Ceramic matrix composite turbine blade inherent frequency calculation method considering damage

Abstract

The invention discloses a damage-considered inherent frequency calculation method for a ceramic matrix composite turbine blade, which comprises the following steps of: establishing a three-dimensional finite element model of a ceramic matrix composite, and calculating according to elastic moduli of a first linear section and a second linear section to obtain a damage-free inherent frequency of the turbine blade and an inherent frequency lower limit in a damage state; predicting the range of the nonlinear inherent frequency by combining the nondestructive state inherent frequency and the damage state inherent frequency lower limit; setting a frequency bandwidth based on the range of the nonlinear inherent frequency, carrying out time-domain frequency sweep analysis on the blade model in a lossless state, gradually applying harmonic loads under different excitation frequencies, extracting steady-state displacement response amplitudes corresponding to the different excitation frequencies, and completing time-domain excitation analysis on the blade model; and extracting the dynamic inherent frequency based on the amplitude result of the time domain excitation analysis. According to the method, the calculation process of the nonlinear vibration response of the CMCs can be realized, and the accuracy of inherent frequency calculation is improved.

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 a ceramic matrix composite turbine blade taking damage into consideration, and is particularly suitable for predicting the mechanical properties of a ceramic matrix composite material in a damaged state. Background Art

[0002] Ceramic matrix composites are widely used in high-temperature structural components such as aircraft engine turbine blades due to their excellent high-temperature performance. However, the high-temperature oxidation environment has a significant impact on the material properties. The oxidation reaction causes the strength and stiffness of the material to decrease, and triggers a complex mesoscopic damage mechanism, which affects the dynamic characteristics and natural frequency of the blades. The traditional natural frequency calculation method fails to fully consider the oxidation damage characteristics of the material, making it difficult to accurately evaluate the performance of turbine blades under service conditions.

[0003] The invention with the publication number CN110852015B discloses a nonlinear calculation method for the modal of ceramic matrix composite materials. The invention proposes to establish a ceramic matrix composite material stiffness model based on damage, and then solve the generalized eigenvalue problem to obtain the natural frequency and natural vibration mode. However, the invention also fails to fully consider the oxidation damage characteristics of the material, making it difficult to accurately evaluate the performance of turbine blades 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 a ceramic matrix composite turbine blade taking into account damage, which can be combined with a three-dimensional finite element model of a ceramic matrix composite material to realize the calculation process of the nonlinear vibration response of CMCs and improve 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 a 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 into account damage, the method comprising the following steps:

[0007] S1, establish a three-dimensional finite element model of a ceramic matrix composite turbine blade, perform a three-segment fitting of the material's tensile curve including a first linear segment, a nonlinear segment, and a second linear segment according to the damage evolution of the ceramic matrix composite, 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; calculate the undamaged natural frequency of the turbine blade 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;

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

[0009] S3, setting the frequency bandwidth based on the range of nonlinear natural frequency, performing time domain frequency sweep analysis on the blade model in the lossless state, gradually applying harmonic loads at different excitation frequencies, extracting the steady-state displacement response amplitudes corresponding to different excitation frequencies, and completing 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 relation of the ceramic matrix composite material is:

[0012]

[0013] In the formula, 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 a 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 damaged 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] In the formula, f und and f da They 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 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 )>>0.2mm) is used 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 damage-considered ceramic matrix composite turbine blade natural frequency calculation method of the present invention establishes a damage-considered stiffness model, and combined with finite element software, can quickly give the modal response of the ceramic matrix composite under vibration load. Compared with the existing linear calculation method, the present invention takes into account the nonlinear constitutive structure of the ceramic matrix composite, can realize the prediction of the natural frequency of the ceramic matrix composite under the damaged state and the acquisition of the amplitude-frequency curve, accurately predict the damage state of the material and its dynamic response characteristics, realize the calculation process of the nonlinear vibration response of CMCs, and improve the accuracy of the natural frequency calculation.

[0033] Second, the natural frequency calculation method of ceramic matrix composite turbine blades considering damage 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 It is a schematic diagram of the three-stage mechanical characteristic curve of the 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 further described in 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, perform a three-segment fitting on the tensile curve of the material according to the damage evolution of the ceramic matrix composite, 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 the turbine structure through a subroutine; calculate the undamaged natural frequency of the turbine blade 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, predicts the range of the nonlinear natural frequency;

[0043] S3, setting the frequency bandwidth based on the range of nonlinear natural frequency, performing time domain frequency sweep analysis on the blade model in the lossless state, gradually applying harmonic loads at different excitation frequencies, extracting the steady-state displacement response amplitudes corresponding to different excitation frequencies, and completing 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 on the tensile curve. Describe the nonlinear constitutive relationship of the material according to the first linear segment, the nonlinear segment, and the second linear segment.

[0047]

[0048] In the formula, 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 described by 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 c ,Right now:

[0056]

[0057] The global stiffness matrix K of the entire system is generated in the finite element software. The global stiffness matrix K is calculated by 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 under the non-destructive state is established to calculate the natural frequency of the blade under 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 by modal analysis steps, and 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 obtain the range of nonlinear natural frequency:

[0070] f da ≤f nonlinear ≤f und .

[0071] Step 5: Time Domain Stimulus Analysis: Set the frequency bandwidth [f min ,f max ], frequency range [f min ,f max ] includes the lower limit of the intact natural frequency and the damaged natural frequency. The blade model in the intact state is subjected to time domain frequency sweep analysis, and different excitation frequencies f are gradually applied. 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 the 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, reduces the frequency step Δf, and 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, the nodes at the root and clamping area of ​​the beam are subjected to fixed support constraints, limiting the displacement in three directions to zero to simulate the fixing effect in the actual test. A sinusoidal gravity field is loaded in the vertical direction, and the acceleration amplitude of the gravity field is 50m / s 2 . Figure 1 Schematic diagram of the three-segment mechanical property curve of ceramic matrix composites.

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

[0081] Step 1: Create a ceramic matrix composite cantilever beam and divide the mesh, such as 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 obtain the range of nonlinear natural frequency:

[0092] 231.3Hz≤f nonlinear ≤669.6Hz.

[0093] Step 4, describing the nonlinear constitutive relationship of the material for 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 [231.3 Hz, 668.6 Hz], perform a 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: Refined analysis of the resonance range: After observing the response amplitude A(f i ) significantly increases the frequency range, reduces the frequency step Δf, and 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 considering damage and the undamaged state.

[0099] Step 7: Plotting the amplitude-frequency response curve and dynamic response analysis: Plot the amplitude-frequency response curve A(f) through the frequency sweep results of the time domain excitation analysis 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 present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present 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 embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal 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 generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. 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 capable of directing a computer or other programmable data processing device to operate 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 A 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 instructions for implementing the process in the computer or other programmable device. 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 other 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 falling within the scope of the present application.

[0105] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also 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, perform a three-segment fitting of the material's tensile curve including a first linear segment, a nonlinear segment, and a second linear segment according to the damage evolution of the ceramic matrix composite, 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; calculate the undamaged natural frequency of the turbine blade 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; S2, combining the natural frequency of the intact state and the lower limit of the natural frequency of the damaged state, predicts the range of the nonlinear natural frequency; S3, setting the frequency bandwidth based on the range of nonlinear natural frequency, performing time domain frequency sweep analysis on the blade model in the lossless state, gradually applying harmonic loads at different excitation frequencies, extracting the steady-state displacement response amplitudes corresponding to different excitation frequencies, and completing 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 method for calculating the natural frequency of a ceramic matrix composite turbine blade considering damage according to claim 1, characterized in that: In step S1, the nonlinear constitutive relation of the ceramic matrix composite material is: In the formula, 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 method for calculating the natural frequency of a ceramic matrix composite turbine blade considering damage 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 to calculate the blade natural frequency f in a lossless state. und : Where k1 is the lossless stiffness of the ceramic matrix composite material, and m is the mass of the turbine blade.

4. The method for calculating the natural frequency of a ceramic matrix composite turbine blade considering damage 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 the damaged 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 method for calculating the natural frequency of a ceramic matrix composite turbine blade considering damage 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 vf und In the formula, f und and f da They are the blade natural frequency in the intact state and the lower limit of the natural frequency in the damaged state, respectively.

6. The method for calculating the natural frequency of a ceramic matrix composite turbine blade considering damage according to claim 1, 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 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 ; F0 is the amplitude of the excitation; The steady-state displacement response amplitude A(f i ) The frequency range when the increase is greater than the preset increase 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 method for calculating the natural frequency of a ceramic matrix composite turbine blade taking into account damage 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 method for calculating the natural frequency of a ceramic matrix composite turbine blade taking into account damage according to claim 1, 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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