A thermo-aero-servoelastic coupling analysis method for aircraft

Abstract

This invention discloses a method for thermo-aerodynamic servo-elastic coupling analysis of an aircraft. Using the time-step size of unsteady aerodynamic forces as the time increment, a reduced-order aerodynamic-thermal model is employed at the current time step to calculate the temperature field of the complete aircraft structure at each discrete moment, obtaining the aircraft's thermal modes. The reduced-order unsteady aerodynamic model is then used to solve for the aerodynamic forces, calculating the aeroelastic response of the aircraft's thermal modes after aerodynamic heating. This aeroelastic response information is then transferred to the servo control system's servo dynamics model, outputting the control force for the next time step. Subsequently, the aero-servo-elastic response under the simultaneous action of aerodynamic forces and control forces at the next time step is solved, until the thermo-aerodynamic-servo-elastic calculation of the entire flight trajectory is completed. This invention considers the influence of friction and clearance in the aircraft's servo control system on the aeroelastic calculation, employing a reduced-order model to calculate aerodynamic forces and aerodynamic heat, thus improving computational efficiency while ensuring solution accuracy.

Description

Technical Field

[0001] This invention relates to a method for thermo-aerodynamic servo-elastic coupling analysis of aircraft, belonging to the field of aircraft aeroelastic analysis technology. Background Technology

[0002] With increasing demands for high speed, high maneuverability, high load, and high flight efficiency in aircraft, the structural weight ratio of aircraft is continuously decreasing. The harsh aerodynamic and thermal environment caused by high-speed flight leads to a further decrease in structural stiffness. The thermo-aerodynamic servo-elasticity problem arising from the complex multi-physics coupling of aerodynamics, aerothermal dynamics, structural dynamics, and control seriously affects the stable operation of aircraft and is a key issue that must be addressed during the aircraft design process.

[0003] The thermal environment of an actual aircraft structure is closely related to its flight trajectory. Ground tests are difficult to accurately simulate the thermal environment of the entire ballistic trajectory of an aircraft. Numerical simulation is the main research method for the design and analysis of aircraft thermo-aeroelastic problems. In terms of research objects, most studies are limited to the thermo-aeroelastic analysis of a single airfoil. The article "Aero-thermoelastic Analysis of Control Surfaces under Different Flow Conditions [J]. Aeronautical Science and Technology, 2023, 34(11):34-43.]" simulated the flutter problem of the control surface model under different flow conditions using Fluent and Ansys coupled simulation. The article "Comprehensive Analysis of Hypersonic Airfoil Aero-thermo- and Static Aero-elasticity [J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, 38(01):53-58.]" adopted a layered solution approach to decouple the thermo-aeroelastic problem and studied the static aeroelastic problem of the aircraft airfoil considering the influence of thermal effects. In these studies, only some state points were selected for thermo-aeroelastic analysis, ignoring the real-time changes of the aircraft's aerodynamic environment along the trajectory, and thus failing to 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 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 this invention is to overcome the shortcomings of the prior art and propose a thermo-aerodynamic servo-elastic coupling analysis method for aircraft. Numerical simulation is performed throughout the entire flight trajectory, and a finite element model of the aircraft is established. A reduced-order model combining intrinsic orthogonal decomposition and surrogate model is used to calculate the aerodynamic forces and aerothermal forces carried by the aircraft. While ensuring accuracy, this method avoids the large amount of time consumption caused by direct CFD calculation, improves computational efficiency, and realizes the thermo-aerodynamic servo-elastic coupling analysis of aircraft.

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

[0006] A method for thermo-aerodynamic servo-elastic coupling analysis of aircraft includes:

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

[0008] Step 2: Construct an aerothermal reduced-order model using a model reduction method that combines intrinsic orthogonal decomposition and surrogate model, which is used to calculate the temperature field of the structure after static aerothermoelastic balancing under given ballistic flight conditions.

[0009] Step 3: Construct an aerodynamic reduced-order model using a model reduction method that combines intrinsic orthogonal decomposition and surrogate model, perform unsteady CFD calculations to solve the aerodynamic load training data, and reduce the dimensionality of the samples based on the training data to obtain the unsteady aerodynamic reduced-order model.

[0010] Step 4: Establish the dynamic model of the servo control system's servo motor;

[0011] Step 5: Calculate the temperature distribution on the surface of the aircraft at each discrete moment under given ballistic flight conditions using an aerodynamic thermal reduced-order model. Interpolate the time-varying temperature distribution on the surface nodes of the structural elastic 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.

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

[0013] Step 7: Solve the aerodynamic forces using an unsteady aerodynamic force reduction model, calculate the aeroelastic response of the aircraft's thermal modes after aerodynamic heating, and update the aerodynamic mesh of the constructed aerodynamic force reduction model by updating the structural deformation using the dynamic mesh method.

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

[0015] Step 9: Advance the time step ΔT using unsteady aerodynamic forces. aero For the time step, based on step 7, the aero-servo elastic response under the simultaneous action of aerodynamic force and control force at the current time step is solved. Then, based on step 8, the control force for the next time step is calculated. After that, step 7 is returned to solve for the aero-servo elastic response under the simultaneous action of aerodynamic force and control force at the next time step. The time step ΔT for the servo system output control force is defined as follows: servo Time-progression step ΔT with unsteady aerodynamic forces aero same;

[0016] Step 10: If the calculation time in step 9 reaches the set time, return to step 5 until the thermo-aerodynamic servo elasticity calculation of the entire flight trajectory is completed.

[0017] Furthermore, in step 1, when establishing the elastic model of the aircraft structure, the factors of clearance and friction between the control surface and the control shaft are incorporated, and contact pairs are used to simulate the nonlinearity of the structure; the control slot gasket and the control shaft form a contact pair, the control slot gasket and the control surface form a contact pair, and the lead screw and the bearing form a contact pair; the mesh of the contact area is refined; among which, the contact stiffness K of the contact pair mating surface is... n and tangential contact stiffness K t They are respectively:

[0018]

[0019] In the formula, D is the fractal dimension; G is the characteristic scale coefficient; δ max δ represents the maximum deformation of the micro-protrusion at the mating surface. c For the critical deformation of the micro-convexity of the mating surface, when δ < δ c The micro-convex body undergoes elastic deformation when δ > δ c Micro-protrusions undergo plastic deformation; E, v and μ are the equivalent elastic modulus, shear modulus, Poisson's ratio, and friction coefficient of the interface; a c The critical contact area; a l T represents the area of ​​the maximum contact point. m For the tangential load on the mating surface, P m This represents the normal load on the mating surface.

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

[0021] Selecting flight Mach number, flight altitude, and flight angle of attack as design variables, sample points X = [x1, x2, ..., x] are obtained in the design space. n ] T The balanced temperature was obtained using CFD unsteady numerical simulation as the sample matrix Y = [y1, y2, ..., y]. n ] T ,and Let be the temperature of the j-th node of the structure at the i-th sample point. There are a total of n sample points and N nodes in the structure.

[0022] Singular value decomposition of the response matrix Y yields the eigenvectors ψ0 and Y of matrix Y. T YV = VΛ, ψ0 = YV, where Λ is the diagonal matrix formed by the eigenvalues ​​ξ; V is a matrix composed of columns Y T The matrix composed of the eigenvectors of Y;

[0023] Based on the eigenvalue ξ, a small portion of the basis vectors, i.e. the truncated m-dimensional (m << n) POD basis ψ, is selected to approximate the characteristics of all sample spaces. The mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model.

[0024] Furthermore, in step 3, an aerodynamic reduced-order model is constructed by combining intrinsic orthogonal decomposition and surrogate model. 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 unsteady aerodynamic forces. The POD method is used to obtain truncated modes and modal coefficients. The mapping relationship between input parameters and POD modal coefficients is constructed through the Kriging surrogate model.

[0025] Furthermore, in step 4, a dynamic model of the servo control system's servo motor is established, specifically using the following method:

[0026] The servo motor transfer function of the servo control system adopts a second-order dynamic model, rewriting the servo motor transfer function in the frequency domain into a state-space form:

[0027]

[0028] In the formula, A c B is the system matrix; c For the control matrix; C c For the output matrix; x c y is the system state vector; c u is the system output vector; u is the servo control command vector; u s This refers to the steering deflection of the control surface;

[0029] State-space equations for elastic bodies and unsteady aerodynamic forces:

[0030]

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

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

[0033]

[0034] In the formula,

[0035]

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

[0037] Combining the above three state-space equations yields the aerodynamic servo-elastic closed-loop control equations for the aircraft:

[0038]

[0039] The system matrix in the formula is as follows:

[0040]

[0041] Furthermore, in step 7, a hybrid method of over-limit interpolation is used to interpolate the aerodynamic calculation grid. The entire flow field grid is divided into multiple blocks, and the static equilibrium equations are solved using an iterative method to linearly distribute the deformation at the grid block boundaries to each node of the grid. The corresponding static equilibrium equations are as follows:

[0042]

[0043] Where k ij It is the spring stiffness of edge ij; k t,jj This is torsional stiffness added to prevent excessive deformation of the element; Δx j It is the displacement of the j-th node connected to the spring; Δx i Let N be the displacement to be determined; N is the number of nodes connected to the node to be determined by springs.

[0044] Furthermore, when the calculation 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 this invention compared to the prior art are:

[0047] This invention, in performing thermo-aerodynamic servo-elastic coupling analysis, incorporates the aircraft's servo control structure into the modeling and considers nonlinear factors such as friction and clearance between the servo motor and the control shaft. Numerical simulation of the complete flight trajectory allows for a more accurate simulation of the aircraft's actual motion. A reduced-order model is used to calculate aerodynamic forces and aerothermal forces, avoiding the significant computational cost of direct CFD solutions. In the time-domain propulsion calculations, loose temporal coupling is employed, calculating aerothermal and structural heat conduction coupling over larger time steps and performing aerodynamic servo-elastic coupling over smaller time steps, ensuring accuracy while improving computational efficiency. Attached Figure Description

[0048] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0049] Figure 1 This is a flowchart of the thermo-aerodynamic servo elastic coupling analysis of an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of a thermo-pneumatic servo elastic bidirectional time-domain loose coupling according to an embodiment of the present invention. Detailed Implementation

[0051] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although 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. Rather, 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-aerodynamic servo-elastic coupling refers to the physical coupling relationship of varying strengths among the thermal environment, aerodynamic forces, elastic forces, inertial forces, and control forces generated by aerodynamic heating during high-speed flight. This invention proposes a method for analyzing aircraft thermo-aerodynamic servo-elastic coupling, such as... Figure 1 As shown, it includes:

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

[0054] The thermodynamic model considers heat transfer between the aircraft surface and its surrounding environment. The aerodynamic model, based on the Navier-Stokes equations, simulates the interaction between the aircraft surface and the surrounding airflow. The servo control system model provides the control forces required for the aircraft's attitude control. The structural elasticity model uses the finite element method to analyze the dynamic response of the aircraft structure under thermal loads, aerodynamic loads, and control forces.

[0055] In establishing the elastic model of the aircraft structure, the factors of clearance and friction between the control surface and the control shaft are incorporated, and contact pairs are used to simulate the nonlinearity of the structure. The control slot gasket and the control shaft form one contact pair, the control slot gasket and the control surface form one contact pair, and the lead screw and the bearing form one contact pair. The mesh in the contact area is refined to ensure computational accuracy during nonlinear calculations. The contact stiffness K of the contact pair mating surface is... n and tangential contact stiffness K t They are respectively:

[0056]

[0057] In the formula, D is the fractal dimension; G is the characteristic scale coefficient; δ max δ represents the maximum deformation of the micro-protrusion at the mating surface. c For the critical deformation of the micro-convexity of the mating surface, when δ < δ c The micro-convex body undergoes elastic deformation when δ > δ c Micro-protrusions undergo plastic deformation; E, v and μ are the equivalent elastic modulus, shear modulus, Poisson's ratio, and friction coefficient of the interface; a c The critical contact area; a l T represents the area of ​​the maximum contact point. m For the tangential load on the mating surface, P m This represents the normal load on the mating surface.

[0058] Step 2: Construct an aerothermal reduced-order model using a model reduction method combining Proper Orthogonal Decomposition (POD) and Surrogate (hereinafter referred to as POD-Surrogate), and calculate the temperature field of the structure after static aero-thermoelastic balancing under given ballistic flight conditions.

[0059] Flight Mach number, flight altitude, and flight angle of attack were selected as design variables, and experimental design methods such as Latin hypercube were used to obtain sample points X = [x1, x2, ..., x...]. n ] T The balanced temperature was obtained using CFD unsteady numerical simulation as the sample matrix Y = [y1, y2, ..., y]. n ] T ,and Let be the temperature of the j-th node of the structure at the i-th sample point. There are a total of n sample points and N nodes in the structure. Perform singular value decomposition on the response matrix Y to obtain the eigenvectors ψ0 and Y' of matrix Y. T YV = VΛ, ψ0 = YV. Where Λ is the diagonal matrix formed by the eigenvalues ​​ξ; V is a matrix composed of columns Y... T The matrix is ​​composed of the eigenvectors of Y. Based on the eigenvalue ξ, a small subset of basis vectors is selected, i.e., the truncated m-dimensional (m << n) POD basis ψ, to approximate the characteristics of all sample spaces. The mapping relationship between input parameters and POD modal coefficients is constructed through a Kriging surrogate model.

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

[0061] The aerodynamic order reduction model selects 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 performed on 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 for the aerodynamic load training data of the sample points under the excitation signal. Based on the training data, the sample is dimensionality reduced, and the truncated modes and modal coefficients are obtained using the POD method. A Kriging surrogate model is used to construct the mapping relationship between the input parameters and the POD modal coefficients, thus obtaining the unsteady aerodynamic order reduction model.

[0062] Step 4: Establish the dynamic model of the servo control system's servo motor.

[0063] The servo motor transfer function of the servo control system adopts a second-order dynamic model:

[0064]

[0065] In the formula, u(s) is the input command for servo control; δ(s) is the output of the servo; k s T represents the steady-state gain of the servo motor. s μ is the time constant of the servo motor. s The damping ratio of the servo motor;

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

[0067]

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

[0069] State-space equations for elastic bodies and unsteady aerodynamic forces:

[0070]

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

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

[0073]

[0074] In the formula,

[0075]

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

[0077] Combining the above three state-space equations yields the aerodynamic servo-elastic closed-loop control equations for the aircraft:

[0078]

[0079] The system matrix in the formula is as follows:

[0080]

[0081] Step 5: Using the aerodynamic thermal reduced-order model established in step S2, 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 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, calculate the corresponding thermal modes of the aircraft using the finite element method.

[0083] Step 7: Solve the aerodynamic forces using the aerodynamic reduced-order model established in step S3, calculate the aeroelastic response of the aircraft thermal modes after aerodynamic heating, and update the aerodynamic mesh of the constructed aerodynamic reduced-order model by updating the structural deformation using the dynamic mesh method.

[0084] In this embodiment, a hybrid method of over-limit interpolation is used to achieve dynamic mesh interpolation. The entire flow field mesh is divided into multiple blocks, and the static equilibrium equations are solved using an iterative method to linearly distribute the deformation at the boundary of the mesh blocks to each node of the mesh. The corresponding static equilibrium equations are as follows:

[0085]

[0086] Where k ij It is the spring stiffness of edge ij; k t,jj This is torsional stiffness added to prevent excessive deformation of the element; Δx j It is the displacement of the j-th node connected to the spring; Δx i Let N be the displacement to be determined; N is the number of nodes connected to the node to be determined by springs.

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

[0088] Step 9: Advance the time step ΔT using unsteady aerodynamic forces. aero For the time step, based on step S7, the aero-servo elastic response under the simultaneous action of aerodynamic force and control force corresponding to the current time step is solved. Then, based on step 8, the control force for the next time step is calculated. After that, the process returns to step S7 to solve for the aero-servo elastic response under the simultaneous action of aerodynamic force and control force corresponding to the next time step. The time step ΔT for the servo system output control force is defined as follows: servo Time-progression step ΔT with unsteady aerodynamic forces aero same.

[0089] When the calculation time of steps 10 and 9 reaches the set time, return to step 5; until the thermo-aerodynamic servo-elasticity calculation of the entire flight trajectory is completed, realizing the coupled analysis of the aircraft's thermo-aerodynamic servo-elasticity.

[0090] Figure 2 This is a schematic diagram of a thermo-aerodynamic servo elastic two-way loosely coupled time domain, from time T to T+ΔT. aero Aerodynamic servo-elastic coupling calculations are performed at all times: based on the thermal modes, aerodynamic loads, and control forces corresponding to the temperature field of the aircraft at time T, aerodynamic servo-elastic solutions are obtained, and so on, until T+ΔT. heat At time ΔT heat Changes in the thermal modes of the aircraft structure are not considered during the time interval.

[0091] In performing NΔT aero The pneumatic servo elasticity solution reaches T+ΔT at each time step. heat After a certain time, it is assumed that the structure has accumulated sufficient deformation, and its impact on the thermal modes of the aircraft is not negligible. At this point, T+ΔT is recalculated. heat The aerodynamic heat distribution under deformation at any time is determined, and then the solution for T+ΔT is obtained. heat thermal modes at time

[0092] At T+ΔT heat Time until T+2ΔT heat Repeat the above aerodynamic servo elasticity calculations at different times, and so on, until the thermo-aerodynamic servo elasticity analysis of the entire trajectory is completed.

[0093] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the thermo-aerodynamic servo-elastic coupling of an aircraft, characterized in that, include: Step 1: Establish the aircraft's thermodynamic model, aerodynamic model, structural elasticity model including control surfaces, and servo control system model; Step 2: Construct an aerothermal reduced-order model using a model reduction method that combines intrinsic orthogonal decomposition and surrogate model, which is used to calculate the temperature field of the structure after static aerothermoelastic balancing under given ballistic flight conditions. Step 3: Construct an aerodynamic reduced-order model using a model reduction method that combines intrinsic orthogonal decomposition and surrogate model, perform unsteady CFD calculations to solve the aerodynamic load training data, and reduce the dimensionality of the samples based on the training data to obtain the unsteady aerodynamic reduced-order model. Step 4: Establish the dynamic model of the servo control system's servo motor; Step 5: Calculate the temperature distribution on the surface of the aircraft at each discrete moment under given ballistic flight conditions using an aerodynamic thermal reduced-order model. Interpolate the time-varying temperature distribution on the surface nodes of the structural elastic 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. Step 6: Calculate the thermal modes of the aircraft based on the temperature field of the complete aircraft structure; Step 7: Solve the aerodynamic forces using an unsteady aerodynamic force reduction model, calculate the aeroelastic response of the aircraft's thermal modes after aerodynamic heating, and update the aerodynamic mesh of the constructed aerodynamic force reduction model by updating the structural deformation using the dynamic mesh method. Step 8: Transmit the aeroelastic response information of the aircraft to the servo control system's servo motor dynamics model, and output control force according to control requirements; Step 9: Advance the time step size ΔT using unsteady aerodynamic forces. aero For the time step, based on step 7, the aero-servo elastic response under the simultaneous action of aerodynamic force and control force at the current time step is solved. Then, based on step 8, the control force for the next time step is calculated. After that, step 7 is returned to solve for the aero-servo elastic response under the simultaneous action of aerodynamic force and control force at the next time step. The time step ΔT for the servo system output control force is defined as follows: servo Time-progression step ΔT with unsteady aerodynamic forces aero same; Step 10: If the calculation time of step 9 reaches the set time, return to step 5 until the thermo-aerodynamic servo elasticity calculation of the entire flight trajectory is completed. In step 1, when establishing the elastic model of the aircraft structure, the factors of clearance and friction between the control surface and the control shaft are included, and contact pairs are used to simulate the nonlinearity of the structure; the control slot gasket and the control shaft form a contact pair, the control slot gasket and the control surface form a contact pair, and the lead screw and the bearing form a contact pair; the mesh of the contact area is refined; among them, the contact stiffness K of the contact pair mating surface is... n and tangential contact stiffness K t They are respectively: In the formula, D is the fractal dimension; G is the characteristic scale coefficient; δ max δ represents the maximum deformation of the micro-protrusion at the mating surface. c For the critical deformation of the micro-convexity of the mating surface, when δ < δ c The micro-convex body undergoes elastic deformation when δ > δ c Micro-protrusions undergo plastic deformation; E, v and μ are the equivalent elastic modulus, shear modulus, Poisson's ratio, and friction coefficient of the interface; a c The critical contact area; a l T represents the area of ​​the maximum contact point. m For the tangential load on the mating surface, P m This represents the normal load on the mating surface.

2. The aircraft thermo-aerodynamic servo-elastic coupling analysis method according to claim 1, characterized in that, In step 2, the method for obtaining the order reduction model of unsteady aerodynamics is as follows: Selecting flight Mach number, flight altitude, and flight angle of attack as design variables, sample points X = [x1, x2, ..., x] are obtained in the design space. n ] T The balanced temperature was obtained using CFD unsteady numerical simulation as the sample matrix Y = [y1, y2, ..., y]. n ] T , and y i =[T i 1 ,T i 2 ,…,T i n ], T i j Let be the temperature of the j-th node of the structure at the i-th sample point; there are a total of n sample points and N nodes in the structure; Singular value decomposition of the response matrix Y yields the eigenvectors ψ0 and Y of matrix Y. T YV = VΛ, ψ0 = YV, where Λ is the diagonal matrix formed by the eigenvalues ​​ξ; V is a matrix composed of columns Y T The matrix composed of the eigenvectors of Y; Based on the eigenvalue ξ, a small portion of the basis vectors, i.e., the truncated m-dimensional POD basis ψ, is selected to approximate the characteristics of all sample spaces. The mapping relationship between the input parameters and the POD modal coefficients is constructed through the Kriging surrogate model; where m << n.

3. The aircraft thermo-aerodynamic servo-elastic coupling analysis method according to claim 1, characterized in that, In step 3, an aerodynamic reduced-order model is constructed by combining intrinsic orthogonal decomposition and surrogate model. 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 unsteady aerodynamic forces. The POD method is used to obtain truncated modes and modal coefficients. The mapping relationship between input parameters and POD modal coefficients is constructed through the Kriging surrogate model.

4. The aircraft thermo-aerodynamic servo-elastic coupling analysis method according to claim 1, characterized in that, In step 4, the dynamic model of the servo control system's servo motor is established. The specific method is as follows: The servo motor transfer function of the servo control system adopts a second-order dynamic model, rewriting the servo motor transfer function in the frequency domain into a state-space form: In the formula, A c B is the system matrix; c For the control matrix; C c For the output matrix; x c y is the system state vector; c u is the system output vector; u is the servo control command vector; u s This refers to the steering deflection of the control surface; State-space equations for elastic bodies and unsteady aerodynamic forces: In the formula, A s B is the system matrix of the generalized controlled object; s For the control matrix; C s D is the output matrix. s For direct transmission of the matrix; x s y is the state vector of the generalized controlled object; s This is the deformation vector caused by elastic vibration; Consider the state-space form of the k-th order control law of a servo control system: In the formula, In the formula, A k B is the system matrix; k For the control matrix; C k D is the output matrix. k For direct transmission of the matrix; x k y is the system state vector; k The system output vector; u k r is the control law command vector; r is the closed-loop system reference input. Combining the above three state-space equations yields the aerodynamic servo-elastic closed-loop control equations for the aircraft: The system matrix in the formula is as follows:

5. The aircraft thermo-aerodynamic servo-elastic coupling analysis method according to claim 1, characterized in that, In step 7, a hybrid method of over-limit interpolation is used to interpolate the aerodynamic calculation grid. The entire flow field grid is divided into multiple blocks, and the static equilibrium equations are solved using an iterative method to linearly distribute the deformation at the grid block boundaries to each node of the grid. The corresponding static equilibrium equations are as follows: In the formula, k ij It is the spring stiffness of edge ij; k t,jj This is torsional stiffness added to prevent excessive deformation of the element; Δx j It is the displacement of the j-th node connected to the spring; Δx i Let N be the displacement to be determined; N is the number of nodes connected to the node to be determined by springs.

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

7. The aircraft thermo-aerodynamic servo-elastic 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.

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