Gear structure strength reliability evaluation method under multiple failure modes

Abstract

The invention provides a method for evaluating the strength reliability of a gear structure in multiple failure modes, which belongs to the technical field of aircraft transmission system gear structure evaluation, and specifically comprises the following steps: establishing a finite element model of an aircraft transmission system gear structure, and obtaining a strength response parameter of the gear structure under the action of an input load; establishing a probability model of related parameters of the gear structure according to a probability statistics theory; establishing a performance function of the gear structure based on strength failure; according to the three failure modes of the gear structure, and in combination with the strength failure performance function, establishing a reliability performance function of the gear structure of the transmission system in each failure mode: obtaining a failure area of the gear structure in each failure mode; and establishing a strength reliability analysis model of the transmission system gear structure by adopting a subset simulation method, and performing reliability analysis on the transmission system gear structure to obtain the failure probability of the system. By means of the processing scheme, the calculation amount can be reduced to a large extent, and the calculation efficiency is improved.

Description

Technical Field

[0001] The present application relates to the field of gear structure assessment of aircraft transmission systems, and in particular to a method for assessing the strength reliability of gear structures under multiple failure modes. Background Art

[0002] Gears are key components in aircraft transmission systems. Failure of the gear structure in aircraft transmission systems will lead to failure of the transmission system, which may cause aircraft failure or even cause aircraft crashes and fatalities. In order to extend service life and improve flight safety, it is necessary to conduct strength reliability assessment of aircraft transmission system gear structures under multiple failure modes.

[0003] At present, the reliability assessment method for gear structures in aircraft transmission systems generally adopts a method combining theoretical analysis and calculation with Monte Carlo simulation. The strength of the gear structure is theoretically analyzed, and the failure probability is directly calculated by the Monte Carlo method to evaluate the reliability of the structure. This method has achieved good results for single failure modes of gear structures, but for gear structure failure problems under multiple failure modes, there are problems such as long calculation time, narrow scope of application, and difficulty in simulating the coupling effect of multiple failure modes. The reason is that the causes of gear structure failure are complex and changeable. Therefore, it is necessary to improve the traditional method of gear structure reliability assessment under multiple failure modes.

[0004] However, it should be pointed out that although the superiority of the Monte Carlo simulation method probability model is more obvious, its requirements for the amount of parameter statistical information are more stringent. For the gear structure of the transmission system, it is expensive and time-consuming to obtain the data information of the objective uncertainty factors of the structural parameters; due to the differences in materials and manufacturing processes, these data are difficult to use. In actual engineering problems, the information on the distribution density of structural parameter information is usually lacking, which cannot meet the requirements of the Monte Carlo simulation method for a large sample size. 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. Obviously, for small probability problems under multiple failure modes, the Monte Carlo simulation method seems powerless. Summary of the invention

[0005] In view of this, the present application provides a method for evaluating the strength reliability of gear structures under multiple failure modes, which solves the problems in the prior art, can greatly reduce the amount of calculation and improve calculation efficiency.

[0006] The present application provides a method for evaluating the reliability of gear structure strength under multiple failure modes using the following technical solutions:

[0007] A method for evaluating the strength reliability of gear structures under multiple failure modes, comprising:

[0008] Step 1, establishing a finite element model of the gear structure of the aircraft transmission system, and obtaining the strength response parameter S of the gear structure under the input load;

[0009] Step 2: According to probability statistics theory, a probability model of gear structure related parameters is established;

[0010] Step 3, establish the gear structure based on strength failure function g = [S] - S, where [S] is the allowable parameter of the material selected for the structure;

[0011] Step 4: According to the three failure modes of the gear structure and combined with the strength failure function function, the reliability function g(x) of the gear structure of the transmission system under each failure mode is established:

[0012] Step 5, obtaining the failure area of ​​each failure mode of the gear structure;

[0013] Step 6: Use the subset simulation method to establish a strength reliability analysis model for the transmission system gear structure, and perform reliability analysis on the transmission system gear structure to obtain the failure probability of the system.

[0014] Optionally, in step 2, the gear structure related parameters include the input load T, thickness h, tooth width b, relative roughness f and elastic modulus E of the gear structure;

[0015] The joint probability density function of input load T, thickness h, tooth width b, relative roughness f and elastic modulus E is f(T, h, b, f, E); where the input load T is an interval variable, T∈[T0, T1].

[0016] Optionally, the function function of the gear structure based on strength failure in step 3 includes both random variables (x1, x2, x3, x4) and interval variables (y1), then the function function of the gear structure based on strength failure is:

[0017] g=[S]-g(x,y)

[0018] =[S]-g(x1,x2,x3,x4,y1);

[0019] Among them, x1 is the thickness h of the gear structure, x2 is the tooth width b of the gear structure, x3 is the relative roughness f of the gear structure, x4 is the elastic modulus E of the gear structure, and y1 is the input load T of the gear structure.

[0020] Optionally, in step 4, the reliability function functions of the gear structure of the transmission system under the three failure modes are:

[0021] The reliability function under the strength failure caused by principal stress is g (σ) (x) = [σ] - σ(x);

[0022] The reliability function under strain-induced strength failure is g (ε) (x) = [ε] - ε(x);

[0023] The reliability function under the strength failure caused by shear stress is g (τ) (x) = [τ] - τ(x).

[0024] Optionally, in step 5:

[0025] The failure areas of the three failure modes are:

[0026] Failure region F under strength failure caused by principal stress (σ) ={(x,y):F=[σ]-g σ (x1,x2,x3,x4,y1)<0};

[0027] Failure region F under strain-induced strength failure (ε) ={(x,y):F=[ε]-g ε (x1,x2,x3,x4,y1)<0};

[0028] Failure region F under shear stress-induced strength failure (τ) ={(x,y):F=[τ]-g τ (x1,x2,x3,x4,y1)<0}.

[0029] Optionally, step 6 specifically includes:

[0030] Obtain the total failure domain of the transmission system gear structure. The total failure domain F of the transmission system gear structure is the sum of the failure areas under the three modes: F = F (σ) ∪F (ε) ∪F (τ) ;

[0031] For failure domain F, introduce b1>b2>…>b m =0 a series of critical values ​​b1, b2, ..., b m , the failure event F with nested relationship is formed by the introduced critical value k ={(x,y):g(x,y)≤b k}(k=1,2,…,m);

[0032] and According to the multiplication theorem and the inclusion relationship of events, the failure probability calculation formula can be obtained as follows:

[0033]

[0034] Let P1 = P{P1}, P k =P{F k |F (k-1)}(k=2,3,…,m);

[0035] Finally, the failure probability of the gear structure of the transmission system is obtained

[0036] In summary, this application includes the following beneficial technical effects:

[0037] Aiming at the situation that there is a lack of information on the distribution density of gear structure parameters in aircraft transmission systems and multiple failure modes of gear structures coexist, a reliability analysis model based on finite element method and subset simulation method is proposed. The model shows better engineering applicability in dealing with problems such as insufficient statistics of gear structure parameters, multiple failure modes of structures and time-consuming calculations, especially when some parameter information is scarce and the parameter probability density function cannot be accurately obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] 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.

[0039] Figure 1 This is a flow chart of the gear structure strength reliability assessment method under multiple failure modes in this application. DETAILED DESCRIPTION

[0040] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0041] 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.

[0042] 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.

[0043] 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.

[0044] 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.

[0045] An embodiment of the present application provides a method for evaluating the strength reliability of a gear structure under multiple failure modes.

[0046] like Figure 1 As shown, a method for evaluating the strength reliability of gear structures under multiple failure modes includes the following steps:

[0047] The finite element model of the gear structure of the aircraft transmission system was established using finite element software, and the strength response parameters S of the gear structure under the input load were obtained: maximum principal stress σ, maximum elongation strain ε and maximum shear stress τ.

[0048] According to the probability statistics theory, the probability model of gear structure related parameters is established. The gear structure strength response parameters are the function of the input load T, thickness h, tooth width b, relative roughness f and elastic modulus E of the gear structure. The joint probability density function of the five parameters is f(T, h, b, f, E); the load T is an interval variable, T∈[T0, T1].

[0049] Establish the function of strength-based failure of gear structure:

[0050] g = [S] - S (1);

[0051] Where [S] is the allowable parameter of the material selected for the structure;

[0052] S=f(σ,ε,τ) (2).

[0053] There are three failure modes of gear structure: 1) Failure of the structure due to the maximum principal stress σ being greater than the allowable stress of the material; 2) Failure of the structure due to the maximum elongation strain ε being greater than the allowable strain of the material; 3) Failure of the structure due to the maximum shear stress τ being greater than the allowable shear stress of the material.

[0054] According to the three failure modes of gear structure combined with the strength failure function function, the reliability function function g(x) of the gear structure of the transmission system is established respectively: the reliability function function under the strength failure caused by the principal stress is g (σ) (x) = [σ] - σ(x), the reliability function under strain-induced strength failure is g (ε) (x) = [ε] - ε(x), the reliability function under the strength failure caused by shear stress is g (τ) (x) = [τ] - τ(x).

[0055] The strength reliability analysis model of the transmission system gear structure is established by using the subset simulation method. The reliability analysis of the transmission system gear structure is performed to obtain the failure probability of the system.

[0056] The embodiment of the present application is described by taking the gear of a certain aircraft transmission system as an example, and a finite element model of the gear structure is established using finite element software.

[0057] During the model processing, geometric parameters that have no effect on structural strength and stiffness, such as holes, chamfers, and small-sized grooves in non-critical areas designed to meet assembly, sealing, production and other requirements are deleted. In addition, the complex shapes of some non-critical areas are also modified.

[0058] For complex parts, high-quality tetrahedral meshes are used for meshing. The size of non-critical parts is selected between 3 and 5 mm according to the meshing requirements. The mesh size of critical parts is selected as 2 mm after multiple trials from large to small. The selection standard is that the reduction of mesh size no longer affects or minimally affects the stress results of critical parts.

[0059] The strength response parameters of the gear structure can be obtained through finite element analysis.

[0060] The gear structure strength response parameters are functions of the gear structure's input load T, thickness h, tooth width b, relative roughness f, and elastic modulus E. Gear thickness h, tooth width b, relative roughness f, and elastic modulus E are random variables, and load T is an interval variable.

[0061] In this embodiment, the gear structure is made of structural steel 30CrMnSiA, and the gear material and structure-related parameters are shown in Tables 1 and 2.

[0062] Table 1 Probability distribution and numerical characteristics of random variables

[0063]

[0064] Table 2 Related parameters of interval variables

[0065]

[0066] For equation (1), which contains both random variables (x1, x2, x3, x4) and interval variables (y1), it can be rewritten as:

[0067] g=[S]-g(x,y)

[0068] =[S]-g(x1,x2,x3,x4,y1) (3);

[0069] The failure region F of the gear structure can be expressed as formula (4);

[0070] F={(x,y):F=[S]-g(x1,x2,x3,x4,y1)<0} (4);

[0071] Among them, x = (x1, x2, x3, x4) is a random vector, y = (y1) is a one-dimensional interval variable, y 1 and are the upper and lower bounds of the interval variable, and the joint probability density function is f (x,y) (x,y).

[0072] There are three failure modes of the transmission system gear structure: 1) Failure of the structure due to the maximum principal stress σ being greater than the allowable stress of the material; 2) Failure of the structure due to the maximum elongation strain ε being greater than the allowable strain of the material; 3) Failure of the structure due to the maximum shear stress τ being greater than the allowable shear stress of the material. According to the working strength design criteria of the transmission system gear structure, the transmission system gear structure function function g is established using the principal stress, strain and shear stress. (σ) , g (ε) and g (τ) , the specific forms are shown in formula (5), formula (6) and formula (7) respectively;

[0073] Principal stress: g (σ) (x,y)=[σ]-σ(x1,x2,x3,x4,y1) (5);

[0074] Strain: g (ε) (x,y)=[ε]-ε(x1,x2,x3,x4,y1) (6);

[0075] Shear stress: g (τ)(x,y)=[τ]-τ(x1,x2,x3,x4,y1) (7).

[0076] Function g (σ) , g (ε) and g (τ) The failure domains are F (σ) 、F (ε) and F (τ) , as shown in equations (8), (9) and (10);

[0077] F (σ) ={(x,y):F=[σ]-g σ (x1,x2,x3,x4,y1)<0} (8);

[0079] F (ε) ={(x,y):F=[ε]-g ε (x1,x2,x3,x4,y1)<0} (9);

[0081] F (τ) ={(x,y):F=[τ]-g τ (x1,x2,x3,x4,y1)<0}

[0082] (10).

[0083] Assume that the failure probabilities of principal stress, strain and shear stress of the gear structure of the transmission system are P f(σ) , P f(ε) and P f(τ) , and the solution formulas are shown in (11), (12) and (13) respectively;

[0084]

[0085] It can be seen from equations (8), (9) and (10) that the intersection of the failure domains of the principal stress, strain and shear stress strength of the transmission system gear structure is an empty set. Therefore, the total failure domain F of the transmission system gear structure is the sum of the three and satisfies equation (14);

[0086] F=F (σ) ∪F (ε) ∪F (τ) (14).

[0087] Therefore, the failure probability P of the gear structure strength failure in the transmission system is f It can be expressed as (15);

[0088]

[0089]

[0090] It can be seen from formula (15) that by obtaining the failure probability of the principal stress, strain and shear stress of the gear structure of the transmission system, the functional reliability of the gear structure under strength failure of the transmission system can be obtained.

[0091] The subset simulation method converts small failure probabilities into the product of a series of larger conditional probabilities by introducing reasonable intermediate failure events. Its basic steps are to start from the joint probability density function of the basic variables, gradually construct the sampling density function on each subset, and then obtain the sampling density function of the required limit state equation, and finally obtain the estimated value of the failure probability.

[0092] For the failure domain F shown in equation (4), we can introduce b1>b2>...>b m =0 a series of critical values ​​b1, b2, ..., b m The introduced critical values ​​can constitute failure events with nested relationships, as shown in formula (16).

[0093] F k ={(x,y):g(x,y)≤b k}(k=1,2,…,m) (16)

[0094] At this time there is And there are According to the multiplication theorem and the inclusion relationship of events, the failure probability calculation formula can be obtained as follows:

[0095]

[0096] Let P1 = P{F1}, P k =P{F k |F (k-1)}(k=2,3,…,m), the above formula can be rewritten as:

[0097]

[0098] Obviously, from the above derivation process, it can be seen that the reliability analysis of the subset simulation method is to convert small probabilities into the product of larger conditional probabilities, thereby improving the efficiency of digital simulation calculations.

[0099] Substituting the principal stress, strain and shear stress values ​​calculated by finite element analysis into equations (11), (12) and (13), respectively, the functional functions of the gear structure of the transmission system under different failure modes can be obtained. The functional reliability is then calculated using the subset simulation method and the Monte Carlo method. The estimated value of the Monte Carlo method is taken as the accurate value, and the relative error of the estimated value of the failure probability of the subset simulation method under strength failure is calculated. The calculation parameters and results are shown in Table 3.

[0100] Table 3 Reliability analysis results of transmission system gear structure strength failure

[0101]

[0102] It can be seen that the estimated value of the Monte Carlo method is an accurate value, and the relative error of the estimated value of the failure probability of the transmission system gear structure strength fault solved by the subset simulation method is 4.44%. The subset simulation method can not only meet the calculation accuracy requirements, but also the sample size required by the subset simulation method is only 20% of that of the Monte Carlo method. According to the above analysis results, the functional reliability calculation results based on the subset simulation method in Table 3 are substituted into formula (15) to obtain the subset simulation method in the sampling of 2×10 4 The following calculation shows that the failure probability of the transmission system gear structure failure is 0.002773.

[0103] This shows that the subset simulation method can greatly reduce the amount of calculation and improve the calculation efficiency, which has great advantages in the practical engineering application of transmission system gear structure.

[0104] 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 method for evaluating the strength reliability of gear structures under multiple failure modes, characterized in that: include: Step 1, establishing a finite element model of the gear structure of the aircraft transmission system, and obtaining the strength response parameter S of the gear structure under the input load; Step 2: According to probability statistics theory, a probability model of gear structure related parameters is established; Step 3, establish the gear structure based on strength failure function g = [S] - S, where [S] is the allowable parameter of the material selected for the structure; Step 4: According to the three failure modes of the gear structure and combined with the strength failure function function, the reliability function g(x) of the gear structure of the transmission system under each failure mode is established: Step 5, obtaining the failure area of ​​each failure mode of the gear structure; Step 6: Use the subset simulation method to establish a strength reliability analysis model for the transmission system gear structure, and perform reliability analysis on the transmission system gear structure to obtain the failure probability of the system.

2. The gear structure strength reliability assessment method under multiple failure modes according to claim 1 is characterized in that: In step 2, the gear structure related parameters include the input load T, thickness h, tooth width b, relative roughness f and elastic modulus E of the gear structure; The joint probability density function of input load T, thickness h, tooth width b, relative roughness f and elastic modulus E is f(T, h, b, f, E); where the input load T is an interval variable, T∈[T0, T1].

3. The gear structure strength reliability assessment method under multiple failure modes according to claim 2 is characterized in that: In step 3, the function function of the gear structure based on strength failure includes both random variables (x1, x2, x3, x4) and interval variables (y1), so the function function of the gear structure based on strength failure is: g=[S]-g(x,y)=[S]-g(x1,x2,x3,x4,y1); Among them, x1 is the thickness h of the gear structure, x2 is the tooth width b of the gear structure, x3 is the relative roughness f of the gear structure, x4 is the elastic modulus E of the gear structure, and y1 is the input load T of the gear structure.

4. The method for evaluating the strength reliability of gear structure under multiple failure modes according to claim 3 is characterized in that: In step 4, the reliability function functions of the gear structure of the transmission system under the three failure modes are: The reliability function under the strength failure caused by principal stress is g (σ) (x) = [σ] - σ(x); The reliability function under strain-induced strength failure is g (ε) (x) = [ε] - ε(x); The reliability function under the strength failure caused by shear stress is g (τ) (x) = [τ] - τ(x).

5. The method for evaluating the reliability of gear structure strength under multiple failure modes according to claim 4 is characterized in that: In step 5: The failure areas of the three failure modes are: Failure region F under strength failure caused by principal stress (σ) ={(x,y):F=[σ]-g σ (x1,x2,x3,x4,y1)<0}; Failure region f under strain-induced strength failure (ε) ={(x,y):F=[ε]-g ε (x1,x2,x3,x4,y1)<0}; Failure region F under shear stress-induced strength failure (τ) ={(x,y):F=[τ]-g τ (x1,x2,x3,x4,y1)<0}.

6. The gear structure strength reliability assessment method under multiple failure modes according to claim 5 is characterized in that: The step 6 specifically includes: Obtain the total failure domain of the transmission system gear structure. The total failure domain F of the transmission system gear structure is the sum of the failure areas under the three modes: F = F (σ) ∪F (ε) ∪F (τ) ; For failure domain F, introduce b1>b2>…>b m =0 a series of critical values ​​b1, b2, ..., b m , the failure event F with nested relationship is formed by the introduced critical value k ={(x,y):g(x,y)≤b k }(k=1,2,…,m); and According to the multiplication theorem and the inclusion relationship of events, the failure probability calculation formula can be obtained as follows: Let p1 = p{F1}, p k =p{F k |F (k-1) }(k=2,3,…,m); finally the failure probability of the gear structure of the transmission system is obtained

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