Bush structure reliability evaluation method

Abstract

The invention provides a bush structure reliability evaluation method, and belongs to the technical field of aircraft transmission system bush structures, and the method specifically comprises the steps: building a finite element model of the aircraft transmission system bush structure, and obtaining the maximum contact stress sigma r and the maximum structural pressure stress sigma p of the bush structure; establishing a lining failure-based performance function Z of the lining structure; a failure region Df of the bushing structure; a sample pi is extracted from the interval variable p through a Latin sampling method, a performance function under the sample pi is obtained, then a random variable is extracted through an important sampling method, the performance function Zij is calculated, and Zijlt is counted; calculating the failure probability of the lining structure according to the failure probability # imgabs0 # corresponding to pi by recording the number of pi, 0 as IMi. Through the processing scheme of the invention, the accuracy of the reliability evaluation result of the bushing structure is improved.

Description

Technical Field

[0001] The present application relates to the field of bushing structures of traveler transmission systems, and in particular to a bushing structure reliability assessment method. Background Art

[0002] The bushing structure is a key component in the aircraft transmission system. In general, the bushing is a type of component that protects the system equipment. The use of the bushing can reduce the wear, vibration and noise of the transmission system and has an anti-corrosion effect. In order to extend the service life of the transmission system and improve flight safety, it is necessary to conduct a structural reliability assessment of the bushing structure of the aircraft transmission system.

[0003] For the bushing structure of the transmission system, on the one hand, it is expensive and time-consuming to obtain data information on the objective uncertainty factors of the structural parameters. The development process of our country's models is short and the tests are relatively few. On the other hand, although relevant foreign literature can provide some reference data, due to the differences in materials and manufacturing processes, these data are difficult to use, which limits the application of traditional methods in bushing performance evaluation. In actual engineering problems, information on the distribution density of uncertain variables is usually lacking. Once the probability distribution assumption of the parameters does not match the actual situation, the use of random models for structural reliability analysis itself loses its meaning. Summary of the invention

[0004] In view of this, the present application provides a bushing structure reliability assessment method, which solves the problems in the prior art and improves the accuracy of bushing structure reliability assessment results.

[0005] A bushing structure reliability assessment method provided in this application adopts the following technical solution:

[0006] A bushing structure reliability assessment method, comprising:

[0007] Step 1: Establish a finite element model of the bushing structure of the aircraft transmission system and obtain the maximum contact stress σ of the bushing structure r and the maximum compressive stress of the structure σ p ;

[0008] Step 2, establishing a functional function Z of the bushing structure based on bushing failure;

[0009] Step 3, Failure area D of bushing structure f ;

[0010] Step 4: First, use the Latin sampling method to extract sample p from the interval variable p i (i=1,2,…,N), get sample p i The performance function under the condition is then used to extract random variables through the importance sampling method to calculate the performance function Z ij (j=1,2,…,Mi ), statistics Z ij <0, denoted as IM i , then p i The corresponding failure probability Calculate the failure probability of the bushing structure.

[0011] Optionally, in step 1, the maximum contact stress σ of the bushing structure r and the maximum compressive stress σ p It is a function of the bushing inner diameter d, bushing elastic modulus E, bushing thickness h, and pressure p; the bushing inner diameter d, elastic modulus E, and bushing thickness h are random variables, and the pressure p is an interval variable.

[0012] Optionally, in step 2, the bushing structure is based on the function function of bushing failure Z=[σ]-σ=[σ]-σ(d, E, h, p);

[0013] With (x1, x2, x3) as random variables and (y1) as interval variables, the function function of the sleeve structure based on the sleeve failure is Z = Z(x, y) = Z(x1, x2, x3, y1) = [v] - σ(x1, x2, x3, y1), where x1 corresponds to the elastic modulus E of the sleeve, x2 corresponds to the inner diameter d of the sleeve, x3 corresponds to the thickness h of the sleeve, and y1 corresponds to the pressure p;

[0014] Among them, [σ] is the allowable stress of the material selected for the structure. When the function function Z is greater than 0, the bushing structure is in a safe state; when the function function Z is equal to 0, the bushing structure is in a critical state; when the function function Z is less than 0, the bushing structure is in a failure state.

[0015] Optionally, in step 3, the failure area D of the bushing structure f ={(x,y):Z=[σ]-σ(x1,x2,x3,y1)<0}, where x=(x1,x2,x3) is a random vector and the joint probability density function is f x (x), y = (y1) is a one-dimensional interval variable, and y 1 are the upper and lower bounds of the interval variable.

[0016] Optionally, step 4 specifically includes:

[0017] Use Latin sampling method to select from the interval Draw samples (y 1i )(i=1,2,…,N), sample(y 1i )(i=1,2,…,N) is the functional function of Z i (x,y 1i )=Z i (x1,x2,x3,y 1i)(i=1,2,…,N);

[0018] Z i (x,y 1i ) corresponds to the failure area D f (i) = {(x,y 1i ):Z i (x1,x2,x3,y 1i )<0};

[0019] For each given sample (y 1i )(i=1,2,…,N), performance function Z i (x,y 1i )=0 is transformed into a probability model containing only random variables, and the random variables d are extracted by the importance sampling method. ij 、E ij ,δ ij (j=1,2,…,M i ), for a given (y 1i )(i=1,2,…,N) and the performance function Z i (x,y 1i )=0, introducing the important sampling function h x (x) for failure probability P f (i) making estimates;

[0020] Estimation of bushing structure failure probability based on importance sampling method for:

[0021]

[0022] Among them, x j The importance sampling function h x (x) The jth sample drawn, I i (x j ) is the indicator function, which satisfies the following functional relationship:

[0023]

[0024] Importance sampling function h x (x) is of the form:

[0025]

[0026] Among them, μ k , τ k are the kth (k=1,2,3) variables x k The mean and standard deviation of

[0027] For (j=1,2,…,N), we get an array of failure probabilities The failure probability of the bushing structure is

[0028] Optionally, in step 1 of 6, a finite element model of the bushing structure of the aircraft transmission system is established using finite element software.

[0029] In summary, this application includes the following beneficial technical effects:

[0030] At present, with the application and development of finite element simulation analysis technology, finite element strength analysis has been widely used in the research and development of aircraft structures. The failure process of the bushing structure is simulated by finite element simulation, and the failure probability is calculated by digital simulation method to evaluate the reliability of the bushing structure. Therefore, the reliability design method using digital simulation method as the theoretical basis in the design and reliability analysis of the structure is more reasonable than the conventional method. In view of the lack of information on some parameters of the aircraft bushing structure, a random-non-probabilistic mixed measurement model is proposed. This model shows better applicability in dealing with the multi-source of unknown parameters of complex structures (random uncertainty, non-probabilistic uncertainty), especially when some parameter information is poor and the parameter probability density function cannot be accurately obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0032] Figure 1 This is a flow chart of the importance sampling method in the embodiment of this application. DETAILED DESCRIPTION

[0033] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0034] The following describes the implementation methods of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.

[0035] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present application, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0036] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application. The illustrations only show the components related to the present application rather than being drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed at will, and the component layout may also be more complicated.

[0037] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0038] An embodiment of the present application provides a bushing structure reliability assessment method.

[0039] A bushing structure reliability assessment method, comprising:

[0040] Step 1: Establish a finite element model of the bushing structure of the aircraft transmission system and obtain the maximum contact stress σ of the bushing structure r and the maximum compressive stress of the structure σ p ; Maximum contact stress of bushing structureσ r and the maximum compressive stress σ p It is a function of the bushing inner diameter d, bushing elastic modulus E, bushing thickness h, and pressure p; the bushing inner diameter d, elastic modulus E, and bushing thickness h are random variables, and the pressure p is an interval variable.

[0041] Step 2, establishing a functional function Z of the bushing structure based on bushing failure;

[0042] Z=[σ]-σ=[σ]-σ(d,E,h,p) (1);

[0043] Wherein, [σ] is the allowable stress of the selected material of the structure. When the function function Z is greater than 0, the bushing structure is in a safe state. When the function function Z is equal to 0, the bushing structure is in a critical state. When the function function Z is less than 0, the bushing structure is in a failure state, as specifically expressed in formula (2);

[0044]

[0045] Step 3, Failure area D of bushing structure f .

[0046] Step 4: First, use the Latin sampling method to extract sample p from the interval variable p i (i=1,2,…,N), sample p i The function under this is Z i =[σ]-σ(d,E,δ,p i ), and then extract the random variable d by the importance sampling method ij 、E ij ,δ ij (j=1,2,…,M i ), calculate the performance function Z ij . Statistics Z ij <0, denoted as IM i , then p i The corresponding failure probability Calculate the failure probability of the bushing structure

[0047] The embodiment of the present application uses a bushing structure of a certain aircraft transmission system to explain the evaluation method of the present application in detail.

[0048] During the model processing, the geometric parameters that have no effect on the strength and stiffness of the structure, such as holes, chamfers, and small-sized slots in non-critical areas designed to meet the needs of assembly, sealing, and production, are deleted. The meshing of different structures is different in fineness, and eight-node hexahedral mesh units are selected as the main unit. For complex parts, high-quality tetrahedral meshes are used as auxiliary units for meshing; the size of non-critical parts is selected between 1 and 4 mm according to the requirements of hexahedral meshing, and the mesh size of critical parts is selected after multiple trials from large to small. 0.5 mm is selected, and the selection standard is that the reduction of mesh size no longer affects or minimally affects the stress results of critical parts. .

[0049] The maximum contact stress and maximum compressive stress of the bushing structure can be obtained through finite element analysis.

[0050] In this example, the bushing structure is made of aluminum bronze QAl7, and the maximum stress σ of the structure is a function of the bushing inner diameter d, elastic modulus E, bushing thickness h, and pressure p. The bushing inner diameter d, elastic modulus E, and bushing thickness h are random variables, and the pressure p is an interval variable.

[0051] In the model, the relevant parameters of the bushing structure are shown in Tables 1, 2, and 3.

[0052] Table 1 Related parameters of random variables

[0053]

[0054] Table 2 Related parameters of interval variables

[0055]

[0056] Table 3 Determination parameters [σ]

[0057]

[0058] Maximum contact stress of bushing structureσ r Greater than the allowable contact stress [σ r ], the contact surface of the bushing structure will be worn, and the structure does not meet the strength safety requirements; the maximum compressive stress of the bushing structure σ p Greater than the allowable compressive stress of the selected structural material [σ p ], the structure will produce mechanical damage such as plastic deformation and fracture, and the structure does not meet the strength safety requirements; therefore, the functional function of the bushing structure based on wear failure and strength failure is established according to the working conditions of the bushing structure.

[0059] For the bushing structure based on the bushing failure function Z, which contains both random variables (x1, x2, x3) and interval variables (y1), it can be rewritten as:

[0060] Z=Z(x,y)=Z(x1,x2,x3,y1)=[σ]-σ(x1,x2,x3,y1) (3);

[0061] Failure area D of bushing structure f It can be expressed as formula (4):

[0062] D f ={(x,y):Z=[σ]-σ(x1,x2,x3,y1)<0} (4);

[0063] Among them, x = (x1, x2, x3) is a random vector, and the joint probability density function is f x (x), y = (y1) is a one-dimensional interval variable, and y 1 are the upper and lower bounds of the interval variable.

[0064] Use Latin sampling method to select from the interval Draw samples (y 1i )(i=1,2,…,N), substitute into the function, and get the sample (y 1i )(i=1,2,…,N) is the functional function of Z i (x,y 1i )=Z i(x1,x2,x3,y 1i )(i=1,2,…,N), which is Z j (x,y 1j )=Z j (x1,x2,x3,y 1j )(j=1,2,…,N).

[0065] Z i (x,y 1i ) corresponds to the failure area D f (i) Calculated by formula (5):

[0066] Z i (x,y 1i ) corresponds to the failure area D f (i) = {(x,y 1i ):Z i (x1,x2,x3,y 1i )<0} (5).

[0067] For each given sample (y 1i )(i=1,2,…,N), performance function Z i (x,y 1i )=0 is transformed into a probability model containing only random variables, and the numerical simulation method is used to obtain (y 1i )(i=1,2,…,N) corresponding to the failure probability For (i=1,2,…,N), we can get an array of failure probabilities: Then the robust reliability index of the structure, that is, the failure probability

[0068] Among them, Figure 1 As shown, for each given sample (y 1i )(i=1,2,…,N), performance function Z i (x,y 1i The specific process of converting )=0 into a probability model containing only random variables is:

[0069] For a given (y 1i )(i=1,2,…,N) and the performance function Z i (x,y 1i )=0, introducing the important sampling function h x (x) for failure probability P f (i) Estimation: The failure probability P f (i) can be written as formula (6):

[0070]

[0071] Estimation of bushing structure failure probability based on importance sampling method It can be written as formula (7):

[0072]

[0073] Among them, x j The joint probability density function h x (x) The jth sample extracted. i (x j ) is the indicator function, which satisfies the following functional relationship:

[0074]

[0075] Importance sampling function h x (x) is in the form of formula (8):

[0076]

[0077] Among them, μ k , τ k are the kth (k=1,2,3) variables x k The mean and standard deviation of .

[0078] Substituting the maximum contact stress and maximum compressive stress of the finite element analysis results into equations (1) and (2), the functional function of the bushing structure failure can be obtained. The reliability of the bushing structure is then calculated using the importance sampling method and the Latin sampling method. The calculation results are shown in Table 4.

[0079] Table 4 Reliability analysis results of bushing

[0080]

[0081] Finally, the interval of the failure probability of the bushing structure is [0.000129, 0.000362], and the length of the interval is 0.000233, so the robust reliability index of the bushing structure is 0.000362.

[0082] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A bushing structure reliability assessment method, characterized in that: include: Step 1: Establish a finite element model of the bushing structure of the aircraft transmission system and obtain the maximum contact stress σ of the bushing structure r and the maximum compressive stress of the structure σ p ; Step 2, establishing a functional function Z of the bushing structure based on bushing failure; Step 3, Failure area D of bushing structure f ; Step 4: First, use the Latin sampling method to extract sample p from the interval variable p i (i=1,2,…,N), get sample p i The performance function under the condition is then used to extract random variables through the importance sampling method to calculate the performance function Z ij (j=1,2,…,M i ), statistics Z ij <0, denoted as IM i , then p i The corresponding failure probability Calculate the failure probability of the bushing structure.

2. The bushing structure reliability assessment method according to claim 1, characterized in that: In step 1, the maximum contact stress σ of the bushing structure r and the maximum compressive stress σ p It is a function of the bushing inner diameter d, bushing elastic modulus E, bushing thickness h, and pressure p; the bushing inner diameter d, elastic modulus E, and bushing thickness h are random variables, and the pressure p is an interval variable.

3. The bushing structure reliability assessment method according to claim 2, characterized in that: In step 2, the bushing structure is based on the function function of bushing failure Z = [σ] - σ = [σ] - σ (d, E, h, p); With (x1, x2, x3) as random variables and (y1) as interval variables, the function function of the sleeve structure based on the sleeve failure is Z = Z(x, y) = Z(x1, x2, x3, y1) = [σ] - σ(x1, x2, x3, y1), where x1 corresponds to the elastic modulus E of the sleeve, x2 corresponds to the inner diameter d of the sleeve, x3 corresponds to the thickness h of the sleeve, and y1 corresponds to the pressure p; Among them, [σ] is the allowable stress of the material selected for the structure. When the function function Z is greater than 0, the bushing structure is in a safe state; when the function function Z is equal to 0, the bushing structure is in a critical state; when the function function Z is less than 0, the bushing structure is in a failure state.

4. The bushing structure reliability assessment method according to claim 3, characterized in that: In step 3, the failure area D of the bushing structure f ={(x,y):Z=[σ]-σ(x1,x2,x3,y1)<0}, where x=(x1,x2,x3) is a random vector and the joint probability density function is f x (x), x = (y1) is a one-dimensional interval variable, and y 1 are the upper and lower bounds of the interval variable.

5. The bushing structure reliability assessment method according to claim 4, characterized in that: The step 4 specifically includes: Use Latin sampling method to select from the interval Draw samples (y 1i )(i=1,2,…,N), sample(y 1i )(i=1,2,…,N) is the functional function of Z i (x,y 1i )=Z i (x1,x2,x3,y 1i )(i=1,2,…,N); Z i (x,y 1i ) corresponds to the failure area D f (i) = {(x,y 1i ):Z i (x1,x2,x3,y 1i )<0}; For each given sample (y 1i )(i=1,2,…,N), performance function Z i (x,y 1i )=0 is transformed into a probability model containing only random variables, and the random variables d are extracted by the importance sampling method. ij 、E ij ,δ ij (j=1,2,…,M i ), for a given (y 1i )(i=1,2,…,N) and the performance function Z i (x,y 1i )=0, introducing the important sampling function h x (x) for failure probability P f (i) making estimates; Estimation of bushing structure failure probability based on importance sampling method for: Among them, x j The importance sampling function h x (x) The jth sample drawn, I i (x j ) is the indicator function, which satisfies the following functional relationship: Importance sampling function h x (x) is of the form: Among them, μ k , τ k are the kth (k=1,2,3) variables x k The mean and standard deviation of For (j=1,2,…,N), we get an array of failure probabilities The failure probability of the bushing structure is 6. The bushing structure reliability assessment method according to claim 3, characterized in that: In the step 1, a finite element model of the bushing structure of the aircraft transmission system is established using finite element software.

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