CN102661729B - Method for confirming sectional dimension of I-shaped hollow beam of high-speed fluttering model of airplane - Google Patents

Abstract

The invention belongs to the field of structural mechanics and relates to a method for confirming a sectional dimension of an I-shaped hollow beam of a high-speed fluttering model of an airplane. The method is characterized in that the steps for confirming the sectional dimension of a thin-wall rectangular hollow beam with four lugs are as follows: calculating a vertical inertia moment Ix and a polar inertia moment J with preset values of the thin-wall rectangular hollow beam and an equivalent width a1 and an equivalent height b1 of a rectangle with a wall thickness being t; adjusting the preset polar inertia moment J; calculating an equivalent width a2 and an equivalent height b2; and taking b2 as the maximum value scope of b3, and iterating, thereby obtaining the sectional dimension a3, b3 and L3 fit for a sectional feature governing equation. According to the method provided by the invention, the precision of the section design of the model is increased, the uncertainty of the model design is reduced, the time for confirming the sectional dimension is shortened and the design efficiency of the fluttering model is increased. The lugs are located at four corners of the rectangle, so that the total height of the section is reduced and the dimensional limit demand is met to a certain degree.

Description

Definite method of the I-shaped hollow beam sectional dimension of a kind of aircraft high speed flutter model

Technical field

The invention belongs to structural mechanics field, relate to definite method of the I-shaped hollow beam sectional dimension of a kind of aircraft high speed flutter model.

Background technology

High speed flutter model can be used for obtaining the Transonic Flutter characteristic of aircraft and parts thereof, and high speed flutter model needs very little roof beam structure quality that very large aerofoil rigidity is provided conventionally, and in order to meet the designing requirement of three-way rigidity, be a desirable design form with the rectangular thin-wall hollow beam cross section of auricle.

Conventionally the method that need to gather by examination is in the past obtained the sectional dimension meeting the demands.The method that examination is gathered has following shortcoming: the first, adjust the experience that sectional dimension data needs designer, the dimensional data providing by rule of thumb often error is very large, even there will be the situation that is difficult to adjust the size meeting design requirement, affect the precision of model section rigidity, increased the uncertainty of modelling; The second, will determine sectional dimension by method of trial and error, need to carry out artificial adjustment and the judgement of many rounds, the time is long, and efficiency is low, has a strong impact on the modelling cycle.

Referring to Chinese patent " with definite method of auricle thin-wall rectangular hollow beam sectional dimension " (application number 201110232656.2), ensure with auricle rectangular thin-wall hollow beam have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _ybe in the situation of t with polar moment of inertia J and wall thickness and auricle thickness, can directly determine equivalent width a, equivalent height b and the hollow beam cross section beam overall L of its rectangle, this method does not need examination to gather, and precision and efficiency all very high.But the feature in cross section corresponding to this method is that auricle is positioned on the neutral surface in cross section, trouble in modelling and processing likely can be brought because equivalent height b value is excessive in this cross section.

Summary of the invention

The object of the invention is: the definite method that proposes the I-shaped hollow beam sectional dimension of a kind of aircraft high speed flutter model, to improve the precision of model section rigidity, reduce the uncertainty of modelling, shorten the time of determining sectional dimension, improve the design efficiency of flutter model, and the auricle of the thin-wall rectangular hollow beam with four auricles that the present invention proposes is positioned at four angle points of rectangle, under the condition of same cross-sectional characteristic desired value, has effectively reduced the overall height in cross section.

Technical solution of the present invention is: definite method of the I-shaped hollow beam sectional dimension of aircraft high speed flutter model, ensure aircraft high speed flutter model I-shaped hollow beam have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _ywith polar moment of inertia J and rectangular thin-wall hollow beam wall thickness be that t and auricle thickness are t _rsituation under, determine the equivalent width a of its rectangle ₃, equivalent height b ₃with hollow beam cross section beam overall L ₃.Here specify that all long measures are mm.It is characterized in that, determine that the step of the I-shaped hollow beam sectional dimension of aircraft high speed flutter model is as follows:

1, make t _r=n _rt;

2, calculate thin-wall rectangular hollow beam have predetermined value vertically to moment of inertia I _xwith polar moment of inertia J and rectangular thin-wall hollow beam wall thickness be t ₁and auricle thickness is t _rtime rectangular equivalent width a ₁with equivalent height b ₁:

2.1, calculate the first intermediate variable p and the second intermediate variable q according to following formula:

$\left\{\begin{array}{c}p=\frac{3}{t}({4I}_x+J)\\ q=\frac{{9I}_x}{t^2}({4I}_x-J)\end{array}\right....\left[1\right]$

2.2, calculate the 3rd intermediate variable s according to following formula:

$s=\frac{1}{2}(p-\sqrt{p^2-4q})...\left[2\right]$

2.3, calculate equivalent width a ₁with equivalent height b ₁:

$\left\{\begin{array}{c}{a}_1=\frac{{2I}_x}{\sqrt[3]{s^{2}t}}-\frac{\sqrt[3]{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00001629009100012.png"\; state="\{\{state\}\}">s</figure-callout>}}}{3}\\ b_1=\sqrt[3]{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00001629009100012.png"\; state="\{\{state\}\}">s</figure-callout>}}\end{array}\right....\left[3\right]$

3, predetermined polar moment of inertia J is adjusted: calculate the value J after polar moment of inertia J adjusts according to following formula ₁:

J ₁＝J[1-t _r/(2b ₁)]……………………………[4]

4, calculate equivalent width a ₂with equivalent height b ₂: change the J in formula [1] into J ₁, then calculate equivalent width a according to the method described in step 2 ₂with equivalent height b ₂;

5, iterative computation cross section property governing equation obtain sectional dimension:

5.1, make b _3k=b ₂-0.1k, variable k=1,2,3 ..., int (10b ₂), wherein int () is bracket function;

5.2, according to b _3kcalculate a _3k:

$a_{3k}=\frac{J_1/\left(4t\right)}{b_{3k}^2}(1+\sqrt{1+\frac{{2b}_{3k}^3}{J_1\left(4t\right)}})...\left[5\right]$

5.3, according to a _3kand b _3kcalculate L _3k:

$L_{3k}=(a_{3k}+t)+\frac{{6I}_x/t-(a_{3k}+t)({3b}_{3k}^2+t^2)-{(b_{3k}-t)}^3}{n_r[3{(b_{3k}+t-t_r)}^2+t_r^2]}...\left[6\right]$

5.4, according to a _3k, b _3kand L _3kcalculate f _k:

5.5, according to f _kcalculate err _k:

${\mathrm{err}}_k=\frac{|f_k-{6I}_y/t|}{{6I}_y/t}\&times;100\%...\left[8\right]$

5.6, obtain sectional dimension:

Error identifying value err _kthe a that minimum is corresponding _3kand b _3kcalculate L _3k, be final sectional dimension a ₃and b ₃calculate L ₃.

Advantage of the present invention is: improved the precision of model section rigidity, reduced the uncertainty of modelling, shortened the time of definite sectional dimension, improved the design efficiency of flutter model.One embodiment of the present of invention are gathered with current examination compared with method, and the present invention determines that the time of sectional dimension is only 10 minutes, and the examination method of gathering needs 25 hours, and the used time of the present invention is only for 1/150th of method is gathered in examination.Meanwhile, reduce overall depth of section, met dimension constraint, brought facility to modelling processing.

Brief description of the drawings

Fig. 1 is the schematic cross section of not being with the thin-wall rectangular hollow beam of auricle.A in figure ₁the equivalent width of the rectangle that calculates of step 1 of the present invention, a ₁outer rim width-walled thickness the t of=rectangle.B ₁the equivalent height of the rectangle that calculates of step 1 of the present invention, b ₁outer rim height-walled thickness the t of=rectangle.The center that the initial point 0 of the two-dimensional coordinate system in Fig. 1 is rectangle, x axle is parallel to the Width of rectangle, and positive dirction is towards the right side, and the positive dirction of y axle is upward.

Fig. 2 is the schematic cross section of the I-shaped hollow beam of aircraft high speed flutter model.Two-dimensional coordinate system in Fig. 2 is identical with Fig. 1.

Embodiment

Below the present invention is described in further details.Referring to Fig. 1,2, definite method of the I-shaped hollow beam sectional dimension of aircraft high speed flutter model, ensure the aircraft I-shaped hollow beam of high speed flutter model cross section have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _ywith polar moment of inertia J and rectangular thin-wall hollow beam wall thickness be that t and auricle thickness are t _rsituation under, determine the equivalent width a of its rectangle ₃, equivalent height b ₃with hollow beam cross section beam overall L ₃.Here specify that all long measures are mm.It is characterized in that, determine that the step of the I-shaped hollow beam sectional dimension of aircraft high speed flutter model is as follows:

1, make t _r=n _rt;

2, calculate thin-wall rectangular hollow beam have predetermined value vertically to moment of inertia I _xwith polar moment of inertia J and rectangular thin-wall hollow beam wall thickness be t ₁and auricle thickness is t _rtime rectangular equivalent width a ₁with equivalent height b ₁:

2.1, calculate the first intermediate variable p and the second intermediate variable q according to following formula:

$\left\{\begin{array}{c}p=\frac{3}{t}({4I}_x+J)\\ q=\frac{{9I}_x}{t^2}({4I}_x-J)\end{array}\right....\left[1\right]$

2.2, calculate the 3rd intermediate variable s according to following formula:

$s=\frac{1}{2}(p-\sqrt{p^2-4q})...\left[2\right]$

2.3, calculate equivalent width a ₁with equivalent height b ₁:

$\left\{\begin{array}{c}{a}_1=\frac{{2I}_x}{\sqrt[3]{s^{2}t}}-\frac{\sqrt[3]{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00001629009100012.png"\; state="\{\{state\}\}">s</figure-callout>}}}{3}\\ b_1=\sqrt[3]{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00001629009100012.png"\; state="\{\{state\}\}">s</figure-callout>}}\end{array}\right....\left[3\right]$

3, predetermined polar moment of inertia J is adjusted: calculate the value J after polar moment of inertia J adjusts according to following formula ₁:

J ₁＝J[1-t _r/(2b ₁)]……………………………[4]

4, calculate equivalent width a ₂with equivalent height b ₂: change the J in formula [1] into J ₁, then calculate equivalent width a according to the method described in step 2 ₂with equivalent height b ₂;

5, iterative computation cross section property governing equation obtain sectional dimension:

5.1, make b _3k=b ₂-0.1k, variable k=1,2,3 ..., int (10b ₂), wherein int () is bracket function;

5.2, according to b _3kcalculate a _3k:

$a_{3k}=\frac{J_1/\left(4t\right)}{b_{3k}^2}(1+\sqrt{1+\frac{{2b}_{3k}^3}{J_1\left(4t\right)}})...\left[5\right]$

5.3, according to a _3kand b _3kcalculate L _3k:

$L_{3k}=(a_{3k}+t)+\frac{{6I}_x/t-(a_{3k}+t)({3b}_{3k}^2+t^2)-{(b_{3k}-t)}^3}{n_r[3{(b_{3k}+t-t_r)}^2+t_r^2]}...\left[6\right]$

5.4, according to a _3k, b _3kand L _3kcalculate f _k:

5.5, according to f _kcalculate err _k:

${\mathrm{err}}_k=\frac{|f_k-{6I}_y/t|}{{6I}_y/t}\&times;100\%...\left[8\right]$

5.6, obtain sectional dimension:

Find out err _ka corresponding to value minimum _3kand b _3kcalculate L _3k, be final sectional dimension a ₃and b ₃calculate L ₃.

Principle of work of the present invention is: derive and parameter correction by mechanics of materials fundamental formular, (seeing " mechanics of materials " Dan Hui ancestral Higher Education Publishing House 1999) obtained a kind of method that obtains the I-shaped hollow beam sectional dimension of aircraft high speed flutter model from cross section property, for definite sectional dimension, this is a kind of half reverse mentality of designing and method, therefore, than needed to gather by artificial examination the method for sectional dimension of obtaining in the past, efficiency and precision are greatly improved.And than ears sheet thin-wall rectangular hollow beam in the past, the I-shaped hollow beam that the present invention proposes can meet certain dimension constraint condition.

Embodiment

To the method for the invention, calculate checking.

Provide three groups of aircraft high speed flutter girder moulder's font hollow beam cross sections, P1～P3 cross section is respectively embodiment 1～embodiment 3.Table 1 has provided the geometrical property predetermined value of three embodiment, i.e. desired value.For P1～P3, carry out sectional dimension design.Table 1 has also provided the geometrical property that uses the design section that the inventive method obtains, i.e. design load, and the error of design load.Table 2 has provided the size design value of three embodiment, and wherein thin-walled and auricle thickness are the value of providing in advance.

The design load of the cross section geometric characteristic of table 1 is according to the sectional dimension of table 2 correspondence, is calculated by FEMAP v9.31.The desired value of comparing, the error of design section characteristic value is all not more than 2%, and from engineering viewpoint, this is a kind of high-precision result of calculation.

Table 1 cross section geometric characteristic mm ⁴

Table 2 cross section geometry design load mm

Claims (1)

1. a definite method for the I-shaped hollow beam sectional dimension of aircraft high speed flutter model, ensure I-shaped thin-walled beam have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _ywith polar moment of inertia J and I-shaped thin-walled beam wall thickness be that t and auricle thickness are t _rsituation under, determine the equivalent width a of its rectangle ₃, equivalent height b ₃with hollow beam cross section beam overall L ₃; Here specify that all long measures are mm, it is characterized in that, determine that the step of thin-wall rectangular hollow beam sectional dimension is as follows:

1.1, make t _r=n _rt;

1.2, calculate thin-wall rectangular hollow beam have predetermined value vertically to moment of inertia I _xwith polar moment of inertia J and I-shaped thin-walled beam wall thickness be that t and auricle thickness are t _rtime rectangular equivalent width a ₁with equivalent height b ₁:

1.2.1, calculate the first intermediate variable p and the second intermediate variable q according to following formula:

$\left\{\begin{array}{c}p=\frac{3}{t}({4I}_x+J)\\ q=\frac{{9I}_x}{t^2}({4I}_x-J)\end{array}\right....\left[1\right]$

1.2.2, calculate the 3rd intermediate variable s according to following formula:

$s=\frac{1}{2}(p-\sqrt{p^2-4q})...\left[2\right]$

1.2.3, calculate equivalent width a ₁with equivalent height b ₁:

$\left\{\begin{array}{c}{a}_1=\frac{{2I}_x}{\sqrt[3]{s^{2}t}}-\frac{\sqrt[3]{s}}{3}\\ b_1=\sqrt[3]{s}\end{array}\right....\left[3\right]$

1.3, predetermined polar moment of inertia J is adjusted: calculate the value J after polar moment of inertia J adjusts according to following formula ₁:

J ₁＝J[1-t _r/(2b ₁)]……………………………[4]

1.4, calculate equivalent width a ₂with equivalent height b ₂: change the J in formula [1] into J ₁, then calculate equivalent width a according to the method described in step 1.2 ₂with equivalent height b ₂;

1.5, iterative computation cross section property governing equation obtain sectional dimension:

1.5.1, make b _3k=b ₂-0.1k, variable k=1,2,3 ..., int (10b ₂), wherein int () is bracket function;

1.5.2, according to b _3kcalculate a _3k:

$a_{3k}=\frac{J_1/\left(4t\right)}{b_{3k}^2}(1+\sqrt{1+\frac{{2b}_{3k}^3}{J_1\left(4t\right)}})...\left[5\right]$

1.5.3, according to a _3kand b _3kcalculate L _3k:

$L_{3k}=(a_{3k}+t)+\frac{{6I}_x/t-(a_{3k}+t)({3b}_{3k}^2+t^2)-{(b_{3k}-t)}^3}{n_r[3{(b_{3k}+t-t_r)}^2+t_r^2]}...\left[6\right]$

1.5.4, according to a _3k, b _3kand L _3kcalculate f _k:

1.5.5, according to f _kerror of calculation value err _k:

${\mathrm{err}}_k=\frac{|f_k-{6I}_y/t|}{{6I}_y/t}\&times;100\%...\left[8\right]$

1.5.6, obtain sectional dimension:

Error identifying value err _kthe a that minimum is corresponding _3kand b _3kcalculate L _3k, be final sectional dimension a ₃and b ₃calculate L ₃.

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