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

Abstract

The invention provides a ground 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 a motion model of the airframe on the undercarriage; establishing a complex three-dimensional shape rotor wing and body coupling mode comprehensive model, and deducing a kinetic equation; and establishing a ground resonance analysis method.

Description

Technical Field

[0001] This application belongs to the technical field of helicopter dynamics modeling and analysis, and specifically relates to a method for modeling and analyzing the ground resonance of a helicopter with a forward-swept and backward-swept upper and lower anti-tip configuration. Background Art

[0002] All along, the blade tip plays an important role in improving the flight performance and handling performance of helicopters. With the wide application of various new materials on helicopter rotors, it has become possible to improve the performance of helicopter rotors by changing the blade tip shape. Advanced blade tip shape designs have been a research hotspot at home and abroad in recent years. As follows Figure 8 Shown are advanced blade tips such as the foreign BERP blade tip and blue-edge blade tip, whose shapes all include the characteristic of blade tip sweep. Aerodynamic research shows that swept blade tips have an important impact on the air compressibility around the advancing blades and the flow separation stall characteristics of the retreating blades, etc.

[0003] When a helicopter flies forward, the oncoming flow Mach number of the advancing rotor blades increases, and shock waves are likely to appear. The angle of attack of the retreating blade sections increases, and dynamic stall is likely to occur. This not only limits the improvement of the helicopter's flight speed but also seriously affects the flight performance of the helicopter. Research has found that by changing the geometric shape of the blade tip, the aerodynamic performance of the rotor can be improved, the noise level can be reduced, and the flight speed of the helicopter can be greatly increased. The successful application of the BERP (British-Experimental-Rotor-Program) rotor with an advanced blade tip shape in the Lynx helicopter has even created a world record for the flight speed of a single-rotor helicopter with a tail rotor.

[0004] Compared with traditional rectangular rotors, the rotor flow field in the area near the blade disc of a complex three-dimensional shape blade tip rotor changes significantly, thus changing the aerodynamic performance and noise level of the rotor. However, changing the blade tip shape will also change the aerodynamic force of the blade tip part, thereby increasing the coupling between the bending and torsional motions of the blade and also having an impact on the ground resonance stability of the helicopter. The research on the ground resonance analysis method for a complex three-dimensional shape blade tip rotor helicopter can provide an important basis for the optimization design and application of complex three-dimensional shape blade tips, ensuring that a blade tip shape with excellent aerodynamic performance will not exhibit unstable ground resonance phenomena.

[0005] Changing the blade tip shape will simultaneously change the coupling between the bending and torsional motions of the blade. The influence on ground resonance is reflected in the movement of the unstable region of the rotor speed and the change in the damping of the rotor flapping mode. Some literature only mentions the influence of the sweep angle or dihedral angle on aeroelastic stability, but does not comprehensively consider the research on the ground resonance stability of a blade tip configuration with forward and backward sweep and upper and lower dihedral angles. To fully understand the influence of the blade tip shape (forward and backward sweep, upper and lower dihedral) on the dynamic stability of ground resonance, a more refined blade aeroelastic dynamics model is required.

[0006] Based on the urgent need to understand the ground resonance dynamic stability mechanism of a helicopter with a complex three - dimensional blade tip configuration rotor, aiming at the problem of the possible adverse effects of forward - swept, backward - swept, up - and - down - swept blade tips on the ground resonance stability of the helicopter, this technology breaks through the ground resonance dynamic modeling and analysis technology for a helicopter with a forward - swept, backward - swept, up - and - down - swept blade tip configuration rotor, providing technical support for the design analysis and safe flight of modern advanced helicopters retrofitted with complex three - dimensional rotors. Summary of the Invention

[0007] Object of the Invention: To propose a method for modeling and analyzing the ground resonance of a helicopter with a forward - swept, backward - swept, up - and - down - swept blade tip configuration rotor, which is used for analyzing the ground resonance stability of modern advanced rotor systems and helicopters with rotors having complex three - dimensional blade tip shapes, calculating the resonance speed range and the stability damping margin, and providing key technical support for carrying out model design and retrofit research and development.

[0008] This application provides a method for modeling and analyzing the ground resonance of a helicopter with a forward - swept, backward - swept, up - and - down - swept blade tip configuration, and the method includes the following steps:

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

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

[0011] 3) Establish the aerodynamic model of the rotor blade;

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

[0013] 5) Establish the motion model of the airframe on the landing gear;

[0014] 6) Establish the coupled - mode synthesis model of the complex three - dimensional rotor and the airframe, and derive the dynamic equation;

[0015] 7) Establish the ground resonance analysis method.

[0016] Preferably, in step 1), the system coordinate system includes: an inertial coordinate system, an airframe coordinate system, a hub coordinate system, a blade rotation coordinate system, a coordinate system before blade deformation, a coordinate system after blade deformation, and a local coordinate system for blade tip deformation, and the relationships between the coordinate systems are the coordinate transformation relationships between the coordinate systems.

[0017] Preferably, in step 2), establishing the structural dynamics model of the rotor blade includes: simplifying the straight section of the blade into a slender elastic beam, assuming that the elastic axis of the blade passes through the rotation center; there is a pre - twist angle θ of the blade section relative to the elastic axis along the span direction, and there is a pre - coning angle β of the blade relative to the rotation plane. C, the geometric nonlinearity of blade deformation is considered; the deformation of the elastic axis at any section r along the span of the blade includes four motions and their structural and inertial couplings: axial displacement u, flapping displacement v, pitch displacement w, and torsional deformation φ; the connection between the blade root and the hub is simulated by boundary conditions and boundary elements for its hinge support, fixed support, or hinge support with spring constraints and multi-channel force transmission relationships.

[0018] Preferably, in step 3), the establishment of the aerodynamic force model of the rotor blade includes: since the blade tip adopts a forward and backward swept and up and down reversed configuration, it will cause sensitive changes in the aerodynamic characteristics of the blade, that is, it has a great influence on the aerodynamics, but has a small influence on the ground resonance stability. Therefore, when performing aerodynamic force modeling in the ground resonance dynamics analysis, on the basis of adopting the quasi-steady aerodynamic force model, considering the non-uniform first-order dynamic inflow model can meet the requirements of ground resonance stability analysis.

[0019] Preferably, in step 4), the establishment of the dynamics and aerodynamic model of the blade tip section includes: when establishing the structural dynamics model of the blade tip section, in terms of processing, as long as the up and down reversed angle is added to the pre-cone angle at the starting position of the forward and backward swept and up and down reversed angles of the blade along the span, and for the forward and backward swept angles, they are considered in the local coordinate transformation matrix; when establishing the aerodynamic force model of the blade tip section, due to the change in the position of the aerodynamic center of the airfoil section caused by the forward and backward swept angles of the blade tip, the aerodynamic force of the section changes; the position of the aerodynamic center needs to be calculated according to the forward and backward swept angles of the blade tip, and the change in the aerodynamic torque is calculated by adjusting the position of the aerodynamic center; when dealing with the oncoming flow velocity of the blade, the forward and backward swept angles need to be considered in the transformation matrix. After the oncoming flow velocity is transformed to the local coordinate of the forward and backward swept section through this transformation matrix, and the aerodynamic force is calculated, then the force transformation matrix formed by this transformation matrix is left-multiplied by the aerodynamic force term to be transformed to the global coordinate.

[0020] Preferably, in step 5), the establishment of the motion model of the airframe on the landing gear: assuming the airframe is a rigid body, considering the elastic constraints and damping provided by the landing gear to the airframe, simplifying the buffer and the wheels as stiffness and damping components; the deformation motion of the landing gear is caused by the displacement and velocity of the airframe movement, so that the landing gear generates elastic and damping constraint forces acting on the airframe; according to D'Alembert's principle, the inertial force of the airframe and the load acting on the airframe by the landing gear are in a balanced state, and thus the motion equation of the airframe on the landing gear is established.

[0021] Preferably, in step 6), the comprehensive model of the coupling mode of the complex three-dimensional shape rotor and the airframe, and the derivation of the dynamic equation include: First, the Hamilton principle is used to derive the coupling dynamic equation of the rotor / airframe system; according to the dynamic models of the airframe, rotor blades and aerodynamic force models, the airframe is used as a sub-structure of the coupling dynamic system, and its kinetic energy, potential energy and virtual work of external loads are described in the modal space, and their generalized coordinates are the vibration modal coordinates of the airframe; Second, the blades are regarded as residual structures, and a hybrid dynamic coupling analysis model of the modal space and the physical space is established. The partial differential equation of blade dynamics is discretized by the finite element method, the vibration characteristics of the isolated blade are calculated, and N P blade modes are selected, and then the blade motion is transformed into the blade modal space to obtain the comprehensive analysis model of the coupling of the rotor and the airframe modes.

[0022] Preferably, in step 7), the ground resonance analysis method includes: based on the non-linear dynamic model of the landing gear, a spatial model is generally used for the airframe; based on the test data of the dynamic characteristics of the hub center, a plane model is usually used for the airframe, that is, the vibration characteristics of the airframe on the landing gear are represented by the modal parameters of the hub center in the rotating plane; for the above-mentioned linear differential equation of the coupling mode of the rotor / airframe, the multi-blade coordinate transformation is used to eliminate the periodic coefficients in the equation, and the complex eigenvalues and eigenvectors of the coupling mode equation are calculated by the eigenvalue QR algorithm. By analyzing the positive and negative values of the real parts of all complex eigenvalues, the ground resonance stability of the dynamic coupling system is judged.

[0023] The present application has the following technical effects:

[0024] The present invention relates to a method for modeling and analyzing the ground resonance of a helicopter with a forward and backward swept and up and down reversed blade tip configuration. The model takes into account the influence of the forward and backward swept and up and down reversed blade tip configuration. The ground resonance dynamic model and analysis method can be used for the ground resonance stability analysis, resonance speed range and stability damping margin calculation of all advanced helicopters (especially modern complex three-dimensional shape rotor helicopters), providing key technical support for the development of new models and the modification of existing models. Description of the Drawings

[0025] Figure 1 is a schematic diagram of the coordinate systems of the airframe, rotor hub and rotor blades involved in the present invention;

[0026] Figure 2 is a schematic diagram of the relationship between the pre-cone angle of the rotor blade and the up and down reverse angle of the blade tip involved in the present invention;

[0027] Figure 3 is a schematic diagram of the blade tip part with the forward and backward swept angle of the blade tip involved in the present invention;

[0028] Figure 4 is a schematic diagram of the position relationship from the overall coordinates to the local coordinates of the aerodynamic center position of the blade tip section involved in the present invention;

[0029] Figure 5 It is a schematic diagram of the airframe model involved in the present invention;

[0030] Figure 6 It is a schematic diagram of the blade aerodynamic force model involved in the present invention;

[0031] Figure 7 It is a schematic diagram of the blade beam element model involved in the present invention;

[0032] Figure 8 They are schematic diagrams of the foreign BERP blade tip and blue-edge blade tip. Specific implementation manner

[0033] A method for ground resonance modeling and analysis of a forward and backward swept and up and down reversed blade tip configuration rotary-wing helicopter provided by the present application belongs to the technical field of helicopter dynamics design, and involves a dynamic modeling method and an analysis method for a whole-aircraft coupling system. It is applicable to the ground resonance dynamics modeling and stability analysis of conventional and rotary-wing helicopters with a forward and backward swept and up and down reversed blade tip configuration. In particular, for a rotary-wing with a forward and backward swept and up and down reversed blade tip configuration, the coupling dynamic model takes into account the influence of the three-dimensional configuration of the blade tip on the ground resonance stability. The modal synthesis technology is used to model the rotor and airframe dynamic systems. The motions of the rotor blade, blade tip, and airframe are described respectively in the established multi-coordinate systems, and the structural dynamics finite element method models of the isolated rotor blade and airframe are established; the quasi-steady and non-uniform first-order dynamic inflow models are used to model the aerodynamic force; the motion model of the airframe on the landing gear is established according to D'Alembert's principle; the Hamilton principle is applied to derive the dynamic equation of the rotor-airframe coupling system. After the finite element discretization of the blade motion space, blade trimming, linearization, and modal analysis, the coupled rotor / airframe dynamic equation is reduced by using a finite number of low-order blade modal coordinates, and the rotor / airframe modal coupling dynamic equation in the corresponding modal coordinates is derived. By using the multi-blade coordinate transformation to eliminate the periodic coefficients in the equation, the complex eigenvalues and eigenvectors are calculated by the eigenvalue QR method to analyze the ground resonance stability. This model and analysis method can be used for the ground resonance stability analysis of all advanced helicopters (especially modern complex three-dimensional shape rotary-wing helicopters), the calculation of the resonance speed range and stability damping margin, and provide key technical support for the development of new models and the modification of models.

[0034] The modal synthesis technique is used to model the rotor and airframe dynamics system. The motions of the rotor blade, blade tip, and airframe are described in the established multi-coordinate systems respectively, and the structural dynamics finite element method models of the isolated rotor blade and airframe are established. The quasi-steady and non-uniform first-order dynamic inflow models are used to model the aerodynamic forces. According to D'Alembert's principle, the motion model of the airframe on the landing gear is established. Hamilton's principle is applied to derive the dynamic equations of the rotor-airframe coupled system. After the finite element discretization of the blade motion space, blade trimming, linearization, and modal analysis, the coupled rotor / airframe dynamic equations are reduced with a finite number of low-order blade modal coordinates, and the rotor / airframe modal coupled dynamic equations in the corresponding modal coordinates are derived. By using the multi-blade coordinate transformation to eliminate the periodic coefficients in the equations, the complex eigenvalues and eigenvectors are calculated by the eigenvalue QR method to analyze the ground resonance stability.

[0035] A method for ground resonance modeling and analysis of a helicopter with a forward-swept and backward-swept, up-and-down-reflected blade tip configuration is provided, including:

[0036] (1) Establish the coordinate systems of each system and the relationships between the coordinate systems. Establish the inertial coordinate system, airframe coordinate system, hub coordinate system, blade rotation coordinate system, pre-deformation coordinate system of the blade, post-deformation coordinate system of the blade, local coordinate system of the blade tip deformation, and establish the coordinate transformation relationships between the coordinate systems.

[0037] (2) Structural dynamics model of the rotor blade. The straight section of the blade is simplified as a slender elastic beam, assuming that the elastic axis of the blade passes through the rotation center; the centroid, tension center, and aerodynamic center of the blade section may not coincide, the mass and tensile stiffness distributions of the section are not symmetric about the chordwise axis η of the section, there is a pre-twist angle θ of the blade section relative to the elastic axis along the span direction, and there is a pre-cone angle β of the blade relative to the rotation plane. C , considering the geometric nonlinearity of the blade deformation. The deformation of the elastic axis at any section r along the span of the blade includes: axial displacement u, flapping displacement v, lag displacement w, and torsional deformation φ, and the structural and inertial couplings of these four motions. The connection between the blade root and the hub is simulated by boundary conditions and boundary elements for its hinge support, fixed support, or hinge support with spring constraints and multi-way force transmission relationships.

[0038] (3) Aerodynamic force model of the rotor blade. Since the blade tip of the blade adopts a forward-swept and backward-swept, up-and-down-reflected configuration, it will cause sensitive changes in the aerodynamic characteristics of the blade, that is, it has a great impact on the aerodynamics, but has a small impact on the ground resonance stability. Therefore, when modeling the aerodynamic forces in the ground resonance dynamics analysis, on the basis of using the quasi-steady aerodynamic force model, considering the non-uniform first-order dynamic inflow model can meet the requirements of the ground resonance stability analysis.

[0039] (4) Structural dynamics treatment of the blade tip section. The forward and backward sweep and up and down reversal configuration of the blade tip has little effect on the dynamic characteristics of the structure itself. When there are forward and backward sweep and up and down reversal angles at the blade tip, the centrifugal force of its mass needs to be projected onto the centrifugal stiffness. If the angle is large, the projected value is small. However, since it is at the blade tip and its centrifugal force is small, it has little effect on the entire blade, especially on the straight section of the blade. Therefore, the centrifugal force at the blade tip has little effect on the centrifugal stiffness of the entire blade. However, the blade pre-cone angle is considered in the model, and the centrifugal force is projected into the local coordinates of the blade beam element to calculate its contribution to the stiffness. In the treatment, as long as the up and down reversal angle is added to the pre-cone angle at the starting position of the spanwise direction of the forward and backward sweep and up and down reversal angles of the blade, and for the forward and backward sweep angles, they are considered in the local coordinate transformation matrix.

[0040] (5) Aerodynamic force treatment of the blade tip section. The change in the aerodynamic center position of the airfoil section caused by the forward and backward sweep angles of the blade tip leads to the change in the sectional aerodynamic force. The aerodynamic center position needs to be calculated based on the forward and backward sweep angles of the blade tip. For the aerodynamic model of the blade airfoil, the 1 / 4 chord length at the leading edge is taken as the blade axis, and this axis is also the aerodynamic center of the blade airfoil. The forward and backward sweep angle design is mainly to change the aerodynamic torque of this section. The backward sweep generates a negative aerodynamic torque, which reduces the angle of attack of the blade, and vice versa increases the angle of attack. Reducing the angle of attack helps to eliminate aeroelastic instability, and the forward sweep is not conducive to aeroelastic stability. The change in the aerodynamic torque is calculated by adjusting the aerodynamic center position.

[0041] (6) Aerodynamic force transformation matrix treatment of the oncoming flow velocity. When dealing with the oncoming flow velocity of the blade, the forward and backward sweep angles need to be considered in the transformation matrix. This transformation matrix includes not only the blade deformation angle, pitch, and blade twist deformation angle, but also the blade flapping deformation angle and forward and backward sweep angles. After the oncoming flow velocity is transformed to the local coordinates of the forward and backward sweep section through this transformation matrix, and the aerodynamic force is calculated, then the force transformation matrix formed by this transformation matrix is left-multiplied by the aerodynamic force term to be transformed to the global coordinates.

[0042] (7) Aerodynamic center value transformation treatment of the aerodynamic torque. The aerodynamic center position of the forward and backward sweep angles of the blade tip calculated in the above (5) is in the global coordinates, while the aerodynamic force of the forward and backward sweep angle section of the blade tip calculates the aerodynamic torque in the local coordinates. Therefore, the aerodynamic center value needs to be transformed to the local coordinates and then transformed back to the moment of the lift force about the blade axis through the force transformation matrix.

[0043] (8) Establishment of the movement model of the airframe on the landing gear. Assume that the airframe is a rigid body. Considering the elastic constraint and damping provided by the landing gear to the airframe, simplify the buffer and the wheel into stiffness and damping components. The deformation movement of the landing gear is caused by the movement displacement and speed of the airframe, which generates elastic and damping constraint forces on the airframe. The acceleration of the airframe results in the inertial force acting on the airframe. The heading and lateral movements of the landing gear are only restricted by the elastic and damping force loads of the wheels, and the vertical movement of the landing gear is jointly affected by the elastic and damping force loads of the wheels and the buffer. The loads of the wheels and the buffer in the vertical direction are in a series relationship, and the inertial loads of the buffer and the wheels are not considered. According to D'Alembert's principle, the inertial force of the airframe and the loads acting on the airframe by the landing gear are in a balanced state, and based on this, the movement equation of the airframe on the landing gear is established.

[0044] (9) Establishment of the comprehensive analysis model of the coupling mode of the rotor with a complex three-dimensional shape and the airframe. When establishing the comprehensive analysis model of the coupling mode of the rotor and the airframe, first regard the blade as a residual structure, and the hub node at the connection interface as a residual node, and establish a dynamic coupling analysis model that mixes the modal space and the physical space. This model is convenient for deriving the coupling dynamic equation of the rotor / airframe system. On this basis, discretize the partial differential equation of the blade dynamics by the finite element method, calculate the vibration characteristics of the isolated blade, select N P blade modes, and then transform the blade movement into the blade modal space. The node displacement of the hub is represented by the modal coordinate {X FP}, and the comprehensive analysis model of the coupling mode of the rotor and the airframe is obtained.

[0045] (10) Derivation of the coupling dynamic equation of the rotor / airframe with a complex three-dimensional shape. Derive the coupling dynamic equation of the rotor / airframe system according to Hamilton's principle. The airframe, as a substructure of the coupled dynamic system, its kinetic energy, potential energy, and virtual work of the external load are described in the modal space, and their generalized coordinates are the vibration modal coordinates of the airframe. The movement of the hub at the connection interface between the rotor and the airframe and the movement of the rotor blades are described in the physical space. The kinetic energy, potential energy, and virtual work of the external load of the rotor blades are expressed by the movement of the hub and the movement of the blades. After establishing the dynamic equation using physical coordinates, then transform the movement of the hub into the modal space. The vibration modal damping force of the airframe and the structural damping and artificial damping of the rotor blades, etc. are regarded as non-ideal constraint forces and classified as external forces, and the virtual work they do is also classified as the virtual work of the external load together. After establishing the blade dynamic equation and discretizing it in space and time, through blade trimming and linearization, blade modal analysis and modal condensation, the blade dynamic modal equation is obtained, which is coupled with the airframe modal equation, and finally the linear differential equation of the coupling mode of the rotor / airframe is obtained.

[0046] (11) Ground resonance analysis method. Based on the non-linear dynamic model of the landing gear, a spatial model is generally used for the airframe; based on the dynamic characteristic test data of the hub center, a plane model is usually used for the airframe, that is, the vibration characteristics of the airframe on the landing gear are represented by the modal parameters of the hub center in the rotation plane. For the above-mentioned rotor / airframe modal coupling dynamic linear differential equation, multi-blade coordinate transformation is used to eliminate the periodic coefficients in the equation, and the eigenvalue QR algorithm is used to calculate the complex eigenvalues and eigenvectors of the coupling modal equation. By analyzing the positive and negative values of the real parts of all complex eigenvalues, the ground resonance stability of the dynamic coupling system is obtained.

[0047] Please refer to Figures 1 - 7 , and make a further detailed description of the ground resonance modeling and analysis method for the forward and backward swept and up and down reversed blade tip configuration rotor helicopter involved in the present invention.

[0048] Step 1: Establish the coordinate systems of each system and the relationships between the coordinate systems. Establish an inertial coordinate system, an airframe coordinate system, a hub coordinate system, a blade rotation coordinate system, a coordinate system before blade deformation, a coordinate system after blade deformation, a local coordinate system for blade tip deformation, and establish the coordinate transformation relationships between each coordinate system. The airframe, rotor hub, and blade coordinate systems are shown in Figure 1 as shown. {O g ,X g ,Y g ,Z g} is the ground fixed coordinate system, and its coordinate vectors are represented by {i g ,j g ,k g}. The aircraft gravity acts along the -k g direction. {O f ,X f ,Y f ,Z f} is the airframe coordinate system, and the coordinate origin O f is selected at the center of gravity of the whole aircraft. Its coordinate vectors are represented by {i f ,j f ,k f}. The six degrees of freedom of the airframe relative to the coordinate system {i g ,j g ,k g} are X f , Y f , Z f , φ Xf , φ Yf , φ Zf . X f is positive forward, Z f is positive upward, and the positive direction of Y f is determined by the right-hand rule. {O H ,X H ,Y H ,ZH} is the rotor hub coordinate system, which is used to describe any {X f ,Y f ,Z f The origin of the coordinate system is at the center of the hub, and the coordinate vector is {i H ,j H ,k H}, the motion of the rotor hub center is X H , Y H , Z H ,φ XH ,φ YH ,φ ZH 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}, relative to the coordinate system before the blade deformation, there are three angles ζ, β, θ, representing the chordwise, flapping, pitching, and torsional deformation displacements of any point on the section of the blade elastic axis, and described by the coordinate system {X i ,Y i ,Z i}, assuming negative blade sweep and negative dihedral. Establish the coordinate transformation relationships between the coordinate systems:

[0049]

[0050]

[0051] Step 2: Establishment of the analysis model.

[0052] 1) Establishment of the structural dynamics model of the rotor blade. The straight section of the blade is simplified as a slender elastic beam, assuming that the elastic axis of the blade passes through the rotation center; the centroid, tension center, and aerodynamic center of the blade section may not coincide, the mass and tensile stiffness distribution of the section are not symmetric about the chordwise axis η of the section, there is a pre-twist angle θ of the blade section relative to the elastic axis along the span direction, and the blade has a pre-cone angle β relative to the rotation plane C , considering the geometric nonlinearity of the blade deformation. The deformation of the elastic axis of any section r along the span of the blade includes: axial displacement u, flapping displacement v, pitching displacement w, and torsional deformation φ, and the coupling of their structures and inertia. The connection between the blade root and the hub is simulated by boundary conditions and boundary elements for its hinge support, fixed support, or hinge support with spring constraints and multi-way 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 is provided by the independent blade deformation.

[0053] 2) Establishment of the aerodynamic model of the rotor blade. Since the blade tip adopts the configuration of forward and backward sweep and dihedral, it will cause sensitive changes in the aerodynamic characteristics of the blade, that is, it has a great influence on the aerodynamics, but has a small influence on the ground resonance stability. Therefore, when modeling the aerodynamic force in the ground resonance dynamics analysis, on the basis of adopting the quasi-steady aerodynamic model, considering the non-uniform first-order dynamic inflow model can meet the requirements of ground resonance stability analysis.

[0054] 3) Structural dynamics treatment of the blade tip section. The configuration of forward and backward sweep and dihedral of the blade tip has a small influence on the dynamic characteristics of the structure itself. When there are forward and backward sweep and dihedral angles at the blade tip, the centrifugal force of its mass needs to be projected onto the centrifugal stiffness. If the angle is large, the projected value is small. However, due to the small centrifugal force at the blade tip, it has little influence on the whole blade, especially on the straight section of the blade. Therefore, the centrifugal force at the blade tip has little influence on the centrifugal stiffness of the whole blade. However, the pre-cone angle of the blade is considered in the model, and the centrifugal force is projected into the local coordinates of the blade beam element to calculate its contribution to the stiffness. In the treatment, as long as the dihedral angle is added to the pre-cone angle at the starting position of the forward and backward sweep and dihedral angles of the blade along the span, such asFigure 2 as shown; for the leading and trailing sweep angles, they are considered in the local coordinate transformation matrix.

[0055] 4) Aerodynamic force treatment of the blade tip section. Due to the leading and trailing sweep angles of the blade tip, the position of the aerodynamic center of the airfoil section changes, thus causing changes in the sectional aerodynamic force. The position of the aerodynamic center needs to be calculated based on the blade width and the leading and trailing sweep angles of the blade tip. For the aerodynamic model of the blade airfoil, the 1 / 4 chord length at the leading edge is taken as the blade axis, and this axis is also the aerodynamic center of the blade airfoil, as shown in Figure 3 as shown, from Figure 3 it can be seen that for the straight section (main section) of the blade, XAC = 0, that is, the aerodynamic center is on the blade axis; for the leading sweep section at the blade tip, the XAC of this section changes from 0 to negative (i.e., less than 0); and for the trailing sweep section, the XAC changes from negative to positive (i.e., greater than 0). The use of leading and trailing sweep angles is mainly to change the aerodynamic torque of this section. Trailing sweep generates negative aerodynamic torque, which reduces the angle of attack of the blade, and vice versa for increasing the angle of attack. Reducing the angle of attack helps to eliminate aeroelastic instability, and leading sweep is not conducive to aeroelastic stability. By adjusting the position of the aerodynamic center, the change in the calculated aerodynamic torque is achieved.

[0056] 5) Treatment of the oncoming flow velocity by the aerodynamic force transformation matrix of the blade tip section. When dealing with the oncoming flow velocity of the blade, the leading and trailing sweep angles need to be considered in the transformation matrix [T T . In this transformation matrix, β is the blade deformation angle, θ is the pitch angle + the blade twist deformation angle, and ζ is the blade flapping deformation angle + the leading and trailing sweep angles. Through the transformation matrix [T T , the oncoming flow velocity is transformed to the local coordinates of the leading and trailing sweep sections. After calculating the aerodynamic force, the force transformation matrix [T T formed by [T SB is left-multiplied by the aerodynamic force term to transform it to the global coordinates (i.e., the coordinates before the blade deformation). The transformation matrix [T T is a coordinate transformation matrix for each coordinate vector, and the local aerodynamic force at the blade tip only has the chordwise S, the vertical T, and the torque M θ , and the force transformation matrix [T SB is the transformation of the blade S, T, and M θ to the three forces and three moments in the global coordinates.

[0057] 6) Transformation of the aerodynamic center value in the blade tip section to process the aerodynamic torque. The above 4 gives the calculation method of the aerodynamic center XAC of the leading and trailing sweep sections at the blade tip. The position of this aerodynamic center is in the global coordinates (i.e., the distance from the local EAC to the blade axis), while the aerodynamic force in the leading and trailing sweep angle sections at the blade tip calculates the aerodynamic torque in the local coordinates (this torque is the lift multiplied by the distance from the blade axis to the local aerodynamic center). Therefore, the XAC value of the aerodynamic center needs to be transformed to the local coordinates, as shown in Figure 4 as shown, that is, EAC in the local coordinates = XAC / cos(leading and trailing sweep angle), and then through the force transformation matrix [T SBMultiply by cos(front and rear sweep angles), and then return to the moment of lift about the blade axis.

[0058] 7) Establishment of the aircraft body motion model on the landing gear. Assume that the aircraft body is a rigid body. Considering the elastic constraint and damping provided by the landing gear to the aircraft body, its constraint stiffness and damping are assumed to be linear within a small range around the compression equilibrium position. If the amplitude is large, the linear assumption cannot be used, and the influence of nonlinear characteristics on the ground resonance stability needs to be considered. The aircraft body and landing gear model is shown in Figure 5 as follows.

[0059] Landing gears generally have different layouts and configurations, but they can all be transformed into a general column-type shock strut-wheel landing gear model. The wheel and the shock absorber are in series, acting as elastic damping on the fuselage. Simplify the shock absorber and the wheel into stiffness and damping components. The displacement and velocity of the aircraft body movement cause the deformation movement of the landing gear, resulting in elastic and damping constraint forces on the landing gear, which act on the aircraft body. The acceleration of the aircraft body leads to inertial forces acting on the aircraft body. The heading and lateral movements of the landing gear are only constrained by the elastic and damping force loads of the wheels, and the vertical movement of the landing gear is jointly affected by the elastic and damping force loads of the wheels and the shock absorber. The loads of the wheels and the shock absorber in the vertical direction are in series, and the inertial loads of the shock absorber and the wheels are not considered. According to D'Alembert's principle, the inertial forces of the aircraft body and the loads acting on the aircraft body by the landing gear are in equilibrium, and based on this, the motion equation of the aircraft body on the landing gear is established in matrix form, where {X} = {X, Y, Z, φ x , φ y , φ z}T is a vector with 6 elements, and [M f , [K f , [C f are the linear matrices of the mass, stiffness, and damping of the aircraft body without the rotor.

[0060] Generally, consider the 6 rigid body motion degrees of freedom at the center of gravity of the aircraft body: heading displacement X, lateral displacement Y, vertical displacement Z, roll Φ X , pitch Φ Y and yaw motion Φ Z . Calculate the vibration characteristics of the aircraft body on the landing gear by the aircraft body calculation model, such as modal parameters: modal mass, damping, stiffness, and vibration mode. According to the vibration mode, the vibration modal parameters of the aircraft body can be transformed into effective quantities (effective mass, effective damping, and effective stiffness) at the hub center, or the spatial aircraft body dynamics model can be transformed into a planar dynamics model to make it consistent with the commonly used hub center dynamic characteristic test model.

[0061] 8) Establishment of a comprehensive analysis model for the coupled modes of a rotor with a complex three-dimensional shape and the airframe. To consider the structural characteristics of the rotor system, as well as the flapping, lagging, and torsional motions of the blades and their various couplings, a comprehensive dynamic model for the coupled stability of a rotor with a complex three-dimensional shape and the airframe is established, which can accurately consider the effects of design parameters such as blade elastic deformation and blade tip configuration on stability.

[0062] When establishing the comprehensive analysis model for the modal coupling of the rotor and the airframe, first, consider the blade as a residual structure and the hub nodes at the connection interface as residual nodes, and establish a dynamic coupling analysis model that combines the modal space and the physical space. This model facilitates the derivation of the coupled dynamic equations of the rotor / airframe system. On this basis, discretize the partial differential equations of blade dynamics using the finite element method, calculate the vibration characteristics of the isolated blade, select N P blade modes, and then transform the blade motion into the blade modal space. The nodal displacements of the hub are represented by the modal coordinates {X FP}, and the comprehensive analysis model for the modal coupling of the rotor and the airframe is obtained.

[0063] Step 3: Derivation of the coupled dynamic equations for a rotor with a complex three-dimensional shape and the airframe.

[0064] The coupled dynamic equations of the rotor / airframe system are derived from Hamilton's principle. According to the dynamic models of the airframe, rotor blades, and aerodynamic forces, the airframe is regarded as a substructure of the coupled dynamic system. Its kinetic energy, potential energy, and virtual work of external loads are described in the modal space, and their generalized coordinates are the vibration modal coordinates of the airframe. The motion of the hub at the connection interface between the rotor and the airframe and the motion of the rotor blades are described in the physical space. The kinetic energy, potential energy, and virtual work of the external loads of the rotor blades are represented by the hub motion [X H Y H Z H φ XH φ YH φ ZH and the blade motion u v wφ. The motion of the hub is the transport motion of the rotor blades, and it has six degrees of freedom of motion. Since the number of modal coordinates used to transform these six physical coordinates into the modal space of the airframe is more than six, physical coordinates are used in the derivation of the dynamic coupling equations. After establishing the dynamic equations, the hub motion [X H Y H Z H φ XH φ YH φ ZH is transformed into the modal space. The vibration modal damping force of the airframe and the structural damping and artificial damping of the rotor blades, etc., are regarded as non-ideal constraint forces and classified as external forces, and their virtual work is also classified as the virtual work of external loads together.

[0065] The variational equation of Hamilton's principle for the coupled dynamic system of the rotor / airframe is:

[0066]

[0067] In the formula, U is the strain energy of the coupling system established based on the strain-displacement field; T is the kinetic energy of the coupling system established according to the motion field; W is the external force work acting on the coupling system, including aerodynamic external forces and other constraint external forces.

[0068] a) Describe the strain-displacement relationship of the blade deformation. Using Hooke's law of strain and stress, obtain the strain potential energy of a single blade, and then sum over the total number of blades of the rotor to obtain the total potential energy of the rotor deformation.

[0069]

[0070] Analyze the motion velocity of a point in an arbitrary airfoil section along the spanwise direction of the blade. According to the kinetic energy formula, deduce the kinetic energy and kinetic energy variation of a single blade, and sum over the total number of blades of the rotor to obtain the total kinetic energy of the rotor.

[0071]

[0072] In the formula, is the motion velocity of a point in an arbitrary airfoil section along the spanwise direction of the blade. of the blade.

[0073] The kinetic energy and potential energy of the blade tip section are also derived in the same way as the above formula. First, through the deformation displacement of a point on any section of the blade tip section, deduce the motion velocity of this point, and then obtain the expressions of strain potential energy and kinetic energy, and add them to the above potential energy and kinetic energy formulas.

[0074] 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. Load the aerodynamic force onto the blade section, multiply it by the corresponding virtual displacement, and then the virtual work of the aerodynamic force of the section can be obtained. Then integrate over the blade to obtain the virtual work of the aerodynamic force of a single blade.

[0075] The quasi-steady aerodynamic force model of the blade adopts the lifting line theory. The acting point of the aerodynamic force is at the quarter-chord length. Calculate the aerodynamic load on the airfoil with the airflow velocity at three-quarters of the chord length. Assume that the induced flow velocity v i of the rotor is evenly distributed, as shown in Figure 6 . Through the aerodynamic force elements L, D, M ac , project them into the airfoil section coordinate system of the blade to obtain the aerodynamic forces T, S, M φa acting on the airfoil section.

[0076] In the aerodynamic force calculation, the inflow distribution of the rotor needs to be obtained first. The commonly used inflow models include the uniform inflow model, Deer's linear inflow model, and dynamic inflow model.

[0077] 1) Uniform inflow model

[0078]

[0079] Among them, \(m\) is the advance ratio, and \(a\) s is the forward tilt angle of the rotor shaft, and \(C\) T is the rotor thrust coefficient.

[0080] 2) Deers inflow model

[0081]

[0082] Among them, \(\psi\) 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 force model that relates the rotor aerodynamic loads (thrust, roll, and pitch aerodynamic moments) to the transient changes in the rotor induced velocity. The induced velocity, which is assumed to be non-uniformly distributed along the blade disk, is a function of the blade spanwise position and the azimuth angle, and can well reflect the physical essence of the rotor inflow. This model can be applied to the aerodynamic elastic stability and response of helicopters. Its first-order harmonic dynamic inflow model represents the linear first-order harmonic distribution of the induced velocity of the rotor wake at the blade disk in the following form:

[0085]

[0086] In the above formula, is the dimensionless induced velocity, \(v\) ie , \(v\) ic , \(v\) is is determined by the following dynamic equations:

[0087]

[0088] In the above formula,

[0089]

[0090] 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 functions of the induced velocity itself. With the dynamic aerodynamic characteristic coefficients of the airfoil, similar to Figure 6 , the aerodynamic loads on any airfoil section of the blade can be obtained. Project the blade aerodynamic force onto the coordinate system , left-multiply the virtual displacement array of the blade, and integrate along the blade span to obtain the virtual work done by the aerodynamic force of one blade on the motion of the blade.

[0091]

[0092] For the virtual work term of the aerodynamic force at the blade tip section, it is necessary to first derive the oncoming flow velocity of each section at the blade tip. The oncoming flow velocity of the blade tip section It is divided into three parts: the wind speed caused by forward flight and the inflow into the rotor disk The oncoming flow velocity generated by the movement at the blade tip is The oncoming flow velocity generated by the movement of the airframe The oncoming flow velocity generated by the movement at the blade tip It is caused by blade deformation and rotation about the rotor axis. After converting it to the coordinate system after blade tip deformation, the velocity of any section at the blade tip is obtained. Using the above method, the aerodynamic load of any section at the blade tip can be determined. After converting it to the coordinate system before blade tip deformation and substituting it into the above formula (18), the virtual work of aerodynamic force of the blade tip section can be obtained.

[0093] c) Derivation of the dynamic modal equation of the rotor blade

[0094] 1) Blade dynamic equation and space-time discretization

[0095] Substitute equations (8), (9) and (18) into the variational equation (7) to derive the blade dynamic equation. The finite element method is used to discretize the blade motion {X rs}, and the blade is divided into several beam elements (see Figure 7 ), and the nodal deformation displacement {q ie} k,i is used to describe the elastic vibration of the blade, and the nonlinear dynamic equation corresponding to all the nodal degrees of freedom of the blade is obtained, which can be expressed as:

[0096]

[0097] 2) Blade trimming

[0098] The trimming equation is: [K xrsxrs (q e )]{q e}+{F xrs0 (q e )}=0 (20)

[0099] The trimming displacements of each node in the blade equilibrium state are solved from equation (20), and let it be {q e0}

[0100] 3) Linearization of the blade dynamic equation

[0101] The displacements of each node of the blade are expressed as: {q e}={q e0}+{Δq e} (21)

[0102] Substitute equation (21) into equation (20) for linearization, retain the first-order term of Δ{q e}, and equation (19) can be linearized as:

[0103]

[0104] 4) Blade Modal Analysis and Modal Reduction

[0105] Calculate the natural frequencies and vibration modes of the blade in the undamped state of equation (22). Select N P low-order modes of the blade's flapping, pitching, and torsional couplings with the airframe through modal analysis for modal synthesis, that is, reduce the coupled equations of the dynamic system. Let the vibration mode matrix corresponding to these N P low-order modes be:

[0106] {Δq e} = [X MB {X bp} (23)

[0107] Substitute equation (23) into the linearized vibration differential equation (22), and pre-multiply by the transpose of the modal matrix [X MB to obtain the dynamic modal equation of the rotor blade.

[0108] d) According to the airframe dynamic model established above, use the NASTRAN analysis software to calculate the airframe vibration modal frequencies and vibration modes. Then, based on the analysis of the airframe vibration modes, select the airframe modes of interest for synthesis with the rotor modes installed on the airframe. Suppose a total of N f airframe modes are selected. Then, the kinetic energy of these modal vibrations can be expressed as:

[0109]

[0110] where M fp is the generalized mass of the N f airframe modes, and X fp is the generalized coordinate of these N f airframe modes. In the synthesis with the rotor blade vibration modes, they can be defined as super-node coordinate variables. According to the variational method, the variational formula of the kinetic energy of the airframe modal vibration is obtained:

[0111]

[0112] The potential energy of the first N f airframe modal vibrations is expressed as the product of the modal stiffness and the square of the generalized modal coordinate (i.e., the super-node coordinate variable):

[0113]

[0114] where K fp is the generalized stiffness of the N f airframe modes.

[0115] When the aircraft takes off and lands on the ground, the landing gear provides stiffness so that the frequencies of these six rigid body modes are not zero, and thus the potential energy is also not zero. Therefore, the six rigid body modes must be included. The variation of the potential energy is:

[0116]

[0117] The virtual work of the damping force of the airframe mode vibration includes the virtual work done by the structural damping force of the airframe and the damping force provided by the artificial damper (such as the damping provided by the landing gear), and can be expressed as:

[0118]

[0119] In the formula, C fpi is the damping coefficient matrix of the N f modes of the airframe.

[0120] e) According to the above-derived strain energy, kinetic energy, virtual work of aerodynamic force, and potential energy, kinetic energy, virtual work of damping force of the airframe, based on the Hamilton's principle formula, according to the variations {δX rs} T and {δX fp} T describing the motion variables of the rotor blade and the airframe, divide the energy equation into two parts: 1) the equation coupling the airframe motion and the rotor blade motion corresponding to the variation {δX fp}, and 2) the equation coupling the rotor blade motion and the airframe motion corresponding to the variation {δX T}. rs} T

[0121] Step 4: Ground resonance analysis method. When performing ground resonance analysis, based on the nonlinear dynamics model of the landing gear, generally the airframe adopts a spatial model (see Figure 5 ); based on the dynamic characteristic test data of the hub center, usually the airframe adopts a planar model, that is, the vibration characteristics of the airframe on the landing gear are represented by the modal parameters of the hub center in the rotation plane.

[0122] After the above linearization process and modal coordinate transformation, the obtained linear differential equation of the rotor / airframe modal coupling dynamics, using the multi-blade coordinate transformation, eliminates the periodic coefficients in the equation, and the finally obtained linear differential equation of the modal coupling dynamics can be expressed in the following form:

[0123]

[0124] Removing the damping matrix in equation (29), the natural frequencies and vibration modes of the rotor-airframe coupling can be calculated using the general eigenvalue calculation method.

[0125] The QR algorithm is used to calculate the complex eigenvalues and eigenvectors of Equation (29). By analyzing the positive and negative values of the real parts of all complex eigenvalues, the ground resonance stability of the dynamic coupling system is obtained. The real part of the eigenvalue represents the damping of the system, and the imaginary part represents the frequency of the system. The stability of the system is judged according to the real part of the eigenvalue of the retreating flap mode of the rotor: if the real part of the eigenvalue of the retreating flap mode is less than zero, the system is stable at this rotor speed; if the real part of the eigenvalue of the retreating flap mode is greater than zero, the system is unstable.

Claims

1. A method for modeling and analyzing the ground resonance of a helicopter with a forward and backward swept and upward and downward anti-twisted blade tip configuration, characterized in that: The method includes the following steps: 1) Establish the system coordinate system and the relationships between coordinate systems; 2) Establish the structural dynamics model of the rotor blade; 3) Establish the aerodynamic force model of the rotor blade; 4) Establish the dynamics and aerodynamic model of the blade tip section; 5) Establish the motion model of the airframe on the landing gear; 6) Establish the comprehensive model of the coupled modes of the complex three-dimensional shape rotor and the airframe, and derive the dynamic equation; 7) Establish the ground resonance analysis method.

2. The method according to claim 1, wherein: In step 1), the system coordinate system includes: inertial coordinate system, airframe coordinate system, hub coordinate system, blade rotation coordinate system, coordinate system before blade deformation, coordinate system after blade deformation, local coordinate system of blade tip deformation. The relationships between the coordinate systems are the coordinate transformation relationships between the coordinate systems.

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

4. The method according to claim 3, characterized in that: In step 3), the establishment of the aerodynamic force model of the rotor blade includes: since the blade tip of the blade adopts the forward and backward swept and up and down reversed configuration, it will cause sensitive changes in the aerodynamic characteristics of the blade, that is, it has a great impact on the aerodynamics, but has a small impact on the ground resonance stability. Therefore, in the aerodynamic force modeling of the ground resonance dynamics analysis, on the basis of adopting the quasi-steady aerodynamic force model, considering the non-uniform first-order dynamic inflow model can meet the requirements of the ground resonance stability analysis.

5. The method according to claim 4, wherein: In step 4), the establishment of the dynamics and aerodynamic model of the blade tip section includes: when establishing the structural dynamics model of the blade tip section, in the treatment, as long as the up and down reversed angle is added to the pre-cone angle at the starting position of the spanwise of the forward and backward swept and up and down reversed angles of the blade, and for the forward and backward swept angles, they are considered in the local coordinate transformation matrix; when establishing the aerodynamic force model of the blade tip section, due to the change of the aerodynamic center position of the airfoil section caused by the forward and backward swept angles of the blade tip, the aerodynamic force of the section changes; the aerodynamic center position needs to be calculated according to the forward and backward swept angles of the blade tip, and the change of the aerodynamic torque is calculated by adjusting the aerodynamic center position; when dealing with the oncoming flow velocity of the blade, the forward and backward swept angles need to be considered in the transformation matrix. After the oncoming flow velocity is transformed to the local coordinate of the forward and backward swept section through this transformation matrix, and the aerodynamic force is calculated, then the force transformation matrix formed by this transformation matrix is left-multiplied by the aerodynamic force term to be transformed to the global coordinate.

6. The method according to claim 5, wherein: In step 5), the establishment of the motion model of the airframe on the landing gear: Assume that the airframe is a rigid body, consider that the landing gear provides elastic constraints and damping to the airframe, and simplify the buffer and the wheel as stiffness and damping components; the deformation motion of the landing gear is caused by the displacement and velocity of the airframe movement, so that the landing gear generates elastic and damping constraint forces acting on the airframe; according to D'Alembert's principle, the inertial force of the airframe and the load acting on the airframe by the landing gear are in a balanced state, and thus the motion equation of the airframe on the landing gear is established.

7. The method according to claim 6, characterized in that: In step 6), the comprehensive model of the coupled modes of the complex three-dimensional shape rotor and the airframe, and the derivation of the dynamic equations include: First, the coupled dynamic equations of the rotor / airframe system are derived using Hamilton's principle; according to the dynamic models of the airframe, rotor blades and aerodynamic force models, the airframe is regarded as a sub-structure of the coupled dynamic system, and its kinetic energy, potential energy and virtual work of the external load are described in the modal space, and their generalized coordinates are the vibration modal coordinates of the airframe; Second, regarding the blade as a residual structure, a hybrid dynamic coupling analysis model of the modal space and the physical space is established, the partial differential equations of blade dynamics are discretized by the finite element method, the vibration characteristics of the isolated blade are calculated, N P blade modes are selected, and then the blade motion is transformed into the blade modal space to obtain the comprehensive analysis model of the rotor and airframe modal coupling.

8. The method according to claim 7, wherein: In step 7), the ground resonance analysis method includes: based on the nonlinear dynamics model of the landing gear, generally the airframe adopts a spatial model; based on the dynamic characteristic test data of the hub center, usually the airframe adopts a plane model, that is, the vibration characteristics of the airframe on the landing gear are represented by the modal parameters of the hub center in the rotation plane; for the above-mentioned coupled modal dynamics linear differential equation of the rotor / airframe, the multi-blade coordinate transformation is adopted to eliminate the periodic coefficients in the equation, and the QR algorithm of eigenvalues is used to calculate the complex eigenvalues and eigenvectors of the coupled modal equation. By analyzing the positive and negative values of the real parts of all the complex eigenvalues, the ground resonance stability of the dynamic coupling system is judged.

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