A design method for hollow blades

Abstract

The present invention discloses a design method for a hollow blade, which includes: S1: obtaining a design domain of an initial two-dimensional cross section of a hollow blade; S2: setting an initial density field of the design domain; S3: obtaining a constraint function and an objective function according to the current density field; S4: analyzing the sensitivity of the objective function and the constraint function to the current density field; S5: optimizing the design domain of the two-dimensional cross section of the hollow blade according to the sensitivity and updating the current density field to obtain an updated current density field; S6: judging whether the updated current density field meets a preset convergence condition, if so, entering step S7; otherwise, returning to step S3; S7: generating a final hollow blade according to the updated current density field. The design method for a hollow blade provided by the present invention can design a hollow blade with a more advanced structure and a larger space.

Description

Technical Field

[0001] The invention relates to the technical field of hollow blades, and in particular to a design method for hollow blades. Background Art

[0002] Hollow blades are key components of aircraft engines, bearing 80% of the engine's thrust. At present, with the continuous improvement of aircraft engine performance, the aerodynamic limit load is also increasing. Under the action of this aerodynamic load, the hollow blades become thinner and longer, which reduces the stiffness and increases the incidence of aeroelastic instability. Aeroelastic instability can cause damage to the blades in a short period of time, resulting in serious consequences. Therefore, the aeroelastic stability of hollow blades has become a very important issue in the design and use of advanced aircraft engines.

[0003] Researchers have conducted a lot of research on the optimal design of blades. Strength, frequency and aerodynamic efficiency are the mechanical properties that these studies mainly focus on. From the perspective of the research object, these studies can be divided into two categories: one is the blade shape optimization of solid blades, and the other is the material layout optimization of the hollow area of ​​hollow blades. In the design of solid blades, in order to improve the aerodynamic efficiency and strength of the blades, researchers have carried out parameter optimization design of the fan blade cross-section. In the design of hollow blades, the material layout of the hollow area becomes the main design variable. Considering mechanical properties such as stress, frequency, and weight, parameter optimization and topology optimization are used to optimize the material layout of the hollow area of ​​the blade.

[0004] Most of the above studies did not consider aeroelastic stability in the optimization. In the current flutter suppression design, researchers usually prevent the aeroelastic instability of the blade by structural detuning and aerodynamic detuning. Some researchers also improve the aeroelastic stability of the blade by optimizing the blade shape, modifying the casing profile, changing the radial distribution of the stagger angle, etc. For hollow blades, the main deformation forms of their flutter are bending and torsion. Therefore, the bending stiffness and torsional stiffness of the hollow blade affect its aeroelastic stability. It can be said that the existence of the hollow area not only reduces the mass of the blade, but also affects the bending, torsional stiffness and flutter speed of the blade. Therefore, the arrangement of the hollow area material is the key to the design of hollow blades. Summary of the invention

[0005] The object of the present invention is to provide a design method for a hollow blade, so as to be able to design a hollow blade with a more advanced structure and a larger space.

[0006] The technical solution of the present invention to solve the above technical problems is as follows:

[0007] The present invention provides a method for designing a hollow blade, and the method for designing a hollow blade comprises:

[0008] S1: Obtain the design domain of the initial hollow blade 2D section;

[0009] S2: Setting the initial density field of the design domain;

[0010] S3: Obtain constraint function and objective function according to the current density field;

[0011] S4: analyzing the sensitivity of the objective function and the constraint function to the current density field;

[0012] S5: Optimizing the design domain of the two-dimensional cross section of the hollow blade according to the sensitivity and updating the current density field to obtain an updated current density field;

[0013] S6: Determine whether the updated current density field meets the preset convergence condition, if so, proceed to step S7; otherwise, return to step S3;

[0014] S7: Generate a final hollow blade according to the updated current density field.

[0015] Optionally, the step S3 includes:

[0016] S31: Obtaining relevant parameters of the current hollow blade according to the current density field;

[0017] S32: obtaining an aeroelastic equation according to the relevant parameters;

[0018] S33: according to the aeroelastic equation, obtaining the objective function, aeroelastic stability constraint function and volume constraint function of the current hollow blade at the target incoming flow velocity;

[0019] S34: Obtaining the constraint function according to the aeroelastic stability constraint function and the volume constraint function.

[0020] Optionally, the step S31 includes:

[0021] S311: Calculating the mass matrix of the current hollow blade according to the current density field;

[0022] S312: Mapping the density field of the two-dimensional cross section of the current hollow blade onto the three-dimensional solid hollow blade to obtain the density field of the three-dimensional solid hollow blade;

[0023] S313: Calculate the stiffness matrix according to the density field of the three-dimensional solid hollow blade;

[0024] S314: determining the blade reduction frequency at the target incoming flow velocity through iterative calculation;

[0025] S315: Obtaining an aerodynamic matrix according to the reduced frequency and geometric parameters;

[0026] S316: Outputting the mass matrix, the stiffness matrix and the aerodynamic matrix as relevant parameters of the current hollow blade.

[0027] Optionally, in step S315, the aerodynamic matrix Q is:

[0028] Q=Q Re +iQ Im

[0029] Among them, Q Re is the real part of the aerodynamic matrix, Q Im is the imaginary part of the aerodynamic matrix.

[0030] Optionally, in step S32, the aeroelastic equation is:

[0031]

[0032] Where M is the mass matrix, is the acceleration vector of the hollow blade heave and pitch motion, K is the stiffness matrix, q(t) is the displacement vector characterizing the blade heave and pitch motion, and ω is the circular frequency of blade vibration, γ is the transient attenuation coefficient, is the mode of simple harmonic vibration of the hollow blade, t is time, ρ ∞ is the atmospheric density, U ∞ is the target incoming flow velocity, Q is the aerodynamic matrix, and p is the complex eigenvalue.

[0033] Optionally, in step S33, the objective function is to maximize the blade vibration circular frequency ω;

[0034] The aeroelastic stability constraint function g(ρ) is:

[0035] g(ρ)=γ≤0

[0036] The volume constraint function h(ρ) is:

[0037]

[0038] Among them, γ is the transient attenuation coefficient; is the cell density of the i0th cell in the design domain, N is the number of cells in the design domain, is the unit volume of the i0th unit in the design domain, V* is the volume of the three-dimensional solid hollow blade design domain, V f is the volume fraction used to characterize the volume constraint function.

[0039] Optionally, the step S4 comprises:

[0040] S41: Obtaining a displacement vector function and a complex eigenvalue expression representing the heave and pitch motion of the blade;

[0041] S42: Obtaining a quadratic eigenvalue equation according to the displacement vector function and the complex eigenvalue expression;

[0042] S43: according to the quadratic eigenvalue equation, obtaining the blade vibration circular frequency and transient attenuation coefficient in the current density field;

[0043] S44: according to the blade vibration circular frequency and the transient attenuation coefficient, using the expression of the complex eigenvalue, obtain a circular frequency sensitivity formula and a transient attenuation coefficient sensitivity formula;

[0044] S45: Establishing complex scalar equations;

[0045] S46: Obtaining, according to the complex scalar equation, the sensitivity of the real part and the imaginary part of the complex eigenvalue to the current density field;

[0046] S47: Obtain the sensitivity of the objective function and the constraint function according to the sensitivity of the real part and the imaginary part of the complex eigenvalue to the current density field, the circular frequency sensitivity formula and the transient attenuation coefficient sensitivity formula.

[0047] Optionally, in step S42, the expression of the complex eigenvalue p is:

[0048] p=ω(γ±i)

[0049] The circular frequency sensitivity formula is:

[0050]

[0051] The transient attenuation coefficient sensitivity formula is:

[0052]

[0053] Among them, ω is the circular frequency of blade vibration, γ is the transient attenuation coefficient, i0 is the i0th unit in the design domain, is the cell density of the i0th cell in the design domain, p Im is the imaginary part of the complex eigenvalue p, p Re is the real part of the complex eigenvalue p.

[0054] Optionally, the step S45 includes:

[0055] S451: Deriving both sides of the quadratic eigenvalue equation to obtain a derivative equation;

[0056] S452: Obtain the complex scalar equation according to the quadratic eigenvalue equation and the derivative equation.

[0057] Optionally, in step S42, the quadratic eigenvalue equation is:

[0058]

[0059] In step S45, the complex scalar equation is:

[0060]

[0061] Where p is the complex eigenvalue, M is the mass matrix, is the mode of simple harmonic vibration of the hollow blade, is the left eigenvector of the jth eigenvalue of the matrix R and the matrix is the sensitivity of the jth eigenvalue to the i0th unit density, M is the mass matrix, is the cell density of the i0th cell in the design domain, ρ ∞ is the atmospheric density, U ∞ is the target flow velocity, p j is the jth complex eigenvalue, K is the stiffness matrix, Q Re is the real part of the aerodynamic matrix, Q Im is the imaginary part of the aerodynamic matrix, k is the reduction frequency and is the mode of simple harmonic vibration of the jth order hollow blade, ω is the circular frequency of blade vibration, b R It is the half chord length of the hollow blade.

[0062] The present invention has the following beneficial effects:

[0063] The present invention establishes a calculation method for aeroelastic stability based on a two-degree-of-freedom oscillator with inertial coupling of heave and pitch motion, and derives the sensitivity of flutter frequency and flutter boundary. The present invention can be used to optimize the material layout of the hollow area of ​​the bending-torsion coupling hollow blade, and obtain a blade design with better aeroelastic stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 A flow chart of the design method of the hollow blade provided by the present invention;

[0065] Figure 2 It is the structural diagram of the hollow blade cross section;

[0066] Figure 3 Schematic diagram of the constraints of bending and torsion motion of the hollow blade;

[0067] Figure 4 is the cross-sectional coordinate system at the shear center and the schematic diagram of unit force and unit moment;

[0068] Figure 5 It is a structural schematic diagram of the hollow area and design domain of the hollow blade;

[0069] Figure 6 The design and analysis results of the hollow blade when the volume-to-body ratio is 0.3;

[0070] Figure 7 The design and analysis results of the hollow blade when the volume-to-body ratio is 0.4;

[0071] Figure 8 Design and analysis results of hollow blades with a volume-to-body ratio of 0.6. DETAILED DESCRIPTION

[0072] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0073] Example

[0074] The present invention provides a design method for a hollow blade, referring to Figure 1 As shown, the design method of the hollow blade includes:

[0075] S1: Obtain the design domain of the initial hollow blade 2D section;

[0076] Here, the design domain of the initial two-dimensional cross section of the hollow blade may be initially given during the design process, or may be the design domain of the two-dimensional cross section of an existing formed hollow blade, which is not specifically limited in the present invention.

[0077] Figure 2 The figure shows the cross section of a hollow blade, where the hollow area is located in the upper middle part of the blade. There are several reinforcing ribs distributed in the hollow area. The hollow blade is modeled as a two-degree-of-freedom oscillator, in which the heave and pitch motions are inertially coupled (see Figure 3 The hollow blade cross section (generally at 75% of the blade height) is taken as the research object. The two-element wing is composed of bending springs K h and torsion spring K α suspension.

[0078] S2: Setting the initial density field of the design domain;

[0079] That is, the design domain is given an initial density field ρ=ρ0.

[0080] S3: Obtain constraint function and objective function according to the current density field;

[0081] Specifically, step S3 includes:

[0082] S31: Obtaining relevant parameters of the current hollow blade according to the current density field;

[0083] Here, the relevant parameters of the current hollow blade include mass matrix, stiffness matrix and aerodynamic matrix. Therefore, further, obtaining the mass matrix, stiffness matrix and aerodynamic matrix includes the following steps:

[0084] S311: Calculating the mass matrix of the current hollow blade according to the current density field;

[0085] The mass matrix M includes the mass m of the hollow blade span, the mass static moment S of the hollow blade section around the elastic axis α And the mass moment of inertia I of the blade section about the elastic axis α , which can all be calculated based on the current density field.

[0086] Specifically, the calculation process of the mass matrix M is:

[0087] Under the current density field, the unit leaf mass static moment around the elastic axis is

[0088] Under the current density field, the unit leaf mass moment of inertia around the elastic axis is

[0089] in dmi is the mass of the ith unit, n is the number of elements in the design domain, and yi is the distance between the elastic axis and the centroid of the ith element.

[0090] S312: Mapping the density field of the two-dimensional cross section of the current hollow blade onto the three-dimensional solid hollow blade to obtain the density field of the three-dimensional solid hollow blade;

[0091] S313: Calculate the stiffness matrix according to the density field of the three-dimensional solid hollow blade;

[0092] Here, it is necessary to first calculate the bending stiffness and torsional stiffness of the hollow blade according to the density field of the three-dimensional solid hollow blade. Of course, the bending stiffness and torsional stiffness are calculated through the bending spring K h and torsion spring K α Therefore, what is actually calculated is the bending stiffness K of the bending spring. h and the torsion stiffness K of the torsion spring α The stiffness matrix K includes the bending stiffness K h and torsional stiffness K α .

[0093] Specifically, the calculation process of the stiffness matrix K is:

[0094] The blade three-dimensional model was used. The section coordinate system was established with the shear center of the 75% blade height section as the origin and the elastic axis as the x-axis. Figure 4 As shown, a unit force and a unit moment are applied at the shear center. The static equilibrium equation of this finite element model is:

[0095] K all U all =F all

[0096] Among them, K all is the stiffness matrix of the three-dimensional blade, U all is the displacement vector of the three-dimensional blade. For the shear center of the blade section, the static equilibrium equation is:

[0097] F sc =K b U sc

[0098] Among them, K b is a 6×6 stiffness matrix, U sc is the displacement matrix of the shear center in the cross-sectional coordinate system, F sc is the load matrix acting on the shear center in the section coordinate system.

[0099]

[0100] For the 6×6 stiffness matrix K b , the following eigenvalue equation can be solved to obtain the stiffness of the blade along the six directions of the cross-sectional coordinate system, where x and M z The corresponding characteristic value is the bending stiffness coefficient K h and torsional stiffness coefficient K α .

[0101] S314: determining the blade reduction frequency at the target incoming flow velocity through iterative calculation;

[0102] S315: Obtaining an aerodynamic matrix according to the reduced frequency and geometric parameters;

[0103] The aerodynamic matrix Q is:

[0104] Q=Q Re +iQ Im

[0105] Among them, Q Re is the real part of the aerodynamic matrix, Q Im is the imaginary part of the aerodynamic matrix.

[0106] Here, an initial guess for the reduction frequency is first calculated:

[0107]

[0108] Afterwards, the initial aerodynamic matrix Q is calculated based on the initial guess of the reduced frequency (0) , and solve Get the eigenvalue p i (0) If the eigenvalue p i (0) The imaginary part of is closest to ω1, then the reduced frequency is updated as:

[0109]

[0110] If the reduction frequency satisfies ||k1 (1) -k1 (0) ||≤10 -3 , then k1 (1) is the target flow velocity U ∞ According to the reduction frequency k1 (1) The aerodynamic matrix Q can be obtained by combining the geometric parameters of the blade. Here, the geometric parameters include the chord length of the hollow blade and the position of the elastic axis. The position of the elastic axis needs to be calculated based on the material layout of the hollow area of ​​the blade. The chord length of the blade is Figure 5 The distance from the leading edge to the trailing edge of the blade cross section, because the design method of the hollow blade provided by the present invention does not change the shape of the outer contour of the blade, but only designs the material layout in the core layer of the blade, so the chord length of the blade is initially given. The material layout of the hollow area of ​​the blade, that is, the density field, will affect the stiffness of the blade cross section, and then affect the position of the elastic axis of the blade. Therefore, the position of the elastic axis needs to be recalculated in each iteration according to the current two-dimensional density field of the blade.

[0111] S316: Outputting the mass matrix, the stiffness matrix and the aerodynamic matrix as relevant parameters of the current hollow blade.

[0112] S32: obtaining an aeroelastic equation according to the relevant parameters;

[0113] Here, since the density field represents the locations with material and without material in the design domain, the density field of each design domain is different, that is, the structural form of the hollow area of ​​the blade in each design domain is different. The density field affects the form of the structure, and the form of the structure affects the mass distribution and stiffness of the structure, and then affects the frequency of the structure. Therefore, it is necessary to determine the objective function by solving the aeroelastic equation.

[0114] The aeroelastic equation needs to be obtained based on the above-mentioned related parameters.

[0115] The aeroelastic equation is:

[0116]

[0117] Where M is the mass matrix, is the acceleration vector of the hollow blade heave and pitch motion, K is the stiffness matrix, q(t) is the displacement vector characterizing the blade heave and pitch motion, and ω is the frequency, γ is the transient attenuation coefficient, is the mode of simple harmonic vibration of the hollow blade, t is time, ρ ∞ is the atmospheric density, U ∞ is the target incoming flow velocity, Q is the aerodynamic matrix, and p is the complex eigenvalue.

[0118] Assuming the blades are in simple harmonic vibration, Substituting this expression into the aeroelastic equation, the aeroelastic equation can be transformed into the following quadratic eigenvalue equation:

[0119]

[0120] p is the complex eigenvalue, ω is the circular frequency of blade vibration, γ is the transient attenuation coefficient, is the mode of simple harmonic vibration of the hollow blade. When the real part of the complex eigenvalue is positive, the vibration of the blade is divergent and flutter will occur.

[0121] S33: according to the aeroelastic equation, obtaining the objective function, aeroelastic stability constraint function and volume constraint function of the current hollow blade at the target incoming flow velocity;

[0122] The objective function is to maximize the blade vibration circular frequency ω;

[0123] The aeroelastic stability constraint function g(ρ) is:

[0124] g(ρ)=γ≤0

[0125] The volume constraint function h(ρ) is:

[0126]

[0127] Where γ is the transient attenuation coefficient; ρ i0 is the cell density of the i0th cell in the design domain, N is the number of cells in the design domain, is the unit volume of the i0th unit in the design domain, V* is the volume of the three-dimensional solid hollow blade design domain, V f is the volume fraction used to characterize the volume constraint function.

[0128] S34: Obtaining the constraint function according to the aeroelastic stability constraint function and the volume constraint function.

[0129] In the present invention, the constraint function includes an aeroelastic stability constraint function and a volume constraint function.

[0130] S4: analyzing the sensitivity of the objective function and the constraint function to the current density field;

[0131] Optionally, the step S4 comprises:

[0132] S41: Obtaining a displacement vector function and a complex eigenvalue expression representing the heave and pitch motion of the blade;

[0133] The displacement vector function that characterizes the blade's heave and pitch motion is q(t) and The complex eigenvalue expression is: p = ω(γ±i).

[0134] S42: Obtaining a quadratic eigenvalue equation according to the displacement vector function and the complex eigenvalue expression;

[0135] The quadratic eigenvalue equation is:

[0136] S43: according to the quadratic eigenvalue equation, obtaining the blade vibration circular frequency and transient attenuation coefficient in the current density field;

[0137] The key point of sensitivity analysis in this method lies in the sensitivity of frequency ω and transient attenuation coefficient γ. These two sensitivities can be derived from the expression of complex eigenvalues, namely:

[0138] S44: according to the blade vibration circular frequency and the transient attenuation coefficient, using the expression of the complex eigenvalue, obtain a circular frequency sensitivity formula and a transient attenuation coefficient sensitivity formula;

[0139] The expression of the complex eigenvalue p is:

[0140] p=ω(γ±i)

[0141] The circular frequency sensitivity formula is:

[0142]

[0143] The transient attenuation coefficient sensitivity formula is:

[0144]

[0145] Among them, ω is the circular frequency of blade vibration, γ is the transient attenuation coefficient, i0 is the i0th unit in the design domain, is the cell density of the i0th cell in the design domain, p Im is the imaginary part of the complex eigenvalue p, p Re is the real part of the complex eigenvalue p.

[0146] It can be seen from the above formula that the sensitivity of the blade vibration circular frequency ω and the transient attenuation coefficient γ can be expressed by the real part and imaginary part of the complex eigenvalue p.

[0147] S45: Establishing complex scalar equations;

[0148] The specific steps to establish the complex scalar equation include:

[0149] S451: performing a derivative operation on both sides of the quadratic eigenvalue function to obtain a derivative equation;

[0150] Here, since the quadratic eigenvalue function is more complicated, the quadratic eigenvalue equation is abbreviated as:

[0151]

[0152] After that, the above content is derived, and the derived equation is:

[0153]

[0154] S452: Obtain the complex scalar equation according to the quadratic eigenvalue function and the derivative equation.

[0155] definition is the left eigenvector of the jth eigenvalue of matrix R, then Combined with the derivative equation, the new equation is:

[0156]

[0157] Expanding the new equation, it becomes a complex scalar equation, that is:

[0158]

[0159] in, is the left eigenvector of the jth eigenvalue of the matrix R and the matrix is the sensitivity of the jth eigenvalue to the i0th unit density, M is the mass matrix, ρ i0 is the cell density of the i0th cell in the design domain, ρ ∞ is the atmospheric density, U ∞ is the target flow velocity, p j is the jth complex eigenvalue, K is the stiffness matrix, Q Re is the real part of the aerodynamic matrix, Q Im is the imaginary part of the aerodynamic matrix, k is the reduction frequency and is the mode of simple harmonic vibration of the jth order hollow blade, ω is the circular frequency of blade vibration, b R is the half chord length of the hollow blade. Among them, the jth eigenvalue corresponds to the performance of the jth order vibration of the blade.

[0160] S46: Obtaining, according to the complex scalar equation, the sensitivity of the real part and the imaginary part of the complex eigenvalue to the current density field;

[0161] In complex scalar equations, is the only unknown complex variable value, and the complex scalar equation can be decomposed into two real equations, so it can be decomposed into and

[0162] S47: Obtain the sensitivity of the objective function and the constraint function according to the sensitivity of the real part and the imaginary part of the complex eigenvalue to the current density field, the circular frequency sensitivity formula and the transient attenuation coefficient sensitivity formula.

[0163] Coming Soon and Substitute into the circular frequency sensitivity formula And the transient attenuation coefficient sensitivity formula In the above example, the sensitivity of the objective function and constraint function can be output.

[0164] S5: Optimizing the design domain of the two-dimensional cross section of the hollow blade according to the sensitivity and updating the current density field to obtain an updated current density field;

[0165] S6: Determine whether the updated current density field meets the preset convergence condition, if so, proceed to step S7; otherwise, return to step S3;

[0166] In the present invention, the preset convergence condition is |ρ-ρ new |≤0.1%. Of course, those skilled in the art can also design and preset convergence conditions according to actual needs, and the present invention does not make specific restrictions. Here, ρ represents the current density field, ρ new Represents the updated current density field.

[0167] S7: generating a final hollow blade according to the current density field;

[0168] Of course, in addition to the current density field provided by the present invention, the blade profile, design domain, and material parameters of the hollow blade (density, elastic modulus, Poisson's ratio, etc. of the blade material) are also required.

[0169] The material layout design of the hollow area of ​​the blade is carried out with the unit density as the design variable. Figure 5 As shown in the figure, the design domain of the blade is located at 28% to 88% of the blade height and 10% to 80% of the blade shape. The thickness of the hollow blade skin is 20% of the blade thickness. The blade section is modeled using a quadrilateral unit with a size of 1 mm. The solid blade is modeled using a hexahedral unit with a size of 1 mm.

[0170] Through the optimization method described in this paper, a set of volume ratios V fThe optimization results are 0.3, 0.4, and 0.6 respectively, and the results are compared with the optimization results of flexibility topology optimization and frequency topology optimization, such as Figure 6 to Figure 8 As shown in the figure. For the aeroelastic stability topology optimization design, the hollow area material is distributed at the leading and trailing edges of the blade, while for the frequency topology optimization design, the hollow area material is distributed in the middle of the blade. The optimized design material obtained by the compliance topology optimization is evenly distributed in the hollow area. Figure 6 (b)- Figure 8 From the results of aeroelastic stability analysis shown in (b), the optimal blades obtained by aeroelastic stability topology optimization are stable at the design point. When the volume fractions are 0.3 and 0.4, the optimal blades obtained by compliance topology optimization are unstable at the design point. In addition, when the volume fractions are 0.5 and 0.6, although the optimal blades and solid blades are aeroelastically stable at the design point, the optimal structure obtained by aeroelastic stability topology optimization also has a higher flutter boundary.

[0171] from Figure 6 (b)- Figure 8 (b) It can be seen that compared with the optimal blades obtained by compliance topology optimization and frequency topology optimization, the optimal blade obtained by aeroelastic stability topology optimization has better aeroelastic stability at the same volume fraction. Compared with the solid blade, the mass of the hollow blade is lower. And at the critical flutter speed of the solid blade, the hollow blade obtained by aeroelastic stability topology optimization is stable.

[0172] The present invention has the following beneficial effects:

[0173] The present invention establishes a calculation method for aeroelastic stability based on a two-degree-of-freedom oscillator with inertial coupling of heave and pitch motion, and derives the sensitivity of flutter frequency and flutter boundary. The present invention can be used to optimize the material layout of the hollow area of ​​the bending-torsion coupling hollow blade, and obtain a blade design with better aeroelastic stability.

[0174] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing a hollow blade, characterized in that: The design method of the hollow blade comprises: S1: Obtain the design domain of the initial hollow blade 2D section; S2: Setting the initial density field of the design domain; S3: Obtain constraint function and objective function according to the current density field; S4: analyzing the sensitivity of the objective function and the constraint function to the current density field; S5: Optimizing the design domain of the two-dimensional cross section of the hollow blade according to the sensitivity and updating the current density field to obtain an updated current density field; S6: Determine whether the updated current density field meets the preset convergence condition, if so, proceed to step S7; otherwise, return to step S3; S7: generating a final hollow blade according to the updated current density field; The step S3 comprises: S31: Obtaining relevant parameters of the current hollow blade according to the current density field; S32: obtaining an aeroelastic equation according to the relevant parameters; S33: according to the aeroelastic equation, obtaining the objective function, aeroelastic stability constraint function and volume constraint function of the current hollow blade at the target incoming flow velocity; S34: Obtaining the constraint function according to the aeroelastic stability constraint function and the volume constraint function.

2. The method for designing a hollow blade according to claim 1, characterized in that: The step S31 comprises: S311: Calculating the mass matrix of the current hollow blade according to the current density field; S312: Mapping the density field of the two-dimensional cross section of the current hollow blade onto the three-dimensional solid hollow blade to obtain the density field of the three-dimensional solid hollow blade; S313: Calculate the stiffness matrix according to the density field of the three-dimensional solid hollow blade; S314: determining the blade reduction frequency at the target incoming flow velocity through iterative calculation; S315: Obtaining an aerodynamic matrix according to the reduced frequency and geometric parameters; S316: Outputting the mass matrix, the stiffness matrix and the aerodynamic matrix as relevant parameters of the current hollow blade.

3. The design method of hollow blade according to claim 2, characterized in that: In step S315, the aerodynamic matrix Q is: Q=Q Re +iQ Im Among them, Q Re is the real part of the aerodynamic matrix, Q Im is the imaginary part of the aerodynamic matrix.

4. The method for designing a hollow blade according to claim 1, characterized in that: In step S32, the aeroelastic equation is: Where M is the mass matrix, is the acceleration vector of the hollow blade heave and pitch motion, K is the stiffness matrix, q(t) is the displacement vector characterizing the blade heave and pitch motion, and ω is the circular frequency of blade vibration, γ is the transient attenuation coefficient, is the mode of simple harmonic vibration of the hollow blade, t is time, ρ ∞ is the atmospheric density, U ∞ is the target incoming flow velocity, Q is the aerodynamic matrix, and p is the complex eigenvalue.

5. The method for designing a hollow blade according to claim 1, characterized in that: In the step S33, the objective function is to maximize the blade vibration circular frequency ω; The aeroelastic stability constraint function g(ρ) is: g(ρ)=γ≤0 The volume constraint function h(ρ) is: Among them, γ is the transient attenuation coefficient; is the cell density of the i0th cell in the design domain, N is the number of cells in the design domain, is the unit volume of the i0th unit in the design domain, V* is the volume of the three-dimensional solid hollow blade design domain, V f is the volume fraction used to characterize the volume constraint function.

6. The method for designing a hollow blade according to claim 1, characterized in that: The step S4 comprises: S41: Obtaining a displacement vector function and a complex eigenvalue expression representing the heave and pitch motion of the blade; S42: Obtaining a quadratic eigenvalue equation according to the displacement vector function and the complex eigenvalue expression; S43: according to the quadratic eigenvalue equation, obtaining the blade vibration circular frequency and transient attenuation coefficient in the current density field; S44: according to the blade vibration circular frequency and the transient attenuation coefficient, using the expression of the complex eigenvalue, obtain a circular frequency sensitivity formula and a transient attenuation coefficient sensitivity formula; S45: Establishing complex scalar equations; S46: Obtaining, according to the complex scalar equation, the sensitivity of the real part and the imaginary part of the complex eigenvalue to the current density field; S47: Obtain the sensitivity of the objective function and the constraint function according to the sensitivity of the real part and the imaginary part of the complex eigenvalue to the current density field, the circular frequency sensitivity formula and the transient attenuation coefficient sensitivity formula.

7. The method for designing a hollow blade according to claim 6, characterized in that: In step S42, the expression of the complex eigenvalue p is: p=ω(γ±i) The circular frequency sensitivity formula is: The transient attenuation coefficient sensitivity formula is: Among them, ω is the circular frequency of blade vibration, γ is the transient attenuation coefficient, i0 is the i0th unit in the design domain, is the cell density of the i0th cell in the design domain, p Im is the imaginary part of the complex eigenvalue p, p Re is the real part of the complex eigenvalue p.

8. The method for designing a hollow blade according to claim 6, characterized in that: The step S45 comprises: S451: Deriving both sides of the quadratic eigenvalue equation to obtain a derivative equation; S452: Obtain the complex scalar equation according to the quadratic eigenvalue equation and the derivative equation.

9. The method for designing a hollow blade according to any one of claims 6 to 8, characterized in that: In step S42, the quadratic eigenvalue equation is: In step S45, the complex scalar equation is: Where p is the complex eigenvalue, M is the mass matrix, is the mode of simple harmonic vibration of the hollow blade, is the left eigenvector of the jth eigenvalue of the matrix R and the matrix is the sensitivity of the jth eigenvalue to the i0th unit density, M is the mass matrix, is the cell density of the i0th cell in the design domain, ρ ∞ is the atmospheric density, U ∞ is the target flow velocity, p j is the jth complex eigenvalue, K is the stiffness matrix, Q Re is the real part of the aerodynamic matrix, Q Im is the imaginary part of the aerodynamic matrix, k is the reduction frequency and is the mode of simple harmonic vibration of the jth order hollow blade, ω is the circular frequency of blade vibration, b R It is the half chord length of the hollow blade.

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