Vibration response modeling and analysis method for front-back sweep and up-down reverse blade tip configuration helicopter

Abstract

The invention provides a vibration response 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 body structure dynamic model; establishing an airframe aerodynamic model; establishing a complex three-dimensional shape rotor wing and body coupling mode comprehensive model, and deducing a kinetic equation; discretizing finite elements of space coordinates of the blades in the kinetic equation; balancing analysis is carried out; solving vibration response by a time finite element method; and transient response analysis.

Description

Technical Field

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

[0002] The blade tip has always played an important role in improving the flight performance and maneuverability of helicopters. With the widespread application of various new materials in helicopter rotors, it has become possible to improve the performance of helicopter rotors by changing the blade tip shape. Advanced blade tip shape design has been a hot topic of research at home and abroad in recent years. Figure 12 The following figure shows advanced propeller tips, such as the BERP tip and the Blue Edge tip, all of which feature a swept tip. Aerodynamic research has shown that the swept tip significantly affects the air compressibility around the leading blade and the airflow separation stall characteristics of the trailing blade.

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

[0004] Compared to traditional rectangular rotors, rotor blades with complex three-dimensional blade tips exhibit significant changes in the 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, significantly impacting the helicopter's vibration response. Research on modeling and analysis methods for the vibration response of rotor helicopters with complex three-dimensional blade tips can provide an important basis for the optimal design of complex three-dimensional blade tip shapes, ensuring that a blade tip shape with excellent aerodynamic performance does not excessively affect the helicopter's vibration response, particularly the vibration response values ​​of certain components that have attracted considerable attention.

[0005] Changing the blade tip shape simultaneously alters the coupling between blade bending and torsional motions, affecting the rotor's aeroelastic properties and, consequently, the vibration response of the rotor-airframe coupling. Early studies often employed simple blade aeroelastic models, approximating the blade tip by modeling it with its center of gravity offset from the section's elastic axis. Tarzanin and Vlaminck systematically investigated the effects of blade tip sweep on hub loads, considering the coupling of blade flapping and torsional motion while ignoring the coupling of shimmy motion with other motions. They demonstrated that the effect of tip sweep on hub loads varies with flight speed and blade parameters (particularly blade section torsional stiffness). However, research on the effects of changing blade tip shape on the overall vibration response of the aircraft is limited. Therefore, to fully understand the influence of blade tip shape (forward and backward sweep, anhedral angle) on the overall vibration response of the aircraft, more sophisticated coupled system aeroelastic models and effective analytical methods are needed.

[0006] This technology is based on the urgent need to understand the influence mechanism of complex three-dimensional blade tip configuration on the vibration response of helicopters. Aiming at the problem of the possible adverse effects of the forward-swept, backward-swept, up-down and down-reversed blade tip configuration on the vibration response of the entire aircraft, it breaks through the dynamic modeling and analysis technology of the vibration response of forward-swept, backward-swept, up-down and down-reversed blade tip configuration rotor helicopters, providing technical support for the design and analysis of complex three-dimensional rotor modification of modern advanced helicopters. Summary of the Invention

[0007] Purpose of the invention: To propose a vibration response 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 vibration response analysis (both steady-state and transient) of modern advanced rotor systems and advanced helicopters with complex three-dimensional rotor shapes, and provide key technical support for model design and modification research and development.

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

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

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

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

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

[0013] 5) Establish the body structure dynamics model;

[0014] 6) Establish an aerodynamic model of the aircraft;

[0015] 7) Establish a comprehensive modal model of the coupling between the complex three-dimensional rotor and the fuselage, and derive the dynamic equations;

[0016] 8) Finite element discretization of blade space coordinates in dynamic equations;

[0017] 9) Trim analysis;

[0018] 10) Time finite element method to solve vibration response;

[0019] 11) Transient response analysis.

[0020] Preferably, in step 1), the system coordinate system includes: an inertial coordinate system, a body coordinate system, a hub non-rotating coordinate system, a hub rotating coordinate system, a blade flapping coordinate system, a blade swing coordinate system and a blade pitch change coordinate system, and the relationship between the coordinate systems is the coordinate transformation relationship between the coordinate systems.

[0021] Preferably, in step 2), the establishment of the rotor blade structural dynamic model includes: simplifying the straight section of the blade into a slender elastic beam, assuming that the blade elastic axis passes through the rotation center; the blade cross section has a pre-twist angle θ relative to the elastic axis along the span direction, and the blade has a pre-cone angle β relative to the rotating surface C , considering the geometric nonlinearity of blade deformation; the deformation of the elastic axis at any section r along the span direction of the blade includes four motions: axial displacement u, swing displacement v, flapping displacement w and torsional deformation φ, and their structural and inertial coupling; the connection between the blade root and the hub is simulated by boundary conditions and boundary elements, including its hinged support, fixed support or hinged support with spring constraints and multi-path force transmission relationships.

[0022] 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. Therefore, when modeling the aerodynamic force in the coupled system vibration response analysis model, the unsteady aerodynamic force model, the ONERA model and the dynamic inflow model are considered on the basis of the quasi-steady aerodynamic force model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the steady-state response, stability and transient response analysis.

[0023] 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.

[0024] Preferably, in step 5), the airframe structure dynamics model is established by adopting the finite element method to establish the airframe structure dynamics model, using the commercial software PATRAN to directly perform finite element mesh division on the designed airframe structure components, and selecting appropriate units from the unit library provided by NASTRAN software to simulate various types of structures according to the force and force transmission of the structural elements and components; using NASTRAN software to calculate the natural frequency and mode shape, and by analyzing the natural frequency and mode shape of the airframe structure, determining the airframe vibration mode, which must include 6 rigid body modes of the airframe.

[0025] Preferably, in step 6), the airframe aerodynamic model is established: the airframe aerodynamic model includes the aerodynamic forces of the fuselage, horizontal tail, vertical tail and tail rotor; the aerodynamic forces and moments of the fuselage are determined directly using the wind tunnel test results, which are functions of the fuselage angle of attack and sideslip angle; the tail includes the horizontal tail and vertical tail, and the aerodynamic force on the tail is replaced by a concentrated force, the point of action of which is at the aerodynamic center of the tail; for helicopters with a main rotor and a tail rotor, only the pull of the tail rotor is considered, and the pull or thrust is considered for balancing the entire aircraft.

[0026] Preferably, in step 7), the complex three-dimensional rotor and body coupling modal integrated model and the derivation of the dynamic equations include: first, using the Hamilton principle to derive the rotor / body system coupling dynamic equations; according to the body, rotor blade dynamics model and aerodynamic model, the body 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 their generalized coordinates are the body vibration modal coordinates; secondly, the blade is used as a residual structure, and a hybrid dynamic coupling analysis model of the modal space and physical space is established, the blade dynamics partial differential equation is discretized using the finite element method, the vibration characteristics of the isolated blade are calculated, and N is selected. P The blade modes are then transformed into the blade modal space to obtain a comprehensive analysis model of rotor and body modal coupling.

[0027] Preferably, in step 8), the finite element discretization of the blade spatial coordinates in the dynamic equation includes: the motion of the blade is a binary function of the spatial coordinates and time; in order to remove spatial correlation, the finite element method is used to discretize the blade motion, the blade is divided into a number of beam units, and the node deformation displacement of the beam unit is used to describe the elastic vibration of the blade.

[0028] Preferably, in step 9), the trim analysis includes: since the rotor / airframe modal coupling dynamics nonlinear differential equation has periodic coefficients, the trim of the airframe and the blades is an iterative process; the parameters output by the airframe trim are the attitude angle of the airframe and the required rotor collective pitch Φ0 and the cyclic pitch Φ 1C , Φ 1S After completing an iterative calculation cycle, the balancing calculation will be divided into two parts. One part is the balancing of the six rigid body modal equations, and the other part is the calculation of the N FP The steady-state response of each mode; when the blade is trimmed, the required rotor collective pitch Φ0 and cyclic pitch Φ 1C , Φ 1S As the total distance θ0 and the periodic variable distance θ 1C ,θ 1S The input value is used to solve the blade modal steady-state response; if the calculation results of the current and subsequent airframe and blade trims meet the error requirements, the iterative cycle is completed.

[0029] This application has the following technical effects:

[0030] The present invention provides a vibration response modeling and analysis method for a rotor helicopter with a forward-and-backward swept and reversed blade tip configuration. The coupled dynamics model takes into account the influence of the forward-and-backward swept and reversed blade tip configuration. The coupled system dynamics model and analysis method can be used for vibration response analysis (including steady-state and transient) of all advanced helicopters (especially modern rotor helicopters with complex three-dimensional shapes), providing key technical support for the design and development of new models and model modifications. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the coordinate system of the airframe, rotor hub and blades involved in the present invention;

[0032] Figure 2 This is a schematic diagram of the aerodynamic model of the blade involved in the present invention;

[0033] 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;

[0034] Figure 4 Schematic diagram of the tip of a blade with forward and backward sweep angles according to the present invention;

[0035] Figure 5It is a schematic diagram of the positional relationship between the overall coordinates and the local coordinates of the aerodynamic center position of the blade tip section involved in the present invention;

[0036] Figure 6 This is a schematic diagram of a finite element model of an aircraft body involved in the present invention;

[0037] Figure 7 This is a schematic diagram of a flat tail aerodynamic model involved in the present invention;

[0038] Figure 8 This is a schematic diagram of the vertical tail aerodynamic model involved in the present invention;

[0039] Figure 9 This is a schematic diagram of a tail rotor aerodynamic model according to the present invention;

[0040] Figure 10 This is a schematic diagram of a blade beam unit model involved in the present invention;

[0041] Figure 11 It is a schematic diagram of the time finite element method involved in the present invention.

[0042] Figure 12 This is a schematic diagram of foreign BERP propeller tips and blue-edge propeller tips. DETAILED DESCRIPTION

[0043] The present application provides a vibration response modeling and analysis method for a rotor helicopter with a forward-and-backward swept up-and-down reverse blade tip configuration. The application belongs to the helicopter dynamics design technology and involves a full-machine coupled system dynamics modeling method and analysis method. The application is applicable to the vibration response analysis of conventional rotor helicopters and rotor helicopters with forward-and-backward swept up-and-down reverse blade tip configurations. In particular, for rotors with forward-and-backward swept up-and-down reverse blade tip configurations, the coupled dynamics model needs to consider the influence of the three-dimensional configuration of the blade tip on the vibration response of the coupled system, which is mainly reflected in the aerodynamics. The modal synthesis technology is used to comprehensively model the rotor and body dynamics coupling system, describe the motion of the body, rotor, and blade tip in different coordinates, and establish structural dynamics finite element method models of isolated rotor blades and body structures respectively. The quasi-steady and unsteady dynamic models, dynamic inflow models, and ONERA models are used to model the aerodynamics. The Hamilton principle is applied to derive the dynamic equations of the rotor / body coupling system. According to the nonlinear modal vibration equation of the isolated blade after spatial finite element discretization, after modal coordinate transformation and modal contraction, the rotor / body modal coupling dynamics nonlinear differential equation is finally obtained. The coupled modal equations are nonlinear differential equations with periodic coefficients. Balancing the airframe and blades is an iterative process, and the time-dependent finite element method is used to solve the steady-state response of the rotor / airframe modal coupling. However, during maneuvering flight, the airframe and blades cannot be trimmed, and the transient response can be obtained by directly solving the differential equations using direct integration. This modeling and analysis method can be applied to vibration and transient response analysis of all advanced helicopters, especially modern rotorcraft with complex three-dimensional geometries, providing key technical support for the design and development of new models and retrofits.

[0044] The technical solution of the present invention is to use modal synthesis technology to comprehensively model the rotor and airframe dynamic coupling system, describe the motion of the airframe, rotor, and blade tip in different coordinates, establish structural dynamics finite element method models of the isolated rotor blade and airframe structure respectively, use quasi-steady and unsteady dynamic models, dynamic inflow models, and ONERA models to model the aerodynamic forces, and apply the Hamilton principle to derive the dynamic equations of the rotor / airframe coupling system. Based on the nonlinear modal vibration equation of the isolated blade after spatial finite element discretization, after modal coordinate transformation and modal contraction, the rotor / airframe modal coupling dynamics nonlinear differential equation is finally obtained. The coupled modal equation is a nonlinear differential equation with periodic coefficients. The balancing of the airframe and blades is an iterative process. The time finite element method is used to solve the steady-state response of the rotor / airframe modal coupling. However, in maneuvering flight, the airframe and blades cannot be balanced, and the transient response can be obtained by directly solving the differential equation using the direct integration method.

[0045] The present application provides a vibration response modeling and analysis method for a forward-and-backward swept rotor helicopter with an up-and-down reversed blade tip configuration, including:

[0046] (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.

[0047] (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.

[0048] (3) Aerodynamic model of rotor blades. Since 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. Therefore, when modeling the aerodynamics in the coupled system vibration response analysis model, the unsteady aerodynamic model, ONERA model and dynamic inflow model are considered on the basis of the quasi-steady aerodynamic model. The aerodynamic model is shown in Figure 2 ,The comprehensive application of these three models can more accurately calculate the aerodynamic loads in steady-state response analysis, stability analysis and transient response analysis.

[0049] (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.

[0050] (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.

[0051] (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.

[0052] (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.

[0053] (8) Airframe structure dynamics model. The airframe structure dynamics model is established using the finite element method. The commercial software PATRAN is used to directly perform finite element meshing on the designed airframe structure components. Based on the forces and force transmission of the structural elements and components, appropriate units are selected from the unit library provided by the NASTRAN software to simulate various types of structures. The natural frequencies and vibration modes are calculated using the NASTRAN software. By analyzing the natural frequencies and vibration modes of the airframe structure, the airframe vibration modes are determined, which must include the rigid body modes of the six airframes.

[0054] (9) Airframe aerodynamic model. The airframe aerodynamic model includes the aerodynamic forces of the fuselage, horizontal tail, vertical tail and tail rotor. The aerodynamic forces and moments of the fuselage are directly determined by the wind tunnel test results, which are the fuselage angle of attack α WF and sideslip angle β WF The tailplane consists of the horizontal and vertical tailplanes. The aerodynamic forces acting on the tailplane (excluding aerodynamic torque) are replaced by a concentrated force acting at the tailplane's aerodynamic center. For helicopters with both a main rotor and a tail rotor, only the pull of the tail rotor is considered; other forces are not considered because they have no effect on the coupled stability and dynamic characteristics of the entire aircraft. The pull (or push) is considered for overall aircraft trim.

[0055] (10) Establishment of a comprehensive analysis model for the coupling modal relationship between the complex three-dimensional rotor and the airframe. First, the blade is taken as a residual structure and the hub node of the connection interface is taken as a residual node. A dynamic coupling analysis model that is a mixture of modal space and physical space is established. This model facilitates the derivation of the rotor / airframe coupling 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 modal coupling comprehensive analysis model is obtained.

[0056] (11) Derivation of the modal coupling dynamic equations of the complex three-dimensional rotor and the fuselage. The coupled dynamic equations of the rotor / airframe system are derived based on Hamilton's principle. The fuselage is 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 their generalized coordinates are the body vibration modal coordinates. The motion of the hub at the interface between the rotor and the fuselage and the motion of the rotor blades are described in the physical space. 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 body vibration modal damping force and 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. The blade motion is transformed into the modal space using the isolated blade vibration modal coordinates, while the hub motion is represented using the modal coordinates {X FP} indicates that the rotor / airframe modal coupling dynamic equations in the modal space are finally derived.

[0057] (12) Finite element discretization of the blade's spatial coordinates in the dynamic equations. The blade's motion is a binary function of spatial coordinates and time. To remove spatial correlation, the finite element method is used to discretize the blade's motion. The blade is divided into several beam elements, and the node deformation and displacement of the beam elements are used to describe the blade's elastic vibration.

[0058] (13) Balancing analysis. Since the obtained rotor / airframe modal coupling dynamics nonlinear differential equation has periodic coefficients, the balancing of the airframe and blades is an iterative process, and the solution obtained is the steady-state response of the rotor / airframe modal coupling. The parameters of the airframe trim output are the attitude angle of the airframe and the required rotor collective pitch Φ0 and the cyclic pitch Φ 1C , Φ 1S After completing an iterative calculation cycle (one for the body trim and one for the blade trim), the trim calculation will be divided into two parts. One part is the trim of the six rigid body modal equations of the body with constant values, and the other part is the N FP The steady-state response of each mode. When the blade is trimmed, the required rotor collective pitch Φ0 and cyclic pitch Φ 1C, Φ 1S As the total distance θ0 and the periodic variable distance θ 1C ,θ 1S The blade modal steady-state response is solved based on the input values. If the results of the two previous calculations of the airframe and blade trim meet the error requirements, the iterative cycle is completed.

[0059] (14) Time finite element method is used to solve the vibration response. The time finite element method is based on the weak Hamilton principle. Similar to the space finite element method, the time finite element method divides a rotation of 2π into N E The rotor blade and fuselage modal coordinates are represented by the shape function [H(ψ)] and the time node displacement {ζ}. Since the coupling equation is obtained by linearizing the nonlinear equation, it is necessary to use an iterative method until the two results meet the steady-state response error requirements, and then the final modal coupling steady-state response can be obtained.

[0060] (15) Transient response analysis. During helicopter maneuvering, neither the fuselage nor the rotor blades can be trimmed, nor does linearization need to be performed. The coupled analysis model considers the ONERA model and the dynamic inflow model (which can more accurately predict the response of the dynamic system). The direct integration method is used to calculate the time history of the aircraft under a certain flight state and analyze the transient response of the fuselage and blades under this state.

[0061] See also Figures 1-11 , the vibration response modeling and analysis method of the forward and backward swept up and down reverse blade tip configuration rotor helicopter involved in the present invention is further described in detail.

[0062] 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 ,kf} indicates that the body is relative to the coordinate system {i g ,j g ,k g The six degrees of freedom of motion of f , Y f , Z f ,φ Xf ,φ Yf ,φ Zf .X f Forward is positive, Z f Upward is positive, Y f The positive direction is determined by the right-hand rule. H ,X H ,Y H ,Z H} is the rotor hub coordinate system, used to describe any {X f ,Y f ,Z f The movement of the rotor at the coordinates of {i H ,j H ,k H}, the movement of the rotor hub center is expressed by X H , Y H , Z H ,φ XH ,φ YH ,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:

[0063]

[0064] Step 2: Establishment of analysis model.

[0065] 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.

[0066] 2) Establishment of the rotor blade aerodynamic model. Since 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. Therefore, when modeling the aerodynamics in the coupled system vibration response analysis model, the unsteady aerodynamic model, ONERA model and dynamic inflow model are considered on the basis of the quasi-steady aerodynamic model. The aerodynamic model is shown in Figure 2 ,The comprehensive application of these three models can more accurately calculate the aerodynamic loads in steady-state response analysis, stability analysis and transient response analysis.

[0067] 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.

[0068] 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.

[0069] 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.

[0070] 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.

[0071] 7) Airframe structure dynamics model. The airframe structure dynamics model is established using the finite element method. The commercial software PATRAN is used to directly divide the finite element mesh of the designed airframe structure components. According to the force and force transmission of the structural elements and components, appropriate units are selected from the unit library provided by NASTRAN software to simulate various types of structures, such as Figure 6 As shown in the figure, the rotor hub is the interface with the airframe, and the hub center is a node in the airframe structural finite element model. Similarly, the aerodynamic action points of the horizontal tail, vertical tail, and tail rotor are also considered nodes in the airframe structural finite element model. Natural frequencies and mode shapes are calculated using NASTRAN software. By analyzing the natural frequencies and mode shapes of the airframe structure, the airframe vibration modes are determined, which must include the six rigid body modes.

[0072] 8) Airframe aerodynamic model. The airframe aerodynamic model needs to be established in the coupled model, including the aerodynamic forces of the fuselage, horizontal tail, vertical tail and tail rotor. The aerodynamic forces and moments of the fuselage are directly determined by the wind tunnel test results, which are the fuselage angle of attack α WF and sideslip angle β WF The aerodynamic drag, side force, lift, roll, pitch, and yaw moment coefficients of the fuselage are taken from wind tunnel test data. These forces and moments act on the entire fuselage, that is, they are considered to act on the center of mass of the fuselage, corresponding to the rigid body motion mode of the fuselage.

[0073] The tail consists of a horizontal tail and a vertical tail. The aerodynamic force on the tail (excluding aerodynamic torque) is replaced by a concentrated force, whose action point is at the aerodynamic center of the tail. The calculation model of the aerodynamic force of the horizontal tail and the vertical tail is shown in Figure 7 and 8 For helicopters with main rotors and tail rotors, only the pull of the tail rotor is considered, and other forces are not considered, because those forces have no effect on the coupling stability and dynamic characteristics of the whole aircraft. Considering the pull (or push) force is used to balance the whole aircraft. Figure 9 shown.

[0074] 9) Establishment of a comprehensive analysis model for the coupled modal analysis of complex three-dimensional rotors and airframes. The interface between the airframe and the rotor blades is the hub. The hub's degrees of freedom are the node displacements at the interface between the airframe and the rotor blade structure. The rotor blade dynamics model includes the hub's associated motion. Therefore, the rotor / airframe modal coupling comprehensive analysis model defines the vibration modes of the airframe and isolated rotor blade in modal space as supernodes of the airframe and rotor blade structures, respectively. The hub at the interface is defined as the residual structure, and the hub's displacements are defined as displacements of the residual nodes.

[0075] In the coupled comprehensive analysis model, the blade is first regarded as a residual structure, and the hub node of the connection interface is regarded as a residual node. A dynamic coupling analysis model of the modal space and physical space hybrid is established. This model facilitates the derivation of the rotor / airframe coupling 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 modal coupling comprehensive analysis model is obtained.

[0076] Step 3: Derive the modal coupling dynamic equations of the complex three-dimensional rotor and fuselage.

[0077] The coupled dynamic equations of the rotor / airframe system are derived from Hamilton's principle. Based on the airframe, rotor blade dynamics, and aerodynamic models, the airframe is used as a substructure of the coupled dynamic system. Its kinetic energy, potential energy, and external virtual work are described in modal space, and their generalized coordinates are the airframe vibration modal coordinates. 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 virtual work of the rotor blades are expressed using the hub motion. 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.

[0078] The variational equation of the Hamilton principle for the rotor / airframe coupled dynamic system is:

[0079]

[0080]

[0081] In the formula, a pair of rotors has N b blade; U f 、T f 、W f They represent the potential energy, kinetic energy and external virtual work of the body respectively; represents the potential energy, kinetic energy and external virtual work of the kth blade of the rotor.

[0082] The rotor / airframe coupling dynamic equation derived from equation (7) is a mixture of modal space and physical space. Then, the blade motion is transformed into the modal space using the isolated blade vibration modal coordinates, while the hub motion is transformed into the modal space using the modal coordinates {X FP} indicates that the rotor / airframe modal coupling dynamic equations in the modal space are finally derived.

[0083] 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.

[0084]

[0085] Analyze the motion velocity of a point in the span of any airfoil section from the upper edge of the blade, derive the kinetic energy and kinetic energy variation of a blade according to the kinetic energy formula, and sum the total kinetic energy of the rotor by the total number of rotor blades.

[0086]

[0087] Where, The span direction of the blade upper edge The velocity of a point within any airfoil section.

[0088] 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.

[0089] In view of the difference between Hodges nonlinear large deformation beam and medium deformation beam, the main difference is that the large deformation beam has additional tensile and torsional increments caused by bending in the tensile and torsional displacements compared with the medium deformation beam.

[0090] 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.

[0091] 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 .

[0092] In aerodynamic calculations, it is necessary to first obtain the inflow distribution of the rotor. Commonly used inflow models include the uniform inflow model, Deer's linear inflow model, and the dynamic inflow model. 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-uniformly distributed induced velocity along the blade 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 helicopter vibration response and stability. Its first-order harmonic dynamic inflow model expresses the linear first-order harmonic distribution of the induced velocity of the rotor wake at the blade disc as follows:

[0093]

[0094] In the above formula, is the dimensionless induced velocity, v ie , v ic , v is Determined by the following kinetic equation:

[0095]

[0096] The rotor lift, roll, and pitch moment coefficients on the right side of the dynamic inflow equation (14) are functions of the blade motion and also of the induced velocity itself.

[0097] 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. When combined with a dynamic inflow model, it provides more accurate aerodynamic calculations. This combined model handles nonlinearities and is used for helicopter transient response and dynamic stability analysis.

[0098] The airfoil lift differential equation established using the ONERA model is:

[0099]

[0100] The differential equation of airfoil aerodynamic drag is:

[0101]

[0102] The differential equation of the airfoil aerodynamic moment is:

[0103]

[0104] ΔC L , ΔC D , ΔC M is the difference between the experimental value of the lift, drag and moment coefficient of the airfoil and its linear value, R λ The other coefficients in equations (18) are parameters of the ONERA model, determined by airfoil test data. Equations (15) (2) to (17) 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.

[0105]

[0106] 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 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 (19).

[0107] c) Based on the established airframe dynamics model, the NASTRAN analysis software is used to calculate the airframe vibration modal frequency and vibration mode. Then, based on the analysis of the airframe vibration mode, the airframe modal of interest is selected and integrated with the rotor mode installed on the airframe. Assume that the selected airframe modes are N f , then the variational formula of the kinetic energy of these modal vibrations is:

[0108]

[0109] 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 modes are defined as super-node coordinate variables in the synthesis with the rotor blade vibration modes.

[0110] For the six rigid body modes with zero frequency in the air, their generalized stiffness is zero and their potential energy is also zero. However, 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, so the six rigid body modes must be included. 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., super-node coordinate variables). The potential energy variation formula is:

[0111]

[0112] Where K fp Yes N f The generalized stiffness of the body mode.

[0113] 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:

[0114]

[0115] Where C fpi It is the body N f The damping coefficient matrix of each mode.

[0116] d) The aerodynamic forces and moments acting on the aircraft's center of gravity are expressed by the generalized virtual displacement of the aircraft's rigid body mode, without considering the aircraft's elastic mode. That is, only the virtual work done by the fuselage's aerodynamic forces and moments on the aircraft's rigid body mode is considered. Therefore, the virtual work of the fuselage's aerodynamic forces is:

[0117]

[0118] Where, F fa The three forces and three moments acting on the center of gravity of the body are the vibration mode matrices corresponding to the six rigid body modes at the center of gravity of the body are the unit matrix. The virtual displacement in the formula is the variation δX of the six rigid body modal coordinates of the body. fp .

[0119] The virtual work done by the horizontal tail aerodynamics on the airframe mode given by the horizontal tail aerodynamics model can be expressed as:

[0120]

[0121] In the formula, {X Pin} is the displacement of the aerodynamic point on the horizontal tail, {F Pin} is the aerodynamic force, which is also divided into two parts. One part is independent of the node motion speed and is a constant term The other part is a linear function of the node's movement speed is the vibration mode matrix of the body mode corresponding to the node displacement.

[0122] The virtual work done by the vertical tail aerodynamic force on the body mode given by the vertical tail aerodynamic model can be expressed as:

[0123]

[0124] In the formula, {X vt} is the displacement of the aerodynamic action point on the vertical tail, {F vt} is the aerodynamic force, [X mvt ] is the vibration mode matrix of the body mode corresponding to the node displacement.

[0125] The pull and airfoil drag acting on the center of the tail rotor hub output by the tail rotor aerodynamic model are projected into the body coordinate system as follows: and {F ltr}, the displacement and velocity of the center point of the tail rotor hub are {X tr}and The vibration mode matrix corresponding to the body mode is [X mtr ] is expressed as follows:

[0126]

[0127] e) Based on the kinetic energy, potential energy and external virtual work of the rotor and the body derived above, according to the Hamilton principle formula, according to the variation {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 equation for coupling the rotor blade motion with the body motion is this dynamic equation describing the rotor / body coupled motion, where each coefficient matrix contains cosnψ k ,sinnψ k Factor, that is, periodic coefficient, and {X rs} T It also contains the non-independent quantity of blade motion, namely the partial derivative of blade deformation displacement, and {X rs} T It is a function of space and time. The following will explain how to use the finite element method to discretize the blade motion in the two parts of the equation and obtain the independent blade motion node coordinates. The equation is transformed into the corresponding body modal coordinates {X fp} T and blade node coordinates The rotor / airframe coupled dynamic modal equations.

[0128] Step 4: Finite element discretization of blade space coordinates in the dynamic equation. The motion of the blade is a binary function of space coordinates and time. In order to remove the spatial correlation, the finite element method is used to discretize the blade motion, dividing the blade into several beam elements, and using the node deformation displacement of the beam element to describe the elastic vibration of the blade. The medium deformation beam element is expressed as each unit contains 15 degrees of freedom, such as Figure 10 As shown. Each beam element has 2 end nodes and 3 internal nodes, and each end node has 6 degrees of freedom u, v, v', w, w', The internal nodes have only one degree of freedom, and the unit center node is the torsional degree of freedom The nodes at the points where the unit is divided into three equal parts are the axial deformation degrees of freedom u.

[0129] For the i-th beam element, using shape function interpolation, the elastic deformation of any point xi inside it can be expressed as:

[0130]

[0131] Where s = x i / l i , l iis the unit length. H is the shape function of the unit's flapping and shimmying bending degrees of freedom, H u and are the shape functions of the axial tensile and torsional degrees of freedom. i is the column vector of the total degrees of freedom for a single element:

[0132]

[0133] Through the above shape functions and the node displacement of the unit, the displacement of any point in the unit. Then the blade energy equation is discretized. After discretization, the blade energy variation can be expressed as

[0134]

[0135] Where q is the total degree of freedom vector of a single blade, M, C, and K are the mass, damping, and stiffness matrices of the blade, respectively, and F is the load vector.

[0136] Step 5: Trim analysis. Based on the spatially discretized nonlinear modal vibration equation of the isolated blade, after modal coordinate transformation and modal contraction, the final forward flight rotor / airframe modal coupling dynamics nonlinear differential equation is as follows (the hovering state can be considered as a forward flight state with zero flight speed):

[0137] The modal equation of the body coupled with the rotor is:

[0138]

[0139] The blade modal equation of the Kth blade of the rotor coupled with the body is:

[0140]

[0141] Equations (30) and (31) are nonlinear differential equations with periodic coefficients. Therefore, trimming the airframe and blades is an iterative process, and the resulting solution is the steady-state response of the rotor / airframe modal coupling. However, for maneuvering flight, the airframe and blades cannot be trimmed, and solving the differential equations directly using direct integration will yield the transient response.

[0142] a) Aircraft trim

[0143] The parameters of the body trim output are the body attitude angle and the required rotor collective pitch Φ0 and cyclic pitch Φ 1C , Φ 1S When the flight state (such as speed) is given, the above parameters are determined by the six rigid body modal equations of the aircraft in equation (30). The first step of the iterative calculation is to take the sum of the 3rd to 5th and 7th terms in equation (30) as zero, where the third term corresponding to the airborne flight state is zero, and solve the attitude angle and the required Φ0, Φ 1C , Φ 1SThe solutions for the other modes of the aircraft and the blade modes are all set to zero. For the ground state, the six rigid body displacements of the aircraft can be set to zero and no balancing calculation is performed.

[0144] After completing an iterative calculation cycle (one for the body trim and one for the blade trim), the trim calculation is divided into two parts. One part is the constant value solution of the six rigid body modal equations of the body, and the other part is the N FP The steady-state response of each mode. When calculating the steady-state response of the body mode from Equation (30), the blade term in the equation is used as the exciting force term. The forced response of Equation (30) under the action of the rotor load can be solved by the integral method or the time finite element method.

[0145] b) Blade trim

[0146] The output of the body trim attitude angle and Φ0, Φ 1C , Φ 1S After the preset value is reached, the first blade trim is performed, and the required rotor collective pitch Φ0 and cyclic pitch Φ 1C , Φ 1S As the total distance θ0 and the periodic variable distance θ 1C ,θ 1S Input value. The steady-state response of the blade mode is solved by equation (31), where the first, second and last terms of (31) are attributed to the exciting force term of the vibration equation, but terms 1 and 2 are zero for the first-order harmonic term, and only the first-order term is considered in the rigid body balancing calculation of the aircraft. There are two methods for solving the steady-state response of the blade mode of equation (31). The time finite element method is used here to solve it. In addition to obtaining the steady-state response of the blade, blade balancing also has a pitch iterative calculation process. After obtaining the steady-state response of the blade, it is necessary to check the actual pitch of the blade at 0.75R. Is it consistent with the required values ​​Φ0, Φ 1C , Φ 1S Meet the error requirements. If not, adjust the rotor collective pitch θ0 and cyclic pitch θ according to the error value. 1C ,θ 1S The input value is With Φ0, Φ 1C , Φ 1S When the two subsequent calculation results of the airframe and blade trim meet the error requirements, the iterative cycle is completed.

[0147] Step 6: Time finite element method is used to solve the vibration response. The time finite element method is based on the weak Hamilton principle, multiplying equation (30) by and equation (31) multiplied by Then from the initial moment ψ i To the end time ψ jSince the response of the body and blades is periodic, we have ψ i =ψ and ψ j =ψ+2π. Therefore, the coupled equation can be written as follows:

[0148]

[0149] in,

[0150] Expand {Q} into a first-order Taylor series:

[0151] {Q}={Q s}+{ΔQ}

[0152]

[0153] Substituting into equation (32), we get:

[0154]

[0155] Similar to the spatial finite element method, the time finite element method divides a rotation of 2π into N E Time units, such as Figure 11 As shown, the rotor blade and body modal coordinates are expressed using the shape function [H(ψ)] and the time node displacement {ζ}:

[0156] {Y}=[H(ψ)]{ζ} (35)

[0157] Therefore, the speed can also be expressed as:

[0158]

[0159] [H(ψ)] and spatial finite element [H u (x)], similarly, (35), (36) and their variations {δY}=[H(ψ)]{δζ} and Substituting into (34), since {δζ} is arbitrary, it is required that in equation (34):

[0160] {HQ s}+[K HH ]{Δζ}=0 (37)

[0161] Where,

[0162]

[0163] [H ψ ] T =[H1 H2 H3 H4]

[0164] Calculate the solution of equation (37). Since equation (34) is obtained by linearizing the nonlinear equation, it is necessary to use an iterative method to make the final steady-state response satisfy equation (32). Let the response value obtained by the kth iteration be {ζ} k , then the response value obtained in the k+1th iteration is {ζ} k+1 , its relationship with the previous time is:

[0165] {ζ} k+1 ={ζ} k +{Δζ} k+1 (38)

[0166] {Δζ} k+1 is the increment of displacement at the time node, and the iterative calculation is repeated until the two results meet a certain error requirement. Then the steady-state response corresponding to the modal coordinates of the fuselage and rotor blades can be expressed as:

[0167] {Y}=[H(ψ)]{ζ} (39)

[0168] For any moment, the steady-state response of the ψ body and blade physical coordinate nodes can be expressed as:

[0169] {X fi}=[X MFP ][H(ψ)]{ζ},{X bi}=[X MBP ][H(ψ)]{ζ} (40)

[0170] Step 7: Transient Response Analysis. The above describes the rotor / airframe coupled steady-state vibration response analysis process during steady-state flight. During helicopter maneuvering, neither the airframe nor the rotor blades can be trimmed, nor does linearization require processing. In this case, the rotor / airframe modal coupling transient response analysis is required. The transient response analysis incorporates the ONERA model and the dynamic inflow model (which more accurately predicts the response of the dynamic system). A direct integration method is used to calculate the time history of the aircraft under a specific flight state, analyzing the transient response of the airframe and blades under that state.

Claims

1. A vibration response modeling and analysis method for 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 the body structure dynamics model; 6) Establish an aerodynamic model of the aircraft; 7) Establish a comprehensive modal model of the coupling between the complex three-dimensional rotor and the fuselage, and derive the dynamic equations; 8) Finite element discretization of blade space coordinates in dynamic equations; 9) Trim analysis; 10) Time finite element method to solve vibration response; 11) Transient response analysis.

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 non-rotating coordinate system, a hub rotating coordinate system, a blade flapping coordinate system, a blade swing coordinate system and a blade pitch change coordinate system, and the relationship between the coordinate systems is the coordinate transformation relationship between the coordinate systems.

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

4. The method according to claim 3, wherein: In step 3), the establishment of the rotor blade aerodynamic model includes: because the blade tip adopts a forward and backward swept up and down reverse configuration, it will cause sensitive changes in the blade aerodynamic characteristics, that is, it has a great impact on the aerodynamics. Therefore, when modeling the aerodynamic force in the coupled system vibration response analysis model, the unsteady aerodynamic force model, the ONERA model and the dynamic inflow model are considered on the basis of the quasi-steady aerodynamic force model. The comprehensive application of these three models can more accurately calculate the aerodynamic load in the steady-state response, stability and transient response 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 airframe structure dynamics model is established by using the finite element method to establish the airframe structure dynamics model, using the commercial software PATRAN to directly perform finite element meshing on the designed airframe structure components, and selecting appropriate units from the unit library provided by the NASTRAN software to simulate various types of structures based on the forces and force transmission of the structural elements and components; using the NASTRAN software to calculate the natural frequencies and vibration modes, and by analyzing the natural frequencies and vibration modes of the airframe structure, determining the airframe vibration modes, which must include 6 rigid body modes of the airframe.

7. The method according to claim 6, characterized in that: In step 6), the airframe aerodynamic model is established: the airframe aerodynamic model includes the aerodynamic forces of the fuselage, horizontal tail, vertical tail, and tail rotor; the airframe aerodynamic forces and moments are directly determined using wind tunnel test results, which are functions of the fuselage angle of attack and sideslip angle; the tail includes the horizontal tail and vertical tail, and the aerodynamic force on the tail is replaced by a concentrated force, the point of action of which is at the aerodynamic center of the tail; for helicopters with a main rotor and a tail rotor, only the pull of the tail rotor is considered, and the pull or thrust is considered for balancing the entire aircraft.

8. The method according to claim 7, wherein: In step 7), the complex three-dimensional rotor and body coupling modal integrated model and the derivation of the dynamic equations include: first, using the Hamilton principle to derive the rotor / body system coupling dynamic equations; according to the body, rotor blade dynamics model and aerodynamic model, the body 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 their generalized coordinates are the body vibration modal coordinates; secondly, the blade is used as a residual structure, and a hybrid dynamic coupling analysis model of the modal space and physical space is established, and the blade dynamics partial differential equation is discretized using the finite element method to calculate the vibration characteristics of the isolated blade, and select N P The blade modes are then transformed into the blade modal space to obtain a comprehensive analysis model of rotor and body modal coupling.

9. The method according to claim 8, characterized in that: In step 8), the finite element discretization of the blade spatial coordinates in the dynamic equation includes: the motion of the blade is a binary function of the spatial coordinates and time; in order to remove spatial correlation, the finite element method is used to discretize the blade motion, the blade is divided into several beam units, and the node deformation displacement of the beam unit is used to describe the elastic vibration of the blade.

10. The method according to claim 9, characterized in that: In step 9), the trim analysis includes: since the rotor / airframe modal coupling dynamics nonlinear differential equation has periodic coefficients, the trim of the airframe and blades is an iterative process; the parameters of the airframe trim output are the attitude angle of the airframe and the required rotor collective pitch Φ0 and the cyclic pitch Φ 1C , Φ 1S After completing an iterative calculation cycle, the balancing calculation will be divided into two parts. One part is the balancing of the six rigid body modal equations, and the other part is the calculation of the N FP The steady-state response of each mode; when the blade is trimmed, the required rotor collective pitch Φ0 and cyclic pitch Φ 1C , Φ 1S As the total distance θ0 and the periodic variable distance θ 1C ,θ 1S The input value is used to solve the blade modal steady-state response; if the calculation results of the current and subsequent airframe and blade trims meet the error requirements, the iterative cycle is completed.

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