CN113408165B - Blade creep-fatigue composite probability life analysis method based on heteroscedastic regression - Google Patents
Blade creep-fatigue composite probability life analysis method based on heteroscedastic regression Download PDFInfo
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Abstract
The invention provides a method for analyzing the creep-fatigue composite probability life of a blade based on heteroscedastic regression, which comprises the following steps: determining the low cycle fatigue probability life according to the test data; determining the creep probability service life according to the test data, and obtaining a creep probability service life model through binary variance regression analysis; establishing a finite element analysis model of the turbine blade, wherein the finite element analysis model comprises establishing a geometric model, setting material properties, applying boundary conditions and external loads and extracting a finite element analysis result; extracting random samples of the probability life auxiliary variable, and obtaining random samples of the low-cycle fatigue life and random samples of the creep life through the analysis of a life equation by combining with a finite element output result; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory; determining a probability density function of creep-fatigue composite life according to a nuclear density method; and obtaining the composite life confidence interval corresponding to the given confidence level under different survival probabilities by a self-service sampling method.
Description
Technical Field
The invention relates to the technical field of engines, in particular to a turbine blade creep-fatigue composite probability life analysis method based on heteroscedastic regression.
Background
Aircraft engines and gas turbines are sources of aircraft and marine power, turbine components are the core, and the life of turbine components largely determines the life of the engine. The turbine component has a complex structure and a severe working environment, is subjected to complex working conditions such as high temperature, high pressure, centrifugal load and vibration load, and is very easy to lose effectiveness such as creep deformation and fatigue.
Therefore, providing a complete set of creep-fatigue life estimation methods is of great importance for analyzing and improving the life performance of turbine components.
It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present invention and therefore may include information that does not constitute prior art known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to provide a blade creep-fatigue composite probability life analysis method based on heteroscedastic regression, which can obtain 95% confidence intervals of life estimation values of turbine blades under different survival probabilities.
According to an aspect of the embodiment of the invention, a method for analyzing the creep-fatigue composite probability life of a blade based on heteroscedastic regression is provided, and the method comprises the following steps:
acquiring fatigue test data of a target turbine blade material, and determining the low-cycle fatigue probability life according to the test data, wherein the determination of the low-cycle fatigue probability life comprises determining preset parameters in a probability life equation and correcting the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio;
determining the creep probability life according to the test data, wherein independent variables in a creep life equation comprise temperature and load-holding stress, and a creep probability life model is obtained through binary variance regression analysis;
establishing a finite element analysis model of the turbine blade, wherein the finite element analysis model comprises establishing a geometric model, setting material properties, applying boundary conditions and external loads and extracting a finite element analysis result;
extracting random samples of the probability life auxiliary variables, and obtaining random samples of the low-cycle fatigue life and random samples of the creep life through analysis of a life equation by combining with finite element output results; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory;
determining a probability density function of creep-fatigue composite life according to the nuclear density;
and obtaining the composite life confidence interval corresponding to the given confidence level under different survival probabilities by a self-service sampling method.
In an exemplary embodiment of the disclosure, the obtaining fatigue test data of a target turbine blade material, and determining a low-cycle fatigue probability life according to the test data, where the determining of the low-cycle fatigue probability life includes determining preset parameters in a probability life equation and performing a modification of the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio, includes:
acquiring fatigue life data of the material under a strain cycle ratio;
establishing a probability-strain-life model of the fatigue life according to the fatigue life data;
and (4) determining a corrected fatigue life probability model by correcting the average stress and replacing the fatigue life standard deviation of the asymmetric cycle with the fatigue life standard deviation of the symmetric cycle.
In an exemplary embodiment of the present disclosure, the probability-strain-life model is:
wherein, delta epsilon t As total strain amplitude, Δ ε e Amplitude of elastic strain, Δ ε p For plastic strain amplitude, u is a standard normal random variable, E is Young's modulus, u is an auxiliary variable and follows a standard normal distribution, N f In order to determine the number of fatigue cycles,
are the mean values, σ, of the four parameters, respectively e0 、σ p0 Respectively representing logarithmic lifetimes y e 、y p In logarithmic strain component x e0 、x p0 Standard deviation of (a), theta e 、θ p Respectively represent σ e 、σ p Slope of the linear change.
In an exemplary embodiment of the present disclosure, the modified fatigue life probability model is:
wherein, delta epsilon t To total strain amplitude, σ m Is the mean stress.
In an exemplary embodiment of the disclosure, the random samples of the probabilistic life auxiliary variables are extracted, and the random samples of the low cycle fatigue life and the random samples of the creep life are obtained through the analysis of a life equation by combining with the finite element output results; obtaining a random sample of creep-fatigue composite life by a linear accumulated damage theory, comprising:
obtaining the creep life of the material at different temperatures and under different holding stresses;
and obtaining a probability creep life equation by using binary variance regression analysis.
In an exemplary embodiment of the present disclosure, the probabilistic creep life equation is:
lg N c ＝b 0 +b 1 T+b 2 lg S+b 3 (lg S) 2 +b 4 (lg S) 3 +σ 0 |1+θ T (T-x T0 )+θ s (S-x s0 )|μ
wherein N is c Denotes creep life, T is temperature, S is holding stress, b i (i =0,1,.., 4) is a model parameter, σ 0 Logarithmic life lg N c At a temperature component x T0 And a holding stress component x S0 Standard deviation of (a), theta T 、θ S The slope of the log life standard deviation with temperature and holding stress, u is an auxiliary variable and follows a standard normal distribution.
In one exemplary embodiment of the present disclosure, the random error term is related to temperature and stress by:
σ(S，T)＝σ 0 |1+θ T (T-T 0 )+θ S (S-S 0 )|
wherein T is 0 Is a standard temperature, S 0 The standard holding stress.
In an exemplary embodiment of the present disclosure, the creep probability lifetime heteroscedastic regression analysis model is:
Y＝2.2252×10 4 -2.8117×10 4 X+1.1845×10 4 X 2 -1.6637×10 3 X 3 +εE～(0，0.0132×(1-0.1295×(X-2.3754))
wherein Y represents a logarithmic lifetime and X represents a logarithmic holding stress.
In an exemplary embodiment of the present disclosure, the creep-fatigue composite life sample is:
wherein, N C-F To compound life, N 1 Fatigue life of the main cycle, N 2 Fatigue life for the sub-cycle, N 3 Creep life is considered.
In an exemplary embodiment of the present disclosure, the probability density function is:
wherein K (u) is a kernel function, n is the number of kernel functions, h i Greater than 0 is window width, alpha i Is the weight of each kernel function, and 0 < alpha i ＜1，
According to the method for analyzing the creep-fatigue composite probability life of the blade based on the heteroscedastic regression, firstly, fatigue life test data of the blade material DZ125 at 800 ℃ can be obtained through tests, and a probability life equation of the DZ125 material at 800 ℃ is obtained through a univariate heteroscedastic regression analysis; creep life test data of the turbine blade material DZ125 under three different temperature and load-holding stresses are obtained through tests, a binary variance regression analysis model is deduced and established, and a creep probability life model of the creep life variance along with the change of creep temperature and load-holding stress is established. Secondly, extracting fatigue life dispersity characterization auxiliary variables and creep life dispersity characterization auxiliary variable samples, obtaining corresponding fatigue life and creep life samples through probability life model analysis, and obtaining creep-fatigue life samples through a linear damage accumulation theory. And finally, obtaining creep-fatigue composite life probability distribution through nuclear density estimation based on a creep-fatigue life sample, and obtaining a 95% confidence interval of the life estimation value of the turbine blade under different survival probabilities through resampling and repeated analysis of the test data by a Bootstrap (self-help sampling method).
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:
FIG. 1 is a flowchart of a method for analyzing a creep-fatigue composite probabilistic life of a blade based on heteroscedastic regression according to an embodiment of the disclosure;
FIG. 2 provides a P- ε -N curve of DZ125 at 800 ℃ for one embodiment of the present disclosure;
FIG. 3 is a graph illustrating creep life at various survival rates at 980 ℃ according to an embodiment of the present disclosure;
FIG. 4 is a flow chart of a creep-fatigue probability life analysis for a turbine blade provided in accordance with an embodiment of the present disclosure;
FIG. 5 is a geometric model of a turbine blade provided by an embodiment of the present disclosure;
FIG. 6 illustrates turbine blade finite element analysis results provided by an embodiment of the present disclosure;
FIG. 7 is a probability density function plot of turbine blade creep-fatigue composite life provided by one embodiment of the present disclosure.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art.
The flow charts shown in the drawings are merely illustrative and do not necessarily include all of the contents and operations/steps, nor do they necessarily have to be performed in the order described. For example, some operations/steps may be decomposed, and some operations/steps may be combined or partially combined, so that the actual execution sequence may be changed according to the actual situation.
Embodiments of the present disclosure provide a method for analyzing a creep-fatigue composite probability life of a blade based on heteroscedastic regression, as shown in fig. 1 and 4, the method including:
s100, obtaining fatigue test data of a target turbine blade material, and determining the low-cycle fatigue probability life according to the test data, wherein the determination of the low-cycle fatigue probability life comprises the steps of determining preset parameters in a probability life equation and correcting the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio;
step S200, determining the creep probability life according to the test data, wherein independent variables in a creep life equation comprise temperature and load-holding stress, and a creep probability life model is obtained through binary different variance regression analysis;
step S300, establishing a turbine blade finite element analysis model, including establishing a geometric model, setting material properties, applying boundary conditions and external loads, and extracting a finite element analysis result;
s400, extracting random samples of the probability life auxiliary variables, and obtaining random samples of the low cycle fatigue life and random samples of the creep life through analysis of a life equation by combining with finite element output results; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory;
s500, determining a probability density function of the creep-fatigue composite life according to a nuclear density method;
and S600, obtaining a composite life confidence interval corresponding to a given confidence level under different survival probabilities by a self-service sampling method.
According to the method for analyzing the creep-fatigue composite probability life of the blade based on the different variance regression, firstly, fatigue life test data of the blade material DZ125 at 800 ℃ can be obtained through tests, and a probability life equation of the DZ125 material at 800 ℃ is obtained through a univariate different variance regression analysis; creep life test data of the turbine blade material DZ125 under three different temperature and load-holding stresses are obtained through tests, a binary variance regression analysis model is deduced and established, and a creep probability life model of the creep life variance along with the change of creep temperature and load-holding stress is established. Secondly, extracting fatigue life dispersity characterization auxiliary variables and creep life dispersity characterization auxiliary variable samples, obtaining corresponding fatigue life and creep life samples through probability life model analysis, and obtaining creep-fatigue life samples through a linear damage accumulation theory. And finally, obtaining creep-fatigue composite life probability distribution through nuclear density estimation based on a creep-fatigue life sample, and obtaining a 95% confidence interval of the life estimation value of the turbine blade under different survival probabilities through resampling and repeated analysis of the test data by a Bootstrap (self-help sampling method).
In the following, each step in the method for analyzing the creep-fatigue composite probability life of the blade based on the variance regression provided by the present disclosure will be described in detail.
In step S100, fatigue test data of a target turbine blade material is obtained, and a low-cycle fatigue probability life is determined according to the test data, where the determination of the low-cycle fatigue probability life includes determining preset parameters in a probability life equation and performing correction of the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio.
Specifically, the fatigue probability life model in step S100 is obtained by a unitary anisotropic regression method, and the probability life of the structural assessment site under the current stress cycle level is obtained by extracting a random sample of the auxiliary variable in combination with the cyclic stress of the structural assessment site. The specific substeps in S100 are as follows:
step S101: fatigue life data for the investigated materials at strain cycle ratios were collected. Taking the turbine blade material DZ125 targeted as an example, table 1 is the DZ125 alloy casting low cycle fatigue life data.
Table 1: low cycle fatigue performance of DZ125 alloy casting
Step S102: and establishing a probability-strain-life model of fatigue life estimation.
The basic theory of heterovariance regression is as follows:
the strain-life curve is more suitable for plastic deformation of a material under large load, and is more suitable for calculating the low cycle fatigue life, the most common model is a Manson-coffee model, and the specific expression is as follows:
wherein, delta epsilon t ＝ε max -ε min ，
Wherein, delta epsilon t Is the total strain amplitude, delta epsilon e Is the elastic strain amplitude, delta epsilon p Is plastic strain amplitude, sigma' f Is fatigue strength coefficient, E is elastic modulus, N f Is fatigue cycle number, b is fatigue strength index, epsilon' f The fatigue plasticity coefficient and the fatigue plasticity index are c.
The P-epsilon-N curve is a set of epsilon-N curves at different survival rates P. This set of curves gives the following information: distribution data of fatigue life N at a given strain cycle.
The core of the Manson-coffee formula is that in a log-log coordinate, the fatigue life is respectively in a linear relation with an elastic strain amplitude and a plastic strain amplitude, and is expressed as follows:
let y e ＝log(2N)，
The standard linear equation for the available elastic threads is:
y e ＝a e +b e x e (4)
in the same way, let y p ＝log(2N)，
The standard linear equation for the resulting plasticity line is:
y p ＝a p +b p x p (5)
a large number of fatigue test data show that the log life dispersion is a function of Δ ε e 、Δε p The standard deviation of logarithmic life is in linear relation with logarithmic elastic strain component and logarithmic plastic strain component, namely:
y＝a+bx+ε (6)
wherein epsilon to N (0, sigma) 2 (x) σ (x) is expressed as:
σ(x)＝σ 0 [1+θ(x-x 0 )] (7)
in the formula, σ 0 Is logarithmic life at x 0 Standard deviation at the strain component.
Suppose that the sample obtained from n independent experiments is (x) 1 ，y 1 )、(x 2 ，y 2 )、...、(x n ，y n ) Then, the estimated quantities of the parameters in equations (6) and (7) are calculated as:
wherein ν is the degree of freedom of the variance, and when θ =0, ν = n-2, i.e. degenerates to the same variance case; when θ ≠ 0, ν = n-3. Other process parameters are as follows:
I(x i ，θ)＝1+θ(x i -x 0 ) (13)
substituting the expressions (16) to (21) into the expression (11) to solve theta, and solving the theta to obtain the subsequent expression (8)) Solving the parameters a, b and sigma 0 。
A in Manson-coffee formula under different survival rates e 、a p 、b e 、b p In contrast, and therefore considering the P-epsilon-N function fitting, these four parameters are random variables,
the mean of these four parameters, respectively, the linear standard deviation of the elastic and plastic lines can be expressed by equation (7):
σ e (x e )＝σ e0 [1+θ e (x e -x e0 )] (22)
σ p (x p )＝σ p0 [1+θ p (x p -x p0 )] (23)
in the formula, σ e0 、σ p0 Respectively representing logarithmic lifetimes y e 、y p In logarithmic strain component x e0 、x p0 Standard deviation of (a), theta e 、θ p Respectively represent σ e 、σ p Slope of the linear change.
Since the log-life follows a normal distribution, the mean value is
(plastic segment)
) Standard deviation of σ e (x e ) (plastic segment σ) p (x p ) Therefore, convert it to standard normal variables:
therefore, the following steps are obtained:
the corresponding plastic line is expressed as:
in the formula, u is a standard normal random variable.
The relationship between the four parameters and the auxiliary variable u in the Manson-coffee formula is as follows:
the DZ 125P-epsilon-N curve is obtained by using the different variance regression analysis theory and combining the fatigue life data of the DZ125 material at 800 ℃ in the step S101, and is shown as follows:
obtaining related estimation parameters of the elastic line according to heteroscedastic regression analysis:
in a similar way, the related estimation parameters of the plastic line are obtained according to the heteroscedastic regression analysis:
therefore, the probability strain-life curve (strain ratio R) based on the univariate variance regression analysis ε Is-1) as follows:
the fatigue life of the material can be estimated from equation (37) for different survival probabilities and different cyclic stress levels, and fig. 2 gives the strain life curves for 0.01, 0.5 and 0.99 survival probabilities P. Fig. 2 shows that the smaller the strain amplitude, the longer the fatigue life, and the greater the dispersion of the fatigue life.
Step S103: by Morrow mean stress correction, replacing the fatigue life standard deviation of the asymmetric cycle with the fatigue life standard deviation of the symmetric cycle, a corrected fatigue life probability model can be obtained, namely:
wherein σ m Is the mean stress, E is the young's modulus, u is the auxiliary variable and follows a standard normal distribution.
In step S200, determining a creep probability life according to the test data, where independent variables in a creep life equation include temperature and holding stress, and the creep probability life model is obtained through a binary variance regression analysis.
Specifically, the creep probability life model in step S200 is obtained by a binary heteroscedastic regression method, and the creep probability life of the structure assessment site under the current holding stress is obtained by extracting random samples of auxiliary variables and combining the cyclic stress of the structure assessment site. The specific substeps in step S200 are as follows:
step S201: the creep life of the material under investigation at different temperatures and different holding stresses was collected, taking the turbine blade material DZ125 as an example, and table 2 shows the creep life data of the DZ125 alloy castings at 760 ℃, 980 ℃ and 1040 ℃.
Table 2: creep life test data of DZ125 under different temperatures and different stresses
Step S202: the following probability creep life equation is obtained by using the binary variance regression analysis, namely:
lg N c ＝b 0 +b 1 T+b 2 lg S+b 3 (lg S) 2 +b 4 (lg S) 3 +σ 0 |1+θ T (T-x T0 )+θ S (S-x S0 )|μ (39)
wherein N is c Denotes creep life, T is temperature, S is holding stress, b i (i =0,1.., 4) is the model parameter, σ 0 Is logarithmic life lg N c At a temperature component x T0 And a holding stress component x S0 Standard deviation of (a), theta T 、θ S The slope of the log life standard deviation with temperature and holding stress, u is an auxiliary variable and follows a standard normal distribution.
The basic theory of the proposed binary heteroscedastic regression is as follows:
in the endurance test and the creep test, as the stress or temperature is increased, the life dispersion is necessarily decreased, i.e., the logarithmic life variance at each stress or temperature is unequal. Therefore, it is necessary to establish a bivariate regression model to solve the problem of establishing the probabilistic creep life model.
First, assume that the relationship between the random error term and temperature and stress is:
σ(S，T)＝σ 0 |1+θ T (T-T 0 )+θ S (S-S 0 )| (40)
wherein, temperature and stress are represented by T and S. The variance term of random error under different temperature and stress is different, generally, the higher the temperature is, the larger the stress is, the smaller the service life is, the smaller the dispersion of the service life is, the smaller the standard deviation of the service life is, therefore, the theta T And theta S And should generally be negative. Using the M-S equation in the analysis of the binary variance creep life, i.e.
lg t c ＝b 0 +b 1 T+b 2 X+b 3 X 2 +b 4 X 3 (41)
The creep life equation can be written as:
Y＝b 0 +b 1 T+b 2 X+b 3 X 2 +b 4 X 3 (42)
wherein Y = lg t c X = lg σ, let X 1 ＝T，X 2 ＝X，X 3 ＝X 2 ，X 4 ＝X 3 Then equation (41) can be expressed as:
Y＝b 0 +b 1 X 1 +b 2 X 2 +b 3 X 3 +b 4 X 4 (43)
consideration of creep life dispersancy with respect to stress X 1 And X 2 The heteroscedasticity of (a) can be obtained as follows, taking into account the random error term, an heteroscedasticity analysis model
Y＝b 0 +b 1 X 1 +b 2 X 2 +b 3 X 3 +b 4 X 4 +ε (44)
Wherein epsilon-N0, sigma (x) 1 ，x 2 )]，σ(x 1 ，x 2 )＝σ 0 |1+θ 1 (x 1 -x 10 )+θ 2 (x 2 -x 20 )|。
Order to
N c ＝b 0 Z 0 +b 1 Z 1 +b 2 Z 2 +b 3 Z 3 +b 4 Z 4 +u (45)
wherein the content of the first and second substances,
then the
The heteroscedastic equivalence can be converted into homoscedastic linear regression by means of weighting through the formula (45).
θ 1 、θ 2 The solution of (2) uses maximum likelihood estimation:
the likelihood function L is maximum, then only need
The minimum, i.e. the sum of the squared residuals of the least squares, is minimized.
Thus, an optimization concept can be employed to solve for θ 1 、θ 2 And coefficient matrix b = [ b = 0 ，b 1 ，b 2 ，b 3 ，b 4 ]。
Solving for theta 1 、θ 2 And coefficient matrix b = [ b = 0 ，b 1 ，b 2 ，b 3 ，b 4 ]The optimization model is as follows:
the calculation of σ 0 is:
obtaining the DZ 125P-T-S-N by combining the heterovariance regression analysis theory with the creep life data of the DZ125 material in the step S201 c The curves, as follows:
Y＝2.2252×10 4 -2.8117×10 4 X+1.1845×10 4 X 2 -1.6637×10 3 X 3 +ε
ε～(0，0.0132×(1-0.1295×(X-2.3754)) (53)
wherein Y represents a logarithmic lifetime, and X represents a logarithmic holding stress.
The probability creep life of the researched material under different temperatures and different holding stresses can be estimated by combining test data with a binary heteroscedastic regression model in the patent.
The fatigue life of the material can be estimated according to the formula (54) under different survival probabilities and different holding stresses, and fig. 3 shows holding stress-life curves under the conditions that the survival probabilities P are 0.01, 0.5 and 0.99. The results of FIG. 3 show that the smaller the holding stress, the longer the lifetime, and the greater the dispersibility of the lifetime.
In step S300, a finite element analysis model of the turbine blade is established, including establishing a geometric model, setting material properties, applying boundary conditions and external loads, and extracting a finite element analysis result.
Specifically, a geometric model of the turbine blade is shown in FIG. 5. The material is DZ125, the working temperature is 800 ℃, and the material attribute and working condition information are shown in tables 3 and 4. Table 5 shows the cyclic stress and cyclic strain information obtained from the finite element analysis results under different conditions. The results of finite element analysis at 13880rpm are shown in FIG. 6.
Table 3: material Properties of DZ125 Material at 800 deg.C
| Material properties | Young's modulus | Modulus of shear | Poisson ratio | Yield strength | Coefficient of linear expansion |
| Unit of | GPa | GPa | - | |
10 -6 ·℃ -1 |
| Longitudinal direction | 102 | 90.5 | 0.43 | 933 | 14.55 |
| Transverse direction | 139.5 | 52.5 | 0.29 | 783 | 14.43 |
Table 4: main cycle and damaged secondary cycle (average rise and fall)
Table 5: stress-strain analysis result for examining air film hole under two working conditions
In step S400, random samples of the probability life auxiliary variables are extracted, and the random samples of the low-cycle fatigue life and the random samples of the creep life are obtained through the analysis of a life equation by combining with the finite element output results; and obtaining a random sample of the creep-fatigue composite life by a linear accumulated damage theory.
Specifically, in step S400, a corresponding life random sample is obtained through the transmission of the auxiliary variable randomness to the fatigue life and the creep life, and a corresponding composite life random sample is obtained through the linear damage accumulation. The method comprises the following specific steps:
step S401: let P Li Survival probability P representing fatigue life of i-th order C Indicating the probability of survival for creep life. Since the survival probability is between 0 and 1, it is in [0,1]Interval(s)Respectively randomly extracting n
And P C Of (2) a sample, i.e.
Obtaining corresponding auxiliary variable samples
Wherein the content of the first and second substances,
the kth sample representing the auxiliary variable in the ith-stage fatigue life analysis equation,
the kth sample of the auxiliary variables in the i-th order creep life analysis equation is represented.
Step S402: setting k =1;
step S403: according to the P-epsilon-N curve and P-T-S-N C The curve calculates the survival rate as
Fatigue life of
Creep life under
Step S404: according to the linear damage accumulation theory, the composite life of the blade is calculated
Step S405: judging whether k is larger than n, and continuing to execute when k is larger than n; otherwise, let k = k +1, and return to step S403;
step S406: to composite life
Are ordered, i.e.
Calculating the composite life of the blade under different survival probabilities according to the sorted data, wherein when the survival probability is p, the corresponding composite life is
Wherein [. ]]Representing a rounding operation.
In step S400, a random sample of the probabilistic life auxiliary variable is extracted, and a random sample of the low cycle fatigue life and a random sample of the creep life are obtained through analysis of a life equation by combining with a finite element output result; obtaining a random sample of the creep-fatigue composite life by a linear accumulated damage theory, wherein the method comprises the following specific steps:
step S410: by using N 1 Representing the fatigue life of the main cycle, N 2 Denotes the fatigue life of the sub-cycle, N 3 Represents creep life;
step S420: mean stress for the first main cycle regime
Total strain amplitude
The sample of the auxiliary normal variable u is extracted as { u (1) ，u (2) ,...,u (n) N, the corresponding n sets of lifetimes are calculated according to equation (37), i.e.:
step S430: mean stress for the second sub-cycle regime
Total strain amplitude
The sample of the auxiliary normal variable u is extracted as { u (1) ,u (2) ,...,u (n) N, the corresponding n sets of lifetimes are calculated according to equation (37), i.e.:
step S440: for the creep case, the dwell stress was σ =415.2125MPa, and the sample for the extracted variable ε was { ε (1) ,ε (2) ,...,ε (n) N, the corresponding n sets of lifetimes are calculated according to equation (37), i.e.:
step S450: from the life samples in the three modes, creep-fatigue composite life samples were calculated as follows:
wherein 100min represents the load-holding time of the average stress of the one-time take-off and landing working condition 1.
In step S500, a probability density function of creep-fatigue life is estimated according to a kernel density method.
Specifically, according to the composite life sample obtained in step S400
Combined nuclear densityThe probability density function of the estimated composite life is estimated. The probability density function of the creep-fatigue composite life distribution is shown in fig. 7. The principle of the nuclear density estimation method is as follows:
assuming that K (u) is a given probability density function over R, then:
referred to as overall probability density f n (x) K (u) is a kernel function (also called a window function), n is the number of kernel functions, h i >0 is window width, α i Is a weight of each kernel function, and 0<α i <1，
In step S600, a Bootstrap sampling method is used to obtain a composite lifetime confidence interval corresponding to a given confidence level under different survival probabilities.
Specifically, step S600 includes: step S601: and obtaining fatigue life test data and creep life test data. Let { (x) (i) ,y (i) )；i＝1,...,S 1 Denotes the amplitude of the strain cycle at the temperature studied as x (i) (i＝1,...,S 1 ) Fatigue test data y (i) (i＝1,...,S 1 )，{(T (i) ,s (i) ,n c (i) )；i＝1,...,S 2 Denotes the temperature T (i) Holding stress of s (i) Creep life test data n c (i) ；
Step S602: let k =1;
step S603: and acquiring a kth set of Bootstrap samples. Sample data of fatigue test { (x) (i) ,y (i) )；i＝1,...,S 1 Withdraw S with a replacement 1 A sample, is marked
Sample data for creep test { (T) (i) ,s (i) ,n c (i) )；i＝1,...,S 2 Withdraw S with a replacement 2 A sample, is marked
Step S604: using samples
And combining with univariate variance regression analysis to obtain model parameters in the probability-strain-fatigue life model under the group of samples and a corresponding probability-strain-fatigue life model; using samples
And obtaining model parameters in the probability-temperature-stress-creep life model and a corresponding probability-temperature-stress-creep life model under the group of samples by combining with the binary different variance regression analysis.
Step S605: let k = k +1, and return to step S603. When k is larger than M (M represents the preset number of Bootstrap sample groups), the following steps are continuously executed.
Step S606: for strain cycles of x * Holding stress of s * At a temperature of T * And estimating by using the life equation under the M groups of resampling samples to obtain M groups of fatigue lives and M groups of creep lives under different survival probabilities P, and performing statistical inference, such as a confidence interval, on the M groups of creep-fatigue composite lives corresponding to the linear damage accumulation theory through the M groups of creep-fatigue composite lives.
In Table 6 are composite life samples obtained by the step S500
The creep-fatigue composite life and the corresponding equivalent flight time (the time of one flight is 100 min) under different survival probabilities are calculated. In Table 7, the results were obtained by the Bootstrap methodTo a 95% confidence interval for creep-fatigue composite life estimation for different probabilities of survival of the turbine blade.
Table 6: creep-fatigue composite life at different survival probabilities
Table 7: 95% confidence intervals for creep-fatigue composite life estimation for turbine blades at different probabilities of survival
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
It will be understood that the invention is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.
Claims (7)
1. A method for analyzing the creep-fatigue composite probability life of a blade based on heteroscedastic regression is characterized by comprising the following steps:
acquiring fatigue test data of a target turbine blade material, and determining the low cycle fatigue probability life according to the test data, wherein the determination of the low cycle fatigue probability life comprises the steps of determining preset parameters in a probability life equation and correcting the probability life equation under a standard strain ratio to the probability life equation under an arbitrary strain ratio;
determining the creep probability life according to the test data, wherein independent variables in a creep life equation comprise temperature and holding stress, and a creep probability life model is obtained through binary different variance regression analysis;
establishing a finite element analysis model of the turbine blade, wherein the finite element analysis model comprises establishing a geometric model, setting material properties, applying boundary conditions and external loads and extracting a finite element analysis result;
extracting random samples of the probability life auxiliary variable, and obtaining random samples of the low-cycle fatigue life and random samples of the creep life through the analysis of a life equation by combining with a finite element output result; obtaining a random sample of creep-fatigue composite life through a linear accumulated damage theory;
determining a probability density function of the creep-fatigue composite life according to a nuclear density method;
obtaining a composite life confidence interval corresponding to a given confidence level under different survival probabilities by a self-service sampling method;
the method comprises the steps of extracting random samples of probability life auxiliary variables, and obtaining random samples of low cycle fatigue life and random samples of creep life through analysis of a life equation by combining finite element output results; obtaining a random sample of creep-fatigue composite life by a linear accumulated damage theory, comprising:
obtaining the creep life of the material at different temperatures and under different holding stresses;
obtaining a probability creep life equation by using a binary variance regression analysis, wherein the probability creep life equation is as follows:
lg N c ＝b 0 +b 1 T+b 2 lg S+b 3 (lg S) 2 +b 4 (lg S) 3 +σ 0 |1+θ T (T-x T0 )+θ s (S-x S0 )|μ
wherein N is c Denotes creep life, T is temperature, S is holding stress, b j (j＝0，1,., 4) are model parameters, σ 0 Logarithmic life lg N c At a temperature component x T0 And a holding stress component x S0 Standard deviation of (a), theta T 、θ S The slope of the log life standard deviation with temperature and holding stress, u is an auxiliary variable and follows a standard normal distribution.
2. The analysis method according to claim 1, wherein the obtaining of fatigue test data of the target turbine blade material, and the determining of the low cycle fatigue probability life according to the test data comprises determining preset parameters in a probability life equation and performing a modification of the probability life equation at a standard strain ratio to the probability life equation at an arbitrary strain ratio, and comprises:
acquiring fatigue life data of the material under a strain cycle ratio;
establishing a probability-strain-life model of the fatigue life according to the fatigue life data;
and determining a corrected fatigue life probability model by mean stress correction and replacing the fatigue life standard deviation of the asymmetric cycle with the fatigue life standard deviation of the symmetric cycle.
3. The analytical method of claim 2, wherein the probability-strain-lifetime model is:
wherein, delta epsilon t As total strain amplitude, Δ ε e Amplitude of elastic strain, Δ ε p For plastic strain amplitude, E is the Young's modulus, u is the auxiliary variable and follows a standard normal distribution, N f In order to determine the number of fatigue cycles,
are the mean values, σ, of the four parameters, respectively e0 、σ p0 Respectively representing logarithmic lifetimes y e 、y p In logarithmic strain component x e0 、x p0 Standard deviation of (a), theta e 、θ p Respectively represent sigma e 、σ p Slope of the linear change.
4. The analytical method of claim 3, wherein the modified fatigue life probability model is:
wherein, delta epsilon t To total strain amplitude, σ m Is the mean stress.
5. The analytical method of claim 1, wherein the creep probability lifetime heteroscedastic regression analysis model is:
Y＝2.2252×10 4 -2.8117×10 4 X+1.1845×10 4 X 2 -1.6637×10 3 X 3 +εε～(0，0.0132×(1-0.1295×(X-2.3754))
wherein Y represents a logarithmic lifetime and X represents a logarithmic holding stress.
6. The analytical method of claim 1, wherein the random sample of creep-fatigue composite life is:
wherein N is C-F To compound life, N 1 Fatigue life of the major cycle, N 2 Fatigue life for the sub-cycle, N 3 Creep life is considered.
7. The analysis method of claim 1, wherein the probability density function is:
where K () is a kernel function, n is the number of kernel functions, h i Greater than 0 is window width, alpha i Is the weight of each kernel function, and 0 < alpha i ＜1，
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