A disc spring structure reliability evaluation method based on subset simulation method

Abstract

The application provides a disc spring structure reliability evaluation method based on a subset simulation method, belongs to the technical field of disc spring structures of aircraft mechanical systems, and specifically: a finite element model of a disc spring structure of an aircraft mechanical system is established, and the maximum stress sigma of the disc spring structure is obtained; a function function of disc spring structure failure is established; a disc spring structure failure area is obtained; samples of variables are extracted from the load range of the disc spring through the subset simulation method, random variables are extracted from the joint probability density function of the random variables through the subset simulation method, the function function is calculated, and finally the failure probability of the disc spring structure is calculated. Through the processing scheme, the evaluation calculation efficiency is improved under the premise of meeting the accuracy requirement.

Description

Technical Field

[0001] This application relates to the field of disc springs in aircraft mechanical systems, and in particular to a method for assessing the structural reliability of disc springs based on subset simulation. Background Technology

[0002] Disc springs, also known simply as disc springs, are thin leaf springs made of steel plates stamped into a disc shape. They are small in size, have a high load-bearing capacity, uniform compression, and strong buffering and vibration damping capabilities. Different combinations (stacked or paired) can achieve different loads. Their nonlinear, incremental, zero-stiffness, and negative-stiffness deformation characteristics allow them to withstand a wide range of loads under very small deformation conditions, thereby greatly reducing the size and weight of the main unit. Therefore, they are widely used in aircraft mechanical systems.

[0003] Current methods for reliability design calculations of disc springs are either not precise enough, or the calculation process is too complex, while some methods have a narrow range of applicability. Disc springs themselves exhibit geometric nonlinearity, combined disc springs exhibit contact nonlinearity, and some special disc springs also exhibit material nonlinearity. Therefore, the calculation of disc springs with multiple nonlinearities is very complex, and some cannot obtain analytical solutions. With the development of computer technology and computational methods, complex engineering problems can be solved using discretized numerical calculation methods and with the help of computers to obtain numerical solutions that meet engineering requirements.

[0004] In the research of strength and reliability assessment methods for disc spring structures, the safety factor method is a conventional and commonly used design approach. However, the safety factor method typically fails to consider the dispersion of load and material properties, using only fixed values. This pursuit of safety leads to overly conservative designs, which, while reducing the chance of structural failure, cannot answer the question of the extent to which the designed product is safe. Furthermore, it often results in material waste and performance degradation. Reliability design, based on probability theory and mathematical statistics, treats the variables involved in the design as random variables, considering the impact of random factors on safety. It represents a deepening and development of conventional design theory. Therefore, in the reliability design and analysis of disc spring structures, the reliability design method based on probability theory is more reasonable than the conventional safety factor method.

[0005] The performance evaluation of disc spring structures in mechanical systems is mainly based on probabilistic models. This model takes into account the objective uncertainties of external loads, material performance parameters, structural geometry, calculation models, initial conditions, and boundary conditions during the design, manufacturing, and use of the structure, and uses probability density functions to describe the uncertain parameters based on probability theory, thus avoiding the influence of subjective human factors on the objective results. Summary of the Invention

[0006] In view of this, this application provides a reliability assessment method for disc spring structures based on subset simulation, which solves the problems in the prior art and improves the assessment calculation efficiency while meeting the accuracy requirements.

[0007] The reliability assessment method for disc spring structures based on subset simulation provided in this application adopts the following technical solution:

[0008] A reliability assessment method for disc spring structures based on subset simulation includes:

[0009] Step 1: Establish a finite element model of the disc spring structure of the aircraft's mechanical system and obtain the maximum stress of the disc spring structure. ;

[0010] Step 2: Establish the functional function for the failure of the disc spring structure;

[0011] Step 3: Obtain the failure area of ​​the disc spring structure;

[0012] Step 4: First, use the subset simulation method to simulate the load on the disc spring. within the interval for variables Sample extraction , Then, random variables are extracted from the joint probability density function of the random variables using the subset simulation method. , , , Calculate the function Finally, the failure probability of the disc spring structure is calculated; among which, The allowable stress for selecting materials for the structure Let t be the outer diameter of the disc spring, and t be the thickness of the disc spring. This is the elastic modulus of the disc spring.

[0013] Optionally, in step 2, the function for determining the failure of the disc spring structure... ;

[0014] by For random variables, Let the variable be an interval; then, the function for determining the failure of the disc spring structure is: ,in, The elastic modulus of the corresponding disc spring , Corresponding to the outer diameter of the disc spring , Corresponding to the thickness of the disc spring t , The load on the corresponding disc spring .

[0015] Optionally, in step 2, the function... The disc spring is safe when the value is greater than 0; function When the function equals 0, the disc spring is in a critical state, and the function is... The disc spring fails when the value is less than 0.

[0016] Optionally, the failure area of ​​the disc spring structure in step 3 as follows:

[0017] ;

[0018] in, Let be a random vector, and its joint probability density function be... , It is a one-dimensional interval variable. , and These are the upper and lower bounds of the interval variable, respectively.

[0019] Optionally, the specific steps for calculating the failure probability of the disc spring structure in step 4 include:

[0020] Let the probability of structural failure of the disc spring be... ,

[0021] ;

[0022] in It is a basic random variable The joint probability density function;

[0023] For the failure area , Introduction A series of critical values , , , The introduced critical values ​​constitute nested failure events. , ;

[0024] ,and Based on the multiplication theorem and the inclusion relationship of events, the following formula for calculating the failure probability can be obtained:

[0025] ;

[0026] make , , ;

[0027] Final failure probability of disc spring structure .

[0028] Optionally, in step 1, a finite element model of the disc spring structure is established using finite element software.

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

[0030] This application proposes a method for assessing the strength and reliability of disc spring structures based on subset simulation. It employs a probabilistic model of structural parameters to handle the random uncertainties in structural materials and manufacturing dimensions, and uses finite element analysis to analyze and solve the stress response of the disc spring structure, thus reducing the impact of structural parameter uncertainties on structural reliability. The subset simulation method has no restrictions on the dimension of variables or the degree of nonlinearity of the limit state equation, making it suitable for analyzing reliability problems with high nonlinearity and low failure probability. The subset simulation reliability analysis method not only meets the accuracy requirements with fewer samplings but also exhibits lower dispersion and faster convergence speed, providing guidance for reliability assessment and optimal design of disc spring structures in engineering to determine the optimal solution. Attached Figure Description

[0031] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of the reliability assessment method for disc spring structures based on subset simulation method in this application;

[0033] Figure 2 This is a schematic diagram illustrating the variation of the strength failure probability estimate calculated by the subset simulation method in this application with the number of samples.

[0034] Figure 3 A schematic diagram illustrating how the strength failure probability estimate calculated using the Monte Carlo method varies with the number of samples. Detailed Implementation

[0035] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0036] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0037] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one 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 set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0038] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0039] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0040] This application provides a reliability assessment method for disc spring structures based on subset simulation.

[0041] like Figure 1 As shown, a reliability assessment method for disc spring structures based on subset simulation includes:

[0042] A finite element model of the disc spring structure in the aircraft's mechanical system was established to obtain the maximum stress of the disc spring structure. Maximum stress of disc spring structure It is the outer diameter of the disc spring ,thickness t elastic modulus The function of the disc spring. The load on the disc spring. Elastic modulus ,thickness t Let be random variables, and the joint probability density function of the three random variables is: ; load For interval variables, .

[0043] Establish a function to prevent the disc spring structure from failing. ;

[0044] (1);

[0045] In the formula The allowable stress of the material selected for the structure.

[0046] Function Satisfying relation (2):

[0047] (2);

[0048] Function The disc spring is safe when the value is greater than 0; function When the function equals 0, the disc spring is in a critical state, and the function is... The disc spring fails when the value is less than 0.

[0049] Obtain the failure region of the disc spring structure.

[0050] First, the load on the disc spring is obtained through subset simulation. within the interval for variables Sample extraction , ,sample The following function is Then, using subset simulation, the joint probability density function of the random variables is... Extracting random variables , , , Calculate the function Finally, the failure probability of the disc spring structure is calculated; among which, The allowable stress for selecting materials for the structure Let t be the outer diameter of the disc spring, and t be the thickness of the disc spring. Let be the elastic modulus of the disc spring.

[0051] This application uses a disc spring structure in an aircraft mechanical system to specifically illustrate the evaluation method:

[0052] During model processing, geometric parameters that do not affect structural strength and stiffness, such as holes, chamfers, and small-sized grooves in non-critical areas designed to meet assembly, sealing, and production requirements, are deleted. Different mesh finenesses are applied to different structures, and eight-node hexahedral mesh elements are selected. The size of non-critical parts is selected between 2 and 4 mm according to the hexahedral mesh requirements. After multiple trial calculations from large to small, the mesh size of critical parts is selected as 0.25 mm. The selection criterion is that the reduction of mesh size no longer affects or has a minimal impact on the stress results of critical parts.

[0053] Finite element analysis can be used to obtain the stress cloud diagram of the disc spring and the maximum contact stress of the structure. .

[0054] Maximum contact stress of disc spring structure It is the outer diameter of the disc spring Thickness t, elastic modulus The function of the disc spring. The load on the disc spring. Elastic modulus Thickness t is a random variable, load It is an interval variable.

[0055] In the model, the relevant parameters of the disc spring structure are shown in Table 1 and Table 2.

[0056] Table 1. Relevant parameters of random variables

[0057]

[0058] Table 2. Relevant parameters for interval variables

[0059]

[0060] Maximum contact stress of disc spring structure The stress is greater than the allowable stress of the material selected for the structure. When the disc spring structure undergoes plastic deformation and fracture, mechanical damage occurs, and the structure fails to meet the strength and safety requirements. Therefore, a failure function function for the disc spring structure is established based on the working conditions of the disc spring.

[0061] For equation (1), which also includes random variables and interval variables Then it can be rewritten as:

[0062] (3).

[0063] Failure area of ​​disc spring structure It can be expressed as equation (4);

[0064] (4).

[0065] in, Let be a random vector, and its joint probability density function be... , It is a one-dimensional interval variable. , and These are the upper and lower bounds of the interval variable, respectively.

[0066] Let the probability of failure of the disc spring be... The solution formula is shown in equation (5);

[0067] (5);

[0068] in It is a basic random variable The joint probability density function.

[0069] The following section uses the strength failure of a disc spring as an example to illustrate its reliability solution process.

[0070] For the failure probability shown in equation (5), the Monte Carlo method uses the joint probability density function To extract a sample and use the sample to estimate the probability of failure. The estimation formula is shown in equation (6) below;

[0071] (6);

[0072] in, For the joint probability density function The first one drawn One sample, To determine the number of samples, It is an indicator function.

[0073] Obviously, It is the probability of failure. An unbiased estimate. When the sample size When large enough, It converges in probability to the true failure probability. .

[0074] In the reliability analysis of disc springs, due to the low failure probability, the number of samples required for numerical simulation using the Monte Carlo method is very large, and the calculation time is very long, which is unacceptable in engineering.

[0075] The subset simulation method transforms a small failure probability into a product of a series of larger conditional probabilities by introducing reasonable intermediate failure events. Its basic steps start with the joint probability density function of the basic variables, construct the sampling density function on each subset step by step, and then obtain the sampling density function of the limit state equation to be obtained, and finally obtain the estimated value of the failure probability.

[0076] First, the load on the disc spring is obtained through subset simulation. within the interval for variables Sample extraction , Then, random variables are extracted from the joint probability density function of the random variables using the subset simulation method. , , Calculate the function Finally, the failure probability of the disc spring structure is calculated; among which, The allowable stress for selecting materials for the structure Let t be the outer diameter of the disc spring, and t be the thickness of the disc spring. This is the elastic modulus of the disc spring.

[0077] Finally, the failure probability of the disc spring structure was calculated.

[0078] For the failure region shown in equation (4) , can be introduced A series of critical values , , , These introduced critical values ​​can constitute failure events with nested relationships, as shown in equation (7);

[0079] , (7).

[0080] At this time there is And there are Based on the multiplication theorem and the inclusion relationship of events, the following formula for calculating the failure probability can be obtained:

[0081] (8);

[0082] make , , Then the above formula can be rewritten as

[0083] (9).

[0084] Clearly, as can be seen from the above derivation process, the reliability analysis of the subset simulation method transforms small probabilities into a product of larger conditional probabilities, thereby improving the efficiency of digital simulation calculations.

[0085] Substituting the maximum contact stress from the finite element analysis results into equation (3), the function function for the failure of the disc spring structure can be obtained. Then, the reliability of the disc spring structure is calculated using the subset simulation method and the Monte Carlo method. The estimated value of the Monte Carlo method is the exact value. The relative error of the subset simulation method in solving the estimated failure probability of the disc spring structure is calculated. The calculation results are shown in Table 3 below.

[0086] like Figure 2 and Figure 3 As shown, the subset simulation method and the Monte Carlo method are used to calculate the variation of the failure probability estimate with the number of samplings. The subset simulation method has a total of 10 sampling times. 4 The sampling interval is 500 times; the total number of samplings for the Monte Carlo method is 10. 5 The sampling interval is 5000 times.

[0087] Table 3 Reliability Analysis Results of Disc Spring Structure

[0088]

[0089] pass Figure 2 and Figure 3 By comparing and analyzing the Monte Carlo method and the subset simulation method in calculating the probability of failure of disc spring structure strength with the number of samples, it can be clearly seen that the subset simulation method has a smaller degree of dispersion in estimating the failure probability and a faster convergence speed.

[0090] The Monte Carlo method yields an accurate estimate, while the subset simulation method yields a relative error of 2.17% for the estimated probability of failure of the disc spring structure. This demonstrates that the subset simulation method not only meets the accuracy requirements but also requires only 1 / 10 the sample size of the Monte Carlo method.

[0091] This demonstrates that using the subset simulation method can significantly reduce the amount of computation and improve computational efficiency, which has great advantages in the practical engineering application of disc spring structures.

[0092] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A reliability assessment method for disc spring structures based on subset simulation, characterized in that, include: Step 1: Establish a finite element model of the disc spring structure of the aircraft's mechanical system and obtain the maximum stress of the disc spring structure. ; Step 2: Establish the functional function for the failure of the disc spring structure; Step 3: Obtain the failure area of ​​the disc spring structure; Step 4: First, use the subset simulation method to simulate the load on the disc spring. within the interval for variables Sample extraction , Then, random variables are extracted from the joint probability density function of the random variables using the subset simulation method. , , , Calculate the function Finally, the failure probability of the disc spring structure is calculated; among which, Let t be the outer diameter of the disc spring, and t be the thickness of the disc spring. This is the elastic modulus of the disc spring.

2. The reliability assessment method for disc spring structures based on subset simulation method according to claim 1, characterized in that, In step 2, the function for determining the failure of the disc spring structure... ; by For random variables, Let the variable be an interval; then, the function for determining the failure of the disc spring structure is: ,in, The elastic modulus of the corresponding disc spring , Corresponding to the outer diameter of the disc spring , Corresponding to the thickness of the disc spring t , The load on the corresponding disc spring .

3. The reliability assessment method for disc spring structures based on subset simulation method according to claim 2, characterized in that, In step 2, the function The disc spring is safe when the value is greater than 0; function When the function equals 0, the disc spring is in a critical state, and the function is... The disc spring fails when the value is less than 0.

4. The reliability assessment method for disc spring structures based on subset simulation method according to claim 2, characterized in that, The specific steps for calculating the failure probability of the disc spring structure in step 4 include: Let the probability of failure of the disc spring structure be... , ； in It is a basic random variable The joint probability density function; For the failure area , Introduction A series of critical values , , , The introduced critical values ​​constitute nested failure events. , ; ,and Based on the multiplication theorem and the inclusion relationship of events, the following formula for calculating the failure probability can be obtained: ； make , , ; Final failure probability of disc spring structure .

5. The reliability assessment method for disc spring structures based on subset simulation method according to claim 1, characterized in that, In step 1, a finite element model of the disc spring structure is established using finite element software.

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