CN102314151B - Quality property micro-adjustment structure of aircraft wind tunnel model formed by light curing and method - Google Patents

Abstract

The invention provides a quality property micro-adjustment structure of an aircraft wind tunnel model quickly formed based on light curing and a method; the method comprises the steps that: 1. the aircraft wind tunnel model in the micro-adjustment structure is designed and processed in advance; 2. an optimal quality property micro-adjustment scheme is obtained through computer-assisted optimization: the quality property parameter of the aircraft wind tunnel model after being processed is measured and compared with a design value, and an error value is calculated as a target function; portfolios which are added or removed from the micro-adjustment structure serve as optimization variables; and an optimal quality property micro-adjustment scheme is obtained through computer-based automatic optimization. The invention provides the quick and automatic quality property micro-adjustment method which can provide the quality property simulation precision of the model.

Description

Fine tuning structure and the method thereof of the mass property of the aircraft wind tunnel model of photocuring moulding

Technical field

The invention belongs to rapid shaping technique and aircraft wind tunnel experiment model and make the field, relate to a kind of method for trimming of aircraft wind tunnel model mass property of photocuring moulding.

Background technology

The aircraft wind tunnel model that utilizes the photocureable rapid shaping technology to make can shorten the manufacturing cycle of model and reduce the assembling link of model, is a new technology that application prospect is arranged.

For the extraordinary wind tunnel test of aircraft (aircraft, body etc.), such as experiments such as free flight, tailspins, the mass property of model (weight, center of gravity and the moment of inertia that comprise model) is strict.Because material, manufacturing and the inevitable loss of significance of assembling link make the mass property of finishing model have certain error.When this error greater than designing requirement is, need carry out trace to the mass property of model and regulate.Finely tune by increase or reduce modes such as small quality, adjusting balance position at model based on mach method.On the one hand, because there is difficulty in process in the processing that classic method is processed complicated external and internal compositions, increased the operation easier of adjusting; On the other hand, such method generally is manual operations, and is lower to the having relatively high expectations of operator's experience, skill level, automaticity.

The photocureable rapid shaping technology can the processed complex external and internal compositions, and has certain machining precision, is fit to the external and internal compositions complexity, to the processing of models such as the high free flight of mass property accuracy requirement, tailspin.Simultaneously because this technology can be in model optional position time processing tiny characteristic structure, make design in advance and workmanship characteristic fine tuning structure, utilize the robotization method for trimming of computer-aided design (CAD) to become possibility.

Summary of the invention

Technical matters to be solved by this invention provides a kind of fine tuning structure and method thereof of mass property of aircraft wind tunnel model of photocuring moulding, utilize photocurable quick shaping process to be easy to the advantage of processed complex structure and the characteristics of computer aided optimum technology Automatic Optimal, reduce operation easier, reduce manual operations, realize the fine setting of aircraft wind tunnel model mass property, thereby improve the simulation precision of model quality characteristic.

To achieve these goals, the present invention adopts following technical scheme:

A kind of fine tuning structure of mass property of aircraft wind tunnel model of photocuring moulding, body at wind tunnel model is distributed with a plurality of weightening finish structures and loss of weight structure, described weightening finish structure is the groove that distributes along the body outer rim, has the aperture that is communicated with groove at described body wall; Described loss of weight structure is the ring texture that is distributed in the body inner chamber, and ring texture is connected on the body by post.

In described weightening finish structure of hollow groove, pour into liquid light-cured resin as required, adopt UV illumination to make its curing at last.

A kind of method for trimming of aircraft wind tunnel model mass property of photocuring moulding may further comprise the steps:

1) designs and processes the aircraft wind tunnel model with fine tuning structure in advance;

2) utilize computer aided optimum to obtain optimum mass property trimming scheme: to measure the mass property parameter that obtains processing back aircraft wind tunnel model, calculate error amount after comparing with design load, as objective function; With fine tuning structure is added or remove operation be combined as the optimization variable; Obtain optimum mass property trimming scheme by the computing machine Automatic Optimal.

Described mass property parameter comprises model weight, model barycentric coordinates and model rotation inertia.

Described fine tuning structure comprises weightening finish structure and loss of weight structure; Described weightening finish structure and loss of weight structure utilize the photocureable rapid shaping technology together to process with model, and single structure has definite weight, barycentric coordinates and moment of inertia, and relative model has definite position and orientation; Utilize the weightening finish structure to increase the method for model weight in pre-processed cavity, filling with liquid resin, through increasing the model constant weight in this position behind the photocuring.

Described objective function is the mass property of actual measurement and the total error ∑ e of design load:

∑ e=e _M+ e _CG+ e _MOI(formula 1)

Wherein, e _MError for the model general assembly (TW); e _CGError for the model centre of gravity place; e _MOIError for model rotation inertia;

Optimizing variable is the operative combination [A] [B] of mass property fine tuning structure, A and B represent respectively to increase weight structure and loss of weight structure.

Obtain optimum mass property trimming scheme by enumerative technique in the step 2, may further comprise the steps:

1) enumerates all [A] [B] combinations; Weightening finish structure and the total number of loss of weight structure are n, and then [A] [B] combination adds up to 2 ⁿ, each combination is designated as [A] [B] _i, i=1,2 ..., 2 ⁿ

2) calculate all [A] [B] _iCorresponding objective function ∑ e value is designated as ∑ e _i, i=1,2 ..., 2 ⁿ

3) search minimum target function is at ∑ e _iMiddle search minimum value is designated as ∑ e _Min, corresponding combination [A] [B] _MinBe optimum mass property trimming scheme.

Fine tuning structure and the method thereof of the aircraft wind tunnel model mass property of photocuring moulding of the present invention have the following advantages at least: the present invention is by the process advantage of photocuring moulding technology, adjusting after the modelling stage, just consideration was processed, design a series of fine tuning structures in advance, and process with model; After mould processing is finished, according to the measured data error of calculation value that check obtains, utilize the operation scheme of computing machine Automatic Optimal fine tuning structure, and adjustment model mass property accordingly.The present invention has utilized photocurable quick shaping process to be easy to the advantage of processed complex structure and the characteristics of computer aided optimum technology Automatic Optimal, realize the robotization fine setting of aircraft wind tunnel model mass property, can reduce operation easier, reduce manual operations, thereby improved the simulation precision of dummy vehicle mass property.The invention provides a kind of mass property method for trimming of quick, robotization, the simulation precision of the mass property that can supply a model.

Description of drawings

Fig. 1 is the relation of model actual measurement coordinate system and design coordinate system, and wherein (a) is original state, (b) postrotational state;

Fig. 2 is the relation of single fine tuning structure coordinate system and design coordinate system, and wherein (a) is original state, (b) is postrotational state;

Fig. 3 is the structural representation of body aircraft of the present invention;

Fig. 4 is the present invention's structural representation that increases weight;

Fig. 5 is loss of weight structural representation of the present invention.

Embodiment

Below in conjunction with accompanying drawing, fine tuning structure and the method thereof of the aircraft wind tunnel model mass property of photocuring moulding of the present invention is described in detail:

See also Fig. 1 to shown in Figure 5, the method for trimming of the aircraft wind tunnel model mass property of a kind of photocuring moulding of the present invention may further comprise the steps:

One, designs and processes " mass property fine tuning structure " in advance

As shown in Figure 3, be body dummy vehicle structural representation.Coordinate origin is in model vertices, and the x axle is for being parallel to body dummy vehicle axis and pointing to the rear, and the y axle is for perpendicular to the vertical plane of symmetry of fuselage and point to right-handly, and the z axle is in the vertical plane of symmetry of fuselage and points upwards.

Design the distribution of weightening finish and loss of weight structure in advance as shown in Figure 3: the weightening finish structure is positioned at two cross sections, totally 8, is designated as A1 ~ A8 respectively; The loss of weight structure distribution totally 2, is designated as B1, B2 in two cross sections.The structural representation of weightening finish structure is as shown in Figure 4: the weightening finish structure be the groove 2 that distributes along body 1 outer rim among the design, and the body wall in the structure centre position has aperture 3 connection grooves 2.The design's purpose is, by aperture 3 liquid light-cured resin is injected groove 2, thereby makes its curing reach the purpose of " gaining in weight " in this position by UV illumination again.The structural representation of loss of weight structure is as shown in Figure 5: the weightening finish structure is the ring texture 4 that is distributed in body 1 inner chamber among the design, and ring texture 4 is connected on the body 1 by post 5.As required, destroy post 5 and make this ring texture 4 come off, be implemented in this position and " reduce weight ".

Two, utilize computer-aided design (CAD) " mass property fine setting " scheme

Fine tuning structure adds up to n among the design _OPT=10, can adopt enumerative technique.

Enumerate all [A] [B] combinations for 1 °.Suppose that weightening finish and the total number of loss of weight structure are 10, then [A] [B] combination adds up to 2 ¹⁰=1024, each combination is designated as [A] [B] _i(i=1,2 ..., 1024).

2 ° are calculated all [A] [B] _iCorresponding objective function ∑ e value.According to formula 1, formula 24a, formula 24b and formula 24c, calculate [A] [B] _iCorresponding ∑ e is designated as ∑ e _i(i=1,2 ..., 2 ⁿ, n=10 wherein)

3 ° of search minimum target functions.At ∑ e _iMiddle search minimum value is designated as ∑ e _Min, corresponding combination [A] [B] _MinBe the optimal adjustment scheme.

Three, high-precision fine setting

In order to improve the mass property precision of model, can carry out duplicate measurements, debugging to model.Method is, after the fine tuning structure in the above-mentioned steps prioritization scheme is operated, measures the mass property parameter of this model again, obtains new error, serves as to optimize variable with remaining fine setting street corner, reuses enumerative technique and is optimized.The number of times of high-precision fine setting can repeatedly repeat as required.

The present invention utilizes in the step of computer-aided design (CAD) " mass property fine setting " scheme, and obtaining of optimal case is defined as optimization problem, and by the computing machine Automatic Optimal.

Measure the mass property parameter that obtains processing back model, calculate error amount after comparing with design load, as objective function; With fine tuning structure is added or remove operation be combined as the optimization variable.

Objective function: the mass property of actual measurement and the total error of design load

∑ e=e _M+ e _CG+ e _MOI(formula 1)

e _MError for the model general assembly (TW)

e _CGError for the model centre of gravity place

e _MOIError for model rotation inertia

Optimize variable: the operative combination of mass property fine tuning structure [A] [B]

A and B represent respectively weightening finish or loss of weight structure.

Each fine tuning structure has implementation and operation or the two states that remains unchanged, and one group of operation of all structures selects just to constitute a value of variable [A] [B].Each value result of corresponding total error ∑ e exists a value to make ∑ e minimum, and this value is exactly optimal value, i.e. the optimal case of enforcement " mass property fine setting ".Under certain algorithm is supported, utilize computer aided optimum to calculate and to find this value.

Implementing key of the present invention is: 1. set up objective function and the mathematical relation (being formula 15c, formula 19a, formula 19b, formula 19c, formula 23) of optimizing variable; 2. set up the algorithm of area of computer aided scheme optimization.Specifically be described below:

1, sets up objective function and the mathematical relation of optimizing variable

A) design load of model quality characteristic

◆ general assembly (TW): the model general assembly (TW) is design load

◆ barycentric coordinates: the design load of model barycentric coordinates

$\stackrel{\‾}{x}=({\stackrel{\‾}{x}}_0,{\stackrel{\‾}{y}}_0,{\stackrel{\‾}{z}}_0)$ (formula 2)

◆ moment of inertia: the design load of model inertial tensor is

$\stackrel{\‾}{I}=\left[\begin{array}{ccc}{\stackrel{\‾}{I}}_{\mathrm{xx}}& -{\stackrel{\‾}{I}}_{\mathrm{xy}}& -{\stackrel{\‾}{I}}_{\mathrm{xz}}\\ -{\stackrel{\‾}{I}}_{\mathrm{yx}}& {\stackrel{\‾}{I}}_{\mathrm{yy}}& -{\stackrel{\‾}{I}}_{\mathrm{yz}}\\ -{\stackrel{\‾}{I}}_{\mathrm{zx}}& -{\stackrel{\‾}{I}}_{\mathrm{zy}}& {\stackrel{\‾}{I}}_{\mathrm{zz}}\end{array}\right]$ (formula 3a)

Be respectively the moment of inertia around three coordinate axis, other are product of inertia.

The delivery type cross center of gravity the main shaft coordinate system (general provision is axially for the x axle, and exhibition is to be the y axle, with it vertically and to satisfy right-hand law be the z axle), then product of inertia is 0, namely the design load of model inertial tensor is

$\stackrel{\‾}{I}=\left[\begin{array}{ccc}{\stackrel{\‾}{I}}_{\mathrm{xx}}& 0& 0\\ 0& {\stackrel{\‾}{I}}_{\mathrm{yy}}& 0\\ 0& 0& {\stackrel{\‾}{I}}_{\mathrm{zz}}\end{array}\right]$ (formula 3b)

B) error analysis of model quality characteristic

Shown in Fig. 1 (a), the main shaft coordinate of the mistake center of gravity of modelling is

Wherein Be center of gravity, its coordinate

Be respectively the principal axis of inertia.The main shaft coordinate of the mistake center of gravity of model actual measurement is Oxyz, and wherein O is center of gravity, its coordinate x=(x ₀, y ₀, z ₀), x, y, z are the principal axis of inertia.

The actual measurement coordinate system designs the direction vector of coordinate system relatively

$r=x-\stackrel{\‾}{x}=(\mathrm{\Δx},\mathrm{\Δy},\mathrm{\Δz})=(x_0-{\stackrel{\‾}{x}}_0,y_0-{\stackrel{\‾}{y}}_0,z_0-{\stackrel{\‾}{z}}_0)$ (formula 4)

Rotation matrix is

$\mathrm{\Λ}=\left[\begin{array}{ccc}{\mathrm{\λ}}_{11}& {\mathrm{\λ}}_{12}& {\mathrm{\λ}}_{13}\\ {\mathrm{\λ}}_{21}& {\mathrm{\λ}}_{22}& {\mathrm{\λ}}_{23}\\ {\mathrm{\λ}}_{31}& {\mathrm{\λ}}_{32}& {\mathrm{\λ}}_{33}\end{array}\right]$ (formula 5)

Wherein, λ _IjFor i coordinate in the actual measurement coordinate system (refer to x, y, z) j coordinate (refers in designing coordinate system

On direction cosine.

The design coordinate system is determined that by design the actual measurement coordinate system is recorded by surveying instrument, so r and Λ all are known.

◆ general assembly (TW)

The model actual measurement general assembly (TW) is M, and design gross weight is

Then the general assembly (TW) error is:

$\mathrm{\ΔM}=M-\stackrel{\‾}{M}$ (formula 6)

◆ barycentric coordinates

The model actual measurement barycentric coordinates are x=(x ₀, y ₀, z ₀), the design gravity coordinate is

Then the center of gravity error is:

$\mathrm{\Δx}=(\mathrm{\Δx},\mathrm{\Δy},\mathrm{\Δz})=(x_0-{\stackrel{\‾}{x}}_0,y_0-{\stackrel{\‾}{y}}_0,z_0-{\stackrel{\‾}{z}}_0)$ (formula 7)

◆ moment of inertia

The model actual measurement inertial tensor is

$I=\left[\begin{array}{ccc}{I}_{\mathrm{xx}}& {-I}_{\mathrm{xy}}& {-I}_{\mathrm{xz}}\\ {-I}_{\mathrm{yx}}& I_{\mathrm{yy}}& {-I}_{\mathrm{yz}}\\ {-I}_{\mathrm{zx}}& {-I}_{\mathrm{zy}}& I_{\mathrm{zz}}\end{array}\right]$ (formula 8a)

Wherein, I _Xx, I _Yy, I _ZzBe the moment of inertia of three axles, other are product of inertia, because the actual measurement coordinate is the inertia principal axes system of the overweight heart, product of inertia is 0, therefore

$I=\left[\begin{array}{ccc}{I}_{\mathrm{xx}}& 0& 0\\ 0& I_{\mathrm{yy}}& 0\\ 0& 0& I_{\mathrm{zz}}\end{array}\right]$ (formula 8b)

As shown in Figure 1, the actual measurement coordinate system be transformed into the design coordinate system need rotate and translation transformation.

Rotational transform: the actual measurement inertial tensor is transformed into the design coordinate system, then

$I^{\′}=\mathrm{\ΛI}=\left[\begin{array}{ccc}{I}_{11}^{\′}& {-I}_{12}^{\′}& {-I}_{13}^{\′}\\ {-I}_{21}^{\′}& I_{22}^{\′}& {-I}_{23}^{\′}\\ {-I}_{31}^{\′}& {-I}_{32}^{\′}& I_{33}^{\′}\end{array}\right]$ (formula 8c)

According to following formula, analytical form is

$I^{\′}=\left[\begin{array}{ccc}{\mathrm{\λ}}_{11}{I}_{\mathrm{xx}}& {\mathrm{\λ}}_{12}{I}_{\mathrm{yy}}& {\mathrm{\λ}}_{13}{I}_{\mathrm{zz}}\\ {\mathrm{\λ}}_{21}{I}_{\mathrm{xx}}& {\mathrm{\λ}}_{22}{I}_{\mathrm{yy}}& {\mathrm{\λ}}_{23}{I}_{\mathrm{zz}}\\ {\mathrm{\λ}}_{31}{I}_{\mathrm{xx}}& {\mathrm{\λ}}_{32}{I}_{\mathrm{yy}}& {\mathrm{\λ}}_{33}{I}_{\mathrm{zz}}\end{array}\right]$ (formula 8d)

Translation transformation: moment of inertia is different with the form of product of inertia translation transformation

According to the moment of inertia parallel axis theorem

$I_{\mathrm{ii}}^{\′\′}=I_{\mathrm{ii}}^{\′}+\stackrel{\‾}{M}{d}_i^2(i=x,y,\mathrm{or\; z})$ (formula 9)

Wherein, M is the model actual measurement general assembly (TW), d _iFor rotating the distance of back actual measurement coordinate system and design coordinate system respective shaft, shown in Fig. 1 (b),

$d_y^2={\mathrm{\Δx}}^2+{\mathrm{\Δz}}^2$ (formula 10a)

Diaxon is similar in addition, then

$d_x^2={\mathrm{\Δy}}^2+{\mathrm{\Δz}}^2$ (formula 10b)

$d_z^2={\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2$ (formula 10c)

According to the product of inertia parallel axis theorem, product of inertia is

$I_{\mathrm{ij}}^{\′\′}=I_{\mathrm{ij}}^{\′}+\stackrel{\‾}{M}{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j(i=x,y,\mathrm{or\; z},i\≠j)$ (formula 11)

Therefore, the model actual measurement inertia matrix has after being transformed into the design coordinate system

$I^{\′\′}=\left[\begin{array}{ccc}{I}_{11}^{\′\′}& {-I}_{12}^{\′\′}& {-I}_{13}^{\′\′}\\ {-I}_{21}^{\′\′}& I_{22}^{\′\′}& {-I}_{23}^{\′\′}\\ {-I}_{31}^{\′\′}& {-I}_{32}^{\′\′}& I_{33}^{\′\′}\end{array}\right]$ (formula 12)

Formula 12 is the matrix form of formula 11.

C) the fine setting principle of model quality characteristic

Shown in Fig. 2 (a), the main shaft coordinate of the mistake center of gravity of modelling is

Wherein

Be center of gravity, coordinate

Be respectively the principal axis of inertia.The main shaft coordinate of the mistake center of gravity of model actual measurement is O _ix _iy _iz _i, O wherein _iBe center of gravity, coordinate x=(x _{0, i}, y _{0, i}, z _{0, i}), x _i, y _i, z _iBe the principal axis of inertia.

The fine tuning structure coordinate system designs the direction vector of coordinate system relatively

$r_i=x_i-{\stackrel{\‾}{x}}_i=({\mathrm{\Δx}}_i,{\mathrm{\Δy}}_i,{\mathrm{\Δz}}_i)=(x_{0,i}-{\stackrel{\‾}{x}}_0,y_{0.i}-{\stackrel{\‾}{y}}_0,z_{0.i}-{\stackrel{\‾}{z}}_0)$ (formula 13)

Rotation matrix is

${\mathrm{\Λ}}_i=\left[\begin{array}{ccc}{\mathrm{\λ}}_{11,i}& {\mathrm{\λ}}_{12,i}& {\mathrm{\λ}}_{13,i}\\ {\mathrm{\λ}}_{21,i}& {\mathrm{\λ}}_{22,i}& {\mathrm{\λ}}_{23,i}\\ {\mathrm{\λ}}_{31,i}& {\mathrm{\λ}}_{32,i}& {\mathrm{\λ}}_{33,i}\end{array}\right]$ (formula 14)

λ wherein _KlFor k coordinate in the fine tuning structure coordinate system (refers to x _i, y _iOr z _i) l coordinate (refers in the design coordinate system

On direction cosine.

Design coordinate system and fine coordinate system are determined by design, so r _iAnd Λ _iAll known.

Symbol description: above i is the label of fine tuning structure, comprises weightening finish structure and loss of weight structure.Design and the total number of making of fine tuning structure are n, are without loss of generality, and (0≤k≤n) be the weightening finish structure, back n-k is the loss of weight structure to preceding k of regulation.The total number p(0 of the structure≤p that implement to regulate≤n), be without loss of generality, before the regulation q (0≤q≤p) be the weightening finish structure, back p-q is individual to be the loss of weight structure.

◆ general assembly (TW)

The weight of single fine tuning structure is m _i, then the influence to general assembly (TW) is Δ m _i, i=1,2, ..., k, k+1 ..., n, according to above regulation, preceding k is weightening finish structure, Δ m _iFor on the occasion of, back n-k be the loss of weight structure, Δ m _iBe negative value.

After implement regulating, fine tuning structure to the entire effect of model general assembly (TW) is,

$\mathrm{\Σm}=\underset{j}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\Δm}}_j$ (formula 15a)

J=1,2, ..., q, q+1 ..., p, the same regulation, preceding q is the weightening finish structure.

The target of regulating is that implementation model actual measurement general assembly (TW) and design gross weight coincide, namely

$M+\mathrm{\Σm}=\stackrel{\‾}{M}$ (formula 15b)

Therefore, the error function of model general assembly (TW) is in the objective function

$e_M=(M-\stackrel{\‾}{M})+\mathrm{\Σm}$ (formula 15c)

◆ barycentric coordinates

The weight of single fine tuning structure is m _i, the model actual measurement general assembly (TW) is M, then single fine tuning structure makes the variable quantity of Model Measured barycentric coordinates be

${\mathrm{\Δx}}_{\mathrm{CG}}^i=\frac{m_i}{M+m_i}{\mathrm{\Δx}}_i$ (formula 16a)

${\mathrm{\Δy}}_{\mathrm{CG}}^i=\frac{m_i}{M+m_i}{\mathrm{\Δy}}_i$ (formula 16b)

${\mathrm{\Δz}}_{\mathrm{CG}}^i=\frac{m_i}{M+m_i}{\mathrm{\Δz}}_i$ (formula 16c)

I=1,2, ..., k, k+1 ..., n, according to above regulation, preceding k is weightening finish structure, m _iGet on the occasion of, back n-k be the loss of weight structure, m _iGet negative value.

After implementing to regulate, fine tuning structure to the entire effect of model barycentric coordinates is

$\mathrm{\Σx}=\underset{j}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\Δx}}_{\mathrm{CG}}^j$ (formula 17a)

$\mathrm{\Σy}=\underset{j}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\Δy}}_{\mathrm{CG}}^j$ (formula 17b)

$\mathrm{\Σz}=\underset{j}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{CG}}^j$ (formula 17c)

J=1,2, ..., q, q+1 ..., p, the same regulation, preceding q is the weightening finish structure.

The target of regulating is that implementation model actual measurement barycentric coordinates and design centre coordinate coincide, namely

$x_0+\mathrm{\Σx}={\stackrel{\‾}{x}}_0$ (formula 18a)

$y_0+\mathrm{\Σy}={\stackrel{\‾}{y}}_0$ (formula 18b)

$z_0+\mathrm{\Σz}={\stackrel{\‾}{z}}_0$ (formula 18c)

Then the centre of gravity place error function is in the objective function

$e_{\mathrm{CG}}^x=(x_0-\stackrel{\‾}{x_0})+\mathrm{\Σx}$ (formula 19a)

$e_{\mathrm{CG}}^y=(y_0-\stackrel{\‾}{y_0})+\mathrm{\Σy}$ (formula 19b)

$e_{\mathrm{CG}}^z=(z_0-\stackrel{\‾}{z_0})+\mathrm{\Σz}$ (formula 19c)

◆ moment of inertia

Single fine tuning structure inertial tensor

$I_i=\left[\begin{array}{ccc}{I}_{\mathrm{xx},i}& {-I}_{\mathrm{xy},i}& {-I}_{\mathrm{xz},i}\\ {-I}_{\mathrm{yx},i}& I_{\mathrm{yy},i}& {-I}_{\mathrm{yz},i}\\ {-I}_{\mathrm{zx},i}& {-I}_{\mathrm{zy},i}& I_{\mathrm{zz},i}\end{array}\right]$ (formula 20a)

I _{Xx, i}, I _{Yy, i}, I _{Zz, i}Be the moment of inertia of three axles, other are product of inertia, because the fine tuning structure coordinate is the inertia principal axes system of the overweight heart, product of inertia is 0, therefore

$I_i=\left[\begin{array}{ccc}{I}_{\mathrm{xx},i}& 0& 0\\ 0& I_{\mathrm{yy},i}& 0\\ 0& 0& I_{\mathrm{zz},i}\end{array}\right]$ (formula 20b)

I=1,2, ..., k, k+1 ..., n, according to above regulation, preceding k is weightening finish structure, m _iGet on the occasion of, back n-k be the loss of weight structure, m _iGet negative value.

As shown in Figure 2, the fine tuning structure coordinate system be transformed into the design coordinate system need rotate and two conversion of translation.Through the conversion identical with last joint " analysis of model quality characteristic error ", after the inertial tensor of single fine tuning structure is transformed into the design coordinate system

$I_i^{\′\′}=\left[\begin{array}{ccc}{I}_{11,i}^{\′\′}& {-I}_{12,i}^{\′\′}& {-I}_{13,i}^{\′\′}\\ {-I}_{21,i}^{\′\′}& I_{22,i}^{\′\′}& {-I}_{23,i}^{\′\′}\\ {-I}_{31,i}^{\′\′}& {-I}_{32,i}^{\′\′}& I_{33,i}^{\′\′}\end{array}\right]$ (formula 21)

I=1,2, ..., k, k+1 ..., n, according to above regulation, preceding k is weightening finish structure, m _iGet on the occasion of, back n-k be the loss of weight structure, m _iGet negative value.

The design coordinate system under, single fine tuning structure is to model inertial tensor I " influence be

Δ I _i"=I _i" (formula 22a)

I=1,2, ..., k, k+1 ..., n, according to above regulation, preceding k is weightening finish structure, m _iGet on the occasion of, back n-k be the loss of weight structure, m _iGet negative value.

After implementing to regulate, fine tuning structure to the entire effect of model inertial tensor is

${\mathrm{\ΣI}}^{\′\′}=\underset{j}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\ΔI}}_j^{\′\′}$ (formula 22b)

J=1,2, ..., q, q+1 ..., p, the same regulation, preceding q is the weightening finish structure.

The target of regulating is that implementation model actual measurement inertial tensor I is " with the design inertial tensor

Coincide, namely

$I^{\′\′}+{\mathrm{\ΣI}}^{\′\′}=\stackrel{\‾}{I}$ (formula 22c)

Then the moment of inertia error function is in the objective function

$e_{\mathrm{MOI}}=(I^{\′\′}-\stackrel{\‾}{I})+{\mathrm{\ΣI}}^{\′\′}$ (formula 23)

Analytical expression is

$e_{\mathrm{MOI}}^{11}=\mathrm{\Σ}[{\mathrm{\λ}}_{11,i}{I}_{\mathrm{xx},i}+m_i({{\mathrm{\Δy}}_i}^2+{{\mathrm{\Δz}}_i}^2)]+{\mathrm{\λ}}_{11}{I}_{\mathrm{xx}}+\stackrel{\‾}{M}({\mathrm{\Δy}}^2+{\mathrm{\Δz}}^2)-{\stackrel{\‾}{I}}_{\mathrm{xx}}$ (formula 23a)

$e_{\mathrm{MOI}}^{12}=\mathrm{\Σ}[{\mathrm{\λ}}_{12,i}{I}_{\mathrm{yy},i}-m_i{\mathrm{\Δx}}_i{\mathrm{\Δy}}_i]+{\mathrm{\λ}}_{12}{I}_{\mathrm{yy}}-\stackrel{\‾}{M}\mathrm{\Δx\Δy}$ (formula 23b)

$e_{\mathrm{MOI}}^{13}=\mathrm{\Σ}[{\mathrm{\λ}}_{13,i}{I}_{\mathrm{zz},i}-m_i{\mathrm{\Δx}}_i{\mathrm{\Δz}}_i]+{\mathrm{\λ}}_{13}{I}_{\mathrm{zz}}-\stackrel{\‾}{M}\mathrm{\Δx\Δz}$ (formula 23c)

$e_{\mathrm{MOI}}^{21}=\mathrm{\Σ}[{\mathrm{\λ}}_{21,i}{I}_{\mathrm{xx},i}-m_i{\mathrm{\Δx}}_i{\mathrm{\Δy}}_i]+{\mathrm{\λ}}_{21}{I}_{\mathrm{xx}}-\stackrel{\‾}{M}\mathrm{\Δx\Δy}$ (formula 23d)

$e_{\mathrm{MOI}}^{22}=\mathrm{\Σ}[{\mathrm{\λ}}_{22,i}{I}_{\mathrm{yy},i}+m_i({{\mathrm{\Δx}}_i}^2+{{\mathrm{\Δz}}_i}^2)]+{\mathrm{\λ}}_{22}{I}_{\mathrm{yy}}+\stackrel{\‾}{M}({\mathrm{\Δx}}^2+{\mathrm{\Δz}}^2)-{\stackrel{\‾}{I}}_{\mathrm{yy}}$ (formula 23e)

$e_{\mathrm{MOI}}^{23}=\mathrm{\Σ}[{\mathrm{\λ}}_{23,i}{I}_{\mathrm{zz},i}-m_i{\mathrm{\Δy}}_i{\mathrm{\Δz}}_i]+{\mathrm{\λ}}_{23}{I}_{\mathrm{zz}}-\stackrel{\‾}{M}\mathrm{\Δy\Δz}$ (formula 23f)

$e_{\mathrm{MOI}}^{31}=\mathrm{\Σ}[{\mathrm{\λ}}_{31,i}{I}_{\mathrm{xx},i}-m_i{\mathrm{\Δx}}_i{\mathrm{\Δz}}_i]+{\mathrm{\λ}}_{31}{I}_{\mathrm{xx}}-\stackrel{\‾}{M}\mathrm{\Δx\Δz}$ (formula 23g)

$e_{\mathrm{MOI}}^{32}=\mathrm{\Σ}[{\mathrm{\λ}}_{32,i}{I}_{\mathrm{yy},i}-m_i{\mathrm{\Δy}}_i{\mathrm{\Δz}}_i]+{\mathrm{\λ}}_{32}{I}_{\mathrm{yy}}-\stackrel{\‾}{M}\mathrm{\Δy\Δz}$ (formula 23h)

$e_{\mathrm{MOI}}^{33}=\mathrm{\Σ}[{\mathrm{\λ}}_{33,i}{I}_{\mathrm{zz},i}+m_i({{\mathrm{\Δx}}_i}^2+{{\mathrm{\Δy}}_i}^2)]+{\mathrm{\λ}}_{33}{I}_{\mathrm{zz}}+\stackrel{\‾}{M}({\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2)-{\stackrel{\‾}{I}}_{\mathrm{zz}}$ (formula 23i)

I=1,2, ..., q, q+1 ..., p, the same regulation, preceding q is the weightening finish structure.

2, set up the algorithm of area of computer aided scheme optimization

Every analytical expression of objective function is as follows:

$e_M=(M-\stackrel{\‾}{M})+\mathrm{\Σm}$ (formula 24a)

$e_{\mathrm{CG}}=\sqrt{{\left(e_{\mathrm{CG}}^x\right)}^2+{\left(e_{\mathrm{CG}}^y\right)}^2+{\left(e_{\mathrm{CG}}^z\right)}^2}$ (formula 24b)

$e_{\mathrm{MOI}}=\sqrt{\underset{i,j}{\mathrm{\Σ}}{\left(e_{\mathrm{MOI}}^{\mathrm{ij}}\right)}^2},(i,j=\mathrm{1,2,3})$ (formula 24c)

Therefore, objective function ∑ e=e _M+ e _CG+ e _MOICan Analytical Expression, objective function with optimize variable and have the mathematical relation of determining, be i.e. the definite value of one group of corresponding objective function ∑ e of [A] [B] value.Optimizing algorithm function and be in [A] [B] value space (all operations to fine tuning structure makes up) searches and makes a group of objective function ∑ e minimum, it is characterized in that to utilize programming language (as C, FORTRAN, language such as MATLAB) realize, and by computer automatic execution.

Involved in the present invention is discrete variable is in the multi-dimensional optimization problem of the finite space, in principle, is applicable to that the algorithm (as enumerative technique, intend discrete method, Fibonacci method etc.) of such problem all is applicable to the present invention.According to the characteristics of problem of the present invention, preferred algorithm enumerative technique and modified algorithm thereof.Specifically be described below:

A) enumerative technique

◆ algorithm principle: list all values of optimizing variable [A] [B], calculate the value of corresponding objective function ∑ e, get and make ∑ e minimum [A] [B] combination be the optimal adjustment scheme of asking.

◆ algorithm steps: this algorithm may further comprise the steps:

Enumerate all [A] [B] combinations for 1 °.Suppose that weightening finish and the total number of loss of weight structure are n, then [A] [B] combination adds up to 2 ⁿ, each combination is designated as [A] [B] _i(i=1,2 ..., 2 ⁿ).

2 ° are calculated all [A] [B] _iCorresponding objective function ∑ e value.According to formula 1, formula 24a, formula 24b and formula 24c, calculate [A] [B] _iCorresponding ∑ e is designated as ∑ e _i(i=1,2 ..., 2 ⁿ)

3 ° of search minimum target functions.At ∑ e _iMiddle search minimum value is designated as ∑ e _Min, corresponding combination [A] [B] _MinBe the optimal adjustment scheme.

◆ the algorithm scope of application: this algorithm principle is simple, realizes easily, generally is applicable to the less situation of variable [A] [B] sum of optimizing.[A] [B] combination adds up to 2 ⁿ, the variable space is with fine tuning structure sum n exponential increase, and when n value is more greatly, assessing the cost of this algorithm can be very big with the cycle.Therefore, this algorithm is used for the occasion of weightening finish and loss of weight structure sum n less (n≤10).When total n big (n〉10), should adopt other algorithms.

B) optimization (adapt to many group objective functions) progressively

◆ algorithm principle: the basis of this algorithm is enumerative technique.This algorithm at first sorts to all objective functions, forward objective function at first uses enumerative technique optimization to sorting, find the combination of satisfying certain error requirements, objective function after in this combination range ordering being leaned on also adopts enumerative technique optimization, and the like, up to all objective functions are all optimized, draw the optimal adjustment scheme at last.

◆ algorithm steps: this algorithm may further comprise the steps:

1 ° is sorted to objective function.1. determine total number n of objective function _OPTCan determine as required, (be ∑ e as 1, suc as formula 1), 3 (general assembly (TW), barycentric coordinates and moment of inertia each 1, suc as formula 24a, formula 24b and formula 24c), 13 (general assembly (TW) suc as formula totally 1 of 15c, barycentric coordinates suc as formula totally 3 of 19a ~ c, moment of inertia suc as formula totally 9 of 23a ~ i) etc. (it should be noted that, when the total number of objective function was 1, this algorithm was changed in quality and is enumerative technique); 2. objective function is sorted.Generally sort according to objective function f ([A] [B]) significance level, forward optimization space is bigger, obtains the littler optimal combination of error easily, and therefore the objective function that emphasis is guaranteed is placed on the front.The meter ranking results is

$f{\left(\right[A\left]\right[B\left]\right)}_1,f{\left(\right[A\left]\right[B\left]\right)}_2,...,f{\left(\right[A\left]\right[B\left]\right)}_{n_{\mathrm{OPT}}}.$

Enumerate for 2 ° and intend optimization aim function f ([A] [B]) _i(1≤i≤n _OPT) [A] [B] combination.According to the result of last round of optimization, enumerate epicycle and optimize space [A] [B] combination.Especially, first objective function f ([A] [B]) ₁Optimizing the space is the total space, i.e. [A] [B] combination adds up to 2 ⁿ, with enumerative technique step 1 °.

3 ° to intending optimization aim function enforcement optimization.With enumerative technique step 2 ° and 3 °.

4 ° according to 2 ° of 1 ° of order repeating steps and 3 °, all optimize up to all objective functions, find final optimal combination.

◆ the algorithm scope of application: when this algorithm is applicable to fine tuning structure sum n big (n〉10).

More than provided fine tuning structure sum n(and comprised weightening finish and loss of weight structure) the optimization algorithm steps that do not adopt simultaneously, generally when n hour (n≤10) adopt an enumerative technique, (n〉10) adopted progressively optimization when n was big.The realization of algorithm can be according to the programming language of selecting (as C, FORTRAN, MATLAB, APDL etc.), and by computer automatic execution.

The above only is one embodiment of the present invention, it or not whole or unique embodiment, the conversion of any equivalence that those of ordinary skills take technical solution of the present invention by reading instructions of the present invention is claim of the present invention and contains.

Claims (7)

1. the fine tuning structure of the mass property of the aircraft wind tunnel model of a photocuring moulding, it is characterized in that: the body at wind tunnel model is distributed with a plurality of weightening finish structures and loss of weight structure, described weightening finish structure is the groove (2) that distributes along body (1) outer rim, has the aperture (3) that is communicated with groove (2) at described body wall; Described loss of weight structure is for being distributed in the ring texture (4) of body (1) inner chamber, and ring texture (4) is connected on the body (1) by post (5).

2. the fine tuning structure of the mass property of the aircraft wind tunnel model of a kind of photocuring moulding as claimed in claim 1, it is characterized in that: in described weightening finish structure of hollow groove, pour into liquid light-cured resin as required, adopt UV illumination to make its curing at last.

3. an application rights requires the method that the fine tuning structure of mass property of the aircraft wind tunnel model of 1 described photocuring moulding is finely tuned, and it is characterized in that, may further comprise the steps:

1) designs and processes the aircraft wind tunnel model with fine tuning structure in advance;

2) utilize computer aided optimum to obtain optimum mass property trimming scheme: to measure the mass property parameter that obtains processing back aircraft wind tunnel model, calculate error amount after comparing with design load, as objective function; With fine tuning structure is added or remove operation be combined as the optimization variable; Obtain optimum mass property trimming scheme by the computing machine Automatic Optimal.

4. method as claimed in claim 3 is characterized in that, described mass property parameter comprises model weight, model barycentric coordinates and model rotation inertia.

5. method as claimed in claim 3 is characterized in that, described fine tuning structure comprises weightening finish structure and loss of weight structure; Described weightening finish structure and loss of weight structure utilize the photocureable rapid shaping technology together to process with model, and single weightening finish structure and loss of weight structure have definite weight, barycentric coordinates and moment of inertia, and relative model has definite position and orientation; Utilize the weightening finish structure to increase the method for model weight in pre-processed cavity, filling with liquid resin, through increasing the model constant weight in this position behind the photocuring; Utilize the method for loss of weight structure decrease model weight for removing pre-processed loss of weight structure, reduce the model constant weight in this position.

6. as claim 3 or 4 described methods, it is characterized in that: described objective function is the mass property parameter of actual measurement and the total error ∑ e of design load:

∑ e=e _M+ e _CG+ e _MOI(formula 1)

Wherein, e _MError for the model general assembly (TW); e _CGError for the model centre of gravity place; e _MOIError for model rotation inertia;

The operative combination [A] [B] that described optimization variable is the mass property fine tuning structure, A and B represent respectively to increase weight structure and loss of weight structure.

7. method as claimed in claim 6 is characterized in that: step 2) in obtain optimum mass property trimming scheme by enumerative technique, may further comprise the steps:

1) enumerates all [A] [B] combinations; Weightening finish structure and the total number of loss of weight structure are n, and then [A] [B] combination adds up to 2 ⁿ, each combination is designated as [A] [B] _i, i=1,2 ..., 2 ⁿ

2) calculate all [A] [B] _iCorresponding objective function ∑ e value is designated as ∑ e _i, i=1,2 ..., 2 ⁿ

3) search minimum target function is at ∑ e _iMiddle search minimum value is designated as ∑ e _Min, corresponding combination [A] [B] _MinBe optimum mass property trimming scheme.

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