A multi-system coupled dynamics modeling method for a multi-propeller tilting wing rotorcraft

Abstract

The application provides a multi-propeller tilting wing rotor aircraft multi-system coupling dynamics modeling method, which comprises the following steps: step 1, establishing each system coordinate system and the relationship between the coordinate systems; step 2, establishing an aerodynamic force model according to the body coordinate system, the wing deformation coordinate system and the blade deformation coordinate system; step 3, establishing a high-aspect-ratio wing dynamics model according to the wing deformation coordinate system; step 4, establishing a nacelle dynamics model according to the wing undeformed coordinate system; step 5, establishing a rotor dynamics model according to the blade deformation coordinate system; and step 6, establishing a multi-propeller / nacelle / high-aspect-ratio wing coupling system dynamics equation according to the high-aspect-ratio wing dynamics model, the nacelle dynamics model and the rotor dynamics model.

Description

Technical Field

[0001] This invention pertains to helicopter dynamics modeling and analysis technology, specifically relating to a multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft. Background Technology

[0002] Multi-rotor / tilt-wing rotorcraft integrates the concepts of distributed rotors and tilt-wings. Its aerodynamic layout adopts a tilt-wing configuration, with multiple distributed rotor units distributed across the fore and aft wings. This configuration enables vertical takeoff and landing, hovering, and high-speed forward flight. Its flight speed and operational radius are more than double that of conventional helicopters, making it a significant development direction for future high-speed rotorcraft. Some international research institutions have already begun strategic planning and preparation, conducting extensive preliminary research on this configuration and achieving significant breakthroughs. Dynamic design technology is crucial among the core technologies of multi-rotor / tilt-wing rotorcraft. Currently, there is an urgent need to conduct relevant fundamental research to understand the mechanisms and laws of its aeroelastic coupling dynamics. Summary of the Invention

[0003] The technical problem to be solved by this invention is to propose a multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft, which can be used for coupled system modal analysis and stability analysis of multi-rotor / tilt-wing rotorcraft, tiltrotor aircraft, distributed high-speed rotorcraft and other aircraft. It can also be used for aeroelastic response analysis of such aircraft, providing key technical support for model design and modification development.

[0004] Technical solution: A multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft, the method comprising:

[0005] Step 1: Establish the coordinate systems for each system and the relationships between the coordinate systems;

[0006] Step 2: Establish the aerodynamic model based on the body coordinate system, wing deformation coordinate system, and blade deformation coordinate system;

[0007] Step 3: Establish a dynamic model of the high aspect ratio wing based on the wing deformation coordinate system;

[0008] Step 4: Establish the nacelle dynamics model based on the undeformed wing coordinate system;

[0009] Step 5: Establish the rotor dynamics model based on the blade deformation coordinate system;

[0010] Step 6: Based on the dynamic model of the high aspect ratio wing, the dynamic model of the nacelle, and the dynamic model of the rotor, establish the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system.

[0011] Furthermore, step 1 specifically includes:

[0012] Establish an inertial coordinate system, a body coordinate system, an undeformed wing coordinate system, a deformed wing coordinate system, a non-rotating rotor hub coordinate system, a rotating rotor hub coordinate system, an undeformed rotor blade coordinate system, and a deformed rotor blade coordinate system, as well as the relationships between these coordinate systems.

[0013] Furthermore, step 3 includes:

[0014] Step 31: Using the formula The virtual deformation energy U of the wing was calculated. w .

[0015] Step 32: Using the formula The virtual kinetic energy T of the wing was calculated. w .

[0016] Step 33: Using the formula Computer wing external force virtual work W w .

[0017] Step 34: Based on the wing's virtual deformation energy U w wing virtual kinetic energy T w And the virtual work of external force on the wing W w Constructing a dynamic model for a high aspect ratio airfoil

[0018] .

[0019] Furthermore, step 5 includes:

[0020] Step 51: Using the formula Calculate the blade virtual deformation energy U b .

[0021] Step 52: Using the formula Calculate the virtual kinetic energy T of the blade. b .

[0022] Step 53: Using the formula Calculate the virtual work W of the propeller blade aerodynamics. b .

[0023] Step 54: Using the blade dynamics equations

[0024] Construct a rotor dynamics model.

[0025] Furthermore, step 4 includes:

[0026] Based on the undeformed coordinate system of the wing, using the formula A nacelle dynamic model was established; and the nacelle mass matrix was extracted. .

[0027] Furthermore, step 6 includes:

[0028] Based on the dynamic models of high aspect ratio wings, nacelles, and rotors, the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system are established.

[0029] .

[0030] Furthermore, step 2 includes:

[0031] Based on the wing deformation coordinate system, establish the aerodynamic model of the wing;

[0032] Based on the body coordinate system, establish the aerodynamic model of the body.

[0033] Furthermore, step 2 includes:

[0034] Based on the blade deformation coordinate system, a blade model is established; then, based on the blade model and the relationship between the hub rotation coordinate system and the blade deformation coordinate system, the aerodynamic model of the rotor is established by summing the number of blades.

[0035] The beneficial effects of this invention are as follows: This invention provides a multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft. Addressing the characteristics of multi-rotor / tilt-wing rotorcraft dynamics problems, it establishes the dynamic equations for a multi-rotor / nacelle / high aspect ratio wing coupled system. This modeling method can be applied to fundamental dynamics research such as modal analysis, stability analysis, and aeroelastic response analysis of multi-rotor / tilt-wing rotorcraft coupled systems. It can also be directly extended to the aeroelastic coupling stability design and analysis of various advanced rotorcraft, tiltrotor aircraft, and distributed high-speed rotorcraft. Attached Figure Description

[0036] Figure 1 This invention relates to the wing and rotor hub coordinate system;

[0037] Figure 2 This is a schematic diagram of the elastic wing involved in the present invention;

[0038] Figure 3 This invention relates to a schematic diagram of the aerodynamic profile of an airfoil.

[0039] Figure 4 This is a schematic diagram of the nacelle configuration involved in the present invention;

[0040] Figure 5 This invention relates to a blade unit and node distribution diagram;

[0041] Figure 6 This is a schematic diagram of the blade degree-of-freedom distribution involved in the present invention. Detailed Implementation

[0042] To retain excellent vertical takeoff and landing and hovering performance while breaking through the speed limitations of traditional helicopter configurations to achieve high-speed flight (up to 600 km / h), multi-rotor / tilt-wing configurations integrate the advantages of multiple technologies. However, they inevitably inherit the inherent problems and defects of these technologies, and may even generate new problems after integration. Aeroelastic instability and excessive vibration resulting from the coupling of distributed multi-rotors with high aspect ratio wings will be key dynamic challenges for multi-rotor tiltrotor aircraft, especially the transient aeroelastic response / load during wing tilt transition and the stability of gyroscopic flutter under high-speed forward axial flow conditions.

[0043] Multi-rotor / tilt-wing rotorcraft employs a high-aspect-ratio wing design, resulting in significant wing structural deformation. Simultaneously, the distributed multi-rotor configuration causes concentrated loads and concentrated mass / inertia, leading to complex aerodynamic / elastic / inertial coupling characteristics during transition and high-speed forward flight. As a novel rotorcraft configuration, domestic research on the coupled dynamics of multi-rotor / tilt-wing rotorcraft and similar tiltrotor aircraft is virtually nonexistent. Therefore, theoretical calculation methods for the complex aeroelastic coupling dynamics between multi-rotors and high-aspect-ratio tiltrotor wings, and understanding their modal characteristics, aeroelastic response, and stability under different flight states, are crucial for the dynamic design of multi-rotor / tilt-wing rotorcraft. However, researching the aeroelastic coupling dynamics of multi-rotor / tilt-wings and addressing fundamental performance issues such as the coupled modal characteristics and motion characteristics of structurally deformable wings and distributed multi-rotors requires a solid foundation in multi-system coupled dynamics modeling methods, which is of great significance for the development of dynamic design technology for high-speed rotorcraft with multi-rotor tiltrotor configurations.

[0044] The technological achievements of this research have broad application prospects and a profound impact on the development of high-speed rotorcraft technology in my country. They strongly support my country's research and development of advanced high-speed rotorcraft and are of great significance. They can be directly applied to the aeroelastic coupling stability design and analysis of various advanced rotorcraft, tiltrotor aircraft, and distributed high-speed rotorcraft. Fundamental research on the dynamics of multi-rotor / tilt-wing rotorcraft has broad market potential and application prospects, and the multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft plays a crucial role.

[0045] Example 1

[0046] The technical solution of this invention is as follows: First, the motion of the rotor, wing, and nacelle is described in different coordinate systems. Structural dynamics finite element models of isolated rotor blades, elastic wings, and nacelles are established respectively. Quasi-steady or unsteady aerodynamic models are used to model the aerodynamics. Based on the theory of moderately deformable beams and quasi-steady / unsteady aerodynamic models, the dynamic equations of the rotor blades, nacelle kinetic energy, and elastic wings are established using the Hamiltonian variational principle. The equations are spatially discretized using the finite element method. The matrix dimension is expanded according to the number of degrees of freedom, and the matrix elements corresponding to the same nodal degrees of freedom are superimposed to obtain the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system. A method for solving the stability model is also given.

[0047] This application provides a multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft, including:

[0048] Step 1: Establish the coordinate systems of each system and the coordinate transformation relationships between them.

[0049] The system coordinate system includes the inertial coordinate system, the body coordinate system, the undeformed wing coordinate system, the deformed wing coordinate system, the non-rotating rotor hub coordinate system, the rotating rotor hub coordinate system, the undeformed rotor blade coordinate system, and the deformed rotor blade coordinate system.

[0050] Step 2: Establish an aerodynamic model.

[0051] Because the coupling stability, aeroelastic response, and aerodynamic forces of multi-rotor / nacelle / high aspect ratio wing coupled systems are related, different aerodynamic models need to be considered for different dynamic analyses. For rotor aerodynamic calculations, a quasi-steady aerodynamic model, an unsteady aerodynamic model, a dynamic inflow model, and the ONERA model were used. The combined application of these three models can more accurately calculate aerodynamic loads in stability analysis, dynamic response analysis, and transient response analysis. For the aerodynamic calculations of the fuselage, horizontal stabilizer, vertical stabilizer, and tiltrotor wings, a blowing test model was used due to the influence of the rotor downwash.

[0052] Step 3: Establish a dynamic model for a high aspect ratio wing.

[0053] The multi-rotor tilting high-aspect-ratio wing considers elastic deformation and is described by a beam model. The wing root is connected to the fuselage through a tilting hinge, on which multiple rigid nacelles are distributed. The motion of the wing is the superposition of bending and torsion of the elastic axis. The wing model is established using the theory of moderate deformation beams, and the virtual deformation energy, virtual kinetic energy, and virtual work of external forces of the high-aspect-ratio wing are established to derive the dynamic equations of the tilting wing.

[0054] Step 4: Establish the nacelle dynamics model.

[0055] The nacelle and power plant are rigidly connected to the elastic wing. Multiple rigid nacelles are distributed and installed on the elastic wing structure, which is equivalent to having multiple points of mass and inertia. Ignoring the effects of aerodynamic drag, we only consider kinetic energy. By using the spatial position vector of any point on the nacelle, we can obtain the velocity vector. Finally, by integration, we can obtain the virtual kinetic energy of the nacelle and derive the dynamic equations of the nacelle.

[0056] Step 5: Establish a rotor dynamics model.

[0057] For the rotor system of a multi-rotor / tilt-wing aircraft, a rotor dynamics model considering the effects of elastic wing motion is established based on Hamilton's variational principle. The blades are constructed using 15-DOF nonlinear moderately deformable beam elements. Considering their elastic motions such as flapping, flaring, torsion, and axial tension, the deformation of the elastic axis at any spanwise section r of the blade is analyzed. This includes four motions: axial displacement u, flaring displacement v, flapping displacement w, and torsional deformation φ, along with their structural and inertial coupling. The virtual deformation energy, virtual kinetic energy, and aerodynamic virtual work of the blades are calculated, and the rotor dynamics equations are derived.

[0058] Step 6: Derivation of the dynamic equations for the coupled system of multi-rotor / nacelle / high aspect ratio wing.

[0059] Based on the dynamic model of the wing, nacelle, and rotor system, and using Hamilton's principle, the mass damping stiffness matrices of the rotor system, nacelle, and elastic wing are integrated into a multi-system coupled model. The force vectors of the rotor and wing, corresponding to their degrees of freedom, are then integrated into the force vectors of the multi-system coupling, yielding the dynamic equations of the rotor / nacelle / wing coupled system model. These coupled dynamic equations are then transformed into state equations. The eigenvalue method is used to solve for the eigenvalues ​​of the state equations. The real part of the eigenvalue represents the system damping, and the imaginary part represents the system frequency. The stability of the coupled system can be determined based on the real part of the eigenvalues.

[0060] Example 2

[0061] The following detailed description, in conjunction with the accompanying drawings, of the multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft involved in this invention is provided in further detail.

[0062] Step 1: Establish the coordinate systems of each system and the relationships between the coordinate systems.

[0063] The system coordinate system includes the inertial coordinate system, the body coordinate system, the undeformed wing coordinate system, the deformed wing coordinate system, the non-rotating rotor hub coordinate system, the rotating rotor hub coordinate system, the undeformed rotor blade coordinate system, and the deformed rotor blade coordinate system.

[0064] To facilitate the description of the spatial positions and motion deformations of the wings, nacelles, and rotor blades, a series of reference coordinate systems need to be established. The coordinate systems of each system and the relationships between them are as follows: inertial coordinate system, body coordinate system, undeformed wing coordinate system, deformed wing coordinate system, non-rotating rotor hub coordinate system, rotating rotor hub coordinate system, undeformed rotor blade coordinate system, and deformed rotor blade coordinate system. The wing and rotor hub coordinate systems are shown below. Figure 1 As shown, coordinates {O} are defined on the tilt axis of the undeformed wing. i ,X i Y i Z i}, denoted by the subscript i. The deformed wing coordinate system is {O w X w , Y w Z w The subscript 'w' indicates the deformation angle that differs from the undeformed coordinate system in three directions. The wing tilts forward about its tilt axis. Angle: The tilt angle is defined as 0° in helicopter mode. Rotor hub coordinate system: Defined at the center of the gimbal, as {O... H X H Y H Z H}, denoted by the subscript h. The rotating coordinate system is {O}. r X r Y r Z r The subscript 'r' indicates the azimuth angle Ψ relative to the Kh axis of the propeller hub coordinate system. The subscript 'β' indicates the flapping coordinate system, with the flapping hinge offset relative to the center of the propeller hub. There exists a swing angle β. The oscillation coordinate system is labeled with the subscript ζ, and the offset is... There is a zeta angle of motion. The method for establishing the coordinate systems for deformed and undeformed wings, and the coordinate system transformation relationships, refer to the method for establishing the coordinate systems for deformed and undeformed rotor blades of conventional helicopters. The establishment and coordinate system transformation relationships of other coordinate systems are consistent with those of conventional helicopters.

[0065] Step 2: Establish the aerodynamic model based on the body coordinate system, wing deformation coordinate system, and blade deformation coordinate system.

[0066] Specifically, step 2 includes: establishing an aerodynamic model of the wing based on the wing deformation coordinate system; establishing a blade model based on the blade deformation coordinate system; establishing an aerodynamic model of the rotor based on the blade model and the relationship between the coordinate systems of the hub rotation coordinate system and the blade deformation coordinate system by summing the number of blades; and establishing an aerodynamic model of the fuselage based on the fuselage coordinate system.

[0067] Because the coupling stability, aeroelastic response, and aerodynamic forces of multi-rotor / nacelle / high aspect ratio wing coupled systems are related, different aerodynamic models need to be considered for different dynamic analyses. For rotor aerodynamic calculations, a quasi-steady aerodynamic model, an unsteady aerodynamic model, a dynamic inflow model, and the ONERA model were used. The combined application of these three models can more accurately calculate aerodynamic loads in stability analysis, dynamic response analysis, and transient response analysis. For the aerodynamic calculations of the fuselage, horizontal stabilizer, vertical stabilizer, and tiltrotor wings, a blowing test model was used due to the influence of the rotor downwash.

[0068] Step 3: Establish a dynamic model of a high aspect ratio wing based on the wing deformation coordinate system.

[0069] The multi-rotor tilt-wing, high-aspect-ratio airfoil, considering elastic deformation, is described using a beam model. The wing root is connected to the fuselage via a tilt-hing, and multiple rigid-body nacelles are distributed along its axis. A schematic diagram of the wing is shown below. Figure 2 As shown. The wing chord length is... The half-length is y TW , The offset between the tilt hinge installation position and the wing's elastic axis is given. The wing's motion is a superposition of the bending and torsion of the elastic axis. An wing model is established using the theory of moderately deformable beams, and the virtual deformation energy, virtual kinetic energy, and virtual work done by external forces for a high aspect ratio wing are calculated to derive the dynamic equations for a missile-like wing.

[0070] Specifically, step 3 includes:

[0071] Step 31: Using the formula The virtual deformation energy U of the wing was calculated. w .

[0072] The elastic airfoil model is established using the moderate deformation beam theory, which assumes the airfoil is an anisotropic beam, resulting in moderate deformation and small strain. The model is then based on the stress and strain of the airfoil and the elastic modulus constant of its material. The relationship between these factors can be integrated along the cross-section and span of the wing to obtain the wing's deformation energy. Taking the variational expression for the deformation energy yields the corresponding virtual deformation energy, expressed as:

[0073] (1)

[0074] Step 32: Using the formula The virtual kinetic energy T of the wing was calculated. w .

[0075] The kinetic energy of an airfoil depends on its own velocity, and its expression and corresponding variables are as follows:

[0076] (2)

[0077] Speed ​​at any point on the wing This depends on the derivative of the point's position vector with respect to time in the inertial frame. The wing's x-radius position and the displacement of its cross-section are defined as {x + u, v, w}, where u, v, and w correspond to the radial, chordal, and vertical displacements of the wing cross-section; the third part is the position vector of any point within this cross-section in the deformable wing coordinate system, defined as {0, ..., ... , By deriving the position vector of any point on the wing in the body coordinate system, the velocity of any point on the wing in the body coordinate system is obtained by differentiation. Substituting the velocity expression into the variational expression (2) of the wing kinetic energy above, the virtual kinetic energy of the wing can be obtained.

[0078] Step 33: Using the formula Computer wing external force virtual work W w .

[0079] Compared to the complex and unsteady aerodynamic environment of a rotor, the aerodynamic environment of an airfoil is much simpler. Therefore, a quasi-steady aerodynamic model is used to describe the aerodynamic loads on the airfoil section. The quasi-steady aerodynamic model for the blades adopts the lift line theory, with its aerodynamic point of application at one-quarter chord length. The aerodynamic loads on the airfoil are calculated using the airflow velocity at three-quarter chord length. A schematic diagram of the aerodynamics of the airfoil section is shown below. Figure 2 As shown.

[0080] To calculate the aerodynamic loads on the airfoil section, the relative velocity between the airfoil section and the air must first be obtained. It is caused by the forward flight speed V W The velocity V caused by the elastic motion of the wing b Composition. The velocity vector V at any point on the wing is obtained by differentiating the displacement vector of any point on the wing in the body coordinate system with respect to time. b By combining the forward velocity, the inflow velocity at the wing section in the deformed wing coordinate system can be obtained. Based on the force and moment equations, the aerodynamic forces and moments of the wing can be derived. Then, based on the coordinate system relationships, the virtual work of the wing aerodynamic forces in the undeformed wing coordinate system can be derived, as expressed below:

[0081] (3)

[0082] Step 34: Based on the wing's virtual deformation energy U w wing virtual kinetic energy T w And the virtual work of external force on the wing W w Constructing a dynamic model for a high aspect ratio airfoil

[0083] .

[0084] Derivation of the dynamic equations for an elastic wing. Based on the distribution of the lift rotor and thrust rotor on the wing, and taking into account computational efficiency, the wing is divided into four spatial beam elements. By assembling the wing element matrix using the finite element method, the mass matrix, damping matrix, stiffness matrix, and force vectors of the entire wing can be obtained.

[0085] After discretization, the variational expression for the wing energy is:

[0086] (4)

[0087] in, It is the total degree of freedom vector of the wing. , and These are the mass, damping, and stiffness matrices of the wing, respectively. It is the load vector.

[0088] Step 4: Based on the undeformed coordinate system of the wing, use the formula ,

[0089] Establish a nacelle dynamic model; and extract the nacelle mass matrix. .

[0090] The nacelle and power unit of a multi-rotor tiltrotor aircraft are rigidly connected to a flexible wing, and its configuration is as follows: Figure 4 As shown, multiple rigid nacelles are distributed and installed on the elastic wing structure, which is equivalent to having multiple points of mass and inertia. Ignoring the influence of aerodynamic drag and only considering the influence of kinetic energy, the nacelles only contribute to the mass matrix of the system. To establish the nacelle model, the spatial position vector of any point on the nacelle must first be transformed to the inertial coordinate system. Then, the first derivative with respect to time is taken to obtain the velocity vector. Finally, the virtual kinetic energy of the nacelle is obtained through volume integral.

[0091] Based on the fundamental theory of multibody dynamics, the arbitrary position vector of the distributed nacelle in the undeformed wing coordinate system can be obtained, and the velocity vector can be derived, thus yielding the virtual kinetic energy of the nacelle:

[0092] (5)

[0093] Extracting the nacelle mass matrix:

[0094] (6)

[0095] in, The nacelle's motion degrees of freedom are represented. The structural characteristic parameters of the rigid nacelle in a multi-rotor tiltrotor aircraft are calculated to form a 6×6 mass matrix. Based on the nacelle's distribution on the wing, the nacelle mass matrix is ​​coupled to the total wing mass matrix to analyze the influence of multiple slings on the structural modes of a high aspect ratio wing.

[0096] Step 5: Establish the rotor dynamics model based on the blade deformation coordinate system.

[0097] For the rotor system of a multi-rotor / tilt-wing aircraft, a rotor dynamics model considering the effects of elastic wing motion is established based on Hamilton's variational principle. The blades are constructed using 15-DOF nonlinear moderately deformable beam elements. Considering their elastic motions such as flapping, flaring, torsion, and axial tension, the deformation of the elastic axis at any spanwise section r of the blade is analyzed. This includes four motions: axial displacement u, flaring displacement v, flapping displacement w, and torsional deformation φ, along with their structural and inertial coupling. The virtual deformation energy, virtual kinetic energy, and aerodynamic virtual work of the blades are calculated, and the rotor dynamics equations are derived.

[0098] Step 51: Using the formula Calculate the blade virtual deformation energy U b .

[0099] The derivation process is consistent with that of the virtual deformation energy derivation process of the wing. The theory of moderately deformable beams is used to establish the elastic blade model, assuming the blade is an anisotropic beam, resulting in moderate deformation and small strain. The model is then derived based on the blade's stress, strain, and the elastic modulus constant of its material. The relationship between these factors can be integrated along the blade's cross-section and span to obtain the blade's deformation energy. Taking the variational expression for the deformation energy yields the corresponding virtual deformation energy, expressed as:

[0100] (1)

[0101] Step 52: Using the formula Calculate the virtual kinetic energy T of the blade. b .

[0102] The derivation process is consistent with that of the virtual kinetic energy derivation of the wing. The kinetic energy of the blade depends on the blade's own velocity, and its expression and corresponding variables are as follows:

[0103] (2)

[0104] The speed of any point on the blade It depends on the derivative of the position vector of that point with respect to time in the inertial frame. The blade's x-radius position and the displacement of its profile are defined as {x + u, v, w}, where u, v, and w correspond to the radial, chordal, and vertical displacements of the blade profile; the third part is the position vector of any point within this profile in the deformed blade coordinate system, defined as {0, ... , By deriving the position vector of any point on the blade in the body coordinate system, and taking the derivative with respect to time, the velocity of any point on the blade in the body coordinate system can be obtained. Substituting the velocity expression into the variational expression (2) of the blade kinetic energy above, the blade virtual kinetic energy can be obtained.

[0105] Step 53: Using the formula Calculate the virtual work W of the propeller blade aerodynamics. b .

[0106] Based on the establishment of the aerodynamic model in the second step, for rotor aerodynamic calculations, quasi-steady aerodynamic models, unsteady aerodynamic models, dynamic inflow models, or the ONERA model are used to establish the aerodynamic forces on the blades. Then, by multiplying the aerodynamic loads of each blade section by the virtual displacement of that section and integrating along the entire blade, the aerodynamic virtual work of the blade can be obtained. The expression for the aerodynamic virtual work on a single blade is:

[0107] (7)

[0108] Step 54: Using the blade dynamics equations

[0109] Construct a rotor dynamics model.

[0110] After discretizing the blade using the finite element method, its dimensionless energy expression is as follows:

[0111] (8)

[0112] Substituting the expressions for virtual deformation energy, virtual kinetic energy, and virtual work done by external forces into the above equation yields the discretized aeroelastic motion equations for the propeller blades.

[0113] The blade is divided into several medium-deformation beam elements, each containing 15 degrees of freedom, such as... Figure 5 As shown. Each element has 2 external nodes and 3 internal nodes. Each external node contains 6 degrees of freedom, as follows: , , , , , The internal nodes have only one degree of freedom, with the central node of the element having the torsional degree of freedom and the nodes at the trisection points of the element having the axial deformation degree of freedom.

[0114] For the i-th beam element, using shape function interpolation, any point inside it... The elastic deformation can be expressed as:

[0115] (9)

[0116] in, , It is the unit length. It is the shape function of the unit's swinging and pendulum bending degrees of freedom. and It is a shape function for axial tension and torsional degrees of freedom. The total degrees of freedom column vector for a single unit:

[0117] (10)

[0118] Will Written as a matrix expression:

[0119] (11)

[0120] in, , and The mass, damping, and stiffness matrices of the i-th element are given in sequence, and all are linear matrices. It is the corresponding load vector, including both linear and nonlinear components.

[0121] Assuming the blade is divided into five elements, the degrees of freedom of a single blade are numbered as follows: Figure 6 As shown. The entire blade has 51 degrees of freedom. After discretization, the variational expression for the blade energy is:

[0122] (12)

[0123] Depending on the different root connection forms of the blades, the boundary conditions of equation (12) also vary. Based on the discretized energy expression, by setting the corresponding boundary conditions, the aeroelastic differential equation of a single blade can be obtained:

[0124] (13)

[0125] For N b Summing the values ​​of each blade yields the dynamic equations of a rotor.

[0126] Step 6: Based on the dynamic models of the high aspect ratio wing, nacelle, and rotor, establish the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system. .

[0127] After establishing the dynamic equations of the elastic wing, the nacelle kinetic energy equation, and the rotor blade dynamic equation, the dynamic matrix equation of the half-span multi-blade / high aspect ratio wing coupled system can be obtained according to the Hamiltonian energy principle.

[0128] rotor system , , , Matrix and nacelle and flexible wings , , , By combining the matrices, a rotor / nacelle / wing coupled system model can be obtained. , , , The matrix assembly method involves expanding the matrix dimension according to the number of degrees of freedom and superimposing the matrix elements corresponding to the same node degrees of freedom to obtain the mass matrix, damping matrix, and stiffness matrix of the entire model. The same method is used for the force vectors, assembling the force vectors of the rotor system and the wing force vectors according to their corresponding degrees of freedom to obtain the force vectors of the rotor / wing coupling system of the half-width model.

[0129] The dynamic equations of the half-span multi-rotor / high aspect ratio wing coupled system model are expressed in matrix form as follows:

[0130] (14)

[0131] Among them, degrees of freedom As shown below:

[0132] (15)

[0133] In the above formula, the subscripts n and m represent the number of discrete units of the wing and the blade, respectively.

[0134] The coupled dynamic equations are transformed into state equations. The eigenvalue method is then used to solve for the eigenvalues ​​of the state equations. The real part of the eigenvalue represents the system's damping, and the imaginary part represents the system's frequency. The stability of the coupled system can be determined based on the real part of the eigenvalues.

[0135] In summary, this application provides a multi-system coupled dynamics modeling method for multi-rotor / tilt-wing rotorcraft, belonging to helicopter dynamics modeling and analysis technology. Considering the characteristics of multi-rotor / tilt-wing rotorcraft dynamics problems, the motion of the rotor, wing, and nacelle is first described in different coordinate systems. Structural dynamics finite element models of isolated rotor blades, elastic wings, and nacelles are established separately, and quasi-steady or unsteady aerodynamic models are used for aerodynamic modeling. Based on the theory of moderately deformable beams and quasi-steady / unsteady aerodynamic models, the dynamic equations of the rotor blades, nacelle kinetic energy, and elastic wings are established using the Hamiltonian variational principle. The equations are spatially discretized using the finite element method. The matrix dimension is expanded according to the number of degrees of freedom, and the matrix elements corresponding to the same nodal degrees of freedom are superimposed to obtain the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system. Finally, the eigenvalues ​​are solved using the eigenvalue method, and the stability of the coupled system is determined by the eigenvalue solutions. This modeling method can be applied to fundamental dynamic research such as modal analysis, stability analysis, and aeroelastic response analysis of coupled systems of multi-rotor / tilt rotorcraft. It can also be directly extended to the aeroelastic coupling stability design and analysis of various advanced rotorcraft, tiltrotor aircraft, and distributed high-speed rotorcraft.

Claims

1. A multi-system coupled dynamics modeling method for a multi-rotor tilt-wing rotorcraft, characterized in that, The method includes: Step 1: Establish the coordinate systems for each system and the relationships between the coordinate systems; Step 2: Establish the aerodynamic model based on the body coordinate system, wing deformation coordinate system, and blade deformation coordinate system; Step 3: Establish a dynamic model of the high aspect ratio wing based on the wing deformation coordinate system; Step 4: Establish the nacelle dynamic model based on the undeformed wing coordinate system; Step 5: Establish the rotor dynamics model based on the blade deformation coordinate system; Step 6: Based on the dynamic models of the high aspect ratio wing, nacelle, and rotor, establish the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system; Step 6 includes: establishing the dynamic equations of the multi-rotor / nacelle / high aspect ratio wing coupled system based on the dynamic models of the high aspect ratio wing, nacelle, and rotor. ,in The total number of degrees of freedom of the system. , , , These are the system's total mass matrix, damping matrix, stiffness matrix, and force matrix, respectively.

2. The method according to claim 1, characterized in that, Step 1 specifically includes: Establish an inertial coordinate system, a body coordinate system, an undeformed wing coordinate system, a deformed wing coordinate system, a non-rotating rotor hub coordinate system, a rotating rotor hub coordinate system, an undeformed rotor blade coordinate system, and a deformed rotor blade coordinate system, as well as the relationships between these coordinate systems.

3. The method according to claim 2, characterized in that, Step 3 includes: Step 31: Using the formula The virtual deformation energy U of the wing was calculated. W Where A is the wing cross-sectional area and L is the wing span. For axial stress, and For engineering shear stress, For axial strain, and For engineering shear strain; Step 32: Using the formula The virtual kinetic energy T of the wing was calculated. w ,in For the wing mass density, Let be the velocity at any point on the wing; Step 33: Using the formula Computer wing external force virtual work W w ,in, , , For external force loads along the undeformed elastic axis of the wing, This is the torque along the undeformed elastic axis of the wing; Step 34: Based on the wing's virtual deformation energy U w wing virtual kinetic energy T w And the virtual work of external force on the wing W w Constructing a dynamic model for a high aspect ratio airfoil ,in This refers to the total number of wing units. Let be the column vector of the total degrees of freedom of the wing. , , , These are the wing's total mass matrix, damping matrix, stiffness matrix, and force matrix, respectively.

4. The method according to claim 3, characterized in that, Step 5 includes: Step 51: Using the formula Calculate the blade virtual deformation energy U b Where R is the blade radius and B is the blade cross-sectional area; Step 52: Using the formula Calculate the virtual kinetic energy T of the blade. b ,in The mass density of the blade, Let be the velocity of any point on the blade; Step 53: Using the formula Calculate the virtual work W of the propeller blade aerodynamics. b ,in, , These are the external force loads along the lateral and vertical directions of the undeformed elastic axis of the blade, respectively. This is the torque along the undeformed elastic axis of the blade; Step 54: Using the blade dynamics equations Construct a rotor dynamics model, where N b This represents the total number of blade units. Let the column vector of blade degrees of freedom be denoted as . , , , These are the total mass matrix, damping matrix, stiffness matrix, and force matrix of the blade, respectively.

5. The method according to claim 1, characterized in that, Step 4 includes: Based on the undeformed coordinate system of the wing, using the formula A nacelle dynamic model was established; and the nacelle mass matrix was extracted. ,in, Indicates the nacelle volume density. S Indicates the volume of the nacelle. This represents the velocity at any point on the nacelle. Indicates the degrees of freedom of the nacelle's motion. This represents the nacelle mass matrix.

6. The method according to claim 2, characterized in that, Step 2 includes: Based on the wing deformation coordinate system, establish the aerodynamic model of the wing; Based on the body coordinate system, establish the aerodynamic model of the body.

7. The method according to claim 2, characterized in that, Step 2 includes: Based on the blade deformation coordinate system, a blade model is established; then, based on the blade model and the relationship between the hub rotation coordinate system and the blade deformation coordinate system, the aerodynamic model of the rotor is established by summing the number of blades.

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