A typical virtual test modeling method for rudder ground buffet considering rudder shaft gap

Abstract

The application relates to the field of dynamics and control research, and specifically discloses a ground flutter virtual test modeling method, which is used for establishing a model with an exciter, a rudder surface and a rudder shaft, and comprises the following steps: constructing a reduced-order rigid-flexible coupling dynamics model, wherein the reduced-order rigid-flexible coupling dynamics model comprises reduced-order masses and reduced-order stiffnesses corresponding to boundary point self-coupling, boundary point and internal point coupling, internal point and boundary point coupling and internal point self-coupling; and solving the reduced-order rigid-flexible coupling dynamics model according to the reduced-order modal degree of freedom displacement, the reduced-order modal degree of freedom velocity, the force of the exciter and the stress of the rudder shaft to obtain the displacement, the velocity and the acceleration of the excitation table, wherein the stress of the rudder shaft is determined according to the displacement of the rudder shaft and the rudder shaft gap. The scheme provided by the application overcomes the problem that the traditional method is difficult to consider the influence of the rudder shaft gap, so that the rudder surface simulation result is more accurate and closer to the actual situation.

Description

Technical Field

[0001] This application relates to the technical field of dynamics and control research, and in particular to a virtual test modeling method for ground flutter of a typical rudder surface considering rudder shaft clearance. Background Technology

[0002] Ground flutter simulation testing technology is a semi-physical simulation verification technique developed in recent years, offering advantages such as low risk, short cycle time, and high accuracy. This technology uses concentrated forces provided by a finite number of exciters to simulate distributed aerodynamic forces acting on the surface of an aircraft, thereby achieving the purpose of testing the flutter boundary of the aircraft on the ground. Currently, ground flutter simulation testing of ambient temperature structures has been validated in the laboratory and is being promoted for engineering applications. Due to the strong openness of ground flutter simulation testing technology, it can easily conduct tests and verifications of thermal flutter, aerodynamic servoelasticity, etc., and has broad application prospects. In summary, when studying ground flutter simulation testing, researchers mainly need to consider key technical points such as unsteady aerodynamic force order reduction and reconstruction methods, and multi-input multi-output system controllers.

[0003] Virtual testing refers to the simulation of complex physical systems in a virtual environment using computer modeling and simulation technology. It primarily assesses whether the functions and performance of the complex physical system meet design requirements. Using virtual testing systems to replace actual complex physical systems allows for unlimited number of tests and ensures repeatability. Virtual testing can lay the foundation for preliminary work in real system testing and can, to some extent, replace tests that cannot be performed in physical systems. In costly, labor-intensive, and time-consuming physical system testing, it can solve resource shortages, shorten testing time, save expenses, and avoid the emission of harmful substances from some real system tests, reducing environmental pollution. With the widespread application of virtual testing technology, its advantages have been recognized in various fields. Unlike ground flutter simulation testing technology, the main challenges of ground flutter virtual testing technology lie in simulating the nonlinear characteristics during test piece installation, modeling the dynamic coupling model between the exciter and the test piece, and simulating the dynamic response of the test piece during flutter. Summary of the Invention

[0004] This application provides a virtual test modeling method for typical control surface ground flutter considering rudder shaft clearance. The purpose is to overcome the problem that traditional methods have difficulty in considering the influence of rudder shaft clearance, so as to make the control surface simulation results more accurate and closer to the actual situation.

[0005] Firstly, a virtual test modeling method for ground flutter is provided. This method is used to establish a model with an exciter, control surfaces, and a control shaft. The modeling method includes:

[0006] A reduced-order rigid-flexible coupled dynamic model is constructed, which includes the reduced-order mass and reduced-order stiffness corresponding to boundary point self-coupling, boundary point-internal point coupling, internal point-boundary point coupling, and internal point self-coupling.

[0007] Based on the reduced-order modal degree of freedom displacement, reduced-order modal degree of freedom velocity, the force of the exciter and the force on the rudder shaft, the reduced-order rigid-flexible coupling dynamic model is solved to obtain the displacement, velocity and acceleration of the excitation table, wherein the force on the rudder shaft is determined based on the rudder shaft displacement and rudder shaft clearance.

[0008] Compared with the prior art, the solution provided in this application has at least the following beneficial technical effects:

[0009] This invention proposes a virtual test modeling method for ground flutter of typical control surfaces based on a rigid-flexible coupled multibody dynamics model, an exciter electromechanical coupling model, an exciter feedback control model, a collision model, and an aerodynamic model. By coupling the collision model with the flexible multibody dynamics model, the model established by this method can take into account the rudder shaft clearance and carry out virtual tests of ground flutter of typical control surfaces.

[0010] In conjunction with the first aspect, in some implementations of the first aspect, the force on the rudder shaft satisfies:

[0011] When |x r |-δ<1×10 -5 At that time, the rudder shaft is subjected to force f r =F s +F d Collision elastic force F s With collision damping force F d for:

[0012] x r δ represents the displacement of the rudder shaft paddle node, and δ represents the initial clearance.

[0013] The solution provided in this application can simultaneously consider both the elastic force and the damping force of the collision, so as to take into account a relatively large number of collision forces and make the analysis results more accurate.

[0014] In conjunction with the first aspect, in some implementations of the first aspect, the force of the exciter is determined based on the displacement, velocity, and acceleration of the excitation platform, as well as the coil current.

[0015] In conjunction with the first aspect, in some implementations of the first aspect, the force of the exciter satisfies:

[0016]

[0017] Kf represents the Ampere force coefficient experienced by the coil when it is energized, i represents the current flowing through the coil, x, and Let be the displacement, velocity, and acceleration of the excitation table, respectively; m, c, and k be the mass, damping, and support stiffness of the exciter's moving coil, respectively; and f be the force exerted by the exciter.

[0018] In conjunction with the first aspect, in some implementations of the first aspect, the coil current i satisfies:

[0019]

[0020] Where K f The induced electromotive force coefficient of the coil is represented by V, the exciter resistance is R, the output voltage is V, the input voltage is V, and the power amplifier coefficient is G.

[0021] In conjunction with the first aspect, in some implementations of the first aspect, the input voltage satisfies:

[0022]

[0023] Where k1, k2, k3, and k4 are manually specified state feedback coefficients, f a This is the output signal of the exciter.

[0024] In conjunction with the first aspect, in some implementations of the first aspect, the exciter output signal f a satisfy:

[0025]

[0026] Where H(s) is the aerodynamic transfer function, u b This is the displacement vector of the boundary nodes.

[0027] In conjunction with the first aspect, in some implementations of the first aspect, the reduced-order rigid-flexible coupling dynamic model satisfies:

[0028]

[0029] in and u b These are the acceleration vector and displacement vector of the boundary nodes, respectively, f b Let η be the load vector at the model boundary nodes. * For reduced-order modal degrees of freedom displacement, Represents the acceleration of the reduced-order modal degrees of freedom. and These represent the reduced quality corresponding to boundary point self-coupling, boundary point-interior point coupling, interior point-boundary point coupling, and interior point self-coupling, respectively. and These represent the reduced-order stiffness corresponding to boundary point self-coupling, boundary point-internal point coupling, internal point-boundary point coupling, and internal point self-coupling, respectively.

[0030] In conjunction with the first aspect, in some implementations of the first aspect, solving the reduced-order rigid-flexible coupled dynamic model includes:

[0031] Solve the state equations:

[0032]

[0033] in

[0034]

[0035]

[0036] C = [I 0 I 0], D = [0]

[0037]

[0038] I is the identity matrix, η * For reduced-order modal degrees of freedom displacement, x represents the acceleration of the reduced-order modal degrees of freedom. r x represents the displacement of the rudder shaft lever node. e For the trailing edge node displacement of the rudder tip, the exciter force f e =-f, f r For the rudder shaft under force, the boundary node displacement signal u b =x, boundary node velocity signal Boundary node acceleration signal

[0039] In a second aspect, an electronic device is provided for performing the ground flutter virtual test modeling method as described in any of the implementations of the first aspect above. Attached Figure Description

[0040] Figure 1 This is a schematic flowchart illustrating a virtual test modeling method for ground flutter provided in an embodiment of this application.

[0041] Figure 2 This is a schematic flowchart illustrating a virtual test modeling method for ground flutter provided in an embodiment of this application.

[0042] Figure 3 This is a schematic structural diagram of an electromagnetic exciter.

[0043] Figure 4 This is a schematic diagram showing the connection between the exciter and the rudder surface.

[0044] Figure 5 This is a schematic structural diagram of a typical finite element model of a rudder surface.

[0045] Figure 6 This is the time-domain signal of acceleration at a typical control surface measurement point without gaps.

[0046] Figure 7 This is the time-domain acceleration signal at a typical control surface measurement point with a gap.

[0047] Figure 8 This is a typical rudder shaft deflection angle signal with gaps. Detailed Implementation

[0048] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0049] Figure 1 This is a schematic flowchart of a virtual test modeling method for ground flutter provided in an embodiment of this application.

[0050] 110. Construct a reduced-order rigid-flexible coupled dynamic model. The reduced-order rigid-flexible coupled dynamic model includes the reduced-order mass and reduced-order stiffness corresponding to boundary point self-coupling, boundary point-internal point coupling, internal point-boundary point coupling, and internal point self-coupling.

[0051] 120. Based on the reduced modal degrees of freedom displacement, reduced modal degrees of freedom velocity, exciter force and rudder shaft force, solve the reduced rigid-flexible coupling dynamic model to obtain the excitation table displacement, velocity and acceleration, where the rudder shaft force is determined based on the rudder shaft displacement and rudder shaft clearance.

[0052] The following is combined with Figure 2 This paper describes one implementation of the modeling method provided in this application.

[0053] Step 1: Aerodynamic Model Building

[0054] The aerodynamic model uses a transfer function form.

[0055]

[0056] Where H(s) is the aerodynamic transfer function, which can be calculated using the commercial software ZAERO or specified manually. The input signal for the aerodynamic model is u. b u b This represents the boundary node displacement vector. The output signal is the exciter output signal f. a In the initial load step, u b It can be specified manually.

[0057] Step 2: Modeling the exciter feedback control system

[0058] The exciter feedback control system adopts a state feedback approach, which includes displacement feedback, velocity feedback, and acceleration feedback. Its theoretical model is as follows:

[0059]

[0060] Where x, and These represent the displacement, velocity, and acceleration of the excitation platform, respectively, x, and Given by the typical control surface output signal. a The input signal is given by the exciter output signal. k1, k2, k3, and k4 are manually specified state feedback coefficients. The input signal of the state feedback control system is x, and f a The output signal is V input. In the initial load step, x, and It can be specified manually.

[0061] Step 3: Modeling the electromechanical coupling of the exciter

[0062] First, an electromechanical coupling model of the exciter is established. The structure of the electromagnetic exciter is shown in [reference needed]. Figure 3 The connection relationship between the exciter and a typical control surface is shown in [reference needed]. Figure 4 Based on the working principle of the vibrator, the mathematical model of the mechanical part of the vibrator can be expressed as:

[0063]

[0064] Among them, K f The coefficient of Ampere force on the coil when it is energized is represented by i, and the current flowing through the coil is represented by x. and These represent the displacement, velocity, and acceleration signals of the excitation platform, respectively; m, c, and k represent the mass, damping, and support stiffness of the exciter's moving coil, respectively; and f represents the typical feedback force signal from the control surface. The electrical components of the exciter include resistance and inductance, and its mathematical model can be expressed as:

[0065]

[0066] Where V 输出 K represents the output voltage of the power amplifier. f R represents the induced electromotive force coefficient of the coil, and R is the exciter resistance. The mathematical model of the power amplifier in the exciter can be expressed as:

[0067] V 输出 =GV 输入 (5)

[0068] Among them, V 输出 V is the output voltage of the power amplifier. 输入Let V be the input voltage of the power amplifier, and G be the power amplifier coefficient. The input signal of the electromechanical coupling model of the exciter is the input voltage V. 输入 and the displacement signal x and velocity signal of the excitation table acceleration signal The output signal is a typical control surface feedback force signal f.

[0069] Step 4: Modeling the rudder shaft clearance collision model

[0070] The initial clearance between the mounting device and the rudder shaft is δ. The formula for determining if the mounting device collides with the rudder shaft lever is:

[0071] |x r |-δ<1×10 -5 (6)

[0072] x r Let F be the displacement of the rudder shaft lever node. When the bearing device and the rudder shaft displacement satisfy the above equation, then there exists a collision elastic force F. s With collision damping force F d for

[0073]

[0074]

[0075] Among them, the maximum collision elastic force constraint x max and maximum collision damping force constraint Parameters are manually defined. Based on the rudder shaft clearance collision model, the parameters can be determined according to the rudder shaft displacement x. r and speed Obtain the collision elastic force F s With collision damping force F d Thus, the force signal f of the rudder shaft is obtained. r =F s +F d .

[0076] Step 5: Modeling typical control surfaces

[0077] A typical finite element model of a control surface was established based on FEM software, specifically as follows: Figure 4 , Figure 5 As shown. Typical control surfaces are selected, with the root node of the control shaft and the trailing edge node of the control tip as boundary nodes. It is assumed that the highest frequency for dynamic analysis is f. max Modal truncation only retains modal frequencies below f. max The modal dynamics of the reduced-order substructure with rigid-flexible coupling are as follows:

[0078]

[0079] in and u bThese are the acceleration vector and displacement vector of the substructure boundary nodes, respectively, f b η is the load vector of the boundary nodes of the substructure model. * For reduced-order modal degrees of freedom displacement, Represents the acceleration of the reduced-order modal degrees of freedom. and These represent the reduced quality corresponding to boundary point self-coupling, boundary point-interior point coupling, interior point-boundary point coupling, interior point-interior point coupling, and interior point self-coupling, respectively. and These represent the reduced-order stiffness corresponding to boundary point self-coupling, boundary point-interior point coupling, interior point-boundary point coupling, and interior point self-coupling, respectively. Transformation matrix H * for

[0080] H * =[Ξ Φ * (10)

[0081] Boundary point constrained mode Ξ and fixed boundary point reduced-order mode matrix Φ* can be obtained by changing the boundary point constraints of the finite element model.

[0082] make

[0083]

[0084] Formula (10) can be transformed into the form of substructure dynamics equations in state-space equations.

[0085]

[0086] in

[0087]

[0088] C = [I 0 I 0], D = [0]

[0089]

[0090] Where I is the identity matrix.

[0091] x r x represents the displacement of the rudder shaft lever node. e This represents the displacement of the trailing edge node of the rudder tip. This step yields a reduced-order model of a typical flexible rudder surface, with the exciter force signal f as the input. e =-f and rudder shaft force signal f r The output is the boundary node displacement signal u. b =x, velocity signal acceleration signal The displacement, velocity, and acceleration signals of the trailing edge node of a typical control surface tip are the corresponding dynamic response signals of the excitation platform.

[0092] According to formula (12), the vector x in the i-th step can be obtained. s Given vector u, solve for the vector in step i. x at step i+1 s It can be derived from the i-th step. The results are obtained. Then, steps one through five are repeated in a loop to obtain the time-domain simulation results of the ground flutter virtual test model.

[0093] In some embodiments, time-domain simulations can be performed in MATLAB by coupling the electromechanical coupling model of the exciter, the typical control surface model, the exciter feedback control model, the control shaft clearance collision model, and the aerodynamic model to obtain the virtual test response signal of typical control surface ground flutter. This virtual experiment considers the clearance, and the acceleration signal remains at zero for a specific time period, which is consistent with the theoretical analysis, proving the modeling is correct.

[0094] This application will be further described in detail below.

[0095] Example 1

[0096] The model to be processed in this example is a virtual test model of ground flutter of a typical control surface considering rudder shaft clearance. The model is divided into an exciter electromechanical coupling model, a typical control surface model, an exciter feedback control model, a rudder shaft clearance collision model, and an aerodynamic model. The geometric model of the typical control surface is as follows: Figure 4 As shown.

[0097] (1) Electromechanical coupling model of exciter

[0098] Given the electromechanical coupling model parameters of the exciter, where the resistance R = 16.8Ω and the induced electromotive force coefficient K of the coil... f =0.9044N / A, exciter mass m =0.2275kg, damping c =4.5N / (m / s), stiffness k =2542.1N / s, power amplifier coefficient G =2.

[0099] (2) Typical control surface model

[0100] Given the parameters of a typical rigid-flexible coupling model of a control surface, f max Given a 100Hz frequency, its finite element model is shown below. Figure 4 and Figure 5 H was subsequently obtained * Generalized mass matrix and generalized stiffness matrix Finally, the coefficient matrices A, B, C, and D of the dynamic equations in state-space form are obtained.

[0101] (3) Exciter feedback control model

[0102] Given the model parameters of the exciter feedback control model, and given k1 = 4.2V / (m / s) 2 ), k2=83.6V / (m / s), k3=4.7E4 V / m and k4=18.5V / N.

[0103] (4) Rudder shaft clearance collision model

[0104] Given the collision model parameters δ = 1 mm for the rudder shaft clearance, x max =0.1mm,

[0105] (5) Aerodynamic Model and Simulation Calculation

[0106] To simplify the calculation, H(s) = 1 was chosen for verification. The electromechanical coupling model of the exciter, the typical control surface model, the exciter feedback control model, the control shaft clearance collision model, and the aerodynamic model were coupled. Discrete-time simulation was conducted. Given a unit pulse force at the trailing edge node of the typical control surface tip, the linear time-domain response without clearance and the nonlinear dynamic time-domain response with clearance at this node are as follows: Figure 6 and Figure 7 As shown, the rudder shaft time-domain deflection angle signal is as follows Figure 8 As shown in the figure, this invention can take into account the rudder shaft clearance, conduct virtual test modeling and simulation of ground flutter of typical rudder surfaces, and facilitate ground flutter analysis of typical rudder surfaces.

[0107] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A method for modeling virtual ground flutter tests, characterized in that, The modeling method is used to establish a model with an exciter, control surface, and control shaft. The modeling method includes: A reduced-order rigid-flexible coupled dynamic model is constructed, which includes the reduced-order mass and reduced-order stiffness corresponding to boundary point self-coupling, boundary point-internal point coupling, internal point-boundary point coupling, and internal point self-coupling. Based on the reduced modal degrees of freedom displacement, reduced modal degrees of freedom velocity, the force of the exciter and the force on the rudder shaft, the reduced rigid-flexible coupling dynamic model is solved to obtain the displacement, velocity and acceleration of the excitation table, wherein the force on the rudder shaft is determined based on the rudder shaft displacement and rudder shaft clearance. The reduced-order rigid-flexible coupling dynamic model satisfies: in and These are the acceleration vector and displacement vector of the boundary nodes, respectively. For the load vectors at the model boundary nodes, For reduced-order modal degrees of freedom displacement, Represents the acceleration of the reduced-order modal degrees of freedom. , , and These represent the reduced quality corresponding to boundary point self-coupling, boundary point-interior point coupling, interior point-boundary point coupling, and interior point self-coupling, respectively. , , and These represent the reduced-order stiffness corresponding to boundary point self-coupling, boundary point-internal point coupling, internal point-boundary point coupling, and internal point self-coupling, respectively.

2. The ground flutter virtual test modeling method according to claim 1, characterized in that, The rudder shaft is subjected to the following forces: when At that time, the rudder shaft is subjected to force Collision elastic force With collision damping force for: , , For the rudder shaft paddle node displacement, This is the initial gap.

3. The ground flutter virtual test modeling method according to claim 1, characterized in that, The force applied by the exciter is determined based on the displacement, velocity, and acceleration of the excitation platform, as well as the current flowing through the coil.

4. The ground flutter virtual test modeling method according to claim 3, characterized in that, The force exerted by the exciter satisfies: This represents the Ampere force coefficient experienced by the coil when it is energized. This indicates the current flowing through the coil. , and These are the displacement, velocity, and acceleration of the excitation platform, respectively. , and These are the exciter moving coil mass, damping, and support stiffness, respectively. The force exerted by the exciter.

5. The ground flutter virtual test modeling method according to claim 4, characterized in that, The coil is energized by current. satisfy: ， ， in This represents the coefficient of the induced electromotive force of the coil. For the exciter resistor, For output voltage, Input voltage, This is the power amplifier coefficient.

6. The ground flutter virtual test modeling method according to claim 5, characterized in that, The input voltage satisfies: ， in , , and Specify the state feedback coefficient manually. This is the output signal of the exciter.

7. The ground flutter virtual test modeling method according to claim 6, characterized in that, The exciter output signal satisfy: in Let be the aerodynamic transfer function. This is the displacement vector of the boundary nodes.

8. The ground flutter virtual test modeling method according to claim 1, characterized in that, Solving the reduced-order rigid-flexible coupling dynamic model includes: Solve the state equations: in ， ， It is the identity matrix. For reduced-order modal degrees of freedom displacement, Represents the acceleration of the reduced-order modal degrees of freedom. For the rudder shaft paddle node displacement, The displacement of the trailing edge node of the rudder tip, and the force of the exciter. , For the rudder shaft under stress, the displacement signal of the boundary node Boundary node velocity signal Boundary node acceleration signal .

9. An electronic device, characterized in that, The electronic device is used to perform the ground flutter virtual test modeling method as described in any one of claims 1 to 8.

Images