Helicopter ship surface resonance modeling and analysis method with front-back sweep and up-down reverse blade tip configuration

Abstract

The invention provides a ship surface resonance modeling and analysis method for a front-back sweep 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 single undercarriage motion model; establishing a motion model of the airframe on the ship surface; establishing a complex three-dimensional shape rotor wing / aircraft body / ship surface coupling kinetic model, and deducing a kinetic equation; and establishing a ship surface resonance analysis method.

Description

Technical Field

[0001] The present application belongs to the field of helicopter technology, and specifically relates to a method for modeling and analyzing deck 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 helicopter rotor performance by changing the blade tip shape.

[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 experience significant changes in the rotor flow field near the 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 deck resonance stability of shipborne helicopters. Research on deck resonance analysis methods for rotor blades with complex three-dimensional blade tips can provide an important basis for the optimized design and application of complex three-dimensional blade tip shapes for shipborne helicopters, ensuring that blade tips with excellent aerodynamic performance will not cause helicopter deck resonance instability.

[0005] Changing the blade tip shape simultaneously alters the coupling between blade bending and torsional motions. This influence on the deck resonance of shipborne helicopters is reflected in a shift in the unstable region of rotor speed and a change in rotor flap modal damping. Currently, no research has been found on the effects of blade sweep or anhedral angles on deck resonance stability. To fully understand the influence of blade tip shape (swept, anhedral) on the dynamic stability of deck resonance, a more sophisticated blade aeroelastic model is needed.

[0006] This technology is based on the urgent need to understand the mechanism of the resonant dynamic stability of the deck of helicopter rotors with complex three-dimensional blade tip configurations. It aims to solve the problem of the possible adverse effects of the forward-swept, backward-swept, up-and-down reverse blade tips on the resonant stability of the helicopter deck, and breaks through the modeling and analysis technology of the resonant dynamics of the deck of helicopter rotors with forward-swept, backward-swept, up-and-down reverse blade tips. It provides technical support for the design analysis and safe flight of modern advanced ship-borne helicopters modified with complex three-dimensional rotors. Summary of the Invention

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

[0008] The present application provides a method for modeling and analyzing deck 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 blade tip section dynamics and aerodynamic model;

[0013] 5) Establish a single landing gear motion model;

[0014] 6) Establish a model of the aircraft's motion on the ship's surface;

[0015] 7) Establish a complex three-dimensional rotor / airframe / ship deck coupled dynamics model and derive the dynamic equations;

[0016] 8) Establish a ship deck 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 CThe blade deformation is geometrically nonlinear, accounting for the deformation of the elastic axis at any spanwise section r. The deformation of the blade along the elastic axis 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.

[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 when the ship surface resonates, especially in gusts and sudden winds. Therefore, when modeling the aerodynamics of the ship surface resonance dynamics analysis, the unsteady aerodynamic model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the rotor / airframe / ship coupled 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 single landing gear motion model is established: when a helicopter takes off and lands on a ship deck, the ship will move up and down, sway left and right, and sway back and forth, and the ship will generate a vertical force on the landing gear, the action point being the landing point of the landing gear wheel on the ship deck; in the free mooring state, the load P exerted by the ship on the landing gear is a time function variable. The load F exerted by the aircraft body on the single landing gear is: Z and buffer axial force F S Balance, while the buffer axial force F S And the vertical stiffness damping force F of the wheel T The ship's motion affects the landing gear by directly considering the motion relationship between the ship and the landing gear. According to the d'Alembert principle, the forces acting on the wheels by the fuselage and the buffer are balanced with the inertial force, and the vertical motion equations of each landing gear wheel are established.

[0022] Preferably, in step 6), the motion model of the aircraft on the ship deck is established by considering the six degrees of freedom of the aircraft and performing force analysis on the aircraft, including the inertial force of the aircraft, the restraint force generated by the landing gear system, and the force exerted by the ship on the aircraft; and establishing the motion equation of the aircraft on the ship deck according to the D'Alembert principle. Before takeoff and landing on the ship deck, when the helicopter is moored with a harpoon, the harpoon exerts constraints on the vertical, roll, and pitch motions of the helicopter. Therefore, the harpoon constraint needs to be added to the vertical, roll, and pitch motion equations of the helicopter, and the motion equations of the helicopter on the ship deck for two landing modes: free landing on the ship deck and harpoon moored landing on the ship deck are established.

[0023] Preferably, in step 7), the complex three-dimensional rotor / airframe / ship deck coupled dynamic model and the derivation of the dynamic equations include: deriving the rotor / airframe / ship deck coupled system dynamic equations based on Hamilton's principle; based on the airframe, rotor blade dynamic model and aerodynamic model and ship motion, the airframe is used as a substructure of the coupled dynamic system, and its kinetic energy, potential energy and external load virtual work are described in the modal space, and the impact of the ship in free landing and harpoon mooring states on the airframe is considered in the airframe and ship deck motion model; the kinetic energy, potential energy and external load virtual work of the rotor blades are represented by hub motion and blade motion, and after establishing the dynamic equations using physical coordinates, after time and space discretization, blade balancing and linearization processing, blade modal analysis and modal contraction, the blade dynamic modal equations are obtained, which are coupled with the airframe modal equations to finally obtain the rotor / airframe / ship deck coupled dynamic linear differential equations.

[0024] Preferably, in step 8), the deck resonance analysis method includes: based on the nonlinear dynamic model of the landing gear and the ship motion, a space model is generally adopted for the airframe; based on the dynamic characteristics test data of the hub center on the deck, a plane model is usually adopted for the airframe, that is, the vibration characteristics of the airframe on the deck are represented by the modal parameters of the hub center in the rotating plane; for the above-mentioned rotor / airframe / deck coupled dynamic linear differential equation, a multi-blade coordinate transformation is adopted to eliminate the periodic coefficient in the equation, and the eigenvalue QR algorithm is adopted to calculate the complex eigenvalues ​​and eigenvectors of the coupling equation, and the deck resonance stability of the dynamic coupling system is obtained by analyzing the positive and negative values ​​of the real part of all complex eigenvalues.

[0025] This application has the following technical effects:

[0026] The present invention provides a deck resonance modeling and analysis method for a rotor helicopter with a forward-and-backward swept, up-and-down reverse blade tip configuration. The model takes into account the influence of the forward-and-backward swept, up-and-down reverse blade tip configuration of the blades. The deck resonance dynamics model and analysis method can be used for deck resonance stability analysis, resonance speed zone and stability damping margin calculation of all advanced ship-borne helicopters (especially modern ship-borne helicopters with complex three-dimensional rotor shapes), providing key technical support for the design and development of new ship-borne helicopter 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 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 The present invention relates to the positional relationship between the global coordinates and the local coordinates of the aerodynamic center of the blade tip section;

[0032] Figure 6 The present invention relates to a vertical force balance of a strut-type landing gear;

[0033] Figure 7 This is a schematic diagram of the movement of a single landing gear wheel involved in the present invention;

[0034] Figure 8 This is the force model of the aircraft body on the ship surface involved in the present invention;

[0035] Figure 9 are the coordinates of the harpoon involved in the present invention;

[0036] Figure 10 This is a blade beam unit model involved in the present invention;

[0037] Figure 11 It is a schematic diagram of the time finite element method involved in the present invention. DETAILED DESCRIPTION

[0038] The present application provides a method for modeling and analyzing the deck resonance of a helicopter rotor with a forward-and-backward swept up-and-down reversed blade tip configuration. The method belongs to the category of helicopter dynamics design technology and involves a method for modeling and analyzing the dynamics of the whole-machine coupled system. The method is applicable to the deck resonance dynamics modeling and stability analysis of conventional helicopter rotors and helicopter rotors 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 configuration rotor, the coupled dynamics model considers the influence of the three-dimensional configuration of the blade tip on the deck resonance stability. The rotor, airframe, and ship dynamics systems are modeled separately using the principles of mechanics. The motion of the rotor blades, blade tips, airframe, landing gear, and ship is described separately in the established multi-coordinate system, and a structural dynamics model of the isolated rotor blades and airframe is established. The aerodynamics model is modeled by considering the unsteady aerodynamic model, the dynamic inflow model, and the ONERA model based on the quasi-steady aerodynamic model. The motion model of the airframe on the deck is established based on the D'Alembert principle. The dynamics equations of the rotor / airframe / deck coupled system are derived using the Hamilton principle. Through space-time discretization, blade balancing, linearization, and modal analysis of the blade dynamics equations, the rotor / airframe / deck modal coupling dynamics equations are reduced using a limited number of low-order blade modal coordinates. After eliminating the periodic coefficients in the equations using multi-blade coordinate transformation, the complex eigenvalues ​​and eigenvectors are calculated using the eigenvalue QR method to analyze the deck resonant stability. This model and analysis method can be used to analyze the deck resonant stability, resonant speed range, and stability damping margin of all advanced shipborne helicopters (especially modern rotorcraft with complex three-dimensional shapes), providing key technical support for the design and development of new models and model upgrades.

[0039] The technical solution of this invention is to model the rotor, airframe, and ship dynamics systems separately using mechanical principles. The motion of the rotor blades, blade tips, airframe, landing gear, and ship is described in the established multi-coordinate system, establishing a structural dynamics model of the isolated rotor blades and airframe. 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 motion model of the airframe on the deck is established based on the d'Alembert principle. The dynamic equations of the rotor / airframe / deck coupled system are derived using the Hamiltonian principle. Through spatiotemporal discretization of the blade dynamic equations, blade balancing, linearization, and modal analysis, the rotor / airframe / deck modal coupling dynamic equations are reduced using finite low-order blade modal coordinates. Multi-blade coordinate transformation is used to eliminate periodic coefficients in the equations. The complex eigenvalues ​​and eigenvectors are calculated using the eigenvalue QR method to analyze the deck resonance stability.

[0040] This application provides a method for modeling and analyzing deck resonance of a forward-and-backward swept rotor helicopter with an up-and-down reversed blade tip configuration, including:

[0041] (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.

[0042] (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.

[0043] (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 great influence on the ship surface resonance, especially in gusts and sudden winds. Therefore, when modeling the aerodynamics of the ship surface resonance dynamics analysis, the unsteady aerodynamic model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic model. The comprehensive application of these three models can more accurately calculate the aerodynamic loads in the rotor / airframe / ship coupled stability analysis.

[0044] (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.

[0045] (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.

[0046] (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.

[0047] (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.

[0048] (8) Load balance analysis of a single landing gear. When a helicopter takes off and lands on a ship's deck, the ship will move up and down, sway left and right, and sway back and forth. The ship will exert a force on the landing gear, and the point of action is the landing point of the landing gear wheel on the ship. In the free mooring state, the load P exerted on the landing gear by the ship is a time function variable. The load F exerted on a single landing gear by the aircraft body is Z and buffer axial force F S Balance, while the buffer axial force F S And the vertical stiffness damping force F of the wheel T The ship's motion affects the landing gear by directly considering the kinematic relationship between the ship and the landing gear. Based on the d'Alembert principle, the forces acting on the wheels from the aircraft body and the buffer are balanced by the inertial forces, establishing the vertical motion equations for each landing gear wheel.

[0049] (9) The motion model of the aircraft on the ship's surface. Considering the six degrees of freedom of the aircraft's motion, the force analysis of the aircraft's motion is carried out, including the inertial force, the constraint force generated by the landing gear system, and the force exerted by the ship on the aircraft. Based on the D'Alembert principle, the motion equation of the aircraft on the ship's surface is established. Before takeoff and landing on the ship deck, when the helicopter is moored with a harpoon, the harpoon exerts constraints on the vertical, roll, and pitch motions of the helicopter. Therefore, the harpoon constraint needs to be added to the vertical, roll, and pitch motion equations of the helicopter, and the motion equations of the helicopter on the ship deck for two landing modes: free landing on the ship deck and harpoon moored landing on the ship deck are established.

[0050] (10) Complex three-dimensional rotor / airframe / ship deck coupled dynamic model.

[0051] When establishing the rotor / airframe / ship deck coupled dynamic model, the blade is first treated as a residual structure, the interface hub node is treated as a residual node, and a dynamic coupling analysis model that mixes modal space and physical space is established. This model facilitates the derivation of the rotor / airframe / ship deck coupled system dynamic equations. On this basis, the finite element method is used to discretize the blade dynamic partial differential equations, calculate the vibration characteristics of the isolated blade, and select N P The blade mode is transformed into the blade modal space, and the hub node displacement is expressed in modal coordinates {X FP} indicates that the rotor / airframe / ship deck modal coupling comprehensive analysis model is obtained.

[0052] (11) Derivation of the coupled dynamic equations of rotor / airframe / ship deck with complex three-dimensional shape. The dynamic equations of the coupled rotor / airframe / ship deck system are derived based on Hamilton's principle. Based on the dynamic model of the airframe, rotor blades, aerodynamic model and ship motion, the airframe is used as a substructure of the coupled dynamic system. Its kinetic energy, potential energy and external load virtual work are described in the modal space. The impact of the ship in free landing and harpoon mooring states on the airframe is considered in the airframe and ship deck motion model. The kinetic energy, potential energy and external load virtual work of the rotor blades are represented by the hub motion and blade motion. After the dynamic equations are established using physical coordinates, the hub motion is converted to the modal space. The damping force of the airframe vibration modal, the rotor blade structural damping, artificial damping, etc. are regarded as non-ideal constraint forces and are classified as external forces. The virtual work they do is also classified as the external load virtual work. After establishing the blade dynamic equation and discretizing it in time and space, the blade dynamic modal equation is obtained through blade balancing and linearization, blade modal analysis and modal reduction. It is coupled with the airframe modal equation to finally obtain the rotor / airframe / ship deck coupled dynamic linear differential equation.

[0053] (12) Ship deck resonance analysis method. Based on the nonlinear dynamic model of the landing gear and the ship motion, the airframe generally adopts a spatial model; based on the dynamic characteristics test data of the hub center on the ship deck (or shaking platform), the airframe usually adopts a planar model, that is, the vibration characteristics of the airframe on the ship deck are expressed by the modal parameters of the hub center in the rotating plane.

[0054] For the above-mentioned rotor / airframe / ship deck coupled dynamic linear differential equation, multi-blade coordinate transformation is used to eliminate the periodic coefficient in the equation, and the eigenvalue QR algorithm is used to calculate the complex eigenvalues ​​and eigenvectors of the coupling equation. By analyzing the positive and negative values ​​of the real part of all complex eigenvalues, the ship deck resonance stability of the dynamic coupling system is obtained.

[0055] See also Figures 1-11 , the modeling and analysis method of the deck resonance 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.

[0056] 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 fThe 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 ,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}, 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:

[0057]

[0058] Step 2: Establishment of analysis model.

[0059] 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.

[0060] 2) Establishment of the aerodynamic model of the rotor blades. Since 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 great impact on the ship surface resonance, especially in gusts and sudden winds. Therefore, when modeling the aerodynamics of the ship surface resonance dynamics analysis, 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 combined application of these three models can more accurately calculate the aerodynamic loads in the ,rotor / airframe / ship coupled stability analysis.

[0061] 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.

[0062] 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 3 It 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.

[0063] 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.

[0064] 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.

[0065] 7) Establishment of landing gear motion model. When a helicopter takes off and lands on a ship's deck, the ship will move up and down, sway left and right, and sway back and forth. The ship will generate a vertical force on the landing gear, and the action point is the landing point of the landing gear wheels on the ship's deck. Figure 6 The force acting on the ship's surface should be balanced with the force acting on it by the aircraft body and the buffer. The effect of the ship's movement on the landing gear is directly reflected in the movement (load) relationship between the ship and the landing gear, see Figure 7 According to the D'Alembert principle, the forces acting on the wheels from the aircraft body and the buffer are balanced with the inertial force, and a vertical motion model of each landing gear wheel is established.

[0066] 7) Load balance analysis of a single landing gear. When a helicopter takes off and lands on a ship's deck, the ship will move up and down, sway left and right, and rock back and forth. The ship will exert a force on the landing gear, and the point of action is the landing point of the landing gear wheels on the ship's deck. The vertical motion of the ship at the landing point can be expressed as Z J =Z J0 sinω J t, Z J0 is the landing point sinking amplitude, ω J is the ship's sinking and floating frequency. Similarly, the ship's heading and lateral motion are expressed as: X J =X J0 sinω J t and Y J =Y J0 sinω J t.

[0067] Vertical force analysis of landing gear in free-tethered state, see Figure 6 , Figure 6 The middle landing gear is subjected to the load P from the ship. The load P N 、 It is a time function variable. The load F exerted by the aircraft on a single landing gear is Z and buffer axial force F S Balance, while the buffer axial force F S And the vertical stiffness damping force F of the wheel T The influence of the ship's motion on the landing gear is directly considered by considering the motion relationship between the ship and the landing gear. Figure 7 . Figure 7 Middle Z J Indicates the movement of the ship, Z T represents the movement of the wheels (each wheel is independent), F S is the force exerted by the buffer on the wheel, M T is the wheel mass, K and C are the vertical stiffness and damping of the wheel. The wheel motion equation is, During the balance calculation, the motion Z at the three landing points JThey are different, Z J It can be expressed as: Z J =Z J0 sinω J t, Z J0 is the initial amplitude of the landing point sinking and floating, ω J is the ship's heaving and surfacing frequency. Based on the d'Alembert principle, the forces acting on the wheels from the aircraft body and the buffer are balanced by the inertial force, and the vertical motion equations of each landing gear wheel are established.

[0068] 8) Establishment of the aircraft's motion model on the ship's deck. Considering the six degrees of freedom of the aircraft's motion, Figure 8 It is the body motion model, which performs force analysis on the body and establishes the body motion equation. Figure 8 The inertial force of the aircraft, the restraint force generated by the landing gear system, and the force exerted by the ship on the aircraft are shown in Figure 2. Based on the d'Alembert principle, the motion equation of the aircraft on the ship is established.

[0069] For situations where a helicopter is not free-landing, that is, before takeoff and landing on the ship's deck, a mooring device is used. The harpoon is currently the most commonly used device, and other devices can be simplified by modeling to represent this type. The harpoon is a hydraulically controlled axial two-force rod. When the harpoon hooks onto the ship's deck grille, the hydraulic system immediately contracts, pulling the helicopter downward and compressing the landing gear. This prevents the wheels from leaving the deck and potentially tipping over, regardless of the ship's turbulence. When moored with the harpoon, the landing gear is subjected to a constant high load, regardless of lift force, essentially maintaining a fixed operating compression state. This ensures that the helicopter's stability characteristics on the ship's deck remain essentially unchanged, effectively controlling the occurrence of deck resonance.

[0070] Figure 9 are the coordinates of the harpoon device, and the connection points between the harpoon device and the fuselage are points A, B and C. For the harpoon landing state, when the harpoon is locked, that is, when the servo valve is closed, the harpoon rod provides a vertical constraint (downward direction) on the movement of the fuselage. The stiffness of this constraint is relatively high and needs to be considered in the model. Assuming that the axial stiffness of the harpoon rod is Kyu, the X and Y distances from its point of action to the center of gravity of the fuselage are Xyu and Yyu (=0) respectively. From this, the distances to the landing points of each wheel are calculated. The X and Y distances from the harpoon's point of action to the center of gravity of the fuselage are used to calculate the constraint force provided by the harpoon when the body moves; and the distance from the harpoon's point of action to the wheel landing point is used to calculate the static load applied by the harpoon to each wheel, which is used for the balance calculation of the entire machine. The harpoon constraint force on the body movement is: F yu =K yu (Z G +φ X Y yu -φ Y X yu), the harpoon imposes constraints on the vertical, roll, and pitch motions of the aircraft. Therefore, the following terms need to be added to the vertical, roll, and pitch motion equations of the aircraft:

[0071] In the vertical equation of the fuselage: K yu (Z G +φ X Y yu -φ Y X yu )

[0072] In the body roll equation: K yu (Z G +φ X Y yu -φ Y X yu )Y yu

[0073] In the body pitch equation: -K yu (Z G +φ X Y yu -φ Y X yu )X yu

[0074] The above establishes the motion equations of the aircraft on the ship deck for two landing modes: free landing on the ship deck and harpoon-tethered landing.

[0075] 8) Establishment of a complex three-dimensional rotor / airframe / deck coupled dynamics model. To account for the rotor system's structural characteristics and blade flapping, shimmying, and torsional motions, as well as their various couplings, and the coupled motions of the ship and the airframe's landing gear, a complex three-dimensional rotor / airframe / deck coupled stability analysis dynamics model was established that accurately considers the effects of design parameters such as blade tip configuration, blade elastic deformation, landing gear deformation, and ship motion on stability.

[0076] When establishing the rotor / airframe / ship deck coupled dynamic model, the blade is first treated as a residual structure, and the interface hub node is used as a residual node to establish a dynamic coupling analysis model that mixes modal space and physical space. This model facilitates the derivation of the rotor / airframe / ship deck coupled system dynamic equations. On this basis, the finite element method is used to discretize the blade dynamic partial differential equations, calculate the vibration characteristics of the isolated blade, and select N P The blade mode is transformed into the blade modal space, and the hub node displacement is expressed in modal coordinates {X FP} indicates that the rotor / airframe / ship deck modal coupling comprehensive analysis model is obtained.

[0077] Step 3: Derive the coupled dynamic equations of rotor / airframe / ship deck with complex three-dimensional shape.

[0078] The coupled dynamic equations of the rotor / airframe / deck system are derived from Hamilton's principle. Based on the dynamic and aerodynamic models of the airframe, rotor blades, and ship motion, the airframe is used as a substructure of the coupled dynamic system. Its kinetic energy, potential energy, and external load virtual work are described in modal space. Their generalized coordinates are the airframe vibration modal coordinates. The effects of the ship in free landing and harpoon mooring states on the airframe are considered in the airframe and deck motion model. 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. The kinetic energy, potential energy, and external load virtual work of the rotor blades are described 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 the associated motion of the rotor blades, which has 6 degrees of freedom. Since the number of modal coordinates used to convert these 6 physical coordinates into the body modal space will be more than 6, the physical coordinates are used in the derivation of the dynamic coupled motion equation. After the dynamic equation is established, the hub motion [X H Y H Z H φ XH φ YH φ ZH ] is converted to modal space. The airframe vibration modal damping force, rotor blade structural damping, artificial damping, etc. are classified as external forces as non-ideal constraints, and the virtual work they do is also classified as external load virtual work.

[0079] The variational equation of the Hamilton principle for the rotor / airframe / deck coupled dynamic system is:

[0080]

[0081] 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.

[0082] 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.

[0083]

[0084] 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.

[0085]

[0086] Where, The span direction of the blade upper edge The velocity of a point within any airfoil section.

[0087] 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.

[0088] 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.

[0089] 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 .

[0090] 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.

[0091] 1) Uniform inflow model

[0092]

[0093] Among them, m is the forward ratio, a s is the rotor shaft tilt angle, C T is the rotor thrust coefficient.

[0094] 2) Deers inflow model

[0095] λ=μtanα s +λ i

[0096]

[0097] k y =-2μ (11)

[0098] where ψ is the azimuth angle of the rotor blade.

[0099] 3) Dynamic inflow model

[0100] 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:

[0101]

[0102] In the above formula, is the dimensionless induced velocity, v ie , v ic , v is Determined by the following kinetic equation:

[0103]

[0104] In the above formula,

[0105]

[0106] 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.

[0107] 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.

[0108] The airfoil lift differential equation established using the ONERA model is:

[0109]

[0110] The differential equation of airfoil aerodynamic drag is:

[0111]

[0112] The differential equation of the airfoil aerodynamic moment is:

[0113]

[0114] Where,

[0115]

[0116] ΔCL , 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.

[0117]

[0118] 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).

[0119] c) Derivation of rotor blade dynamic modal equations.

[0120] 1) Blade dynamic equations and time-space discretization

[0121] Substituting equations (8), (9) and (22) into variational equation (7) yields the blade dynamic equation. The finite element method is used to calculate the blade motion {X rs} to discretize and divide the blade into several beam elements (see Figure 10), using the node deformation displacement of the beam element {q ie} k,i Describing the elastic vibration of the blade, the nonlinear dynamic equation corresponding to all the nodal degrees of freedom of the blade is obtained, which can be expressed as:

[0122]

[0123] Since the dynamic equation is a nonlinear equation group about generalized degrees of freedom and time, similar to the spatial finite element method, the time finite element method is used to divide a rotor rotation period into N e time units, each unit contains n nodes (the number of nodes depends on the order of the unit shape function) (see Figure 11 ). After time discretization, the blade energy equation is simplified to the following form:

[0124]

[0125] 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. Using the boundary condition y(2π)=y(0) of the periodic system, the steady-state periodic solution of the blade is obtained.

[0126] 2) Blade balancing

[0127] The balancing equation is: [K xrsxrs (q e )]{q e}+{F xrs0 (q e )}=0 (25)

[0128] The trim displacement of each node in the blade equilibrium state is solved by equation (25) and is set as {qe0}.

[0129] 3) Linearization of blade dynamic equations

[0130] The displacement of each node of the blade is expressed as: {q e}={q e0}+{Δq e} (26)

[0131] Substitute (26) into equation (25) for linearization, and retain until Δ{q e}, equation (24) can be linearized as:

[0132]

[0133] 4) Blade modal analysis and modal reduction

[0134] Calculate the natural frequency and vibration mode of the blade in the undamped state in equation (27), and select N through modal analysis. P The blade flapping, shimmying and torsion coupling low-order modes are modally integrated with the body, that is, the dynamic system coupling equation is condensed. P The vibration matrix of the low-order mode is:

[0135] {Δq e}=[X MB ]{X bp} (28)

[0136] Substitute Equation (28) into the linearized vibration differential equation (27) and multiply it by the modal matrix [X MB ] is transposed to obtain the rotor blade dynamic modal equation.

[0137] d) Based on the above-established dynamic model of the airframe on the ship deck, the vibration modal frequencies and vibration modes of the airframe on the ship deck are calculated using NASTRAN analysis software. Then, based on the analysis of the airframe vibration modes, the airframe modal on the ship deck of interest is selected and integrated with the rotor modal mounted on the airframe. Assume that the total number of selected airframe modalities on the ship deck is N. f The kinetic energy of these modal vibrations can be expressed as:

[0138]

[0139] Where M fp Yes N f The generalized mass of the body mode, X fp It's this N f The generalized coordinates of the airframe modal can be defined as super-node coordinate variables in the synthesis with the rotor blade vibration mode. According to the variational method, the variational formula of the modal vibration kinetic energy of the airframe on the ship is obtained:

[0140]

[0141] N on the front of the fuselage on the ship f The potential energy of a modal vibration is expressed as the product of the modal stiffness and the square of the generalized modal coordinates (i.e., supernode coordinate variables):

[0142]

[0143] Where K fp Yes N f The generalized stiffness of the body mode.

[0144] When an aircraft takes off and lands on the ship, 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, so the six rigid body modes must be included. The potential energy variation is:

[0145]

[0146] The virtual work of the damping force of the airframe modal 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), which can be expressed as:

[0147]

[0148] Where C fpi It is the body N f The damping coefficient matrix of each mode.

[0149] e) Based on the above-derived rotor strain energy, kinetic energy, aerodynamic virtual work and the ship's body potential energy, kinetic energy, and damping force virtual work, according to the Hamilton principle formula, according to the variational formula {δX rs} T and {δX fp} T The energy equation is divided into two parts: 1) the strain equation {δX fp} T The equations for coupling the body motion with the rotor blade motion, and 2) the strain {δX rs} T The equations for coupling the rotor blade motion with the body motion.

[0150] Step 4: Ship deck resonance analysis method. When analyzing ship deck resonance, based on the nonlinear dynamic model of the landing gear and the ship motion, the general body adopts a spatial model (see Figure 8 ); Based on the dynamic characteristics test data of the hub center on the ship deck (or shaking platform), the airframe usually adopts a plane model, that is, the vibration characteristics of the airframe on the ship deck are expressed by the modal parameters of the hub center in the rotating plane.

[0151] After the above linearization and modal coordinate transformation, the rotor / airframe / ship deck coupled dynamic linear differential equation is obtained. By using multi-blade coordinate transformation to eliminate the periodic coefficient in the equation, the final coupled dynamic linear differential equation can be expressed as follows:

[0152]

[0153] The QR algorithm is used to calculate the complex eigenvalues ​​and eigenvectors of equation (34). By analyzing the positive and negative values ​​of the real part of all complex eigenvalues, the deck resonance stability of the dynamic coupling system is obtained. The real part of the eigenvalue represents the system damping, and the imaginary part represents the system frequency. The stability of the system is determined based on the real part of the eigenvalue of the rotor shimmy mode: if the real part of the eigenvalue of the shimmy mode is less than zero, the system is stable at that rotor speed. If the real part of the eigenvalue of the shimmy mode is greater than zero, the system is unstable.

Claims

1. A method for modeling and analyzing deck 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 a single landing gear motion model; 6) Establish a model of the aircraft's motion on the ship's surface; 7) Establish a complex three-dimensional rotor / airframe / ship deck coupled dynamics model and derive the dynamic equations; 8) Establish a ship deck 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 The blade deformation is geometrically nonlinear, accounting for the deformation of the elastic axis at any spanwise section r. The deformation of the blade along the elastic axis 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.

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 when the ship surface resonates, especially in gusts and sudden winds. Therefore, when modeling the aerodynamics of the ship surface resonance dynamics analysis, the unsteady aerodynamic model, the dynamic inflow model and the ONERA model are considered on the basis of the quasi-steady aerodynamic model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the rotor / airframe / ship coupled 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 motion model of a single landing gear is established: when a helicopter takes off and lands on a ship deck, the ship will move up and down, sway left and right, and sway back and forth. The ship will generate a vertical force on the landing gear, and the action point is the landing point of the landing gear wheel on the ship deck; in the free mooring state, the load P exerted by the ship on the landing gear is a time function variable. The load F exerted by the aircraft body on the single landing gear is Z and buffer axial force F S Balance, while the buffer axial force F S And the vertical stiffness damping force F of the wheel T The ship's motion affects the landing gear by directly considering the motion relationship between the ship and the landing gear. According to the d'Alembert principle, the forces acting on the wheels by the fuselage and the buffer are balanced with the inertial force, and the vertical motion equations of each landing gear wheel are established.

7. The method according to claim 6, characterized in that: In step 6), the motion model of the aircraft on the ship's deck is established by considering the six degrees of freedom of the aircraft's motion and performing force analysis on the aircraft's motion, including the inertial force, the restraint force generated by the landing gear system, and the force exerted by the ship on the aircraft's motion; and establishing the motion equation of the aircraft on the ship's deck based on the D'Alembert principle. Before takeoff and landing on the ship deck, when the helicopter is moored with a harpoon, the harpoon exerts constraints on the vertical, roll, and pitch motions of the helicopter. Therefore, the harpoon constraint needs to be added to the vertical, roll, and pitch motion equations of the helicopter, and the motion equations of the helicopter on the ship deck for two landing modes: free landing on the ship deck and harpoon moored landing on the ship deck are established.

8. The method according to claim 7, wherein: In step 7), the complex three-dimensional rotor / airframe / ship deck coupled dynamic model and the derivation of the dynamic equations include: deriving the rotor / airframe / ship deck coupled system dynamic equations based on the Hamilton principle; based on the airframe, rotor blade dynamic model and aerodynamic model and ship motion, the airframe is used as a substructure of the coupled dynamic system, and its kinetic energy, potential energy and external load virtual work are described in the modal space, and the impact of the ship in the free landing and harpoon mooring states on the airframe is considered in the airframe ship deck motion model; the kinetic energy, potential energy and external load virtual work of the rotor blades are represented by the hub motion and the blade motion, and after the dynamic equations are established using physical coordinates, after time and space discretization, the blades are balanced and linearized, and the blade modal analysis and modal reduction are performed to obtain the blade dynamic modal equations, which are coupled with the airframe modal equations to finally obtain the rotor / airframe / ship deck coupled dynamic linear differential equations.

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

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