CN204855125U - Measure device of three degree of freedom dynamic stability parameters in aircraft in high -speed wind tunnel - Google Patents

Abstract

The utility model relates to a measure device of three degree of freedom dynamic stability parameters in aircraft in high -speed wind tunnel has every single move excitation piezoceramics vibration exciter in tail branch, its one end links to each other with tail branch, and the other end is supported on tail branch through the elasticity hinge by the rear end hinged joint of parallelly connected back of frame and first connecting rod, the middle part of first connecting rod, the front end of first connecting rod and vibration section of thick bamboo hinged joint, there is T type branch in the inner chamber of a vibration section of thick bamboo, the both ends and the vibration section of thick bamboo hinged joint of the vertical axle of T type branch, T type branch the improve level both ends and cylinder balance hinged joint of axle, be equipped with first, second driftage / lift -over piezoceramics vibration exciter in the cylinder balance, one end first, second driftage / lift -over piezoceramics vibration exciter is fixed respectively on a vibration section of thick bamboo, the other end respectively with the second connecting rod hinged joint that corresponds. The device is put in the wind -tunnel, but three degree of freedom dynamic stability parameters in the aircraft in the precision measurement high -speed wind tunnel.

Description

The device of aircraft three-freedom moving steadiness parameter is measured in a kind of high-speed wind tunnel

Technical field

The utility model relates to aircraft three-freedom moving steadiness parameter field of measuring technique, specifically a kind of device measuring aircraft three-freedom moving steadiness parameter in high-speed wind tunnel.

Background technology

The dynamic and static steadiness parameter of aircraft or dynamic and static stable derivative are the important parameters weighing aircraft control and stability, and it is the characteristic parameter that the time rate of change of kinematic parameter (angular displacement, linear velocity or angular velocity component) or kinematic parameter causes the change of aerodynamic force suffered by aircraft or moment (coefficient).

Modern military fighter plane is in order to improve its combat performance, and often requirement can carry out various highly difficult maneuvering flight.Aircraft not only will have enough stability, especially will have accurate navigability maybe guidance property.The maneuverability of aircraft is better, and navigability performance number is higher, and the fighting capacity of aircraft and viability are also stronger.But, under large attack angle and high maneuver flying condition, flow field around aircraft is very complicated, in addition the aerodynamic configuration become increasingly complex and various forms of burbling, vortex, make the method for method of engineering calculation in the past, Fluid Mechanics Computation all be difficult to meet the estimation requirement of aircraft flight performance number.The test of wind-tunnel Dynamic stability becomes the necessary component in aircraft development.

For transporter, passenger plane and other civil aircrafts, improve the stable performance number of aircraft under various interference and atmospheric turbulence condition and trajectory stability also becomes more and more important.Such as, modern passenger plane is to security, and especially comfortableness, has more and more higher requirement, and this has become the essential condition buying modern passenger plane.This just requires that aircraft has good damping capacity to various atmospheric turbulence, microexplosion.When taking off or land, because aircraft speed is lower, correction can be utilized few highly again, and the dynamic and static stability indicator of aircraft is just even more important.

In a word, to contemporary aircraft, no matter being military fighter aircraft or seating plane, accurately giving in accurate different degree of freedom, the dynamic and static stable derivative especially under high-speed condition, has been the problem that must solve in aircraft development.But the structure space allowed due to high wind tunnel testing is very little, and aerodynamic loading, particularly normal force and pitching moment are very large again.In such a situa-tion, not only want the load of energy suffered by support model, and the motion of three degree of freedom and enough spaces and enough driving moments can be provided, and also will aerodynamic loading accurately suffered by rating model and model angular displacement, be very difficult task.This is also the dynamic device only having single-degree-of-freedom so far in high-speed wind tunnel, and there is no the reason of Three Degree Of Freedom wind tunnel test equipment.

A kind of balance measurement device for the experiment of pitching dynamic derivative disclosed in Chinese patent CN101726401.This device with the motor be contained in pole as drive source, the parts such as the transmission shaft supported by bearing, the eccentric wheel of front end, projection in chute drive cross flexible member front end, make five COMPONENT BALANCE be attached thereto make pitch vibration around the center of cross element.The suffered load signal of model is exported by five COMPONENT BALANCE, and angle signal is exported by the foil gauge on cross element, tries to achieve aerodynamic parameter thus.Except can only doing the test of pitching single-degree-of-freedom, because pole space is to the restriction of motor, motor size and corresponding power can not be very large.In addition, the gap of bearing, slide block and chute etc. and their uncertainty also can bring to moving wave shape the distortion and corresponding measuring error that can not ignore.Further, the moment of driving model pitching is through that an elongated round bar carrys out transmitting torque to realize.The angular distortion of elongate rod under moment of torsion also can bring impact to the waveform of model luffing and measuring error.

The dynamic derivative experimental provision of another kind disclosed in Chinese patent CN102998082 in pitch orientation.Except can only doing the test of pitching single-degree-of-freedom, this device by motor through parallel double crank mechanism drive pole and and then promote model do pitch vibration.This mechanism only may carry out support model by the form of abdomen supporting and driving model makes pitch vibration, only uses in low-speed wind tunnel; In addition, the gap in all bearings and supporting device bring error all can to model sport waveform, thus brings very large impact to measurement result.

Utility model content

The purpose of this utility model is to provide a kind of device measuring aircraft three-freedom moving steadiness parameter in high-speed wind tunnel.

The technical scheme in the invention for solving the technical problem is: the device measuring aircraft three-freedom moving steadiness parameter in high-speed wind tunnel, it is characterized in that, it comprises pitch vibration cylinder, cartridge type balance, pitching vibrator, the first and second driftage/rolling vibrators, tee T pole, framework, the first and second connecting rods, slide bar, support sting, dummy vehicle, rear end elastic hinge, middle part elastic hinge, front end elastic hinge, pitching elastic hinge, driftage elastic hinge, rolling elastic hinge, roll sensor etc.

Pitching exciting piezoelectric actuator group is provided with in described support sting, described pitching exciting piezoelectric actuator group is connected with the rear end elastic hinge of first connecting rod after being joined by frame set, the middle part of described first connecting rod is connected with the middle part elastic hinge on support sting, the front end of described first connecting rod is connected by front end elastic hinge with vibrating barrel, and described vibrating barrel is connected by pitching elastic hinge with support sting;

Further, tee T pole is provided with in the inner chamber of described pitch vibration cylinder, the two ends of the upper vertical axes of described tee T pole are connected by elastic hinge of going off course with vibrating barrel, and the two ends of the upper transverse axis of described tee T pole are connected by rolling elastic hinge with cartridge type balance;

Further, the first driftage/rolling piezoelectric actuator and the second driftage/rolling piezoelectric actuator is provided with in described cartridge type balance, one end of first, second driftage/rolling piezoelectric actuator is fixed on vibrating barrel, the other end of first, second driftage/rolling piezoelectric actuator connects with corresponding second connecting rod elastic hinge respectively, and second connecting rod described in two is all connected by elastic hinge with cartridge type balance;

Further, the flexure strip of the elastic hinge of described vibrating barrel and support sting is provided with foil gauge, in order to measure the change of the angle of pitch, in described cartridge type balance, the front end of tee T pole is provided with flexure strip, which is provided with the foil gauge of reaction roll angle, the flexure strip of the driftage elastic hinge be connected with vibrating barrel at the upper and lower end of tee T pole also there is foil gauge, to measure the change of crab angle.

Further, first, second driftage/rolling piezoelectric actuator is fixed with guide rail end block, described support sting is provided with guide rod, described guide rod and guide rail end block are slidably connected.

Further, described cartridge type balance is thin-wall construction.

The beneficial effects of the utility model are: the device measuring aircraft three-freedom moving steadiness parameter in the high-speed wind tunnel that the utility model provides, use the mode of two-stage motion platform: the pitch vibration in the pitch plane of the relative support sting of vibrating barrel, the vibration of driftage and rolling done by balance Relative Vibration cylinder.The driftage of model and roll oscillation axle and pitch vibration axle keep orthogonality relation forever, thus make model be obtained three-degree-of-freedom motion around three Z-axises; The joint of all moving components is all connected by elastic hinge; Thin-walled boxlike five COMPONENT BALANCE provides high rigidity, high sensitivity and large inside installing space.The utility model is placed in wind-tunnel, accurately can measure aircraft three-freedom moving steadiness parameter in high-speed wind tunnel.

Accompanying drawing explanation

Fig. 1 is one-piece construction figure of the present utility model;

Fig. 2 is the tomograph of cartridge type balance;

The mechanism map that Fig. 3 is cartridge type sky mean longitude tee T pole, elastic hinge is connected with vibrating barrel;

Fig. 4 is the driftage/rolling piezoelectric actuator of parallel placement and vibration gentle with sky

Connection layout between cylinder;

Fig. 5 is placed on pitching exciting piezoelectric actuator in support sting and yi word pattern, ten

Font hinge set and linkage assembly;

Fig. 6 is the structural drawing that the gentle model in cartridge type sky connects;

Fig. 7 is wind-tunnel dynamic test flow chart of data processing figure;

Fig. 8 is the front elevation of Fig. 2;

Fig. 9 is the A-A cut-open view in Fig. 8;

In figure: 101 support stings, 102 pitching exciting piezoelectric actuators, 103 frameworks, 104 rear end elastic hinges, 105 middle-end elastic hinges, 106 front end elastic hinges, 107 second cross hinges, 108 first connecting rods, 109 cartridge type balances, 110 dummy vehicles, 111 indulge, transversely strengthening pin, 112 slide bars, 113 chutes, 114 pitch vibration cylinders, 115 tee T poles, 116 driftage elastic hinges, 117 tommys, rolling elastic hinge after 118, rolling elastic hinge before 119, 120 first driftage/rolling piezoelectric actuators, 121 second driftage/rolling piezoelectric actuators, 122 second connecting rods, 123 rolling flexure strips, 124 guide rods, 125 guide rail end blocks, 126 flexure strips, pin after 127, dowel bushing in 128, pin before 129, 130 pitching tommys, 131 driftage tommys, 132 balance inner cones, 133 pitching moments and normal force load-sensing unit, 134 yawings and side force load-sensing unit, 135 rolling moment load-sensing units.

Embodiment

Below in conjunction with accompanying drawing, the utility model is described in detail.

As shown in Fig. 1 to Fig. 7, install dummy vehicle 110 in the front end of cartridge type balance, the pitching exciting piezoelectric actuator group 102 be arranged in support sting 101 promotes the axle center pitch vibration of first connecting rod 108 around the first cross hinge 105 by yi word pattern hinge 104 after framework 103 groups connection.First connecting rod front end premenstrual yi word pattern hinge 106 is connected with vibrating barrel 114 and promotes the axle center pitch vibration of the second cross hinge 107 that vibrating barrel 114 is connected with support sting along vibrating barrel.Like this, when the upper and lower straight-line oscillation of piezoelectric actuator, first connecting rod can make pitch vibration by the rotation center in the middle part of first connecting rod.Circular arc is compensated to the radial difference of rectilinear motion by the lateral flexibility of yi word pattern hinge.When the pitching amplitude 1.5 degree of vibrating barrel, on connecting rod, the brachium of pitch vibration is 100 millimeters, and this radial variations is only 0.021 millimeter.Under such lateral deformation, although yi word pattern hinge bears the drawing of 1125 newton, compressive load, it is still in the scope allowed band of pressure bar stabilization.

A tee T pole 115 is had in vibrating barrel, the upper and lower side of the Z-axis of tee T pole is connected with vibrating barrel through cross hinge, and after the transverse axis of tee T pole having T-shaped bar, before cross hinge 118, T-shaped bar, cross hinge 119 is connected with cartridge type balance 109.Like this, cartridge type balance can make yaw oscillation around the upper and lower cross hinge Relative Vibration cylinder of the Z-axis of tee T pole.Cartridge type balance also can make roll oscillation by the cross hinge Relative Vibration cylinder on the transverse axis of tee T pole.

Parallelly in cartridge type balance placed two piezoelectric actuators, be respectively the first driftage/rolling piezoelectric actuator 120 and the second driftage/rolling piezoelectric actuator 121, the direction of placement is orthogonal with pitch orientation.In addition, one end of these two piezoelectric actuators is fixed on vibrating barrel, and the other end is connected with respective second connecting rod 122, and is connected with cartridge type balance through elastic hinge 123.Here, effect and the aforesaid yi word pattern hinge of elastic hinge are similar, and only its lateral deformation is the lateral deformation sum that second connecting rod and balance circular motion cause.If balance pivoted arm is 20 millimeters, this lateral deformation is 0.012 millimeter to the maximum, within the pressure bar stabilization scope of a word slice.

In addition, in order to make vibrator can accurately Linear Driving, avoid the impact of side load, support sting has the guide rod 124 of vertical movement, the guide hole on the guide rail end block 125 of the moved end (top) of this guide rod and vibrator have employed the form be slidably matched.Like this, just ensure that the upper and lower accurately rectilinear motion with vibrator.

By above-mentioned arrangement, these two piezoelectric actuators both can order about that balance Relative Vibration cylinder is gone off course, roll oscillation, can order about again the combination vibration that balance Relative Vibration cylinder does driftage and rolling.

On the second cross hinge 107, foil gauge is posted in the appropriate location of spoke, and forms Wheatstone bridge, to reflect the instantaneous corner course of balance relative to the driftage of pole.In cartridge type balance 109, the front end of tee T pole 115, have the flexure strip 126 of a reaction roll angle, be connected with tee T pole 115 with cartridge type balance 109 respectively, be stained with the foil gauge of reflection model roll angle above.

Cartridge type balance 109 can be five COMPONENT BALANCE, in order to meet the requirement that longitudinal loading is comparatively large and side load is less, cartridge type balance there are three cover load-sensing unit groups, i.e. pitching power and normal force load-sensing unit 133, yawing and side force load-sensing unit 134 and rolling load-sensing unit 135, correspondingly respectively to measure longitudinally, side direction and rolling aerodynamic loading.Each element component is not made up of four post beam type composition elements on two different cross sections.Respective side is larger than the distances surveying longitudinal load-sensing unit with the distance between cross section to two of load-sensing unit, to meet the requirement of balance to side load and the different sensitivity to longitudinal loading.Cartridge type balance 109 is also provided with pitching tommy 130, driftage tommy 131 and balance inner cone 132.

At pitching moment M _zwith yawing M _yunder effect, the stress and strain of cross section I and cross section II is calculated by following formula respectively:

To pitching moment M _z, ${\mathrm{\σ}}_{IYmax}={\mathrm{\σ}}_{IIYmax}=\frac{3({\mathrm{\ρ}}_2+h_2)M_Z}{b_1{h}_1^3+b_2{h}_2^3+12{\mathrm{\ρ}}_2^2{b}_2{h}_2}$

${\mathrm{\ϵ}}_{IY\max }={\mathrm{\ϵ}}_{IIY\max }=\frac{3({\mathrm{\ρ}}_2+h_2)M_Z}{E(b_1{h}_1^3+b_2{h}_2^3+12{\mathrm{\ρ}}_2^2{b}_2{h}_2)}$

To yawing M _y, ${\mathrm{\σ}}_{IZmax}={\mathrm{\σ}}_{IIZmax}=\frac{3(2{\mathrm{\ρ}}_1+b_1)M_Y}{b_1^3{h}_1+b_2^3{h}_2+12{\mathrm{\ρ}}_1^2{b}_1{h}_1}$

${\mathrm{\ϵ}}_{IZmax}={\mathrm{\ϵ}}_{IIZ\max }=\frac{3(2{\mathrm{\ρ}}_1+b_1)M_Y}{b_1^3{h}_1+b_2^3{h}_2+12{\mathrm{\ρ}}_1^2{b}_1{h}_1}$

To rolling moment M _x,

Due to structural limitations, two cross sections of cartridge type balance 109 can not be across the both sides of model rotation center (the second cross hinge 107), can only try one's best near the rotation center of model.Appropriate location on the strain beam of cartridge type balance 109 is posted foil gauge and forms electric bridge, measures instantaneous normal direction, side force and pitching, driftage, rolling moment, input store and computing machine respectively.

In order to reduce the impact of the measuring error such as gas, the load signal that when the model angular displacement signal that hinge exports and blowing, cartridge type balance 109 exports, after the parameter identification of cross correlation process and three period equations, provides relevant quiet, dynamic Aerodynamic Coefficient.

Balance input (i.e. main motion signal) is X (t)=P ₀sin ω t

Balance exports as Y (t)=S ₀sin (ω t+ η)+n (t)

If noise is uncorrelated with main motion, then above formula can be write as

$R_{XY}\left(\mathrm{\τ}\right)=\frac{P_0{S}_0}{2}cos(\mathrm{\ω}\mathrm{\τ}+\mathrm{\η})$

Equally, if the average that X (k) and Y (k) is wide steady each state Pianli is the departure process of zero, then the cross correlation function of sequence X (k) and Y (k) is

R _xy(l)＝E{X(k)Y(k+l)}

Corresponding estimator or sample this cross correlation function and be

${\hat{R}}_{xy},L\left(l\right)=\frac{1}{L}\underset{k=1}{\overset{L-1}{\Σ}}X\left(k\right)Y(k+l)$

l＝0,±1,±2,…,±(L-1)

L is data length

During data processing, first should deduct the mean value of each signal, to eliminate constant term, then carry out related operation.Wherein sampling interval, total number of samples, maximum delayed several L etc., determine according to factors such as test frequency, signal to noise ratio, permissible accuracy and system passbands.

When Three Degree Of Freedom vibration done by model, Dynamic stability parameter will be tried to achieve through the modulus identification of three periodic motions:

When model is around center of gravity three-degree-of-freedom motion, three cyclical theorys of the available description precession of motion of model, nutating and rolling movement describe:

$I\stackrel{\·\·}{\mathrm{\α}}-p\stackrel{\·}{\mathrm{\β}}{I}_x-M_{\mathrm{\α}}\mathrm{\α}-(M_{\stackrel{\·}{\mathrm{\α}}}+M_q)\stackrel{\·}{\mathrm{\α}}-M_{\mathrm{\δ}}\mathrm{\δ}\cos pt-M_{p\mathrm{\β}}P\mathrm{\β}=0$

$I\stackrel{\·\·}{\mathrm{\β}}-p\stackrel{\·}{\mathrm{\α}}{I}_x-N_{\mathrm{\β}}\mathrm{\β}-(N_{\mathrm{\γ}}-N_{\stackrel{\·}{\mathrm{\β}}})\stackrel{\·}{\mathrm{\β}}-M_{\mathrm{\δ}}\mathrm{\δ}\sin pt-N_{p\mathrm{\α}}P\mathrm{\α}=0$

Introduce multiple dihedral formula

ξ＝iα+β

Above-mentioned equation can be written as after simplifying:

$\stackrel{\·\·}{\mathrm{\ξ}}+\[-ip\left(\frac{I_x}{I}\right)-\frac{M_q+M_{\stackrel{\·}{\mathrm{\α}}}}{1}\]\stackrel{\·}{\mathrm{\ξ}}+\[-ip\frac{M_{pb}}{I}-\frac{M_{\mathrm{\α}}}{I}\]\mathrm{\ξ}-\frac{M_{\mathrm{\δ}}}{I}(-\sin pt+i\cos pt)\mathrm{\δ}=0$

Solution of equation can be written as

$\mathrm{\ξ}=k_1{e}^{({\mathrm{\λ}}_1+{\mathrm{i\ω}}_1)t}+k_2{e}^{({\mathrm{\λ}}_2+{\mathrm{i\ω}}_2)t}+k_3{e}^{ipt}$

In formula, the right three parts are nutating precession, precession and rolling three mode.Wherein k ₁, k ₂, k ₃for plural number, above formula being written as two real variable forms has

$\mathrm{\α}\left(t\right)=(A_1{\mathrm{cos\ω}}_{1}t+B_1{\mathrm{sin\ω}}_{1}t)e^{{\mathrm{\λ}}_{1}t}+(A_2{\mathrm{cos\ω}}_{2}t+B_2{\mathrm{sin\ω}}_{2}t)e^{{\mathrm{\λ}}_{2}t}+(A_3\cos pt+B_3\sin pt)$

$\mathrm{\β}\left(t\right)=(B_1{\mathrm{cos\ω}}_{1}t-A_1{\mathrm{sin\ω}}_{1}t)e^{{\mathrm{\λ}}_{1}t}+(B_2{\mathrm{cos\ω}}_{2}t-A_2{\mathrm{sin\ω}}_{2}t)e^{{\mathrm{\λ}}_{2}t}+(B_3\cos pt-A_3\sin pt)$

A in above formula ₁, B ₁, A ₂, B ₂be and starting condition α ₀, β ₀, relevant constant.Frequency leads and damping term ω ₁, ω ₂, λ ₁, λ ₂be and remove M _δthe parameter that aerodynamic parameter to be asked beyond δ is relevant:

M _α＝-Iω ₁ω ₂

M _q＝I(λ ₁+λ ₂)

$p=\frac{I}{I_x}({\mathrm{\ω}}_1+{\mathrm{\ω}}_2)$

$M_{p\mathrm{\β}}=-\[\frac{{\mathrm{\λ}}_1{\mathrm{\ω}}_2+{\mathrm{\λ}}_2{\mathrm{\ω}}_1}{{\mathrm{\ω}}_1+{\mathrm{\ω}}_2}\]I_x$

Present vector to be estimated is:

[ξ]＝[A ₁,B ₁,A ₂,B ₂,A ₃,B ₃,ω ₁,ω ₂,λ ₁,λ ₂] ^T

Wherein A ₁to B ₃for the linear function of α, β, and ω ₁to λ ₂for the nonlinear function of α, β.

Set up evaluation function

J＝∑[α(t)-α _i] ²+[β(t)-β _i] ²

Wherein α _i, β _ifor t=t _idata point.

By α (t), β (t) to often organizing variable ω ₁, ω ₂, λ ₁, λ ₂launch at discreet value ξ place, have

Wherein extremely for discreet value, ω ₁to λ ₂for the increment of discreet value.

By the optimal estimation of ξ can be tried to achieve.Its component form as have

$\begin{array}{c}\frac{\∂}{\∂\mathrm{\ω}}\[\underset{i}{\Σ}\left\{{\left(\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}{\mathrm{\ω}}_1+\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_2}{\mathrm{\ω}}_2+\frac{\∂\mathrm{\α}}{\∂{\mathrm{\λ}}_1}{\mathrm{\λ}}_1\frac{\∂\mathrm{\α}}{\∂{\mathrm{\λ}}_2}{\mathrm{\λ}}_2\right)}^2\right\}\]\\ +2\frac{\∂}{\∂{\mathrm{\ω}}_1}\[\underset{i}{\Σ}\left(R_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}{\mathrm{\ω}}_1+R_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_2}{\mathrm{\ω}}_2+R_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_1}{\mathrm{\λ}}_1+R_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_2}{\mathrm{\λ}}_2\right)+\underset{i}{\Σ}\left(Q_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}{\mathrm{\ω}}_1+Q_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_2}{\mathrm{\ω}}_2+Q_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_1}{\mathrm{\λ}}_1+Q_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_2}{\mathrm{\λ}}_2\right)\]+\end{array}$

$+\frac{\∂}{\∂{\mathrm{\ω}}_1}\[\underset{i}{\Σ}{R}_i^2+\underset{i}{\Σ}{Q}_i^2\]=0^{+}$

Wherein residual error

Owing to being at precompensation parameter place's value, therefore deng being constant, the above formula left side first sport is zero, and has

$\begin{array}{c}\underset{i}{\Σ}\[{\left(\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}\right)}^2+{\left(\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\right)}^2\]{\mathrm{\ω}}_1+\underset{i}{\Σ}\mathrm{\[(}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_2}\mathrm{)+(}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_2}\mathrm{)\]}{\mathrm{\ω}}_2+\underset{i}{\Σ}\[(\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\λ}}_1}\mathrm{)+(}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_1})\]{\mathrm{\λ}}_1\\ +\underset{i}{\Σ}\mathrm{\[(}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\λ}}_2}\mathrm{)+(}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_2}\mathrm{)\]}{\mathrm{\λ}}_2\mathrm{=-}\underset{i}{\Σ}\[R_i\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}+Q_i\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\]\end{array}$

If make [C _j]=[ω ₁, ω ₂, λ ₁, λ ₂] ^tthen above formula is write as matrix expression and is:

[F _kj][C _j]＝[Rl _k]

Wherein [F _kj] be square formation, row k j column element is

$F_{kj}=\underset{i}{\Σ}(\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ξ}}_k}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ξ}}_j}+\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ξ}}_k}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ξ}}_j})$ Such as

$F_{11}=\underset{i}{\Σ}\[{\left(\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}\right)}^2+{\left(\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\right)}^2\]$

$F_{12}=\underset{i}{\Σ}\[\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_2}+\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_2}\]$

$F_{44}=\underset{i}{\Σ}\[{\left(\frac{\∂\mathrm{\α}}{\∂{\mathrm{\λ}}_2}\right)}^2+{\left(\frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_2}\right)}^2\]$

[Rl _k] be column vector, and have

$\[{\mathrm{Rl}}_k\]=\underset{i}{\Σ}\[\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ξ}}_k}{R}_i+\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ξ}}_k}{Q}_i\]$

Such as

$\[{\mathrm{Rl}}_1\]=\underset{i}{\Σ}\[\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}{R}_i+\frac{\∂\mathrm{\β}}{\∂{\mathrm{\ω}}_1}{Q}_i\]$

By matrix expression, if [F _kj] without singular point, nonopiate again, then have

{ξ _j}＝[F _kj] ^-1{Rl _k}＝[F _jk]{Rl _k}

By above formula, as long as [F _kj, R _lk] try to achieve, just can solution to make new advances there is increment type again

Continue iteration, until residual sum of squares (RSS) is less than a certain required amount.

And [F _kj] and [ _rlk] in every α, β to ω ₁to λ ₂partial derivative also can try to achieve:

$\begin{array}{c}\frac{\∂\mathrm{\α}}{\∂{\mathrm{\ω}}_1}=\left(t\right)(B_1{\mathrm{cos\ω}}_{1}t-A_1{\mathrm{sin\ω}}_{1}t)e^{{\mathrm{\λ}}_{1}t}\\ \·\\ \·\\ \·\\ \frac{\∂\mathrm{\β}}{\∂{\mathrm{\λ}}_2}=\left(t\right)(B_2{\mathrm{cos\ω}}_{2}t-A_2{\mathrm{sin\ω}}_{2}t)e^{{\mathrm{\λ}}_{2}t}\end{array}$

Ask A now ₁, B ₁, A ₂, B ₂, A ₃, B ₃, the angle of attack and yaw angle can be written as:

$\mathrm{\α}=\left(\frac{\∂\mathrm{\α}}{\∂A_1}\right)A_1+\left(\frac{\∂\mathrm{\α}}{\∂B_1}\right)B_1+\left(\frac{\∂\mathrm{\α}}{\∂A_2}\right)A_2+\left(\frac{\∂\mathrm{\α}}{\∂B_2}\right)B_2+\left(\frac{\∂\mathrm{\α}}{\∂A_3}\right)A_3+\left(\frac{\∂\mathrm{\α}}{\∂B_3}\right)B_3$

$\mathrm{\β}=\left(\frac{\∂\mathrm{\β}}{\∂A_1}\right)A_1+\left(\frac{\∂\mathrm{\β}}{\∂B_1}\right)B_1+\left(\frac{\∂\mathrm{\β}}{\∂A_2}\right)A_2+\left(\frac{\∂\mathrm{\β}}{\∂B_2}\right)B_2+\left(\frac{\∂\mathrm{\β}}{\∂A_3}\right)A_3+\left(\frac{\∂\mathrm{\β}}{\∂B_3}\right)B_3$

Due to

$\frac{\∂\mathrm{\α}}{\∂A_1}=cos\left({\mathrm{\ω}}_{1}t\right)e^{{\mathrm{\λ}}_{1}t}$

$\frac{\∂\mathrm{\β}}{\∂A_1}=-sin\left({\mathrm{\ω}}_{1}t\right)e^{{\mathrm{\λ}}_{1}t}$

In front formula, other partial derivative also can similarly be tried to achieve.So by

$\frac{\∂J}{\∂\mathrm{\ξ}}=\frac{\∂}{\∂\mathrm{\ξ}}\{\underset{i}{\Σ}\{{\[\mathrm{\α}\left(t\right)-{\mathrm{\α}}_i\]}^2+{\[\mathrm{\β}\left(t\right)-{\mathrm{\β}}_i\]}^2\}\}=0$

Above formula is to certain component (such as A ₁) expression formula be

$\frac{\∂}{\∂A_1}\{\underset{i}{\Σ}{\[\frac{\∂\mathrm{\α}}{\∂A_1}{A}_1+...+\frac{\∂\mathrm{\α}}{\∂B_3}{B}_3-{\mathrm{\α}}_i\]}^2+\underset{i}{\Σ}{\[\frac{\∂\mathrm{\β}}{\∂A_1}{A}_1+...+\frac{\∂\mathrm{\β}}{\∂B_3}{B}_3-{\mathrm{\β}}_i\]}^2\}$

Consider deng being constant at i point, so have:

$\underset{i}{\Σ}\[\frac{\∂\mathrm{\α}}{\∂A_1}{A}_1+...+\frac{\∂\mathrm{\α}}{\∂B_3}{B}_3-{\mathrm{\α}}_i\]\frac{\∂\mathrm{\α}}{\∂A_1}+\underset{i}{\Σ}\[\frac{\∂\mathrm{\β}}{\∂A_1}{A}_1+...+\frac{\∂\mathrm{\β}}{\∂B_3}{B}_3-{\mathrm{\β}}_i\]\frac{\∂\mathrm{\β}}{\∂A_1}={\mathrm{\α}}_i\frac{\∂\mathrm{\α}}{\∂A_1}+{\mathrm{\β}}_i\frac{\∂\mathrm{\β}}{\∂A_1}$

Maybe can be rewritten as:

$\begin{array}{c}{A}_1\{\underset{i}{\Σ}\[{\left(\frac{\∂\mathrm{\α}}{\∂A_1}\right)}^2+{\left(\frac{\∂\mathrm{\β}}{\∂A_1}\right)}^2\]\}+B_1\{\underset{i}{\Σ}\[\left(\frac{\∂\mathrm{\α}}{\∂A_1}\right)\left(\frac{\∂\mathrm{\α}}{\∂B_1}\right)+\left(\frac{\∂\mathrm{\β}}{\∂A_1}\right)\left(\frac{\∂\mathrm{\β}}{\∂B_1}\right)\]\}+...+\\ +B_3\{\underset{i}{\Σ}\[\left(\frac{\∂\mathrm{\α}}{\∂A_1}\right)\left(\frac{\∂\mathrm{\α}}{\∂B_3}\right)+\left(\frac{\∂\mathrm{\β}}{\∂A_1}\right)\left(\frac{\∂\mathrm{\β}}{\∂B_3}\right)\]\}=\underset{i}{\Σ}\[\frac{\∂\mathrm{\α}}{\∂A_1}{\mathrm{\α}}_i+\frac{\∂\mathrm{\β}}{\∂A_1}{\mathrm{\β}}_i\]\end{array}$

Above-mentioned equation has six, can solve A ₁to B ₃six unknown numbers, thus obtain every Dynamic stability parameter.

Claims (9)

1. in a high-speed wind tunnel, measure the device of aircraft three-freedom moving steadiness parameter, it is characterized in that, its involving vibrations cylinder, cartridge type balance, pitching vibrator, first and second driftage/rolling vibrators, tee T pole, framework, first and second connecting rods, slide bar, support sting, dummy vehicle, rear end elastic hinge, middle part elastic hinge, front end elastic hinge, pitching elastic hinge, driftage elastic hinge, rolling elastic hinge, roll sensor, pitching vibrator is provided with in described support sting, described pitching vibrator is connected by rear end elastic hinge with first connecting rod, the middle part of described first connecting rod is connected with the middle part elastic hinge of support sting, the front end of described first connecting rod and vibrating barrel are by front end chain connection, described vibrating barrel is connected by pitching elastic hinge with support sting, in the inner chamber of described vibrating barrel, be provided with tee T pole, the two ends of the upper vertical axes of described tee T pole and vibrating barrel are by chain connection of going off course, and the two ends of the upper transverse axis of described tee T pole and cartridge type balance are by rolling chain connection, the first driftage/rolling vibrator and the second driftage/rolling vibrator is provided with in described cartridge type balance, one end of first, second driftage/rolling vibrator is separately fixed on vibrating barrel, the other end of first, second driftage/rolling vibrator respectively with corresponding second connecting rod chain connection, the other end of second connecting rod described in two all with cartridge type balance chain connection.

2. in a kind of high-speed wind tunnel according to claim 1, measure the device of aircraft three-freedom moving steadiness parameter, it is characterized in that being provided with foil gauge on described pitching elastic hinge, driftage elastic hinge and roll sensor, react the pitching of the relative support sting of dummy vehicle, driftage and roll angle respectively.

3. in a kind of high-speed wind tunnel according to claim 1, measure the device of aircraft three-freedom moving steadiness parameter, it is characterized in that, first, second driftage/rolling vibrator is fixed with guide rail end block, described support sting is provided with guide rod, described guide rod and guide rail end block are slidably connected.

4. measure the device of aircraft three-freedom moving steadiness parameter in a kind of high-speed wind tunnel according to claim 1, it is characterized in that, described second connecting rod is connected with cartridge type balance by elastic hinge.

5. measure the device of aircraft three-freedom moving steadiness parameter in a kind of high-speed wind tunnel according to claim 1, it is characterized in that, described cartridge type balance is thin-wall construction.

6. in a kind of high-speed wind tunnel according to claim 5, measure the device of aircraft three-freedom moving steadiness parameter, described cartridge type balance is five COMPONENT BALANCE, and the outer wall of described cartridge type balance is provided with pitching moment and normal force load-sensing unit, yawing and side force load-sensing unit and rolling moment load-sensing unit.

7. measure the device of aircraft three-freedom moving steadiness parameter in a kind of high-speed wind tunnel according to claim 1, described pitching vibrator is piezoelectric actuator.

8. measure the device of aircraft three-freedom moving steadiness parameter in a kind of high-speed wind tunnel according to claim 1, first, second driftage/rolling vibrator described is piezoelectric actuator.

9. measure the device of aircraft three-freedom moving steadiness parameter in a kind of high-speed wind tunnel according to claim 1, the adjustable length of described second connecting rod.