A dual evaluation method for static strength design and reliability of aero-engine structures

Abstract

The present application provides a dual evaluation method for static strength design and reliability of aircraft engine structures, including: obtaining basic data required for evaluation, including stress of dangerous parts at design point temperature, reserve coefficient, static strength design criteria of corresponding structural parts, and material ultimate strength mechanical property test data; processing the material ultimate strength mechanical property test data at design point temperature to obtain the mean and standard deviation of the ultimate strength, and then obtaining the ultimate strength variation coefficient; deriving the relationship between reliability and reserve coefficient, and material ultimate strength variation coefficient to obtain preliminary reliability; constructing a regression model, fitting the preliminary reliability and variation coefficient to obtain a regression curve, and obtaining structural reliability based on the regression curve; judging the structural reliability and the minimum reliability index requirement value in the corresponding structural reliability index requirement. If the structural reliability meets the minimum reliability index requirement value, it indicates that the structural reliability meets the requirement, otherwise it does not meet the requirement.

Description

Technical Field

[0001] The present application belongs to the technical field of aero-engine design, and in particular relates to a dual evaluation method for static strength design and reliability of an aero-engine structure. Background Art

[0002] Aero-engines mainly use static strength design criteria based on reserve coefficients to carry out static strength design evaluation and verification. Reserve coefficients are used to characterize various uncertainties in structural design, but they cannot quantify the uncertainties in the design. Due to the introduction of new materials and new technologies, the mechanical properties of new engine materials are unstable. During model development, the mechanical properties of some new materials have large dispersion. The existing strength design criteria cannot fully include the uncertainty of material mechanical properties, which reduces the effectiveness of deterministic simulation evaluation.

[0003] Reliability evaluation for electronic products can be performed through a large number of statistical reliability tests to determine their reliability level. However, due to the complex structure, advanced materials, and complex working load environment of aircraft engines, the reliability testing costs are very high. Reliability indicators can only be verified through simulation. Academic methods mainly include reliability coefficient method, moment estimation method, Monte Carlo simulation analysis method, and surrogate model method. However, these methods cannot be directly applied to engineering development, mainly in the following aspects:

[0004] 1) In the field of engineering applications, all four methods face the problem of missing reliability design data and cannot be applied;

[0005] 2) The strength design criteria for aircraft engines have been verified through years of application and are irreplaceable in their authority. The above four methods are not directly compatible with the current strength design criteria.

[0006] 3) The first two methods require explicit limit state equations and the distribution parameters of stress and strength. Since engines adopt the maximum load design principle, it is generally difficult to obtain stress distribution parameters, which cannot reflect the influence of the dispersion of major material properties, and the calculation accuracy is also low.

[0007] 4) The latter two methods can be used to perform corresponding reliability assessments based on the current data. However, for complex aircraft engine structures, a single simulation takes a long time, and Monte Carlo simulation analysis requires at least 10 6 The above calculations have low computational efficiency and are difficult to apply in engine engineering development. The validity of the proxy model in the proxy model method cannot be verified, and its computational accuracy is difficult to guarantee. At the same time, the establishment of the proxy model itself also has many technical difficulties and is difficult to implement in engineering. Summary of the Invention

[0008] The purpose of this application is to provide a dual evaluation method for static strength design and reliability of aircraft engine structures to solve or alleviate at least one problem in the background technology.

[0009] The technical solution of the present application is: a method for dual evaluation of static strength design and reliability of aircraft engine structure, the method comprising:

[0010] Obtaining basic data required for the evaluation, including stresses in critical locations for strength calculation and analysis of aircraft engine structural components at the engine design temperature, allowable values ​​of material ultimate strength, reserve factors, static strength design criteria for corresponding structural components, and material ultimate strength mechanical property test data;

[0011] The ultimate strength mechanical property test data of the material at the design point temperature are processed to obtain the mean and standard deviation of the ultimate strength, and then the ultimate strength variation coefficient is obtained based on the mean and standard deviation;

[0012] The relationship between reliability, reserve factor and coefficient of variation of material ultimate strength is derived using conditional failure probability, thus obtaining preliminary reliability.

[0013] Constructing a regression model, fitting the preliminary reliability and the coefficient of variation through the regression model to obtain a regression curve, and obtaining the structural reliability according to the regression curve;

[0014] The structural reliability is judged against the minimum reliability index requirement value in the corresponding structural reliability index requirement. If the structural reliability meets the minimum reliability index requirement value, it indicates that the structural reliability meets the requirement, otherwise it does not meet the requirement.

[0015] Furthermore, the sample size n of the material ultimate strength mechanical properties test data corresponding to the engine design point temperature satisfies:

[0016] Where 1-γ represents the significance level, and p represents the failure probability.

[0017] Furthermore, when the minimum material mechanical properties test sample size cannot meet the requirements, the test sample size must be at least greater than 28 pieces.

[0018] Furthermore, the ultimate strength variation coefficient satisfies the following relationship with the mean and standard deviation of the ultimate strength:

[0019] Where C v is the coefficient of variation of ultimate strength, μ is the mean of ultimate strength, and σ is the standard deviation of ultimate strength.

[0020] Furthermore, when the strength check of aircraft engine structural parts uses the mean value of the material mechanical properties, the mean reliability

[0021] When the strength check of aero-engine structural parts uses the -3σ value of the material mechanical properties, the -3σ reliability

[0022] Where, is the normal distribution cumulative failure probability function, Cv is the coefficient of variation, and n is the reserve coefficient.

[0023] Furthermore, when reliability calculation is not performed, only the reliability of the structure under the dispersion of material properties is evaluated, and the minimum reserve coefficient based on the mean value of material properties satisfies The minimum reserve coefficient based on the material mechanical properties-3σ value meets

[0024] Where u 1-R is the (1-R) ​​quantile of the normal distribution.

[0025] Furthermore, the process of fitting the reliability and the coefficient of variation to obtain the regression curve includes:

[0026] A polynomial regression model is constructed, and the expression of the regression model is:

[0027] y=a0+a1x+…+a m x m

[0028] Where a0~a m are polynomial coefficients, m is the number of polynomial terms;

[0029] Determine the parameters of the above polynomial expression. The process includes:

[0030] 1) Let the coefficient of variation C v is the independent variable x, reliability R is the variable y, and the required value of the reserve coefficient n is selected according to the static strength design criterion;

[0031] 2) Uniformly select p (p>m) coefficients of variation C between [0.05, 0.2] v The variable values ​​(x1, x2, ..., x p );

[0032] 3) According to the reliability calculation formula and the given reserve coefficient n, calculate x1, x2, ..., x p Corresponding y1, y2, ..., y p Get (x i ,y i );

[0033] 4) Calculate the coefficient a of the polynomial using the least squares fitting method: i ;

[0034]

[0035] 5) Calculate the correlation coefficient r(x,y) according to the following formula. Ensure that the correlation coefficient r>0.999, then the reliability can be estimated based on the polynomial;

[0036]

[0037] 6) If the correlation coefficient r>0.999 cannot be guaranteed, the sample size should be increased (x i ,y i ), repeat steps 3 to 5 until the correlation coefficient r>0.999.

[0038] Furthermore, the number m of terms in the polynomial is 2 or 3.

[0039] Furthermore, it also includes:

[0040] The reliability is converted into a failure rate corresponding to a single flight mission time, and the reliability of the structural static strength is further evaluated by the failure rate.

[0041] Furthermore, the failure rate and reliability satisfy: λ = -lnR / t

[0042] Among them, λ is the failure rate, R is the reliability, and t is the single task time.

[0043] The evaluation method provided in this application can be effectively compatible with the existing engine structural strength design criteria system, thereby realizing the dual evaluation of aircraft engine structural reliability and deterministic strength design. The evaluation method is simple, computationally efficient, and easy to apply. In engineering, it can effectively control the stability of material mechanical properties caused by reliability uncertainty factors caused by missing engineering data, improve the existing deterministic strength design system, and improve the reliability of aircraft engine structural design. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions provided by this application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of this application.

[0045] Figure 1 Schematic diagram of the dual evaluation method for static strength design and reliability of aero-engine structure in this application.

[0046] Figure 2 FIG. 4 is a fitting curve of the coefficient of variation and reliability according to an embodiment of the present application. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0048] At present, the maximum load principle is used in the design of engine structural integrity to carry out structural strength design analysis. When checking strength, the stress of the most dangerous part is selected and compared with the allowable value of the material mechanical properties to calculate the reserve coefficient to determine whether the requirements of the strength design criteria are met. This method can basically ensure the reliability of aircraft engine structural design. However, due to the introduction of new materials and new technologies, and the unstable mechanical properties of new materials, the mechanical properties of materials are highly dispersed, which has a significant impact on the static strength analysis results. Therefore, the application is mainly based on the stress-strength interference model, assuming the maximum load, and using the conditional failure probability to establish a mapping relationship between the strength design reserve coefficient, mechanical property dispersion, and reliability index. Based on the principle of determining the minimum reliability index, a reliability assessment based on the existing strength design criteria is achieved. In combination with the current demand status of reliability index parameters in engineering, an index conversion relationship is given to meet engineering needs.

[0049] like Figure 1 As shown, the dual evaluation method for static strength design and reliability of aircraft engine structures provided in this application mainly includes the following steps:

[0050] 1) Obtain basic data

[0051] Before conducting a static strength reliability assessment of an aero-engine structure, the following basic data must be obtained first, including: stresses in critical locations from strength calculations and analysis of aero-engine structural components at the engine design temperature, allowable values ​​of material ultimate strength, reserve factors, static strength design criteria for corresponding structural components, and test data from material ultimate strength mechanical property tests.

[0052] The requirements for test data are as follows:

[0053] Corresponding to the material ultimate strength mechanical properties test data at the engine design point temperature, the sample size n is required to meet the following formula requirements:

[0054] Among them, 1-γ represents the significance level, p represents the failure probability, the failure probability can be determined according to the minimum reliability requirements of the structural components, and the significance level can be flexibly adjusted according to engineering needs.

[0055] When the minimum reliability level of a structural component is high and the minimum material mechanical properties test sample size in actual engineering cannot meet the requirements, the test sample size should be at least greater than 28 pieces.

[0056] 2) Estimation of material property dispersion parameters based on normal distribution

[0057] The ultimate strength mechanical properties test data of the material at the design point temperature are processed to obtain the mean μ and standard deviation σ of the ultimate strength. Then, the ultimate strength variation coefficient Cv is calculated based on the mean μ and standard deviation σ:

[0058] 3) Calibration of material performance dispersion parameters, reserve coefficients and reliability indicators;

[0059] The relationship between reliability, reserve factor and coefficient of variation of material ultimate strength is derived using conditional failure probability.

[0060] At present, when checking the strength of aircraft engine structural parts, the mean value μ and -3σ value of the material mechanical properties are usually used for strength verification. When the mean value is used for verification, the reliability is calculated according to formula (3). When the -3σ value is used for strength verification, the reliability is calculated according to formula (4):

[0061] Mean reliability

[0062] -3σ reliability

[0063] In the above formula, is the normal distribution cumulative failure probability function, C v is the coefficient of variation, and n is the reserve coefficient.

[0064] When reliability calculation is not required, it is only necessary to evaluate whether the structure is reliable under the dispersion of material properties. The reserve coefficient can be calculated according to the minimum reserve coefficient based on the mean value of material properties in formula (5) and the minimum reserve coefficient based on the material properties-3σ value in formula (6):

[0065] Mean reserve coefficient

[0066] -3σ minimum reserve coefficient

[0067] In the above formula, u 1-R is the (1-R) ​​quantile of the normal distribution.

[0068] 4) Establish a response surface model considering the dispersion of material properties

[0069] Due to professional limitations in engineering applications, the calculation of quantiles and cumulative failure probabilities involved in the reliability and reserve coefficient in the above calibration is relatively cumbersome. Therefore, this application further provides a response surface model that considers the dispersion of material properties on the basis of the above, and conducts rapid evaluation by constructing a regression model and fitting the regression curve of reliability and coefficient of variation, making it more convenient for engineering applications.

[0070] The regression model constructed in this application is expressed as follows:

[0071] y=a0+a1x+…+a m x m (7)

[0072] m is generally taken as m=2 or m=3, that is, the polynomial is generally a quadratic polynomial or a cubic polynomial.

[0073] After that, the parameters of the above polynomial expression are determined. The process includes:

[0074] 4.1) Assume the coefficient of variation C v is the independent variable x, reliability R is the variable y, and the reserve coefficient requirement value n is selected according to the static strength design criteria, which is generally 1.25;

[0075] 4.2) Uniformly select p (p>m) variable values ​​(x1, x2, ..., x) with coefficient of variation Cv between [0.05, 0.2]. p );

[0076] 4.3) According to formula 3 and the given reserve coefficient n, calculate x1, x2, ..., x p Corresponding y1, y2, ..., y p , we get (x i ,y i );

[0077] 4.4) Calculate the coefficient a of 7 using the least squares fitting method listed in formula 8 i ;

[0078]

[0079] 4.5) Calculate the correlation coefficient r(x,y) according to Formula 9, ensuring that r>0.999, and obtain the specific form of the polynomial. Based on this polynomial, the structural reliability can be obtained, and thus the reliability assessment can be carried out;

[0080]

[0081] 4.6) If r > 0.999 cannot be guaranteed, the sample size should be increased (x i ,y i ), repeat steps 4.3, 4.4, and 4.5 until the correlation coefficient r>0.999.

[0082] like Figure 2 The figure shows the reliability and variation coefficient fitting curve y=50.465x when the polynomial number m=3, the reserve coefficient requirement value n=1.25, and the correlation coefficient r=0.9995 (satisfying r>0.999) in one embodiment of the present application. 3-23.127x 2 +2.0612x+0.9505.

[0083] 5) Reliability evaluation

[0084] Table 1 shows the structural reliability requirements for fighter jets according to one embodiment of the present application. During the design, severity levels are assigned based on the impact of the most severe consequences of structural static strength failure on the engine. The probability value corresponding to the minimum reliability requirement is selected based on Table 1. The reliability value calculated using Formulas 3 and 4 is compared with the minimum reliability requirement. If it exceeds the minimum reliability requirement, the structural reliability meets the requirements. If it does not, design improvements are necessary, including improvements to structural parameters or material property dispersion (improving material property dispersion can make material properties more stable).

[0085] For example, if the impact of a certain structural component on the engine is "causing personal injury or death; engine damage", the corresponding minimum reliability index requirement is 0.9999999, then the mean reliability R calculated by formula 3 and formula 4 is u and -3σ reliability R -3σ Both must be greater than 0.9999999.

[0086] Table 1 Structural reliability index requirements for fighter aircraft

[0087]

[0088] 6) Failure rate evaluation

[0089] In engineering practice, for specific failure modes, we not only focus on reliability, but also need to consider the failure rate corresponding to a single flight mission time. According to formula 10, the conversion between failure rate and reliability index is performed to evaluate the corresponding failure rate. The conversion relationship between failure rate and reliability is: λ = -lnR / t(10)

[0090] Among them, λ is the failure rate, R is the reliability, and t is the single task time.

[0091] According to the above formula, the failure rates of single mission time of up to 2 hours and single mission time of up to 10 hours are calculated respectively, and compared with the failure rate index requirements of single mission time of up to 2 hours and single mission time of up to 10 hours, thus completing the dual evaluation of static strength design and reliability.

[0092] For example, in this embodiment of the present application, the reliability calculated by the above process is 0.9999998, so the failure rate with a maximum single task time of 2 hours is 1.0000001e-7.

[0093] The evaluation method provided in this application can be effectively compatible with the existing engine structural strength design criteria system, thereby realizing the dual evaluation of aircraft engine structural reliability and deterministic strength design. The evaluation method is simple, computationally efficient, and easy to apply. In engineering, it can effectively control the stability of material mechanical properties caused by reliability uncertainty factors caused by missing engineering data, improve the existing deterministic strength design system, and improve the reliability of aircraft engine structural design.

[0094] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A dual evaluation method for static strength design and reliability of aircraft engine structures, characterized by: The method comprises: Obtaining basic data required for the evaluation, including stresses in critical locations for strength calculation and analysis of aircraft engine structural components at the engine design temperature, allowable values ​​of material ultimate strength, reserve factors, static strength design criteria for corresponding structural components, and material ultimate strength mechanical property test data; The ultimate strength mechanical property test data of the material at the design point temperature are processed to obtain the mean and standard deviation of the ultimate strength, and then the ultimate strength variation coefficient is obtained based on the mean and standard deviation; The relationship between reliability, reserve factor and coefficient of variation of material ultimate strength is derived using conditional failure probability, thus obtaining preliminary reliability. Constructing a regression model, fitting the preliminary reliability and the coefficient of variation through the regression model to obtain a regression curve, and obtaining the structural reliability according to the regression curve; The structural reliability is judged against the minimum reliability index requirement value in the corresponding structural reliability index requirement. If the structural reliability meets the minimum reliability index requirement value, it indicates that the structural reliability meets the requirement, otherwise it does not meet the requirement.

2. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 1, characterized in that: The sample size n of the material ultimate strength mechanical properties test data corresponding to the engine design point temperature satisfies: Where 1-γ represents the significance level, and p represents the failure probability.

3. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 2, characterized in that: When the minimum material mechanical properties test sample size cannot meet the requirements, the test sample size shall be at least greater than 28 pieces.

4. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 1, characterized in that: The ultimate strength variation coefficient satisfies the following relationship with the mean and standard deviation of the ultimate strength: Where C v is the coefficient of variation of ultimate strength, μ is the mean of ultimate strength, and σ is the standard deviation of ultimate strength.

5. The method for dual static strength design and reliability evaluation of an aircraft engine structure according to claim 4, characterized in that: When the strength check of aircraft engine structural parts uses the mean value of material mechanical properties, the mean reliability When the strength check of aero-engine structural parts uses the -3σ value of the material mechanical properties, the -3σ reliability Where, is the normal distribution cumulative failure probability function, C v is the coefficient of variation, and n is the reserve coefficient.

6. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 5, characterized in that: When reliability calculation is not performed, only the reliability of the structure under the dispersion of material properties is evaluated, and the minimum reserve coefficient based on the mean value of material properties satisfies The minimum reserve coefficient based on the material mechanical properties-3σ value meets Where u 1-R is the (1-R) ​​quantile of the normal distribution.

7. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 6, characterized in that: The process of fitting the reliability and coefficient of variation to obtain the regression curve includes: A polynomial regression model is constructed, and the expression of the regression model is: y=a0+a1x+...+a m x m Where a0~a m are polynomial coefficients, m is the number of polynomial terms; Determine the parameters of the above polynomial expression. The process includes: 1) Let the coefficient of variation C v is the independent variable x, reliability R is the variable y, and the required value of the reserve coefficient n is selected according to the static strength design criterion; 2) Uniformly select p (p>m) coefficients of variation C between [0.05, 0.2] v The variable values ​​(x1, x2, ..., x p ); 3) According to the reliability calculation formula and the given reserve coefficient n, calculate x1, x2, ..., x p Corresponding y1, y2, ..., y p Get (x i ,y i ); 4) Calculate the coefficient a of the polynomial using the least squares fitting method: i ; 5) Calculate the correlation coefficient r(x,y) according to the following formula. Ensure that the correlation coefficient r>0.999, then the reliability can be estimated based on the polynomial; 6) If the correlation coefficient r>0.999 cannot be guaranteed, the sample size should be increased (x i ,y i ), repeat steps 3) to 5) until the correlation coefficient r>0.

999.

8. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 7, characterized in that: The number of terms m in the polynomial is 2 or 3.

9. The method for dual evaluation of static strength design and reliability of an aircraft engine structure according to any one of claims 1 to 8, characterized in that: Also includes: The reliability is converted into a failure rate corresponding to a single flight mission time, and the reliability of the structural static strength is further evaluated by the failure rate.

10. The method for dual evaluation of static strength design and reliability of aircraft engine structure according to claim 9, characterized in that: The failure rate and reliability satisfy: λ = -lnR / t Among them, λ is the failure rate, R is the reliability, and t is the single task time.

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