Small sample ultra-high cycle fatigue strength prediction method

Abstract

The invention belongs to the technical field of engine material reliability design, and provides a small sample ultra-high cycle fatigue strength prediction method. According to the method, a fatigue strength dispersive model is fused into a three-parameter S-N curve model, model parameters are solved through a maximum likelihood method, the utilization rate of test data in the fitting process is increased, and on the basis of ultra-high-cycle fatigue test data of small samples, ultra-high-cycle fatigue strength prediction with specified confidence and reliability can be achieved. According to the method, under the condition that the data sample size is limited, a reliable method is provided for ultrahigh-cycle fatigue strength evaluation of the engine material at low economic cost, the accuracy of ultrahigh-cycle fatigue strength prediction is improved, and the test cost and the calculation complexity are remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engine reliability design, and specifically to a small-sample ultra-high cycle fatigue strength prediction method. This method incorporates the fatigue strength dispersion into the three-parameter S-N curve model, and uses the maximum likelihood method to solve the model, improving the utilization efficiency of test data in the solution process. By using small-sample test data, it realizes the fatigue strength prediction within the ultra-high cycle fatigue range. Background Art

[0002] With the rapid development of modern aviation industry, as the "heart" of an aircraft, the performance and quality of an aero-engine directly determine the overall performance and safety of the aircraft. Among them, the fatigue strength of engine materials is one of the key indicators to measure its service life and reliability. The traditional fatigue strength assessment of engine materials is mainly based on high cycle fatigue (HCF) data, that is, fatigue performance data based on 10 million cycle times. However, with the continuous improvement of aero-engine design requirements, especially for the new generation of engines with long service life and high reliability, relying solely on high cycle fatigue data can no longer meet the design needs.

[0003] At present, the aero-engine design criteria at home and abroad have clearly put forward the requirements for ultra-high cycle fatigue (VHCF) performance data based on 1 billion cycle times. This means that engine materials need to maintain stable fatigue performance under a longer number of cycles to ensure the safe operation of the engine. However, the implementation of ultra-high cycle fatigue tests faces many challenges, such as long test cycles, high costs, large data dispersion, etc. Therefore, how to accurately and efficiently predict the ultra-high cycle fatigue strength of engine materials has become a key problem to be solved urgently in the field of aero-engine material reliability design.

[0004] Based on the above background, the present invention proposes a method for predicting the ultra-high cycle fatigue strength of engine materials for reliability design, which makes a probabilistic description of the S-N curve, realizes the prediction of ultra-high cycle fatigue strength for small-sample data, and combines a series of advanced data processing techniques and algorithms to further improve the accuracy and efficiency of the prediction Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting the ultra-high cycle fatigue strength of engine materials for reliability design. This method incorporates a probability model into the three-parameter S-N curve model, and through fitting and analyzing small-sample ultra-high cycle fatigue test data, it realizes the fatigue strength prediction of engine materials within the ultra-high cycle fatigue range. This method has the advantages of short test cycle, low cost, high accuracy, etc., and is applicable to the reliability design of aero-engine materials.

[0006] The technical solution of the present invention: A small-sample ultra-high cycle fatigue strength prediction method includes the following steps:

[0007] Step 1: Small-sample very high cycle fatigue test;

[0008] Step 2: Construct a fatigue strength probability model;

[0009] The specific form of the fatigue strength probability model is:

[0010] ln(N) = a + b×ln(S - S RFL ) (1)

[0011] where N is the fatigue life; S is the stress level; a is the slope of the logarithmic S-N curve, b is the intercept of the logarithmic S-N curve; S RFL is the fatigue limit of a certain test piece itself, which follows a normal distribution, with its mean value being S 0 , and the standard deviation being σ; the set θ of four undetermined parameters (a, b, σ, S 0 ) is established for subsequent parameter optimization;

[0012] Let V = S RFL , W = ln(N); define the probability density function of W as: f W (w; S, θ); define the cumulative probability distribution function of W as F W (w; S, θ); define the parameter likelihood function as:

[0013]

[0014] Step 3: Solve the likelihood function and optimize the parameters

[0015] After n tests are completed, n groups of (S i , N i ) data are substituted into formula (1) for fitting to obtain the fitted value a 0 of parameter a, the fitted value b 0 of parameter b, the fitted value S RFL of parameter S 00 ; let θ 0 = [a 0 , b 0 , S 00 , c·S 00 , where c is the dispersion factor, with a value range of 0.01 - 0.2; take θ 0 as the initial value of parameter optimization and substitute it into formula (4) to calculate the likelihood function

[0016] Define the upper limit θ 0 *t of the solution interval and the lower limit θ 0 / t, where t ranges from 2 to 10; the gradient descent method is used to continuously optimize θ between the upper limit and the lower limit of the solution, so that the likelihood function takes the maximum value; at this time, the four parameters (a, b, σ, S 0 ) in θ are the optimal solutions of the model;

[0017] Step 4: Fatigue strength prediction

[0018] The number of cycles N' to be predicted on the S-N curve is set in sequence, which are 1×10 6 , 3×10 6 , 1×10 7 , 3×10 7 , 1×10 8 , 3×10 8 , 1×10 9 ; then, by mapping n test points to the number of cycles N', n strength mapping values S' are obtained:

[0019] Calculate the average value of the n strength mapping values S' and denote it as χ, which is the median fatigue strength corresponding to the number of cycles N';

[0020] Set the required prediction confidence level as γ and reliability as p. First, refer to the HB Z / 112 standard to calculate the minimum sample size for whether the n S' values meet the requirements of the required prediction confidence level γ and reliability p; if not, increase the number of test samples; if satisfied, calculate the fatigue strength χ corresponding to the specified confidence level γ and reliability p γ,p ;

[0021] Use a smooth curve to successively connect the fatigue strengths χ corresponding to different predicted numbers of cycles N' γ,p , and then the p-S-N curve with confidence level γ and reliability p can be obtained.

[0022] The specific small-sample ultra-high cycle fatigue test is to prepare ultra-high cycle fatigue samples of n samples. First, use the up-and-down method to test 2 up-and-down pairs in the test stress range corresponding to 1×10 7 to 1×10 9 cycle times, and then carry out the group method test in the stress range corresponding to 1×10 5 to 1×10 7 cycles in the medium and short life regions. There are no less than 4 stress levels, and there are 1-2 valid data for each stress level; when there are sufficient samples, appropriately increase the number of specimens; for each test, record the test serial number i, the test stress S i , the number of cycles N i , and the test result δ i .

[0023] For the n samples mentioned above, n > 12.

[0024] The test result δ i : The specimen fracture is recorded as 1, and the specimen without fracture is recorded as 0.

[0025] The described f W (w; S, θ) has the formula:

[0026]

[0027] The described F W (w; S, θ) has the formula:

[0028]

[0029] The formula for the described n strength mapping values S’ is:

[0030]

[0031] The fatigue strength χ corresponding to the specified confidence level γ and reliability p γ,p The formula is:

[0032]

[0033] where β represents the unbiased correction coefficient of the standard deviation; k γ,p is the one-sided tolerance coefficient.

[0034] The described k γ,p The solution formula is:

[0035]

[0036] where: u P represents the standard normal deviate related to the reliability P, and u γ represents the standard normal deviate related to the confidence level γ, both of which are obtained by looking up the table.

[0037] The beneficial effects of the present invention are as follows:

[0038] The accuracy of ultra-high cycle fatigue strength prediction is improved: By introducing the fatigue strength dispersion into the three-parameter S-N curve model and using the maximum likelihood estimation method, the data utilization efficiency during S-N curve fitting is maximally improved. The present invention can more accurately describe the ultra-high cycle fatigue behavior of metal materials, improve the accuracy of fatigue strength prediction, and reduce the test cost and time: The present invention uses small sample data for ultra-high cycle fatigue tests, and compared with the traditional staircase method and S-N curve method, the test period is shorter and the cost is lower. The ultra-high cycle fatigue strength prediction method provided by the present invention can provide an important basis for the reliability design of aero-engine materials, and helps to improve the performance and reliability of aero-engines. Description of the Drawings

[0039] Figure 1 Flow chart of the present invention Detailed implementation manners

[0040] The present invention will be further described below in conjunction with the accompanying drawings:

[0041] As Figure 1 shown, a small-sample ultra-high cycle fatigue strength prediction method includes the following steps:

[0042] First step: Small-sample ultra-high cycle fatigue test

[0043] Prepare ultra-high cycle fatigue samples of n samples (n > 12). First, test 2 lift pairs using the staircase method in the test stress range corresponding to 1×10 7 to 1×10 9 cycle numbers, and then conduct group testing in the stress range corresponding to 1×10 5 to 1×10 7 cycles. There are no less than 4 stress levels, and there are 1 - 2 valid data for each stress level. When there are sufficient samples, the number of specimens can be appropriately increased. For each test, record the test serial number i, the test stress S i , the cycle number N i , and the test result δ i (the specimen fracture is recorded as 1, and the specimen not fractured is recorded as 0).

[0044] Second step: Construct a fatigue strength probability model

[0045] The fatigue strength model adopted by the present invention is based on the three-parameter S-N curve and introduces a fatigue strength probability model to describe the ultra-high cycle fatigue behavior of the alloy. The specific form of the model is:

[0046] ln(N) = a + b×ln(S - S RFL ) (1)

[0047] where N is the fatigue life; S is the stress level; a is the slope of the logarithmic S-N curve, b is the intercept of the logarithmic S-N curve; S RFL is the fatigue limit of a certain test piece itself, showing a random distribution. When S RFL is normally distributed, its mean value is S 0 , and the standard deviation is σ. The set θ of four undetermined parameters (a, b, σ, S 0 ) is established for subsequent parameter optimization.

[0048] Let V = S RFL , W = ln(N). Define the probability density function of W as:

[0049]

[0050] Define the cumulative probability distribution function of W as:

[0051]

[0052] Define the parametric likelihood function as:

[0053]

[0054] Step 3: Solve the likelihood function and optimize the parameters

[0055] After n trials are completed, n sets of (S i , N i ) data are substituted into formula (1) for fitting to obtain the fitted value a 0 of parameter a, the fitted value b 0 of parameter b, the fitted value S RFL of parameter S 00 . Let θ 0 = [a 0 , b 0 , S 00 , c·S 00 , where c is the dispersion factor with a value range of 0.01 - 0.2; Take θ 0 as the initial value of parameter optimization and substitute it into formula 4 to calculate the likelihood function

[0056] Define the upper limit θ 0 *t of the solution interval and the lower limit θ 0 / t of the solution interval, where t generally takes a value of 2 - 10. Use the gradient descent method to continuously optimize θ between the upper limit and the lower limit of the solution to make the likelihood function take the maximum value. At this time, the four parameters (a, b, σ, S 0 ) in θ are the optimal solutions of the model.

[0057] Step 4: Fatigue strength prediction

[0058] Set the number of cycles N' to be predicted on the S-N curve in sequence, which are 1×10 6 , 3×10 6 , 1×10 7 , 3×10 7 , 1×10 8 , 3×10 8 , 1×10 9 . Then, n test points can be mapped to the number of cycles N' through formula (5) to obtain n strength mapping values S':

[0059]

[0060] Calculate the average value of n strength mapping values (S’), denoted as which is the median fatigue strength corresponding to the number of cycles N’.

[0061] Set the required confidence level to be γ and the reliability to be p. First, refer to the HB Z / 112 standard to calculate whether the n S’ values meet the requirements of the minimum sample size for the specified confidence level γ and reliability p. If not, increase the number of test samples; if satisfied, calculate the fatigue strength χ corresponding to the specified confidence level γ and reliability p according to formulas (6) and (7). γ,p .

[0062]

[0063]

[0064] where β represents the unbiased correction coefficient of the standard deviation; u P represents the standard normal deviate related to the reliability P, and u γ represents the standard normal deviate related to the confidence level γ, both of which can be obtained by looking up the table.

[0065] Use a smooth curve to successively connect the fatigue strengths χ corresponding to different N’ γ,p , then the p-S-N curve of the confidence level γ and reliability p can be obtained.

[0066] The beneficial effects of the present invention are as follows:

[0067] Improve the accuracy of ultra-high cycle fatigue strength prediction: By introducing the fatigue strength dispersion into the three-parameter S-N curve model and using the maximum likelihood estimation method to maximize the data utilization efficiency during S-N curve fitting. The present invention can more accurately describe the ultra-high cycle fatigue behavior of metal materials, improve the accuracy of fatigue strength prediction, and reduce the test cost and time: The present invention uses small sample data for ultra-high cycle fatigue tests, which has a shorter test cycle and lower cost compared with the traditional staircase method and S-N curve method. The ultra-high cycle fatigue strength prediction method provided by the present invention can provide an important basis for the reliability design of aeroengine materials and contribute to improving the performance and reliability of aeroengines.

Claims

1. A small sample ultra-high cycle fatigue strength prediction method, characterized in that: The following steps are involved: Step 1: Small sample ultra-high cycle fatigue test; Step 2: Construct fatigue strength probability model; The specific form of the fatigue strength probability model is: ln(N)=a+b×ln(S-S RFL ) (1) Where, N is fatigue life; S is stress level; a is the slope of the logarithmic SN curve, b is the intercept of the logarithmic SN curve; S RFL is the fatigue limit of a test piece itself, which is normally distributed, with an average value of S0 and a standard deviation of σ; the established set θ of the four unknown parameters (a, b, σ, S0) is used for subsequent parameter optimization; Let V = S RFL , W = ln(N); define the probability density function of W as: f W (w; S, θ); define the cumulative probability distribution function of W as F W (w; S, θ); define the parameter likelihood function for: Step 3: Solve the likelihood function and optimize the parameters After completing n trials, we will get n groups (S i ,N i ) data into formula (1) for fitting, and the fitting value of parameter a is obtained as a0, the fitting value of parameter b is b0, and the parameter S RFL Fitting value S 00 ; Let θ0=[a0,b0,S 00 ,c.S 00 ], c is the dispersion factor, ranging from 0.01 to 0.2; θ0 is used as the initial value of parameter optimization and is substituted into formula (4) to calculate the likelihood function Define the upper limit of the solution interval θ0*t, and the lower limit of the solution interval θ0 / t, where t is 2 to 10; use the gradient descent method to continuously optimize θ between the upper limit and the lower limit, so that the likelihood function The value is the largest; at this time, the four parameters in θ (a, b, σ, S0) This is the optimal solution of the model; Step 4: Fatigue Strength Prediction The number of cycles N' to be predicted on the SN curve is set to 1×10 6 , 3×10 6 , 1×10 7 , 3×10 7 , 1×10 8 , 3×10 8 , 1×10 9 ; Then by mapping n test points to the cycle number N', n intensity mapping values ​​S' are obtained: Calculate the average value of n intensity mapping values ​​S' and record it as That is the median fatigue strength corresponding to the cycle number N'; Set the required prediction confidence level as γ and reliability level as p. First, refer to the HB Z / 112 standard to calculate whether n S' values ​​meet the minimum sample number required for the required prediction confidence level γ and reliability level p. If not, increase the number of test samples. If yes, calculate the fatigue strength χ corresponding to the specified confidence level γ and reliability level p. γ,p ; The fatigue strength χ corresponding to different predicted cycle numbers N' is sequentially plotted using a smooth curve. γ,p , we can get the pSN curve of confidence γ and reliability p.

2. The small sample ultra-high cycle fatigue strength prediction method according to claim 1 is characterized in that: The small sample ultra-high cycle fatigue test specifically comprises preparing n samples of ultra-high cycle fatigue samples, firstly 7 Up to 1×10 9 The test stress range corresponding to the number of cycles is tested by the lifting method with two lifting pairs, and then in the medium and short life range 1×10 5 Up to 1×10 7 Carry out group test within the stress range corresponding to the cycle, with no less than 4 stress levels and 1-2 valid data for each stress level; increase the number of samples appropriately when sufficient samples are available; record the test number i and test stress S for each test i , number of cycles N i , test results δ i .

3. The small sample ultra-high cycle fatigue strength prediction method according to claim 2 is characterized in that: The n samples, n>12.

4. The small sample ultra-high cycle fatigue strength prediction method according to claim 2 is characterized in that: The test results δ i : The sample fracture is recorded as 1, and the sample non-fracture is recorded as 0.

5. The small sample ultra-high cycle fatigue strength prediction method according to claim 1 is characterized in that: The f W The formula for (w; S, θ) is:

6. The small sample ultra-high cycle fatigue strength prediction method according to claim 1 is characterized in that: The F W The formula for (w; S, θ) is:

7. The small sample ultra-high cycle fatigue strength prediction method according to claim 1 is characterized in that: The formula of the n intensity mapping values ​​S' is:

8. The small sample ultra-high cycle fatigue strength prediction method according to claim 1 is characterized in that: The fatigue strength x corresponding to the specified confidence γ and reliability p γ,p The formula is: Where β represents the unbiased correction coefficient of the standard deviation; k γ,p is the one-sided tolerance factor.

9. The small sample ultra-high cycle fatigue strength prediction method according to claim 1, characterized in that: The k γ,p The solution formula is: Where: u P represents the standard normal deviation associated with reliability P, u γ Represents the standard normal deviation related to the confidence level γ, which is obtained by looking up the table.

Images