Aircraft hot pneumatic servo elastic coupling analysis method

Abstract

The invention discloses a thermal aerodynamic servo elastic coupling analysis method for an aircraft, which comprises the following steps: by taking a time propulsion step length of unsteady aerodynamic force as a time step length, calculating a temperature field of a complete structure of the aircraft at each discrete moment by adopting an aerodynamic thermal reduced-order model at the current time step to obtain a thermal mode of the aircraft; solving aerodynamic force by adopting an unsteady aerodynamic force reduced-order model, calculating aeroelastic response analysis of a thermal mode of the aircraft after aerodynamic heating, transmitting aeroelastic response information of the aircraft to a servo control system steering engine dynamical model, outputting control force of a next time step, and calculating the aeroelastic response of the aircraft. And then solving the pneumatic servo elastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the next time step until the hot pneumatic servo elastic calculation of the whole flight trajectory is completed. According to the method, the influence of friction and clearance of the aircraft servo control system on aeroelasticity calculation is considered, the aerodynamic force and the aerodynamic heat are calculated by adopting the reduced-order model, and the calculation efficiency is improved while the solving precision is ensured.

Description

Technical Field

[0001] The invention relates to an aircraft thermo-aerodynamic servoelastic coupling analysis method, belonging to the technical field of aircraft aeroelastic analysis. Background Art

[0002] With the requirements for high speed, high maneuverability, high load and high flight efficiency of aircraft, the proportion of aircraft structure weight is constantly decreasing, and the harsh aerodynamic thermal environment caused by high-speed flight leads to a further decrease in structural stiffness. The thermo-aerodynamic servoelasticity problem caused by the coupling of complex multi-physics fields such as aerodynamics, aerodynamic heat, structural dynamics and control seriously affects the stable operation of the aircraft and is a key problem that must be solved in the aircraft design process.

[0003] The thermal environment of the actual aircraft structure is closely related to its flight trajectory. It is difficult to accurately simulate the thermal environment of the entire trajectory of the aircraft in ground tests. Numerical simulation is the main research method for the design and analysis of aircraft thermoaeroelastic problems. In terms of research objects, most studies are limited to the thermoaeroelastic analysis of a single wing. The article "Aerodynamic thermoelastic analysis of rudder surface under different flow states [J]. Aviation Science and Technology, 2023, 34(11): 34-43.]" simulates the flutter problem of the rudder model under different flow states through Fluent and Ansys coupling. The article "Comprehensive analysis of aerodynamic heat and static aeroelasticity of hypersonic wing surface [J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, 38(01): 53-58.]" decouples the thermoaeroelastic problem by using a hierarchical solution approach, and studies the static aeroelastic problem of the aircraft wing surface considering the influence of thermal effects. In these studies, some state points are selected for thermoaeroelastic analysis, ignoring the real-time changes of the aircraft aerodynamic environment along the trajectory, and cannot fully describe the real flight state. In terms of aerodynamic calculation, Chinese patent CN103077259A proposes an unsteady aerodynamic expression applicable to arbitrary shapes based on the local piston theory, but does not consider the influence of gas viscosity on aerodynamic calculation. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, to propose a method for analyzing the thermal aerodynamic servoelastic coupling of an aircraft, to perform numerical simulation in the entire flight trajectory and to establish a finite element model of the aircraft, to use a reduced-order model combining intrinsic orthogonal decomposition and a proxy model to calculate the aerodynamic force and aerodynamic heat carried by the aircraft, to avoid the large amount of time consumption caused by direct CFD calculation while ensuring accuracy, to improve calculation efficiency, and to realize the thermal aerodynamic servoelastic coupling analysis of the aircraft.

[0005] The technical solution of the present invention is:

[0006] A method for analyzing aircraft thermo-aerodynamic-servoelastic coupling, comprising:

[0007] Step 1: Establish the aircraft thermodynamic model, aerodynamic model, structural elastic model including control surfaces and servo control system model;

[0008] Step 2: A model reduction method combining intrinsic orthogonal decomposition and surrogate model is used to construct an aerodynamic thermal reduction model to calculate the temperature field of the structure after static aerodynamic thermoelastic trimming under given ballistic flight conditions;

[0009] Step 3: Use the model reduction method combining intrinsic orthogonal decomposition and surrogate model to construct an aerodynamic reduced-order model, perform unsteady CFD calculations to solve aerodynamic load training data, reduce the dimension of samples based on the training data, and obtain an unsteady aerodynamic reduced-order model;

[0010] Step 4: Establish a servo control system steering gear dynamics model;

[0011] Step 5: Use the aerodynamic thermal reduction model to calculate the temperature distribution of the aircraft surface at each discrete moment under given ballistic flight conditions, interpolate the time-varying aircraft surface temperature distribution at the surface nodes of the structural elastic model, obtain the finite element boundary conditions for calculating transient heat conduction, and use the CFD method to calculate the temperature field of the complete structure of the aircraft at each discrete moment;

[0012] Step 6: Calculate the thermal mode of the aircraft based on the temperature field of the complete structure of the aircraft;

[0013] Step 7: Use the unsteady aerodynamic reduced-order model to solve the aerodynamic force, calculate the aeroelastic response analysis of the aircraft thermal mode after aerodynamic heating, and update the aerodynamic mesh of the aerodynamic reduced-order model by the dynamic mesh method based on the structural deformation;

[0014] Step 8: Transmit the aircraft aeroelastic response information to the servo control system steering gear dynamics model, and output the control force according to the control requirements;

[0015] Step 9: Advance the time step ΔT of the unsteady aerodynamic force aero is the time step, based on step 7, the aerodynamic servoelastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the current time step is solved, and then the control force for the next time step is calculated based on step 8, and then the control force for the next time step is calculated by returning to step 7 to solve the aerodynamic servoelastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the next time step; wherein, the time advancement step ΔT of the servo system output control force servo The time step length ΔT of the unsteady aerodynamic force aero same;

[0016] Step 10: If the calculation time of step 9 reaches the set time, return to step 5 until the thermoaero-servoelastic calculation of the full flight trajectory is completed.

[0017] Furthermore, in step 1, when establishing the aircraft structural elastic model, the gap and friction factors between the rudder surface and the rudder shaft are added, and the nonlinearity of the structure is simulated by contact pairs; the rudder seam gasket and the rudder shaft constitute a contact pair, the rudder seam gasket and the rudder surface constitute a contact pair, and the screw and the bearing constitute a contact pair; the mesh of the contact area is encrypted; wherein, the contact stiffness K of the contact pair interface normal is n and tangential contact stiffness K t They are:

[0018]

[0019] Where D is the fractal dimension; G is the characteristic scale coefficient; δ max is the maximum deformation of the micro-convex body on the bonding surface; δ c is the critical deformation of the micro-convex body of the bonding surface, when δ<δ c The microconvex body undergoes elastic deformation. When δ>δ c The micro-convex body undergoes plastic deformation; E. v and μ are the equivalent elastic modulus, shear modulus, Poisson's ratio and friction coefficient of the bonding surface; a c is the critical contact area; a l is the area of ​​the maximum contact point, T m is the tangential load on the joint surface, P m is the normal load on the joint surface.

[0020] Furthermore, in step 2, the method for obtaining the unsteady aerodynamic reduced-order model is specifically as follows:

[0021] Select the flight Mach number, flight altitude and flight angle of attack as design variables and obtain the sample points X=[x1,x2,…,x n ] T , the balanced temperature is obtained by CFD unsteady numerical simulation as the sample corresponding matrix Y = [y1, y2, ..., y n ] T ,and is the temperature of the jth node of the structure at the i-th sample point. There are n sample points in total and N nodes in the structure;

[0022] Perform singular value decomposition on the response matrix Y to obtain the eigenvector ψ0 of the matrix Y, Y T YV=VΛ,ψ0=YV, where Λ is a diagonal matrix formed by eigenvalue ξ; V is a matrix with columns Y T The matrix of eigenvectors of Y;

[0023] According to the eigenvalue ξ, a small part of the first basis vectors, namely the truncated m-dimensional (m<<n) POD basis ψ, is selected to approximately fit the spatial characteristics of all samples, and the mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model.

[0024] Furthermore, in step 3, a method combining intrinsic orthogonal decomposition and surrogate model is used to construct an aerodynamic reduction model, the flight Mach number, flight Reynolds number and flight angle of attack are selected as design variables, the Latin hypercube experimental design method is used to obtain n sample points in the design space, excitation signals are applied to all structural degrees of freedom to calculate the solution of the unsteady aerodynamic force, the POD method is used to obtain the truncated mode and modal coefficients, and the mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model.

[0025] Furthermore, in step 4, a servo control system steering gear dynamics model is established, and the specific method is as follows:

[0026] The servo control system's servo transfer function uses a second-order dynamics model, which rewrites the servo transfer function in the frequency domain into a state space form:

[0027]

[0028] In the formula, A c is the system matrix; B c is the control matrix; C c is the output matrix; x c is the system state vector; y c is the system output vector; u is the servo control command vector; u s is the rudder surface deflection vector;

[0029] The state-space equations for an elastic body and unsteady aerodynamic forces:

[0030]

[0031] In the formula, A s is the system matrix of the generalized controlled object; B s is the control matrix; C s is the output matrix; D s is a direct transfer matrix; x s is the state vector of the generalized controlled object; y s is the deformation vector caused by elastic vibration;

[0032] Consider the k-order control law state space form of the servo control system:

[0033]

[0034] In the formula,

[0035]

[0036] In the formula, A k is the system matrix; B k is the control matrix; C k is the output matrix; D k is a direct transfer matrix; x k is the system state vector; y k is the system output vector; u k is the control law command vector; r is the reference input of the closed-loop system;

[0037] The above three state-space equations are combined to obtain the closed-loop control equation of the aircraft aeroservoelasticity:

[0038]

[0039] The system matrix is ​​in the following form:

[0040]

[0041] Furthermore, in step 7, the hybrid method of super-finite interpolation is used to realize the grid interpolation of aerodynamic calculation, the entire flow field grid is divided into multiple blocks, and the static equilibrium equation is solved by the iterative method to linearly distribute the deformation at the boundary of the grid block to each node of the grid. The corresponding static equilibrium equation is as follows:

[0042]

[0043] In the formula, k ij is the spring stiffness of edge ij; k t,jj It is to avoid excessive deformation of the unit to add torsional stiffness; Δx j is the displacement of the jth node connected to the spring; Δx i is the displacement to be calculated; N is the number of points connected to the node to be calculated by springs.

[0044] Furthermore, when the calculated time reaches the set time, return to step 5 and set the time ΔT heat , ΔT heat =NΔT aero , N is a positive integer.

[0045] Furthermore, the aerodynamic model is based on the Navier-Stokes equations to simulate the interaction between the aircraft surface and the surrounding airflow.

[0046] The advantages of the present invention compared with the prior art are:

[0047] When the present invention performs thermal aerodynamic servoelastic coupling analysis, the servo control structure of the aircraft is covered during modeling and nonlinear factors such as friction and clearance between the servo and the rudder shaft are considered. Numerical simulation is carried out for the complete flight trajectory, which can more accurately simulate the real motion state of the aircraft. The reduced-order model is used to calculate aerodynamic force and aerodynamic heat, avoiding the large amount of computational consumption of direct CFD solution. In the time domain advancement calculation, time loose coupling is adopted, and the aerodynamic heat and structural heat conduction coupling are calculated in a larger time step, and aerodynamic servoelastic coupling is performed in a smaller time step, which ensures accuracy while improving calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0049] Figure 1 This is a flow chart of thermal aerodynamic servoelastic coupling analysis according to an embodiment of the present invention;

[0050] Figure 2 Schematic diagram of bidirectional time-domain loose coupling of thermoaerodynamic servoelasticity according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0052] Aircraft thermo-aero-servoelastic coupling refers to the physical coupling relationship of different strengths among the thermal environment, aerodynamic force, elastic force, inertial force and control force formed by aerodynamic heating when the aircraft is flying at high speed. The present invention proposes an aircraft thermo-aero-servoelastic coupling analysis method, such as Figure 1 As shown, including:

[0053] Step 1: Establish the aircraft thermodynamic model, aerodynamic model, structural elasticity model and servo control system model.

[0054] The thermodynamic model takes into account the heat exchange between the aircraft surface and the surrounding environment. The aerodynamic model is based on the Navier-Stokes equations to simulate the interaction between the aircraft surface and the surrounding airflow. The servo control system model provides the control force required for the aircraft attitude control. The structural elastic model uses the finite element method to analyze the dynamic response of the aircraft structure under the action of thermal loads, aerodynamic loads and control forces.

[0055] When establishing the aircraft structural elastic model, the gap and friction factors between the rudder surface and the rudder shaft are added, and the nonlinearity of the structure is simulated by contact pairs. The rudder seam gasket and the rudder shaft form a contact pair, the rudder seam gasket and the rudder surface form a contact pair, and the screw and the bearing form a contact pair. The mesh of the contact area is encrypted to ensure the calculation accuracy during nonlinear calculation. Among them, the contact stiffness K of the contact pair interface normal n and tangential contact stiffness K t They are:

[0056]

[0057] Where D is the fractal dimension; G is the characteristic scale coefficient; δ max is the maximum deformation of the micro-convex body on the bonding surface; δ c is the critical deformation of the micro-convex body of the bonding surface, when δ<δ c The microconvex body undergoes elastic deformation. When δ>δ c The micro-convex body undergoes plastic deformation; E. v and μ are the equivalent elastic modulus, shear modulus, Poisson's ratio and friction coefficient of the bonding surface; a c is the critical contact area; a l is the area of ​​the maximum contact point, T m is the tangential load on the joint surface, P m is the normal load on the joint surface.

[0058] Step 2: A model reduction method combining proper orthogonal decomposition (POD) and surrogate model (hereinafter referred to as POD-Surrogate) is used to construct an aerodynamic thermal reduction model to calculate the temperature field of the structure after static aerodynamic thermoelastic balancing under given ballistic flight conditions.

[0059] The flight Mach number, flight altitude and flight angle of attack are selected as design variables, and the Latin hypercube and other experimental design methods are used to obtain the sample points X = [x1, x2, ..., x n ] T , the balanced temperature is obtained by CFD unsteady numerical simulation as the sample corresponding matrix Y = [y1, y2, ..., y n ] T ,and is the temperature of the jth node of the structure at the i-th sample point. There are n sample points in total and N nodes in the structure. Perform singular value decomposition on the response matrix Y to obtain the eigenvector ψ0 of the matrix Y, Y T YV=VΛ,ψ0=YV. Where Λ is a diagonal matrix formed by eigenvalue ξ; V is a matrix with columns Y T The matrix is ​​composed of the eigenvectors of Y. According to the eigenvalue ξ, a small number of the first basis vectors, that is, the truncated m-dimensional (m<<n) POD basis ψ, are selected to approximately fit the spatial characteristics of all samples. The mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model.

[0060] Step 3: Use the POD-Surrogate reduction method to construct an aerodynamic reduction model, use FLUENT to perform unsteady CFD (Computational Fluid Dynamics, hereinafter referred to as CFD) calculations to solve the aerodynamic load training data, reduce the dimensionality of the samples based on the training data, and obtain an unsteady aerodynamic reduction model.

[0061] The aerodynamic reduction model selects the flight Mach number, flight Reynolds number and flight angle of attack as design variables. Experimental design methods such as Latin hypercube are used to obtain n sample points in the design space. First, steady CFD is solved for each sample point to provide initial values ​​for the calculation of the unsteady flow field. Then, FLUENT is used to perform unsteady CFD calculations to solve the aerodynamic load training data of the sample point under the excitation signal. The sample is reduced in dimension based on the training data, and the POD method is used to obtain the truncated mode and modal coefficients. The mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging proxy model to obtain the unsteady aerodynamic reduction model.

[0062] Step 4: Establish the servo control system steering gear dynamics model

[0063] The servo control system's steering gear transfer function uses a second-order dynamics model:

[0064]

[0065] Where u(s) is the input command of the steering gear control; δ(s) is the output of the steering gear; k s is the steady-state gain of the servo; T s is the time constant of the servo; μ s is the damping ratio of the servo;

[0066] Rewrite the servo transfer function G(s) in the frequency domain into the state space form:

[0067]

[0068] In the formula, A c is the system matrix; B c is the control matrix; C c is the output matrix; x c is the system state vector; y c is the system output vector; u is the servo control command vector; u s is the rudder surface deflection vector.

[0069] The state-space equations for an elastic body and unsteady aerodynamic forces:

[0070]

[0071] In the formula, A s is the system matrix of the generalized controlled object; B s is the control matrix; C s is the output matrix; D s is a direct transfer matrix; x s is the state vector of the generalized controlled object; y s is the deformation vector caused by elastic vibration;

[0072] Consider the k-order control law state space form of the servo control system:

[0073]

[0074] In the formula,

[0075]

[0076] In the formula, A k is the system matrix; B k is the control matrix; C k is the output matrix; D k is a direct transfer matrix; x k is the system state vector; y k is the system output vector; u k is the control law command vector; r is the reference input of the closed-loop system.

[0077] The above three state-space equations are combined to obtain the closed-loop control equation of the aircraft aeroservoelasticity:

[0078]

[0079] The system matrix is ​​in the following form:

[0080]

[0081] Step 5: Use the aerodynamic thermal reduction model established in step S2 to calculate the temperature distribution of the aircraft surface at each discrete moment under given ballistic flight conditions. Interpolate the time-varying temperature distribution of the aircraft surface at the surface nodes of the finite element model to obtain the finite element boundary conditions for calculating transient heat conduction. Use the CFD method to calculate the temperature field of the complete structure of the aircraft at each discrete moment.

[0082] Step 6: Based on the temperature field of the complete structure of the aircraft in step S5, the corresponding thermal mode of the aircraft is calculated using the finite element method.

[0083] Step 7: Use the aerodynamic reduction model established in step S3 to solve the aerodynamic force, calculate the aeroelastic response analysis of the aircraft thermal mode after aerodynamic heating, and update the aerodynamic mesh of the aerodynamic reduction model by the dynamic mesh method based on the structural deformation.

[0084] In this embodiment, a hybrid method of transfinite interpolation is used to implement dynamic mesh interpolation. The entire flow field mesh is divided into multiple blocks. The static equilibrium equation is solved by an iterative method to linearly distribute the deformation at the boundary of the mesh block to each node of the mesh. The corresponding static equilibrium equation is as follows:

[0085]

[0086] In the formula, k ij is the spring stiffness of edge ij; k t,jj It is to avoid excessive deformation of the unit to add torsional stiffness; Δx j is the displacement of the jth node connected to the spring; Δx i is the displacement to be calculated; N is the number of points connected to the node to be calculated by springs.

[0087] Step 8: The unsteady aeroelastic response information of the aircraft is transmitted to the servo control system. According to the control requirements, the servo control system outputs the control force and torque.

[0088] Step 9: Advance the time step ΔT of the unsteady aerodynamic force aero is the time step, based on step S7, the aerodynamic servoelastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the current time step is solved, and then the control force of the next time step is calculated based on step 8, and then the step S7 is returned to solve the aerodynamic servoelastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the next time step; wherein, the time advancement step ΔT of the servo system output control force servo The time step length ΔT of the unsteady aerodynamic force aero same.

[0089] When the calculation time of step 10 and step 9 reaches the set time, return to step 5; until the thermoaerodynamic servoelastic calculation of the full flight trajectory is completed, the coupled analysis of the thermoaerodynamic servoelasticity of the aircraft is realized.

[0090] Figure 2 Schematic diagram of the loose coupling of thermo-aero-servoelasticity in the two-way time domain, from time T to T+ΔT aero Perform aero-servoelastic coupling calculation at all times: Perform aero-servoelastic solution based on the thermal mode, aerodynamic load and control force corresponding to the temperature field of the aircraft at time T, and so on until T+ΔT heat Moment. At ΔT heat During the time interval, the changes in the thermal modes of the aircraft structure are not considered.

[0091] In NΔT aero The aeroservoelastic solution of time steps reaches T+ΔT heat After time T+ΔT, it is considered that the structure has accumulated enough deformation and the impact on the thermal mode of the aircraft cannot be ignored. At this time, T+ΔT is recalculated. heat Aerodynamic heat distribution under time deformation, and then solve T+ΔT heat Thermal mode at time

[0092] At T+ΔT heat From time to T+2ΔT heat The above aerodynamic servoelastic calculation is repeated between the times, and so on, until the thermal aerodynamic servoelastic analysis of the entire trajectory is completed.

[0093] The above-described embodiments are only preferred specific implementations of the present invention. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing aircraft thermo-aerodynamic-servoelastic coupling, characterized in that: include: Step 1: Establish the aircraft thermodynamic model, aerodynamic model, structural elastic model including control surfaces and servo control system model; Step 2: A model reduction method combining intrinsic orthogonal decomposition and surrogate model is used to construct an aerodynamic thermal reduction model to calculate the temperature field of the structure after static aerodynamic thermoelastic trimming under given ballistic flight conditions; Step 3: Use the model reduction method combining intrinsic orthogonal decomposition and surrogate model to construct an aerodynamic reduced-order model, perform unsteady CFD calculations to solve aerodynamic load training data, reduce the dimension of samples based on the training data, and obtain an unsteady aerodynamic reduced-order model; Step 4: Establish a servo control system steering gear dynamics model; Step 5: Use the aerodynamic thermal reduction model to calculate the temperature distribution of the aircraft surface at each discrete moment under given ballistic flight conditions, interpolate the time-varying aircraft surface temperature distribution at the surface nodes of the structural elastic model, obtain the finite element boundary conditions for calculating transient heat conduction, and use the CFD method to calculate the temperature field of the complete structure of the aircraft at each discrete moment; Step 6: Calculate the thermal mode of the aircraft based on the temperature field of the complete structure of the aircraft; Step 7: Use the unsteady aerodynamic reduced-order model to solve the aerodynamic force, calculate the aeroelastic response analysis of the aircraft thermal mode after aerodynamic heating, and update the aerodynamic mesh of the aerodynamic reduced-order model by the dynamic mesh method based on the structural deformation; Step 8: Transmit the aircraft aeroelastic response information to the servo control system steering gear dynamics model, and output the control force according to the control requirements; Step 9: Advance the time step ΔT of the unsteady aerodynamic force aero is the time step, based on step 7, the aerodynamic servoelastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the current time step is solved, and then the control force for the next time step is calculated based on step 8, and then the control force for the next time step is calculated by returning to step 7 to solve the aerodynamic servoelastic response under the simultaneous action of the aerodynamic force and the control force corresponding to the next time step; wherein, the time advancement step ΔT of the servo system output control force servo The time step length ΔT of the unsteady aerodynamic force aero same; Step 10: If the calculation time of step 9 reaches the set time, return to step 5 until the thermoaero-servoelastic calculation of the full flight trajectory is completed.

2. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: In step 1, when establishing the aircraft structural elastic model, the gap and friction factors between the rudder surface and the rudder shaft are added, and the nonlinearity of the structure is simulated by contact pairs; the rudder seam gasket and the rudder shaft constitute a contact pair, the rudder seam gasket and the rudder surface constitute a contact pair, and the screw and the bearing constitute a contact pair; the mesh of the contact area is encrypted; among them, the contact stiffness K of the contact pair interface normal is n and tangential contact stiffness K t They are: Where D is the fractal dimension; G is the characteristic scale coefficient; δ max is the maximum deformation of the micro-convex body on the bonding surface; δ c is the critical deformation of the micro-convex body of the bonding surface, when δ<δ c The microconvex body undergoes elastic deformation. When δ>δ c The micro-convex body undergoes plastic deformation; E. v and μ are the equivalent elastic modulus, shear modulus, Poisson's ratio and friction coefficient of the bonding surface; a c is the critical contact area; a l is the area of ​​the maximum contact point, T m is the tangential load on the joint surface, P m is the normal load on the joint surface.

3. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: In step 2, the method for obtaining the unsteady aerodynamic reduced-order model is as follows: Select the flight Mach number, flight altitude and flight angle of attack as design variables and obtain the sample points X=[x1,x2,…,x n ] T , the balanced temperature is obtained by CFD unsteady numerical simulation as the sample corresponding matrix Y = [y1, y2, ..., y n ] T , and y i =[T i 1 ,T i 2 ,…,T i n ], T i j is the temperature of the jth node of the structure at the i-th sample point; there are n sample points in total and N nodes in the structure; Perform singular value decomposition on the response matrix Y to obtain the eigenvector ψ0 of the matrix Y, Y T YV=VΛ,ψ0=YV, where Λ is a diagonal matrix formed by eigenvalue ξ; V is a matrix with columns Y T The matrix of eigenvectors of Y; According to the eigenvalue ξ, a small part of the first basis vectors, namely the truncated m-dimensional (m<<n) POD basis ψ, is selected to approximately fit the spatial characteristics of all samples, and the mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model.

4. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: In step 3, the aerodynamic reduction model is constructed by combining the proper orthogonal decomposition and the surrogate model. The flight Mach number, flight Reynolds number and flight angle of attack are selected as design variables. The Latin hypercube experimental design method is used to obtain n sample points in the design space. The excitation signal is applied to all structural degrees of freedom to calculate the solution of the unsteady aerodynamic force. The POD method is used to obtain the truncated mode and modal coefficients. The mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model.

5. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: In step 4, the servo control system steering gear dynamics model is established. The specific method is as follows: The servo control system's servo transfer function uses a second-order dynamics model, which rewrites the servo transfer function in the frequency domain into a state space form: In the formula, A c is the system matrix; B c is the control matrix; C c is the output matrix; x c is the system state vector; y c is the system output vector; u is the servo control command vector; u s is the rudder surface deflection vector; The state-space equations for an elastic body and unsteady aerodynamic forces: In the formula, A s is the system matrix of the generalized controlled object; B s is the control matrix; C s is the output matrix; D s is a direct transfer matrix; x s is the state vector of the generalized controlled object; y s is the deformation vector caused by elastic vibration; Consider the k-order control law state space form of the servo control system: In the formula, In the formula, A k is the system matrix; B k is the control matrix; C k is the output matrix; D k is a direct transfer matrix; x k is the system state vector; y k is the system output vector; u k is the control law command vector; r is the reference input of the closed-loop system; The above three state-space equations are combined to obtain the closed-loop control equation of the aircraft aeroservoelasticity: The system matrix is ​​in the following form:

6. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: In step 7, the hybrid method of super-finite interpolation is used to realize the grid interpolation of aerodynamic calculation. The entire flow field grid is divided into multiple blocks. The static equilibrium equation is solved by the iterative method to linearly distribute the deformation at the boundary of the grid block to each node of the grid. The corresponding static equilibrium equation is as follows: In the formula, k ij is the spring stiffness of edge ij; k t,jj It is to avoid excessive deformation of the unit to add torsional stiffness; Δx j is the displacement of the jth node connected to the spring; Δx i is the displacement to be calculated; N is the number of points connected to the node to be calculated by springs.

7. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: When the calculated time reaches the set time, return to step 5 and set the time ΔT heat , ΔT heat =NΔT aero , N is a positive integer.

8. The aircraft thermo-aerodynamic-servoelastic coupling analysis method according to claim 1, characterized in that: The aerodynamic model is based on the Navier-Stokes equations and simulates the interaction between the aircraft surface and the surrounding airflow.

Images