CN104143032A - Method for automatically solving assembly pose during plane large-size component digital assembling - Google Patents

Abstract

The invention provides a method for automatically solving assembly pose during plane large-size component digital assembling and belongs to the technical field of research of modern manufacturing technology of advanced manufacturing. The method is effective in correctly resolving the large-size component assembly pose and provides an accurate adjusting matrix for the following automatic adjustment. The method adopting key characteristics to position a component assembly position includes selecting and analyzing the key characteristics of the large-size component; matching the key characteristic to the assembly position; designing a normalized evaluation function to coordinating sizes; adopting an optimization algorithm to coordinate key sizes; achieving accurate assembly pose of the large-size component and outputting the adjustment matrix. By the use of the method, the problem that during flexible assembly of plane components, overmuch error accumulation during assembly causes that a data model is difficult in calculating space positions of the large-size components so as to fail to accurately assemble the plane components is solved, and an effective way to apply automatic equipment in the digital assembly of the plane large-size components is provided.

Description

The method of automatic calculation assembling pose in Large Aircraft Components digitizing assembling process

Technical field

The present invention relates to the method for automatic calculation assembling pose in Large Aircraft Components digitizing assembling process, belong to the research contents of advanced manufacturing technology field Modern Manufacturing Technology.

Background technology

Large Aircraft Components digitizing assembling is the important component part in the digitizing flexible assembly technology of aircraft, has applied the gordian techniquies such as measuring technique, cooperative motion planning and control technology in airplane digital flexible assembly technology, assembly information integrated management technology, Kinematic Simulation Technology.It adopts digitizing means to coordinate the complex relationship in large parts assembling, has realized the Large Aircraft Components Digital Assembly that meets strict pneumatic requirement.Wherein, how to make large parts product optional position and attitude from space be adjusted to exactly correct assembling attitude, it is the key that realizes Large Aircraft Components digitizing assembling, therefore solving and obtaining it and adjust matrix large parts assembling attitude, drive automation equipment to complete automatic assembling, be that large part numbers is disguised the research emphasis of joining always.

Because manufacture exists error, people are devoted to research always and how utilize product data model and measure feedback data, obtain exactly the method for assembling pose.Progressively develop now: 1) only can meet 3 pose computing methods that accurately manufacture a product, 2) the decomposition of singular matrix method (SVD) of energy absorption portion error, 3) reach the least square method of error sum of squares minimum, 4) solve the inconsistent weighted least-squares method of each point permissible error.But these algorithms all do not have to solve pose Solve problems completely.In the assembling with high-precision requirement, in the assembling of especially multiple high precision assembly features combination, be difficult to solve correct rigging position.

Summary of the invention

Solving scheme for traditional pose is difficult to obtain the large parts problem of rigging position accurately herein, adopts the pose solution technique based on key characteristic accurately to obtain large parts assembling attitude.

In order to solve the problem of large parts assembling pose determination in Large Aircraft Components digitizing assembling process, provide adjustment matrix to realize robotization assembling, a kind of large parts assembling attitude method for solving based on key characteristic has been proposed herein.The method is by key characteristic Degree of Freedom Analysis, and independence and freedom degree mates, and cooperative dimensioning is unified to be evaluated, the four partial contents compositions such as cooperative dimensioning optimization.Under the method is supported, can realize in large part numbers assembling process, the accurate location of large space of components pose, and matrix is adjusted in output.

The method, first by the analysis to aircraft technique and assembly technology parting plane part, obtains the key characteristic of large parts assembling, and analyzes the degree of freedom that assembly properties retrain.Construct normalized assembly quality evaluation function by Taguchi quality loss function, and by this function application in the design of hereditary function fitness function, adopt the required adjustment angle of the large parts assembling of SVD method primary Calculation attitude and along change in coordinate axis direction adjusted value, set it as according to initialization genetic algorithm initial population, adopt the Real-valued heredity function of roulette method design to solve the degree of freedom with cooperative dimensioning, finally export assembling attitude and adjust matrix.

The present invention, for automatic calculation assembling pose in Large Aircraft Components digitizing assembling process provides a kind of accurate pose determination method, provides a kind of effective technological means for realizing Large Aircraft Components digitizing assembling.

Brief description of the drawings

Fig. 1 straight line is adjusted schematic diagram

The loss of Fig. 2 oeverall quality

Embodiment

One, Large Aircraft Components assembling key characteristic is chosen and Degree of Freedom Analysis

Large parts assembling key characteristic refers to the geometry, the dimensional characteristic that in assembling process, assembly quality are had the greatest impact, has comprised airplane design benchmark, the morpheme characteristic of large parts, critical size characteristic etc.Airplane design benchmark is the main benchmark in airplane design, in assembling, determines part residing position in product by this benchmark.Design basis has often comprised the plane that some are important, as aircraft plane of symmetry etc.The morpheme characteristic of large parts has comprised important axis and the plane of large components interior, and as the wingchordpiston of horizontal tail, the inverted diherdral that large parts are determined wing by it, is the key characteristic that need to pay close attention to when horizontal tail is installed.Critical size characteristic refers in large parts assembling to have the dimensional requirement of production breakdown interface and the characteristic of morpheme requirement of higher matching requirements.

The basic goal that key characteristic is chosen is by the measurement of key characteristic is located completely to the locus of large parts product.Because single key characteristic can not limit degree of freedom after large parts have assembled completely (as axis feature, movement in the axial direction and the degree of freedom of rotating around axis still need other key characteristic points to retrain), large parts assembling attitude solves to need to obtain and meets the key characteristic set that large parts are located completely.So the analysis purpose on large parts key characteristic degree of freedom is: one, analyze the affect situation of each key characteristic on large parts degree of freedom; Two, whether analyze the selection of passing through key characteristic to large parts Complete Bind.Its concrete implementation step is as follows:

Step 1: each key characteristic limits Degree of Freedom Analysis and mark

Large parts key characteristic can be divided into point, line, surface characteristic.The sequencing of selecting key characteristic, each key characteristic is inconsistent on the impact of large parts degree of freedom (DOF), and the rigid body coordinate system building also exists difference.Three-dimensional key characteristic (point, line, face) is as follows to large parts three-dimensional constraining relation:

Wherein TDOC represents translation freedoms, and RDOC represents rotary freedom, known after key characteristic calculates by analyzing, and can obtain large parts and determine degree of freedom and still needed to determine degree of freedom.

Step 2: key characteristic limits large parts degree of freedom judgement completely

By obtaining the impact of each key characteristic on large space of components degree of freedom to the analysis of key characteristic degree of freedom degree.By the key characteristic after selecting is asked to the method for friendship, allow the degree of freedom of final restriction be 6 or when being expressed as spatial degrees of freedom and limiting completely, the attitude of large parts in space and position just can obtain uniquely determining:

CS=FS-(FTD ₁∩FTD ₂∩...∩FTD _n)∪(FRA ₁∩FRA ₂∩...∩FTA _n) (1)

Wherein, CS is constraint space, free space when FS is nothing constraint completely.Known in the time of CS=FS, large parts are by key characteristic Complete Bind.In the time that the change in coordinate axis direction of key characteristic direction vector or normal vector and global coordinate system has arbitrarily angular relationship, the degree of freedom constraint of key characteristic can not decompose in set coordinate axis completely, presents the relation of mutual constraint with the degree of freedom of coordinate axis mark.The now analysis of degree of freedom can not be carried out reasoning by said method.Can be by judging that whether equation has the method acquisition constraint judgement of solution, obtains the degree of freedom constraint of single key characteristic by the method for rotatable coordinate axis.Now, in the time forming direction vector, do not determine that degree of freedom should be according to x, y, z and α, beta, gamma in-line arrangement row.

Straight line is:

Plane is:

Then CS set is sought common ground, judge whether full rank of transposed matrix and rotation matrix, full rank represents that displacement degree of freedom or translation freedoms are completely definite.

As flatness of the response and flatness of the response combination

Wherein by and

$\left\{\begin{array}{c}{A}_{1}x+B_{1}y-Z_1=0\\ A_{2}x+B_{2}y-Z_2=0\end{array}---\left(5\right)\right.$

If $\left[\begin{array}{ccc}{A}_1& B_1& -1\\ A_2& B_2& -1\end{array}\right]$ Full rank, but line number is less than columns, and linear algebra still has one degree of freedom not determine without solution on translation direction.

In rotary freedom direction, by can obtain matrix:

$\left[\begin{array}{ccc}{A}_1& -1& 0\\ A_2& -1& 0\\ 0& B_1& -1\\ 0& B_2& -1\end{array}\right]---\left(6\right)$

In one degree of freedom, there are multiple constraints therein in equation redundant description, and in revolution space Complete Bind.According to above principle, can judge that whether the combination of many group characteristics is by completely definite large parts six-freedom degree, and according to property combination order, get rid of redundant degree of freedom constraint.

Two, large parts independently assemble attitude matching

Pass through the Degree of Freedom Analysis to key characteristic, can obtain the impact of each key characteristic on large parts degree of freedom.Can utilize accordingly key characteristic by progressively extremely correct assembling pose of computing of large parts.Between key characteristic, exist primary and secondary relation, for a certain key characteristic, if the degree of freedom that key characteristic can limit all needs strict guarantee, this key characteristic is main key characteristic so, should first solve it carrying out when key characteristic pose solves.Less important key characteristic, refers to that those degree of freedom that only have the restriction of part key characteristic are applied to the key characteristic of the pose determination of large parts.Because main key characteristic limits completely to the degree of freedom in some directions of large parts, do not allow less important key characteristic to modify to it, less important key characteristic must be abandoned the control to this part degree of freedom, and by meeting less important key characteristic assembling standard with the incoherent degree of freedom adjustment of main key characteristic control freedom degree.All there is equal decisive action or the less degree of freedom of decisive gap for multiple key characteristics, can adopt the method for cooperative dimensioning optimization that this degree of freedom is optimized and is solved.

Step 1: main key characteristic attitude matching

It is that large parts assembling attitude solves the problem that first needs solution that main key characteristic solves, and solving before this assembling attitude, there is no degree of freedom constraint, and its solution procedure is comparatively flexible.In order to coordinate main key characteristic to solve, can increase auxiliary degree of freedom constraint, meet completely after assembly features at key characteristic, this degree of freedom is discharged.Because key characteristic mostly is line, face characteristic, line face characteristic all can utilize its proper vector to describe.Adopt space vector matching method that main key characteristic degree of freedom matching problem is described herein.Due to the vector of any mistake initial point in space, all can arrive in the coordinate axis of specifying, as shown in Figure 1 by twice conversion.Known α angle and γ angle can solve according to following formula.

$\mathrm{\γ}=A\sin \left(\frac{\mathrm{Lx}}{\sqrt{{\mathrm{Lx}}^2+{\mathrm{Ly}}^2}}\right)---\left(7\right)$

$\left[\begin{array}{c}{\mathrm{Lx}}^{\′}\\ {\mathrm{Ly}}^{\′}\\ {\mathrm{Lz}}^{\′}\\ 1\end{array}\right]={\left[\begin{array}{cccc}\cos \mathrm{\γ}& -\sin \mathrm{\γ}& 0& 0\\ \sin \mathrm{\γ}& \cos \mathrm{\γ}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]}_{\mathrm{RZ}}\left[\begin{array}{c}\mathrm{Lx}\\ \mathrm{Ly}\\ \mathrm{Lz}\\ 1\end{array}\right]---\left(8\right)$

$\mathrm{\α}=-A\tan \frac{{\mathrm{Lz}}^{\′}}{{\mathrm{Ly}}^{\′}}---\left(9\right)$

L' just can make straight line overlap with y axle around x axle rotation alpha angle.L' is RX around y axle coincidence matrix:

$\mathrm{RX}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\α}& -\sin \mathrm{\α}& 0\\ 0& \sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 0& 1\end{array}\right]---\left(10\right)$

In large parts assembling based on key characteristic, adjust large component axes and known dead in line, can be using the unique point on target axis as true origin, the reference point in component axes overlaps with unique point on known axis after by translation T greatly.Then known according to above-mentioned theory:

L _end=RX _t ^-1RZ _t ^-1RZ _lcRX _lcL _lc (11)

Wherein: L _lcfor the coordinate of large component axes in space, RZ _lc, RX _lcfor large component axes is adjusted to the rotation matrix RX of Y-axis _t, RZ _tfor target axis is adjusted to the rotation matrix of Y-axis.

Step 2: inferior key characteristic attitude matching

In order to ensure the correctly involutory of main key characteristic, main key characteristic defines the multiple degree of freedom of large parts, and it is changed while not allowing less important key characteristic to adjust.So less important key characteristic, when to large parts attitude computing, must strictly limit these degree of freedom, and allow other degree of freedom to adjust.From space matrix theory, large parts its true origin invariant position in rotary course, while swaying, on axle, each point does not also change.Less important key characteristic attitude solves, and can utilize above characteristic to solve, but now rigid body must be rotated around coordinate axis.As described above, axis can utilize its direction vector, and plane can utilize its normal vector to express characteristic.After supposing by rotation translation, key characteristic vector to be overlapped with coordinate axis X, carry out around the rotation of X-axis and move along X-axis, its attitude is asked and is expressed as:

${P_{\mathrm{end}}}^{\′}=\left[\begin{array}{cccc}1& 0& 0& x\\ 0& \cos \mathrm{\α}& -\sin & 0\\ 0& \sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 0& 1\end{array}\right]{P_{\mathrm{start}}}^{\′}---\left(12\right)$

Wherein P _start' be through main key characteristic calculate and coordinate axis transform after the residing locus of characteristic point on large parts, P _end' target location after coordinate axis transform.The adjustment matrix R obtaining in integrating step one _nr ₂r ₁just can obtain the final assembling attitude P of large parts _end.

$P_{\mathrm{end}}=R_n\·\·\·R_2{R}_1{P}_{\mathrm{start}}---\left(13\right)$

Three, cooperative dimensioning is unified evaluates

Discussed the computing method of single key characteristic point to large parts degree of freedom above, these methods are to be based upon large parts key characteristic large parts degree of freedom is had on the basis of independent effect.When the influence of certain single-degree-of-freedom of many groups key characteristic to large parts is close, upwards there is complicated size rapport the party, can not utilize single key characteristic to position this degree of freedom.In assembly technology, assembly quality is coordinated to control and is formed by many sizes often.Because the error size that each cooperative dimensioning allows is inconsistent, cause the size of product quality loss also not identical so be offset same size, and error numerical values recited, unit that key characteristic allows are all inconsistent, need to adopt normalized evaluation function to process it, formation has evaluation amount of equal value and adds up, and the attitude of overall assessment value optimum is as its final carriage.As allowed in key characteristic around X-axis angular error be ± 0.001rad, and the permissible error of one of them key point is ± 0.2mm.By adjust in the time that the angle of X-axis meets above two evaluation indexes simultaneously, due to unit and the upper and lower deviation constraint of the margin of error inconsistent, can not simply add error and.Need to adopt the method for normalizing that it is carried out comprehensive and is evaluated.Getting the Definite purpose function of Taguchi quality loss function herein plans.In conjunction with field mouth mass function, establish evaluation function and be:

$f_i\left(q_i\right)=\frac{1}{K{(q_i-t)}^2+B}---\left(14\right)$

Wherein:

△ is that upper and lower absolute value of the bias a is evaluation of estimate corresponding to upper lower deviation

B is 1 $K=\frac{1-\mathrm{aB}}{{\mathrm{\Δ}}^{2}a}$

According to above requiring, the evaluation amount after normalization is added up and forms overall assessment index, due to the unified evaluation in order to adapt to the key characteristic scoring item formation with varying number, and form unified optimization assembly evaluation amount, need to be by accumulation amount divided by key characteristic scoring item number, getting its mean value is overall assessment index, has assembly quality overall loss value:

Wherein M (X) adjusts function for attitude, and it is made up of large part pose adjustment matrix, and has different expression-forms according to undetermined degree of freedom.Suppose only to need the degree of freedom of opposing connection X-axis to adjust, the visible formula of the expression formula of this function (10).P _ifor the residing locus of large parts key point; E _ifor forming evaluation of estimate characteristic point with large parts key point, this characteristic point can be the point of fixity in space, can be also other key points on large parts. for the theoretical value of this size.Wherein f _i(X) function has multiple different form, and it is identical with formula (14) form, but by cooperative dimensioning requirement, will be converted into value q to be evaluated, as get Z-direction coordinate as evaluation,

Four, cooperative dimensioning optimization

Parts cooperative dimensioning Optimization Solution technology, belongs to large parts attitude regulating technology, and its initial population can be determined scope according to other attitude method for solving.As the large part pose obtaining by SVD method, the assembling weak effect of key characteristic point, definite degree of freedom direction also can change because of solving, but the result solving by SVD method can be dwindled cooperative dimensioning range of search.While adopting Population in Genetic Algorithms initialization, first solve large part pose by SVD method, and get required attitude and position result as central point, and estimate that according to large parts setting range the upper lower deviation of increase scope forms range of search, generate population at random in range of search.The overall evaluation function of then unifying to obtain in evaluation by cooperative dimensioning, as fitness function, is constructed hereditary function, carries out cooperative dimensioning computing final output adjustment matrix.

Step 1: adopt SVD method tentatively to solve angle of assembling, along coordinate translation amount

Choose four point coordinate in large parts digital-to-analogue and form matrix:

$P=\left[\begin{array}{cccc}{P}_1& P_2& P_3& P_4\end{array}\right]---\left(16\right)$

$P_i={[x_i,y_i,z_i]}^T---\left(17\right)$

The actual coordinate of these four characteristic points in space is:

$P^{\′}=\left[\begin{array}{cccc}{P_1}^{\′}& {P_2}^{\′}& {P_3}^{\′}& {P_4}^{\′}\end{array}\right]---\left(18\right)$

${P_i}^{\′}={[{x_i}^{\′},{y_i}^{\′}{z_i}^{\′}]}^T---\left(19\right)$

The centre of gravity place of asking two point sets to form, the translation vector of centre of gravity place i.e. translational movement between two point sets:

$T=\frac{\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{P_i}^{\′}-\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{P}_i}{4}---\left(20\right)$

The centre of gravity place of two point sets is made as to initial point, now between two point sets, only has rotation relationship, their rotation R matrix is:

${\mathrm{U\ΣV}}^T=\mathrm{svd}\left(P_{\mathrm{MoveToOrigin}}{P_{\mathrm{MoveToOrigin}}}^{\′T}\right)---\left(21\right)$

R=UV ^T (22)

Wherein P _moveToOriginand P _moveToOrigin' ^tbe the coordinate amount after point set separately arranges, be embodied as:

$P_{\mathrm{MoveToOrigin}}=\left[\begin{array}{cccc}1& & & \\ & 1& & \frac{-\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{P}_i}{4}\\ & & 1& \\ & & & 1\end{array}\right]P---\left(23\right)$

$P_{\mathrm{MoveToOrigin}}=\left[\begin{array}{cccc}1& & & \\ & 1& & \frac{-\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{P_i}^{\′}}{4}\\ & & 1& \\ & & & 1\end{array}\right]P^{\′}---\left(24\right)$

Get the correlative of Metzler matrix and T vector as the matrix angle in genetic algorithm and the design of coordinate direction translational movement.

Step 2: hereditary function initial population initialization

Adopt the angle of previous step acquisition and along coordinate axis translational movement, carry out matrix design according to the required coordination direction of cooperative dimensioning, as need are coordinated around X-axis rotational freedom and along X-axis translation freedoms.Design matrix is:

$\mathrm{MX}=\left[\begin{array}{cccc}1& 0& 0& X\\ 0& \cos \mathrm{\α}& -\sin \mathrm{\α}& 0\\ 0& \sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 0& 1\end{array}\right]---\left(25\right)$

The wherein numerical value of α and the numerical value of X, chooses near the numerical value obtaining in previous step, has:

X=Radom(x-dx,x+dx) (27)

Wherein:

for the angle obtaining according to SVD method; for the angle fluctuation scope of estimating voluntarily;

X be according to SVD method obtain along x axle translational movement; Dx is the translational movement fluctuation range of estimating voluntarily;

Population gene inside comprises two chromosome: gene (x, α)

Step 3: fitness function is set

Using the overall assessment formula obtaining in unified cooperative dimensioning evaluation as fitness function.And fitness is reached to 0.9 as algorithm termination condition.

Step 4:

Use genetic algorithm to obtain the large parts key characteristic position after optimizing.The set of the position of supposing key characteristic point now in space is P _end, be P in the set of initial measurement time point _start, adopt SVD method mentioned above to carry out computing.Obtain from P _startto P _endangular transformation and translation vector, and obtain rotation matrix R, R is also the adjustment matrix that instructs automatic mounting to join simultaneously.Use adjustment matrix can plan adjustment track, drive Digital assembly system, accurately large parts are assembled to installation site.

Claims (2)

1. for a method for automatic calculation assembling pose in Large Aircraft Components digitizing assembling process, described method comprises key characteristic Degree of Freedom Analysis, independence and freedom degree coupling, and cooperative dimensioning is unified to be evaluated, and four partial contents such as cooperative dimensioning optimization, is characterized in that:

1) first the method is analyzed large parts key characteristic degree of freedom.By the design basis of analysis of aircraft, critical size, large parts morpheme features etc., obtain large parts key characteristic.Then, and judge whether location completely of large parts by the key characteristic of choosing, obtain each key characteristic and determine the spatial degrees of freedom of large parts.

2) according to key characteristic Degree of Freedom Analysis, further distinguish primary and secondary relation, the rapport of key characteristic, main key characteristic is adopted to autonomous degree of freedom matching process completely, less important key characteristic adopts constrained degree of freedom matching process.Identify for the key characteristic with rapport, for cooperative dimensioning error distribution provides foundation.

3) characteristic of acquisition cooperative dimensioning, and according to the interior cooperative dimensioning evaluation method of claim 1 content, utilize the nominal size of cooperative dimensioning, upper and lower deviate regulation cooperative dimensioning optimum evaluation of estimate, meet dimensional requirement evaluation of estimate scope, discontented sufficient dimensional requirement evaluation of estimate scope, and the evaluation of estimate after normalizing is cumulative, construct overall evaluation function.

4) utilize the preliminary required adjustment matrix of large parts final carriage that obtains of SVD method, generation foundation using angle relevant to cooperative dimensioning in matrix or coordinate direction size as hereditary function initial population, utilize 3) in the overall assessment function of composition of content as fitness function, by making its optimization obtain the final assembling attitude of large parts.

2. the method for automatic calculation assembling pose in Large Aircraft Components digitizing assembling process according to claim 1, is characterized in that specifically comprising the steps:

Step 1: utilize airplane data model and technical papers, extract large parts key characteristic.

Step 2: large parts key characteristic is determined to large parts degree of freedom analyzes, judge whether it locates completely to large parts, and obtain the large space of components degree of freedom of each key characteristic control situation.

Step 3: key characteristic is classified, obtain main key characteristic, less important key characteristic, has the key characteristic of rapport.

Step 4: adopt unconfined key characteristic matching method, mate main key characteristic locus.

Step 5: adopt constrained key characteristic matching method, mate less important key characteristic locus.

Step 6: analyze nominal size, the upper lower deviation of cooperative dimensioning, and be normalized evaluation.

Step 7: utilize normalized evaluation function, construct the fitness function of hereditary function.

Step 8: select on large parts four not points of the key characteristic on same straight line, utilize SVD method to obtain and adjust matrix.

Step 9: according to the angle of required coupling or change in coordinate axis direction, choose the correlation values of adjusting in matrix as hereditary function initialization population foundation, generate initialization population.

Step 10: adopt the Real-valued heredity function of roulette design to be optimized calculating to cooperative dimensioning.

Step 11: according to this final carriage, select key characteristic point, and compare with the key characteristic point of large parts actual measurement acquisition, adopt SVD method to obtain and adjust matrix.