A method for calculating the natural frequency of a ceramic matrix composite turbine blade considering damage

Abstract

The application discloses a kind of inherent frequency calculation methods of ceramic matrix composite turbine blade considering damage, comprising: establishing the three-dimensional finite element model of ceramic matrix composite, the inherent frequency of turbine blade without damage and the inherent frequency lower limit under damage state are calculated by the elastic modulus of first linear segment and second linear segment;Inherent frequency range of non-linear is predicted by combining the inherent frequency of non-damage state and the inherent frequency lower limit under damage state;Frequency bandwidth is set based on the range of non-linear inherent frequency, time-domain sweep analysis is carried out on the blade model under non-damage state, harmonic load under different excitation frequencies is gradually applied, the steady-state displacement response amplitude corresponding to different excitation frequencies is extracted, and time-domain excitation analysis of blade model is completed;Dynamic inherent frequency is extracted based on the amplitude result of time-domain excitation analysis.The application can realize the calculation process of CMCs non-linear vibration response, and improve the accuracy of inherent frequency calculation.

Description

Technical Field

[0001] The present invention relates to the field of mechanical property prediction of nonlinear structural materials, and in particular to a method for calculating the natural frequency of ceramic matrix composite turbine blades taking damage into consideration, and is particularly suitable for predicting the mechanical properties of ceramic matrix composite materials in a damaged state. Background Art

[0002] Ceramic-matrix composites (CMCs) are widely used in high-temperature structural components such as aircraft engine turbine blades due to their excellent high-temperature performance. However, high-temperature oxidizing environments significantly affect material properties. Oxidation reactions cause a decrease in the material's strength and stiffness, and trigger complex microscopic damage mechanisms, affecting the blade's dynamic characteristics and natural frequency. Traditional natural frequency calculation methods fail to fully account for the material's oxidative damage characteristics, making it difficult to accurately assess the performance of turbine blades under service conditions.

[0003] Patent application CN110852015B discloses a nonlinear method for calculating ceramic matrix composite modal properties. This method proposes establishing a damage-based stiffness model for the ceramic matrix composite, then solving a generalized eigenvalue problem to obtain natural frequencies and modes. However, this method fails to fully consider the material's oxidative damage characteristics, making it difficult to accurately assess turbine blade performance under service conditions. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for calculating the natural frequency of ceramic matrix composite turbine blades taking into account damage. The method can be combined with a three-dimensional finite element model of ceramic matrix composites to realize the calculation process of the nonlinear vibration response of CMCs, thereby improving the accuracy of the natural frequency calculation. The present invention can be widely used in the performance evaluation of ceramic matrix composite turbine blades and has strong engineering application value.

[0005] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0006] A method for calculating the natural frequency of a ceramic matrix composite turbine blade taking damage into account, the method comprising the following steps:

[0007] S1. Establish a three-dimensional finite element model of a ceramic matrix composite turbine blade. According to the damage evolution of the ceramic matrix composite, perform a three-segment fitting of the material's tensile curve, including a first linear segment, a nonlinear segment, and a second linear segment. Describe the nonlinear constitutive relationship of the ceramic matrix composite based on the elastic moduli of the first linear segment, the nonlinear segment, and the second linear segment. Calculate the undamaged natural frequency of the turbine blade and the lower limit of the natural frequency in the damaged state using the elastic moduli of the first linear segment and the second linear segment, respectively.

[0008] S2, combining the natural frequency of the intact state and the lower limit of the natural frequency of the damaged state to predict the range of the nonlinear natural frequency;

[0009] S3: Set the frequency bandwidth based on the range of the nonlinear natural frequency, perform time-domain frequency sweep analysis on the blade model in the intact state, gradually apply harmonic loads at different excitation frequencies, extract the steady-state displacement response amplitudes corresponding to different excitation frequencies, and complete the time-domain excitation analysis of the blade model;

[0010] S4, based on the amplitude results of the time domain excitation analysis, draw the amplitude-frequency response curve, take the peak frequency of the amplitude-frequency response curve as the dynamic natural frequency, and extract the nonlinear response characteristics of the turbine blade.

[0011] As a preferred example, in step S1, the nonlinear constitutive relationship of the ceramic matrix composite material is:

[0012]

[0013] Where, E c is the elastic modulus of the material, E1 is the elastic modulus of the first linear segment of the material, ε1 is the end strain of the first linear segment of the material, E2 is the elastic modulus of the second linear segment of the material, ε2 is the end strain of the second linear segment of the material, a1, a2, a3, a4 are the fitting parameters of the nonlinear segment of the material, and ε is the current strain of the material.

[0014] As a preferred example, in step S1, based on the elastic modulus of the first linear segment of the ceramic matrix composite material, a material mechanics model in a lossless state is established to calculate the blade natural frequency f in the lossless state. und :

[0015]

[0016] Where k1 is the lossless stiffness of the ceramic matrix composite material, and m is the mass of the turbine blade.

[0017] As a preferred example, in step S1, based on the elastic modulus of the second linear segment of the ceramic matrix composite material, the lower limit of the natural frequency f under the damage state is calculated. da :

[0018]

[0019] Where k2 is the damage stiffness of the ceramic matrix composite.

[0020] As a preferred example, in step S2, the nonlinear natural frequency f nonlinear The following conditions are met:

[0021] f da ≤f nonlinear≤f und

[0022] Where, f und and f da are the blade natural frequency in the intact state and the lower limit of the natural frequency in the damaged state, respectively.

[0023] As a preferred example, step S3 further includes:

[0024] Set the frequency bandwidth [f min ,f max ] and frequency step Δf, gradually applying different excitation frequencies f i Harmonic load F under i (t), perform time domain frequency sweep analysis on the blade model in the intact state and extract different excitation frequencies f i The steady-state displacement response amplitude A(f i ), where F(t) = F0sin(2πf i t), f da =f min , f und =f max ;

[0025] Where F0 is the amplitude of the excitation.

[0026] The steady-state displacement response amplitude A(f i ) when the increase is greater than the preset increase threshold (for example, when the increase ΔA(f i The frequency range of )>>0.2mm is taken as the resonance range. For the resonance range, the frequency step Δf is reduced to perform refined scanning to capture the resonance characteristics of the nonlinear material.

[0027] As a preferred example, in step S3, the initial value of the frequency step Δf is 1 Hz, and the frequency step Δf in the resonance range is 0.1 Hz.

[0028] As a preferred example, the formula for the steady-state displacement response amplitude A(f) corresponding to different excitation frequencies f is:

[0029]

[0030] Where K is the stiffness matrix, M is the mass matrix, C is the damping matrix, and ω = 2πf.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] First, the present invention's damage-considered natural frequency calculation method for ceramic matrix composite (CMC) turbine blades establishes a damage-considered stiffness model. Combined with finite element software, it can rapidly determine the modal response of CMCs under vibration loads. Compared to existing linear calculation methods, this method considers the nonlinear constitutive properties of CMCs, enabling prediction of the natural frequency of CMCs under damage and acquisition of amplitude-frequency curves. This allows for accurate prediction of the material's damage state and dynamic response characteristics, enabling the calculation of the nonlinear vibration response of CMCs and improving the accuracy of natural frequency calculations.

[0033] Second, the damage-considered natural frequency calculation method of the ceramic matrix composite turbine blade of the present invention can be widely used in the performance evaluation of ceramic matrix composite turbine blades and has strong engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of three-segment mechanical property curve of ceramic matrix composite material;

[0035] Figure 2 It is a schematic diagram of the structure of the blade finite element model;

[0036] Figure 3 Schematic diagram of harmonic load under different excitation frequencies;

[0037] Figure 4 Schematic diagram of the comparison between the vibration response with damage and the undamaged state;

[0038] Figure 5 Flowchart of the calculation method for the natural frequency of ceramic matrix composite turbine blades considering damage. DETAILED DESCRIPTION

[0039] The embodiments of the present invention are described in further detail below with reference to the accompanying drawings.

[0040] This embodiment discloses a method for calculating the natural frequency of a ceramic matrix composite turbine blade taking into account damage, the method comprising the following steps:

[0041] S1. Establish a three-dimensional finite element model of a ceramic matrix composite turbine blade. According to the damage evolution of the ceramic matrix composite, perform a three-segment fitting on the tensile curve of the material. Describe the nonlinear constitutive relationship of the ceramic matrix composite according to the elastic modulus of the first linear segment, the nonlinear segment, and the second linear segment, and assign it to the turbine structure through a subroutine. Calculate the natural frequency of the turbine blade without damage and the lower limit of the natural frequency in the damaged state through the elastic modulus of the first linear segment and the second linear segment respectively.

[0042] S2, combining the natural frequency of the intact state and the lower limit of the natural frequency of the damaged state to predict the range of the nonlinear natural frequency;

[0043] S3: Set the frequency bandwidth based on the range of the nonlinear natural frequency, perform time-domain frequency sweep analysis on the blade model in the intact state, gradually apply harmonic loads at different excitation frequencies, extract the steady-state displacement response amplitudes corresponding to different excitation frequencies, and complete the time-domain excitation analysis of the blade model;

[0044] S4, based on the amplitude results of the time domain excitation analysis, draw the amplitude-frequency response curve, take the peak frequency of the amplitude-frequency response curve as the dynamic natural frequency, and extract the nonlinear response characteristics of the turbine blade.

[0045] See also Figure 5 , the method specifically comprises the following steps:

[0046] Step 1: Establish a three-dimensional finite element model of the ceramic matrix composite material. According to the damage evolution of the ceramic matrix composite material, perform a three-segment fitting of the tensile curve. The nonlinear constitutive relationship of the material is described according to the first linear segment, the nonlinear segment, and the second linear segment.

[0047]

[0048] Where, E c is the elastic modulus of the material, E1 is the elastic modulus of the first linear segment of the material, ε1 is the end strain of the first linear segment of the material, E2 is the elastic modulus of the second linear segment of the material, ε2 is the end strain of the second linear segment of the material, a1, a2, a3, a4 are the fitting parameters of the nonlinear segment of the material, and ε is the current strain of the vortex material.

[0049] Under anisotropic conditions, the stiffness matrix C of ceramic matrix composites ij The various terms are composed of the elastic modulus E(ε), shear modulus G ij and Poisson's ratio v ij In this embodiment, the stiffness matrix C ij is a 6x6 stiffness matrix defined as follows:

[0050]

[0051] Stiffness matrix C ij The components of can be expressed using the material elastic modulus and Poisson's ratio:

[0052]

[0053] C 12 =v 12 C 11 ,C 13 =v 13 C 11

[0054] C44 =G 12 ,C 55 =G 23 ,C 66 =G 13

[0055] Among them, C 11 The corresponding elastic modulus depends on the E of the current stage c ,Right now:

[0056]

[0057] Generate the global stiffness matrix K of the entire system in the finite element software. The global stiffness matrix K is calculated using the following formula:

[0058]

[0059] Where B is the unit strain-displacement matrix; D is the elastic matrix of the material (including information such as elastic modulus and Poisson's ratio), and V is the blade volume.

[0060] Step 2: Based on the first linear segment elastic modulus of the ceramic matrix composite material, a material mechanics model in the non-destructive state is established to calculate the natural frequency of the blade in the non-destructive state.

[0061]

[0062] Where k1 is the lossless stiffness and m is the mass.

[0063] Step 3: Calculation of the natural frequency in the damaged state: Based on the second linear segment elastic modulus of the ceramic matrix composite material, calculate the lower limit of the natural frequency in the damaged state:

[0064]

[0065] Where k2 is the damage stiffness.

[0066] The modal analysis under the lossless state is completed by finite element software. The natural frequency and vibration mode are calculated using the modal analysis steps. The natural frequency of the blade is obtained by solving the modal equation. The basic form of the modal equation is:

[0067] [K-ω 2 M]Φ=0

[0068] Where M is the mass matrix, ω is the angular frequency, and the natural frequency f is related to it as follows: Φ is the vibration mode vector.

[0069] Step 4: Nonlinear natural frequency range prediction: Combined with the lossless state natural frequency f und , the lower limit of the natural frequency of the damage state f da, and the range of nonlinear natural frequency is obtained:

[0070] f da ≤f nonlinear ≤f und .

[0071] Step 5: Time domain excitation analysis: Set the frequency bandwidth [f min ,f max ], frequency range [f min ,f max ] includes the lower limit of the natural frequency of damage and the natural frequency of damage, and performs a time domain frequency sweep analysis on the blade model in the intact state, gradually applying different excitation frequencies f i Harmonic loads under:

[0072] F(t)=F0sin(2πf i t);

[0073] Extract f i The steady-state displacement response amplitude A(f i The harmonic load amplitude in the time domain excitation analysis is kept constant, and the peak change of the displacement response amplitude A(f) and its corresponding frequency f are extracted. peak Characterization is performed, and the relationship between the response amplitude and frequency satisfies the following formula:

[0074]

[0075] Where K is the stiffness matrix, M is the mass matrix, C is the damping matrix, and ω = 2πf.

[0076] Step 6: Refined analysis of the resonance range: After observing the response amplitude A(f i ) significantly increases the frequency range, shortens the frequency step Δf, and reduces the possible resonance frequency f dynamic Perform refined scans to capture the resonant properties of nonlinear materials.

[0077] S7: Amplitude-frequency response curve drawing and dynamic response analysis: Based on the amplitude results of time domain excitation analysis, draw the amplitude-frequency response curve A(f) and extract the dynamic natural frequency f dynamic And nonlinear response characteristics. Dynamic natural frequency f dynamic According to the peak frequency f of the amplitude-frequency response curve peak Sure.

[0078] Examples

[0079] The embodiment of the present invention provides a specific example. In this example, a finite element model of a CMCs beam is first established, with a geometric size of (140×10×3) mm and a density of 1771 kg / m 3In the finite element model of the CMCs beam, fixed support constraints are applied to the nodes at the root and clamping area of ​​the beam, limiting the displacement in three directions to zero to simulate the fixing effect in the actual test. A sinusoidal gravity field with an acceleration amplitude of 50m / s is loaded in the vertical direction. 2 . Figure 1 Schematic diagram of the three-segment mechanical property curve of ceramic matrix composites.

[0080] The natural frequency calculation method for this example includes the following steps:

[0081] Step 1: Create a ceramic matrix composite cantilever beam and divide the mesh, as shown in the following example: Figure 2 As shown. The damage-free elastic parameters of the composite material are as follows:

[0082] E 11 =274.8GPa,E 22 =65GPa,

[0083] G 12 =G 13 =G 23 =25.2GPa,

[0084] v 12 =v 13 =v 23 =0.3;

[0085] Calculate its natural frequency f in the undamaged state und =669.6Hz.

[0086] Step 2: The damage elastic parameters of the composite material are as follows:

[0087] E 11 =32.8GPa,E 22 =65GPa,

[0088] G 12 =G 13 =G 23 =25.2GPa,

[0089] v 12 =v 13 =v 23 =0.3;

[0090] Calculate its damage state natural frequency f da =231.3Hz.

[0091] Step 3, nonlinear natural frequency range prediction: combined with the lossless state natural frequency f und , the lower limit of the natural frequency of the damage state f da , and the range of nonlinear natural frequency is obtained:

[0092] 231.3Hz≤f nonlinear ≤669.6Hz.

[0093] Step 4: describe the nonlinear constitutive relationship of the material using the first linear segment, the nonlinear segment, and the second linear segment of the tensile stress-strain curve.

[0094]

[0095] Step 5: Set the frequency bandwidth to [231.3Hz, 668.6Hz], perform time domain frequency sweep analysis on the blade model in the intact state, and gradually apply different excitation frequencies f i Harmonic loads under:

[0096] F(t)=50sin(2πf i t);

[0097] Extract f i The steady-state displacement response amplitude A(f i ). Figure 3 Schematic diagram of harmonic load under different excitation frequencies.

[0098] Step 6, fine-grained analysis of the resonance range: After observing the response amplitude A(f i ) significantly increases the frequency range, shortens the frequency step Δf, and reduces the possible resonance frequency f dynamic Perform refined scans to capture the resonant properties of nonlinear materials. Figure 4 Schematic diagram of the comparison between the vibration response with damage and the undamaged state.

[0099] Step 7: Plotting the amplitude-frequency response curve and dynamic response analysis: Using the frequency sweep results of the time domain excitation analysis, plot the amplitude-frequency response curve A(f) and extract the dynamic natural frequency f dynamic =576.9Hz and nonlinear response characteristics.

[0100] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0101] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0102] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0103] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions for executing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0104] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0105] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A method for calculating the natural frequency of a ceramic matrix composite turbine blade taking into account damage, characterized in that: The method comprises the following steps: S1. Establish a three-dimensional finite element model of a ceramic matrix composite turbine blade. According to the damage evolution of the ceramic matrix composite, perform a three-segment fitting of the material's tensile curve, including a first linear segment, a nonlinear segment, and a second linear segment. Describe the nonlinear constitutive relationship of the ceramic matrix composite based on the elastic moduli of the first linear segment, the nonlinear segment, and the second linear segment. Calculate the undamaged natural frequency of the turbine blade and the lower limit of the natural frequency in the damaged state using the elastic moduli of the first linear segment and the second linear segment, respectively. S2, combining the natural frequency of the intact state and the lower limit of the natural frequency of the damaged state to predict the range of the nonlinear natural frequency; S3: Set the frequency bandwidth based on the range of the nonlinear natural frequency, perform time-domain frequency sweep analysis on the blade model in the intact state, gradually apply harmonic loads at different excitation frequencies, extract the steady-state displacement response amplitudes corresponding to different excitation frequencies, and complete the time-domain excitation analysis of the blade model; S4, based on the amplitude results of the time domain excitation analysis, draw the amplitude-frequency response curve, take the peak frequency of the amplitude-frequency response curve as the dynamic natural frequency, and extract the nonlinear response characteristics of the turbine blade.

2. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 1, characterized in that: In step S1, the nonlinear constitutive relationship of the ceramic matrix composite material is: Where, E c is the elastic modulus of the material, E1 is the elastic modulus of the first linear segment of the material, ε1 is the end strain of the first linear segment of the material, E2 is the elastic modulus of the second linear segment of the material, ε2 is the end strain of the second linear segment of the material, a1, a2, a3, a4 are the fitting parameters of the nonlinear segment of the material, and ε is the current strain of the material.

3. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 1, characterized in that: In step S1, based on the elastic modulus of the first linear segment of the ceramic matrix composite material, a material mechanics model in a lossless state is established, and the blade natural frequency f in the lossless state is calculated. und : Where k1 is the lossless stiffness of the ceramic matrix composite material, and m is the mass of the turbine blade.

4. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 1, characterized in that: In step S1, based on the elastic modulus of the second linear segment of the ceramic matrix composite material, the lower limit of the natural frequency f under damage state is calculated. da : Where k2 is the damage stiffness of the ceramic matrix composite material, and m is the mass of the turbine blade.

5. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 1, characterized in that: In step S2, the nonlinear natural frequency f nonlinear The following conditions are met: f da ≤f nonlinear ≤f und Where, f und and f da are the blade natural frequency in the intact state and the lower limit of the natural frequency in the damaged state, respectively.

6. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 5, characterized in that: Step S3 further comprises: Set the frequency bandwidth [f min ,f max ] and frequency step Δf, gradually applying different excitation frequencies f i Harmonic load F under i (t), perform time domain frequency sweep analysis on the blade model in the intact state and extract different excitation frequencies f i The steady-state displacement response amplitude A(f i ), where F i (t) = F0sin(2πf i t), f da =f min , f und =f max ; F0 is the amplitude of the excitation; The steady-state displacement response amplitude A(f i ) The frequency range when the amplification is greater than the preset amplification threshold is taken as the resonance range. For the resonance range, the frequency step Δf is reduced to perform a refined scan to capture the resonance characteristics of the nonlinear material.

7. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 6, characterized in that: In step S3 , the initial value of the frequency step Δf is 1 Hz, and the frequency step Δf in the resonance range is 0.1 Hz.

8. The damage-considered natural frequency calculation method for ceramic matrix composite turbine blades according to claim 6, characterized in that: The formula for the steady-state displacement response amplitude A(f) corresponding to different excitation frequencies f is: Where K is the stiffness matrix, M is the mass matrix, C is the damping matrix, and ω = 2πf.

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