CN103577649A - Method for determining goods cabin floor load when transportation aircraft drops goods - Google Patents

Abstract

The invention belongs to the technical field of aircraft flying load design, and relates to the improvement on a method for determining a goods cabin floor load when a transportation aircraft drops goods. The method for determining the goods cabin floor load is characterized by comprising the step of initializing aircraft air-dropping goods parameters, the step of analyzing aircraft limited element modals, the step of carrying out aircraft non-steady aerodynamic calculation, the step of calculating an aircraft air-dropping goods dynamic response, the step of calculating a goods cabin floor structure load dynamic response and the step of determining the design load of a goods cabin floor in the process of air-dropping. By means of the improved method for determining the goods cabin floor load when the transportation aircraft drops the goods, the determining precision of the goods cabin floor load is improved, and the structural safety of the goods cabin floor and the flying safety of the aircraft are guaranteed.

Description

Definite method of cargo deck load during airplane in transportation category cargo dropping

Technical field

The invention belongs to aircraft flight load design field, the improvement of definite method of cargo deck load while relating to airplane in transportation category cargo dropping.

Background technology

Air-drop is one of important process pattern of airplane in transportation category.During air-drop, generally need to determine the design load of the parts such as aircraft hold floor, goods bridge, web member, wing.During current airplane in transportation category cargo dropping, aircraft is considered as to rigid body, only consider the pneumostatic dynamic elasticity correction of aerodynamic force, rely on rigid body fight dynamics equation to solve, concrete technology is shown in document: " the flight dynamics building model and simulation of transporter air-drop ", Yang Miaosheng, Qu Xiangju, < < flight mechanics > >, 2010,28 volumes (the 3rd phase), P.9-12.

During current airplane in transportation category cargo dropping, the shortcoming of definite method of cargo deck load is: the first, determined cargo deck load error is large.Because airplane in transportation category has the advantages that structural flexibility is large, frequency is low, cargo dropping, the especially excitation load of reshipment air-drop process have wider frequency band, can encourage the vibration of the more Elastic mode of aircraft, and this dynamic response may be become larger by aeroelasticity effect, and then causing the increase of aircaft configuration load, these can cause adverse influence to the safety of structure of aircraft and flight safety.The second, in For Elastic Aircraft cargo dropping dynamic response modeling process, do not consider moving process in cargo compartment, discrete fitful wind excitation load does not superpose in air-drop process, the deficiency of these work had both been difficult to meet the requirement of airplane design standard, also in the time of can causing aircraft cargo air-drop, cargo deck design load is less than normal, and then the safety of structure of aircraft and flight safety are caused to adverse influence.

Summary of the invention

The object of the invention is: a kind of definite method of cargo deck load when improved airplane in transportation category cargo dropping is provided, to improve definite precision of cargo deck load, guarantees the safety of structure of cargo deck and the flight safety of aircraft.

Technical scheme of the present invention is: definite method of cargo deck load during airplane in transportation category cargo dropping, it is characterized in that, and determine that the step of cargo deck load is as follows:

1, airplane air dropping goods parameter initialization: carry out airplane air dropping goods parameter initialization according to the air-drop fitful wind criterion in national military standard GJB67.2A-2008, need initialized para-cargo parameter to be: finite element model FEM, the quality m of aircraft of input aircraft _a, aircraft flight height H, aircraft flight speed V, mean aerodynamic chord c, goods quality m _b, the initial " loaded " position x of goods in aircraft hold ₀, goods moment of inertia I _by, the acceleration a that moves in cargo hold of goods _b, mode number k, discrete fitful wind intensity u _w, discrete fitful wind yardstick L _w;

2, aircraft finite element modal analysis: finite element model FEM, the mode number k of above-mentioned aircraft of take be to control parameter, adopt Nastran software to carry out model analysis to the finite element model FEM of aircraft, obtain the modal matrix Φ of aircraft, the vibration circular frequency of every rank mode, general mass matrix M _qqwith the generalized stiffness matrix K _qq, the rigid motion mode that modal matrix Φ comprises aircraft and elastic vibration mode;

3, the non-Unsteady Flow matrix of coefficients of aircraft calculates: with above-mentioned modal matrix Φ, aircraft flight height H, aircraft flight speed V, mean aerodynamic chord c, discrete fitful wind intensity u _wwith discrete fitful wind yardstick L _wfor input variable, carry out the non-Unsteady Flow matrix of coefficients of time domain and calculate, adopt subsonic speed Doubiet Lattice Method to calculate the non-Unsteady Flow matrix of coefficients Q that structural vibration causes _a, adopt fitful wind hybrid modeling method to calculate the wind-induced exciting force matrix of coefficients Q of battle array _w;

4, airplane air dropping goods dynamic response calculates:

4.1, reconstruct For Elastic Aircraft cargo dropping dynamic response differential matrix equation: at 12 parameters of step 1, the modal matrix Φ of step 2, the vibration circular frequency of every rank mode, general mass matrix M _qqwith the generalized stiffness matrix K _qqthe non-Unsteady Flow matrix of coefficients Q causing with the structural vibration of step 3 _aand the wind-induced exciting force matrix of coefficients Q of battle array _wbasis on, reconstruct For Elastic Aircraft cargo dropping dynamic response differential matrix equation:

$\begin{array}{c}(M_{\mathrm{qq}}+{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_b{\mathrm{\&Phi;}}_{\mathrm{bz}})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&xi;}}+[{\left(\frac{{\&PartialD;\mathrm{\&Phi;}}_{\mathrm{bz}}}{\&PartialD;x}\right)}^T{m}_b{V}_{b2a}{\mathrm{\&Phi;}}_{\mathrm{bz}}+{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_b{V}_{b2a}\frac{\&PartialD;{\mathrm{\&Phi;}}_{\mathrm{bz}}}{\&PartialD;x}]\stackrel{\&CenterDot;}{\mathrm{\&xi;}}+K_{\mathrm{qq}}\mathrm{\&xi;}=\\ Q_a\mathrm{\&xi;}+Q_w{u}_w-\begin{array}{}\end{array}\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]g-{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_{b}g\end{array}---\left(1\right)$

Wherein, ξ is the generalized coordinate displacement corresponding to modal matrix Φ, comprises the generalized coordinate displacement of rigid motion mode and the generalized coordinate displacement of elastic vibration mode corresponding to aircraft;

for the generalized coordinate speed corresponding to modal matrix Φ, comprise the generalized coordinate speed of rigid motion mode and the generalized coordinate speed of elastic vibration mode corresponding to aircraft;

for the generalized coordinate acceleration corresponding to modal matrix Φ, comprise the generalized coordinate acceleration of rigid motion mode and the generalized coordinate acceleration of elastic vibration mode corresponding to aircraft; Φ _bzaircraft Modes matrix component for place, goods present position; V _b2afor the movement velocity of goods relative aircraft in cargo hold, by the acceleration a that goods is moved in cargo hold _ban integration can obtain; X is the displacement of goods in cargo hold, by the acceleration a that goods is moved in cargo hold _btwice integration can obtain; Q _aξ is the non-Unsteady Flow that the structural vibration of aircraft causes; Q _wu _wfor the wind-induced exciting force of battle array; G is acceleration of gravity; $\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]$ It is a column vector that length is k;

For utilizing Runge-Kutta method to solve differential matrix equation, formula (1) is organized into single order differential matrix equation:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{ae}}=A_{\mathrm{ae}}{x}_{\mathrm{ae}}+B_{\mathrm{aw}}{u}_w+B_{\mathrm{ag}}{m}_{b}g---\left(2\right)$

Wherein, A _aestate matrix for For Elastic Aircraft body and non-Unsteady Flow composition system; B _awfor the perturbation matrix of discrete fitful wind to For Elastic Aircraft dynamic response; B _agfor because goods movement produces the perturbation matrix of acting force to aircraft; u _wfor discrete fitful wind intensity; x _aefor state vector:

$x_{\mathrm{ae}}=\left[\begin{array}{c}{x}_a\\ \mathrm{\&xi;}\\ \stackrel{\&CenterDot;}{\mathrm{\&xi;}}\end{array}\right]---\left(3\right)$

Wherein, x _afor the hysteresis root Element of non-Unsteady Flow, the whirlpool that simulation comes off from plane airfoil;

4.2, solve generalized coordinate displacement ξ when aircraft 1g is flat to fly ^trim: aircraft 1g puts down while flying and meets the following conditions:

4.2.1, generalized coordinate acceleration

with generalized coordinate speed

be null vector;

4.2.2, the relative airplane motion speed of goods and displacement are 0;

4.2.3, without discrete fitful wind exciting force;

According to above-mentioned condition, aircraft 1g puts down the generalized coordinate displacement ξ while flying ^trimcalculating as shown in formula (4):

${\mathrm{\&xi;}}^{\mathrm{Trim}}=-{(K_{\mathrm{qq}}-Q_a)}^{-1}(\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]+{\mathrm{\&Phi;}}_{\mathrm{bz}0}^T{m}_b)g---\left(4\right)$

Wherein, Φ _bz0modal matrix component for goods aircraft of initial stowage position in cargo hold;

4.3, solve aircraft cargo air-drop dynamic response differential matrix equation: the generalized coordinate displacement ξ while flying so that aircraft 1g is flat ^trimfor the initial solving condition of formula (2), adopt variable step Runge-Kutta method to solve aircraft cargo air-drop dynamic response differential matrix equation, obtain dynamic response, the generalized coordinate speed of the generalized coordinate displacement ξ of aircraft

dynamic response and generalized coordinate acceleration

dynamic response:

$y_{\mathrm{ae}}=\left[\begin{array}{c}\mathrm{\&xi;}\\ \stackrel{\&CenterDot;}{\mathrm{\&xi;}}\\ \stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&xi;}}\end{array}\right]=C_{\mathrm{ae}}{x}_{\mathrm{ae}}+D_{\mathrm{aw}}{u}_w+D_{\mathrm{ag}}{m}_{b}g---\left(5\right)$

Wherein, C _aeoutput matrix for For Elastic Aircraft body and non-Unsteady Flow composition system; D _awfor the transfer matrix of discrete fitful wind to the output of For Elastic Aircraft dynamic response; D _agfor the transfer matrix of aircraft dynamic response being exported due to goods movement;

5, calculate cargo deck load dynamic response: according to dynamic response, the generalized coordinate speed of the generalized coordinate displacement ξ of the aircraft of step 4

dynamic response and generalized coordinate acceleration

dynamic response, calculate the used load of goods to aircraft hold floor dynamic response, shown in (6):

${\stackrel{\&RightArrow;}{F}}_{b2a}\left(t\right)=-m_b({\stackrel{\&RightArrow;}{a}}_{\mathrm{CG}}+\stackrel{\stackrel{\&RightArrow;}{\&CenterDot;}}{q}\&times;{\stackrel{\&RightArrow;}{X}}_b+2\stackrel{\&RightArrow;}{q}\&times;{\stackrel{\&RightArrow;}{V}}_{b2a}-\stackrel{\&RightArrow;}{g})---\left(6\right)$

Wherein, acceleration for aircraft barycenter place;

angle of pitch acceleration for aircraft;

rate of pitch for aircraft;

for the distance of goods apart from aircraft barycenter;

The design load of cargo deck while 6, determining air-drop: according to the cargo deck load dynamic response obtaining in step 5

select

maximum value and minimal value as the air-drop design load of cargo deck.

Advantage of the present invention is: a kind of definite method of cargo deck load when improved airplane in transportation category cargo dropping is provided, improved definite precision of cargo deck load, and guaranteed the safety of structure of cargo deck and the flight safety of aircraft.

Accompanying drawing explanation

Fig. 1 is the dynamic response figure of the goods of one embodiment of the invention to aircraft hold floor load, transverse axis is the time, the longitudinal axis is that goods is to aircraft hold floor load, the dynamic response of the goods that represents to have in air-drop process fitful wind excitation with the curve of circle to aircraft hold floor load, with the curve of triangle, represent in air-drop process goods without the fitful wind excitation dynamic response to aircraft hold floor load, the goods of the fitful wind that superposes in as can be seen from the figure air-drop process excitation to aircraft hold floor load than large to aircraft hold floor load without the goods of fitful wind excitation.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.During airplane in transportation category cargo dropping, definite method of cargo deck load, is characterized in that, determines that the step of cargo deck load is as follows:

1, airplane air dropping goods parameter initialization: carry out airplane air dropping goods parameter initialization according to the air-drop fitful wind criterion in national military standard GJB67.2A-2008, need initialized para-cargo parameter to be: finite element model FEM, the quality m of aircraft of input aircraft _a, aircraft flight height H, aircraft flight speed V, mean aerodynamic chord c, goods quality m _b, the initial " loaded " position x of goods in aircraft hold ₀, goods moment of inertia I _by, the acceleration a that moves in cargo hold of goods _b, mode number k, discrete fitful wind intensity u _w, discrete fitful wind yardstick L _w;

In above-mentioned 12 parameters, the finite element model FEM of aircraft is important input of the present invention, the finite element model FEM of general aircraft is roof beam structure model, the finite element model FEM of aircraft reduces degree of freedom (DoF) to true aircraft by static(al) polycondensation and obtains, wherein corresponding point concentrates mass distribution to finite element node, can greatly reduce like this analysis degree of freedom of aircraft, the definite speed of cargo deck load while improving airplane in transportation category cargo dropping; The mode of choosing the 0～20Hz that need to cover aircraft of mode number k, the dynamic response result that simulation calculation obtains like this has enough precision; Other 10 parameters require to carry out initialization according to the air-drop fitful wind criterion in national military standard GJB67.2A-2008;

2, aircraft finite element modal analysis: finite element model FEM, the mode number k of above-mentioned aircraft of take be to control parameter, adopt Nastran software to carry out model analysis to aircraft finite element model, obtain the modal matrix Φ of aircraft, the vibration circular frequency of every rank mode, general mass matrix M _qqwith the generalized stiffness matrix K _qq, the rigid motion mode that modal matrix Φ comprises aircraft and elastic vibration mode;

The present invention adopts " stablizing mode substrate method " thought, aircraft finite element model is only carried out to a model analysis, the modal matrix Φ obtaining, carries out in cargo dropping dynamic response computation process at aircraft, by the project in the linear combination renewal equation to modal matrix Φ; Technology is shown in document " to stablize mode substrate method ": " A general approach to modal analysis for time-varying system ", Browder A M, AIAA88-2356,1988;

Aircraft is an aircraft for middle free flight on high, must consider its rigid motion mode; Aircraft is subject to the external load function motion that also can deform, also need to consider its elastic vibration mode, based on mode superposition theory, can obtain by the rigid motion mode to aircraft and the linear combination of elastic vibration mode displacement and the distortion of any point on aircraft, these displacements and distortion are the inputs that the non-Unsteady Flow of aircraft calculates; FEM model analysis principle is shown in document: " Aeroelastic analysis user ' s guide ", MSC.Software Corporation, MSC.Software Corporation, 2004;

3, the non-Unsteady Flow matrix of coefficients of aircraft calculates: with above-mentioned modal matrix Φ, aircraft flight height H, aircraft flight speed V, mean aerodynamic chord c, discrete fitful wind intensity u _wwith discrete fitful wind yardstick L _wfor input variable is carried out the calculating of the non-Unsteady Flow matrix of coefficients of time domain, adopt subsonic speed Doubiet Lattice Method to calculate the non-Unsteady Flow matrix of coefficients Q that structural vibration causes _a, adopt fitful wind hybrid modeling method to calculate the wind-induced exciting force matrix of coefficients Q of battle array _w, Q _aand Q _wall by ZAERO software, calculated and obtained, their Computing Principle is shown in document: " ZAERO theoretical manual ", ZONA Technology, Inc, ZONA Technology, Inc, 2008;

4, airplane air dropping goods dynamic response calculates:

4.1, reconstruct For Elastic Aircraft cargo dropping dynamic response differential matrix equation: aircraft carries out needing in cargo dropping process the air-drop design load of definite cargo deck, this dynamic response equation that just need to carry out the whole process of cargo dropping to aircraft is reconstructed, the action Mechanics Simulation of going forward side by side; The invention provides a kind of reconstructing method of airplane in transportation category cargo dropping dynamic response equation, shown in (7), at 12 parameters of step 1, the modal matrix Φ of step 2, the vibration circular frequency of every rank mode, general mass matrix M _qqwith the generalized stiffness matrix K _qqthe non-Unsteady Flow matrix of coefficients Q causing with the structural vibration of step 3 _aand the wind-induced exciting force matrix of coefficients Q of battle array _wbasis on, reconstruct For Elastic Aircraft cargo dropping dynamic response differential matrix equation:

$\begin{array}{c}(M_{\mathrm{qq}}+{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_b{\mathrm{\&Phi;}}_{\mathrm{bz}})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&xi;}}+[{\left(\frac{{\&PartialD;\mathrm{\&Phi;}}_{\mathrm{bz}}}{\&PartialD;x}\right)}^T{m}_b{V}_{b2a}{\mathrm{\&Phi;}}_{\mathrm{bz}}+{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_b{V}_{b2a}\frac{\&PartialD;{\mathrm{\&Phi;}}_{\mathrm{bz}}}{\&PartialD;x}]\stackrel{\&CenterDot;}{\mathrm{\&xi;}}+K_{\mathrm{qq}}\mathrm{\&xi;}=\\ Q_a\mathrm{\&xi;}+Q_w\mathrm{\&xi;}-\begin{array}{}\end{array}\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]g-{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_{b}g\end{array}---\left(7\right)$

Wherein, ξ is the generalized coordinate displacement corresponding to modal matrix Φ, comprises the generalized coordinate displacement of rigid motion mode and the generalized coordinate displacement of elastic vibration mode corresponding to aircraft;

for the generalized coordinate speed corresponding to modal matrix Φ, comprise the generalized coordinate speed of rigid motion mode and the generalized coordinate speed of elastic vibration mode corresponding to aircraft;

for the generalized coordinate acceleration corresponding to modal matrix Φ, comprise the generalized coordinate acceleration of rigid motion mode and the generalized coordinate acceleration of elastic vibration mode corresponding to aircraft; Φ _bzfor the modal components at place, goods present position, due to the movement of goods in aircraft hold, Φ _bzfor time dependent variable, by obtaining modal matrix Φ interpolation, goods leaves Φ after aircraft _bz=0, mode interpolation method is shown in document: " aircraft aeroelasticity handbook ", Guan De, aircraft industry publishing house, 1994; V _b2afor the movement velocity of goods relative aircraft in cargo hold, by the acceleration a that goods is moved in cargo hold _ban integration can obtain; X is the displacement of goods in cargo hold, by the acceleration a that goods is moved in cargo hold _btwice integration can obtain; Q _aξ is the non-Unsteady Flow that the structural vibration of aircraft causes; Q _wu _wfor the wind-induced exciting force of battle array; G is acceleration of gravity; $\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]$ It is a column vector that length is k;

In order to utilize Runge-Kutta method to solve differential matrix equation, formula (7) need to be arranged for single order differential matrix equation:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{ae}}=A_{\mathrm{ae}}{x}_{\mathrm{ae}}+B_{\mathrm{aw}}{u}_w+B_{\mathrm{ag}}{m}_{b}g---\left(8\right)$

Wherein, A _aestate matrix for For Elastic Aircraft body and non-Unsteady Flow composition system; B _awfor the perturbation matrix of discrete fitful wind to For Elastic Aircraft dynamic response; B _agfor because goods movement produces the perturbation matrix of acting force to aircraft; u _wfor discrete fitful wind intensity; x _aefor state vector:

$x_{\mathrm{ae}}=\left[\begin{array}{c}{x}_a\\ \mathrm{\&xi;}\\ \stackrel{\&CenterDot;}{\mathrm{\&xi;}}\end{array}\right]---\left(9\right)$

Wherein, x _afor the hysteresis root Element of non-Unsteady Flow, the whirlpool that simulation comes off from plane airfoil, concrete calculating seen document: " ZAERO theoretical manual ", ZONA Technology, Inc, ZONA Technology, Inc, 2008;

4.2, solve generalized coordinate displacement ξ when aircraft 1g is flat to fly ^trim: aircraft 1g puts down while flying and meets the following conditions:

4.2.1, generalized coordinate acceleration

with generalized coordinate speed

be zero;

4.2.2, the relative airplane motion speed of goods and displacement are 0;

4.2.3, without discrete fitful wind disturbance;

According to above-mentioned condition, aircraft 1g puts down the generalized coordinate displacement ξ while flying ^trimcalculating as shown in formula (10):

${\mathrm{\&xi;}}^{\mathrm{Trim}}=-{(K_{\mathrm{qq}}-Q_a)}^{-1}(\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]+{\mathrm{\&Phi;}}_{\mathrm{bz}0}^T{m}_b)g---\left(10\right)$

Wherein, Φ _bz0modal matrix component for goods aircraft of initial stowage position in cargo hold;

Formula (10) is for surely separating Algebraic Equation set, the generalized coordinate displacement ξ in the time of can obtaining by algebraic operation that aircraft 1g is flat to fly ^trim;

4.3, solve aircraft cargo air-drop dynamic response differential matrix equation: definite dynamic response, generalized coordinate speed being by generalized coordinate displacement ξ of any one components ' load of aircraft

dynamic response and generalized coordinate acceleration

dynamic response and the computing of modal matrix Φ realize; Determining of cargo deck load need to realize by the dynamic response of mode generalized coordinate displacement ξ; Generalized coordinate displacement ξ while flying so that aircraft 1g is flat ^trimfor the initial solving condition of formula (8), adopt variable step Runge-Kutta method to solve aircraft cargo air-drop dynamic response differential matrix equation, obtain dynamic response, the generalized coordinate speed of generalized coordinate displacement ξ

dynamic response and generalized coordinate acceleration

dynamic response:

$y_{\mathrm{ae}}=\left[\begin{array}{c}\mathrm{\&xi;}\\ \stackrel{\&CenterDot;}{\mathrm{\&xi;}}\\ \stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&xi;}}\end{array}\right]=C_{\mathrm{ae}}{x}_{\mathrm{ae}}+D_{\mathrm{aw}}{u}_w+D_{\mathrm{ag}}{m}_{b}g---\left(11\right)$

Wherein, C _aeoutput matrix for For Elastic Aircraft body and non-Unsteady Flow composition system; D _awfor the transfer matrix of discrete fitful wind to the output of For Elastic Aircraft dynamic response; D _agfor the transfer matrix of aircraft dynamic response being exported due to goods movement;

5, calculate cargo deck load dynamic response: according to dynamic response, the generalized coordinate speed of the generalized coordinate displacement ξ of the aircraft of step 4

dynamic response and generalized coordinate acceleration

dynamic response, calculate the used load of goods to aircraft hold floor dynamic response, shown in (12)::

${\stackrel{\&RightArrow;}{F}}_{b2a}\left(t\right)=-m_b({\stackrel{\&RightArrow;}{a}}_{\mathrm{CG}}+\stackrel{\stackrel{\&RightArrow;}{\&CenterDot;}}{q}\&times;{\stackrel{\&RightArrow;}{X}}_b+2\stackrel{\&RightArrow;}{q}\&times;{\stackrel{\&RightArrow;}{V}}_{b2a}-\stackrel{\&RightArrow;}{g})---\left(12\right)$

Wherein, acceleration for aircraft barycenter place;

angle of pitch acceleration for aircraft;

rate of pitch for aircraft;

for the distance of goods apart from aircraft barycenter, the displacement x by goods in cargo hold and subtracting each other of the centroid position of aircraft obtain; According to the dynamic response of generalized coordinate displacement ξ, generalized coordinate speed

dynamic response and generalized coordinate acceleration

dynamic response, with

computing method see document: " ZAERO theoretical manual ", ZONA Technology, Inc, ZONA Technology, Inc, 2008;

The design load of cargo deck while 6, determining air-drop: the cargo deck load obtaining in step 5

dynamic response result be not the final design load of cargo deck, select in maximum value and minimal value as the air-drop design load of cargo deck.

Principle of work of the present invention is: two shortcomings of definite method of cargo deck load during for current airplane in transportation category cargo dropping: the first, determined cargo deck load error is large; The second,, in For Elastic Aircraft cargo dropping dynamic response modeling process, do not consider moving process in cargo compartment, discrete fitful wind exciting force does not superpose in air-drop process.Definite precision of cargo deck load when the present invention takes following measures to improve airplane in transportation category cargo dropping:

(1) take the finite element model FEM of aircraft is main foundation, and airplane in transportation category cargo dropping process is carried out to the reconstruct of kinetics equation; Based on mode superposition theory, utilize the rigid motion mode of aircraft and the elastic vibration mode of aircraft by linear combination, to represent the motion and deformation of aircraft, this method has improved the precision that airplane motion and distortion are described;

(2) in setting up the process of airplane in transportation category cargo dropping dynamic response differential matrix equation, consider the moving process of goods in aircraft hold, set up the dynamic response equation that can more truly reflect cargo movement process;

(3) in cargo dropping process, transporter has been superposeed and met the discrete fitful wind that national military standard GJB67.2A-2008 requires, be that gust velocity section shape is that 1-cos shape, equivalent gust velocity are 7.6m/s, by such calculating, cargo deck design load more accurately in the time of can obtaining cargo dropping;

(4) mode of aircraft finite element model FEM solves with the calculating of non-Unsteady Flow matrix of coefficients and all adopts maturation, stable, reliable business software, computational solution precision is high, and during for airplane in transportation category cargo dropping, cargo deck load definite provides reliable input data.

Embodiment

Adopt the present invention, when definite certain type transporter is carried out to cargo dropping, cargo deck load has been carried out simulation calculation.

Certain type transporter is separated into finite element model FEM, so just aircraft simulation can be become to For Elastic Aircraft; The mass ratio of goods and aircraft is 0.13; The barycenter place that the initial " loaded " position of goods in aircraft hold is aircraft; The translational acceleration a of goods in cargo hold _bfor 2.5m/s ²; The flying height H of aircraft is 30m; The flying speed V of aircraft is 150m/s; Mean aerodynamic chord c is 4.5m; Choose the front 40 rank mode of aircraft; The discrete fitful wind intensity of equivalent u _wfor 7.6m/s; Discrete fitful wind yardstick L _wfor 112.5m.Take above-mentioned parameter as initiation parameter.

Utilize business software Nastran to carry out model analysis to the finite element model FEM of aircraft, obtain the front 40 rank modal matrix Φ of aircraft, and vibration circular frequency, the general mass matrix M of the every rank mode corresponding with modal matrix Φ _qqwith the generalized stiffness matrix K _qq, 6 rigid motion mode that front 6 rank of modal matrix Φ are transporter, the elastic vibration mode that 34 remaining rank mode are transporter.

Above-mentioned modal matrix Φ, aircraft flight height 30m, aircraft flight speed 150m/s, mean aerodynamic chord 4.5m, equivalent discrete fitful wind intensity 7.6m/s and discrete fitful wind yardstick 112.5m are input in business software ZAERO, carry out the non-Unsteady Flow matrix of coefficients of time domain and calculate; The non-Unsteady Flow matrix of coefficients Q that selects subsonic speed Doubiet Lattice Method to cause structural vibration in software ZAERO _acalculate; In software ZAERO, select fitful wind hybrid modeling method to be poised for battle wind-induced exciting force matrix of coefficients Q _wcalculate.

By modal matrix Φ, general mass matrix M _qq, the generalized stiffness matrix K _qq, goods and aircraft the non-Unsteady Flow matrix of coefficients Q that causes of the discrete fitful wind intensity of quality, equivalent 7.6m/s, structural vibration _awith the wind-induced exciting force matrix of coefficients of battle array Q _wsubstitution For Elastic Aircraft cargo dropping dynamic response differential matrix equation, be in formula (8), complete the reconstruct to For Elastic Aircraft cargo dropping dynamic response differential matrix equation.

Initial " loaded " position-aircraft barycenter place according to goods in aircraft hold, carries out to modal matrix Φ the modal matrix component Φ that interpolation obtains goods initial stowage position in cargo hold _bz0, and then utilize generalized coordinate displacement ξ when aircraft 1g is flat to fly ^trimcomputing formula (10) calculate generalized coordinate displacement ξ ^trim.

Generalized coordinate displacement ξ while flying so that aircraft 1g is flat ^trimfor the initial solving condition of formula (8), adopt variable step Runge-Kutta method to solve aircraft cargo air-drop dynamic response differential matrix equation, detailed process is: the translational acceleration 2.5m/s according to goods in cargo hold ², the movement velocity V of integral and calculating goods current time _b2adisplacement x with relative cargo hold; Modal matrix Φ is carried out to the modal matrix component Φ that mode interpolation obtains place, goods current time present position _bz; V based on current time _b2a, x and Φ _bz, the project in new formula (8) more; Adopt Runge-Kutta method iteration one step, complete a step simulation calculation.Meanwhile, utilize formula (11) to obtain dynamic response, the generalized coordinate speed of the generalized coordinate displacement ξ of aircraft

dynamic response and generalized coordinate acceleration

dynamic response.

According to dynamic response, the generalized coordinate speed of the above-mentioned generalized coordinate displacement ξ calculating

dynamic response and generalized coordinate acceleration

dynamic response, utilize formula (12) to calculate the dynamic response of goods to the used load of cargo deck

Select

in maximum value and minimal value as the air-drop design load of cargo deck, for the Structural Strength Design of cargo deck.

Simulation result as shown in Figure 1, in figure, contrasted the dynamic response result to cargo deck with/without the goods in fitful wind excitation situation, transverse axis is the time, and the goods of the fitful wind that superposes in as can be seen from the figure air-drop process excitation is larger to aircraft hold floor load than the goods encouraging without fitful wind to aircraft hold floor load.

By the analysis of simulation result to embodiment, while showing the present invention to airplane in transportation category cargo dropping process, definite result rule of cargo deck load is good, numerical value magnitude is suitable; When carrying out airplane in transportation category cargo dropping process in the deterministic process of cargo deck load, must be in strict accordance with the air-drop fitful wind criterion of national military standard GJB67.2A-2008, stack meets the discrete fitful wind of code requirement, to reach the boundary value of cargo deck air-drop design load.

Claims (1)

1. definite method of cargo deck load during airplane in transportation category cargo dropping, is characterized in that, determines that the step of cargo deck load is as follows:

1.1, airplane air dropping goods parameter initialization: carry out airplane air dropping goods parameter initialization according to the air-drop fitful wind criterion in national military standard GJB67.2A-2008, need initialized para-cargo parameter to be: finite element model FEM, the quality m of aircraft of input aircraft _a, aircraft flight height H, aircraft flight speed V, mean aerodynamic chord c, goods quality m _b, the initial " loaded " position x of goods in aircraft hold ₀, goods moment of inertia I _by, the acceleration a that moves in cargo hold of goods _b, mode number k, discrete fitful wind intensity u _w, discrete fitful wind yardstick L _w;

1.2, aircraft finite element modal analysis: finite element model FEM, the mode number k of above-mentioned aircraft of take be to control parameter, adopt Nastran software to carry out model analysis to the finite element model FEM of aircraft, obtain the modal matrix Φ of aircraft, the vibration circular frequency of every rank mode, general mass matrix M _qqwith the generalized stiffness matrix K _qq, the rigid motion mode that modal matrix Φ comprises aircraft and elastic vibration mode;

1.3, the non-Unsteady Flow matrix of coefficients of aircraft calculates: with above-mentioned modal matrix Φ, aircraft flight height H, aircraft flight speed V, mean aerodynamic chord c, discrete fitful wind intensity u _wwith discrete fitful wind yardstick L _wfor input variable, carry out the non-Unsteady Flow matrix of coefficients of time domain and calculate, adopt subsonic speed Doubiet Lattice Method to calculate the non-Unsteady Flow matrix of coefficients Q that structural vibration causes _a, adopt fitful wind hybrid modeling method to calculate the wind-induced exciting force matrix of coefficients Q of battle array _w;

1.4, airplane air dropping goods dynamic response calculates:

1.4.1, reconstruct For Elastic Aircraft cargo dropping dynamic response differential matrix equation: at 12 parameters of step 1.1, the modal matrix Φ of step 1.2, the vibration circular frequency of every rank mode, general mass matrix M _qqwith the generalized stiffness matrix K _qqthe non-Unsteady Flow matrix of coefficients Q causing with the structural vibration of step 1.3 _aand the wind-induced exciting force matrix of coefficients Q of battle array _wbasis on, reconstruct For Elastic Aircraft cargo dropping dynamic response differential matrix equation:

$\begin{array}{c}(M_{\mathrm{qq}}+{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_b{\mathrm{\&Phi;}}_{\mathrm{bz}})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&xi;}}+[{\left(\frac{{\&PartialD;\mathrm{\&Phi;}}_{\mathrm{bz}}}{\&PartialD;x}\right)}^T{m}_b{V}_{b2a}{\mathrm{\&Phi;}}_{\mathrm{bz}}+{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_b{V}_{b2a}\frac{\&PartialD;{\mathrm{\&Phi;}}_{\mathrm{bz}}}{\&PartialD;x}]\stackrel{\&CenterDot;}{\mathrm{\&xi;}}+K_{\mathrm{qq}}\mathrm{\&xi;}=\\ Q_a\mathrm{\&xi;}+Q_w{u}_w-\begin{array}{}\end{array}\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]g-{\mathrm{\&Phi;}}_{\mathrm{bz}}^T{m}_{b}g\end{array}---\left(1\right)$

Wherein, ξ is the generalized coordinate displacement corresponding to modal matrix Φ, comprises the generalized coordinate displacement of rigid motion mode and the generalized coordinate displacement of elastic vibration mode corresponding to aircraft;

for the generalized coordinate speed corresponding to modal matrix Φ, comprise the generalized coordinate speed of rigid motion mode and the generalized coordinate speed of elastic vibration mode corresponding to aircraft;

for the generalized coordinate acceleration corresponding to modal matrix Φ, comprise the generalized coordinate acceleration of rigid motion mode and the generalized coordinate acceleration of elastic vibration mode corresponding to aircraft; Φ _bzaircraft Modes matrix component for place, goods present position; V _b2afor the movement velocity of goods relative aircraft in cargo hold, by the acceleration a that goods is moved in cargo hold _ban integration can obtain; X is the displacement of goods in cargo hold, by the acceleration a that goods is moved in cargo hold _btwice integration can obtain; Q _aξ is the non-Unsteady Flow that the structural vibration of aircraft causes; Q _wu _wfor the wind-induced exciting force of battle array; G is acceleration of gravity; $\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]$ It is a column vector that length is k;

For utilizing Runge-Kutta method to solve differential matrix equation, formula (1) is organized into single order differential matrix equation:

${\stackrel{\&CenterDot;}{x}}_{\mathrm{ae}}=A_{\mathrm{ae}}{x}_{\mathrm{ae}}+B_{\mathrm{aw}}{u}_w+B_{\mathrm{ag}}{m}_{b}g---\left(2\right)$

Wherein, A _aestate matrix for For Elastic Aircraft body and non-Unsteady Flow composition system; B _awfor the perturbation matrix of discrete fitful wind to For Elastic Aircraft dynamic response; B _agfor because goods movement produces the perturbation matrix of acting force to aircraft; u _wfor discrete fitful wind intensity; x _aefor state vector:

$x_{\mathrm{ae}}=\left[\begin{array}{c}{x}_a\\ \mathrm{\&xi;}\\ \stackrel{\&CenterDot;}{\mathrm{\&xi;}}\end{array}\right]---\left(3\right)$

Wherein, x _afor the hysteresis root Element of non-Unsteady Flow, the whirlpool that simulation comes off from plane airfoil;

1.4.2, solve generalized coordinate displacement ξ when aircraft 1g is flat to fly ^trim: aircraft 1g puts down while flying and meets the following conditions:

1.4.2.1, generalized coordinate acceleration

with generalized coordinate speed

be null vector;

1.4.2.2, the relative airplane motion speed of goods and displacement are 0;

1.4.2.3, without discrete fitful wind exciting force;

According to above-mentioned condition, aircraft 1g puts down the generalized coordinate displacement ξ while flying ^trimcalculating as shown in formula (4):

${\mathrm{\&xi;}}^{\mathrm{Trim}}=-{(K_{\mathrm{qq}}-Q_a)}^{-1}(\left[\begin{array}{c}{m}_a\\ 0\end{array}\right]+{\mathrm{\&Phi;}}_{\mathrm{bz}0}^T{m}_b)g---\left(4\right)$

Wherein, Φ _bz0modal matrix component for goods aircraft of initial stowage position in cargo hold;

1.4.3, solve aircraft cargo air-drop dynamic response differential matrix equation: the generalized coordinate displacement ξ while flying so that aircraft 1g is flat ^trimfor the initial solving condition of formula (2), adopt variable step Runge-Kutta method to solve aircraft cargo air-drop dynamic response differential matrix equation, obtain dynamic response, the generalized coordinate speed of the generalized coordinate displacement ξ of aircraft dynamic response and generalized coordinate acceleration

dynamic response:

$y_{\mathrm{ae}}=\left[\begin{array}{c}\mathrm{\&xi;}\\ \stackrel{\&CenterDot;}{\mathrm{\&xi;}}\\ \stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&xi;}}\end{array}\right]=C_{\mathrm{ae}}{x}_{\mathrm{ae}}+D_{\mathrm{aw}}{u}_w+D_{\mathrm{ag}}{m}_{b}g---\left(5\right)$

Wherein, C _aeoutput matrix for For Elastic Aircraft body and non-Unsteady Flow composition system; D _awfor the transfer matrix of discrete fitful wind to the output of For Elastic Aircraft dynamic response; D _agfor the transfer matrix of aircraft dynamic response being exported due to goods movement;

1.5, calculate cargo deck load dynamic response: according to dynamic response, the generalized coordinate speed of the generalized coordinate displacement ξ of the aircraft of step 1.4

dynamic response and generalized coordinate acceleration

dynamic response, calculate the used load of goods to aircraft hold floor

dynamic response, shown in (6):

${\stackrel{\&RightArrow;}{F}}_{b2a}\left(t\right)=-m_b({\stackrel{\&RightArrow;}{a}}_{\mathrm{CG}}+\stackrel{\stackrel{\&RightArrow;}{\&CenterDot;}}{q}\&times;{\stackrel{\&RightArrow;}{X}}_b+2\stackrel{\&RightArrow;}{q}\&times;{\stackrel{\&RightArrow;}{V}}_{b2a}-\stackrel{\&RightArrow;}{g})---\left(6\right)$

Wherein,

acceleration for aircraft barycenter place;

angle of pitch acceleration for aircraft;

rate of pitch for aircraft;

for the distance of goods apart from aircraft barycenter;

The design load of cargo deck while 1.6, determining air-drop: according to the cargo deck load dynamic response obtaining in step 1.5

select

maximum value and minimal value as the air-drop design load of cargo deck.

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