CN106773782A - A kind of aeroelastic divergence hybrid modeling method - Google Patents

Abstract

The invention belongs to aeroelastic divergence field, it is related to a kind of aeroelastic divergence modeling method.Structural model is set up by test data, calculating is set up aeroelasticity motion model and Controlling model, objectively reduces the model free degree, improves computational efficiency.

Description

A kind of aeroelastic divergence hybrid modeling method

Technical field

The invention belongs to aeroelastic divergence field, it is related to a kind of aeroelastic divergence modeling method.

Background technology

For the aircraft with servo-control system, aeroelastic divergence stability problem is one and inevitably asks Topic.For aircraft first-fly and the great remodeling of aircraft, it is required for carrying out aeroelastic divergence stability analysis.

At present, aeroelastic divergence stability problem is mainly analyzed by Computer Simulation, and Computer Simulation is modeled There is larger difference with aircraft actual conditions, thus simulation model is modified by test method mainly, but model Amendment difficulty is than larger, and correction result also is difficult to fit like a glove.

The content of the invention

The purpose of the present invention：In order to solve, simulation model and actual airplane differ greatly and simulation model is difficult to amendment Problem, is analyzed by test data, sets up test model, then enters promoting the circulation of qi by the mixed model tested and emulate Dynamic servo flexibility analysis.

Technical scheme：A kind of aeroelastic divergence hybrid modeling method, it is characterised in that described method bag Include following steps：

(1) n test point is chosen as the Degree of Structure Freedom, structural model is set up, full machine ground resonance test is carried out, and is measured Modal frequency ω, Mode Shape Φ_h, modal damping C_hh, modal mass M_hh；

(2) according to the modal mass M for measuring_hhModal stiffness K is obtained with modal frequency ω_hh；

K_hh=ω²M_hh

(3) chain of command mode Φ is set up on its Degree of Structure Freedom according to test model_c；

(4) according to Mode Shape Φ_hWith modal mass M_hhMass M in the computation structure free degree_g；

(5) according to structural modal Φ_hWith chain of command mode Φ_cAnd mass M_gSolve structural modal with

Coupling mass M between chain of command mode_hc；

(6) structure motion equation is set up：

ξ in formula, δ represent generalized structure displacement with control deflecting facet respectively；

(7) modal data obtained according to experiment, calculates unsteady using flow field calculation device or other numerical computation methods Aerodynamic force, and identify broad sense aerodynamic force matrix Q_h(s)；

Q in formula_h=[Q_hh Q_hc], A_n=[A_hhn A_hcn] (n=0,1,2), E=[E_h E_c].L is reference length, and V is air-flow Speed,_sIt is Laplace variable；

(8) using the broad sense aerodynamic force matrix Q of fitting_hS () obtains broad sense aerodynamic force f_a；

Q in formula_∞Represent to flow pressure, q is generalized displacement, q=[ξ δ]^T, including generalized structure displacement ξ and control surface deflection δ；

(9) aerodynamic force state variable is taken：

It is transformed into time domain space：

Time domain broad sense aerodynamic force can be write as：

(10) the aeroelasticity equation of motion is set up：

(11) aeroelasticity equation is write as state space form：

In formula

(12) frequency response function of steering wheel is measured according to experiment, steering wheel state equation is obtained：

(13) due to x_act=u_ae, the state equation of controlled device (plant) can represent with following formula：

In formula

C_p=[C_ae D_ae], D_p=0；

(14) consider control system state equation, can be obtained by simulation model：

(15) open-loop transfer function of controlled device and control system is set up：

In formulaC_o=[D_cC_p C_c], D_o=D_cD_p；

(16) state space equation is converted into frequency response function：

H (s)=C_o(sI-A_o)^-1B_o+D_o

Bode figures and Nyquist figures are drawn, stability analysis can be carried out and analyzed with stability margin.

Beneficial effects of the present invention：Structural model is set up by test data, aeroelasticity motion mould is set up by calculating Type and Controlling model, objectively reduce the model free degree, improve computational efficiency.

Specific embodiment

(1) n test point is chosen as the Degree of Structure Freedom, structural model is set up, full machine ground resonance test is carried out, and is measured Modal frequency ω, Mode Shape Φ_h, modal damping C_hh, modal mass M_hh。

(2) according to the modal mass M for measuring_hhModal stiffness K is obtained with modal frequency ω_hh。

K_hh=ω²M_hh

(3) chain of command mode Φ is set up on its Degree of Structure Freedom according to test model_c。

(4) according to mass M_gWith modal matrix Φ_hWith modal mass matrix M_hhBetween relation：

Can obtain：

Thus it is possible to obtain the coupling mass matrix between following structural modal and chain of command mode：

(5) modal data obtained according to experiment, solves broad sense aerodynamic force, is fitted broad sense aerodynamic force matrix：

Q_h(p)=A₀+A₁p+A₂p²+D(Ip-R)^-1Ep

Q in formula_h=[Q_hh Q_hc], A_n=[A_hhn A_hcn] (n=0,1,2), E=[E_h E_c].L is reference length, and V is air-flow Speed, dimensionless Laplace variable p=sL/V, s are Laplace variable.Therefore, broad sense aerodynamic force matrix can be write as：

So, broad sense aerodynamic force can be write as：

Q in formula_∞Represent to flow pressure, q is generalized displacement, including generalized structure displacement ξ and control surface deflection δ, q=[ξ δ ]^T。

Take aerodynamic force state variable：

It is transformed into time domain space：

So, aerodynamic force can be write as：

(6) the aeroelastic divergence equation of motion can be write as：

Then, aeroelastic divergence equation can be write as state space form：

In formula

(7) frequency response function of steering wheel is measured according to experiment, steering wheel state equation is obtained：

(8) due to x_act=u_ae, the state equation of controlled device (plant) can represent with following formula：

In formula

C_p=[C_ae D_ae], D_p=0.

(9) consider control system state equation, can be obtained being measured by experiment by simulation model：

(10) open-loop transfer function of controlled device and control system is set up

In formulaC_o=[D_cC_p C_c], D_o=D_cD_p

(11) state space equation is converted into frequency response function：

H (s)=C_o(sI-A_o)^-1B_o+D_o

Bode figures are drawn with Nyquist figures.Stability analysis can be carried out to be analyzed with stability margin.

Claims (1)

1. a kind of aeroelastic divergence hybrid modeling method, it is characterised in that described method comprises the following steps：

(1) n test point is chosen as the Degree of Structure Freedom, structural model is set up, and carries out full machine ground resonance test, measurement mode Frequencies omega, Mode Shape Φ_h, modal damping C_hh, modal mass M_hh；

(2) according to the modal mass M for measuring_hhModal stiffness K is obtained with modal frequency ω_hh；

K_hh=ω²M_hh

(3) chain of command mode Φ is set up on its Degree of Structure Freedom according to test model_c；

(4) according to Mode Shape Φ_hWith modal mass M_hhMass M in the computation structure free degree_g；

$M_g={\mathrm{\Φ}}_k{M}_{kk}{\mathrm{\Φ}}_k^T$

(5) according to structural modal Φ_hWith chain of command mode Φ_cAnd mass M_gSolve between structural modal and chain of command mode Coupling mass M_hc；

$M_{kc}={\mathrm{\Φ}}_k^T{M}_g{\mathrm{\Φ}}_c$

(6) structure motion equation is set up：

$M_{kk}\stackrel{\·\·}{\mathrm{\ξ}}+C_{kk}\stackrel{\·}{\mathrm{\ξ}}+K_{kk}\mathrm{\ξ}+M_{kc}\stackrel{\·\·}{\mathrm{\δ}}=0$

In formulaRepresent generalized structure displacement with control deflecting facet respectively；

(7) modal data obtained according to experiment, calculates unsteady pneumatic using flow field calculation device or other numerical computation methods Power, and identify broad sense aerodynamic force matrix Q_h(s)；

$Q_k\left(s\right)=A_0+\frac{L}{V}{A}_{1}s+\frac{L^2}{V^2}{A}_2{s}^2+D{(sI-\frac{V}{L}R)}^{-1}Es$

Q in formula_h=[Q_hh Q_hc], A_n=[A_hhn A_hcn] (n=0,1,2), E=[E_h E_c].L is reference length, and V is gas velocity Degree, s is Laplace variable；

(8) using the broad sense aerodynamic force matrix Q of fitting_hS () obtains broad sense aerodynamic force f_a；

$f_a=q_{\mathrm{\∞}}{Q}_{h}q=q_{\mathrm{\∞}}(A_0+\frac{L}{V}{A}_{1}s+\frac{L^2}{V^2}{A}_2{s}^2+D{(Is-\frac{V}{L}R)}^{-1}Es)q$

Q in formula_∞Represent to flow pressure, q is generalized displacement, q=[ξ δ]^T, including generalized structure displacement ξ and control surface deflection δ；

(9) aerodynamic force state variable is taken：

$x_a\left(s\right)={(Is-\frac{V}{L}R)}^{-1}Eqs$

${\mathrm{sx}}_a\left(s\right)=\frac{V}{L}{\mathrm{Rx}}_a\left(s\right)+Eqs$

It is transformed into time domain space：

${\stackrel{\·}{x}}_a=\frac{V}{L}{\mathrm{Rx}}_a+E\stackrel{\·}{q}$

Time domain broad sense aerodynamic force can be write as：

$f_a=q_{\mathrm{\∞}}{Q}_{h}q=q_{\mathrm{\∞}}(A_{0}q+\frac{L}{V}{A}_1\stackrel{\·}{q}+\frac{L^2}{V^2}{A}_2\stackrel{\·\·}{q}+{\mathrm{Dx}}_a)$

(10) the aeroelasticity equation of motion is set up：

$\begin{array}{c}(M_{hh}+q_{\mathrm{\∞}}\frac{L^2}{V^2}{A}_{hh2})\stackrel{\·\·}{\mathrm{\ξ}}+(C_{hh}+q_{\mathrm{\∞}}\frac{L}{V}{A}_{hh1})\stackrel{\·}{\mathrm{\ξ}}+(K_{hh}+q_{\mathrm{\∞}}{A}_{hh0})\mathrm{\ξ}+\\ (M_{hc}+q_{\mathrm{\∞}}\frac{L^2}{V^2}{A}_{hc2})\stackrel{\·\·}{\mathrm{\δ}}+q_{\mathrm{\∞}}\frac{L}{V}{A}_{hc1}\stackrel{\·}{\mathrm{\δ}}+q_{\mathrm{\∞}}{A}_{kc0}\mathrm{\δ}+{\mathrm{Dx}}_a=0\end{array}$

(11) aeroelasticity equation is write as state space form：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{ae}\left(t\right)=A_{ae}{x}_{ae}\left(t\right)+B_{ae}{u}_{ae}\left(t\right)\\ y_{ae}\left(t\right)=C_{ae}{x}_{ae}\left(t\right)+D_{ae}{u}_{ae}\left(t\right)\end{array}\right.$

In formula

(12) frequency response function of steering wheel is measured according to experiment, steering wheel state equation is obtained：

${\stackrel{\·}{x}}_{act}\left(t\right)=A_{act}{x}_{act}\left(t\right)+B_{act}{u}_{act}\left(t\right)$

(13) due to x_act=u_ae, the state equation of controlled device (plant) can represent with following formula：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_p\left(t\right)=A_p{x}_p\left(t\right)+B_p{u}_p\left(t\right)\\ y_p\left(t\right)=C_p{x}_p\left(t\right)+D_p{u}_p\left(t\right)\end{array}\right.$

In formula

C_p=[C_ae D_ae], D_p=0；

(14) consider control system state equation, can be obtained by simulation model：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_c\left(t\right)=A_c{x}_c\left(t\right)+B_c{u}_c\left(t\right)\\ y_c\left(t\right)=C_c{x}_c\left(t\right)+D_c{u}_c\left(t\right)\end{array}\right.$

(15) open-loop transfer function of controlled device and control system is set up：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_o\left(t\right)=A_o{x}_o\left(t\right)+B_o{u}_o\left(t\right)\\ y_o\left(t\right)=C_o{x}_o\left(t\right)+D_o{u}_o\left(t\right)\end{array}\right.$

In formulaC_o=[D_cC_p C_c], D_o=D_cD_p；

(16) state space equation is converted into frequency response function：

H (s)=C_o(sI-A_o)^-1B_o+D_o

Bode figures and Nyquist figures are drawn, stability analysis can be carried out and analyzed with stability margin.