CN108460183A - Materials for aeroengines high cycle fatigue P-S-N curve test methods are determined in a kind of measurement of small sample - Google Patents
Materials for aeroengines high cycle fatigue P-S-N curve test methods are determined in a kind of measurement of small sample Download PDFInfo
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Abstract
The invention discloses a kind of measurements of small sample to determine materials for aeroengines high cycle fatigue P S N curve test methods, including：Based on same sample under different stress levels fatigue life identical probability distribution point meeting formula (4) expression formula in respective estimator of parent distribution：In formula (4), njiThe logarithm service life for being sample i under jth stress level, μjFor the logarithm service life mean value under jth stress level, σjFor the logarithm life standard error under jth stress level；Meaning is identical when subscript j is changed to k；There are one-to-one relationships between each service life sample point under different stress levels, according to the correspondence of formula (4), fatigue life on a certain stress level is equivalent on another stress level, realize sample information aggregation, and then tested to obtain equivalent large sample by small sample, and carry out service life distributed constant statistics according to equivalent big-sample data.Method provided by the invention is to be based on sample building up principle, can obtain FATIGUE LIFE DISTRIBUTION by a small amount of test data, and obtain more accurate P S N curves.
Description
Technical field
The present invention relates to materials for aeroengines fatigue property test technical fields, and in particular to a kind of small sample measurement is fixed
Materials for aeroengines high cycle fatigue P-S-N curve test methods.
Background technology
Current Domestic is to the common high-cycle fatigue test method of materials for aeroengines：Method measures the longevity in material in groups
Area's fatigue life is ordered, lifting and lowering method determines the fatigue limit of materials；Generally P-S-N curves are determined with 40~60 samples.Room temperature is tried
The 20 days time of needs is tested, the hot test period needs nearly 40 days time.For research preparation process, processing technology and
Component design influences engine component fatigue of materials performance rule to need a large amount of high cycle fatigue performance test, including high temperature height
The problems such as all fatigue tests, conventional method is long, testing expenses are high there are the test period.
The working environment of aeroengine components is severe, needs to bear the alternation machinery load that amplitude and frequency change greatly
Lotus has high cycle fatigue performance very high requirement.The characteristics of Development of Novel aeroengine components moulding process and size,
Cause the problems such as sampling of fatigue testing specimen is difficult and waste material is more.Using Small Sample Database processing method can reduce experiment quantity, shorten
Test period saves experimentation cost.
Obtaining P-S-N curves for how handling Small Sample Database has certain research both at home and abroad, on the basis of theory
Domestic and international research level is suitable.But evaluate disunity, small sample amount due to calculating cumbersome and result of calculation credibility
Test method is in solving the problems, such as Practical Project using less.At home, each colleges and universities and scientific research department still use tradition method in groups
The high cycle fatigue performance (national standard GB/T 24176) of material is measured with the method for lifting and lowering method.
Foreign countries are complex for the method for P-S-N curve matchings, calculation amount is larger, are suitable for comprehensive utilization history number
According to obtaining small sample problem using conventional method processing priori data and more correctly estimate, to obtain higher curve precision.
For by improving large sample statistical method, being allowed to be suitable for small sample problem as far as possible, since confidence level is not high, in engineering department
Door is difficult to carry out.
Invention content
Purpose of the invention is to overcome the shortcomings in the prior art, provides a kind of measurement of small sample and determines aero-engine
Material high cycle fatigue P-S-N curve test methods.The present invention is to be based on sample building up principle, the smaller sample size of use (20
Sample or so) method that measures metal material fatigue behaviour (P-S-N curves) at a room temperature and a high temperature, by this method for navigating
In empty engine key member titanium alloy, high temperature alloy high cycle fatigue performance test, Dependence Results can be directly used for evaluating
The fatigue behaviour of titanium alloy, the forging of high temperature alloy, ingot casting, influence of the processing technology to key member fatigue behaviour.
In order to achieve the above object, the invention is realized by the following technical scheme：
Materials for aeroengines high cycle fatigue P-S-N curve test methods determine in a kind of measurement of small sample, which is characterized in that wrap
It includes：
Based on same sample under different stress levels fatigue life identical probability distribution point in respective estimator of parent distribution
Meeting formula (4) expression formula：
In formula (4), njiThe logarithm service life for being sample i under jth stress level, μjFor the logarithm longevity under jth stress level
Order mean value, σjFor the logarithm life standard error under jth stress level；Meaning is identical when subscript j is changed to k；
There are one-to-one relationships between each service life sample point under different stress levels, according to the correspondence of formula (4)
Relationship, the fatigue life on a certain stress level is equivalent on another stress level, realizing sample information aggregation, Jin Eryou
Small sample is tested to obtain equivalent large sample, and carries out service life distributed constant statistics according to equivalent big-sample data.
According to a preferred embodiment of the invention, formula (4) is obtained by following steps：
Based on same sample under different stress levels fatigue life identical probability distribution point in respective estimator of parent distribution
Meeting formula (1) expression formula：
p(n'ji)=p (n'ki) (1)
In formula (1), j stress level parent service life NjLess than sample i service life n is obtained in the stress leveljiProbability (p
(n'ji)=P (N'j＜ n'ji), formula (2) obtains n less than same sample i with k stress level parent service life Nk in k stress levelski
Probability it is identical；
High-Cycle Fatigue Life Prediction obeys logarithm normal distribution, i.e. lgN~N (μ, σ 2) has formula (3) expression formula：
Then formula (1) is expressed as formula (4) expression formula：
In formula (4), njiThe logarithm service life for being sample i under jth stress level, μjFor the logarithm longevity under jth stress level
Order mean value, σjFor the logarithm life standard error under jth stress level；Meaning is identical when subscript j is changed to k.
According to a preferred embodiment of the invention, the test method further includes：Determine the tired longevity under stress levels at different levels
Life dispersibility determines that logarithm standard deviation-stress level relationship, the relationship of logarithm standard deviation σ and stress s are expressed as formula (6)：
σ(sj)=σ (s1)+K(sj-s1) (6)
In formula (6), σ (Sj) be j-th stage stress level under logarithm life standard error, K is straight slope；When a certain stress
Horizontal s1Under life standard error determine after, remaining stress level standard deviation is determined by formula (6).
According to a preferred embodiment of the invention, the test method further includes：Compared with small sample amount, fit
Intermediate value S-N linear equations, equation form are formula (5)：
S=Cnb (5)
In formula (5), s is stress amplitude, and n is fatigue life, and C, b are fitting constant.
Compared with prior art, it is bent to determine materials for aeroengines high cycle fatigue P-S-N for a kind of small sample of the invention measurement
Wire testing method has the advantages that：Method provided by the invention is to be based on sample building up principle, can be by testing on a small quantity
Data obtain FATIGUE LIFE DISTRIBUTION, and obtain more accurate P-S-N curves, Dependence Results can be directly used for evaluation titanium alloy,
The forging of high temperature alloy, the fatigue behaviour of ingot casting.
Specific implementation mode
Below in conjunction with specific embodiment, the present invention will be further described.It should be understood that following embodiment is merely to illustrate this
The range of invention and is not intended to limit the present invention.
Materials for aeroengines high cycle fatigue P-S-N curve test methods are determined in a kind of measurement of small sample, including：
Based on same sample under different stress levels fatigue life identical probability distribution point in respective estimator of parent distribution
Meeting formula (1) expression formula：
p(n'ji)=p (n'ki) (1)
In formula (1), j stress level parent service life NjLess than sample i service life n is obtained in the stress leveljiProbability (p
(n'ji)=P (N'j＜ n'ji), formula (2) and k stress level parent service life NkLess than same sample i n is obtained in k stress levelski's
Probability is identical；
High-Cycle Fatigue Life Prediction obeys logarithm normal distribution, i.e. lgN~N (μ, σ 2) has formula (3) expression formula：
Then formula (1) can be expressed as formula (4) expression formula：
In formula (4), njiThe logarithm service life for being sample i under jth stress level, μjFor the logarithm longevity under jth stress level
Order mean value, σjFor the logarithm life standard error under jth stress level；Meaning is identical when subscript j is changed to k；
There are one-to-one relationships between each service life sample point under different stress levels, are closed according to this correspondence
System, can be equivalent to sample information aggregation on another stress level, is realized the fatigue life on a certain stress level, in turn
It can be tested to obtain equivalent large sample by small sample, and service life estimation of distribution parameters is carried out according to equivalent big-sample data.
P-S-N curves are obtained for example, by the experiment of 4 grades of stress levels, several experiments are carried out on every grade of stress level
(to determine that FATIGUE LIFE DISTRIBUTION, conventional method require 15 or more).(every grade of stress level 3 compared with small sample amount
~5), intermediate value S-N linear equations are gone out according to test data fitting first, equation form is formula (5)：
S=Cnb (5)
In formula (5), s is stress amplitude, and n is fatigue life, and C, b are fitting constant.
For intermediate value S-N curves, even if can reach higher test accuracy if test data is less.In order to determine difference
S-N curves under survival rate, i.e. P-S-N families of curves also need to determine the fatigue life dispersibility under stress levels at different levels, that is, determine
Logarithm standard deviation-stress level relationship.A large number of experiments proves, linear between logarithm standard deviation σ and stress s, logarithm mark
The relationship of quasi- difference σ and stress s is represented by formula (6)：
σ(sj)=σ (s1)+K(sj-s1) (6)
In formula (6), σ (Sj) be j-th stage stress level under logarithm life standard error, K is straight slope；When a certain stress
Horizontal s1Under life standard error determine after, remaining stress level standard deviation can be determined by formula (6).With a certain stress level (example
Such as s1, usually high stress level) under FATIGUE LIFE DISTRIBUTION on the basis of, have the test life data under other stress levels
It is transformed into s1Under stress level, equivalent lifetime distribution is obtained, so that it is determined that life standard error-stress level relationship.The present invention's
Method can cover 10 by the selection of 4 grades of stress levels4~106P-S-N curve matchings between secondary cycle.
When verifying sample building up principle processing small sample test data method, verification test devises two kinds of experiment sides
Case：One kind is (15-x-x), and effective increment number of high stress level is 15 and is used to determine service life distributed constant, other two
Stress level respectively tests x parts sample (x=15,5 or 3)；Another kind is (x-x-x), i.e. three-level stress level test x part samples (x
=5 or 3).Wherein (15-15-15) methods of sampling is tradition method test method, remaining methods of sampling, including (15-5- in groups
5), (15-3-3), (5-5-5), (3-3-3) are the small sample methods of sampling.
Experiment has selected three stress levels, test data to be listed by actual tests sequence, as shown in table 1.
The method fatigue test lifetime data in groups of table 1
If two compared under low stress level respectively only have 5 (or 3) a data of fatigue life, i.e., in 200MPa and 300MPa
Under all only respectively preceding 5 (or 3) a test data, then constitute the data of fatigue life (table of small sample (15-5-5) scheme
Or the data of fatigue life (table 3) of small sample (15-3-3) scheme 2).If there was only 5 or 3 under each stress level
A lifetime data is then small sample (5-5-5) or the fatigue life data (table 4 and table 5) of (3-3-3) scheme.
2 small sample of table (15-5-5) scheme fatigue test lifetime data table
3 small sample of table (15-3-3) scheme fatigue test lifetime data table
4 small sample of table (5-5-5) scheme fatigue test lifetime data table
5 small sample of table (3-3-3) scheme fatigue test lifetime data table
The P-S-N curves for comparing the fitting of two kinds of methods of samplings, can obtain：
A. the method methods of sampling (45 samples) obtains the intermediate value S-N curves that each small sample methods of sampling obtains in groups with tradition
To intermediate value S-N curves essentially coincide.Curve matching precision is reduced with the reduction of sample size, but difference and little, intermediate value S-N
The relative error of the slope of curve is less than 1%, slope error and is less than 4%.
B. the P-S-N curves (p=90%, 99%) being fitted by each methods of sampling, with the increase of reliability p, each pumping
The difference that quadrat method obtains curve increases, and curve matching precision is also reduced with the reduction of sample size；As p=99%, P-S-N
The relative error of the slope of curve is less than 5%, intercept error and is less than 10%.
Experiment proves that method of the invention also maintains relatively high precision while greatly reducing experiment quantity, has
There is extensive popularizing application prospect.
Compared with prior art, it is bent to determine materials for aeroengines high cycle fatigue P-S-N for a kind of small sample of the invention measurement
Wire testing method has the advantages that：Method provided by the invention is to be based on sample building up principle, can be by testing on a small quantity
Data obtain FATIGUE LIFE DISTRIBUTION, and obtain more accurate P-S-N curves, Dependence Results can be directly used for evaluation titanium alloy,
The forging of high temperature alloy, the fatigue behaviour of ingot casting.
Specific embodiments of the present invention are described in detail above, but it is only used as example, the present invention is not intended to limit
In particular embodiments described above.To those skilled in the art, it is any to the invention carry out equivalent modifications and replace
In generation, is also all among scope of the invention.Therefore, without departing from the spirit and scope of the invention made by impartial conversion and repair
Change, all should be contained within the scope of the invention.
Claims (4)
1. materials for aeroengines high cycle fatigue P-S-N curve test methods are determined in a kind of small sample measurement, which is characterized in that packet
It includes：
Based on same sample, fatigue life identical probability distribution point in respective estimator of parent distribution meets under different stress levels
Formula (4) expression formula：
In formula (4), njiThe logarithm service life for being sample i under jth stress level, μjIt is equal for the logarithm service life under jth stress level
Value, σjFor the logarithm life standard error under jth stress level；Meaning is identical when subscript j is changed to k；
There are one-to-one relationship between each service life sample point under different stress levels, according to the correspondence of formula (4),
Fatigue life on a certain stress level is equivalent on another stress level, realizing sample information aggregation, and then by sample
This experiment obtains equivalent large sample, and carries out service life distributed constant statistics according to equivalent big-sample data.
2. the test of materials for aeroengines high cycle fatigue P-S-N curves is determined in a kind of small sample measurement according to claim 1
Method, which is characterized in that formula (4) is obtained by following steps：
Based on same sample, fatigue life identical probability distribution point in respective estimator of parent distribution meets under different stress levels
Formula (1) expression formula：
p(n'ji)=p (n'ki) (1)
In formula (1), j stress level parent service life NjLess than sample i service life n is obtained in the stress leveljiProbability (p (n'ji)=
P(N'j＜ n'ji), formula (2) and k stress level parent service life NkLess than same sample i n is obtained in k stress levelskiProbability phase
Together；
High-Cycle Fatigue Life Prediction obeys logarithm normal distribution, i.e. lgN~N (μ, σ 2) has formula (3) expression formula：
Then formula (1) is expressed as formula (4) expression formula：
In formula (4), njiThe logarithm service life for being sample i under jth stress level, μjIt is equal for the logarithm service life under jth stress level
Value, σjFor the logarithm life standard error under jth stress level；Meaning is identical when subscript j is changed to k.
3. the test of materials for aeroengines high cycle fatigue P-S-N curves is determined in a kind of small sample measurement according to claim 1
Method, which is characterized in that further include：It determines the fatigue life dispersibility under stress levels at different levels, that is, determines that logarithm standard deviation-is answered
The relationship of power horizontal relationship, logarithm standard deviation σ and stress s is expressed as formula (6)：
σ(sj)=σ (s1)+K(sj-s1) (6)
In formula (6), σ (Sj) be j-th stage stress level under logarithm life standard error, K is straight slope；When a certain stress level
s1Under life standard error determine after, remaining stress level standard deviation is determined by formula (6).
4. the test of materials for aeroengines high cycle fatigue P-S-N curves is determined in a kind of small sample measurement according to claim 1
Method, which is characterized in that further include：Compared with small sample amount, intermediate value S-N linear equations are fitted, equation form is
Formula (5)：
In formula (5), s is stress amplitude, and n is fatigue life, and C, b are fitting constant.
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| CN115186393A (en) * | 2022-08-16 | 2022-10-14 | 中国航发沈阳发动机研究所 | Low-sample-size C-P-S-N curve acquisition method for aeroengine structural part |
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Application publication date: 20180828 |