High-precision prediction method for aeroelastic vibration load of rotor blade with trailing edge winglet

Abstract

The invention discloses a high-precision prediction method for the aeroelastic vibration load of a rotor blade with a trailing edge winglet, and belongs to the field of helicopter rotor aeroelastic dynamics. According to the method, the influence of a trailing edge winglet inertia load generated by trailing edge winglet high-frequency motion and a complex blade section shape change generated by trailing edge winglet high-frequency motion on a rotor blade section unsteady aerodynamic load and a rotor time-varying wake is accurately calculated; and high-precision prediction of the aeroelastic vibration load of the rotor blade with the trailing edge winglet is realized. The high-precision prediction method for the aeroelastic vibration load of the rotor blade with the trailing edge winglet is suitable for the rotor blade which is in an unsteady incoming flow and has any movement and deformation, any section shape and any material distribution characteristic; the anisotropy of the composite material and the influence of non-classical effects such as transverse shear deformation, section warping and elastic coupling caused by the anisotropy of the composite material can be accurately calculated, and the method has good engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of helicopter rotor aeroelastic dynamics, specifically referring to a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing edge winglets. Background Technology

[0002] Rotor blades with trailing-edge winglets control the deflection of winglets mounted on the outer trailing edge of the blade, altering the distribution of aerodynamic loads and aeroelastic responses along the azimuth and span, thereby suppressing rotor aeroelastic vibration loads. The active control system for trailing-edge winglets is small in size and consumes relatively little power, allowing it to be fully integrated within the blade to avoid generating additional aerodynamic drag. Its engineering implementation is relatively simple and highly feasible. Furthermore, adding winglets to the trailing edge of the rotor blade does not affect the helicopter's control system, including the automatic swashplate, ensuring high safety. Related experiments conducted both domestically and internationally have demonstrated the value and application prospects of rotor blades with trailing-edge winglets in helicopter vibration control. However, accurately predicting the aeroelastic vibration loads, especially their higher-order components, of rotor blades with trailing-edge winglets is extremely complex and difficult. On the one hand, although the trailing-edge winglet is small in size, its distance from the rotor hub center means that the additional mass it brings contributes significantly to the rotor root moment. Therefore, the influence of the trailing-edge winglet's inertial load generated by its high-frequency motion on the dynamic characteristics of the rotor blade with trailing-edge winglet structure must be considered. On the other hand, the complex blade profile geometry changes generated by the high-frequency motion of the trailing-edge winglet significantly affect the unsteady aerodynamic loads and time-varying wake of the rotor blade with trailing-edge winglet. This aeroelastic coupling makes the influence of the high-frequency motion of the trailing-edge winglet on the aeroelastic vibration load of the rotor blade with trailing-edge winglet more complex and difficult to predict accurately. To date, an accurate and efficient method for predicting the aeroelastic vibration load of rotor blades with trailing-edge winglets is still lacking. Summary of the Invention

[0003] To address the shortcomings of the existing technology, the present invention aims to provide a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing edge winglets, laying a solid foundation for the design and application of active control systems for rotor blades with trailing edge winglets.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] The present invention provides a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing edge winglets, comprising the following steps:

[0006] S1. Accurately incorporate the inertial load of the trailing edge winglet generated by the high-frequency motion of the trailing edge winglet, and simultaneously consider the geometric nonlinearity of the large deformation of the blade, the transverse shear deformation caused by the anisotropy of the composite material, the non-classical effects of section warping and elastic coupling, and the arbitrary section shape and material distribution characteristics of the blade, to establish a geometrically accurate structural model of the rotor blade with trailing edge winglet. The structural model includes the analysis of the two-dimensional section characteristics of the rotor blade with trailing edge winglet and the establishment of the one-dimensional geometrically accurate nonlinear motion equation.

[0007] S2. Considering the complex airfoil profile shape changes caused by unsteady incoming flow, arbitrary airfoil motion, and active control of trailing edge winglets, based on potential flow theory, and utilizing the impenetrability condition of the airfoil surface and the Runge-Kutta condition of the airfoil trailing edge, a two-dimensional unsteady aerodynamic load calculation model of rotor blades with trailing edge winglets is established. Taking into account the influence of trailing edge winglets on the distribution of attached vortex rings and time-varying wake of rotor blades, and utilizing the impenetrability condition of the blade surface and the far wake control equation, a time-varying free wake model of rotor blades with trailing edge winglets is established.

[0008] S3. The two-dimensional profile unsteady aerodynamic load model and the time-varying free wake model are introduced into the established geometrically accurate structural model of the rotor blade with trailing edge winglet. The coupled trim algorithm is used to establish the geometrically accurate aeroelastic model of the rotor blade with trailing edge winglet. Finally, the geometrically accurate aeroelastic equation set of the rotor blade with trailing edge winglet is obtained. The geometrically accurate aeroelastic equation set of the rotor blade with trailing edge winglet includes one-dimensional geometrically accurate nonlinear motion equations, attachment circulation equations, far wake control equations and trim equations.

[0009] S4. The partial differential geometric exact aeroelastic equations of the rotor blade with trailing edge winglet in the spatial and time domains are discretized using the finite element method to obtain the ordinary differential geometric exact aeroelastic equations of the rotor blade with trailing edge winglet in the time domain. The ordinary differential geometric exact aeroelastic equations of the time domain are integrated by step integration using the Newmark numerical integration method and the Newton-Raphson method to obtain the periodically changing steady-state convergent solution, that is, the steady-state aeroelastic response of the rotor blade with trailing edge winglet. The root loads of each blade obtained by solving the steady-state aeroelastic response are summed to obtain the hub vibration load of the rotor blade with trailing edge winglet. The hub vibration load is Fourier expanded to obtain the harmonic components of the hub vibration load of the rotor blade with trailing edge winglet.

[0010] Furthermore, S1 includes:

[0011] S11. Based on the three-dimensional deformation of a rotor blade with trailing edge winglets, without making assumptions about deformation and rotation angle, a method is established to describe the blade from an undeformed state to a deformed state.

[0012] Including the displacement of the blade reference axis, the rotation of the reference section, and the three-dimensional warping of any point within the reference section, based on the relationship between one-dimensional generalized strain and blade three-dimensional deformation, the deformation gradient tensor of any point within the blade section of the rotor with trailing edge winglet is derived. The three-dimensional strain of any point within the blade section of the rotor with trailing edge winglet is obtained by decomposing the deformation gradient tensor using the rotation tensor decomposition method.

[0013] S12. For a rotor blade with trailing edge winglets that has arbitrary cross-sectional shape and arbitrary material distribution characteristics, the Patran software is used to sequentially establish the geometric model, generate the finite element mesh and assign material properties to the blade cross-section according to its cross-sectional structural dimensions and material property parameters, so as to obtain the node, element and element property information of the rotor blade cross-section with trailing edge winglets. Then, combined with the three-dimensional strain at any point in the blade cross-section, the strain energy of the discrete type of the rotor blade cross-section with trailing edge winglets is obtained.

[0014] S13. The variational asymptotic method is used to analyze the strain energy of the discrete type of the blade profile. By minimizing the variation of the strain energy of the discrete type of the blade profile under specified constraints, the three-dimensional warping, generalized Timoshenko strain energy and corresponding profile stiffness characteristic matrix of any point of the rotor blade profile with trailing edge winglet are determined.

[0015] The same numerical integration method along the profile is used to determine the mass characteristic matrix of the blade profile;

[0016] S14. Establish a geometrically accurate description method for the velocity at any point on the blade section and the trailing edge winglet section of a rotor blade with trailing edge winglet, accurately take into account the trailing edge winglet inertial load generated by the high-frequency motion of the trailing edge winglet, and derive the kinetic energy per unit length of blade.

[0017] By introducing virtual displacement and virtual rotation, the variational values ​​of strain energy and kinetic energy per unit length of blade, as well as the virtual work done by external load, are derived. Substituting the variational values ​​of strain energy and kinetic energy per unit length of blade, and the virtual work done by externally distributed forces and torques on the blade per unit length of blade, into the generalized Hamiltonian principle, the one-dimensional geometrically accurate nonlinear equation of motion for a rotor blade with trailing edge winglets is obtained.

[0018] Furthermore, S2 specifically refers to:

[0019] S21. Considering the complex airfoil profile changes caused by unsteady incoming flow, arbitrary airfoil motion, and active control of trailing edge winglets, establish the relationship between the induced velocity caused by the attachment circulation and wake circulation and the airfoil motion and deformation based on the impenetrable boundary conditions of the airfoil surface; establish the relationship between the pressure difference between the upper and lower airfoil surfaces and the attachment circulation based on the vorticity equation.

[0020] Based on the condition that the wake is not subject to force, establish the relationship between the induced velocity caused by the wake circulation and the total attached circulation.

[0021] Based on the relationship between the pressure difference between the upper and lower wing surfaces and the amount of attached circulation, as well as the relationship between the induced velocity caused by the wake circulation and the total amount of attached circulation, the two-dimensional unsteady aerodynamic load of the rotor blade with trailing edge winglet is derived.

[0022] S22. A lifting surface model is used to simulate a rotor blade with trailing edge winglets. The lifting surface coincides with the mid-arc surface of the blade, and the attached vortices on the lifting surface are represented by quadrilateral vortex lattices. The wake of the rotor blade with trailing edge winglets is divided into two parts: a near wake and a far wake. The vortex plates of the near wake are represented by quadrilateral vortex lattices and are kept in the tangential plane of the trailing edge of the mid-arc surface of the blade. The tip vortex of the far wake is represented by a single vortex filament. At the same time, the wake trailed out from the tip of the trailing edge winglet is introduced to account for the influence of the trailing edge winglet on the distribution of attached vortex annulus and the time-varying wake of the rotor blade.

[0023] S23. Calculate the circulation of the attached vortex grid on the curved surface of the rotor blade using the condition that the object surface is impenetrable; determine the shape of the tip vortex wake by solving the control equation of the tip vortex wake; determine the shape of the trailing edge winglet tip vortex wake by solving the control equation of the trailing edge winglet tip vortex wake; determine the final convergent solution by iterative calculation of the attached vortex circulation and the shapes of the tip vortex and trailing edge winglet tip vortex wake, and obtain the distribution of the induced velocity of the rotor blade with trailing edge winglet along the blade azimuth and blade span.

[0024] Furthermore, S3 includes:

[0025] S31. Under the specified rotor shaft tilt angle and advance ratio, the Auto-pilot trim algorithm is used to establish a set of second-order differential equations about the control quantities for trim calculation, and to determine the rotor blade collective pitch control and longitudinal and lateral cyclic pitch control that match the specified trim target quantity.

[0026] S32. Using the kinematic parameters of the geometrically accurate structural model of the rotor blade with trailing edge winglet, the descriptions of the geometrically accurate structural model of the rotor blade with trailing edge winglet, the unsteady aerodynamic load model, the free wake model and the trim algorithm are unified. The models are coupled together by the deformation, control, induced velocity and aerodynamic load of the blade to establish a geometrically accurate aeroelastic model of the rotor blade with trailing edge winglet.

[0027] The final established geometrically accurate aeroelastic equation set for rotor blades with trailing edge winglets includes one-dimensional geometrically accurate nonlinear motion equations, Auto-pilot trim equations, attachment circulation equations, blade tip vortex wake control equations, and trailing edge winglet tip vortex wake control equations.

[0028] Furthermore, the trim target quantities include the thrust coefficient, roll moment coefficient, or lateral tip plane tilt angle, and pitch moment coefficient or longitudinal tip plane tilt angle.

[0029] Furthermore, S4 includes:

[0030] S41. Establish an aeroelastic response solution module for rotor blades with trailing edge winglets. Solve the system of equations consisting of one-dimensional geometrically accurate nonlinear motion equations and Auto-pilot balancing equations, which are characterized by strongly nonlinear second-order partial differential equations with periodic coefficient matrices. First, perform finite element space discretization to obtain a system of strongly nonlinear second-order ordinary differential equations with periodic coefficient matrices that are only related to time. Then, use the Newmark numerical integration method and the Newton-Raphson method to perform step integration on the time-domain ordinary differential geometrically accurate aeroelastic equations to obtain a periodically changing steady-state convergent solution, i.e., the steady-state aeroelastic response of the rotor blade with trailing edge winglets. Extract the absolute velocity at the blade control point within one rotation cycle from the obtained blade aeroelastic response and pass it to the free wake solution module for rotor blades with trailing edge winglets.

[0031] S42. Through external circulation iteration and internal wake geometry iteration, determine the final converged attached vortex circulation and the wake shapes of the blade tip vortex and trailing edge winglet tip vortex, and obtain an attached vortex circulation distribution and wake shape corresponding to the absolute velocity of the blade; calculate the distribution of blade induced velocity along the blade azimuth and blade span during one rotation cycle, and pass it to the aeroelastic response solution module of the rotor blade with trailing edge winglet.

[0032] S43. The aeroelastic response solution module and the free wake solution module of the rotor blade with trailing edge winglet exchange blade motion and induced velocity information and iterate repeatedly to obtain the final converged solution, that is, the aeroelastic response and induced velocity distribution of the rotor blade with trailing edge winglet that converge simultaneously; by summing the root loads of each blade obtained from the aeroelastic response solution, the hub vibration load of the rotor blade with trailing edge winglet is obtained; the obtained hub vibration load is subjected to Fourier expansion to obtain the harmonic components of the hub vibration load of the rotor blade with trailing edge winglet.

[0033] Furthermore, in the process of solving a system of equations consisting of one-dimensional geometrically accurate nonlinear motion equations and Auto-pilot balancing equations, which are characterized by strongly nonlinear second-order partial differential equations with periodic coefficient matrices, the induced velocity distribution is provided by the free wake solving module and remains unchanged during the solution process.

[0034] The beneficial effects of this invention are:

[0035] This invention establishes a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing-edge winglets. By accurately incorporating the inertial load of the trailing-edge winglet generated by its high-frequency motion and precisely handling the influence of complex blade profile changes caused by the high-frequency motion of the trailing-edge winglet on the unsteady aerodynamic loads of the rotor blade profile and the time-varying wake of the rotor, this method provides an accurate and efficient calculation method for predicting aeroelastic vibration loads on rotor blades with trailing-edge winglets. Simultaneously, this method can also accurately calculate the influence of composite material anisotropy and its resulting non-classical effects such as lateral shear deformation, profile warping, and elastic coupling. Through the synergistic design of aeroelastic tailoring of rotor blades with trailing-edge winglets and high-frequency motion of the trailing-edge winglets, the vibration reduction capability of the trailing-edge winglets is further improved. Attached Figure Description

[0036] Figure 1 This is a system block diagram of a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing edge winglets according to the present invention.

[0037] Figure 2 A comparison of the calculation results of the rotor hub vibration load under uncontrolled stationary and controlled motion of the trailing edge winglet of a rotor blade with trailing edge winglet;

[0038] Figure 3 A comparison of the calculation results of the rotor hub vibration load under uncontrolled stationary and controlled motion of the trailing edge winglet of the rotor blade with uncoupled flapping / torsional trailing edge winglet.

[0039] Figure 4 A comparison of the calculation results of the rotor hub vibration load under uncontrolled stationary and controlled motion of the trailing edge winglet of the rotor blade with flapping / torsional positive coupling.

[0040] Figure 5 A comparison of the calculated results of the rotor hub vibration load under uncontrolled stationary and controlled motion of the trailing edge winglet of the rotor blade with a flapping / torsional negative coupling zone. Detailed Implementation

[0041] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0042] Reference Figure 1 As shown, the present invention provides a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing edge winglets, comprising the following steps:

[0043] S1. Accurately incorporating the trailing-edge winglet inertial load generated by high-frequency motion, the large deformation geometric nonlinearity of the blade, the lateral shear deformation caused by the anisotropy of composite materials, non-classical effects such as section warping and elastic coupling, and arbitrary blade section shapes and material distribution characteristics, a geometrically accurate structural model of a rotor blade with a trailing-edge winglet is established. This includes methods for calculating the two-dimensional section characteristics of the rotor blade with a trailing-edge winglet and establishing one-dimensional geometrically accurate nonlinear motion equations. The specific implementation is as follows:

[0044] S11. Starting from the three-dimensional deformation of the rotor blade with trailing edge winglet, without making any assumptions about deformation and rotation, a method is established to describe the blade from an undeformed state to a deformed state, including the displacement of the blade reference axis, the rotation of the reference section, and the three-dimensional warping at any point within the reference section. Based on the relationship between one-dimensional generalized strain and the three-dimensional deformation of the blade, the deformation gradient tensor at any point within the section of the rotor blade with trailing edge winglet is derived. The three-dimensional strain at any point within the section of the rotor blade with trailing edge winglet is obtained by decomposing the deformation gradient tensor using the rotational tensor decomposition method.

[0045] S12. For a rotor blade with a trailing-edge winglet and arbitrary cross-sectional shape and material distribution characteristics, the geometric model of the blade cross-section is established, material properties are defined, and finite element discretization is performed using Patran software based on its cross-sectional structural dimensions and material property parameters. This yields the node, element, and element attribute information of the rotor blade cross-section with trailing-edge winglet. Based on the obtained node, element, and element attribute information of the blade cross-section and the three-dimensional strain at any point within the blade cross-section, the strain energy of the discretized form of the rotor blade cross-section with trailing-edge winglet is obtained.

[0046] S13. The variational asymptotic method is used to analyze the strain energy of the discrete form of the blade profile. By minimizing the variation of the discrete strain energy of the blade profile under specified constraints, the three-dimensional warpage, generalized Timoshenko strain energy, and corresponding profile stiffness characteristic matrix at any point on the rotor blade profile with trailing edge winglet are determined. The same numerical integration method along the profile is used to determine the mass characteristic matrix of the blade profile. The generalized Timoshenko strain energy and its corresponding constitutive equation can be expressed as follows:

[0047]

[0048]

[0049] In equations (1) and (2), matrix S represents the stiffness characteristic matrix of the blade profile, reflecting the influence of composite material anisotropy and its resulting non-classical effects such as transverse shear deformation, profile warping, and elastic coupling. Subscript 1 indicates tension, 2 and 3 indicate shear, 4 indicates torsion, and 5 and 6 indicate bending. The diagonal element S... ii(i = 1, 2, 3, 4, 5, 6) represent the tensile stiffness coefficient, the shear stiffness coefficients in both directions, the torsional stiffness coefficients, and the bending stiffness coefficients in both directions, respectively. Off-diagonal element S ij (i,j=1,2,3,4,5,6,i≠j) represents the corresponding coupling stiffness coefficient. For example, S 14 S represents the tensile / torsional coupling stiffness coefficient. 45 This represents the torsional / bending coupling stiffness coefficient.

[0050] The mass characteristic matrix M of the blade profile can be represented as:

[0051]

[0052] In the formula, μ represents the mass per unit length, and x m2 x m3 Indicates the location of the centroid of the cross section, i 22 i 33 Let i represent the moment of inertia of mass about the two coordinate axes of the cross section. 23 This represents the product of inertia of a cross section.

[0053] S14. Establish a geometrically precise method for describing the velocity at any point on the blade section and the trailing edge winglet section of a rotor blade with a trailing edge winglet. Accurately account for the inertial load of the trailing edge winglet generated by its high-frequency motion, and derive the kinetic energy per unit length of blade. Introduce virtual displacement and virtual rotation to derive the variational values ​​of strain energy and kinetic energy per unit length of blade, as well as the virtual work done by the externally distributed forces and torques on the blade. Substitute the obtained variational values ​​of strain energy and kinetic energy per unit length of blade, and the virtual work done by the externally distributed forces and torques on the blade, into the generalized Hamiltonian principle to obtain the one-dimensional geometrically precise nonlinear equation of motion for the rotor blade with a trailing edge winglet. According to the generalized Hamiltonian principle, the equation of motion for the rotor blade with a trailing edge winglet can be expressed as:

[0054]

[0055] In the formula, T and U represent the kinetic energy and strain energy per unit length of the blade, respectively. This represents the virtual work done by the externally distributed force and externally distributed torque on a unit length blade. In the process of deriving the one-dimensional geometrically precise nonlinear motion equation of the rotor blade with trailing edge winglet using equation (4), no assumptions are made about deformation and rotation angle. The influence of the trailing edge winglet inertial load generated by the high-frequency motion of the trailing edge winglet is accurately included in the form of additional kinetic energy. The two-dimensional unsteady aerodynamic load of the rotor blade with trailing edge winglet, which accurately handles the influence of the complex airfoil profile shape change generated by the active control of the trailing edge winglet, is substituted into equation (4) as the externally distributed force and externally distributed torque.

[0056] S2. Considering the complex airfoil profile changes caused by unsteady incoming flow, arbitrary airfoil motion, and active control of the trailing-edge winglet, based on potential flow theory, and utilizing the impenetrability condition of the airfoil surface and the Runge-Kutta condition of the airfoil trailing edge, a two-dimensional unsteady aerodynamic load calculation method for a rotor blade with a trailing-edge winglet is established. Taking into account the influence of the trailing-edge winglet on the distribution of attached vortex rings and the time-varying wake of the rotor blade, and utilizing the impenetrability condition of the blade surface and the far-wake control equation, a time-varying free wake model of a rotor blade with a trailing-edge winglet is established. The specific implementation is as follows:

[0057] S21. Considering the complex airfoil profile changes caused by unsteady incoming flow, arbitrary airfoil motion, and active control of the trailing edge winglet, establish the relationship between the induced velocity caused by the attachment circulation and wake circulation and the airfoil motion and deformation based on the impenetrable boundary conditions of the airfoil surface. Establish the relationship between the pressure difference between the upper and lower airfoil surfaces and the attachment circulation based on the vorticity equation. Establish the relationship between the induced velocity caused by the wake circulation and the total attachment circulation based on the wake-free condition. Combine these relationships to derive the two-dimensional unsteady aerodynamic loads on the rotor blade with trailing edge winglet.

[0058] S22. A lifting surface model is used to simulate a rotor blade with trailing edge winglets. The lifting surface coincides with the mid-curvature surface of the blade, and the attached vortices on the lifting surface are represented by quadrilateral vortex lattices. The wake of the rotor blade with trailing edge winglets is divided into two parts: a near wake and a far wake. The vortex plates of the near wake are represented by quadrilateral vortex lattices and are kept in the tangential plane of the trailing edge of the mid-curvature surface of the blade. The tip vortex of the far wake is represented by a single vortex filament. At the same time, the wake trailing from the winglet tip is introduced to account for the influence of the trailing edge winglet on the distribution of attached vortex annulus and the time-varying wake of the rotor blade.

[0059] S23. Calculate the circulation of the attached vortex grid on the curved surface of the rotor blade using the condition that the surface is impenetrable. Determine the shape of the tip vortex wake by solving the control equations for the tip vortex wake. Determine the shape of the trailing-edge winglet tip vortex wake by solving the control equations for the trailing-edge winglet tip vortex wake. Determine the final convergent solution through iterative calculations of the attached vortex circulation and the shapes of the tip vortex and trailing-edge winglet tip vortex wakes, obtaining the distribution of the induced velocity of the rotor blade with trailing-edge winglet along the blade azimuth and span.

[0060] S3. The established two-dimensional profile unsteady aerodynamic load model and time-varying free wake model of the rotor blade with trailing edge winglet are introduced into the established geometrically accurate structural model of the rotor blade with trailing edge winglet, and a trim algorithm is coupled to establish a geometrically accurate aeroelastic model of the rotor blade with trailing edge winglet. Finally, a geometrically accurate aeroelastic equation set for the rotor blade with trailing edge winglet, including one-dimensional geometrically accurate nonlinear motion equations, attachment circulation equations, far wake control equations, and trim equations, is obtained. The specific implementation is as follows:

[0061] S31. Under the specified rotor shaft tilt angle and advance ratio, the Auto-pilot trim algorithm is used to establish a set of second-order differential equations about the control variables for trim calculation, and to determine the rotor blade collective pitch control and longitudinal and lateral cyclic pitch control that match the specified thrust coefficient, roll moment coefficient (or lateral tip plane tilt angle) and pitch moment coefficient (or longitudinal tip plane tilt angle).

[0062] S32. Using the kinematic parameters of the geometrically accurate structural model of the rotor blade with trailing edge winglet, the descriptions of the geometrically accurate structural model, unsteady aerodynamic load model, free wake model, and trim algorithm of the rotor blade with trailing edge winglet are unified. By coupling the various models through blade deformation, control, induced velocity, and aerodynamic load, a geometrically accurate aeroelastic model of the rotor blade with trailing edge winglet is established. The final geometrically accurate aeroelastic equation set of the rotor blade with trailing edge winglet consists of one-dimensional geometrically accurate nonlinear motion equations, Auto-pilot trim equations, attachment circulation equations, tip vortex wake control equations, and trailing edge winglet tip vortex wake control equations. It is a set of strongly nonlinear second-order partial differential equations with periodic coefficient matrices.

[0063] S4. The partial differential geometric exact aeroelastic equations for the rotor blade with trailing edge small blade in both the spatial and time domains are discretized using the finite element method to obtain the ordinary differential geometric exact aeroelastic equations for the rotor blade with trailing edge small blade in the time domain. The Newmark numerical integration method and the Newton-Raphson method are used to perform step integration on the ordinary differential geometric exact aeroelastic equations for the time domain to obtain the periodically varying steady-state convergent solution, i.e., the steady-state aeroelastic response of the rotor blade with trailing edge small blade. By summing the root loads of each blade obtained from the aeroelastic solution, the hub vibration load of the rotor blade with trailing edge small blade is obtained. The Fourier expansion of the obtained hub vibration load yields the harmonic components of the hub vibration load of the rotor blade with trailing edge small blade. The specific implementation is as follows:

[0064] S41. A module for solving the aeroelastic response of a rotor blade with a trailing edge winglet is established. The system of equations, consisting of one-dimensional geometrically accurate nonlinear equations and Auto-pilot balancing equations, exhibiting characteristics of strongly nonlinear second-order partial differential equations with periodic coefficient matrices, is first discretized in finite element space to obtain a system of strongly nonlinear second-order ordinary differential equations with periodic coefficient matrices that are only related to time. Then, the Newmark numerical integration method and the Newton-Raphson method are used to perform step integration on the time-domain ordinary differential geometrically accurate aeroelastic equations to obtain a periodically varying steady-state convergent solution, i.e., the steady-state aeroelastic response of the rotor blade with a trailing edge winglet. The induced velocity distribution in the above solution process is provided by the free wake solution module and remains unchanged during the solution process. The absolute velocity at the blade control point within one rotation cycle is extracted from the obtained blade aeroelastic response and passed to the free wake solution module for the rotor blade with a trailing edge winglet.

[0065] S42. Establish a free wake solution module for rotor blades with trailing edge winglets, receiving the absolute velocity at the blade control point within one rotation cycle from the aeroelastic response solution module for rotor blades with trailing edge winglets. Through external circulation iteration (solving the attached circulation linear equations) and internal wake geometry iteration (solving the control equations for the tip vortex wake and the trailing edge winglet tip vortex wake using the PIPC method), determine the final converged attached vortex circulation and the wake shapes of the tip vortex and trailing edge winglet tip vortex, obtaining a wake periodic steady-state solution corresponding to the transmitted absolute blade velocity. Calculate the distribution of blade-induced velocity along the blade azimuth and spanwise direction within one rotation cycle and transmit it to the aeroelastic response solution module for rotor blades with trailing edge winglets.

[0066] S43. The aeroelastic response solution module and the free wake solution module for the rotor blades with trailing edge winglets exchange blade motion and induced velocity information and iteratively solve the problem to determine the final convergent solution, which is the simultaneously convergent aeroelastic response and induced velocity distribution of the rotor blades with trailing edge winglets. By summing the root loads of each blade obtained from the aeroelastic response solution, the hub vibration load of the rotor blades with trailing edge winglets is obtained. The Fourier expansion of the obtained hub vibration load yields the harmonic components of the hub vibration load of the rotor blades with trailing edge winglets.

[0067] This invention provides a high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing edge winglets, offering an accurate and efficient calculation method for predicting aeroelastic vibration loads on rotor blades with trailing edge winglets. Furthermore, the method of this invention can further improve the vibration reduction capability of the trailing edge winglets through the coordinated design of aeroelastic trimming of rotor blades with trailing edge winglets and high-frequency motion of the trailing edge winglets. Figure 2The calculation results of the rotor hub vibration load under uncontrolled stationary and controlled motion of the trailing edge winglet of the rotor blade with trailing edge winglet are presented. As can be seen from the figure, the calculation results of the method of the present invention show a significant reduction in rotor hub vibration load under the controlled motion state of the trailing edge winglet. Figures 3 to 5 The calculation results of rotor hub vibration load under uncoupled flapping / torsion, positively coupled flapping / torsion, and negatively coupled flapping / torsion rotor blade trailing edge winglet uncontrolled stationary and controlled motion are presented. As can be seen from the figure, the calculation results of the method of the present invention reflect the anisotropy of composite materials and the resulting non-classical effects such as transverse shear deformation, section warping and elastic coupling, that is, the influence of aeroelastic shearing on the vibration reduction effect of trailing edge winglets. It can provide a reliable analysis method for the collaborative design of aeroelastic shearing of rotor blades with trailing edge winglets and high-frequency motion of trailing edge winglets.

[0068] The high-precision prediction method for aeroelastic vibration loads of rotor blades with trailing-edge winglets established in this invention is applicable to rotor blades in unsteady flow with arbitrary motion and deformation, arbitrary cross-sectional shape, and arbitrary material distribution characteristics. It can accurately calculate the influence of composite material anisotropy and its resulting non-classical effects such as lateral shear deformation, cross-sectional warping, and elastic coupling, demonstrating significant engineering application value. Finally, it should be particularly noted that one of the main differences between the aeroelastic modeling method of this invention and commonly used aeroelastic modeling methods is the use of a hybrid variational geometrically accurate nonlinear equation of motion to describe the motion of rotor blades with trailing-edge winglets. Therefore, the unknowns in the equation of motion for rotor blades with trailing-edge winglets include not only general displacements, rotations, and their derivatives, but also the resultant force and resultant moment, linear momentum, and angular momentum of the blade cross-section. This hybrid variational model of the blade motion equations offers several advantages. First, it allows for simple shape function discretization in the finite element space, simplifying the solution process. Second, since the blade root load is an unknown in the motion equations, solving the aeroelastic equations directly yields the root load, which can then be used to synthesize the rotor hub load. This eliminates the integration operations required in traditional hub load calculations and avoids computational errors introduced by numerical integration. Traditional aeroelastic modeling methods require integrating the aerodynamic and inertial loads along the spanwise direction of each blade section to obtain the root load, before synthesizing the hub load, which is complex and prone to integration errors.

[0069] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A high-precision prediction method for aeroelastic vibration loads on rotor blades with trailing-edge winglets, characterized in that, The steps include the following: S1. Accurately incorporate the inertial load of the trailing edge winglet generated by the high-frequency motion of the trailing edge winglet, and simultaneously consider the geometric nonlinearity of the large deformation of the blade, the transverse shear deformation caused by the anisotropy of the composite material, the non-classical effects of section warping and elastic coupling, and the arbitrary section shape and material distribution characteristics of the blade, to establish a geometrically accurate structural model of the rotor blade with trailing edge winglet. The structural model includes the analysis of the two-dimensional section characteristics of the rotor blade with trailing edge winglet and the establishment of the one-dimensional geometrically accurate nonlinear motion equation. S2. Considering the complex airfoil profile shape changes caused by unsteady incoming flow, arbitrary airfoil motion, and active control of trailing edge winglets, based on potential flow theory, and utilizing the impenetrability condition of the airfoil surface and the Runge-Kutta condition of the airfoil trailing edge, a two-dimensional unsteady aerodynamic load calculation model of rotor blades with trailing edge winglets is established. Taking into account the influence of trailing edge winglets on the distribution of attached vortex rings and time-varying wake of rotor blades, and utilizing the impenetrability condition of the blade surface and the far wake control equation, a time-varying free wake model of rotor blades with trailing edge winglets is established. S3. The two-dimensional profile unsteady aerodynamic load model and the time-varying free wake model are introduced into the established geometrically accurate structural model of the rotor blade with trailing edge winglet. The coupled trim algorithm is used to establish the geometrically accurate aeroelastic model of the rotor blade with trailing edge winglet. Finally, the geometrically accurate aeroelastic equation set of the rotor blade with trailing edge winglet is obtained. The geometrically accurate aeroelastic equation set of the rotor blade with trailing edge winglet includes one-dimensional geometrically accurate nonlinear motion equations, attachment circulation equations, far wake control equations and trim equations. S4. The partial differential geometric exact aeroelastic equations of the rotor blade with trailing edge winglet in the spatial and time domains are discretized using the finite element method to obtain the ordinary differential geometric exact aeroelastic equations of the rotor blade with trailing edge winglet in the time domain. The ordinary differential geometric exact aeroelastic equations of the time domain are integrated by step integration using the Newmark numerical integration method and the Newton-Raphson method to obtain the periodically changing steady-state convergent solution, that is, the steady-state aeroelastic response of the rotor blade with trailing edge winglet. The root loads of each blade obtained by solving the steady-state aeroelastic response are summed to obtain the hub vibration load of the rotor blade with trailing edge winglet. The hub vibration load is Fourier expanded to obtain the harmonic components of the hub vibration load of the rotor blade with trailing edge winglet.

2. The method for high-precision prediction of aeroelastic vibration load on rotor blades with trailing edge winglets according to claim 1, characterized in that, The S1 includes: S11. Based on the three-dimensional deformation of a rotor blade with trailing edge winglets, without making assumptions about deformation and rotation angle, a method is established to describe the blade from an undeformed state to a deformed state. Including the displacement of the blade reference axis, the rotation of the reference section, and the three-dimensional warping of any point within the reference section, based on the relationship between one-dimensional generalized strain and blade three-dimensional deformation, the deformation gradient tensor of any point within the blade section of the rotor with trailing edge winglet is derived. The three-dimensional strain of any point within the blade section of the rotor with trailing edge winglet is obtained by decomposing the deformation gradient tensor using the rotation tensor decomposition method. S12. For a rotor blade with trailing edge winglets that has arbitrary cross-sectional shape and arbitrary material distribution characteristics, the Patran software is used to sequentially establish the geometric model, generate the finite element mesh and assign material properties to the blade cross-section according to its cross-sectional structural dimensions and material property parameters, so as to obtain the node, element and element property information of the rotor blade cross-section with trailing edge winglets. Then, combined with the three-dimensional strain at any point in the blade cross-section, the strain energy of the discrete type of the rotor blade cross-section with trailing edge winglets is obtained. S13. The variational asymptotic method is used to analyze the strain energy of the discrete type of the blade profile. By minimizing the variation of the strain energy of the discrete type of the blade profile under specified constraints, the three-dimensional warping, generalized Timoshenko strain energy and corresponding profile stiffness characteristic matrix of any point of the rotor blade profile with trailing edge winglet are determined. The same numerical integration method along the profile is used to determine the mass characteristic matrix of the blade profile; S14. Establish a geometrically accurate description method for the velocity at any point on the blade section and the trailing edge winglet section of a rotor blade with trailing edge winglet, accurately take into account the trailing edge winglet inertial load generated by the high-frequency motion of the trailing edge winglet, and derive the kinetic energy per unit length of blade. By introducing virtual displacement and virtual rotation, the variational values ​​of strain energy and kinetic energy per unit length of blade, as well as the virtual work done by external load, are derived. Substituting the variational values ​​of strain energy and kinetic energy per unit length of blade, and the virtual work done by externally distributed forces and torques on the blade per unit length of blade, into the generalized Hamiltonian principle, the one-dimensional geometrically accurate nonlinear equation of motion for a rotor blade with trailing edge winglets is obtained.

3. The method for high-precision prediction of aeroelastic vibration load on rotor blades with trailing edge winglets according to claim 1, characterized in that, Specifically, S2 is: S21. Considering the complex airfoil profile changes caused by unsteady incoming flow, arbitrary airfoil motion, and active control of trailing edge winglets, establish the relationship between the induced velocity caused by the attachment circulation and wake circulation and the airfoil motion and deformation based on the impenetrable boundary conditions of the airfoil surface; establish the relationship between the pressure difference between the upper and lower airfoil surfaces and the attachment circulation based on the vorticity equation. Based on the condition that the wake is not subject to force, establish the relationship between the induced velocity caused by the wake circulation and the total attached circulation. Based on the relationship between the pressure difference between the upper and lower wing surfaces and the amount of attached circulation, as well as the relationship between the induced velocity caused by the wake circulation and the total amount of attached circulation, the two-dimensional unsteady aerodynamic load of the rotor blade with trailing edge winglet is derived. S22. A lifting surface model is used to simulate a rotor blade with trailing edge winglets. The lifting surface coincides with the mid-arc surface of the blade, and the attached vortices on the lifting surface are represented by quadrilateral vortex lattices. The wake of the rotor blade with trailing edge winglets is divided into two parts: a near wake and a far wake. The vortex plates of the near wake are represented by quadrilateral vortex lattices and are kept in the tangential plane of the trailing edge of the mid-arc surface of the blade. The tip vortex of the far wake is represented by a single vortex filament. At the same time, the wake trailed out from the tip of the trailing edge winglet is introduced to account for the influence of the trailing edge winglet on the distribution of attached vortex annulus and the time-varying wake of the rotor blade. S23. Calculate the circulation of the vortex grid attached to the arc surface of the rotor blade using the condition that the object surface is impenetrable; determine the shape of the vortex wake by solving the control equation of the vortex wake at the tip of the rotor blade; determine the shape of the vortex wake at the tip of the vortex wake by solving the control equation of the vortex wake at the tip of the vortex. The final convergent solution is determined by iterative calculation of the attached vortex ring quantity and the shape of the tip vortex and trailing edge winglet tip vortex wake, thus obtaining the distribution of the induced velocity of the rotor blade with trailing edge winglet along the blade azimuth and blade span.

4. The method for high-precision prediction of aeroelastic vibration load on rotor blades with trailing edge winglets according to claim 1, characterized in that, S3 includes: S31. Under the specified rotor shaft tilt angle and advance ratio, the Auto-pilot trim algorithm is used to establish a set of second-order differential equations about the control quantities for trim calculation, and to determine the rotor blade collective pitch control and longitudinal and lateral cyclic pitch control that match the specified trim target quantity. S32. Using the kinematic parameters of the geometrically accurate structural model of the rotor blade with trailing edge winglet, the descriptions of the geometrically accurate structural model of the rotor blade with trailing edge winglet, the unsteady aerodynamic load model, the free wake model and the trim algorithm are unified. The models are coupled together by the deformation, control, induced velocity and aerodynamic load of the blade to establish a geometrically accurate aeroelastic model of the rotor blade with trailing edge winglet. The final established geometrically accurate aeroelastic equation set for rotor blades with trailing edge winglets includes one-dimensional geometrically accurate nonlinear motion equations, Auto-pilot trim equations, attachment circulation equations, blade tip vortex wake control equations, and trailing edge winglet tip vortex wake control equations.

5. The method for high-precision prediction of aeroelastic vibration load on rotor blades with trailing edge winglets according to claim 4, characterized in that, The trim target quantities include the tension coefficient, the roll moment coefficient, or the lateral tip plane tilt angle, and the pitch moment coefficient or the longitudinal tip plane tilt angle.

6. The method for high-precision prediction of aeroelastic vibration load on rotor blades with trailing edge winglets according to claim 1, characterized in that, The S4 includes: S41. Establish an aeroelastic response solution module for rotor blades with trailing edge winglets. Solve the system of equations consisting of one-dimensional geometrically accurate nonlinear motion equations and Auto-pilot balancing equations, which are characterized by strongly nonlinear second-order partial differential equations with periodic coefficient matrices. First, perform finite element space discretization to obtain a system of strongly nonlinear second-order ordinary differential equations with periodic coefficient matrices that are only related to time. Then, use the Newmark numerical integration method and the Newton-Raphson method to perform step integration on the time-domain ordinary differential geometrically accurate aeroelastic equations to obtain a periodically changing steady-state convergent solution, i.e., the steady-state aeroelastic response of the rotor blade with trailing edge winglets. Extract the absolute velocity at the blade control point within one rotation cycle from the obtained blade aeroelastic response and pass it to the free wake solution module for rotor blades with trailing edge winglets. S42. Through external circulation iteration and internal wake geometry iteration, determine the final converged attached vortex circulation and the wake shapes of the blade tip vortex and trailing edge winglet tip vortex, and obtain an attached vortex circulation distribution and wake shape corresponding to the absolute velocity of the blade; calculate the distribution of blade induced velocity along the blade azimuth and blade span during one rotation cycle, and pass it to the aeroelastic response solution module of the rotor blade with trailing edge winglet. S43. The aeroelastic response solution module and the free wake solution module of the rotor blade with trailing edge winglet exchange blade motion and induced velocity information and iterate repeatedly to obtain the final converged solution, that is, the aeroelastic response and induced velocity distribution of the rotor blade with trailing edge winglet that converge simultaneously; by summing the root loads of each blade obtained from the aeroelastic response solution, the hub vibration load of the rotor blade with trailing edge winglet is obtained; the obtained hub vibration load is subjected to Fourier expansion to obtain the harmonic components of the hub vibration load of the rotor blade with trailing edge winglet.

7. A high-precision prediction method for aeroelastic vibration loads of rotor blades with trailing-edge winglets according to claim 6, characterized in that, In the process of solving a system of equations consisting of a one-dimensional geometrically accurate nonlinear motion equation and an Auto-pilot balancing equation, which are characterized by a strongly nonlinear second-order partial differential equation with a periodic coefficient matrix, the induced velocity distribution is provided by the free wake solution module and remains unchanged during the solution process.

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