constructed by adopting a cubic spline interpolation method on the basis, and the circle centers of the edges are expanded to intersect with the leaf-shaped splines along the tangential direction, so that the final complete leaf-shaped mean camber line is obtained.
The measured data of the aviation blade profile is processed by adopting an equal-radius search camber line construction method based on cubic non-uniform closed B-spline interpolation, and the result is shown in FIG. 6. The searching process is continuously carried out along the air inlet edge to the air outlet edge, and all inscribed circles in the graph are final searching results. The continuous model of the circle center of the inscribed circle and the extension line form a blade-shaped mean camber line. From the search results of the air inlet and exhaust edges, the leaf basin and the leaf back, the method for constructing the mean camber line can accurately determine the inscribed circle defined by the mean camber line. Due to the adoption of the step length changing idea, the search efficiency is accelerated, and meanwhile, the convergence precision of the inscribed circle is improved. The final camber line can reflect the actual processing condition of the blade more accurately.
Claims (3)
1. The blade profile mean camber line construction method based on equal radius search is characterized by comprising the following steps of:
1) constructing a leaf-shaped continuous model;
2) constructing a blade profile mean camber line based on radius search according to the blade profile continuous model obtained in the step 1).
2. The method for constructing the blade-shaped mean camber line based on the equal-radius search according to claim 1, wherein the specific implementation method of the step 1) is as follows:
step 1.1, pretreatment
Dividing the curve into two sections through an extreme value of the X coordinate of the measuring point, and reordering the two divided sections according to the X coordinate;
step 1.2 parameterizing node vectors
And d is a total chord length by using an accumulated chord length parameterization method:
then there are:
the data points of the leaf shapes correspond to the nodes in the definition domain, and the nodes in the definition domain can be determined by using an accumulated chord length parameterization method;
step 1.2, back-computing the control vertex of the B-spline
The adopted interpolation curve is a cubic B spline, and k is made to be 3; interpolation from curvesWill define the domain u3,un+1]Substituting the inner nodes into the expression of the B spline:
m +1 linear equation sets are obtained:
for C2A continuous B-spline closed curve, wherein the equation (4) has m effective equations due to the repetition of the first and last measuring points of the leaf profile; the k at the first end and the k at the last end are the same as 3 control points in sequence, and n-2 residual equations about the control points in the formula (4) are left; determining N according to constructed node vector U and basis function recursionj,3(ui) A value of (d); therefore, the equations for the remaining m unknown control points can be calculated, and the matrix form of the equations is as follows:
the final leaf curve interpolation result is represented by the determined node vector U and the back-calculated control vertex.
3. The method for constructing the mean camber line based on the equal-radius search as claimed in claim 1, wherein the specific implementation method of step 2) is as follows:
step 2.1, determining an initial search condition, a radius r, an initial point and a normal direction thereof, and calculating a normal distance d from a circle center to a blade back profile;
2.2, constructing an auxiliary search circle, namely constructing an auxiliary search circle which passes through a lower half section of curve point and has the radius r equal to the radius of the front edge;
step 2.3, taking the normal vector direction of the division point of the front edge as a search direction, and continuously adjusting the search direction according to the difference value of the normal distance d between the circle center and the upper half leaf profile and the radius r of the auxiliary search circle;
when d is larger than r, the searching circle 1 and the blade back molded line have no intersection point, and r ═ r + delta is used as the radius of a new searching circle; when d is less than r, two intersection points are formed between the search circle 2 and the leaf back, and r' is r-delta and is used as the radius of a new search circle; repeating the judgment condition until a set threshold value condition | d-r | is less than epsilon; to this end, a point on the mean camber line and the size of the tangent circle radius at that point have been determined; after the construction process of the inscribed circle is completed once, moving a point in the direction of the rear edge, and repeating the construction process;
step 2.4, constructing a continuous model of the mean camber line
The circle centers of all the inscribed circles obtained through the search form a discretization model of the mean camber line, a continuity model of the mean camber line is constructed by adopting a cubic spline interpolation method on the basis, and the circle centers of the edges are expanded to be intersected with the leaf-shaped splines along the tangential direction, so that the final complete leaf-shaped mean camber line is obtained.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107288690A (en) * | 2017-07-07 | 2017-10-24 | 厦门大学 | A kind of turbine blade film cooling holes morpheme parameter correction method based on parameter of curve |
| CN109356666A (en) * | 2018-12-14 | 2019-02-19 | 中国航发沈阳发动机研究所 | A kind of Blade Design Method of axial-flow turbine big and small blade combination cascade |
| CN109918778A (en) * | 2019-03-04 | 2019-06-21 | 天津工业大学 | Wind energy conversion system aerofoil with blunt tail edge optimum design method under the conditions of a kind of rime ice |
| CN109948299A (en) * | 2019-04-11 | 2019-06-28 | 哈尔滨电气股份有限公司 | Camber line calculation method in a kind of compressor blade |
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107288690A (en) * | 2017-07-07 | 2017-10-24 | 厦门大学 | A kind of turbine blade film cooling holes morpheme parameter correction method based on parameter of curve |
| CN109356666A (en) * | 2018-12-14 | 2019-02-19 | 中国航发沈阳发动机研究所 | A kind of Blade Design Method of axial-flow turbine big and small blade combination cascade |
| CN109918778A (en) * | 2019-03-04 | 2019-06-21 | 天津工业大学 | Wind energy conversion system aerofoil with blunt tail edge optimum design method under the conditions of a kind of rime ice |
| CN109948299A (en) * | 2019-04-11 | 2019-06-28 | 哈尔滨电气股份有限公司 | Camber line calculation method in a kind of compressor blade |
Non-Patent Citations (2)
| Title |
|---|
| 张现东;卜昆;刘连喜;窦杨柳;: "空心涡轮叶片复杂陶芯弯扭变形分析方法比较" * |
| 杨金广;刘振德;邵伏永;吴虎;: "基于渗透边界条件的三维粘性叶轮机械气动设计反方法应用研究" * |
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