A strength simulation method for CMC turbine blades considering dispersion

Abstract

The present invention discloses a CMC turbine blade strength simulation method that takes dispersion into consideration. The random factors are determined by deterministic analysis of composite turbine blades from a microscopic perspective to a macroscopic perspective, a nested proxy model is used to establish the relationship between input and output with high precision, and the failure probability of the blade is calculated by an optimized subset simulation collaborative analysis method. The present invention breaks through the current research field of strength prediction from a microscopic to a macroscopic perspective and the low precision of a single proxy model. Multiple proxy models are nested to ensure data fitting accuracy, and the failure probability calculation interval is narrowed by calling the optimized subset simulation collaborative analysis. While solving the problem of the influence of microscopic dispersion on macroscopic strength, the efficiency of calculating blade strength probability and the accuracy of blade strength probability analysis are improved at the same time.

Description

Technical Field

[0001] The present invention relates to the field of composite blade strength analysis, and in particular to a method for simulating the strength of a ceramic matrix composite (CMC) blade based on a nested proxy model and a combination thereof, taking into account the dispersion of the structure from micro to macro, especially in the field of turbine blade strength analysis. Background Art

[0002] Ceramic-based composites have the characteristics of low density, high temperature resistance, and impact resistance. They have been used in the manufacture of high-temperature and medium-load stationary parts such as engine tail nozzle adjustment plates, inner cones, and turbine blades. CMCs materials are extremely hard and have uneven components, making them difficult to process. Therefore, ceramic-based composites will inevitably cause damage and defects during production and processing. The presence of microstructures such as microcracks and pores in the material will cause stress concentration. When the load exceeds the critical stress, the microcracks will expand and cause structural damage.

[0003] The turbine blade studied in the present invention is made of CMCs material. From a microscopic scale, the ceramic matrix itself is a porous material, and the fiber bundles are spatially staggered. It is very easy to leave pores at the intersection of the fiber bundles during the matrix deposition process. Therefore, the size of the porosity has a certain randomness. It is inevitable that there are defects in the fiber bundles during the manufacturing process. Defects of different forms and degrees are randomly distributed on the surface and inside, resulting in a certain randomness in the mechanical performance parameters of the fiber bundles. From a macroscopic scale, due to the influence of the preparation process, the turbine blades have more or less deviations from the design values ​​during processing and manufacturing. The geometric size parameters of the turbine blades, such as the leading edge of the blade tip, the trailing edge of the blade tip, and the leading edge of the blade root, which are difficult to process, also have a certain dispersion. The main load borne by the blade during operation is centrifugal force. There are two types of blade failure modes, one is the fracture of the blade root, and the other is excessive deformation. The blade weaving direction adopts the method of coinciding the longitudinal direction of the material with the warp direction of the blade, so that the blade can withstand more loads in the warp direction.

[0004] A surrogate model is a method of fitting the relationship between input and output variables by constructing an approximate model through a small number of sample points. There are many types of surrogate models. The polynomial response surface model is used to approximate and predict the output response of a complex system or process. It is suitable for models with low nonlinearity. Since the nonlinearity of functions in most engineering examples is high, the Kriging model has high computational accuracy in solving problems with high dimensions and high nonlinearity. The Kriging model has global and local statistical characteristics and can efficiently analyze the trend of changes. It is an unbiased estimation model that predicts the response value of unknown sample points through known sample points in space. Therefore, the surrogate model can be nested, and a high-fidelity model can be obtained by identifying the relevant proportional coefficients of the function sample points.

[0005] The optimized subset simulation collaborative analysis method is an extended subset simulation technique used to estimate the failure probability of complex systems or structures under specific conditions. It improves efficiency by decomposing the calculation of failure probability into a series of more manageable sub-problems, and can efficiently handle the characteristics of high-dimensional and small failure probability problems. The optimized subset simulation collaborative analysis method is a method that combines optimized subset simulation and collaborative analysis. It converts small failure probabilities into the product of a sequence of larger conditional probabilities by adaptively introducing a series of nested intermediate events, that is, a series of large conditional event simulation processes are used to represent the small failure probability event simulation process. The optimized subset simulation collaborative analysis is used to improve the efficiency and accuracy of structural reliability analysis.

[0006] In the structural reliability analysis of turbine blades, turbine blades contain multiple failure modes. In addition to the influence of external loads, many failure modes are still closely related to the dispersion of microstructure and macrostructure. Therefore, from a microscopic perspective, studying the dispersion of microstructure and dispersion of macrostructure parameters for blade strength analysis is an important issue that has never been addressed in this field. Therefore, in order to solve this type of problem, the nested proxy model and optimized subset simulation collaborative analysis can be combined to reduce the number of samples, improve the accuracy of the results, and enhance the convergence of the algorithm. Summary of the invention

[0007] In order to overcome the shortcomings of the prior art, the present invention proposes a ceramic matrix composite (CMC) blade strength simulation method based on a nested proxy model and optimized subset simulation collaborative analysis taking into account dispersion. First, the blade determinism is analyzed, the failure load and failure form when considering dispersion are analyzed, and the random factors are determined. The nested proxy model and optimized subset simulation collaborative analysis are combined to perform uncertainty analysis and blade strength probability analysis, which can effectively improve the accuracy and calculation efficiency of the actual failure probability of the model.

[0008] The technical solution of the present invention is as follows:

[0009] Step 1: From a microscopic perspective, a unit cell model including the microstructural parameters of the CMCs fibers and pores is established, and from a macroscopic perspective, a blade macroscopic model is established.

[0010] Step 2, perform finite element analysis on the unit cell model, first take the dispersed porosity and fiber strength as meso-random factors, use probability test method to identify the distribution type of random factors, and ensure the validity of probability when sampling meso-random factors; then calculate the meso-mechanical performance parameters of CMC materials under different working conditions, and identify the distribution type and dispersion of meso-mechanical performance parameters. Meso-random factors (including meso-mechanical performance parameters) affect the failure probability and will be used for calculations in subsequent steps.

[0011] Step 3, a new CMCs failure criterion is established based on the strain Hashin criterion. The internal parameters of the criterion are the mechanical performance parameters of the unit cell model obtained in step 2. Based on the criterion, four failure modes, namely, longitudinal tensile fracture, longitudinal compression fracture, latitudinal tensile fracture and latitudinal compression fracture, are judged. That is, by setting different load intervals, it is judged whether the CMC blade will produce tensile fracture or compression fracture failure under longitudinal or latitudinal loads.

[0012] Step 4, based on the blade macro model in step 1, perform a deterministic analysis on the blade strength, take the mean of the microscopic mechanical performance parameters and the dimensional parameters of the blade macro model as input, calculate the stress distribution of the blade when it is about to fail through finite element method, and determine the failure section, failure form and load form on the blade macro model when it is most prone to failure.

[0013] Step 5: performing uncertainty analysis on the turbine blade strength based on the blade macro model to obtain macro random factors and their distribution types that affect the blade probabilistic strength.

[0014] Step 6. According to the different randomness, sampling is performed based on micro-random factors, macro-random factors and multi-scale parameters including micro- and macro-factors. A new optimized partial sorting random sampling method is designed to extract sufficient samples, such as: longitudinal tensile strength, latitudinal tensile elastic modulus, blade tip leading edge thickness and blade root trailing edge thickness as input parameters of the blade model. The polynomial response surface and the Kriging proxy model are nested to form a new nested proxy model, and the connection between the input and output is established. The optimized subset simulation collaborative analysis method is used to evaluate the blade failure probability, output the probability density, and form a probability intensity distribution diagram.

[0015] Preferably, in step 2, the probability test method includes abnormal data screening, consistency test and distribution type selection:

[0016] First, abnormal data is screened, and the maximum normed residual test method is used to detect and eliminate outliers. Secondly, a probability distribution model is selected, and the observed significance level (OSL) values ​​of each probability distribution model are compared to select a suitable distribution model and test method. The mechanical property parameters with greater dispersion influence among the meso-random factors are selected. Finally, the observed significance level values ​​of the mechanical property parameter probability distribution models (including normal distribution, two-parameter Weibull distribution, lognormal distribution and exponential distribution, etc.) are observed, and a suitable distribution model is selected and a consistency test is performed. The consistency test uses the Anderson-Darling test method and the Bayesian hypothesis test.

[0017] Preferably, in step 3, a new CMCs failure criterion is established based on the strain Hashin criterion, and the judgment equation is:

[0018]

[0019] Where 1 and 2 indicate that the fiber reinforcement direction is warp or weft, ε t represents the tensile positive strain, ε c represents the compressive normal strain, γ represents the shear strain, σ is the normal stress, E is the Young's modulus, and G is the shear modulus.

[0020] Preferably, in step 5, two failure modes, blade damage and excessive blade deformation, are considered, and the blade strength is characterized by the ratio of the rotational speed corresponding to the blade failure divided by the operating speed. Several groups of input parameters are extracted based on the new optimized partial sorting random sampling method.

[0021] Preferably, in step 6, the new optimized partial sorting random sampling method is: adaptive sampling based on Latin hypercube sampling, dynamically adjusting the positions of subsequent sampling points according to the existing sample point information, that is, stratifying the nested proxy model according to different proportional coefficients and dividing it into multiple parameter spaces, and adaptively sampling each level space in turn.

[0022] Preferably, in step 6, the nested surrogate model is an unbiased estimation model that predicts the response value of an unknown sample point through known sample points in space, and its expression is:

[0023]

[0024] In the formula, is the final prediction of the nested model, is the prediction of the polynomial response surface,

[0025] is the prediction of the Kriging model, a1 and a2 are their proportions, and satisfy a1+a2=1.

[0026] Preferably, in step 6, a1 and a2 are determined by their linearity and nonlinearity, and the correlation degree can be expressed as:

[0027]

[0028] Where i = 1 or 2, indicating a polynomial response surface or a Kriging proxy model, m indicates the number of sample points close to the fitting points, and n represents the number of remaining sample points. The degree of fit within 5% is considered to meet the closeness requirement.

[0029] Preferably, in step 6, the optimized subset simulation collaborative analysis method adaptively introduces a series of mutually nested intermediate events (i.e., load intervals), converts a small failure probability into a product of a sequence of larger conditional probabilities, and calculates the failure probability based on the collaborative analysis method, which is expressed as:

[0030]

[0031] Where M is the total number of intermediate events. When the conditional probability is a constant p0, the intermediate events can be determined adaptively. j is the indicator function of the jth sample point, N is the number of samples, and the indicator function I j It is used to determine whether the jth sample point meets the failure condition. If the sample point belongs to the failure area and meets the failure condition, Ij=1; if the sample point does not belong to the failure area and does not meet the failure condition, Ij=0; ξ is the collaborative analysis factor, which is adjusted according to the collaborative analysis results.

[0032] As a preference, in step 6, given the coefficient of variation δ and the probability of failure Then the number of samples in the optimized subset simulation collaborative analysis is:

[0033]

[0034] Where r≤3 and the failure probability of each layer is estimated is determined by the correlation between them, γ is the correlation coefficient, and P0 is the failure probability of the intermediate event.

[0035] Beneficial Effects

[0036] 1. The present invention is directed to a strength simulation method for composite turbine blades that takes dispersion into consideration. First, a microscopic-scale woven CMCs unit cell model of the blade and a macroscopic-scale blade model are established. The woven CMCs are regarded as uniform anisotropic materials using homogenization theory. Unlike finite element analysis, the present invention simplifies the blade model into an equivalent proxy model, which can more efficiently solve problems with high dimensions and high nonlinearity, can convert deterministic models into uncertainty analysis problems, and can improve the accuracy of strength simulation.

[0037] 2. The present invention uses optimized subset simulation collaborative analysis to calculate the failure probability of small failure probability events with fewer samples, especially for turbine blade failure probability with a coefficient of variation less than 0.16 at a 95% confidence level. The traditional Monte Carlo method requires at least 10 8 sample points, while the optimized subset simulation collaborative analysis requires 1800 sample points, which can effectively reduce the number of samples and greatly improve the efficiency of solving the failure probability.

[0038] 3. In order to meet the requirements of both calculation accuracy and efficiency, the present invention considers a strength simulation method based on a combination of a nested proxy model and optimized subset simulation collaborative analysis. Under multi-scale objectives and considering the working conditions of blade dispersion, compared with traditional finite element simulation analysis, it can not only improve the accuracy of blade failure probability calculation, but also improve its calculation efficiency.

[0039] 4. The present invention utilizes a new optimized partial sorting random sampling method for experimental design sampling, combines it with a nested proxy model, and utilizes an optimized subset simulation collaborative analysis algorithm for strength analysis, which greatly improves computational efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The probability intensity analysis flow chart established by the present invention;

[0041] Figure 2 A schematic diagram of a turbine blade weaving method in one embodiment of the present invention;

[0042] Figure 3 A schematic diagram of a cross-section of a blade tip in an embodiment of the present invention;

[0043] Figure 4 A schematic diagram of a cross-section of a blade root in one embodiment of the present invention;

[0044] Figure 5 A schematic diagram of turbine blade mesh division in one embodiment of the present invention;

[0045] Figure 6 is the stress distribution on the back of turbine blade;

[0046] Figure 7 is the stress distribution of turbine blade basin;

[0047] Figure 8 Probabilistic strength distribution diagram of turbine blade considering mesoscopic randomness;

[0048] Fig. 9 Probabilistic strength distribution diagram of turbine blades considering macroscopic randomness;

[0049] Fig.10 Probabilistic strength distribution diagram of turbine blades considering multi-scale randomness;

[0050] Fig.11 is the radial displacement distribution diagram of turbine blades;

[0051] Fig.12 This is the probability distribution diagram of turbine blade radial displacement considering multi-scale randomness. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] Composite turbine blades have parameters with large dispersion at the micro and macro scales, including the randomness of the porosity and fiber strength of the unit cell model at the micro perspective, the macroscopic structure size and variation range of the turbine blade at the macro perspective, and the randomness of considering multiple scales. The present invention determines the random factors by performing deterministic analysis on the composite turbine blade from the micro perspective to the macro perspective, uses a nested proxy model to establish the relationship between input and output with high precision, and calculates the blade failure probability by optimizing the subset simulation collaborative analysis method.

[0054] A strength simulation method for ceramic matrix composite (CMC) blades considering dispersion is proposed based on nested surrogate model and optimized subset simulation collaborative analysis. Figure 1-Figure 12 As shown, take the engine turbine blade model as an example:

[0055] Step 1: Based on the real turbine blade, a CMCs unit cell model and a blade macro model are constructed from the microscopic and macroscopic perspectives respectively.

[0056] Step 2: Perform finite element analysis on the unit cell model. First, the dispersed porosity and fiber strength are taken as meso-random factors, and the probability test method is used to identify the distribution type of the random factors to ensure the validity of the probability when sampling the meso-random factors. Then, the meso-mechanical performance parameters of the CMC material under different working conditions are calculated, and the distribution type and dispersion of the meso-mechanical performance parameters are identified.

[0057] Probabilistic testing methods include abnormal data screening, consistency testing, and distribution type selection:

[0058] First, abnormal data is screened, and the maximum normed residual test method is used to detect and eliminate outliers. Secondly, a probability distribution model is selected, and the observed significance level (OSL) values ​​of each probability distribution model are compared to select a suitable distribution model and test method. The mechanical property parameters with greater dispersion influence among the meso-random factors are selected. Finally, the observed significance level values ​​of the mechanical property parameter probability distribution models (including normal distribution, two-parameter Weibull distribution, lognormal distribution and exponential distribution, etc.) are observed, and a suitable distribution model is selected and a consistency test is performed. The consistency test uses the Anderson-Darling test method and the Bayesian hypothesis test.

[0059] In this embodiment, considering that the load on the blade is generally in the form of centrifugal force, the failure modes of the blade generally include blade root fracture and excessive deformation (the above two conclusions are also verified by the deterministic analysis of step 4). Therefore, the blade weaving direction in this embodiment adopts a method in which the longitudinal direction of the material coincides with the warp direction of the blade, so that the blade can withstand more load in the warp direction. The microscopic weaving structure is as follows: Figure 2 As shown, the tip section and root section are as follows Figure 3 and Figure 4 shown.

[0060] In the example of the present invention, the influence of random factors on the probability distribution of blade strength is studied under the condition of a turbine rotor blade rotating at a speed of 12000 rpm. Body force is applied in finite element analysis software to simulate the centrifugal force on the blade, and coupling constraints are applied at the root of the blade to limit the radial displacement of the blade.

[0061] Step 3, a new CMCs failure criterion is established based on the strain Hashin criterion. The internal parameters of the criterion are the mechanical performance parameters of the unit cell model obtained in step 2. Based on the criterion, four failure modes, namely, longitudinal tensile fracture, longitudinal compression fracture, latitudinal tensile fracture and latitudinal compression fracture, are judged. That is, by setting different load intervals, it is judged whether the CMC blade will produce tensile fracture or compression fracture failure under longitudinal or latitudinal loads.

[0062] In this embodiment, the woven ceramic-based composite material is an anisotropic material, and due to its complex microstructure, the material has multiple failure modes. The load borne by the blade is centrifugal force, and the radial direction of the blade coincides with the warp direction of the material in the weaving direction, and the circumferential direction of the blade coincides with the weft direction of the material. Therefore, the centrifugal force borne by the blade in the material is manifested as tensile loads in the warp and weft directions. The failure theories such as Cai Xier and Cai Wu, which are commonly used in the analysis of the mechanical properties of composite materials, are not suitable for accurately describing the failure process of woven composite materials. This paper uses the strain-based Hashin criterion to establish a new turbine blade failure criterion for judging the failure of woven composite materials, and judges the four failure modes of warp pull-off, warp fracturing, weft pull-off and weft fracturing. The judgment equation is:

[0063]

[0064] Where 1 and 2 indicate that the fiber reinforcement direction is warp or weft, ε t represents the tensile positive strain, ε c represents the compressive normal strain, γ represents the shear strain, σ is the normal stress, E is the Young's modulus, and G is the shear modulus.

[0065] Step 4, based on the blade macro model in step 1, a deterministic analysis is performed on the blade strength, the mean of the microscopic mechanical performance parameters and the size parameters of the blade macro model are used as input, and the stress distribution of the blade when it is about to fail is calculated by finite element method to determine the failure section, failure form and load form when the blade macro model is most susceptible to failure. In this embodiment, the failure forms when the blade macro model is most susceptible to failure are determined to be blade damage and excessive blade deformation, and the load form when the blade macro model is most susceptible to failure is determined to be centrifugal load.

[0066] In this embodiment, the stress distribution is as follows: Figure 6 and Figure 7As shown in the figure, the stress distribution of the blade when it is about to break at the failure speed (109.86% of the working speed). Under the centrifugal load, there is obvious stress concentration at the root of the blade. Among the six stress components, the warp, weft and in-plane shear stresses are relatively large, with an order of magnitude of 10 2 MPa, and the magnitude of the remaining stress components is 10 1 MPa, which is much smaller than the strength value. If the load continues to rise, the blade root will be damaged first.

[0067] The radial stress distribution on the blade basin side and the blade back side is slightly different, which is related to the blade macro model and loading method. The geometric dimensions of the blade tip section in the chord length and thickness directions are smaller than the blade root section, and the projection of the blade tip chord length direction in the blade root section is not parallel to the blade root chord length direction, but at a small acute angle. Therefore, under centrifugal load, the blade will produce a slight warp, and the blade warp failure mode should focus on the blade root on the blade basin side and the lower middle part on the blade back side.

[0068] Except for the blade root, the latitudinal stress is evenly distributed throughout the blade, about 10MPa, which is much smaller than the latitudinal tensile strength. The latitudinal stress at the blade root, especially on the blade basin side, is relatively high, about 291MPa, close to the latitudinal tensile strength (329MPa). The high latitudinal stress at the blade root is mainly affected by the applied boundary conditions and has little correlation with the load on the blade.

[0069] The in-plane shear stress distribution is similar to the latitudinal stress distribution, and this distribution is also affected by the applied boundary conditions. The difference is that the location with larger shear stress is not the entire blade root, but the leading and trailing edges of the blade root.

[0070] Step 5, uncertainty analysis is performed on the strength of turbine blades based on the macroscopic model of the blades. Uncertainty analysis is to study the failures caused by different loads on the entire turbine blade, and obtain the macroscopic random factors and their distribution types that affect the probability strength of the blades. For example, when the porosity at the root of the turbine blade is low, the failure load is 80MPa, but if the porosity of the back of the blade is large, its failure load will be reduced to 70MPa relative to the low porosity (failure load is 150MPa), and the back of the blade will fail first.

[0071] Step 6, according to the different randomness, sampling is performed based on micro-random factors, macro-random factors and multi-scale parameters including micro- and macro-factors, and a new optimized partial sorting random sampling method is designed to extract sufficient samples. The polynomial response surface and the Kriging surrogate model are nested to form a new nested surrogate model, and the connection between the input and output is established. The optimized subset simulation collaborative analysis method is used to evaluate the blade failure probability, output the probability density, and form a probability intensity distribution diagram.

[0072] The proxy model is represented as:

[0073]

[0074] In the formula, is the final prediction of the nested model, is the prediction of the polynomial response surface, is the prediction of the Kriging model, a1 and a2 are weights, satisfying a1+a2=1.

[0075] a1 and a2 are determined by their linearity and nonlinearity, and the correlation can be expressed as:

[0076]

[0077] Where i = 1 or 2, indicating a polynomial response surface or a Kriging proxy model, m indicates the number of sample points close to the fitting points, and n represents the number of remaining sample points. The degree of fit within 5% is considered to meet the closeness requirement.

[0078] The optimized subset simulation collaborative analysis method adaptively introduces a series of mutually nested intermediate events, converts the small failure probability into the product of a sequence of larger conditional probabilities, and calculates the failure probability based on the collaborative analysis method, which is expressed as:

[0079]

[0080] Where M is the total number of intermediate events. When the conditional probability is a constant p0, the intermediate events can be determined adaptively. j is the indicator function of the jth sample point, N is the number of samples, and the indicator function I j It is used to determine whether the j-th sample point meets the failure condition. If the sample point belongs to the failure area and meets the failure condition, Ij=1; if the sample point does not belong to the failure area and does not meet the failure condition, Ij=0 to retain the interval where the failure occurs; ξ is the collaborative analysis factor, which is adjusted according to the collaborative analysis results.

[0081] Given the coefficient of variation δ and the failure probability The number of samples described in the optimized subset simulation collaborative analysis is:

[0082]

[0083] In the formula, r≤3 and the failure probability of each layer is estimated by is determined by the correlation between them, γ is the correlation coefficient, and P0 is the failure probability of the intermediate event.

[0084] Specifically,

[0085] In this embodiment, a probabilistic strength analysis is performed on the turbine blades. After step 4, two failure modes are obtained: blade damage and excessive blade deformation. Therefore, in this embodiment, the blade strength is characterized by the ratio of the speed corresponding to the blade failure divided by the operating speed, such as Figures 8 to 10 The horizontal axis of the probability intensity distribution diagram. In order to evaluate the random distribution type and dispersion of the strength of woven ceramic matrix composite material turbine blades, a new optimized partial sorting random sampling method based on Latin hypercube sampling is used in this example. The optimization method is based on Latin hypercube sampling for adaptive sampling. An adaptive process is added to the original sampling method. According to the existing sample point information, the position of subsequent sampling points is dynamically adjusted, such as stratifying the nested proxy model according to different proportional coefficients, dividing multiple parameter spaces according to the nested proxy model proportional coefficients, and adaptively sampling each hierarchical space in turn.

[0086] Consider three situations and perform three samplings:

[0087] 30 sets of input parameters are extracted for the two cases of considering only micro-random factors and only macro-random factors respectively; when multi-scale random factors (including macro- and micro-random factors) are considered, there are more random factors, so 90 sets of input parameters are extracted according to the sample point requirements of the proxy model.

[0088] The random factors included in the mesostructure are the porosity and fiber bundle strength considered when establishing the unit cell model. The randomness of porosity and fiber bundle strength is reflected in the randomness of the macroscopic mechanical properties of the material, and the macroscopic model size of the blade is a fixed value. The macroscopic mechanical performance parameters with greater influence, such as the warp tensile elastic modulus, warp tensile strength, weft tensile elastic modulus, and weft tensile failure stress, are selected as random factors. Figure 8 The probability distribution of blade strength when considering micro-random factors is shown. After the Anderson-Darling test, the significance level of normal distribution is 0.4856, the significance level of lognormal distribution is 0.4863, and the significance level of Weibull distribution is 0.0731. Since the significance level of normal distribution is similar to that of lognormal distribution and the probability distribution of data is slightly right-skewed, the blade strength is accepted to obey the lognormal distribution. The coefficient of variation of blade strength is less than the coefficient of variation of material longitudinal tensile strength, which is 0.53%. This is because when the blade is close to failure under centrifugal load, a small increase in speed will cause a large increase in stress at the root of the blade.

[0089] Affected by material preparation and process factors during the processing, the macroscopic dimensional parameters of the blade have a certain degree of randomness. When considering the influence of the randomness of the macroscopic structural dimensional parameters of the blade model on the blade strength, a parameterized CMCs turbine blade analysis model is established under the premise that the microstructural parameters of the woven composite material remain unchanged. The macroscopic structural dimension definition of typical turbine blades is analyzed, and a macroscopic structural parameterized model of the thickness at the leading edge, trailing edge, leading edge, and trailing edge of the CMCs turbine blade tip is established. This is used as a random influencing factor for probability analysis to analyze the influence of macroscopic structural randomness on blade strength. Taking the thickness of the blade root trailing edge as an example, the thickness of the blade root trailing edge is measured by the arc diameter of the blade root trailing edge. Fig. 9 The Anderson-Darling test shows that the significance level of normal distribution is 0.6082, the significance level of lognormal distribution is 0.6088, and the significance level of Weibull distribution is 0.0944. Since the significance level of normal distribution is close to that of lognormal distribution and the probability distribution of data has no obvious bias, the coefficient of variation of blade strength is 0.38% when only macroscopic randomness is considered, which is smaller than the coefficient of variation of blade strength when only microscopic random factors are considered. This is because the influence of blade macroscopic size change on blade strength is small.

[0090] In this embodiment, the probability distribution type and influence law of turbine blade strength under the combined effect of material performance randomness caused by the microstructure of turbine blade material and macroscopic structural size randomness are studied, and the failure probability analysis of turbine blades under typical working conditions is carried out in combination with the proxy model.

[0091] Since there are many random factors when considering multi-scale randomness, sufficient training samples are needed to ensure the fitting accuracy of the subsequent proxy model. Therefore, 90 macro-micro input parameter samples are obtained by sampling in this example. Table 1 lists the failure speed and operating speed ratios calculated by the 90 models. Fig.10 In order to consider the probability distribution of blade strength with multi-scale randomness, the Anderson-Darling test showed that the significance level of normal distribution of blade strength was 0.3023, the significance level of lognormal distribution was 0.307, and the significance level of Weibull distribution was 0.00002. Since the significance level of lognormal distribution was slightly higher than that of normal distribution and there was a certain bias in the probability distribution of data, it was accepted that the blade strength obeyed the lognormal distribution. Considering multi-scale randomness, there are more random factors. Even if the macroscopic random factors have little effect on the blade, the dispersion of blade strength is still improved. Therefore, the coefficient of variation of blade strength is slightly greater than that of only considering the microscopic random factors and only considering the macroscopic random factors, which is 0.82%.

[0092] Table 1 Ratio of failure speed to operating speed

[0093]

[0094]

[0095] Since two failure modes of the blade are considered in this embodiment, namely, damage when the blade stress reaches the strength and excessive deformation of the blade, the probability distribution of the deformation when the blade is about to be damaged must also be considered. In this example, the maximum value of the radial displacement of the blade is used to represent the blade deformation. The maximum value distribution of the radial displacement of the blade when it is subjected to centrifugal load is shown in the following figure: Fig.11 Its probability distribution is shown as Fig.12 As shown. After the Anderson-Darling test, the significance level of the normal distribution of the blade deformation is 0.0897, the significance level of the log-normal distribution is 0.1422, and the significance level of the Weibull distribution is 0.0002. Since the significance level of the normal distribution of the maximum value of the blade radial displacement is low and the data shows obvious bias, it is accepted that it obeys the log-normal distribution. The coefficient of variation of the maximum value of the blade radial displacement is large, which is 4.8%. This is because the blade radial displacement is affected by more material mechanical properties parameters. The failure speed is mainly controlled by the material's longitudinal tensile strength, but the blade radial displacement is also affected by the material stiffness parameters.

[0096] Comparing the calculated predicted value with the actual value of this example, it can be seen from Tables 2 and 3 that the use of nested surrogate model combined with optimized subset simulation collaborative analysis can effectively improve the calculation efficiency and accuracy.

[0097] Table 2 Predicted and actual values ​​of the ratio of failure speed to operating speed

[0098]

[0099]

[0100] Table 3 Predicted and actual values ​​of the maximum radial displacement of the blade

[0101]

[0102] The parameters of the optimized subset simulation collaborative analysis method used in the present invention are set as follows: the number of samples per layer N = 3000, the conditional probability of the intermediate event is P0 = 0.2, and the maximum number of iterations is 6 to cover the failure probability range. After 15 independent runs, the failure probability interval of the turbine blade under the preset working conditions with a confidence level of 95% is calculated to be [1.1242×10 -5 , 8.1678×10 -5 ].

[0103] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A CMC turbine blade strength simulation method considering dispersion, characterized in that: The following steps are involved: Step 1, from a microscopic perspective, a unit cell model including the microstructural parameters of the CMCs fibers and pores is established, and from a macroscopic perspective, a blade macroscopic model is established; Step 2, performing finite element analysis on the unit cell model, firstly taking the dispersed porosity and fiber strength as meso-random factors, using probability test method to identify the distribution type of random factors, and ensuring the validity of probability when sampling meso-random factors; then calculating the meso-mechanical performance parameters of CMC materials under different working conditions, and identifying the distribution type and dispersion of the meso-mechanical performance parameters; Step 3, based on the strain Hashin criterion, a new failure criterion of turbine blade CMCs is established, wherein the internal parameters of the criterion are the mechanical performance parameters of the unit cell model obtained in step 2, and based on the criterion, four failure modes, namely, longitudinal tensile fracture, longitudinal compression fracture, latitudinal tensile fracture and latitudinal compression fracture, are judged, that is, by setting different load intervals, it is judged whether the CMC blade will produce tensile fracture or compression fracture failure under the longitudinal or latitudinal load; Step 4, based on the blade macro model in step 1, a deterministic analysis is performed on the blade strength, the mean value of the microscopic mechanical performance parameter and the size parameter of the blade macro model is used as input, the stress distribution of the blade when it is about to be destroyed is calculated by finite element method, and the failure section, failure form and load form when the blade macro model is most susceptible to failure are determined; Step 5, performing uncertainty analysis on the strength of the turbine blade based on the blade macro model to obtain macro random factors affecting the blade probability strength and their distribution types; Step 6, according to the different randomness, sampling is performed based on micro-random factors, macro-random factors and multi-scale parameters including micro- and macro-factors, and a new optimized partial sorting random sampling method is designed to extract sufficient samples. The polynomial response surface and the Kriging surrogate model are nested to form a new nested surrogate model, and the connection between the input and output is established. The optimized subset simulation collaborative analysis method is used to evaluate the blade failure probability, output the probability density, and form a probability intensity distribution diagram.

2. The method according to claim 1, characterized in that In step 2, the probability test method is: First, abnormal data is screened and the maximum normed residual test method is used to detect and eliminate outliers; Secondly, select the probability distribution model, compare the observed significance level (OSL) values ​​of each probability distribution model, and select the appropriate distribution model and test method; select the mechanical property parameters with greater dispersion influence among the mesoscopic random factors; Finally, the observed significance level of the probability distribution model of the mechanical property parameters is observed, and the appropriate distribution model is selected and a consistency test is performed.

3. The method according to claim 1, characterized in that In step 3, the new turbine blade CMCs failure criterion is expressed as: Where 1 and 2 indicate that the fiber reinforcement direction is warp or weft, ε t represents the tensile positive strain, ε c represents the compressive normal strain, γ represents the shear strain, σ is the normal stress, E is the Young's modulus, and G is the shear modulus.

4. The method according to claim 1, characterized in that: In step 4, deterministic analysis determines that the most vulnerable failure modes on the blade macro model are blade damage and excessive blade deformation, and determines that the most vulnerable load form on the blade macro model is centrifugal load; in step 5, considering the failure mode, the blade strength is characterized by the ratio of the speed corresponding to the blade failure divided by the operating speed, and several groups of input parameters are extracted based on the new optimized partial sorting random sampling method.

5. The method according to claim 4, characterized in that In step 6, when sampling is performed based on micro-random factors, the random factors included are the porosity and fiber bundle strength described in step 2, and the blade macro-model size is a fixed value; when sampling is performed based on macro-random factors, a parameterized CMCs turbine blade analysis model is established under the premise that the microstructure parameters of the woven composite material remain unchanged, and based on the definition of the macro-structure size of the turbine blade, a macro-structure parameterized model of the thickness at the leading edge of the CMCs turbine blade tip, the trailing edge of the blade tip, the leading edge of the blade root, and the trailing edge of the blade root is established as a random influencing factor.

6. The method according to claim 1, characterized in that In step 6, the new optimized partial sorting random sampling method is: adaptive sampling based on Latin hypercube sampling, dynamically adjusting the positions of subsequent sampling points according to the existing sample point information, that is, stratifying the nested proxy model according to different proportional coefficients and dividing it into multiple parameter spaces, and adaptively sampling each level space in turn.

7. The method according to any one of claims 1 to 6, characterized in that: In step 6, the nested proxy model is expressed as: In the formula, is the final prediction of the nested model, is the prediction of the polynomial response surface, is the prediction of the Kriging model, a1 and a2 are weights, satisfying a1+a2=1.

8. The method according to claim 7, characterized in that In step 6, a1 and a2 are determined by their linearity and nonlinearity, and the correlation can be expressed as: Where i = 1 or 2, indicating a polynomial response surface or a Kriging proxy model, m indicates the number of sample points close to the fitting points, and n represents the number of remaining sample points. The degree of fit within 5% is considered to meet the closeness requirement.

9. The method according to claim 8, characterized in that In step 6, the optimized subset simulation collaborative analysis method adaptively introduces a series of mutually nested intermediate events to transform the small failure probability into the product of a sequence of larger conditional probabilities. The failure probability is calculated based on the collaborative analysis method, which is expressed as: Where M is the total number of intermediate events. When the conditional probability is a constant p0, the intermediate events can be determined adaptively. j is the indicator function of the jth sample point, N is the number of samples, and the indicator function I j It is used to determine whether the jth sample point meets the failure condition. If the sample point belongs to the failure area and meets the failure condition, Ij=1; if the sample point does not belong to the failure area and does not meet the failure condition, Ij=0; ξ is the collaborative analysis factor, which is adjusted according to the collaborative analysis results.

10. The method according to claim 9, characterized in that In step 6, given the coefficient of variation δ and the failure probability The number of samples described in the optimized subset simulation collaborative analysis is: In the formula, r≤3 and the failure probability of each layer is estimated by is determined by the correlation between them, γ is the correlation coefficient, and P0 is the failure probability of the intermediate event.

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