Aerial resonance modeling and analysis method for helicopter with front-back sweep and up-down reverse blade tip configuration

Abstract

The invention provides an air resonance modeling and analysis method for a forward-backward swept and up-down reverse blade tip configuration helicopter. The method comprises the following steps: establishing system coordinate systems and a relationship between the coordinate systems; establishing a rotor blade structure dynamic model; establishing a rotor blade aerodynamic model; establishing dynamic and pneumatic models of the blade tip section; establishing an airframe kinetic model; establishing a complex three-dimensional shape rotor wing and fuselage coupling air resonance kinetic equation for derivation; balancing calculation and linearization processing are carried out; and establishing an air resonance analysis method.

Description

Technical Field

[0001] The present application belongs to the technical field of helicopter dynamics modeling and analysis, and specifically relates to a method for modeling and analyzing the aerial resonance of a helicopter with a forward and backward swept up and down reverse blade tip configuration. Background Art

[0002] The blade tip has always played an important role in improving the flight performance and maneuverability of helicopters. With the widespread application of various new materials in helicopter rotors, it has become possible to improve the performance of helicopter rotors by changing the blade tip shape. Advanced blade tip shape design has been a hot topic of research at home and abroad in recent years. Figure 8 The following figure shows advanced propeller tips, such as the BERP tip and the Blue Edge tip, all of which feature a swept tip. Aerodynamic research has shown that the swept tip significantly affects the air compressibility around the leading blade and the airflow separation stall characteristics of the trailing blade.

[0003] When a helicopter flies forward, the Mach number of the incoming airflow from the leading rotor blade increases, making shock waves more likely to form, while the angle of attack of the trailing blade increases, making dynamic stall more likely. This not only limits the helicopter's flight speed but also seriously affects its flight performance. Research has found that by changing the geometry of the blade tip, the rotor's aerodynamic performance can be improved, noise levels can be reduced, and the helicopter's flight speed can be significantly increased. The successful application of the BERP (British-Experimental-Rotor Program) rotor with an advanced blade tip shape in the Lynx helicopter has even set a world speed record for a single-rotor helicopter with a tail rotor.

[0004] Compared to traditional rectangular rotors, rotor blades with complex three-dimensional blade tips exhibit significant changes in the flow field near the rotor disc, altering the rotor's aerodynamic performance and noise level. However, changing the blade tip shape also alters the aerodynamic forces at the tip, increasing the coupling between blade bending and torsional motion, and impacting the helicopter's in-flight resonance stability. Research on in-flight resonance analysis methods for rotor helicopters with complex three-dimensional blade tips can provide an important basis for the optimized design and application of complex three-dimensional blade tip shapes, ensuring that blade tips with excellent aerodynamic performance will not cause in-flight resonance instability.

[0005] Changing the blade tip shape simultaneously alters the coupling between blade bending and torsional motions, affecting airborne resonance through shifts in the rotor speed instability zone and changes in rotor flapping modal damping. Some literature only mentions the effects of sweep angle or anhedral angle on aeroelastic stability, but lacks comprehensive consideration of the airborne resonance stability of blade tip configurations with sweep, anhedral, and dihedral angles. To fully understand the influence of blade tip shape (sweep, anhedral, and dihedral) on airborne resonance dynamic stability, a more sophisticated blade aeroelastic dynamics model is required.

[0006] This technology is based on the urgent need to understand the air resonance dynamic stability mechanism of rotor helicopters with complex three-dimensional blade tip configurations. Aiming at the problem of the possible adverse effects of forward-swept, backward-swept, upper and lower reverse blade tips on the air resonance stability of helicopters, it breaks through the air resonance dynamic modeling and analysis technology of forward-swept, backward-swept, upper and lower reverse blade tip configurations, and provides technical support for the design analysis and safe flight of modern advanced helicopters modified with complex three-dimensional rotors. Summary of the Invention

[0007] Purpose of the invention: To propose a method for modeling and analyzing the aerial resonance of a forward-and-backward swept rotor helicopter with an up-and-down reverse blade tip configuration, which can be used for the aerial resonance stability analysis of modern advanced rotor systems and rotor helicopters with complex three-dimensional blade tip shapes, calculate the resonant speed zone and stability damping margin, and provide key technical support for model design and modification research and development.

[0008] The present application provides a method for modeling and analyzing the aerial resonance of a helicopter with a forward and backward swept up and down reversed blade tip configuration, the method comprising the following steps:

[0009] 1) Establish the system coordinate system and the relationship between coordinate systems;

[0010] 2) Establish a rotor blade structural dynamics model;

[0011] 3) Establish a rotor blade aerodynamic model;

[0012] 4) Establish the dynamic and aerodynamic model of the blade tip section;

[0013] 5) Establish an organism dynamics model;

[0014] 6) Establish and derive the dynamic equations for the complex three-dimensional rotor and fuselage coupling resonance in the air;

[0015] 7) Balancing calculation and linearization processing;

[0016] 8) Establish an aerial resonance analysis method.

[0017] Preferably, in step 1), the system coordinate system includes: an inertial coordinate system, a body coordinate system, a hub coordinate system, a blade rotation coordinate system, a blade pre-deformation coordinate system, a blade post-deformation coordinate system, and a blade tip deformation local coordinate system, and the relationship between the coordinate systems is the coordinate transformation relationship between the coordinate systems.

[0018] Preferably, in step 2), the establishment of the rotor blade structural dynamic model includes: simplifying the straight section of the blade into a slender elastic beam, assuming that the blade elastic axis passes through the rotation center; the blade cross section has a pre-twist angle θ relative to the elastic axis along the span direction, and the blade has a pre-cone angle β relative to the rotating surface C, considering the geometric nonlinearity of blade deformation; the deformation of the elastic axis at any section r along the span direction of the blade includes four motions: axial displacement u, swing displacement v, flapping displacement w and torsional deformation φ, and their structural and inertial coupling; the connection between the blade root and the hub is simulated by boundary conditions and boundary elements, including its hinged support, fixed support or hinged support with spring constraints and multi-path force transmission relationships.

[0019] Preferably, in step 3), the establishment of the rotor blade aerodynamic model includes: because the blade tip adopts a forward and backward swept up and down reverse configuration, it will cause sensitive changes in the blade aerodynamic characteristics, that is, it has a great impact on the aerodynamics, and the aerodynamic factors have a greater impact during air resonance, especially in the case of high forward flight speed and high lift. Therefore, when modeling the aerodynamic force of air resonance dynamics analysis, the unsteady aerodynamic force model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic force model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the air resonance stability analysis.

[0020] Preferably, in step 4), the establishment of the tip segment dynamics and aerodynamic models includes: when establishing the tip segment structural dynamics model, the upper and lower reverse angles are added to the pre-cone angle at the starting position of the blade's forward and backward sweep direction, and the forward and backward sweep angles are considered in the local coordinate transformation matrix; when establishing the tip segment aerodynamic model, the tip forward and backward sweep angles cause the change in the aerodynamic center position of the airfoil profile, thereby changing the profile aerodynamic force; the aerodynamic center position needs to be calculated based on the tip forward and backward sweep angles, and the change in the calculated aerodynamic torque is achieved by adjusting the aerodynamic center position; when processing the blade incoming flow velocity, the forward and backward sweep angles need to be considered in the transformation matrix, and the incoming flow velocity is converted to the local coordinates of the forward and backward swept segment through the transformation matrix. After calculating the aerodynamic force, the force conversion matrix formed by the transformation matrix is ​​multiplied by the aerodynamic term on the left and converted to the overall coordinates.

[0021] Preferably, in step 5), the fuselage dynamics model is established: assuming that the fuselage is a rigid body, elastic deformation is not considered, and the fuselage has 6 degrees of freedom in the air; when flying in the air, the vibration mode of the helicopter is not affected by the landing gear; the articulated rotor fuselage mode is 6 zero-frequency modes; and for bearingless or hingeless rotors, the fuselage roll and pitch modes are closely related to the rotor flapping stiffness, and air resonance instability occurs under these modes, while other modes of the fuselage can be considered as zero-frequency modes, so the fuselage motion only needs to include pitch and roll motion; the fuselage motion equation can be obtained by balancing three opposite forces and moments at the center of gravity of the fuselage.

[0022] Preferably, in step 6), the derivation of the airborne resonance dynamic equation of the coupling of the complex three-dimensional rotor and the fuselage includes: the airborne resonance dynamic equation can adopt the universal theorem of dynamics, such as Newton's law, d'Alembert-Lagrange theorem, Hamilton's principle, and Lagrange's equation; Hamilton's principle is used here to establish the airborne resonance equation, and according to the dynamic model of the fuselage and rotor blades and the aerodynamic model, the kinetic energy, potential energy and external load virtual work of the fuselage and rotor are described in physical space, the fuselage vibration modal damping force and the rotor blade structural damping, artificial damping, etc. are regarded as non-ideal constraint forces and classified as external forces, and the virtual work done by them is also classified as external load virtual work, and the nonlinear differential equation of the rotor / airframe coupling dynamics is established.

[0023] Preferably, in step 7), the balancing calculation and linearization processing: according to the stability theory of nonlinear differential equations, the balancing calculation needs to be completed first. In the air resonance analysis, it is believed that the balancing solution of the rigid body freedom degree of the corresponding aircraft is zero. Therefore, the rotor lift balancing and blade balancing calculations are also required. The solution of the balancing state is used to linearize the coupled nonlinear differential equations at the system equilibrium position to obtain the coupled linear dynamic differential equations corresponding to the balancing state, which is converted into an analysis of the stability of the coupled system at the equilibrium position for small disturbances.

[0024] Preferably, in step 8), the air resonance analysis method is established, and the solution to the air resonance stability of the rotor and the fuselage coupling usually includes the eigenvalue method and the time domain response damping identification method. The eigenvalue method is to solve the complex eigenvalue of the second-order differential equation containing the damping term, and judge the dynamic instability of the system according to the real part of the eigenvalue; and the time domain response solution is combined with the damping identification method, first solving the transient time domain dynamic response after a given external excitation, and then performing modal damping identification on the attenuated time domain dynamic response, and judging the stability by the positive and negative values ​​of the modal damping.

[0025] This application has the following technical effects:

[0026] The present invention discloses a method for modeling and analyzing the aerial resonance of a rotor helicopter with a forward-and-backward swept, up-and-down reversed blade tip configuration. The model takes into account the influence of the forward-and-backward swept, up-and-down reversed blade tip configuration. The aerial resonance dynamics model and analysis method can be used for aerial resonance stability analysis, resonant speed range, and stability damping margin calculation of all advanced helicopters (especially modern rotor helicopters with complex three-dimensional shapes), providing key technical support for the design and development of new models and model modifications. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the coordinate system of the airframe, rotor hub and blades involved in the present invention;

[0028] Figure 2 The present invention relates to a blade aerodynamic model;

[0029] Figure 3 This is a schematic diagram of the relationship between the blade pre-cone angle and the blade tip anhedral angle involved in the present invention;

[0030] Figure 4 Schematic diagram of the blade tip with forward and backward sweep angles according to the present invention;

[0031] Figure 5 It is a schematic diagram of the positional relationship between the overall coordinates and the local coordinates of the aerodynamic center position of the blade tip section involved in the present invention;

[0032] Figure 6 This is a schematic diagram of a blade beam unit model involved in the present invention;

[0033] Figure 7 This is a schematic diagram of a time finite element model according to the present invention;

[0034] Figure 8 This is a schematic diagram of foreign BERP propeller tips and blue-edge propeller tips. DETAILED DESCRIPTION

[0035] The present application provides a method for modeling and analyzing the air resonance of a forward-and-backward swept up-and-down reversed blade tip rotor helicopter. The method belongs to the helicopter dynamics design technology and involves a method for modeling the dynamics of the whole-machine coupled system and an analysis method. The method is applicable to the air resonance dynamics modeling and stability analysis of conventional rotor helicopters and rotor helicopters with forward-and-backward swept up-and-down reversed blade tip configurations. In particular, for the forward-and-backward swept up-and-down reversed blade tip rotor, the coupled dynamics model takes into account the influence of the three-dimensional configuration of the blade tip on the air resonance stability. The rotor and body dynamics systems are modeled separately using the principles of mechanics, and the motion of the rotor blades, blade tips, and body is described separately in the established multi-coordinate system. The body considers the six-degree-of-freedom rigid body motion; a finite element method model of the isolated rotor blade structure dynamics is established; on the basis of the quasi-steady aerodynamic model, the unsteady aerodynamic model, the dynamic inflow model, and the ONERA model are considered to model the aerodynamic force; and the Hamilton principle is applied to derive the air resonance dynamics equations of the rotor and body coupling. By discretizing the blade motion in space and time using finite elements, rotor lift trim and blade trim are calculated. The solution to the trimmed state is used to linearize the coupled nonlinear differential equations for the system's equilibrium position, resulting in the linear dynamic differential equations for the coupled system corresponding to the trimmed state. The in-flight resonance stability is typically solved using the eigenvalue method and time-domain response damping identification. The eigenvalue method solves the complex eigenvalues ​​of a second-order differential equation containing a damping term, and the system's dynamic instability is determined based on the real part of the eigenvalue. The time-domain response solution is combined with the damping identification method, first solving the transient time-domain dynamic response after a given external excitation. Modal damping is then identified for the decaying time-domain dynamic response, and stability is determined by the positive or negative values ​​of the modal damping. This model and analysis method can be used for in-flight resonance stability analysis, resonant speed range calculation, and stability damping margin calculation for all advanced helicopters (especially modern rotorcraft with complex three-dimensional geometries), providing key technical support for the design and development of new models and model upgrades.

[0036] The rotor and airframe dynamics systems are modeled separately using mechanical principles. The motion of the rotor blades, blade tips, and airframe is described in the established multi-coordinate system, with the airframe considering six-degree-of-freedom rigid body motion. A finite element model of the isolated rotor blade structure dynamics is established. Based on the quasi-steady aerodynamic model, the aerodynamics are modeled by considering the unsteady aerodynamic model, the dynamic inflow model, and the ONERA model. The Hamiltonian principle is applied to derive the dynamic equations for the coupled rotor and airframe in mid-air resonance. By discretizing the blade motion in space and time using finite elements, calculating the rotor lift and blade trim, and linearizing the coupled nonlinear differential equations at the equilibrium position using the solutions to the trimmed state, the linear dynamic differential equations for the coupled system corresponding to the trimmed state are obtained. The in-air resonance stability is typically solved using the eigenvalue method and time-domain response damping identification. The eigenvalue method solves the complex eigenvalues ​​of a second-order differential equation containing a damping term, and the real part of the eigenvalue is used to determine the dynamic instability of the system. The time domain response solution is combined with the damping identification method. First, the transient time domain dynamic response after a given external excitation is solved. Then, the modal damping is identified for the attenuated time domain dynamic response. The stability is judged by the positive and negative values ​​of the modal damping.

[0037] This application provides a method for modeling and analyzing the aerial resonance of a forward-and-backward swept rotor helicopter with an up-and-down reversed blade tip configuration, including:

[0038] (1) Establish the coordinate systems of each system and the relationship between coordinate systems. Establish the inertial coordinate system, the body coordinate system, the hub coordinate system, the blade rotation coordinate system, the blade deformation coordinate system, the blade deformation coordinate system, the blade deformation coordinate system, the blade tip deformation local coordinate system, and establish the coordinate transformation relationship between each coordinate system.

[0039] (2) Dynamic model of rotor blade structure. The straight section of the blade is simplified to a slender elastic beam. It is assumed that the blade elastic axis passes through the center of rotation. The center of mass, tension center and aerodynamic center of the blade section may not coincide. The mass and tensile stiffness distribution of the section are not symmetrical about the section chord axis η. The blade section has a pre-twist angle θ relative to the elastic axis along the span direction, and the blade has a pre-cone angle β relative to the rotation plane. C , accounting for geometric nonlinearity in blade deformation. The deformation of the elastic axis at any spanwise section r includes four motions: axial displacement u, shimmy displacement v, flapping displacement w, and torsional deformation φ, along with their structural and inertial coupling. The connection between the blade root and the hub is simulated using boundary conditions and boundary elements, including hinged, clamped, or hinged with spring constraints, as well as multi-path force transmission.

[0040] (3) Aerodynamic model of rotor blades. Because the blade tip adopts a forward and backward swept up and down reverse configuration, it will cause sensitive changes in the aerodynamic characteristics of the blade, that is, it has a great impact on the aerodynamics. In addition, the aerodynamic factors have a greater impact during air resonance, especially in the case of high forward flight speed and high lift (high forward ratio, high overload). Therefore, when modeling the aerodynamic force of air resonance dynamics analysis, the unsteady aerodynamic force model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic force model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the air resonance stability analysis.

[0041] (4) Dynamic treatment of the blade tip structure. The blade tip adopts a forward and backward swept and reversed configuration, which has little effect on the dynamic characteristics of the structure itself. When the blade tip has a forward and backward swept and reversed angle, its mass centrifugal force needs to be projected on the centrifugal stiffness. If the angle is large, the projected value is small. However, since the centrifugal force is small at the blade tip, it has little effect on the entire blade, especially on the straight section of the blade. Therefore, the centrifugal force of the blade tip has little effect on the centrifugal stiffness of the entire blade. However, the blade pre-cone angle is taken into account in the model, and the centrifugal force is projected into the local coordinates of the blade beam unit to calculate its contribution to the stiffness. In terms of treatment, it is only necessary to add the reverse angle to the pre-cone angle at the starting position of the forward and backward swept and reversed angles in the span direction of the blade, and the forward and backward swept angles are considered in the local coordinate transformation matrix.

[0042] (5) Aerodynamic treatment of the blade tip section. The aerodynamic center position of the airfoil section changes due to the forward and backward sweep angle of the blade tip, thereby changing the aerodynamic force of the section. The aerodynamic center position needs to be calculated based on the forward and backward sweep angle of the blade tip. For the aerodynamic model of the blade airfoil, the 1 / 4 chord length of its leading edge is used as the blade axis, which is also the aerodynamic center of the blade airfoil. The design of the forward and backward sweep angles is mainly to change the aerodynamic torque of the section. The backward sweep produces a negative aerodynamic torque, even if the blade reduces the angle of attack, and vice versa, it increases the angle of attack. Reducing the angle of attack helps to eliminate aeroelastic instability, while forward sweep is not conducive to aeroelastic stability. The change in aerodynamic torque is calculated by adjusting the aerodynamic center position.

[0043] (6) The aerodynamic conversion matrix of the blade tip section processes the incoming flow velocity. When processing the incoming flow velocity of the blade, the forward and backward sweep angles need to be considered in the conversion matrix. This conversion matrix not only includes the blade deformation angle, pitch and blade torsion deformation angle, but also the blade swing deformation angle and the forward and backward sweep angle. The incoming flow velocity is converted to the local coordinates of the forward and backward sweep section through this conversion matrix. After calculating the aerodynamic force, the force conversion matrix formed by this conversion matrix is ​​multiplied by the aerodynamic term on the left and converted to the global coordinates.

[0044] (7) Conversion of the aerodynamic center value of the blade tip section to process the aerodynamic torque. The aerodynamic center position of the blade tip sweep angle calculated in the above step 5 is in the global coordinates, while the aerodynamic force of the blade tip sweep angle section is used to calculate the aerodynamic torque in the local coordinates. Therefore, it is necessary to convert the aerodynamic center value to the local coordinates and then convert it back to the torque of the lift on the blade axis through the force conversion matrix.

[0045] (8) Airframe dynamics model. Assuming the airframe is a rigid body and ignoring elastic deformation, the airframe has 6 degrees of freedom in the air. When flying in the air, unlike on the ground, the vibration mode of the helicopter is not affected by the landing gear. The articulated rotor airframe mode is 6 zero-frequency modes. For bearingless or hingeless rotors, the roll and pitch modes of the airframe are closely related to the rotor flapping stiffness. Resonant instability in the air occurs in these modes, while the other modes of the airframe can be considered as zero-frequency modes. Therefore, the airframe motion only includes pitch and roll motion. The airframe motion equation can be obtained by balancing the three opposite forces and moments at the center of gravity of the airframe.

[0046] (9) Derivation of the dynamic equations for airborne resonance of complex three-dimensional rotor / airframe coupling. The dynamic equations for airborne resonance can be derived using general dynamic theorems, such as Newton's law, d'Alembert-Lagrange theorem, Hamilton's principle, Lagrange's equations, etc. Hamilton's principle is used here to establish the airborne resonance equations. According to the dynamic model of the airframe, rotor blades and aerodynamic model, the kinetic energy and potential energy of the airframe and the external load virtual work are described in physical space, and their generalized coordinates are the physical coordinates of the airframe. The motion of the hub at the interface between the rotor and the airframe and the motion of the rotor blades are described in physical space, and the kinetic energy, potential energy and external load virtual work of the rotor blades are represented by the hub motion and blade motion. The motion of the hub is the associated motion of the rotor blades, which has 6 degrees of freedom of motion. Physical coordinates are used in the derivation of the dynamic coupled motion equations. The damping force of the airframe vibration mode and the rotor blade structural damping, artificial damping, etc. are regarded as non-ideal constraints and are classified as external forces. The virtual work they do is also classified as the external load virtual work.

[0047] (10) Balancing calculation and linearization. According to the stability theory of nonlinear differential equations, the balancing calculation needs to be completed first. In the air resonance analysis, the balancing solution of the rigid body freedom degree of the corresponding body is considered to be zero. Therefore, the rotor lift balancing and blade balancing calculations are also required. The solution of the balancing state is used to linearize the coupled nonlinear differential equations at the system equilibrium position, and the coupled linear dynamic differential equations corresponding to the balancing state are obtained, which is converted into an analysis of the stability of the coupled system at the equilibrium position for small disturbances.

[0048] (11) Airborne resonance analysis method. The solution to the airborne resonance stability of the rotor and fuselage coupling usually includes the eigenvalue method and the time-domain response damping identification method. The eigenvalue method solves the complex eigenvalue of the second-order differential equation containing the damping term, and judges the dynamic instability of the system based on the real part of the eigenvalue. The time-domain response solution is combined with the damping identification method. First, the transient time-domain dynamic response after a given external excitation is solved, and then the modal damping is identified for the attenuated time-domain dynamic response. The stability is judged by the positive and negative values ​​of the modal damping.

[0049] See also Figure 1-Figure 7, the air resonance modeling and analysis method of the forward and backward swept up and down reverse blade tip configuration rotor helicopter involved in the present invention is further described in detail.

[0050] Step 1: Establish the coordinate systems of each system and the relationship between the coordinate systems. Establish the inertial coordinate system, the body coordinate system, the hub coordinate system, the blade rotation coordinate system, the blade deformation coordinate system, the blade deformation coordinate system, the blade deformation local coordinate system, and establish the coordinate transformation relationship between the coordinate systems. See the coordinate system of the body, rotor hub, and blades for details. Figure 1 As shown, {O g ,X g ,Y g ,Z g} is the ground-fixed coordinate system, and its coordinate vector is represented by {i g ,j g ,k g} indicates that the aircraft gravity along -k g Direction. f ,X f ,Y f ,Z f} is the body coordinate system, the coordinate origin O f The center of gravity of the whole machine is selected, and its coordinate vector is {i f ,j f ,k f} indicates that the body is relative to the coordinate system {i g ,j g ,k g The six degrees of freedom of motion of f , Y f , Z f ,φ Xf ,φ Yf ,φ Zf .X f Forward is positive, Z f Upward is positive, Y f The positive direction is determined by the right-hand rule. H ,X H ,Y H ,Z H} is the rotor hub coordinate system, used to describe any {X f ,Y f ,Z f The movement of the rotor at the coordinates of {i H ,j H ,k H}, the movement of the rotor hub center is expressed by X H , Y H , Z H ,φ XH ,φ YH ,φZH Description. The blade rotation coordinate system {i k ,j k ,k k The blade rotates counterclockwise (looking down) at a speed of Ω, and the azimuth angle is ψ k is the kth blade pitch to the hub coordinate axis i H Negative angle. The coordinate system before blade deformation {i s ,j s ,k s} Rotation coordinate system relative to the blade {i k ,j k ,k k There is a pre-cone angle β C The origin of the blade coordinate system is selected at the blade root, which is E away from the hub center. H At any point on the blade in the coordinate system {i s ,j s ,k s} is represented by the coordinates {X s ,Y s ,Z s} description. The coordinate system of any section of the blade after deformation is {i b ,j b ,k b}, the deformation displacement of the point on the blade elastic axis at the section is represented by u, v, w, φ, relative to the coordinate system {i s ,j s ,k s Rotated three angles With coordinates {X b ,Y b ,Z b} description. The coordinate system of the blade tip deformation into any cross section is {i i ,j i ,k i}, with respect to the coordinate system before blade deformation, there are three angles ζ, β, θ, which are expressed as the deformation displacement in the chord direction, swing direction, flap direction and torsion direction of any point on the blade elastic axis. The coordinate system {X i ,Y i ,Z i}, set the blade sweep to negative and the blade inversion to negative. Establish the coordinate transformation relationship between the coordinate systems:

[0051]

[0052]

[0053] Step 2: Establishment of analysis model.

[0054] 1) Establishment of the rotor blade structural dynamics model. The straight section of the blade is simplified to a slender elastic beam. The blade's elastic axis is assumed to pass through the center of rotation. The blade's cross-section center of mass, tension center, and aerodynamic center may not coincide. The cross-section's mass and tensile stiffness distribution are not symmetrical about the cross-section's chord axis η. The blade cross-section has a pre-twist angle θ along the span direction relative to the elastic axis, and a pre-taper angle β relative to the rotation plane. C , considering the geometric nonlinearity of blade deformation. The deformation of the elastic axis at any section r along the span direction of the blade includes four motions: axial displacement u, swing displacement v, flapping displacement w and torsional deformation φ, as well as their structural and inertial coupling. The connection between the root of the blade and the hub is simulated by boundary conditions and boundary elements, including its hinged, fixed or hinged with spring constraints and multi-path force transmission relationships. The partial differential equation of blade dynamics is derived from Hamilton's principle. Since the deformation of the blade is relative to the hub, its deformation energy can be provided by the deformation of the independent blade.

[0055] 2) Establishment of the aerodynamic model of the rotor blade. Because the blade tip adopts a forward and backward swept up and down reverse configuration, it will cause the blade aerodynamic characteristics to change sensitively, that is, it has a great impact on the aerodynamics. In addition, the aerodynamic factors have a greater impact during air resonance, especially in the case of high forward flight speed and high lift (high forward ratio and high overload). Therefore, when analyzing the aerodynamic model of air resonance dynamics, the unsteady aerodynamic model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic model. The aerodynamic model is shown in Figure 2 ,The comprehensive application of these three models can more accurately calculate the aerodynamic loads in the ,analysis of air resonance stability.

[0056] 3) Structural dynamics treatment of the blade tip section. The blade tip adopts a forward and backward swept up and down reverse configuration, which has little effect on the dynamic characteristics of the structure itself. When the blade tip has forward and backward swept up and down reverse angles, its mass centrifugal force needs to be projected on the centrifugal stiffness. If the angle is large, the projected value is small. However, since the centrifugal force is small at the blade tip, it has little effect on the entire blade, especially on the straight section of the blade. Therefore, the centrifugal force of the blade tip has little effect on the centrifugal stiffness of the entire blade. However, the blade pre-cone angle is taken into account in the model, and the centrifugal force is projected into the local coordinates of the blade beam unit to calculate its contribution to the stiffness. In terms of treatment, it is only necessary to add the up and down reverse angles to the pre-cone angle at the starting position of the forward and backward swept up and down reverse angles of the blade in the span direction, such as Figure 3 As shown; the front and rear sweep angles are considered in the local coordinate transformation matrix.

[0057] 4) Aerodynamic treatment of the blade tip section. The aerodynamic center position of the airfoil section changes due to the blade tip sweep angle, thus changing the aerodynamic force of the section. The aerodynamic center position needs to be calculated based on the blade width and the blade tip sweep angle. For the blade airfoil aerodynamic model, the 1 / 4 chord length of its leading edge is taken as the blade axis, which is also the aerodynamic center of the blade airfoil. Figure 4 As shown, from Figure 3It can be seen from the figure that in the straight section (main section) of the blade, XAC = 0, that is, the aerodynamic center is on the blade axis; in the forward-swept section at the blade tip, XAC changes from 0 to negative (i.e., less than 0); while in the swept-back section, XAC changes from negative to positive (i.e., greater than 0). The main purpose of adopting the forward and backward sweep angle design is to change the aerodynamic torque of the section. The backward sweep produces a negative aerodynamic torque, even if the blade reduces the angle of attack, while the reverse increases the angle of attack. Lowering the angle of attack helps eliminate aeroelastic instability, while forward sweep is not conducive to aeroelastic stability. The change in aerodynamic torque is calculated by adjusting the position of the aerodynamic center.

[0058] 5) The aerodynamic conversion matrix of the blade tip section processes the incoming flow velocity. When processing the incoming flow velocity of the blade, the forward and backward sweep angles need to be considered in the conversion matrix [T T ], in the conversion matrix, β is the blade deformation angle, θ is the pitch + blade torsion deformation angle, and ζ is the blade swing deformation angle + forward and backward sweep angle. T ]Convert the incoming flow velocity to the local coordinates of the forward and backward swept segments, calculate the aerodynamic force, and then use [T T ] array formed by the force conversion matrix [T SB ] is multiplied by the aerodynamic term on the left and converted to global coordinates (i.e., coordinates before blade deformation). T ] is the coordinate transformation matrix, for each coordinate vector, and the local aerodynamic force of the blade tip is only the chord direction S, vertical T and torque M θ , force conversion matrix [T SB ] are blades S, T and M θ The three forces and three moments transformed into global coordinates.

[0059] 6) The aerodynamic center value of the blade tip is converted to process the aerodynamic torque. The above 4 gives the calculation method of the aerodynamic center XAC of the blade tip forward and backward sweep section. The aerodynamic center position is in the global coordinate (that is, the distance from the local EAC to the blade axis), and the aerodynamic torque of the blade tip forward and backward sweep angle section is calculated in the local coordinate (the torque is the lift multiplied by the distance from the blade axis to the local aerodynamic center). Therefore, the aerodynamic center XAC value must be converted to the local coordinate, as shown in the following example: Figure 5 As shown, that is, EAC in the local coordinates = XAC / cos (front and back sweep angle), and then through the force conversion matrix [T SB ]Multiply cos (forward and backward sweep angles) to get the moment of lift on the blade axis.

[0060] 7) Establishment of the airframe dynamics model. Assuming the airframe is a rigid body and ignoring elastic deformation, the airframe has six degrees of freedom in the air. When flying in the air, unlike on the ground, the vibration modes of the helicopter are not affected by the landing gear. The articulated rotor airframe modes are six zero-frequency modes. For bearingless or hingeless rotors, the roll and pitch modes of the airframe are closely related to the rotor flapping stiffness. Resonant instability in the air occurs in these modes, while the other modes of the airframe can be considered as zero-frequency modes. Therefore, the airframe motion only includes pitch and roll motion. The airframe motion equation can be obtained by balancing the three opposing forces and moments at the center of gravity of the airframe.

[0061] Step 3: Derivation of the complex three-dimensional rotor / airframe coupled air resonance dynamic equations.

[0062] The resonance dynamics equation in the air can be based on universal dynamics theorems, such as Newton's law, d'Alembert-Lagrange theorem, Hamilton's principle, Lagrange's equation, etc. Hamilton's principle is used here to establish the resonance equation in the air. Based on the dynamic model of the airframe, rotor blades and aerodynamic model, the kinetic energy and potential energy of the airframe and the external virtual work are described in physical space, and their generalized coordinates are the physical coordinates of the airframe. The motion of the hub at the interface between the rotor and the airframe and the motion of the rotor blades are described in physical space, and the kinetic energy, potential energy and external virtual work of the rotor blades are expressed using the hub motion [X H Y H Z H φ XH φ YH φ ZH ] and blade motion uv wφ. The hub motion is a coupled motion of the rotor blades, possessing six degrees of freedom. Physical coordinates are used in the derivation of the dynamic coupled motion equations. Airframe vibration modal damping, rotor blade structural damping, and artificial damping are considered non-ideal constraints and are classified as external forces. The virtual work they perform is also considered as external load virtual work.

[0063] The variational equation of the Hamilton principle for the rotor / airframe coupled dynamic system is:

[0064]

[0065] Where U is the strain energy of the coupled system established based on the strain-displacement field; T is the kinetic energy of the coupled system established based on the motion field; and W is the external work acting on the coupled system, including aerodynamic forces and other constraining forces.

[0066] a) Describe the strain-displacement relationship of blade deformation. Use Hooke's law of strain and stress to obtain the strain potential energy of a blade. Then, sum it over the total number of rotor blades to obtain the total rotor deformation potential energy.

[0067]

[0068] The velocity of a point in the span of any airfoil section along the upper edge of the blade is analyzed, and the kinetic energy and kinetic energy variation of a blade are derived according to the kinetic energy formula. The total kinetic energy of the rotor is obtained by summing the total number of rotor blades.

[0069]

[0070] Where, The span direction of the blade upper edge The velocity of a point within any airfoil section.

[0071] The kinetic energy and potential energy of the blade tip section are also deduced in the same way as the above formula. First, the deformation displacement of a point on any cross-section of the blade tip section is used to deduce the movement speed of the point, and then the expressions of strain potential energy and kinetic energy are obtained and added to the above deformation potential energy and kinetic energy formulas.

[0072] b) The external force acting on the blade is the aerodynamic force, so the virtual work of the external force is the virtual work of the aerodynamic force. Applying the aerodynamic force to the blade cross section and multiplying it by the corresponding virtual displacement gives the cross-sectional aerodynamic virtual work. Then, integrating this over the blade gives the aerodynamic virtual work of the single blade.

[0073] The quasi-steady aerodynamic model of the blade adopts the lift line theory. The aerodynamic force action point is at one-quarter of the chord length. The airflow velocity at three-quarters of the chord length is used to calculate the aerodynamic load on the airfoil. Assuming that the rotor induced flow velocity v i Evenly distributed, see Figure 2 As shown. Through the aerodynamic elements L, D, M ac , projected into the blade airfoil section coordinate system, the aerodynamic forces T, S, and M acting on the airfoil section are obtained φa .

[0074] In aerodynamic calculations, the rotor inflow distribution must be determined first. Common inflow models include the uniform inflow model, Deer's linear inflow model, and the dynamic inflow model.

[0075] 1) Uniform inflow model

[0076]

[0077] Among them, m is the forward ratio, a s is the rotor shaft tilt angle, C T is the rotor thrust coefficient.

[0078] 2) Deers inflow model

[0079] λ=μtanα s +λ i

[0080]

[0081] k y =-2μ (11)

[0082] where ψ is the azimuth angle of the rotor blade.

[0083] 3) First-order dynamic inflow model

[0084] The dynamic inflow model is a two-dimensional unsteady aerodynamic model that links the rotor aerodynamic loads (thrust, roll, and pitch aerodynamic moments) with the transient changes in the rotor induced velocity. The non-uniform distribution of induced velocity along the rotor disc is assumed to be a function of the blade spanwise position and azimuth angle, which can well reflect the physical nature of the rotor inflow. This model can be applied to the aeroelastic stability and response of helicopters. Its first-order harmonic dynamic inflow model expresses the linear first-order harmonic distribution of the induced velocity of the rotor wake at the rotor disc as follows:

[0085]

[0086] In the above formula, is the dimensionless induced velocity, v ie , v ic , v is Determined by the following kinetic equation:

[0087]

[0088] In the above formula,

[0089]

[0090]

[0091] The rotor lift, roll, and pitch moment coefficients on the right side of the dynamic inflow equation (13) are functions of the blade motion and also of the induced velocity itself.

[0092] The ONERA model is an aerodynamic model that calculates the response characteristics of an airfoil's lift, drag, and moment coefficients in unsteady airflow environments based on experimental data from airfoil aerodynamic characteristics. It accounts for compressibility and includes dynamic stall. Combining it with a dynamic inflow model allows for more accurate aerodynamic calculations. This combined model can handle nonlinearities and is used for rotor transient response and dynamic stability analysis.

[0093] The airfoil lift differential equation established using the ONERA model is:

[0094]

[0095] The differential equation of airfoil aerodynamic drag is:

[0096]

[0097] The differential equation of the airfoil aerodynamic moment is:

[0098]

[0099] Where,

[0100]

[0101] ΔC L , ΔC D , ΔC M is the difference between the experimental value of the lift, drag and moment coefficient of the airfoil and its linear value, R λ The other coefficients in equations (21) are parameters of the ONERA model, determined by airfoil test data. Equations (18) (2) to (20) are derived from ΔC L , ΔC D , ΔC M The part of the airfoil aerodynamic characteristics change caused by L , ΔC D , ΔC M The aerodynamic lift, drag and moment forced response of the airfoil induced by the angle of attack reflect the dynamic changes of the aerodynamic characteristics of the airfoil. The aerodynamic lift coefficient C can be obtained. YD , drag coefficient C DD and moment coefficient C MD , with the dynamic aerodynamic coefficient of the airfoil, similar to Figure 2 , the aerodynamic load on any airfoil section of the blade can be obtained. Project the blade aerodynamic force onto the coordinate system In the equation ( ), multiply the virtual displacement array of the blade on the left and integrate along the span of the blade to obtain the virtual work done by the aerodynamic force of a blade on the motion of the blade.

[0102]

[0103] For the aerodynamic virtual work term of the blade tip section, it is necessary to first derive the incoming flow velocity of each section on the blade tip. It is divided into three parts: wind speed caused by forward flight and propeller disc inflow The velocity of the incoming flow generated by the movement at the blade tip is Incoming flow velocity generated by body movement The incoming flow velocity at the blade tip due to movement The velocity of any section of the blade tip can be obtained by converting it to the coordinate system after blade tip deformation. The aerodynamic load of any section of the blade tip can be determined by the above method. The aerodynamic virtual work of the blade tip section can be obtained by converting it to the coordinate system before blade tip deformation and substituting it into the above equation (22).

[0104] c) Finite element discretization of rotor blades. The motion of the blade is a binary function of spatial coordinates and time. In order to remove spatial correlation, the finite element method is used to discretize the blade motion. The blade is divided into several beam elements, and the node deformation displacement of the beam element is used to describe the elastic vibration of the blade. The medium deformation beam element is represented as each unit containing 15 degrees of freedom, such as Figure 6 As shown. Each beam element has 2 end nodes and 3 internal nodes, and each end node has 6 degrees of freedom u, v, v', w, w', The internal nodes have only one degree of freedom, and the unit center node is the torsional degree of freedom The nodes at the points where the unit is divided into three equal parts are the axial deformation degrees of freedom u.

[0105] For the i-th beam element, using shape function interpolation, any point x inside it i The elastic deformation can be expressed as:

[0106]

[0107] Where s = x i / l i , l i is the unit length. H is the shape function of the unit's flapping and shimmying bending degrees of freedom, H u and are the shape functions of the axial tensile and torsional degrees of freedom. i is the column vector of the total degrees of freedom for a single element:

[0108]

[0109] Through the above shape functions and the node displacement of the unit, the displacement of any point in the unit. Then the blade energy equation is discretized. After discretization, the blade energy variation can be expressed as

[0110]

[0111] Where q is the total degree of freedom vector of a single blade, M, C, and K are the mass, damping, and stiffness matrices of the blade, respectively, and F is the load vector.

[0112] d) Time finite element method. Using Hamilton's principle, the rotor equation (25) can be rewritten as:

[0113]

[0114] Where ψ is the blade azimuth angle. After integrating the above formula by parts, considering the periodic characteristics of the rotor motion, in both hovering and steady flight states, we have Therefore, the above equation is equivalent to:

[0115]

[0116] in,

[0117]

[0118] Since the nonlinear load vector F is considered, equation (27) is a nonlinear equation system about generalized degrees of freedom and time. Using the time finite element method, a rotor rotation cycle is divided into N e time units, each unit contains n nodes (the number of nodes depends on the order of the unit shape function). Figure 7 As shown, in one cycle of time, the total number of time nodes is: N d =(n-1)N e +1.

[0119] After time discretization, equation (27) can be written as follows:

[0120]

[0121] Where ψ1=0, After expanding the above equation into a first-order Taylor series at the equilibrium point p0, the displacement at any moment in the unit can be calculated by interpolation based on the node displacement and shape function of the corresponding time unit to obtain q i =H t (s)ξ i , where ξ i is the node displacement vector of the i-th element, H t (s)Time shape function.

[0122] For periodic systems, the equation of motion (27) has the following boundary conditions:

[0123] y(2π)=y(0) (30)

[0124] After introducing the element stiffness matrix and load vector into Equation (29), it is organized into the following form:

[0125] Q G +K G Δξ G =0 (31)

[0126] After solving equation (31), the steady-state periodic response of the rotor can be obtained, that is, q, and Equation (31) is a nonlinear algebraic system of equations because vector Q contains nonlinear terms.

[0127] e) Based on the body motion analysis, the body motion speed and acceleration are obtained:

[0128] Body movement displacement: XY Zφ X φ Y φ Z ;

[0129] Body movement speed:

[0130] Body motion acceleration:

[0131] According to the calculus of variations, the variational formula of the body's kinetic energy is obtained:

[0132]

[0133] Where M f is the mass of the body, X f are the generalized coordinates of the body.

[0134] The potential energy of the body motion is expressed as the product of stiffness and the square of the generalized coordinates. When the aircraft is flying in the air, the landing gear does not provide stiffness and damping, and the six rigid body modal frequencies of the body are zero. The potential energy variation is:

[0135]

[0136] Where K f is the stiffness of the body.

[0137] The virtual work of the damping force of the body motion is the virtual work done by the structural damping force of the body, which can be expressed as:

[0138]

[0139] Where C f is the damping coefficient matrix of the body.

[0140] f) Based on the rotor kinetic energy, potential energy and aerodynamic virtual work derived above, and the airframe kinetic energy, potential energy and damping force virtual work, the total kinetic energy, potential energy and external force work of the complex three-dimensional rotor / airframe coupling system are obtained.

[0141]

[0142]

[0143] In the formula They represent the kinetic energy, elastic potential energy and external work corresponding to the i-th beam section of the k-th blade, respectively. N b is the total number of blades, N e is the total number of units divided into each blade. Substituting the above formula into the Hamilton principle formula, it can be simplified into a general second-order differential equation:

[0144]

[0145] where {f(t)} is the column vector of external forces acting on the coupled system.

[0146] Step 4: Trim calculation and linearization. According to the stability theory of nonlinear differential equations, trim calculations must be completed first. In mid-air resonance analysis, the trim solution corresponding to the rigid body degrees of freedom is assumed to be zero. Therefore, rotor lift trim and blade trim calculations are also required. The solution to the trimmed state is used to linearize the coupled nonlinear differential equations at the system's equilibrium position, resulting in the coupled linear dynamic differential equations corresponding to the trimmed state. This is then transformed into an analysis of the stability of the coupled system at equilibrium with respect to small perturbations.

[0147] a) Balancing calculation

[0148] The balancing equation is: [K xrsxrs (q e )]{q e}+{F xrs0 (q e )}=0(39)

[0149] Solve equation (39) to obtain the balancing displacement of each node in the system equilibrium state, and set it as {q e0}.

[0150] b) Linearization of the kinetic equations

[0151] The displacement of each node of the blade and fuselage is expressed as: {q e}={q e0}+{Δq e}(40)

[0152] In the formula, the motion components of the blades and fuselage are divided into equilibrium components and disturbance components:

[0153]

[0154] where x, y, Ф x ,Ф y The equilibrium component is zero.

[0155] Substitute (40) into equation (39) for linearization, and retain until Δ{q e}, equation (38) can be linearized as:

[0156]

[0157] Step 4: In-flight resonance analysis. The in-flight resonance stability of the coupled rotor and airframe is typically solved using the eigenvalue method and time-domain response damping identification. The eigenvalue method solves the complex eigenvalues ​​of a second-order differential equation containing a damping term, and the system's dynamic instability is determined based on the real part of the eigenvalue. The time-domain response solution is combined with the damping identification method, first solving the transient time-domain dynamic response after a given external excitation. Modal damping is then identified for the attenuated time-domain dynamic response, and stability is determined by the positive or negative values ​​of the modal damping.

[0158] The eigenvalue solution method ignores the external force term of the coupled motion equation (38), and the free vibration equation of the coupled dynamics containing the damping term is:

[0159]

[0160] Among them, C is the damping matrix of the system, M is a symmetric positive definite matrix, and C and K are generally nonsymmetric matrices.

[0161] For hovering and small forward ratio flight states, equation (43) can be linearized into a second-order differential equation with constant coefficients or approximately constant coefficients for a time-invariant system; for other forward flight speeds, the equation will be a second-order differential equation for a linear periodic time-varying system with periodic coefficients.

[0162] 1) Method for solving coupled stability of linear time-invariant systems

[0163] Similar to the ground resonance solution method, the response solution of equation (43) is q = Φe λt (44)

[0164] Where λ is usually a complex vector, expressed as λ = σ + iω D t(45)

[0165] σ is the real part of the complex eigenvalue. When σ>0, the system is unstable, when σ<0, the system is stable, and when σ=0, the system is critically stable. ω D is the modal frequency of the damped free vibration of the system. Substituting equation (45) into equation (43) yields:

[0166] (Mλ 2 +Cλ+K)Φe λt =0 (46)

[0167] The eigenvalues ​​of the system can be obtained by using the QR solution of the eigenvalues ​​of asymmetric matrices.

[0168] 2) Method for solving coupled stability of linear periodic time-varying systems (Floquet theory)

[0169] For equation (43) with periodic coefficients, the state vector is introduced:

[0170]

[0171] The corresponding second-order homogeneous ordinary differential equations can be reduced to a first-order differential equation system:

[0172]

[0173] Among them, F(T+t)=F(t).

[0174] If [U(t)] 2N×2N is a set of basic solutions of equation (48), then At the same time, U(T+t) is also a set of basic solutions of formula (48), that is,

[0175]

[0176] Then there must be the following linear transformation relationship between the two sets of basic solution systems:

[0177] U(T+t)=AU(t) (50)

[0178] Among them, A is a non-singular constant matrix, and its eigenvalue λ k is the characteristic multiplier,

[0179] if Then the coupled system is stable.

Claims

1. A method for modeling and analyzing the aerial resonance of a helicopter with forward and backward swept and reversed blade tips, characterized by: The method comprises the following steps: 1) Establish the system coordinate system and the relationship between coordinate systems; 2) Establish a rotor blade structural dynamics model; 3) Establish a rotor blade aerodynamic model; 4) Establish the dynamic and aerodynamic model of the blade tip section; 5) Establish an organism dynamics model; 6) Establish and derive the dynamic equations for the complex three-dimensional rotor and fuselage coupling resonance in the air; 7) Balancing calculation and linearization processing; 8) Establish an aerial resonance analysis method.

2. The method according to claim 1, wherein: In step 1), the system coordinate system includes: an inertial coordinate system, a body coordinate system, a hub coordinate system, a blade rotation coordinate system, a blade pre-deformation coordinate system, a blade post-deformation coordinate system, and a blade tip deformation local coordinate system. The relationship between the coordinate systems is the coordinate transformation relationship between the coordinate systems.

3. The method according to claim 2, wherein: In step 2), the establishment of the rotor blade structure dynamic model includes: simplifying the straight section of the blade into a slender elastic beam, assuming that the blade elastic axis passes through the rotation center; the blade section has a pre-twist angle θ relative to the elastic axis along the span direction, and the blade has a pre-cone angle β relative to the rotating surface C , considering the geometric nonlinearity of blade deformation; the deformation of the elastic axis at any section r along the span direction of the blade includes four motions: axial displacement u, swing displacement v, flapping displacement w and torsional deformation φ, and their structural and inertial coupling; the connection between the blade root and the hub is simulated by boundary conditions and boundary elements, including its hinged support, fixed support or hinged support with spring constraints and multi-path force transmission relationships.

4. The method according to claim 3, wherein: In step 3), the establishment of the rotor blade aerodynamic model includes: because the blade tip adopts a forward and backward swept up and down reverse configuration, it will cause sensitive changes in the blade aerodynamic characteristics, that is, it has a great impact on the aerodynamics, and the aerodynamic factors have a greater impact during air resonance, especially in the case of high forward flight speed and high lift. Therefore, when modeling the aerodynamic force of air resonance dynamics analysis, the unsteady aerodynamic force model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic force model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the air resonance stability analysis.

5. The method according to claim 4, characterized in that: In step 4), the establishment of the blade tip segment dynamics and aerodynamic models includes: when establishing the blade tip segment structural dynamics model, the upper and lower reverse angles are added to the pre-cone angle at the starting position of the blade's forward and backward sweep direction, and the forward and backward sweep angles are considered in the local coordinate conversion matrix; when establishing the blade tip segment aerodynamic model, the blade tip forward and backward sweep angles cause the change in the aerodynamic center position of the airfoil profile, thereby changing the cross-section aerodynamic force; the aerodynamic center position needs to be calculated based on the blade tip forward and backward sweep angles, and the change in the aerodynamic torque is calculated by adjusting the aerodynamic center position; when processing the blade incoming flow velocity, the forward and backward sweep angles need to be considered in the conversion matrix, and the incoming flow velocity is converted to the local coordinates of the forward and backward swept segment through the conversion matrix. After calculating the aerodynamic force, the force conversion matrix formed by the conversion matrix is ​​multiplied by the aerodynamic term on the left and converted to the overall coordinates.

6. The method according to claim 5, characterized in that: In step 5), the fuselage dynamics model is established: assuming that the fuselage is a rigid body, elastic deformation is not considered, and the fuselage has 6 degrees of freedom in the air; when flying in the air, the vibration mode of the helicopter is not affected by the landing gear; the articulated rotor fuselage mode is 6 zero-frequency modes; and for bearingless or hingeless rotors, the fuselage roll and pitch modes are closely related to the rotor flapping stiffness, and air resonance instability occurs under these modes, while other modes of the fuselage can be considered as zero-frequency modes, so the fuselage motion only includes pitch and roll motion; the fuselage motion equation can be obtained by balancing three opposite forces and moments at the center of gravity of the fuselage.

7. The method according to claim 6, characterized in that: In step 6), the derivation of the airborne resonance dynamic equation of the complex three-dimensional rotor and fuselage coupling includes: the airborne resonance dynamic equation can adopt universal dynamics theorems, such as Newton's law, d'Alembert-Lagrange theorem, Hamilton's principle, and Lagrange's equation; Hamilton's principle is used here to establish the airborne resonance equation, and according to the dynamic model of the fuselage and rotor blades and the aerodynamic model, the kinetic energy, potential energy and external load virtual work of the fuselage and rotor are described in physical space, and the fuselage vibration modal damping force and the rotor blade structural damping, artificial damping, etc. are regarded as non-ideal constraint forces and classified as external forces. The virtual work done by them is also classified as external load virtual work, and the nonlinear differential equation of the rotor / airframe coupling dynamics is established.

8. The method according to claim 7, wherein: In step 7), the balancing calculation and linearization processing: According to the stability theory of nonlinear differential equations, the balancing calculation needs to be completed first. In the air resonance analysis, it is believed that the balancing solution of the rigid body freedom degree of the corresponding body is zero. Therefore, the rotor lift balancing and blade balancing calculations are also required. The solution of the balancing state is used to linearize the coupled nonlinear differential equations at the system equilibrium position to obtain the coupled linear dynamic differential equations corresponding to the balancing state, which is converted into an analysis of the stability of the coupled system at the equilibrium position for small disturbances.

9. The method according to claim 8, characterized in that: In step 8), the airborne resonance analysis method is established to solve the airborne resonance stability of the rotor and the fuselage coupling. There are usually eigenvalue methods and time domain response damping identification methods. The eigenvalue method solves the complex eigenvalues ​​of the second-order differential equation containing the damping term and determines the dynamic instability of the system based on the real part of the eigenvalue. The time domain response solution is combined with the damping identification method. First, the transient time domain dynamic response after a given external excitation is solved. Then, the modal damping is identified for the attenuated time domain dynamic response. The stability is judged by the positive and negative values ​​of the modal damping.

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