CN102968525B

CN102968525B - Method for determining overweight ratio of plane flutter model

Info

Publication number: CN102968525B
Application number: CN201210451712.6A
Authority: CN
Inventors: 罗务揆
Original assignee: Xian Aircraft Design and Research Institute of AVIC
Current assignee: Xian Aircraft Design and Research Institute of AVIC
Priority date: 2012-11-12
Filing date: 2012-11-12
Publication date: 2015-04-29
Anticipated expiration: 2032-11-12
Also published as: CN102968525A

Abstract

The invention belongs to the field of aviation structural mechanics, and relates to a design method for obtaining the overweight ratio of a flutter model in the design of the flutter model. The method comprises the following steps of: calculating the equivalent mass mBE of a reference beam frame according to a reference beam frame model, and calculating the equivalent mass ratio nBE of the reference beam frame in combination with the component mass mA; calculating a design scale coefficient ndss; specifying a section shape coefficient ns; specifying the mass ratio kb of a flutter model beam; and calculating the overweight ratio nG of the flutter model. In According to the method disclosed by the invention, a reverse design method is used for replacing a trial and error method adopted in the conventional model design, so that various factors possibly influencing model weight and mathematical relations thereof are considered at the start of model design, the overweight ratio of the model is further obtained, the uncertainty of model design is reduced, and the model design period is shortened greatly.

Description

Method for determining overweight ratio of airplane flutter model

Technical Field

The invention belongs to the field of aeronautical structure mechanics, and particularly relates to a method for determining an overweight ratio of an airplane flutter model.

Background

The flutter model can be used to obtain the flutter characteristics of the aircraft and its components. In flutter model design, the interference of overweight problem is often encountered, especially the design of high-speed flutter model usually needs small beam frame mass to provide large wing surface rigidity, and the overweight problem of flutter model design is more emphasized. In addition, for some low-speed flutter model design problems, the situation is just opposite, namely the target mass is overlarge, if the flutter model design meets the target mass, the static deformation of the model is larger, and further the test is not favorable, so that an 'overweight ratio' which is smaller than 1 in numerical value is correspondingly added.

In the past, a basic scale of model design is selected and a scale is derived, a certain structural form is selected according to working experience, a flutter model is directly designed, after a model main body is designed, comparison is carried out according to estimated quality and target quality, and if the estimated quality of a model exceeds the target quality, redesign is often carried out at an additional overweight ratio, or redesign is carried out after the structural form of the model and the design scale are adjusted. This method has the following disadvantages:

firstly, the model design seriously depends on the experience of designers, and the uncertainty of the model design is increased;

secondly, the super-weight ratio is acquired by carrying out multiple rounds of redesign and calculation, the time is long, the efficiency is low, and the design period of the model after severe dragging influences the development progress of the airplane.

Disclosure of Invention

The purpose of the invention is:

the invention aims to obtain a method for determining the overweight ratio of a flutter model, which improves the working efficiency, shortens the model design period and changes the original laggard method which depends heavily on experience and needs to be designed by repeated trial and error in the past.

The technical scheme of the invention is as follows:

a method for determining the overweight ratio of airplane flutter model features that the flutter model with reference beam frame is ensured, which includes the mass m of airplane_ABeam frame section characteristic moment of inertia I_x、I_yHarmonic polar moment of inertia J, high speed flutter model design basic scale speed-pressure ratio eta_qAnd density ratio η_ρOr the basic scale speed ratio eta of the low-speed flutter model_VAnd density ratio η_ρOn the basis of the above-mentioned parameters, determining overweight ratio n of flutter model design_G(ii) a Order toUnifying high and low speed flutter models; the specific determination steps are as follows:

step one, calculating the equivalent mass ratio n of the reference beam frame of the airplane_BEThe calculation method is as follows:

1.1, calculating to obtain the equivalent mass m of the reference beam frame_BE：

Moment of inertia I according to beam frame section characteristics_x、I_yAnd polar inertia moment J, calculating the corresponding rectangular section size with the lug, and further obtaining a reference beam frame model with the section size; giving a beam frame material density to obtain the equivalent mass m of the reference beam frame_BE(ii) a From the section characteristic moment of inertia I_x、I_yAnd the polar inertia moment J, the method for obtaining the rectangular section size with the lug is as follows:

1.1.1 for a rectangular cross-section, the iterative formula for the dimensions of the rectangular cross-section is:

wherein,

first, alpha is set to alpha₀0.96, with formula [1]B/a is calculated and is according to the formula [2 ]]Calculating alpha, substituting into equation [1 ]]Through iteration, alpha is converged to a stable value finally, and then a and b can be obtained;

1.1.2 for rectangular cross-section with ear, let the ear thickness

t＝0.2b ……………………………[3]

1.1.3 adjusting J

J1＝J-(t/2b)²] ……………………………[4]

1.1.4 according to the target value I_xAnd J₁And repeating the step 1.1.1 to obtain a₁And b₁；

1.1.5 according to the target value I_yAnd a₁、b₁And t value, obtaining the half width l of the section with the lug;

l = \sqrt[3]{\frac{{3 I}_{y} - {4 a}_{1}^{3} b_{1}}{2 t}} + a_{1}^{3} \begin{matrix} . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . \end{matrix} [5]

finally obtaining the cross section size 2a of the rectangular beam with the lug plates₁、2b₁T and 2 l;

1.2, calculating the equivalent mass ratio n of the reference beam frame_BE：

n_BE＝m_BE/m_A ……………………………[6]

Step two, calculating a coefficient n of a design scale_dss：

Step three, specifying a section shape coefficient n_s：

n_sThe designation of (c) is divided into two cases:

if the actually adopted main beam section form is also a rectangular beam section form with lugs

n_s＝1 ……………………………[8]

If the actually adopted section form of the main beam is a rectangular thin-walled beam with lugs, the section form of the main beam is as follows

0.3≤n_s≤1 ……………………………[9]

In this case n_sThe specific numerical value can be obtained according to specific conditions, and the specific method is obtained by adjusting the thickness parameter of the section thin wall;

step four, specifying the mass ratio k of the flutter model beam_b：

0.25≤k_b≤0.4 ……………………………[10]

Wherein,

in the case of the low-speed flutter model,k_bis small; in the case of the high-speed flutter model, k_b2, partial enlargement;

step five, calculating the overweight ratio n of the flutter model_G：

n_G＝n_sn_dssn_BE/k_b ……………………………[11]

Overweight ratio n of flutter model_GThe control is carried out in the following range as much as possible:

05≤n_G≤20 ……………………………[12]

if it is out of this range, the formula [7 ] can be adjusted]To the formula [10]Obtaining the overweight ratio n of the flutter model meeting the requirements_G；

If 0.9. ltoreq. n_GIf n is less than or equal to 1.1, directly taking n_G＝1。

The invention has the advantages that:

because the invention uses the reverse design thinking to replace the trial and error method adopted in the past model design, various factors which can influence the model weight and the mathematical relationship of the influencing factors are considered at the beginning of the model design, and the model overweight ratio is further obtained. According to the invention, the weight characteristic of the flutter model beam can be conveniently obtained only by adjusting related design parameters, so that the uncertainty of model design is reduced; the work which needs to be finished for several days in the past can be finished within several minutes at present, so that the model design period is greatly shortened; the invention has clear and smooth form, is very suitable for the programming and operation of various general calculation programs and is easy to be mastered by engineering technicians, thereby improving the design efficiency of the flutter model and bringing convenience to the test work of the flutter model and the development of an airplane.

Drawings

FIG. 1 is a schematic view in rectangular section; where a is the half width of the rectangle calculated in step one of the present invention; b is the half height of the rectangle calculated in step one of the present invention; the origin o of the two-dimensional coordinate system in fig. 1 is the center of the rectangle, the x-axis is parallel to the width direction of the rectangle, the positive direction is towards the right, and the positive direction of the y-axis is towards the upper.

FIG. 2 is a schematic view of a rectangular cross section with tabs; the two-dimensional coordinate system in fig. 2 is the same as in fig. 1. In the figure a₁Is the half width of the rectangle calculated in step one of the invention; b1 is the half height of the rectangle calculated in step one of the present invention, t is the thickness of the tab calculated in step one of the present invention; in the figure, l is the calculated half width of the cross section at the first step of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings, referring to fig. 1 and 2.

A method for determining the overweight ratio of airplane flutter model features that the flutter model with reference beam frame (including the mass m of airplane) is ensured_ABeam frame section characteristic moment of inertia I_x、I_yPolar moment of inertia J) and high-speed flutter model design basic scale speed-pressure ratio eta_qAnd density ratio η_ρOr the basic scale speed ratio eta of the low-speed flutter model_VAnd density ratio η_ρOn the basis of the above-mentioned parameters, determining overweight ratio n of flutter model design_G(ii) a The basic scale is defined in handbook of aeroelasticity mechanics of airplanes (tubular, published by aeronautical industry, 1994); order toTherefore, the high-speed flutter model and the low-speed flutter model can be unified under a set of design system; the specific determination steps are as follows:

1.1.1 referring to the rectangular cross-section shown in FIG. 1, the iterative formula for the dimensions of the rectangular cross-section:

wherein,

first, alpha is set to alpha₀0.96, with formula [1]B/a is calculated and is according to the formula [2 ]]Calculating alpha, substituting into equation [1 ]]Through iteration, α is finally converged to a stable value, and a and b can be obtained.

1.1.2 rectangular cross-section with ears as shown in reference to FIG. 2, making the ears thick

t＝0.2b ……………………………[3]

1.1.3 adjusting J

J₁＝J[1-(t/2b)²] ……………………………[4]

1.1.4 according to the target value I_xAnd J₁And repeating the step 1.1.1 to obtain a₁And b₁。

1.1.5 according to the target value I_yAnd a₁、b₁And t, the half width l of the section with the ear can be obtained.

l = \sqrt[3]{\frac{{3 I}_{y} - {4 a}_{1}^{3} b_{1}}{2 t}} + a_{1}^{3} \begin{matrix} . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . & . . . \end{matrix} [5]

Finally obtaining the cross section size 2a of the rectangular beam with the lug plates₁、2b₁T and 2 l.

1.2, calculating the equivalent mass ratio n of the reference beam frame_BE：

n_BE＝m_BE/m_A ……………………………[6]

n_BEThe structural efficiency of the aircraft component is reflected to a certain extent;

step two, calculating a coefficient n of a design scale_dss：

Step three, specifying a section shape coefficient n_s：

n_sThe physical meaning of the expression is that the moment of inertia I is the same in section characteristic_x、I_yAnd the ratio of the area corresponding to the actually adopted main beam section form to the area corresponding to the lug-carrying rectangular beam section form under the polar inertia moment J; there are two cases:

3.1, if the section form of the actually adopted main beam is also the section form of the rectangular beam with the lugs

n_s＝1 ……………………………[8]

3.2, if the actually adopted section form of the main beam is the section form of the rectangular thin-walled beam with the lugs, then

0.3≤n_s≤1 ……………………………[9]

step four, specifying the mass ratio k of the flutter model beam_b：

0.25≤k_b≤0.4 ……………………………[10]

Wherein,

in the case of the low-speed flutter model, k_bGenerally, the size is small; in the case of the high-speed flutter model, k_bGenerally, it is larger;

k_bthe physical meaning is the ratio of the beam mass in the flutter model to the total mass of the model;

step five, calculating the overweight ratio n of the flutter model_G：

n_G＝n_sn_dssn_BE/k_b ……………………………[11]

0.5≤n_G≤2.0 ……………………………[12]

Examples

Taking a low-speed and high-speed flutter model of a certain airplane wing and vertical fin as an example, calculating and verifying:

(1) calculating the equivalent mass m of the reference beam frame according to the reference beam frame model_BEMass m of the bonded member_ACalculating the equivalent mass ratio n of the reference beam frame_BE；

(2) Calculating the coefficient n of the design scale according to the basic scale of the flutter model design_dss；

(3) Specifying a coefficient of cross-sectional shape n_s；

(4) Mass ratio k of flutter mode beam_b；

(5) Calculating the overweight ratio n of the flutter model_G。

Table 1 shows the corresponding data results, and the units of the data are dimensionless. Because the method of the invention uses a reverse design method to replace the prior trial and error method, when the model is not designed, the overweight ratio of the flutter model can be obtained only according to the corresponding design parameters, the calculation efficiency is greatly improved, the work which needs to be finished for several days in the past can be finished, and only several minutes are needed at present.

TABLE 1 calculation data and result of overweight ratio of airplane flutter model

Claims

1. A method for determining the overweight ratio of airplane flutter model features that the flutter model with reference beam frame is ensured, which includes the mass m of airplane_ABeam frame section characteristic moment of inertia I_x、I_yHarmonic polar moment of inertia J, high speed flutter model design basic scale speed-pressure ratio eta_qAnd density ratio η_ρOr the basic scale speed ratio eta of the low-speed flutter model_VAnd density ratio η_ρOn the basis of the above-mentioned parameters, determining overweight ratio n of flutter model design_G(ii) a Order toUnifying high and low speed flutter models; the method is characterized by comprising the following specific steps of:

wherein,

first, alpha is set to alpha₀0.96, with formula [1]B/a is calculated and is according to the formula [2 ]]Calculating alpha, substituting into equation [1 ]]Through iteration, alpha is converged to a stable value finally, and then a and b can be obtained; wherein a is the half width of the rectangle calculated in the step; b is the half height of the rectangle calculated in this step;

1.1.2 for rectangular cross-section with ear, let the ear thickness

t＝0.2b……………………………[3]

1.1.3 adjusting J

J₁＝J[1-(t/2b)²]……………………………[4]

1.1.4 according to the target value I_xAnd J₁And repeating the step 1.1.1 to obtain a₁And b₁(ii) a Wherein a is₁Is the half width of the rectangle calculated in this step; b₁Is the half height of the rectangle calculated in this step;

l = \sqrt[3]{\frac{{3 I}_{y} - {4 a}_{1}^{3} b_{1}}{2 t} + a_{1}^{3}} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [5]

1.2, calculating the equivalent mass ratio n of the reference beam frame_BE：

n_BE＝m_BE/m_A……………………………[6]

Step two, calculating a coefficient n of a design scale_dss：

Step three, specifying a section shape coefficient n_s：

n_sThe designation of (c) is divided into two cases:

n_s＝1……………………………[8]

0.3≤n_s≤1……………………………[9]

step four, specifying the mass ratio k of the flutter model beam_b：

0.25≤k_b≤0.4……………………………[10]

Wherein,

in the case of the low-speed flutter model, k_bIs small; in the case of the high-speed flutter model, k_b2, partial enlargement;

step five, calculating the overweight ratio n of the flutter model_G：

n_G＝n_sn_dssn_BE/k_b……………………………[11]

0.5≤n_G≤2.0……………………………[12]

If it is not0.9≤n_GIf n is less than or equal to 1.1, directly taking n_G＝1。