Dynamic modeling method for reliability of fastening connection system

Abstract

The invention provides a fastening connection system reliability dynamic modeling method which comprises the following steps: establishing a reliability model of fracture failure and loosening failure of a single threaded connection pair to obtain the reliability of the single threaded connection pair in different failure modes; based on a multi-competitive failure mode of a single threaded connection pair, establishing a dynamic reliability model of the fastening connection system under consideration of dynamic degradation by introducing an exponential decay model; wherein the exponential decay model is used for representing the decay process of the bolt pre-tightening force and strength along with time; and constructing a general generation function of each threaded connection pair for performing dynamic reliability calculation on the dynamic reliability model of the fastening connection system, and determining an optimal maintenance interval. According to the method, the multi-competition failure problem of fracture failure and loosening failure of a single threaded connection layer is effectively solved, the method better conforms to engineering practice, calculation is convenient and easy, implementation is easy, and engineering technicians can conveniently master the method.

Description

Technical Field

[0001] This application belongs to the field of reliability analysis technology for fastening connection systems, and particularly relates to a dynamic modeling method for the reliability of fastening connection systems. Background Technology

[0002] In modern engineering and manufacturing, the reliability of fastening systems (such as threaded connections) is a key factor in ensuring structural safety and performance. However, in practical applications, fastening systems face multiple failure modes, including fracture and loosening. These failure modes not only compete with each other, but their probabilities and influencing factors are also highly dynamic and complex. Therefore, accurately modeling and calculating the reliability of fastening systems has become an important and challenging issue.

[0003] Traditional reliability analysis methods for fastening systems are typically based on static assumptions, failing to adequately consider the competing relationships between failure modes and the dynamic changes in the system during actual operation. This approach ignores the potential changes in the reliability of fastening systems over time, due to variations in environmental conditions and loads. Furthermore, as system complexity increases, the dimensionality of failure modes explodes, making it difficult for traditional reliability calculation methods to handle these high-dimensional issues, thus impacting computational accuracy and efficiency. Simultaneously, determining the required maintenance intervals for fastening systems is a crucial safety-related technical issue to ensure high reliability. Summary of the Invention

[0004] In view of this, this application aims to propose a dynamic modeling method for the reliability of fastening connection systems to solve at least one of the above-mentioned problems.

[0005] To achieve the above objectives, the technical solution of this application is implemented as follows:

[0006] This application provides a dynamic modeling method for the reliability of fastening connection systems, including:

[0007] Reliability models for fracture failure and loosening failure of a single threaded connection pair are established to obtain the reliability of a single threaded connection pair under different failure modes.

[0008] Based on the multiple competing failure modes of a single threaded connection pair, a dynamic reliability model of the fastening connection system considering dynamic degradation is established by introducing an exponential decay model; wherein, the exponential decay model is used to characterize the decay process of bolt preload and strength over time.

[0009] By constructing a general generation function for each threaded connection pair, dynamic reliability calculations are performed on the dynamic reliability model of the fastening connection system, and the optimal maintenance interval is determined.

[0010] Furthermore, the parameters are modeled based on the normal distribution function to obtain the reliability calculation formulas for fracture failure and loosening failure;

[0011] ;

[0012] ;

[0013] in, , ;

[0014] In the formula, This indicates the stress in the threaded connection pair under fracture failure mode. This indicates the tensile strength of the threaded connection pair under fracture failure mode. This indicates the stress in the threaded connection under the loosening failure mode. This indicates the resistance to loosening of the threaded connection under the loosening failure mode. Indicates preload. Indicates external load, This represents the cross-sectional area of ​​the bolt. Indicates the coefficient of friction. Indicates the reliability of fracture failure. Indicates reliability in the case of loosening failure. This represents the mean. Indicates standard deviation, This represents the standard normal distribution function.

[0015] Furthermore, the reliability of a single threaded connection under competing failure is expressed as follows:

[0016] ;

[0017] In the formula, Indicates preload Expected value Its representative fastening connection system is numbered as Threaded connection pair.

[0018] Furthermore, by introducing a preload exponential decay model and a tensile strength exponential decay model, and replacing the preload and tensile strength in the modeling; wherein, the preload exponential decay formula is: The formula for the decrease in tensile strength exponent is: and define ;

[0019] The stress formula in the fracture failure mode is: To make the fracture condition be After deformation, the result is ;

[0020] The strength formula in the loosening failure mode is: The loosening conditions are ;

[0021] when At that time, the reliability of fracture failure and loosening failure is as follows:

[0022] ;

[0023] ;

[0024] Based on the reliability of fracture failure and loosening failure, the reliability of a single bolt can be obtained as follows:

[0025] ;

[0026] In the formula, Indicates the initial preload. This represents a random variable representing the initial preload.

[0027] Furthermore, the fastening connection system is composed of Composed of one or more threaded connection pairs Dynamic reliability of the system and fastening connection system It is expressed as follows:

[0028] ;

[0029] In the formula, Indicates an intermediate variable.

[0030] Furthermore, a universal generating function for all threaded connections in the fastening system is constructed, and the formula for the universal generating function is as follows:

[0031] ;

[0032] initialization make ;

[0033] right The following steps are executed repeatedly:

[0034] Through calculation and remove In Item, will The coefficients keep accumulating ;

[0035] in, , Representative number is Check if the threaded connection is working properly.

[0036] Furthermore, by dynamically updating the reliability index of individual threaded connections in the fastening system, the updated dynamic reliability of the fastening system can be obtained. And based on the dynamic reliability of the fastening connection system, a reliability curve is constructed to determine the optimal maintenance interval.

[0037] Compared with existing technologies, the dynamic modeling method for the reliability of fastening connection systems described in this application has the following advantages:

[0038] The dynamic modeling method for the reliability of fastening connection systems described in this application effectively solves the problem of multiple competing failures, such as fracture failure and loosening failure, at the level of a single threaded connection. It considers the dynamic characteristics of the reliability at the level of the fastening connection system and solves the problem of dimensional explosion in the reliability calculation of fastening connection systems. At the same time, it establishes a link between reliability indicators and maintenance intervals, which has important practical significance and application value. In addition, this method is more in line with engineering practice, is convenient and simple to calculate, easy to implement, and easy for engineering technicians to master. Attached Figure Description

[0039] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0040] Figure 1 This is a flowchart of a dynamic reliability modeling method for a fastening connection system as described in an embodiment of this application;

[0041] Figure 2 This is a graph showing the relationship between bolt failure rate and time as described in the embodiments of this application;

[0042] Figure 3 This is a graph showing the relationship between the reliability of the bolt dynamic system described in this application and time.

[0043] Figure 4 This is a reliability analysis diagram of dynamic fracture failure of threaded connection pair considering degradation, as described in the embodiments of this application.

[0044] Figure 5 This is a graph showing the deviation in reliability calculations for fracture-failed fasteners considering degradation and not considering degradation, as described in the embodiments of this application.

[0045] Figure 6 This is a reliability analysis diagram of the threaded connection pair dynamic loosening failure fastener described in the embodiments of this application;

[0046] Figure 7 This is a deviation diagram for the reliability calculation of loosening failure of the threaded connection assembly described in the embodiments of this application;

[0047] Figure 8This is a reliability analysis diagram of the threaded connection pair as described in the embodiments of this application, showing the variation of flight time and preload multiple.

[0048] Figure 9 This is a reliability analysis diagram of the disc-shaft threaded connector described in the embodiments of this application;

[0049] Figure 10 This is a reliability diagram of the system under different maintenance rates as described in the embodiments of this application;

[0050] Figure 11 This is a schematic diagram illustrating the impact of minor changes in maintenance rate on reliability as described in the embodiments of this application. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0052] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this application should have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "first," "second," and similar terms used in the embodiments of this application do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are only used to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0053] The embodiments of this application are described in detail below with reference to the accompanying drawings.

[0054] Please see Figure 1 As shown in the figure, this embodiment provides a dynamic modeling method for the reliability of a fastening connection system, which specifically includes the following steps:

[0055] Step S101: Establish reliability models for fracture failure and loosening failure of a single threaded connection pair to obtain the reliability of a single threaded connection pair under different failure modes.

[0056] Specifically, in this embodiment, this step mainly establishes reliability models for fracture failure and loosening failure, and calculates the reliability index of a single threaded connection pair under different failure modes, denoted as . ,in, The number in the fastening connection system is Threaded connection, Representing the Types of failure modes.

[0057] Assume that all parameters follow a normal distribution, i.e. , , , The reliability calculation formulas for fracture failure and loosening failure are obtained as follows:

[0058] ;

[0059] ;

[0060] Among them, stress in fracture failure mode By preload and external loads Together they are generated, and their expression is: , Resistance to loosening under loosening failure mode Determined by the frictional force generated by the preload. ;

[0061] In the formula, This indicates the stress in the threaded connection pair under fracture failure mode. This indicates the tensile strength of the threaded connection pair under fracture failure mode. This indicates the stress in the threaded connection under the loosening failure mode. This indicates the resistance to loosening of the threaded connection under the loosening failure mode. Indicates preload. Indicates external load, This represents the cross-sectional area of ​​the bolt. Indicates the coefficient of friction. Indicates the reliability of fracture failure. Indicates reliability in the case of loosening failure. This represents the mean. Indicates standard deviation, This represents the standard normal distribution function.

[0062] Step S102: Based on the multiple competing failure modes of a single threaded connection pair, a dynamic reliability model of the fastening connection system considering dynamic degradation is established by introducing an exponential decay model; wherein, the exponential decay model is used to characterize the decay process of bolt preload and strength over time.

[0063] Specifically, in this embodiment, due to the competitive failure characteristic among different failure modes of a single threaded connection pair, it is considered that... Competition-based failures among various failure modes are considered. Combining the failure modes and reliability indicators from step S101, a reliability model for a single threaded connection pair is established. At this point, the reliability of the single threaded fastening pair is: When considering that the failure modes of individual fasteners are independent of each other, the reliability of a single-threaded fastener pair is... as follows:

[0064] ;

[0065] Based on the stress intensity model, assuming preload... These are common influencing factors and follow a normal distribution. ,because These are common variables; when calculating, they need to be calculated in the given context. The reliability of the conditions at that time, and then... integral.

[0066] When a bolt breaks, the fracture condition is: . and Under the condition that the components are independent and follow a normal distribution, the fracture reliability is obtained. :

[0067] ;

[0068] When a bolt becomes loose, the loosening condition is: .because The reliability of loosening is:

[0069] ;

[0070] Based on bolt competitive failure, the reliability of a single bolt can be obtained as the expectation of the conditional reliability with respect to the distribution:

[0071] ;

[0072] in for The probability density function of . That is, the reliability of a single bolt under competing failure can be expressed as:

[0073] ;

[0074] Common degradation models include exponential decay models, linear degradation models, and stochastic degradation models. Considering that the working environment of the fastener is a long-term vibration environment, this embodiment introduces an exponential decay model, in which the preload decays exponentially. and tensile strength index decay For the preload in the modeling and The substitution is performed, and the result still follows a normal distribution. For ease of calculation, both are made to follow the same decay model. .

[0075] The stress in the fracture failure mode is To make the fracture condition be The transformed form is obtained The strength under the loosening failure mode is The loosening conditions are .

[0076] when At that time, the reliability of fracture failure and loosening failure is as follows:

[0077] ;

[0078] ;

[0079] Based on the reliability of fracture failure and loosening failure, the reliability of a single threaded connection pair can be obtained as follows:

[0080] ;

[0081] Considering the dynamic nature of threaded connections in a fastener connection system during use, the reliability of individual threaded connections within the system is not uniform and also exhibits dynamic characteristics. The fastener connection system consists of... The threaded connection assembly, together forming a system, must include at least the following components to complete the system's function: Only a single threaded connection can guarantee normal use. Therefore, the reliability of a fastening connection system can be considered as being determined by… Composed of one or more threaded connections System. Reliability of fastening connection systems. as follows:

[0082] ;

[0083] Step S103: By constructing a general generation function for each threaded connection pair, dynamic reliability calculations are performed on the dynamic reliability model of the fastening connection system, and the optimal maintenance interval is determined.

[0084] Specifically, in this embodiment, due to the dimensionality explosion problem when calculating the reliability of the fastening connection system in step S102, a general generating function method is proposed to simplify the calculation. Representative number is Whether the threaded connection is working properly, among which, This represents normal work; This indicates that the representation is invalid. At this point, , Because the threaded connection in a fastening system must not be lower than the normal operating condition. Given a given number of elements, the calculation relationship is defined as follows:

[0085] ;

[0086] The specific calculation process is as follows:

[0087] Step S301: Construct a general generation function for all threaded connections in the fastening system. The general generation function is as follows:

[0088]

[0089] Step S302, Initialization make .

[0090] Step S303, for The following loop is executed:

[0091] ①Calculation ;

[0092] ②Remove middle Item, and will The coefficients keep accumulating .

[0093] Due to changes in the operating environment, fastening systems require periodic monitoring of individual fastener loads and preload over time. When a fastener failure is detected, the reliability index of the individual threaded connection in the fastening system is dynamically updated, and the updated reliability is denoted as [missing information]. At this point, according to step S103, the updated dynamic reliability of the fastening connection system can be obtained. At the same time, according to sex The reliability curve is used to determine the minimum maintenance interval.

[0094] The method described in this embodiment can effectively solve the problem of multiple competing failures, such as fracture failure and loosening failure, at the level of a single threaded connection. It considers the dynamic characteristics of the reliability at the level of the fastening connection system and solves the problem of dimensional explosion in the reliability calculation of the fastening connection system. At the same time, it establishes a link between reliability indicators and maintenance intervals, which has important practical significance and application value. In addition, this method is more in line with engineering practice, the calculation is convenient and simple, it is easy to implement, and it is easy for engineering technicians to master.

[0095] Example 1

[0096] The following uses a certain type of aircraft engine disc-shaft threaded connector as an example to further illustrate the above embodiment. This disc-shaft threaded connector connects the engine's high-pressure turbine disc to the high-pressure compressor's rear journal connector through 24 sets of threaded connections. Each set of threaded connections consists of a twelve-corner high-pressure rotor self-locking nut and a D-type high-pressure rotor bolt. The specific implementation steps are as follows:

[0097] Step 1: Reliability analysis of fracture and loosening failures of a single threaded connection pair.

[0098] FMECA analysis of the disc-shaft threaded connector revealed that the main failure modes are fracture failure and loosening failure (as shown in the bolt failure rate versus time curve). Figure 2 (as shown)

[0099] 1) Bolt / Nut Fracture Failure Cause Analysis and Reliability Distribution Determination: During engine operation, the high-pressure turbine disc and high-pressure compressor rear journal are subjected to extremely high temperatures and pressures, leading to thermal expansion, thermal stress, and a reduction in material strength in the connector material. The tensile strength of the disc / shaft threaded connector was determined using reliability test data and monitoring data. Follows a normal distribution ,stress Follows a normal distribution Preload Follows a normal distribution , This is a multiple of the preload force; at this point, the stress distribution is... for

[0100] Based on the stress-strength interference theory, the reliability distribution of stress fracture failure is established as follows: .

[0101] 2) Analysis of the causes of loosening failure in threaded connections and determination of reliability distribution: Threaded connections can loosen under vibration and impact loads. Pre-tightening force can be used to prevent loosening failure. Based on historical installation data, the strength of the pre-tightening force is determined. Follows a normal distribution ,stress Follows a normal distribution Based on the stress-strength interference theory, the reliability distribution of connection loosening failure is established as follows: .

[0102] Step 2: Consider the reliability modeling of a single threaded connection pair with multiple competing failures.

[0103] Based on the above failure analysis and reliability distribution, the reliability distributions of stress fracture failure and connection loosening failure for individual threaded connections with different numbers were determined. Since stress fracture failure and connection loosening failure are competing failures, a reliability distribution for single threaded connections with competing failures was established: ,in, .

[0104] The curve showing the relationship between the dynamic reliability of bolts and time. (Example:) Figure 3 As shown, the system's dynamic reliability begins to decline around 6000 hours, and the rate of decline accelerates over the next few hundred hours. If a target reliability is set... Therefore, the system will become unreliable after approximately 6500 working hours. The maintenance interval determined by the parameter settings is approximately 250 hours, meaning the system needs to be returned to the factory for major overhaul before 6500 hours.

[0105] Step 3: Consider dynamic information The disc-shaft threaded connector uses reliability modeling.

[0106] The threaded connection pairs in the disc-shaft threaded connector exhibit dynamic characteristics during engine operation. Under high temperature, high pressure, vibration, and impact loads during engine operation, the threaded connection materials undergo thermal expansion, thermal stress, and a decrease in material strength, leading to fracture and loosening failure. Considering these factors and dynamic changes, the reliability of the threaded connection pairs in the disc-shaft threaded connector is not uniform and exhibits dynamic characteristics. The reliability levels of 24 sets of threaded connection pairs are discussed. As the engine operates, information such as load and impact changes dynamically and is updated, and these values ​​are not equal.

[0107] A disc-shaft threaded connector consists of 24 sets of threaded connections that work together to complete the system's functions. At least 20 threaded connections are required to ensure normal operation. Therefore, the reliability of a disc-shaft threaded connector can be considered as being determined by 20 or more threaded connections. The system, in particular, utilizes reliable threaded connectors for its disc shafts. The formula can be used for calculation, as shown below:

[0108] ;

[0109] This section considers the strength of threaded fasteners. Due to the effects of high temperature, high pressure, and random loads, degradation occurs over time, and its degradation rate... At this point, the strength of the MJ14 specification bolt... mean It will decrease over time; at the same time, considering the dispersion of preload accuracy during actual installation, it will cause the preload multiple to decrease. The change in force. At this point, the designed expected force of 80.95 kN will deviate. At this point, the preload force... Follows a normal distribution There are differences. Meanwhile, considering a disc-shaft threaded connector composed of 24 MJ14 bolts, when one or more threaded connections fail, the stress distribution of the remaining threaded connections will change, and the residual stress... It will no longer follow a normal distribution. This requires recalculation and real-time updates of the stress distribution.

[0110] Considering the reliability of dynamic fracture failure of degraded threaded connections, by Figure 4 As shown. Considering the strength degradation effect, the reliability of threaded connection pair fracture failure is 0.999999991733985, 0.999984785558222, 0.996487007021501, 0.888954622775846, and 0.399888744980576 for flight times of 1000h, 2000h, 3000h, 4000h, and 5000h, respectively. Figure 5 As shown, when the flight time exceeds 3000 hours, the reliability of the threaded connection pair begins to decline significantly due to fracture failure. When degradation effects are not considered, such as... Figure 5 As shown, the reliability calculation deviation for fracture failure of threaded connection pairs considering degradation and not considering degradation is 8.266 × 10⁻⁶ for flight times of 1000h, 2000h, 3000h, 4000h, and 5000h, respectively. -9 1.5214×10 -5 , 0.003513, 0.111045 and 0.6001. Depend on Figure 4 It can be seen that after more than 3000 hours of flight, the deviation in the reliability calculation of threaded connection failure due to strength degradation increases significantly.

[0111] Considering the strength degradation of threaded connections, the reliability of threaded connection pairs to fracture failure decreases with flight time. Figure 4 and Figure 5 It is known that when the flight time exceeds 4000 hours, the threaded connection pair experiences a rapid increase in fracture failure due to decreased strength, resulting in a rapid decline in reliability and a high likelihood of sudden failure. For example... Figure 5It is evident that, compared to analyses that do not consider strength degradation, the deviation in reliability assessments increases after 3000 flight hours. Therefore, considering the dynamic effects of strength degradation in threaded connections can prevent sudden failures and fractures that could lead to significant safety issues. It is therefore recommended to conduct an inspection or overhaul at 3000 flight hours intervals, replacing threaded connections with degraded strength.

[0112] When considering the impact of the preload accuracy control range on the reliability of threaded connections in the event of loosening failure, such as Figure 6 and Figure 7 According to design requirements, the target preload... In practice, fluctuations in the precision of installation tools and the skill of installers can affect the preload ratio. Fluctuations. For example... Figure 6 and Figure 7 As shown, with the increase of the preload multiple With the increase of [something], the reliability against loosening failure initially increases rapidly and then decreases slowly.

[0113] Considering the competing failure relationship between fracture failure and loosening failure, the influence of flight time variation and preload ratio variation on the reliability analysis of threaded connections is analyzed, such as... Figure 8 As shown. By Figure 8 It is known that the reliability of threaded connections is currently more affected by flight time, mainly due to the decrease in strength. Figure 9 This is a reliability analysis diagram for a disc-shaft threaded connector consisting of 24 bolts. It is assumed that at least 20 threaded connections are required to guarantee normal operation. Figure 9 It is known that the overall reliability of the disc-spindle threaded connector decreases rapidly after 5000 flight hours. Therefore, a major overhaul of the disc-spindle threaded connector is required before 5000 hours, and the threaded pair needs to be replaced.

[0114] The above examples demonstrate the importance of considering dynamic information such as strength degradation and preload changes in assessing the reliability of aero-engine disc-shaft threaded connectors, and the necessity of conducting dynamic reliability assessments that comprehensively consider multiple competing failure modes, including fracture and loosening failures. Furthermore, by incorporating dynamic information such as strength degradation and preload changes, it is possible to analyze and determine the maintenance intervals of the threaded connection pairs and the overhaul intervals of the disc-shaft threaded connectors.

[0115] Step 4: Determine the maintenance interval based on dynamic information.

[0116] The analysis of maintenance intervals is conducted based on different maintenance rates. The relationship between system reliability and time, obtained based on different maintenance rates, is as follows: Figure 10 As shown, the maintenance rate The values ​​are 0.0005, 0.001, 0.004 and 0.005, and the corresponding maintenance intervals are 2000 hours, 1000 hours, 250 hours and 200 hours, respectively.

[0117] The relationship between the 2000-hour and 1000-hour maintenance intervals reveals a significant difference in reliability maintenance time. With the 2000-hour interval, system reliability drops below the target reliability before 6000 hours, while the 1000-hour interval extends this time by nearly 500 hours, reaching unreliability close to 6500 hours. While these interval values ​​reflect the different ways maintenance intervals maintain system reliability, their implementation is still incomplete. The 1000-hour interval is more effective at maintaining reliability than the other intervals, but because the interval is set at 1000 hours, the system needs to be returned to the factory for major overhaul around 6000 hours, thus not fully utilizing the system's reliability within this interval. Therefore, further adjustments to the maintenance rate selection are needed to achieve better time utilization.

[0118] like Figure 11 The diagram shown is a relational graph constructed based on the above maintenance rate analysis. It uses 0.0001 as the unit to find the maintenance rate that can determine a better maintenance interval. According to the relational graph, when... At this maintenance interval, the maintenance interval is 910 hours. Based on the reliability under this maintenance rate, the corresponding overhaul time should be controlled at around 6400 hours. Under this maintenance interval, six maintenance operations are required, with a major overhaul on the seventh operation, resulting in a return-to-factory time of 6370 hours. This represents an optimization to varying degrees compared to the other selected maintenance intervals. At that time, the dynamic reliability of the system is hour, The utilization rate of reliable time reached 98%, while the maintenance interval was 1000 hours and 833 hours ( The reliability utilization rates of these systems are only 92% and 90%. Therefore, setting the maintenance interval at 910 hours is a relatively reasonable maintenance interval that makes high utilization of system reliability.

[0119] In summary, this application provides a dynamic reliability modeling method for fastening connection systems. First, reliability modeling is performed on the fracture and loosening failures of a single threaded connection. Second, a single-threaded connection reliability model considering multiple competing failures of fracture and loosening is established. Based on this, a model incorporating dynamic degradation and maintenance information is constructed. A dynamic reliability model for the fastening connection system is presented, and a reliability calculation method based on a general generating function is employed to improve computational efficiency. Finally, based on safety-related reliability requirements, minimum maintenance interval requirements are given.

[0120] Compared with current single-failure-mode fastener reliability modeling methods, this application solves the problem of multiple competing failures in the dynamic degradation of fracture and loosening failures, which is more in line with engineering practice and safety requirements. It is also convenient and simple to calculate, easy to implement, and easy for engineering technicians to master and use. The method is scientific and easy to apply and promote.

[0121] It should be noted that the above description describes some embodiments of this application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0122] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this application (including the claims) is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this application as described above, which are not provided in the details for the sake of brevity.

[0123] The embodiments of this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this application should be included within the protection scope of this application.

Claims

1. A dynamic modeling method for the reliability of a fastening connection system, characterized in that, include: Reliability models for fracture failure and loosening failure of a single threaded connection pair are established to obtain the reliability of a single threaded connection pair under different failure modes. Based on the multiple competing failure modes of a single threaded connection pair, a dynamic reliability model of the fastening connection system considering dynamic degradation is established by introducing an exponential decay model; wherein, the exponential decay model is used to characterize the decay process of bolt preload and strength over time. By constructing a general generating function for each threaded connection pair, dynamic reliability calculations are performed on the dynamic reliability model of the fastening connection system, and the optimal maintenance interval is determined.

2. The method according to claim 1, characterized in that: The parameters are modeled based on the normal distribution function to obtain the reliability calculation formulas for fracture failure and loosening failure; ； ； in, , ; In the formula, This indicates the stress in the threaded connection pair under fracture failure mode. This indicates the tensile strength of the threaded connection pair under fracture failure mode. This indicates the stress in the threaded connection under the loosening failure mode. This indicates the resistance to loosening of the threaded connection under the loosening failure mode. Indicates preload. Indicates external load, This represents the cross-sectional area of ​​the bolt. Indicates the coefficient of friction. Indicates the reliability of fracture failure. Indicates reliability in the case of loosening failure. This represents the mean. Indicates standard deviation, This represents the standard normal distribution function.

3. The method according to claim 2, characterized in that, The reliability of a single threaded connection under competing failure is expressed as follows: ； In the formula, Indicates preload Expected value It represents the fastening connection system numbered as Threaded connection pair.

4. The method according to claim 3, characterized in that: By introducing a preload exponential decay model and a tensile strength exponential decay model, and replacing the preload and tensile strength in the modeling, the preload exponential decay formula is as follows: The formula for the decrease in tensile strength exponent is: and define ; The stress formula in the fracture failure mode is: To make the fracture condition be After deformation, the result is ; The strength formula in the loosening failure mode is: The loosening conditions are ; when At that time, the reliability of fracture failure and loosening failure is as follows: ； ； Based on the reliability of fracture failure and loosening failure, the reliability of a single bolt can be obtained as follows: ； In the formula, Indicates the initial preload. This represents a random variable representing the initial preload.

5. The method according to claim 4, characterized in that: The fastening connection system is composed of Composed of one or more threaded connection pairs Dynamic reliability of the system and fastening connection system It is expressed as follows: ； In the formula, Indicates an intermediate variable.

6. The method according to claim 5, characterized in that: A general generating function is constructed for all threaded connections in the fastening system. The formula for the general generating function is as follows: ； initialization make ; right The following steps are executed repeatedly: Through calculation and remove In Item, will The coefficients keep accumulating ; in, , Representative number is Check if the threaded connection is working properly.

7. The method according to claim 1, characterized in that: By dynamically updating the reliability index of individual threaded connections in the fastening system, the dynamic reliability of the updated fastening system can be obtained. And based on the dynamic reliability of the fastening connection system, a reliability curve is constructed to determine the optimal maintenance interval.

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