CN102620694A - Method for calculating fine-machining attitude of wing - Google Patents

Abstract

The invention provides a method for calculating a fine-machining attitude of a wing. The method comprises the following steps of: firstly, extracting a wing theoretical attitude curved surface S; secondly, horizontally measuring the wing to be finely machined, and thus obtaining real measuring points Pi,0 of wing horizontal measuring points; thirdly, according to the wing theoretical attitude curved surface S and the real measuring points Pi,0 of N wing horizontal measuring points, calculating matching points Ci of the real measuring points Pi,0 of the wing horizontal measuring points on the wing theoretical attitude curved surface by using an iterative closet point algorithm; and finally, according to the real measuring points of the wing horizontal measuring points and the corresponding matching points, calculating attitude parameters of the wing. The method has the advantages that the characteristics of a wing fine-machining process are fully combined; on the basis of wing horizontal measurement data which are easily obtained, calculation of the fine-machining attitude of the wing is realized by using the iterative closet point algorithm; and the problem that the fine-machining attitude of the wing cannot be accurately calculated by the conventional advanced measuring equipment such as a laser tracker is solved.

Description

A kind of wing finishing computation method for attitude

Technical field

The present invention relates to the aero-manufacturing technology field, be specially a kind of wing finishing computation method for attitude.

Background technology

The finishing of wing joint is one of important step of the big parts assembling of aircraft, and the coordinating order of accuracy that improves wing assembling accuracy and wing and other parts is had a very important role.The spatial attitude adjustment is the accurately machined basic link of wing as the important means that improves wing finishing quality, and Attitude Calculation then is the basis of carrying out the spatial pose adjustment, and therefore, the accurate Calculation of realization wing finishing attitude has important practical and is worth.

The patent (application number 200810121358) of Zhejiang University's application discloses a kind of computation method for attitude of aircraft fuselage based on laser tracker; Its main contents are: adopt the measurement point of expressing aspect on a plurality of laser tracker survey aircraft fuselages; Measured value through these measurement points be in the theoretical value under the ideal designs attitude, calculate the current attitude of aircraft components.Other aircraft components computation method for attitude are like document " the some matching algorithm of band engineering constraint " (Yu Cijun, Li Jiangxiong; Yu Fengjie, " mechanical engineering journal ", method of 2010.5:p.183-190.) introducing and document " based on the theoretical horizontal attitude of wing appraisal procedure of Saddle Point Programming " (Zhang Bin; Yao Baoguo, Ke Yinglin, " journal of Zhejiang university "; 2009.10:1761-1765.) method introduced, be similar approach.These class methods have been successfully applied to the Attitude Calculation of fuselage, have to calculate simply the characteristics that precision is high; But this method can not be applicable to the accurate Calculation of wing finishing pose fully, is mainly reflected in: on the one hand, because this method is when reality is used; Need on product, arrange the point that is used to express pose in advance according to the product digital-to-analogue; And use laser tracker that these physical locations in the space are measured, yet, with regard to wing finishing; Because the curved surface enclosed construction of its product object and the structural compactness characteristics of finishing type frame; Make on wing, to be difficult for arranging pose expression point, and use laser tracker that these spatial point are measured, thereby cause the use that is difficult to of this method; On the other hand, the aerofoil horizontal survey is as requisite link in the wing finishing process, and its measured value can reflect the wing posture information; But because the measured point of this measurement is not to arrange fixed point really on the aerofoil in advance; But depend on a certain random point of wing attained pose, at this moment, can't foresee the theoretical coordinate value of measurement point; Therefore, also can't directly apply mechanically the calculating that the preamble method is carried out pose.

Summary of the invention

The technical matters that solves

For solving the deficiency that exists in the prior art, the present invention proposes a kind of wing finishing computation method for attitude.

Technical scheme

Technical scheme of the present invention is:

Said a kind of wing finishing computation method for attitude is characterized in that: may further comprise the steps:

Step 1: extractor airfoil theory curved face S from the digital model of wing, said wing theory curved face are the appearance curved surface of wing lower aerofoil when being in theoretical attitude;

Step 2: treat accurately machined wing and carry out horizontal survey, obtain the eyeball P of wing horizontal survey point _{I, 0}, i=1,2 ..., N, i represent the horizontal survey point sequence number, N representes horizontal survey point sum, P _{I, 0}=(P _{Ix, 0}P _{Iy, 0}P _{Iz, 0}) ^TRepresent i horizontal survey point P _{I, 0}Coordinate under wing design coordinate system;

Step 3: by the eyeball P of wing theory curved face S and N horizontal survey point _{I, 0}, adopt iterative closest point algorithms to calculate the eyeball P of wing horizontal survey point _{I, 0}Match point on the wing theory curved face; Said iterative closest point algorithms is:

Steps A: S is last from P for iterative computation wing theory curved face _{I, 0}Nearest some B _{I, 0}: take up an official post at curved surface S and to get primary iteration point D ₀=S (u ₀, v ₀), u wherein ₀, v ₀Be respectively D ₀U on curved surface S, the v parameter; The span of iteration precision epsilon is 0＜epsilon＜0.01; M=0,1,2 ..., the step of the m+1 time iteration is:

Step a: calculate curved surface S at a D _mThe u at place is to cutting arrow

With v to cutting arrow

${D_{u_m}}^{\′}=\frac{\∂S}{\∂u}{|}_{u=u_m,v{=v}_m},{D_{v_m}}^{\′}=\frac{\∂S}{\∂v}{|}_{u=u_m,v{=v}_m},$

Calculate curved surface S and go up some D _mThe per unit system at place is vowed:

$n_m=\frac{{D^{\′}}_{u_m}\×{D^{\′}}_{v_m}}{|{D^{\′}}_{u_m}\×{D^{\′}}_{v_m}|}$

Step b: compute vector Wherein The expression starting point is D _m, terminal point is P _{I, 0}Vector; Calculate u to v to increment Delta u _m, Δ v _m:

${\mathrm{\Δu}}_m=\frac{{\mathrm{\τ}}_m\×{D^{\′}}_{v_m}}{{D_{u_m}}^{\′}\×{D^{\′}}_{v_m}},$ ${\mathrm{\Δv}}_m=\frac{{\mathrm{\τ}}_m\×{D^{\′}}_{u_m}}{{D_{v_m}}^{\′}\×{D^{\′}}_{u_m}}$

Step c: calculation level D _M+1=S (u _m+ Δ u _m, v _m+ Δ v _m); If D _mWith D _M+1Between distance | D _M+1-D _m|＞epsilon, then repeating step a～c carries out iteration the m+2 time, otherwise gets D _M+1Be B _{I, 0}

Step B: calculate

Wherein || P _{I, 0}-B _{I, 0}|| expression P _{I, 0}With B _{I, 0}Distance;

Step C: the eyeball P of iterative computation horizontal survey point _{I, 0}Match point on curved surface S: the span of iteration precision epsilon1 is 0＜epsilon1＜0.05; K=0,1,2 ..., wherein the step of the k+1 time iteration is:

Steps d: adopt the Levenberg-Marquardt algorithm computation to make function

Parameter vector w=(w when getting minimum value ₁w ₂w ₃) ^T, function f wherein _I1(w), f _I2(w), f _I3(w) be respectively:

$\left\{\begin{array}{c}{f}_{i1}\left(w\right)=R_{k+1}(1,:)P_{i,k}-B_{\mathrm{ix},k}\\ f_{i2}\left(w\right)=R_{k+1}(2,:)P_{i,k}-B_{\mathrm{iy},k}\\ f_{i3}\left(w\right)=R_{k+1}(3,:)P_{i,k}-B_{\mathrm{iz},k}\end{array}\right.$

R _K+1(1 :), R _K+1(2 :), R _K+1(3 :) corresponding respectively expression rotation matrix R _K+1(w) the row vector that 1,2,3 row are formed, rotation matrix R _K+1(w) be:

$R_{k+1}\left(w\right)=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}w}_1\cos w_2& {\mathrm{<figure-callout\; id="1"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}w}_1\sin w_2\sin w_3-\mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\cos w_3& \mathrm{<figure-callout\; id="1"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}{w}_{}{}_1\sin w_2\mathrm{<figure-callout\; id="3"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}{w}_{}{}_3+\mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\mathrm{<figure-callout\; id="3"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_3\\ \mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\cos w_2& \mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\sin w_2\mathrm{<figure-callout\; id="3"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_3+\cos w_1{\cos w}_3& \mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\sin w_2\cos w_3-\cos w_1\sin w_3\\ -\sin w_2& \cos w_2\mathrm{<figure-callout\; id="3"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_3& \cos w_2{\mathrm{<figure-callout\; id="3"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}w}_3\end{array}\right]$

Step e: the rotation matrix R that obtains according to steps d _K+1(w) calculate P _{I, k+1}=R _K+1(w) P _{I, k}

Step f: it is last from P that the method iterative computation in the employing steps A obtains wing theory curved face S _{I, k+1}Nearest some B _{I, k+1}

Step g: calculate

If 1-d _K+1/ d _k>=epsilon1, then repeating step d～step g is carried out iteration the k+2 time, otherwise gets a B _{I, k+1}Eyeball P for horizontal survey point _{I, 0}Match point C on wing theory curved face S _i

Step 4: adopt the Levenberg-Marquardt algorithm computation to make function Parameter vector v=when getting minimum value (α β γ) ^T, v=(α β γ) wherein ^TBe the wing attitude parameter of being asked, α, β, γ represent wing by the x axle rotation alpha radian of initial attitude elder generation around wing design coordinate system, again around y axle rotation β radian, reach current attitude around z axle rotation γ radian at last; Function f _I1(v), f _I2(v), f _I3(v) be respectively:

$\left\{\begin{array}{c}{f}_{i1}\left(v\right)=R(1,:)C_i-P_{\mathrm{ix},0}\\ f_{i2}\left(v\right)=R(2,:)C_i-P_{\mathrm{iy},0}\\ f_{i3}\left(v\right)=R(3,:)C_i-P_{\mathrm{iz},0}\end{array}\right.$

R (1 :), R (2 :), R (3 :) corresponding respectively expression rotation matrix R (the row vector that 1,2,3 row are v) formed, rotation matrix R (v) be:

$R\left(v\right)=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}\\ \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}\\ -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}\end{array}\right].$

Beneficial effect

The present invention has fully combined wing fine-processing technique characteristics; Wing horizontal survey data with easy acquisition are the basis; Through adopting iterative closest point algorithms to realize the calculating of wing finishing attitude, the also insurmountable wing finishing of advanced measuring equipment pose accurate Calculation problems such as existing employing laser tracker have been solved.

Description of drawings

Fig. 1: the example model synoptic diagram in the embodiment of the invention.

Embodiment

Below in conjunction with specific embodiment the present invention is described.

Wing finishing computation method for attitude in the present embodiment may further comprise the steps:

Step 1: extractor airfoil theory curved face S from the digital model of wing, said wing theory curved face are the appearance curved surface of wing lower aerofoil when being in theoretical attitude; Represent the wing theory curved face with the face of cylinder in the present embodiment, like the curved surface S in the accompanying drawing 1;

Step 2: treat accurately machined wing and carry out horizontal survey, obtain the eyeball P of wing horizontal survey point _{I, 0}, i=1,2 ..., N, i represent the horizontal survey point sequence number, N representes horizontal survey point sum, P _{I, 0}=(P _{Ix, 0}P _{Iy, 0}P _{Iz, 0}) ^TRepresent i horizontal survey point P _{I, 0}Coordinate under wing design coordinate system.

The wing that has actual attitude for simulation in the present embodiment sets an attained pose v for the theoretical curved face S that obtains in the last step _Sta=(0.01745 0.01745 0.01745) ^T, the wing with actual attitude is carried out horizontal survey, obtain the eyeball of wing horizontal survey point.Measured 8 points in the example model altogether, with sequence number 1,2 ..., 8 expressions, referring to Fig. 1, the measurement coordinate figure of 8 horizontal survey points is seen table 1.

Step 3: by the eyeball P of wing theory curved face S and N horizontal survey point _{I, 0}, adopt iterative closest point algorithms to calculate the eyeball P of wing horizontal survey point _{I, 0}Match point on the wing theory curved face; Said iterative closest point algorithms is:

Steps A: S is last from P for iterative computation wing theory curved face _{I, 0}Nearest some B _{I, 0}: take up an official post at curved surface S and to get primary iteration point D ₀=S (u ₀, v ₀), u wherein ₀, v ₀Be respectively D ₀U on curved surface S, the v parameter; The span of iteration precision epsilon is 0＜epsilon＜0.01, gets epsilon=0.005 in the present embodiment; M=0,1,2 ..., the step of the m+1 time iteration is:

Step a: calculate curved surface S at a D _mThe u at place is to cutting arrow

With v to cutting arrow

${D_{u_m}}^{\&prime;}=\frac{\&PartialD;S}{\&PartialD;u}{|}_{u=u_m,v{=v}_m},$ ${D_{v_m}}^{\&prime;}=\frac{\&PartialD;S}{\&PartialD;v}{|}_{u=u_m,v{=v}_m},$

Calculate curved surface S and go up some D _mThe per unit system at place is vowed:

$n_m=\frac{{D^{\&prime;}}_{u_m}\&times;{D^{\&prime;}}_{v_m}}{|{D^{\&prime;}}_{u_m}\&times;{D^{\&prime;}}_{v_m}|}$

Step b: compute vector

Wherein

The expression starting point is D _m, terminal point is P _{I, 0}Vector; Calculate u to v to increment Delta u _m, Δ v _m:

${\mathrm{\&Delta;u}}_m=\frac{{\mathrm{\&tau;}}_m\&times;{D^{\&prime;}}_{v_m}}{{D_{u_m}}^{\&prime;}\&times;{D^{\&prime;}}_{v_m}},$ ${\mathrm{\&Delta;v}}_m=\frac{{\mathrm{\&tau;}}_m\&times;{D^{\&prime;}}_{u_m}}{{D_{v_m}}^{\&prime;}\&times;{D^{\&prime;}}_{u_m}}$

Step c: calculation level D _M+1=S (u _m+ Δ u _m, v _m+ Δ v _m); If D _mWith D _M+1Between distance | D _M+1-D _m|＞epsilon, then repeating step a～c carries out iteration the m+2 time, otherwise gets D _M+1Be B _{I, 0}

Step B: calculate

Wherein || P _{I, 0}-B _{I, 0}|| expression P _{I, 0}With B _{I, 0}Distance;

Step C: the eyeball P of iterative computation horizontal survey point _{I, 0}Match point on curved surface S: the span of iteration precision epsilon1 is 0＜epsilon1＜0.05; K=0,1,2 ..., wherein the step of the k+1 time iteration is:

Steps d: adopt the Levenberg-Marquardt algorithm computation to make function

Parameter vector w=(w when getting minimum value ₁w ₂w ₃) ^T, function f wherein _I1(w), f _I2(w), f _I3(w) be respectively:

$\left\{\begin{array}{c}{f}_{i1}\left(w\right)=R_{k+1}(1,:)P_{i,k}-B_{\mathrm{ix},k}\\ f_{i2}\left(w\right)=R_{k+1}(2,:)P_{i,k}-B_{\mathrm{iy},k}\\ f_{i3}\left(w\right)=R_{k+1}(3,:)P_{i,k}-B_{\mathrm{iz},k}\end{array}\right.$

R _K+1(1 :), R _K+1(2 :), R _K+1(3 :) corresponding respectively expression rotation matrix R _K+1(w) the row vector that 1,2,3 row are formed, rotation matrix R _K+1(w) be:

$R_{k+1}\left(w\right)=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="1"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}w}_1\cos w_2& {\mathrm{<figure-callout\; id="1"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}w}_1\sin w_2\sin w_3-\mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\cos w_3& \mathrm{<figure-callout\; id="1"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}{w}_{}{}_1\sin w_2\mathrm{<figure-callout\; id="3"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}{w}_{}{}_3+\mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\mathrm{<figure-callout\; id="3"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_3\\ \mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\cos w_2& \mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\sin w_2\mathrm{<figure-callout\; id="3"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_3+\cos w_1{\cos w}_3& \mathrm{<figure-callout\; id="1"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_1\sin w_2\cos w_3-\cos w_1\sin w_3\\ -\sin w_2& \cos w_2\mathrm{<figure-callout\; id="3"\; label="sin\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">sin</figure-callout>}{w}_{}{}_3& \cos w_2{\mathrm{<figure-callout\; id="3"\; label="cos\; w"\; filenames="HDA0000149645450000011.png"\; state="\{\{state\}\}">cos</figure-callout>}w}_3\end{array}\right]$

Step e: the rotation matrix R that obtains according to steps d _K+1(w) calculate P _{I, k+1}=R _K+1(w) P _{I, k}

Step f: it is last from P that the method iterative computation in the employing steps A obtains wing theory curved face S _{I, k+1}Nearest some B _{I, k+1}:

Step g: calculate

If 1-d _K+1/ d _k>=epsilon1, then repeating step d～step g is carried out iteration the k+2 time, otherwise gets a B _{I, k+1}Eyeball P for horizontal survey point _{I, 0}Match point C on wing theory curved face S _iThe match point of trying to achieve in the present embodiment is seen table 1.

Step 4: the eyeball of the wing horizontal survey point that obtains according to step 2 and the corresponding match point that step 3 obtains, calculate the attitude parameter of wing: adopt the Levenberg-Marquardt algorithm computation to make function

Parameter vector v=when getting minimum value (α β γ) ^T, v=(α β γ) wherein ^TBe the wing attitude parameter of being asked, α, β, γ represent wing by the x axle rotation alpha radian of initial attitude elder generation around wing design coordinate system, again around y axle rotation β radian, reach current attitude around z axle rotation γ radian at last; Function f _I1(v), f _I2(v), f _I3(v) be respectively:

$\left\{\begin{array}{c}{f}_{i1}\left(v\right)=R(1,:)C_i-P_{\mathrm{ix},0}\\ f_{i2}\left(v\right)=R(2,:)C_i-P_{\mathrm{iy},0}\\ f_{i3}\left(v\right)=R(3,:)C_i-P_{\mathrm{iz},0}\end{array}\right.$

R (1 :), R (2 :), R (3 :) corresponding respectively expression rotation matrix R (the row vector that 1,2,3 row are v) formed, rotation matrix R (v) be:

$R\left(v\right)=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}\\ \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}\\ -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}\end{array}\right].$

The wing attitude parameter that calculates is seen table 2.Can find out that from table 2 the wing attitude parameter v that calculates is with the attitude parameter v of embodiment setting _StaBetween the non-difference of error little, almost consistent.

Table 1 horizontal survey point eyeball and match point thereof

Table 2 Attitude Calculation result

Levenberg-Marquardt algorithm in steps d and the step 4 see reference book " optimization method and Matlab program design thereof " (Ma Changfeng .2010, Beijing: the .102-109. of Science Press).

Claims (1)

1. wing finishing computation method for attitude is characterized in that: may further comprise the steps:

Step 1: extractor airfoil theory curved face S from the digital model of wing, said wing theory curved face are the appearance curved surface of wing lower aerofoil when being in theoretical attitude;

Step 2: treat accurately machined wing and carry out horizontal survey, obtain the eyeball P of wing horizontal survey point _{I, 0}, i=1,2 ..., N, i represent the horizontal survey point sequence number, N representes horizontal survey point sum, P _{I, 0}=(P _{Ix, 0}P _{Iy, 0}P _{Iz, 0}) ^TRepresent i horizontal survey point P _{I, 0}Coordinate under wing design coordinate system;

Step 3: by the eyeball P of wing theory curved face S and N horizontal survey point _{I, 0}, adopt iterative closest point algorithms to calculate the eyeball P of wing horizontal survey point _{I, 0}Match point on the wing theory curved face; Said iterative closest point algorithms is:

Steps A: S is last from P for iterative computation wing theory curved face _{I, 0}Nearest some B _{I, 0}: take up an official post at curved surface S and to get primary iteration point D ₀=S (u ₀, v ₀), u wherein ₀, v ₀Be respectively D ₀U on curved surface S, the v parameter; The span of iteration precision epsilon is 0＜epsilon＜0.01; M=0,1,2 ..., the step of the m+1 time iteration is:

Step a: calculate curved surface S at a D _mThe u at place is to cutting arrow With v to cutting arrow

${D_{u_m}}^{\&prime;}=\frac{\&PartialD;S}{\&PartialD;u}{|}_{u=u_m,v{=v}_m},$ ${D_{v_m}}^{\&prime;}=\frac{\&PartialD;S}{\&PartialD;v}{|}_{u=u_m,v{=v}_m},$

Calculate curved surface S and go up some D _mThe per unit system at place is vowed:

$n_m=\frac{{D^{\&prime;}}_{u_m}\&times;{D^{\&prime;}}_{v_m}}{|{D^{\&prime;}}_{u_m}\&times;{D^{\&prime;}}_{v_m}|}$

Step b: compute vector

Wherein

The expression starting point is D _m, terminal point is P _{I, 0}Vector; Calculate u to v to increment Delta u _m, Δ v _m:

${\mathrm{\&Delta;u}}_m=\frac{{\mathrm{\&tau;}}_m\&times;{D^{\&prime;}}_{v_m}}{{D_{u_m}}^{\&prime;}\&times;{D^{\&prime;}}_{v_m}},$ ${\mathrm{\&Delta;v}}_m=\frac{{\mathrm{\&tau;}}_m\&times;{D^{\&prime;}}_{u_m}}{{D_{v_m}}^{\&prime;}\&times;{D^{\&prime;}}_{u_m}}$

Step c: calculation level D _M+1=S (u _m+ Δ u _m, v _m+ Δ v _m); If D _mWith D _M+1Between distance | D _M+1-D _m|＞epsilon, then repeating step a～c carries out iteration the m+2 time, otherwise gets D _M+1Be B _{I, 0}

Step B: calculate Wherein || P _{I, 0}-B _{I, 0}|| expression P _{I, 0}With B _{I, 0}Distance;

Step C: the eyeball P of iterative computation horizontal survey point _{I, 0}Match point on curved surface S: the span of iteration precision epsilon1 is 0＜epsilon1＜0.05; K=0,1,2 ..., wherein the step of the k+1 time iteration is:

Steps d: adopt the Levenberg-Marquardt algorithm computation to make function

Parameter vector w=(w when getting minimum value ₁w ₂w ₃) ^T, function f wherein ₁₁(w), f _I2(w), f _I3(w) be respectively:

$\left\{\begin{array}{c}{f}_{i1}\left(w\right)=R_{k+1}(1,:)P_{i,k}-B_{\mathrm{ix},k}\\ f_{i2}\left(w\right)=R_{k+1}(2,:)P_{i,k}-B_{\mathrm{iy},k}\\ f_{i3}\left(w\right)=R_{k+1}(3,:)P_{i,k}-B_{\mathrm{iz},k}\end{array}\right.$

R _K+1(1 :), R _K+1(2 :), R _K+1(3 :) corresponding respectively expression rotation matrix R _K+1(w) the row vector that 1,2,3 row are formed, rotation matrix R _K+1(w) be:

$R_{k+1}\left(w\right)=\left[\begin{array}{ccc}{\cos w}_1\cos w_2& {\cos w}_1\sin w_2\sin w_3-\sin w_1\cos w_3& \cos w_1\sin w_2\cos w_3+\sin w_1\sin w_3\\ \sin w_1\cos w_2& \sin w_1\sin w_2\sin w_3+\cos w_1{\cos w}_3& \sin w_1\sin w_2\cos w_3-\cos w_1\sin w_3\\ -\sin w_2& \cos w_2\sin w_3& \cos w_2{\cos w}_3\end{array}\right]$

Step e: the rotation matrix R that obtains according to steps d _K+1(w) calculate P _{I, k+1}=R _K+1(w) P _{I, k}

Step f: it is last from P that the method iterative computation in the employing steps A obtains wing theory curved face S _{I, k+1}Nearest some B _{I, k+1}

Step g: calculate

If 1-d _K+1/ d _k>=epsilon1, then repeating step d～step g is carried out iteration the k+2 time, otherwise gets a B _{I, k+1}Eyeball P for horizontal survey point _{I, 0}Match point C on wing theory curved face S _i

Step 4: adopt the Levenberg-Marquardt algorithm computation to make function

Parameter vector v=when getting minimum value (α β γ) ^T, v=(α β γ) wherein ^TBe the wing attitude parameter of being asked, α, β, γ represent wing by the x axle rotation alpha radian of initial attitude elder generation around wing design coordinate system, again around y axle rotation β radian, reach current attitude around z axle rotation γ radian at last; Function f _I1(v), f _I2(v), f _I3(v) be respectively:

$\left\{\begin{array}{c}{f}_{i1}\left(v\right)=R(1,:)C_i-P_{\mathrm{ix},0}\\ f_{i2}\left(v\right)=R(2,:)C_i-P_{\mathrm{iy},0}\\ f_{i3}\left(v\right)=R(3,:)C_i-P_{\mathrm{iz},0}\end{array}\right.$

R (1 :), R (2 :), R (3 :) corresponding respectively expression rotation matrix R (the row vector that 1,2,3 row are v) formed, rotation matrix R (v) be:

$R\left(v\right)=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}\\ \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}\\ -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}\end{array}\right].$

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