A method for determining the failure risk rate of a rotor disk in an aeroengine

Abstract

A method for determining the failure risk rate of a rotor disk in an aeroengine, comprising: assuming that the crack initiation cycle life N of the rotor disk i follows a lognormal distribution ln N i ~N(μ, σ 2 ), where μ is the mean of ln N i , and σ is the standard deviation of ln N i ; constructing the relationship between N i and the crack propagation cycle life N p : N p = kN i , where k is the proportionality coefficient between N i and N p ; constructing the relationship between N i and the crack initiation hour life H of the rotor disk i : H i β i = N i , where β i is the proportionality coefficient between N i and H i ; constructing the relationship between N p and the crack propagation hour life H of the rotor disk p : H p β p = N p , where β p is the proportionality coefficient between N p and H p ; constructing the relationship between β i and β p : β p = mβ i ; constructing the logarithmic relationship between the total hour service life H of the rotor disk and N i : #imgabs0# Calculate the probability p that H is less than the given total hour service life H0 of the rotor disk: #imgabs1##imgabs2#σ ln H = σ, where μ ln is the mean of lnH, and σ ln H is the standard deviation of lnH; calculate the failure risk rate of the rotor disk at H0 #imgabs3##imgabs4# where, #imgabs5# is the probability density function of ln H.

Description

Technical Field

[0001] This application belongs to the technical field of determining the failure risk rate of rotor disks in aeroengines, and particularly relates to a method for determining the failure risk rate of rotor disks in aeroengines. Background Art

[0002] The rotor disk in an aeroengine bears a large load. Once a fracture failure occurs, it will cause non-contained damage, and the consequences are catastrophic.

[0003] To ensure the safety of aeroengines, the rotor disk is managed as a life-limiting component, and when determining the service life of the rotor disk, the "worst" rotor disk is assumed as a premise. This results in a large number of actual rotor disks not having cracks and not experiencing fracture failures when reaching the service life, and still having a long available life. However, due to reasons such as cost, spare parts, and maintenance cycle, the service life of the rotor disk will be extended. Extending the service life of the rotor disk will inevitably increase the risk of fracture failure during use. How to quickly and accurately evaluate the failure risk rate of the rotor disk has become an urgent problem to be solved in engineering, but there is currently a lack of a reliable systematic method.

[0004] In view of the deficiencies of the prior art, this application is proposed.

[0005] It should be noted that the disclosure of the above background art content is only for assisting in understanding the inventive concept and technical solution of the present invention, and it does not necessarily belong to the prior art of this patent application. Without clear evidence indicating that the above content was publicly available on the filing date of this application, the above background art should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0006] The purpose of this application is to provide a method for determining the failure risk rate of rotor disks in aeroengines to overcome or mitigate at least one aspect of the known technical deficiencies.

[0007] The technical solution of this application is as follows:

[0008] A method for determining the failure risk rate of rotor disks in aeroengines includes:

[0009] Assume that the crack initiation cycle life N i of the rotor disk follows a lognormal distribution ln N i ~N(μ, σ 2 ), where p is the mean of ln N i and σ is the standard deviation of ln N i ;

[0010] Construct the relationship between N i and the crack propagation cycle life N p : Np = kN i , where k is the proportionality coefficient between N i and N p ;

[0011] Construct the relationship between N i and the crack initiation hourly life H of the rotor disk i : H i β i = N i , where β i is the proportionality coefficient between N i and H i ;

[0012] Construct the relationship between N p and the crack propagation hourly life H of the rotor disk p : H p β p = N p , where β p is the proportionality coefficient between N p and H p ;

[0013] Construct the relationship between β i and β p : β p = mβ i , where m is the conversion coefficient between β i and β p ;

[0014] Construct the logarithmic relationship between the total hourly service life H and N of the rotor disk i :

[0015] Calculate the probability p that H is less than the given total hourly service life H0 of the rotor disk: σ ln H = σ, where μ ln H is the mean of lnH, and σ ln H is the standard deviation of lnH;

[0016] Calculate the failure risk rate of the rotor disk at H0 where is the probability density function of ln H.

[0017] According to at least one embodiment of the present application, in the above method for determining the failure risk rate of the rotor disk in an aeroengine,

[0018] where

[0019] ln He is the estimated value of ln H, obtained by statistically analyzing n rotor disk fatigue tests;

[0020] e is the mean error between ln H e and ln H;

[0021] f e (e) is the probability density function of e.

[0022] is the estimated value of μ ln H , obtained by statistically analyzing n rotor disk fatigue tests.

[0023] According to at least one embodiment of the present application, in the method for determining the rotor disk failure risk rate in the above aeroengine,

[0024] According to at least one embodiment of the present application, in the method for determining the rotor disk failure risk rate in the above aeroengine,

[0025]

[0026]

[0027] Wherein,

[0028] A r is the safe service life of the rotor disk;

[0029] y is the divergence coefficient of the rotor disk life;

[0030] GeoMean(N i ) is the geometric mean of N i , obtained by statistically analyzing n rotor disk fatigue tests.

[0031] According to at least one embodiment of the present application, in the method for determining the rotor disk failure risk rate in the above aeroengine,

[0032] According to at least one embodiment of the present application, in the method for determining the rotor disk failure risk rate in the above aeroengine, k = 0.5, m = 2.5, σ = ln 6 / 6,

[0033] The present application has at least the following beneficial technical effects:

[0034] Provided is a method for determining the rotor disk failure risk rate in an aeroengine, which, based on the assumption that the crack initiation cycle life N of the rotor disk i obeys a lognormal distribution, constructs N i, the crack growth cycle life N p The relationship between: N p = kN i , N i , the rotor disk crack initiation hour life H i The relationship between: H i β i = N i , N p , the rotor disk crack growth hour life H p The relationship between: H p β p = N p , and constructing the relationship between βi and β p The relationship between: β p = mβi, and then constructing the logarithmic relationship between the total hour service life H and N of the rotor disk i The logarithmic relationship between: Thus, calculating the probability p that H is less than the total hour given service life H0 of the rotor disk: Calculating the failure risk rate of the rotor disk at H0 Provides a reliable systematic method for quickly and accurately evaluating the failure risk rate of the rotor disk. Brief Description of the Drawings

[0035] Figure 1 Is a schematic diagram of the method for determining the failure risk rate of the rotor disk in the aero-engine provided by the embodiment of the present application. Detailed Embodiment

[0036] To make the technical solutions and their advantages of the present application clearer, the technical solutions of the present application will be further clearly and completely described in detail below with reference to the drawings. It can be understood that the specific embodiments described herein are only partial embodiments of the present application, which are only used to explain the present application and are not intended to limit the present application. It should be noted that for the sake of description, only the parts related to the present application are shown in the drawings, and other related parts can refer to the usual design. Without conflict, the embodiments and the technical features in the embodiments of the present application can be combined with each other to obtain new embodiments.

[0037] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application shall have the ordinary meanings understood by those of ordinary skill in the art to which this application pertains. The words indicating directions such as "upper", "lower", "left", "right", "center", "vertical", "horizontal", "inner", "outer", etc. used in the description of this application are only used to indicate relative directions or positional relationships, rather than implying that the device or component must have a specific orientation, be constructed and operated in a specific orientation. When the absolute position of the object being described changes, its relative positional relationship may also change accordingly. Therefore, it should not be construed as a limitation to this application. The terms "first", "second", "third", and similar terms used in the description of this application are only for descriptive purposes to distinguish different components, and should not be construed as indicating or implying relative importance. The similar words such as "a", "an", or "the" used in the description of this application should not be construed as an absolute limitation on the quantity, but should be understood as having at least one. The similar words such as "including" or "comprising" used in the description of this application are intended to mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects.

[0038] In addition, it should be noted that, unless otherwise clearly specified and limited, the similar words such as "installed", "connected", "joined", etc. used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and can also be the communication inside two components. Those skilled in the art can understand its specific meaning in this application according to the specific situation.

[0039] The following further elaborates on this application with reference to the attached Figure 1 drawings.

[0040] Crack initiation cyclic life: Under cyclic loading, the life value when the first semi-circular crack with a fixed depth appears on the rotor disk, counted in reference cycles, denoted as N i ;

[0041] Crack propagation cyclic life: Under cyclic loading, the life value when the first semi-circular crack with a fixed depth on the rotor disk propagates to the unstable state, counted in reference cycles, denoted as N p ;

[0042] Total cyclic life: The sum of the crack initiation cyclic life and the crack propagation cyclic life, denoted as N t 。

[0043] Crack initiation life in hours: For a given flight mission profile, the number of flight hours when the first semi-circular crack with a fixed depth is generated on the rotor disk under cyclic loading, denoted as H i ;

[0044] Crack propagation life in hours: For a given flight mission profile, the number of hours when the first semi-circular crack with a fixed depth on the rotor disk under cyclic loading propagates to the unstable state, denoted as H p ;

[0045] Total service life in hours: For a given flight mission profile, the sum of the crack initiation life in hours and the crack propagation life in hours, denoted as H.

[0046] Assume that the crack initiation cycle life N i follows a lognormal distribution, that is, ln N i ~N(μ, σ 2 ), where μ and σ represent the mean and standard deviation of ln N i respectively;

[0047] Assume that there is an approximately constant relationship between the crack initiation cycle life N i and the crack propagation cycle life N p , that is, N p =kN i ;

[0048] Assume that during the crack initiation stage, the conversion rate between flight hours and the reference cycle number is β i , then: H i β i =N i ;

[0049] Assume that during the crack propagation stage, the conversion rate between flight hours and the reference cycle number is β p , then: H p β p =N p ;

[0050] And, assume that β p =mβ i ,

[0051] Obtain the relationship between the total service life in hours H and the crack initiation cycle life N i :

[0052]

[0053] It is easy to see that the total service life in hours H also follows a lognormal distribution, the mean of ln H is and the variance is

[0054] From the monotonicity of the logarithmic function and according to the definition of the failure rate, it can be known that the probability that the life is less than the given service life H0 in total hours is equal to the probability that the logarithm of the life is less than ln H0, that is, there is a failure probability. Then the failure risk rate of the rotor disk at H0 is:

[0055]

[0056] Among them,

[0057] represents the probability density function of ln H.

[0058] Since the true value of is generally unknown and needs to be estimated as follows:

[0059] Assume that according to the reference cyclic load spectrum, n low-cycle fatigue tests of rotor disks are carried out, and a set of crack initiation life values Ni(k) (k = 1, 2,..., n) are obtained. Then, according to (1), the estimated value of ln H can be obtained, and the mean error between it and the mean value of ln H is denoted as e. It is easy to prove that e follows a normal distribution, and its mean value is μ e = 0, and the variance is

[0060] Using the sample to estimate the population, the estimation of the position of the population distribution depends on the sample. Then the value of can be regarded as the difference caused by the different positions of the estimated value of H due to the sample error. The average value of the value and its error probability, that is:

[0061]

[0062] Among them,

[0063] f e (e) represents the probability density function of e and can be defined as:

[0064]

[0065] By the life divergence coefficient method, the safe service life A i(k) corresponding to a set of crack initiation life values N r (k = 1, 2,..., n) can be obtained, and its relationship with the geometric mean GeoMean(N i(k) ) is as follows:

[0066]

[0067] Among them,

[0068] y is the life divergence coefficient;

[0069] As defined by H: H = H i + H p ;

[0070] From the above H i , N i ; H p , N p ; β i , β p The relationship between them can be obtained as:

[0071]

[0072] From formulas (5) and (6), define the variable n Hcb :

[0073]

[0074] (It is easy to know that n Hcb is also a random variable subject to the lognormal distribution, and the mean of ln n Hcb is and the variance is

[0075] From the above definition, it is easy to know that:

[0076]

[0077] Furthermore, from formula (7), we can obtain:

[0078]

[0079] Furthermore, we get:

[0080]

[0081] (Combining formulas (2), (3), (4) and (10), and by convolution integral, we can get:

[0082]

[0083] Existing experience shows that k = 0.5, m = 2.5, σ = ln6 / 6, Then substituting into formula (11) we get:

[0084]

[0085] In a specific example, the designed service life of the rotor disk is 1600 hours, and the safety life A r obtained from 3 rotor disk fatigue tests is 4000 cycles, β i= 2.0, the failure risk rate for the design service life is 2.2239e-07 according to formula (12). If the service life is extended by 200 hours each time for a total of 5 times, the calculated values of the failure risk rate under the service life are shown in the following table. It can be seen from the table that as the number of times of extending the service life of the rotor disk increases, the failure risk rate of the rotor disk increases significantly:

[0086] Number of life extensions Service life Failure risk rate Initial 1600 2.2239e-07 The first life extension 1800 7.5397e-07 The second life extension 2000 2.0282e-06 The third life extension 2200 4.5672e-06 The fourth life extension 2400 8.9418e-06 The fifth life extension 2600 1.5649e-05

[0087] The various embodiments in the specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other.

[0088] So far, the technical solution of the present application has been described in conjunction with the preferred embodiments shown in the drawings. Those skilled in the art should understand that the protection scope of the present application is obviously not limited to these specific embodiments. Without departing from the principle of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the protection scope of the present application.

Claims

1. A method for determining the failure risk rate of a rotor disk in an aeroengine, characterized in that, including: Assume that the crack initiation cycle life N of the rotor disk i obeys the lognormal distribution lnN i ~N(μ,σ 2 ), where μ is the mean of lnN i and σ is the standard deviation of lnN i ; Construct N i and the crack propagation cycle life N p The relationship between them is: N p = kN i , where k is the proportionality coefficient between N i and N p ; Construct N i and the rotor disk crack initiation life in hours H i The relationship between them is: H i β i = N i where β i is the proportionality coefficient between N i and H i ; Construct N p and the rotor disk crack growth small-hour life H p The relationship between: H p β p = N p where β p is the proportionality coefficient between N p and H p ; Construct β i , β p The relationship between: β p = mβ i , where m is the conversion coefficient between β i , β p ; Construct the logarithmic relationship between the total hourly service life H and N of the rotor disk i between: Calculate the probability p that H is less than the given total service life H0 of the rotor disk in hours: σ ln H = σ, where μ ln H is the mean of ln H, and σ ln H is the standard deviation of ln H; Calculate the failure risk rate of the rotor disk under H0 where is the probability density function of ln H 2. The method for determining the failure risk rate of a rotor disk in an aeroengine according to claim 1, characterized in that, wherein, ln H e is the estimated value of ln H, obtained by statistically analyzing n rotor disk fatigue tests; e is the mean error between ln H e and ln H; f e (e) is the probability density function of e; is the estimated value of μ ln H obtained from the statistical results of n rotor disk fatigue tests.

3. The method for determining the failure risk rate of a rotor disk in an aeroengine according to claim 2, characterized in that, 4. The method for determining the failure risk rate of a rotor disk in an aeroengine according to claim 3, characterized in that, wherein, A r is the safe service life of the rotor disk; y is the divergence coefficient of the rotor disk life; GeoMean(N i ) is the geometric mean of N i , obtained by performing n rotor disk fatigue tests for statistics.

5. The method for determining the failure risk rate of a rotor disk in an aeroengine according to claim 4, characterized in that, 6. The method for determining the failure risk rate of a rotor disk in an aeroengine according to claim 5, characterized in that, k = 0.5, m = 2.5, σ = ln 6 / 6,

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