Aeroelastic analysis method and device for multi-propeller tilting wing

Abstract

The invention provides a multi-propeller tilt wing aeroelastic analysis method and device, and the method comprises the steps: building a motion expression of any point on a coupling system in a ground inertial coordinate system; carrying out structural modeling on the multi-paddle / tilting wing coupling system to obtain strain energy variation expressions of paddles and wings and kinetic energy variation expressions of paddles, nacelles and wings; performing pneumatic modeling on the multi-paddle / tilting wing coupling system to obtain aerodynamic virtual work variation expressions of paddles and wings; establishing a multi-propeller / tilting wing aeroelastic coupling kinetic equation; the method can more accurately predict the vibration load of the pneumatic structure of the multi-propeller / tilt wing coupling system, avoids the aeroelastic instability phenomenon caused by insufficient nacelle rigidity or unreasonable distribution in different flight modes, can guide the optimization design of a nacelle supporting structure, and can improve the reliability of the nacelle supporting structure on the premise of ensuring the structural strength and aeroelastic stability. Lightweight design is realized to reduce the weight of the whole aircraft and improve the voyage and load of the aircraft.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of helicopter rotor dynamics, and particularly relates to a multi-rotor tilting wing aeroelastic analysis method and device. BACKGROUND

[0002] As one of the electrically driven vertical take-off and landing aircrafts, the multi-rotor / tilting wing high-speed rotor aircraft adopts a distributed multi-rotor (divided into lift rotors and thrust rotors) layout. The multi-rotors are arranged at the leading edge of the wing through rotor nacelles. Due to the space requirement of the rotor arrangement, the wing must be designed with a large aspect ratio, which causes the geometric nonlinear effect of the wing deformation to be unable to be ignored. Moreover, the distributed multi-rotors are hung on the wing, which changes the inherent characteristics of the wing structure, and the connection part between the rotor and the wing generally has the typical nonlinear characteristics of elastic connection, so that the nacelles produce a pitching motion relative to the wing. The support stiffness of the connection part has a great influence on the aeroelastic dynamic characteristics of the multi-rotor / tilting wing coupling system. At the same time, when the multi-rotor system is in high-speed forward flight and the tilting transition process, the nonlinear structure large deformation and large angle of attack of the large-aspect-ratio wing produce significant nonlinear effects of the wing aerodynamic force. The coupling of the nonlinear effects of the wing aerodynamic force and the nonlinear factors of the elastic connection of the distributed multi-rotor nacelles produces a complex aeroelastic / structural / inertial coupling effect. Therefore, the nonlinear aeroelastic dynamics problem caused by the aeroelastic coupling effect of the distributed multi-rotor and the large-aspect-ratio wing considering the support stiffness of the rotor nacelles will be a key and basic dynamic problem to be faced by the aeroelastic dynamic characteristics research of the multi-rotor / tilting wing high-speed rotor aircraft.

[0003] At present, a lot of researches have been carried out on the large-aspect-ratio wing with external hanging. The influence of the nonlinear structural large deformation of the wing, the distributed external hanging pod and the support stiffness of the pod on the aeroelastic coupling dynamic characteristics of the wing, especially the flutter characteristics, is analyzed. It is found that as the wing deformation amplitude increases, the wing torsional frequency decreases, the bending-torsional coupling intensifies, the wing flutter critical speed is significantly smaller, the wing stability is higher when the external hanging pod is closer to the middle of the wing and the pod is more biased in the chordwise and vertical positions of the wing, and the wing flutter stability is reduced when the mass distribution of the distributed pod is uneven. When the support stiffness of the pod is low, the wing critical flutter speed is increased, and the influence of the pod position change on the wing flutter speed is reduced. However, there are few analyses on the influence of the support stiffness of the nacelle on the aeroelastic coupling dynamic characteristics of the distributed multi-rotor / large-aspect-ratio tilting wing system. The coupling of the nonlinear effects of the wing aerodynamic force and the nonlinear factors of the elastic connection of the distributed multi-rotor nacelles produces a complex aeroelastic / structural / inertial coupling mechanism, which is not fully understood.

[0004] Therefore, it is necessary to provide a multi-rotor tilting wing aeroelastic analysis method considering the support stiffness of the nacelle. SUMMARY

[0005] In order to solve the problem that the influence of short boom support stiffness on the aeroelastic coupling dynamic characteristics of a distributed multi-blade / large aspect ratio tilt wing system is less analyzed, the nonlinear effects of wing aerodynamic force and the nonlinear factors of elastic connection of the distributed multi-rotor short boom are coupled to produce a complex aeroelastic / structure / inertia coupling mechanism, and the influence mechanism of the distributed multi-rotor short boom support stiffness on the dynamic characteristics, aeroelastic response, stability and vibration load of the multi-blade coupled system is not fully understood, the present application provides a multi-blade tilt wing aeroelastic analysis method considering short boom support stiffness, which provides a basis for the dynamic design of multi-blade / tilt wing high-speed rotor aircraft. The technical scheme is as follows: In the first aspect, a multi-blade tilt wing aeroelastic analysis method is provided, and the method comprises: Step 1, defining a multi-blade / tilt wing coupled system coordinate system, which comprises a ground inertial coordinate system; Step 2, establishing a motion expression of any point on the coupled system in the ground inertial coordinate system; Step 3, based on the motion expression, performing multi-blade / tilt wing coupled system structure modeling to obtain strain energy variational expressions of blades and wings, and kinetic energy variational expressions of blades, short booms and wings; Step 4, based on the motion expression, performing multi-blade / tilt wing coupled system aerodynamic modeling to obtain aerodynamic force virtual work variational expressions of blades and wings; Step 5, establishing multi-blade / tilt wing aeroelastic coupling dynamics equations according to the strain energy variational expressions, the kinetic energy variational expressions and the aerodynamic force virtual work variational expressions.

[0006] Optionally, step 1 specifically comprises: Defining a multi-blade / tilt wing coupled system coordinate system: taking the point where the wing root is connected with the fuselage as the origin, establishing a ground fixed inertial coordinate system, which is the wing undeformed coordinate system X I Y I Z I , then establishing a wing deformed coordinate system X W Y W Z W , a rotor short boom coordinate system X P Y P Z P , a hub non-rotating coordinate system X H Y HZ H , hub rotating coordinate system X R Y R Z R , hub plane coordinate system X U Y U Z U , blade undeformed coordinate system X B Y B Z B and blade deformed coordinate system ξ D η D ς D , and the conversion matrix of each coordinate system is obtained T WI , T PW , T HP , T RH , T UR , T RB , T BD .

[0007] Optionally, step 2 specifically comprises: establishing a motion expression of any point on the coupling system in the ground inertial coordinate system, the motion expression including a motion expression of the wing in the ground inertial coordinate system, a motion expression of the nacelle in the ground inertial coordinate system, and a motion expression of the blade in the ground inertial coordinate system, wherein the motion expression of the blade in the ground inertial coordinate system includes a vector expression of the blade in the ground inertial coordinate system and a velocity expression of the blade in the ground inertial coordinate system, and the vector expression of the blade in the ground inertial coordinate system is:

[0008] vector of the blade in the inertial coordinate system consists of four parts: a vector from any point on the blade profile to the center of the rotor hub, a vector of the hub center in the nacelle coordinate system, a vector of the nacelle rotating center in the wing deformed coordinate system, a vector of the wing nacelle connecting point in the wing undeformed coordinate system, wherein and Both on the nacelle, the sum of which can be used to find the vector radius of the hub center in the wing deformation coordinate system ; x 1、 y 1、 z 1 is the distance from any point on the blade to the hub center in the x, y, z directions, x CG 、 y CG 、 h is the distance from the hub center to the tilt center in the x, y, z directions, x h 、 y h 、 z h is the distance from the tilt center to the nacelle joint profile elastic axis in the x, y, z directions, R w is the distance from the nacelle joint to the wing root in the y direction, The expression of the blade velocity in the ground inertial coordinate system is:

[0009] The blade velocity in the inertial coordinate system is composed of two parts: the blade's own velocity and the induced velocity caused by the wing , which can be further divided into blade translation , hub rotation induced blade motion , wing rotation induced blade motion , wing rotation induced wing motion , wing translation , where and need to consider the influence of wing tilt motion and nacelle pitch motion, where , , T BI and T PI are the transformation matrices between the blade undeformed coordinate system, the rotor nacelle coordinate system and the wing undeformed coordinate system, ϕ s 、 α s 、 ψ s is the rotational freedom at the wing nacelle joint, is the blade pre-cone angle, is the wing tilt angle, is the nacelle pitch angle.

[0010] Optionally, step 3 specifically comprises: The multi-blade / tilt-wing coupling system structure modeling is performed to obtain the strain energy expression of the blade and the wing, and the kinetic energy variational expression of the blade, the nacelle and the wing, the strain energy expression of the blade is:

[0011] The strain energy expression of the wing is:

[0012] In the formula: σ , ε are the stress and strain of the blade or the wing section respectively; η , ζ are the y and z coordinates of any point on the section in the section coordinate system, L represents the rotor radius or the wing span, and the strain σ , ε are calculated by Hooke's law and deformation compatibility relationship respectively; u , v , w , ϕ are the translational degrees of freedom of the blade in the x, y and z directions, and the rotational degree of freedom in the x direction, The kinetic energy variational expression of the blade is as follows:

[0013] In the formula: x h , y h , z h , ϕ s , α s , ψ s are the translational degrees of freedom and the rotational degrees of freedom of the nacelle connection point P in the x, y and z directions, The kinetic energy variational expression of the wing is:

[0014] In the formula: are the translational degrees of freedom and the rotational degrees of freedom of any point on the wing in the x, y and z directions, The kinetic energy variational expression of the nacelle is:

[0015] In the formula: are the translational degrees of freedom and the rotational degrees of freedom of any point on the nacelle in the x, y and z directions.

[0016] Optionally, step 4 specifically comprises: The aerodynamic modeling of the multi-propeller / tilt-wing coupling system is performed to obtain the virtual work variational expressions of the aerodynamic forces of the propeller and the wing, the virtual work variational expression of the aerodynamic force of the propeller being:

[0017] The relative airspeed of the airfoil profile is contributed by the incoming flow speed and the inflow contribution of the propeller disc and the coupling motion of the propeller and the wing , then the airspeed of the airfoil profile in the deformed coordinate system of the propeller is

[0018] In the formula: is the radial airspeed, the air flow is positive when flowing inward along the propeller; is the tangential airspeed, the air flow is positive when flowing from the leading edge to the trailing edge of the airfoil; is the vertical airspeed, the air flow is positive when flowing downward; Based on the strip theory, the aerodynamic force of the propeller profile is the superposition of the quasi-steady circulation and the non-circulation aerodynamic force, that is:

[0019] In the formula: are the combined aerodynamic forces of the airfoil profile in the undeformed coordinate system of the propeller in the directions of the degrees of freedom, respectively, is the combined aerodynamic force distance of the airfoil profile in the undeformed coordinate system of the propeller in the directions of the degrees of freedom, ρ is the air density, h is the chord length of the propeller, c u , c d , c l , c m is the aerodynamic coefficient of the propeller in the direction of the degree of freedom, ( ) c C is the quasi-steady circulation, ( ) NC is the non-circulation aerodynamic force, The virtual work variational expression of the aerodynamic force of the wing is:

[0020] The airspeed of the wing profile V W is divided into the airspeed of the free flow region V W1 and the airspeed of the slip flow region V W2 ,​​​ where V is the free stream velocity V W1 The free stream velocity is divided into: V f and the wing motion velocity V w0 The wake shape in the slipstream region can be regarded as a cylindrical uniform flow with a radius contraction, and the radius contraction formula is:

[0021] wherein: R , C T are the rotor radius and the drag coefficient, respectively, h is the nacelle length, R h is the radius of the slipstream region, The flow in the slipstream region satisfies the gas continuity equation, v i is the average rotor induced inflow, v 1 is the chord-wise velocity increment in the slipstream region, and has the following relationship:

[0022] wherein: v i is the average rotor induced inflow, U Tw is the velocity component of the free stream velocity in the chord-wise direction of the wing, The free stream velocity of the slipstream region in the wing deformation coordinate system is: V W2

[0023] The wing profile aerodynamic force is: .

[0024] Optionally, step 5 establishes the multi-blade / tilt-wing aeroelastic coupling dynamics equation, specifically including: Step 51, convert the blade group set into a rotor equation through a multi-blade coordinate conversion method, and then couple it with the nacelle and wing considering support stiffness, and the motion equation expression is:

[0025] Step 52, convert the above equation into a matrix form, i.e., group set to obtain the total matrix of the multi-blade / tilt-wing configuration coupling system dynamics considering support stiffness:

[0026] wherein: is the degree of freedom of the blade in the non-rotating coordinate system;​ the degrees of freedom for the wing to nacelle junction, the remaining degrees of freedom on the wing; M bb 、C bb 、K bb 、F b M, D, K and F are respectively the total mass, damping, stiffness matrix and force vector for the blade; M btp 、C btp 、K btp M, D, K are respectively the total mass, damping, stiffness matrix for the blade-nacelle pitch coupling; M tpb 、C tpb 、K tpb M, D, K are respectively the total mass, damping, stiffness matrix for the nacelle pitch-blade coupling; M tptp 、C tptp 、K tptp 、F tp M, D, K and F are respectively the total mass, damping, stiffness matrix and force vector for the nacelle pitch-nacelle pitch coupling; M bxh 、C bxh 、K bxh M, D, K are respectively the total mass, damping, stiffness matrix for the blade-wing coupling; M xhb 、C xhb 、K xhb M, D, K are respectively the total mass, damping, stiffness matrix for the wing-blade coupling; M xhxh 、C xhxh 、K xhxh 、F xh M, D, K and F are respectively the total mass, damping, stiffness matrix and force vector for the wing-wing coupling; , M, D, K and F are respectively the mass, damping, stiffness matrix and force vector for the wing except the wing to nacelle junction, The system dynamics global matrix is reduced to: , where: It is the system's structural modal mass, damping, and stiffness matrix; It is the system's generalized coordinate vector; F ( t ) is a force independent of the response. F ( These are forces related to the response, including structural nonlinear terms and aerodynamic terms. Step 53: The simplified overall system dynamics matrix is ​​a nonlinear equation. Let the first... k The solution for the equilibrium position after the next iteration is: To find using the finite difference approximation F ( Regarding the equilibrium position The derivative, and the derivative matrix is ​​the aerodynamic mass, damping, and stiffness matrix, expressed as: , Step 54: Establish the aeroelastic coupling dynamic equations for the multi-rotor / tilt wing as follows:

[0027] , The above formula is transformed into:

[0028] Where I is an N×N identity matrix and 0 is an N×N zero matrix, let the motion Then the above formula can be written as: , in: .

[0029] In a second aspect, a multi-rotor tilt-wing aeroelastic analysis device is provided for performing any of the methods described in the first aspect, the device comprising: Create a module for: Define a coordinate system for the multi-rotor / tilt wing coupled system, which includes the ground inertial coordinate system; Establish the motion expression of any point on the coupled system in the ground inertial coordinate system; Based on the kinematic expressions, a structural model of a multi-bladed / tilt wing coupled system is performed to obtain the variational expressions for the strain energy of the blades and the wing, as well as the variational expressions for the kinetic energy of the blades, nacelles, and the wing. Based on the motion expression, aerodynamic modeling of the multi-blade / tilt wing coupled system is performed to obtain the variational expression of the aerodynamic virtual work of the blades and the wing; Based on the variational expressions for strain energy, kinetic energy, and aerodynamic virtual work, the aeroelastic coupling dynamic equations for a multi-rotor / tilt airfoil are established.

[0030] In a third aspect, a multi-propeller tilting wing aeroelastic analysis device comprises a processor and a memory, the memory storing a program, and the processor executing the program in the memory to implement the method of any one of the first aspect.

[0031] The present application has at least the following beneficial effects: The present application can more accurately predict the aerodynamic structural vibration load of a multi-propeller / tilting wing coupling system, avoid the aerodynamic elastic instability phenomenon caused by insufficient or unreasonable distribution of the nacelle stiffness in different flight modes, guide the optimization design of the nacelle support structure, and realize lightweight design to reduce the weight of the whole machine, improve the flight range and load of the aircraft under the premise of ensuring the structural strength and aeroelastic stability. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 A schematic diagram of wing vertical flapping response calculation results for a wing with a flexible support nacelle, Figure 2 A schematic diagram of the calculation results of the influence of different rotor nacelle numbers and lift rotor deployment of a multi-propeller system on the first-order torsional damping of the wing, Figure 3 A schematic diagram of the calculation results of the system flutter speed under different rotor nacelle numbers and lengths of a multi-propeller system, Figure 4 A schematic diagram of the wing flow region division, Figure 5 A flowchart of the method of the present application. DETAILED DESCRIPTION

[0033] To make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be described clearly and completely below in conjunction with the drawings of the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0034] The features and illustrative embodiments of various aspects of the present application will be described in detail below. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one of ordinary skill in the art that the present application can be practiced without some of these specific details. The following description of embodiments is merely exemplary in nature and is provided to give a better understanding of the present application. The present application is not limited to any particular setting and method set forth below, but covers any improvements, replacements and modifications of structures, methods and devices without departing from the spirit of the present application. In the drawings and the following description, well-known structures and techniques are not shown to avoid unnecessary obscuring of the present application.

[0035] It should be noted that the features of the embodiments and the features in the embodiments can be combined with each other without conflict, and each embodiment can be referred to and cited by each other.

[0036] The application will be described in detail below with reference to the drawings and specific embodiments.

[0037] In view of the nonlinear aeroelastic dynamics problems existing in the high-speed forward flight and the transition process of the tilt of the multi-propeller / tilt wing high-speed rotor aircraft, an analysis method is provided for considering the influence of different nacelle support stiffness on the aeroelastic coupling dynamic characteristics of the distributed multi-rotor / flexible large-aspect-ratio tilt wing coupling system. The influence mechanism of the distributed multi-rotor nacelle support stiffness and the like on the dynamic characteristics, aeroelastic response, stability and vibration load of the multi-propeller coupling system is studied, thereby providing a basis for the dynamic design of the multi-propeller / tilt wing high-speed rotor aircraft.

[0038] Referring to Figure 5 In an embodiment, the method of the application is implemented as follows: (1) Based on the Lagrange coordinate system, the position of any point on the coupling system in the inertial coordinate system is described relative to the inertial coordinate system, and the Hamilton principle is used to derive the multi-propeller / tilt wing coupling dynamics equation, which is expressed as follows:

[0039] In the formula: δU , the strain energy of the system; δT , the kinetic energy of the system; δW , the virtual work of the external force of the system, which is composed of the following parts:

[0040] In the formula: the subscripts W , P , b respectively represent the wing, the nacelle, the blade, N b , N r respectively represent the number of blades and rotors. The nacelle is assumed to be a rigid body, and the influence of its support stiffness on the wing and the rotor is not considered, and its kinetic energy is considered.

[0041] (2) The multi-propeller / tilt wing coupling system coordinate system is defined, the ground fixed inertial coordinate system is established with the wing root and the fuselage connection point as the origin, and then the wing undeformed coordinate system X I Y I Z I , the wing deformed coordinate system XW Y W Z W , rotor nacelle coordinate system X P Y P Z P , hub non-rotating coordinate system X H Y H Z H , hub rotating coordinate system X R Y R Z R , hub planar coordinate system X U Y U Z U , blade undeformed coordinate system X B Y B Z B and blade deformed coordinate system ξ D η D ς D , simultaneously deriving transformation matrices for each coordinate system T WI , T PW , T HP , T RH , T UR , T RB , T BD (wherein there are T UI = T UR T RH T HP T PW T WI , T PI = T PWT WI , T UD =T UR T RB T BD ).

[0042] (3) Establish the motion expression of the multi-propeller / tilt-wing coupling system, and calculate the expression of any point on the coupling system in the ground inertial coordinate system. The motion expressions of the wing and nacelle in the ground inertial coordinate system can be referred to the existing technology, while the motion expression of the propeller in the ground inertial coordinate system needs to consider the influence of the motion expressions of the wing and nacelle, The vector radius of the propeller in the inertial coordinate system It is composed of four parts: The vector radius of any point on the propeller section to the hub center of the rotor, The vector radius of the hub center in the nacelle coordinate system, The vector radius of the rotation center of the nacelle in the wing deformation coordinate system, The vector radius of the wing-nacelle coupling point in the wing undeformed coordinate system, where And Both are on the nacelle, and their sum can be represented by the vector radius of the hub center in the wing deformation coordinate system The position vector radius of any point on the propeller is as follows:

[0043] In the formula: x 1, y 1, z 1 is the distance of any point on the propeller to the hub center in x, y, and z directions, x CG , y CG , h is the distance of the hub center to the tilt center in x, y, and z directions, x h , y h , z h is the distance of the tilt center to the nacelle coupling point section elastic axis in x, y, and z directions, R w is the distance of the nacelle coupling point to the wing root in y direction, The velocity of the propeller in the inertial coordinate system is composed of the propeller's own velocity and the induced velocity caused by the wing , which can be further divided into the translational velocity of the propeller blade motion due to hub rotation blade motion due to wing rotation wing motion due to wing rotation wing translation where and The influence of wing tilt motion and nacelle pitch motion (i.e. motion due to nacelle support stiffness) is considered, where , blade velocity The expression is as follows,

[0044] where: T BI and T PI are the transformation matrices between the blade undeformed coordinate system, the rotor nacelle coordinate system and the wing undeformed coordinate system, ϕ s , α s , ψ s is the rotational freedom at the wing nacelle joint, is the blade precone angle, is the wing tilt angle, is the nacelle pitch angle.

[0045] (4) The structural modeling of the multi-blade / tilt-wing coupled system is performed. The blade and the wing can be analyzed using the moderately deformed beam model, and the nacelle can be regarded as a rigid body. The strain energy expression of the blade is:

[0046] The strain energy expression of the wing is:

[0047] where: σ , ε are the stress and strain of the blade or wing section respectively; η , ζ are the y and z coordinates of any point on the section in the section coordinate system, L represents the rotor radius or the wing semi-span, and the strain σ , ε are calculated by Hooke's law and the deformation compatibility relationship respectively; u , v , w , ϕ are the translational freedom of the blade in the x, y, z directions and the rotational freedom of the blade in the x direction respectively.

[0048] For the blade kinetic energy, the influence of nacelle and wing coupled motion should be considered, the blade kinetic energy variational expression is as follows:

[0049] In the formula: x h 、 y h 、z h 、 ϕ s 、 α s 、 ψ s The translational and rotational degrees of freedom of the nacelle at the connection point P in the x, y, and z directions.

[0050] The nacelle is regarded as a rigid body, and its kinetic energy needs to consider the influence of its own pitch motion and wing coupled motion. The kinetic energy variational expression of the nacelle is: , In the formula: The translational and rotational degrees of freedom of any point on the nacelle in the x, y, and z directions.

[0051] The wing kinetic energy only needs to consider the influence of its own motion, and the kinetic energy variational expression of the wing is: , In the formula: The translational and rotational degrees of freedom of any point on the wing in the x, y, and z directions. (5) The aerodynamic modeling of the multi-blade / tilt-wing coupled system is carried out, and the aerodynamic force virtual work variational expression of the blade and wing is obtained, The aerodynamic force calculation of the airfoil is carried out in the airfoil section coordinate system. For the elastic blade, it is carried out in the deformed blade coordinate system. The airfoil section relative airflow velocity comes from: the incoming flow velocity and the contribution of the blade disc inflow , the contribution of the coupled motion of the blade and wing . The airfoil section airflow velocity in the deformed blade coordinate system is as follows:

[0052] In the formula: The radial airflow velocity is positive when the airflow flows inward along the blade, The tangential airflow velocity is positive when the airflow flows from the leading edge to the trailing edge of the airfoil, The vertical airflow velocity is positive when the airflow flows downward; Based on the strip theory, the section aerodynamic force is the superposition of the quasi-steady circulation (subscript C) and the non-circulation (subscript NC) aerodynamic force, that is:

[0053] where: are the airfoil profiles in the blade undeformed coordinate system the total aerodynamic force in the degree of freedom, are the airfoil profiles in the blade undeformed coordinate system the total aerodynamic force in the degree of freedom, and p is the air density, c h is the blade chord length, c u , c d , c l , c m is the blade the aerodynamic coefficient in the degree of freedom, and C is the quasi-steady circulation, NC is the non-circulation aerodynamic force, The aerodynamic virtual work and its variation of the blade can be written as: , The virtual work expression of the wing aerodynamic force is similar to that of the blade. However, due to the unique configuration of the distributed multi-blade / tilt-wing aircraft, a part of the wing area is always affected by the rotor wake, which is the wing slipstream area, and the rest is the free flow area. Referring to Figure 4 , the free flow area wing profile air flow velocity V W1 is divided into: a ) incoming flow velocity V f ; b ) wing movement velocity V w0 ; ignoring the influence of the wake circumferential velocity, and the axial velocity is approximately uniform flow, then the slipstream area wake shape can be regarded as a cylindrical uniform flow with radius contraction, and its radius contraction formula is: , where: R , C T are the rotor radius and the tension coefficient, respectively, h is the nacelle length, R h is the radius of the slipstream area.

[0054] The airflow in the slipstream area satisfies the gas continuity equation, v i is the rotor induced inflow average, v 1 is the slipstream area chord-wise velocity increment, and has the following relationship: , where v i is the rotor induced inflow mean value, U Tw is the velocity component of the incoming flow in the chord direction of the wing.

[0055] Profile inflow velocity of the slipstream V W2 is:

[0056] The wing profile aerodynamic force is:

[0057] The wing aerodynamic force virtual work variational expression is as follows:

[0058] (6) The multi-blade / tilt wing aeroelastic coupling dynamics equation is established, according to Hamilton's principle, the blade group is converted into a rotor equation through multi-blade coordinate conversion, and then coupled with the short cabin and wing considering support stiffness, and the expression of the motion equation is as follows:

[0059] The above equation is converted into a matrix form, that is, the group is obtained The total matrix of the multi-blade / tilt wing configuration coupling system dynamics considering support stiffness:

[0060] wherein: is the degree of freedom of the blade in the non-rotating coordinate system; is the degree of freedom of the wing and the short cabin connection point, is the remaining degree of freedom of the wing; M bb 、C bb 、K bb 、F b is the total mass, damping, stiffness matrix and load vector of the blade, respectively; M btp 、C btp 、K btp is the total mass, damping, stiffness matrix of the blade-short cabin pitch coupling, respectively; M tpb 、C tpb 、K tpb is the total mass, damping, stiffness matrix of the short cabin pitch-blade coupling, respectively;M tptp 、C tptp 、K tptp 、F tp These are the nacelle pitch-nacelle pitch total mass, damping, stiffness matrix, and load vector, respectively; M bxh 、C bxh 、K bxh These represent the total mass, damping, and stiffness matrices of the blade-wing coupling, respectively. M xhb 、C xhb 、K xhb These are the total mass, damping, and stiffness matrices of the wing-blade coupling, respectively. M xhxh 、C xhxh 、K xhxh 、F xh These are the wing-wing coupled total mass, damping, stiffness matrix, and load vector, respectively; , These represent the mass, damping, stiffness matrix, and load vector of the wing excluding the wing-nacelle connection point. The overall dynamic matrix of the system can be simplified to: , In the formula: It is the system's structural modal mass, damping, and stiffness matrix; It is the system's generalized coordinate vector; F ( t ) is a force independent of the response. F ( ) is the force related to the response (including nonlinear terms of the structure and aerodynamic terms).

[0061] The simplified system dynamics global matrix is ​​a nonlinear equation, let the first equation be... k The solution for the equilibrium position after the next iteration is: To find using the finite difference approximation F ( Regarding the equilibrium position The derivative of , the derivative matrix is ​​the aerodynamic mass, damping, and stiffness matrix, and its expression is as follows:

[0062] The aeroelastic equation of the coupled system is then:

[0063] wherein:

[0064] The above equation can be written as:

[0065] where I is the N x N identity matrix and 0 is the N x N zero matrix. Let the motion be F(t) = M(t) x(t) + G(t). Then the above equation can be written as: , wherein:

[0066] Thus, 2N first order differential equations are obtained. Note that the above equation is valid only if M(t) is not singular. Let F(t) = 0, i.e. G = 0, and solve the above equation for the eigenvalues. The real part of the eigenvalues represents the modal damping, while the imaginary part represents the frequency of the mode, from which the aeroelastic stability characteristics of the coupled system can be analyzed.

[0067] The aeroelastic response of a large aspect ratio flexible wing with three flexible support nacelles in forward flight is analyzed. Figure 1 The time domain response, phase diagram and PSD diagram of the wing vertical deformation in flutter state are given. It can be seen from the diagrams that the wing has experienced the classic flutter of coupled bending and torsional modes.

[0068] The half-span system with three flexible support nacelles and rotors, wing attack angle of 3 deg and blade effective angle of attack of 6 deg is calculated. The first order torsion of the system under different rotor nacelle numbers and lift blade retraction is as shown in Figure 2 The flutter speed of the system under different rotor nacelle numbers and nacelle lengths is as shown in Figure 3 Increasing the number of rotor nacelles and opening the lift blades can expand the range of the slipstream area, thereby significantly increasing the wing torsional mode damping. The forward movement of the mass center of the multi-rotor system increases the nacelle length, which makes the wing torsional frequency decrease, and it is easier to cause torsional instability. The flutter speed of the multi-rotor system also decreases.

[0069] The application summarizes and induces the aeroelastic dynamic characteristics of the high-aspect-ratio wing with flexible support external hanging pod, establishes an aeroelastic dynamic model and an aeroelastic analysis method of a distributed multi-blade / tilt-wing coupled system considering support stiffness, studies the dynamic characteristics of the multi-blade / tilt-wing coupled system with flexible support external hanging pod, especially the influence law of the geometric position and support stiffness of the external hanging pod on the dynamic characteristics, aeroelastic response and flutter characteristics of the coupled system, can more accurately predict the aeroelastic vibration load of the multi-blade / tilt-wing coupled system, avoid the aeroelastic instability phenomenon caused by insufficient or unreasonable distribution of the pod stiffness in different flight modes, guide the optimization design of the pod support structure, realize the lightweight design under the premise of ensuring the structural strength and aeroelastic stability, and reduce the weight of the whole machine to improve the flight range and load of the aircraft.

[0070] The above only expresses the embodiments of the application, which are described in detail and in detail, but cannot be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the application, which belong to the protection scope of the application. In addition, the parts of the application not described in detail are all conventional technologies.

Claims

1. A method for aeroelastic analysis of a multi-rotor tiltrotor aircraft, characterized in that, The method includes: Step 1: Define the coordinate system of the multi-rotor / tilt wing coupling system, which includes the ground inertial coordinate system; Step 2: Establish the motion expression of any point on the coupled system in the ground inertial coordinate system; Step 3: Based on the motion expression, perform structural modeling of the multi-bladed / tilt wing coupled system to obtain the variational expressions of strain energy for the blades and the wing, as well as the variational expressions of kinetic energy for the blades, nacelles, and the wing. Step 4: Based on the motion expression, perform aerodynamic modeling of the multi-blade / tilt wing coupled system to obtain the variational expression of the aerodynamic virtual work of the blades and the wing; Step 5: Based on the variational expressions for strain energy, kinetic energy, and aerodynamic virtual work, establish the aeroelastic coupling dynamic equations for the multi-rotor / tilt wing.

2. The method according to claim 1, characterized in that, Step 1 specifically includes: Define the coordinate system for the multi-rotor / tilt wing coupled system: Establish a fixed ground-based inertial coordinate system with the wing root and fuselage connection point as the origin; this is the wing's undeformed coordinate system. X I Y I Z I Next, establish the wing deformation coordinate system. X W Y W Z W Rotor nacelle coordinate system X P Y P Z P non-rotating coordinate system of the propeller hub X H Y H Z H Rotating coordinate system of propeller hub X R Y R Z R Hub plane coordinate system X U Y U Z U Undeformed blade coordinate system X B Y B Z B Blade Deformation Coordinate System ξ D η D ς D Simultaneously, the transformation matrices for each coordinate system are obtained. T WI , T PW , T HP , T RH , T UR , T RB , T BD .

3. The method according to claim 1, characterized in that, Step 2 specifically includes: Establish the motion expression for any point on the coupled system in the ground inertial coordinate system. This motion expression includes the motion expressions for the wing, the nacelle, and the blades in the ground inertial coordinate system. The blade motion expression in the ground inertial coordinate system includes the radius vector and velocity expression for the blade in the ground inertial coordinate system. The radius vector expression for the blade in the ground inertial coordinate system is: The radius vector of the blade in the inertial coordinate system It consists of four parts: Let be the radius vector from any point on the blade profile to the center of the rotor hub. Let the radius vector of the rotor hub center in the nacelle coordinate system be denoted as . Let be the radius vector of the nacelle rotation center in the wing deformation coordinate system. Let be the radius vector of the wing nacelle connection point in the undeformed coordinate system of the wing, where and Both are located on the nacelle, and their sum can be expressed as the radius vector of the rotor hub center in the wing deformation coordinate system. express; x 1. y 1. z 1 represents the distance in the x, y, and z directions from any point on the blade to the center of the blade hub. x CG , y CG , h It represents the distance in the x, y, and z directions from the center of the propeller hub to the center of tilt. x h , y h , z h It is the distance in the x, y, and z directions of the elastic axis of the section from the tilting center to the nacelle connection point. R w It is the distance in the y-direction from the nacelle connection point to the wing root. The velocity expression of the blade in the ground inertial coordinate system is: The velocity of the blade in the inertial coordinate system Speed ​​of the blade itself and the pull speed caused by the wing It consists of two parts, which can be further divided into blade translation. The blade motion caused by the rotation of the rotor hub The propeller motion caused by wing rotation Wing motion caused by wing rotation Wing translation ,in and The effects of wing tilting motion and nacelle pitching motion need to be considered, among which , , T BI and T PI These are the transformation matrices between the undeformed blade coordinate system, the rotor nacelle coordinate system, and the undeformed wing coordinate system. ϕ s , α s , ψ s The rotational degree of freedom at the wing nacelle connection point. The pre-cone angle of the blade, For wing tilt angle, The pitch angle of the nacelle.

4. The method according to claim 1, characterized in that, Step 3 specifically includes: A structural model of the multi-bladed / tilt wing coupled system was performed to obtain the strain energy expressions for the blades and the wing, as well as the variational expressions for the kinetic energy of the blades, nacelles, and the wing. The strain energy expression for the blades is as follows: The strain energy expression for the wing is: In the formula: σ , ε These are the stress and strain of the blade or airfoil cross-section, respectively. η , ζ Let be the coordinates of any point on the cross section in the y and z directions of the cross section coordinate system, respectively. L Represents rotor radius or wing half-span, strain σ , ε The results were obtained from Hooke's law and deformation compatibility relations, respectively. u , v , w , ϕ These represent the translational degrees of freedom of the blade in the x, y, and z directions, and the rotational degrees of freedom in the x direction, respectively. The variational expression for the kinetic energy of the blade is as follows: In the formula: x h , y h z h , ϕ s , α s , ψ s Let P be the translational and rotational degrees of freedom in the x, y, and z directions at the nacelle connection point P. The variational expression for the kinetic energy of the wing is: In the formula: The translational and rotational degrees of freedom of any point on the wing in the x, y, and z directions. The variational expression for the kinetic energy of the nacelle is: In the formula: The translational and rotational degrees of freedom of any point on the nacelle in the x, y, and z directions.

5. The method according to claim 1, characterized in that, Step 4 specifically includes: Aerodynamic modeling of the multi-bladed / tilt wing coupled system was performed to obtain the variational expressions for the aerodynamic virtual work of the blades and the wing. The variational expression for the aerodynamic virtual work of the blades is as follows: relative airflow velocity of airfoil profile Sources: Incoming flow velocity and propeller disk inflow contribution The contribution of the coupled motion of the propeller blades and the wing Then, in the blade deformation coordinate system, the combined airflow velocity of the airfoil profile is... In the formula: The radial airflow velocity is positive when the airflow flows inward along the blades; The tangential airflow velocity is positive when the airflow flows from the leading edge to the trailing edge of the airfoil. The vertical airflow velocity is positive when the airflow flows downwards; Based on the blade strip theory, the aerodynamic force of the blade profile is a superposition of quasi-steady circulation and non-circulation aerodynamic forces, that is: In the formula: These are the airfoil profiles in the undeformed blade coordinate system. Combined aerodynamic forces in the directions of freedom For the airfoil profile in the undeformed blade coordinate system The resultant aerodynamic torque in the direction of degrees of freedom, where ρ is the air density. c h For the blade chord length, c u , c d , c l , c m For propeller blades Aerodynamic coefficients in the directions of degrees of freedom, ( ) C For a quasi-steady circulation quantity, ( ) NC For non-circular gas dynamics, The variational expression for the aerodynamic virtual work of the wing is: Airflow velocity in airfoil profile V W Airflow velocity divided into free flow region V W1 and the airflow velocity in the slip zone V W2 , The airflow velocity in the airfoil section of the free flow region V W1 Divided into: Incoming flow velocity V f and wing motion speed V w0 The wake shape of the slipstream region can be considered as a cylindrical uniform flow with radius contraction, and its radius contraction formula is: In the formula: R , C T These are the rotor radius and thrust coefficient, respectively. h For nacelle length, R h The radius of the slipstream region. The airflow in the slipstream region satisfies the gas continuity equation. v i The mean value of the rotor-induced inflow. v 1 represents the chordal velocity increment in the slipstream region, and the following relationship applies: In the formula: v i The mean value of the rotor-induced inflow. U Tw This refers to the velocity component of the incoming flow in the chord direction of the wing. Incoming flow velocity in the glide slope profile of the wing deformable coordinate system V W2 for: The aerodynamic forces of the airfoil section are: 。 6. The method according to claim 1, characterized in that, Step 5 establishes the aeroelastic coupling dynamic equations for multi-rotor / tilt wings, specifically including: Step 51: Convert the blade assembly into rotor equations using a multi-blade coordinate transformation method, and then couple it with the nacelle and wing considering support stiffness. The expression for its motion equations is: Step 52: Convert the above equations into matrix form, that is, assemble them to obtain the overall dynamic matrix of the multi-rotor / tilt wing configuration coupled system considering support stiffness: In the formula: Let be the degrees of freedom of the blade in the non-rotating coordinate system; For the degrees of freedom at the wing-nacelle connection point, The remaining degrees of freedom on the wing; M bb 、C bb 、K bb 、F b These represent the total mass of the blades, damping, stiffness matrix, and load vector, respectively. M btp 、 C btp 、K btp These are the total mass, damping, and stiffness matrices of the blade-nacelle pitch coupling, respectively. M tpb 、C tpb 、K tpb These are the total mass, damping, and stiffness matrices of the nacelle pitch-blade coupling; M tptp 、C tptp 、K tptp 、F tp These are the nacelle pitch-nacelle pitch total mass, damping, stiffness matrix, and load vector, respectively; M bxh 、C bxh 、K bxh These represent the total mass, damping, and stiffness matrices of the blade-wing coupling, respectively. M xhb 、 C xhb 、K xhb These are the total mass, damping, and stiffness matrices of the wing-blade coupling, respectively. M xhxh 、C xhxh 、K xhxh 、F xh These are the wing-wing coupled total mass, damping, stiffness matrix, and load vector, respectively; , These represent the mass, damping, stiffness matrix, and load vector of the wing excluding the wing-nacelle connection point. The overall system dynamics matrix simplifies to: ， In the formula: It is the system's structural modal mass, damping, and stiffness matrix; It is the system's generalized coordinate vector; F ( t ) is a force independent of the response. F ( These are forces related to the response, including structural nonlinear terms and aerodynamic terms. Step 53: The simplified overall system dynamics matrix is ​​a nonlinear equation. Let the first... k The solution for the equilibrium position after the next iteration is: To find using the finite difference approximation F ( Regarding the equilibrium position The derivative, and the derivative matrix is ​​the aerodynamic mass, damping, and stiffness matrix, expressed as: ， Step 54: Establish the aeroelastic coupling dynamic equations for the multi-rotor / tilt wing as follows: ， The above formula is transformed into: Where I is an N×N identity matrix and 0 is an N×N zero matrix, let the motion Then the above formula can be written as: , in: .

7. A multi-rotor tilt-wing aeroelastic analysis device, characterized in that, The apparatus for performing the method according to any one of claims 1 to 6, the apparatus comprising: Create a module for: Define a coordinate system for the multi-rotor / tilt wing coupled system, which includes the ground inertial coordinate system; Establish the motion expression of any point on the coupled system in the ground inertial coordinate system; Based on the kinematic expressions, a structural model of a multi-bladed / tilt wing coupled system is performed to obtain the variational expressions for the strain energy of the blades and the wing, as well as the variational expressions for the kinetic energy of the blades, nacelles, and the wing. Based on the motion expression, aerodynamic modeling of the multi-blade / tilt wing coupled system is performed to obtain the variational expression of the aerodynamic virtual work of the blades and the wing; Based on the variational expressions for strain energy, kinetic energy, and aerodynamic virtual work, the aeroelastic coupling dynamic equations for a multi-rotor / tilt wing are established.

8. A multi-rotor tilt-wing aeroelastic analysis device, characterized in that, include: A processor and a memory, the memory storing a program, the processor executing the program in the memory to implement the method of any one of claims 1 to 6.

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